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The chemistry of polymorphism in semiconductor nanocrystals

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The chemistry of polymorphism in semiconductor nanocrystals

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THE CHEMISTRY OF POLYMORPHISM IN SEMICONDUCTOR NANOCRYSTALS

by

Bryce Arend Tappan

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA

In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMISTRY)

December 2021

Copyright 2021 Bryce Arend Tappan

ii

“Life breaks free; it expands to new territories, and crashes through barriers painfully, maybe
even dangerously…Life finds a way.”
- Dr. Ian Malcolm

iii

For Mom

iv

Acknowledgements
Five years ago, I came to Los Angeles unsure of myself as a scientist and not knowing entirely who
I wanted to be as I transitioned out of college and into adulthood. Over the past five years, through the
wisdom, knowledge, mentorship, and friendship of those around me, and through experiences the world
has thrust upon us, I have grown tremendously.
Richard – when you first reached out to me over five years ago, you immediately made me feel
welcome and like I had what it took to succeed in graduate school. Thank you for that, and for investing in
me by giving me opportunity after opportunity in your research lab. I am very proud of the research we
have accomplished together.
Thank you to so many Brutchey Group members over the years. Haipeng, thanks for all the
basketball games and for our continued discussions of science throughout my Ph.D. Carrie, thank you for
always being open to questions and for all the rock climbing adventures we had together. Lucia, thank you
for being one of my very closest friends. I will always look back fondly at late nights in lab and our
discussions of science, music, Spanish, and philosophy. Patrick, thank you for being a fantastic friend and
collaborator throughout my Ph.D., and for your willingness to give me advice and honest, fresh
perspectives. Gözde, thank you for being a friend to me in the lab and for collaborating on my first paper.
I still think of the awesome concert we went to at the Hollywood Bowl! Sara, thank you for figuring out
the life of a graduate student with me! It’s been awesome to have someone right there with me in the group,
every step of the way. Kris, thank you for all the insightful office discussions of topics ranging from science,
to music, to meme stocks. You’re always ahead of the curve and thinking outside of the box, and I respect
that. Lanja, thank you for being my office buddy and for all of the great conversations we’ve had over the
years. You are a constant source of positivity! Emily, thank you for being a great friend and lab mate. It
was an unexpected privilege to be able to publish with you this year! Kyle and Marissa, thank you for being
receptive, enthusiastic, and resilient (COVID made things so tough) graduate students. You bring new
energy into the group, and it’s been fun to get to know you.
v

Thank you to the USC Chemistry Department as a whole. I have felt incredibly supported by the
department throughout my years here. Special thanks to Prof. Prakash, Prof. Melot, Prof. Mark Thompson,
Prof. Marinescu and their respective groups for letting me pop in and out of their labs once in a while when
I needed help with an experiment, needed advice, or just wanted to chat. Thank you to Prof. Brutchey, Prof.
Melot, Prof. Dawlaty, Prof. Feakins, and Dr. Haiges for presiding on my screening, qualifying exam, and
dissertation defense committees. Thank you to Prof. Reisler for leadership advice and for advocating for
graduate students. Thank you to Prof. Williams for stimulating conversations on various subjects
throughout graduate school. Thank you to Michele and Magnolia for running the whole show. Thank you
to the janitorial staff for all your hard work in our chemistry buildings, especially through the pandemic.
Thank you to all the folks who have supported efforts in CGSO and Graduate Student Government over
the years; this works makes for a cohesive graduate student community in the Chemistry Department.
Thank you Prof. Misha Barybin for always being a force for good, a role model, and a close friend
in my life. I wouldn’t be standing where I am today without you. Thank you Zach and Colby for all the
great memories, both at KU and USC.
To all of the Adams House Roommates (Sanket, Nick, Victor, Mami, Robert, Alon, Ana, Anna,
Jeremiah, Seda, Aneesh, Lucia, Abby, Pliny, Doge, and Randy): I’ve loved having you all as my surrogate
family in LA. Living together in our crumbing green mansion on 1516 West Adams made Los Angeles feel
like home, something that was particularly valuable during the hard lock downs of the pandemic. Through
thick and thin, I always felt like I could come back to our house, decompress, and enjoy myself in the
company of such great roommates. Thank you Kevin, for being such a strong and supportive friend
throughout the course of our time together at USC.
Geo, Carlos, and Aaron – you are the best friends anyone could hope for. Thank you for always
being there for me, in every capacity possible. In some way or another, you three have touched nearly all
of my most fond memories of living in LA over the last five years. Thank you Aaron LaRue for all the great
times we’ve had as running buddies. Kris and Joycelyn, thank you for teaching me how to be a determined,
responsible leader, while also being such supportive friends. Thank you Van and Billy for watching the
vi

Mandalorian with me. Thank you Robert N., Mu’azzam, Narcisse, Adam, Jeff, and Courtney for being such
great friends within the department. Thank you Michael and Jacky for your contributions to our research as
undergraduates.
Thank you to all of my childhood and college friends (Gabe, Jon, Jackson, Dan, Myung Ha, Aaron,
Devesh, Jeff, Ad, Peter, Jenny, Ashu, Evan, Adebayo, Joe, Jordyn) that have supported me all throughout
my life, including through my Ph.D. Through continuous friendship over the course of my life, you have
all inspired and challenged me intellectually and we have grown together.
Thank you to my family. First and foremost, thank you to my Mom and Dad. You both always let
me follow my heart’s desire, and encouraged me no matter what path I chose to take. You both have been
the most significant source of inspiration for me. Dad, your career as a scientist, your curiosity and
creativity, and your deep fascination for the natural world has led me to follow in your footsteps. I wouldn’t
have wanted it any other way. Mom, your perseverance, humility, pragmatism, artistry, strength, and most
of all, the optimism and kindness you shared with us will never cease to move me. You made me who I am,
and your memory fuels a fire within me to go out into the world and do the best I can to help people, and
to help solve some of the biggest problems we face in the world today. Thank you Taylor and Erin, for
being the principal role models in my life, second only to Mom and Dad. In so many ways, you both have
forged paths in your lives that have helped me find direction in mine. I know I can always count on support
from you, as well as from Silvia and Jon. Thank you Tim for visiting me, calling me, and always checking
in on me. I am fortunate to have a close cousin like you. Thank you Margy, Michael, Emma, Sarah, Trey
and Jonathan. You’ve always made me feel at home in California, and I am thankful for the time we’ve
been able to spend together here in the last five years. Thank you Dwight, Scott, Diana, Keith, Linda, Bruce,
and Becky, for your continuous enthusiasm and support.
Lastly, thank you Keying. You have been my anything and everything in graduate school. You
supported me through some of the darkest moments of my life, and you shared the brightest moments with
me as well. You motivate me to broaden my horizons intellectually, personally, and culinarily. Your sharp
intellect, cunning wit, and your happiness make being with you the joy of my life.
vii

Table of Contents
Epigraph ........................................................................................................................................................ ii
Dedication .................................................................................................................................................... iii
Acknowledgements ...................................................................................................................................... iv
List of Tables ............................................................................................................................................... xi
List of Figures ............................................................................................................................................. xii
Abstract ..................................................................................................................................................... xxv
Chapter 1. Polymorphic Metastability in Colloidal Semiconductor Nanocrystals ....................................... 1
1.1 Abstract ............................................................................................................................................... 1
1.2 Introduction ......................................................................................................................................... 2
1.2.1 Principles of Metastability ........................................................................................................... 2
1.2.2 Syntheses of Colloidal Semiconductor Nanocrystals with Metastable Crystal Structures .......... 3
1.3 Nanocrystal Polymorph Dependence on Reaction Conditions ........................................................... 6
1.3.1 Phase Control of ZnSe Nanocrystals via Modulation of Rate of Precursor Addition .................. 6
1.3.2 Temperature-Dependent Phase Control of Cu 2SnSe 3 Nanocrystals ........................................... 10
1.4 Tuning Precursor Reactivities for Polymorphic Phase Control on the Nanoscale ............................ 13
1.5 Ligand and Solvent Effects on Nanocrystal Polymorphism ............................................................. 18
1.5.1 Surface Stabilization of Metastable Ag 2Se Nanocrystals........................................................... 18
1.6 The Future of Metastable Nanocrystal Synthesis.............................................................................. 26
1.7 Properties and Applications of Semiconductor Nanocrystals with Metastable Crystal Structures ... 30
1.7.1 Optical Properties and Electrochemiluminescence Applications of Wurtzite ZnSe Nanocrystals
............................................................................................................................................................ 31
1.7.2 Metastable Wurtzite-Like CuInSe 2 Nanocrystals ...................................................................... 34
1.7.3 Persistence of Wurtzite-like CuInSe 2 Nanocrystals ................................................................... 36
1.7.4 Metastable Ag 2Se Nanocrystals ................................................................................................. 36
1.7.5 Optoelectronic Properties of Anti-PbCl 2-Like Ag 2Se Nanocrystals .......................................... 39
1.7.6 Core-Shell Effects on the High-Temperature Stability of Anti-PbCl 2-Like Ag 2Se Nanocrystals
............................................................................................................................................................ 40
1.8 Conclusions ....................................................................................................................................... 41
1.9 References ......................................................................................................................................... 42
Chapter 2. Utilizing Diselenide Precursors towards the Rationally Controlled Synthesis of Metastable
CuInSe 2 Nanocrystals ................................................................................................................................. 51
2.1 Abstract ............................................................................................................................................. 51
2.2 Introduction ....................................................................................................................................... 51
2.3 Experimental ..................................................................................................................................... 54
2.3.1 Materials and General Procedures ............................................................................................. 54
viii

2.3.2 Synthesis of Cu(II) oleate .......................................................................................................... 54
2.3.3 Synthesis of CuInSe 2 Nanocrystals ............................................................................................ 54
2.3.4 Synthesis of CuInSe 2 Nanocrystals using Me 2Se 2 ..................................................................... 55
2.3.5 Synthesis of Copper Selenide Nanocrystals ............................................................................... 55
2.3.6 Characterization ......................................................................................................................... 56
2.3.7 Density Functional Theory (DFT) ............................................................................................. 56
2.4 Results and Discussion ..................................................................................................................... 57
2.4.1 CuInSe2 Formation Pathways .................................................................................................... 60
2.4.2 Assessing the Persistence of the Wurtzite-Like Phase ............................................................... 70
2.5 Conclusions ....................................................................................................................................... 75
2.6 References ......................................................................................................................................... 76
Chapter 3. Ligand-Mediated Phase Control in Colloidal AgInSe 2 Nanocrystals........................................ 81
3.1 Abstract ............................................................................................................................................. 81
3.2 Introduction ....................................................................................................................................... 81
3.3 Experimental ..................................................................................................................................... 83
3.3.1 Materials and General Procedures ............................................................................................. 83
3.3.2 Synthesis of Orthorhombic AgInSe 2 Nanocrystals .................................................................... 84
3.3.3 Synthesis of Chalcopyrite AgInSe 2 Nanocrystals ...................................................................... 84
3.3.4 Nanocrystal Workup .................................................................................................................. 84
3.3.5 Electrostatic Site Potential and Madelung Energy Calculations ................................................ 85
3.3.6 Characterization ......................................................................................................................... 85
3.3.7 Density Functional Theory (DFT) ............................................................................................. 86
3.4 Results and Discussion ..................................................................................................................... 86
3.4.1 Formation of Chalcopyrite AgInSe 2 ........................................................................................... 92
3.4.2 Formation of Orthorhombic AgInSe 2 and the Role of Cation Exchange-Mediating Ligands ... 96
3.4.3 Crystal Chemistry of the Orthorhombic Ag 2Se to Orthorhombic AgInSe 2 Conversion and
Computational Results ...................................................................................................................... 102
3.4.4 Predicting the Syntheses of Novel Metastable Polymorphs on the Nanoscale ........................ 107
3.5 Conclusions ..................................................................................................................................... 109
3.6 References ....................................................................................................................................... 110
Chapter 4. Discovery of a Wurtzite-like Cu 2FeSnSe 4 Semiconductor Nanocrystal Polymorph and
Implications for Related CuFeSe 2 Materials ............................................................................................. 114
4.1 Abstract ........................................................................................................................................... 114
4.2 Introduction ..................................................................................................................................... 114
4.3 Experimental ................................................................................................................................... 117
ix

4.3.1 Materials and General Procedures ........................................................................................... 117
4.3.2 Aliquot Studies of Wurtzite-Like Cu 2FeSnSe 4 Nanocrystals ................................................... 118
4.3.3 Direct Synthesis of Wurtzite-Like Cu 2FeSnSe 4 Nanocrystals ................................................. 119
4.3.4 Characterization ....................................................................................................................... 120
4.3.5 Density Functional Theory Calculations .................................................................................. 120
4.4 Results and Discussion ................................................................................................................... 121
4.4.1 Electronic Structure Calculations for Wurtzite-Like and Stannite Cu 2FeSnSe 4 Polymorphs .. 131
4.4.2 Learning from Wurtzite-Like Cu 2FeSnSe 4: Implications for Unknown Wurtzite-Like CuFeSe 2
and the Stabilizing Effect of Tin ....................................................................................................... 136
4.5 Conclusions ..................................................................................................................................... 141
4.6 Determination of band gap from inverse logarithmic derivative (ILD) method: ............................ 142
4.7 References ....................................................................................................................................... 143
Chapter 5. Crystal Structure of Colloidally Prepared Metastable Ag 2Se Nanocrystals ............................ 149
5.1 Abstract ........................................................................................................................................... 149
5.2 Introduction ..................................................................................................................................... 149
5.3 Nanocrystal Preparation .................................................................................................................. 152
5.4 Structure Determination .................................................................................................................. 153
5.5 Density Functional Theory.............................................................................................................. 164
5.6 Experimental ................................................................................................................................... 167
5.6.1 PVP Solvothermal Synthesis of Ag 2Se Nanocrystals .............................................................. 167
5.6.2 Oleylamine Synthesis of Ag 2Se Nanocrystals ......................................................................... 167
5.6.3 NHC Synthesis of Ag 2Se Nanocrystals .................................................................................... 168
5.6.4 Characterization ....................................................................................................................... 168
5.6.5 Density Functional Theory Calculations .................................................................................. 169
5.7 Conclusions ..................................................................................................................................... 170
5.8 References ....................................................................................................................................... 170
Chapter 6. Synthesis and Electrocatalytic HER Studies of Carbene-Ligated Cu 3-xP Nanocrystals .......... 174
6.1 Abstract ........................................................................................................................................... 174
6.2 Introduction ..................................................................................................................................... 174
6.3 Experimental ................................................................................................................................... 176
6.3.1 Materials and General Procedures ........................................................................................... 176
6.3.2 Preparation of (TMS) 3P Stock Solution ................................................................................... 176
6.3.3 Synthesis of NHC-Stabilized Cu 3-xP Nanocrystals .................................................................. 176
6.3.4 Characterization ....................................................................................................................... 177
6.3.5 Electrochemical Methods ......................................................................................................... 178
x

6.3.6 Density Functional Theory ....................................................................................................... 179
6.4 Results and Discussion ................................................................................................................... 180
6.4.1 Synthesis and Characterization ................................................................................................ 180
6.4.2 Electrocatalytic HER Studies ................................................................................................... 188
6.4.3 Density Functional Theory Calculations .................................................................................. 196
6.5 Conclusions ..................................................................................................................................... 198
6.6 Ligand Density Calculations ........................................................................................................... 198
6.7 References ....................................................................................................................................... 200
Bibliography ............................................................................................................................................. 204

xi

List of Tables
Table 2.1 Bond dissociation energies calculated for different selenium precursors. Geometry optimizations were
performed using the 6-31G(d) basis set and the BMK functional. Then, single-point energy
calculations were carried out with the 6-311G(d,p) basis set and the BMK functional. Thiophenol was
used was a control calculation to gauge the accuracy of these estimates. The experimentally
determined bond C–S dissociation energy of thiophenol is 86.5 ± 2 kcal/mol., 59
Table 4.1 Bader charges of the Cu, Fe, and Se atoms in the different phases of CuFeSe 2., 141
Table 5.1 Refined values of the anti-PbCl 2-like Ag 2Se phase for PVP-capped nanocrystals. Parameters correspond
to the Rietveld refinement shown in Figure 5.2a., 155
Table 5.2 Crystallographic parameters of the predominant Ag 2Se phase for PVP-capped nanocrystals from each
of the PDF fits at different temperatures., 159
Table 5.3 Crystallographic parameters of the predominant Ag 2Se phase for PVP-capped nanocrystals from each
of the Rietveld refinement fits at different temperatures using beamline 11-ID-B., 162
Table 6.1 Overview of the HER performance of 1 and 3, 188
Table 6.2 R ct values of 1 extracted from EIS at variable potentials, 190
Table 6.3 R ct values of 3 extracted from EIS at variable potentials, 192
Table 6.4 Comparison of the characteristic values of 1 and 3 before and after electrolysis, 193
Table 6.5 Energy decomposition analysis results of proton binding to the ligated Cu 9P 3 clusters., 197

xii

List of Figures
Figure 1.1 (a) and (b) show the difference in packing along the c-axis for the wurtzite and zinc blende structures,
respectively. (c) and (d) highlight the fact that the wurtzite structure has an eclipsed dihedral
conformation while the zinc blende structure has a staggered dihedral conformation. Adapted with
permission from reference 45. Copyright 1992, American Physical Society., 7
Figure 1.2. (a) Powder X-ray diffraction (XRD) of ZnSe nanocrystals; pattern 1 corresponds to spherical zinc
blende nanocrystals and patterns 2-4 correspond to ZnSe nanorods with aspect ratios of 3, 6, and 8,
respectively. (b) Transmission electron micrographs (TEM) of isotropic zinc blende ZnSe
nanocrystals. (c) TEM of ZnSe nanorods. (d) TEM of ZnSe multipods. All scale bars shown represent
100 nm. Adapted with permission from reference 9. Copyright 2005, American Chemical Society., 8
Figure 1.3 (a) Powder XRD patterns and (b,c) TEM and HR-TEM micrographs, respectively, of wurtzite-like
Cu 2SnSe 3 nanocrystals synthesized from a hot-injection method at 240 °C. (d) Powder XRD patterns
of zinc blende Cu 2SnSe 3 nanocrystals synthesized from hot-injection reactions using (i-ii) Ph 2Se 2 and
(iii) Se powder. Note that patterns i-ii contain a small amount of the wurtzite-like phase, marked by
an asterisk. (e,f) TEM and HR-TEM micrographs, respectively, of zinc blende nanocrystals
synthesized with Ph 2Se 2. Adapted with permission from reference 52. Copyright 2014, American
Chemical Society., 11
Figure 1.4 (a) TEM image of polytypic nanocrystalline tetrapods in which the arms are wurtzite-like and the
central seed/core is zinc blende. (b) TEM image of polytypic linear nanocrystals in which the central
domain/seed is wurtzite-like and the tips are zinc blende. Adapted with permission from reference 52.
Copyright 2014, American Chemical Society., 13
Figure 1.5 (a) Cu 2S-In 2S 3 pseudo-binary phase diagram. Three phases of CuInS 2 exist in the bulk: the low-
temperature chalcopyrite phase (labeled γ), a higher-temperature zinc blende phase (labeled δ), and
the high-temperature wurtzite phase (labeled ζ). (b) Cu 2Se-In 2Se 3 pseudo-binary phase diagram. Two
phases of CuInSe 2 exist in the bulk: the low-temperature chalcopyrite phase (labeled α), and the high-
temperature zinc blende phase (also known as sphalerite, labeled δ). (c) Shown from left to right are
the chalcopyrite structure type, the zinc blende structure type, and the wurtzite structure type for these
ternary materials. For the chalcopyrite structure, blue atoms = Cu
+
, pink atoms = In
3+
, green atoms =
S
2-
/Se
2-
. Note that the cations are ordered within the structure. For the zinc blende and wurtzite
structure types, cations randomly occupy the tetrahedral holes, thus blue atoms represent both Cu
+
and
In
3+
in these structures, and green atoms = S
2-
/Se
2-
. Only CuInS 2 exhibits the wurtzite structure in bulk,
so for this structure, yellow atoms = S
2-
. Phase diagrams adapted with permission from reference 74,
copyright 2000, AIP Publishing, and from reference 76, copyright 1980, Elsevier., 15
Figure 1.6 (a) Powder XRD patterns corresponding to CuInSe 2 nanocrystals synthesized with various diorganyl
diselenide precursors. For R = benzyl and methyl, the resulting nanocrystals have the chalcopyrite
structure, whereas for R = phenyl, the nanocrystals crystallize with a metastable wurtzite-like
structure. (b) TEM micrographs of the CuInSe 2 nanocrystals derived from each respective precursor.
Adapted with permission from reference 66. Copyright 2018, American Chemical Society., 17
Figure 1.7 (a) Pseudo-hexagonal Se
2-
sub-lattice of Cu 3Se 2. (b) Hexagonal Se
2-
sub-lattice of CuInSe 2.
(c) Wurtzite-like structure of CuInSe 2. (d) Side-view of Cu 3Se 2; edge-sharing configurations are
highlighted in yellow, teal, and red. (e) Top-view of Cu 3Se 2; periodic tetrahedral holes within the
structure are traced with dotted red lines. (f) Cu 3Se 2 structure visualized whereby all edge-sharing
tetrahedra have been omitted and the periodic vacant tetrahedral holes in the structure have been traced
with dotted red lines. This suggestive depiction of the Cu 3Se 2 structure appears nearly identical to the
wurtzite structure shown in (c). In all structures, green = Se
2-
. For the wurtzite-like structure, blue
tetrahedra = Cu
+
/In
3+
. For the Cu 3Se 2 structures, pink and blue tetrahedra represent the two
crystallographically unique copper sites within the crystal structure. Adapted with permission from
reference 66. Copyright 2018, American Chemical Society., 18

xiii

Figure 1.8 (a) Differential scanning calorimetry curves for trioctylphosphine-stabilized anti-PbCl 2-like Ag 2Se
nanocrystals (bottom curve) and bulk Ag 2Se powder (top curve). (b) Heating and (c) cooling in
variable-temperature powder XRD scans of 8.6 nm trioctylphosphine-stabilized anti-PbCl 2-like Ag 2Se
nanocrystals. Adapted with permission from reference 86. Copyright 2014, American Chemical
Society., 19
Figure 1.9 (a) Chalcopyrite structure of AgInSe 2. (b) Orthorhombic wurtzite-like structure of AgInS 2. For both
structures, gray atoms = Ag
+
, pink atoms = In
3+
, green atoms = Se
2-
, and yellow atoms = S
2-
.
(c) Pseudo-binary bulk phase diagram of the Ag 2Se-In 2Se 3 system. AgInSe 2 exists at the 50 mol%
composition. Regions 10, 11, and 12 represent AgInSe 2 with the zinc blende structure, zinc blende +
chalcopyrite structures, and the chalcopyrite structure, respectively. The point at 1060 K between
regions 1 and 10 lies on the liquidus curve and represents the melt temperature of AgInSe 2. (d) Pseudo-
binary bulk phase diagram of the Ag 2S-In 2S 3 system. Region 5 = liquid + AgIn 5S 8, region 11 =
orthorhombic AgInS 2 + AgIn 5S 8, region 14 = chalcopyrite AgInS 2. Phase diagrams adapted with
permission from reference 102, copyright 2001, Elsevier, and reference 104, copyright 2008, Elsevier.,
22
Figure 1.10 Powder XRD patterns corresponding to aliquots taken from reactions in which (a) oleic acid was
employed as the coordinating ligand, and (b) oleylamine was employed as the coordinating ligand. (c)
TEM micrographs corresponding to the XRD patterns shown in (b). Adapted with permission from
reference 68. Copyright 2020, American Chemical Society., 23
Figure 1.11 (a) Pseudo-hexagonal Se
2-
sub-lattice of orthorhombic Ag 2Se. (b) Hexagonal Se
2-
sub-lattice of
orthorhombic AgInSe 2. (c) Demarcation of the periodic tetrahedral holes in orthorhombic Ag 2Se. If
this site was occupied with a cation, the resulting tetrahedron would be corner sharing with
neighboring tetrahedra along the edges highlighted in yellow. (d) Side-on view of orthorhombic
Ag 2Se, with the two crystallographically unique Ag
+
sites shown in grey and blue. (e) Orthorhombic
Ag 2Se when viewed by omitting all edge-sharing coordination sites while highlighting periodic
tetrahedral holes within the structure with dotted red lines. (f) Orthorhombic AgInSe 2 structure; grey
tetrahedra = Ag
+
sites, pink tetrahedra = In
3+
sites, green atoms = Se
2-
. Adapted with permission from
reference 68. Copyright 2020, American Chemical Society., 24
Figure 1.12 (a) Probability density of metastable binary metal oxide polymorphs vs the polymorph energies above
the ground state. The blue curve represents the trend for experimentally observed polymorphs, while
the red curve represents the trend for hypothetical, unobserved metastable polymorphs. (b) Graph
demonstrating the requirement of “remnant stability” for the syntheses of metastable polymorphs. (c)
Plot of the calculated energies of experimentally observed polymorphs (blue points) and unobserved
polymorphs (red points) for different binary metal oxides. Note that for each material, there exist
hypothetical polymorphs that fall energetically between experimentally observed polymorphs, proving
that energy above the ground state is not the only factor in determining synthesizability of metastable
polymorphs. Reprinted from reference 112. 2016 © The Authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. Distributed under a Creative
Commons Attribution Non-Commercial License 4.0 (CC BY-NC)., 28
Figure 1.13 (a) Simplified pseudo-binary Ag 2Se-In 2Se 3 phase diagram. Lattice mismatches between phases are
color-coded, where red = body-centered cubic Se
2-
sub-lattice, blue = pseudo-hexagonal Se
2-
sub-
lattice, and white = face-centered cubic Se
2-
sub-lattice. (b) Reaction scheme demonstrating how the
lattice mismatch between orthorhombic Ag 2Se and chalcopyrite AgInSe 2 prevents the thermodynamic
pathway from operating, allowing the system to follow the kinetically faster pathway to yield
metastable orthorhombic AgInSe 2. Adapted with permission from reference 68, copyright 2020,
American Chemical Society, and reference 102, copyright 2001, Elsevier., 30

xiv

Figure 1.14 (a) Depiction of the defect-free ABAB stacking in wurtzite ZnSe. The alternating direction of the Zn-
Se bond is indicated by red and green arrows. (b) Aberration-corrected high-angle annular-dark-field
(HAADF) image of wurtzite ZnSe nanocrystals containing symmetry-breaking defects. In the upper
left corner, a structural model is superimposed upon the image. The bottom right corner is a simulated
HAADF representation of the experimental data. (c) Model representing the atomic structure found in
(b); note that the translational symmetry of the direction of the Zn-Se bond is broken here, as compared
to in (a). Adapted with permission from reference 123, copyright 2016, American Chemical Society., 32
Figure 1.15 (a) ECL mechanism that elucidates interactions between SO 4
●-
and negatively charged ZnSe. (b) Plot
of ECL signal intensity as a function of the net charge of defect regions in different forms of ZnSe, as
measured by electron holography. Note that wurtzite ZnSe has the highest charge and also the greatest
ECL intensity. (c) Potential-dependent ECL intensity for wurtzite ZnSe, zinc blende ZnSe, bulk ZnSe,
and the bare glassy-carbon electrode. (d) The ECL signal (blue curve) is significantly red shifted from
the intrinsic photoluminescence (black curve) of wurtzite ZnSe nanocrystals, suggesting ECL
originates from an intra-gap surface trap state. Adapted with permission from reference 123, copyright
2016, American Chemical Society., 33
Figure 1.16 (a) Calculated density of states for Cu d-states for wurtzite-like (top) and chalcopyrite (bottom)
CuInSe 2. The Fermi energy is set to zero. (b) Calculated band structure for wurtzite-like CuInSe 2. (c)
Calculated band structure for chalcopyrite CuInSe 2. (d) Simulated electronic absorption profiles for
wurtzite-like and chalcopyrite CuInSe 2; note that the wurtzite-like phase is expected to display
comparable or superior absorption to the chalcopyrite phase from 920 – 613 nm (1.35 – 2.0 eV) of the
electromagnetic spectrum. Adapted with permission from reference 127, copyright 2012, Royal
Society of Chemistry., 35
Figure 1.17 (a) Scheme illustrating the proposed solution-solid-solid mechanism of cubic Ag 2Se-catalyzed ZnSe
nanowire growth. (b) TEM micrograph of ZnSe nanowires grown via Ag 2Se catalysis. Note that the
nanowires are capped with Ag 2Se tips. (c) Scanning TEM micrograph and energy-dispersive
spectroscopy elemental mapping of ZnSe nanowires capped with the Ag 2Se tip. Adapted with
permission from reference 93, copyright 2013, American Chemical Society., 38
Figure 1.18 (a) Mid-infrared absorption spectra for anti-PbCl 2-like Ag 2Se nanocrystals of different sizes. The
large peak at 0.35 eV corresponds to a solvent absorption peak. (b) Plot of the lowest transition
energies for anti-PbCl 2-like Ag 2Se nanocrystals as a function of nanocrystal diameter. (c) Lowest
transition energies vs 1/nanocrystal radius. The red curve represents the predicted lowest transition
energies as a function of 1/radius as calculated through effective mass theory. This relationship is
linear when plotted lowest transition energies versus 1/radius
2
(inset). Adapted with permission from
reference 142, copyright 2012, Royal Society of Chemistry., 39
Figure 2.1 (a) FT-IR spectra of Cu 2-xSe and Cu 3Se 2 intermediates that were isolated from aliquot studies during
the synthesis of chalcopyrite and wurtzite-like CuInSe 2, respectively. Both indicate that oleylamine
ligands are bound to the surface of these intermediates as the spectra display IR bands characteristic
of oleylamine (2800-3000 cm
-1
ν C-H, 1520 – 1700 cm
-1
δ N-H, 1460 cm
-1
δ C-H, 1384 cm
-1
ν C-N). (b)
Normalized TGA curves of intermediate Cu 2-xSe and Cu 3Se 2 nanocrystals that were obtained from
aliquots in the synthesis of chalcopyrite and wurtzite-like CuInSe 2, respectively. The two curves have
qualitatively similar profiles and both exhibit distinct mass loss events near 350 °C, which is the
boiling point of oleylamine. This further supports that oleylamine is the ligand bound to these
intermediates., 57
Figure 2.2 (a) Powder X-ray diffraction patterns of CuInSe 2 nanocrystals derived from the corresponding
diselenide precursors shown at right. The C–Se bond dissociation energies that were calculated by
DFT are given below each precursor.

(b) Transmission electron micrographs of the nanocrystals that
result from syntheses using the four different selenium precursors., 59

xv

Figure 2.3 (a,b) Phase progression of chalcopyrite CuInSe 2 nanocrystals when using the Bn 2Se 2 precursor, as
monitored by XRD. Times correspond to the time after injection of InCl 3. A clear progression can be
seen from these copper selenide intermediates to the final chalcopyrite CuInSe 2 product. After 3 min,
Cu 2–xSe and CuSe intermediates are both observed. (c,d) Phase progression of the wurtzite-like
CuInSe 2 nanocrystals when using the Ph 2Se 2 precursor, as monitored by XRD. After 3 min, the
umangite Cu 3Se 2 phase is the primary intermediate., 61
Figure 2.4 XRD patterns of aliquots taken from the reaction between Bn 2Se 2 and Cu(oleate) 2 heated in oleylamine
to 220 °C in the absence of InCl 3. Aliquots of the reaction solution were removed as the flask was
heated and after the reaction flask reached 220 °C. The aliquot at 2 min reveals that some crystalline
products begin to form at relatively low temperatures., 61
Figure 2.5 XRD pattern of the product resulting from a control reaction between Bn 2Se 2 and Cu(oleate) 2 at 220 °C
in the absence of InCl 3. The same Cu 2–xSe and CuSe intermediates were observed as those in Figure
2.3a,b., 62
Figure 2.6 XRD patterns of aliquots taken from a control reaction between Bn 2Se 2 and Cu(oleate) 2 at 220 °C in
the absence of InCl 3. CuSe does not convert to Cu 2–xSe in the absence of In
3+
in solution., 63
Figure 2.7 (a) XRD patterns of aliquots taken under the same conditions as the reaction shown in Figure 2.3a,b
except performed at a final reaction temperature of 255 °C. The same Cu 2–xSe intermediate is observed
at early times, which is consistent with our hypothesis that Cu 2–xSe is the reactive intermediate that
produces chalcopyrite CuInSe 2. (b) XRD patterns of aliquots taken under the same conditions as the
reaction shown in Figure 2.3c,d except performed at a final reaction temperature of 255 °C. The same
Cu 3Se 2 intermediate was observed, consistent with our hypothesis that Cu 3Se 2 is the reactive
intermediate that produces wurtzite-like CuInSe 2., 64
Figure 2.8 UV-vis-NIR absorption spectra of the aliquots of the reaction shown at left in Figure 2.7; at early times,
Cu 2–xSe intermediates are present and display a significant localized surface plasmon resonance
(LSPR) feature in the near infrared. As Cu 2–xSe is consumed to yield CuInSe 2, this feature disappears
as the aliquots at later times display an absorption spectrum characteristic of chalcopyrite CuInSe 2
nanocrystals., 65
Figure 2.9 XRD pattern of the product resulting from a reaction with Me 2Se 2; full conversion to chalcopyrite
CuInSe 2 is not observed under these conditions (held at a low temperature, 220 °C for 20 min) as
indicated by the presence of the Cu 2–xSe intermediates., 65
Figure 2.10 Illustration of the phase transformation of the cubic antifluorite-type Cu 2–xSe structure to the
tetragonal chalcopyrite CuInSe 2 structure upon exchange of Cu for In cations (Cu = blue, In = pink,
Se = green). The fcc Se sub-lattice is effectively unchanged in this transformation; the high-
temperature lattice constant (433 K) for Cu 2Se is 5.787 Å, which would require an expansion of only
0.078% to match the lattice constant of the chalcopyrite Se sub-lattice lattice parameter of 5.792 Å at
433 K.
46,47
CIF files for the Cu 2-xSe and chalcopyrite CuInSe 2 phases were taken from references
48,49., 66
Figure 2.11 XRD pattern of the product resulting from a control reaction between Ph 2Se 2 and Cu(oleate) 2 at
220 °C for 3 min in the absence of InCl 3. The same Cu 3Se 2 phase was produced, consistent with the
observations in Figure 2.3c,d and Figure 2.7., 68

xvi

Figure 2.12 (a) Se sub-lattice of Cu 3Se 2. Each Se atom has six nearest neighbors that are nearly in plane. These
planes of Se alternate in an ABAB fashion along the [010] direction. (b) Se sub-lattice of wurtzite-like
CuInSe 2. Close packing occurs along the [001] direction. By XRD, the experimental d-spacing for the
(002) planes in our wurtzite-like CuInSe 2 nanocrystals is 3.343(2) Å, which requires a 4.44%
expansion of the interplanar Se•••Se distance within umangite as obtained from the crystal structure
of Cu 3Se 2. (c) Wurtzite-like structure of CuInSe 2; it was assumed that Cu and In cations are randomly
distributed throughout the tetrahedral sites in the structure, so the blue tetrahedra represent both Cu
and In positions. (d) Side view of the Cu 3Se 2 structure along the [001] direction. Note that the first Cu
position (blue) shares four edges (highlighted in yellow) with second Cu position (pink). Each pink
tetrahedron shares two edges (highlighted in red) with a blue tetrahedron and one edge (highlighted in
teal) with an adjacent pink tetrahedron. (e) Top view of Cu 3Se 2 looking down the direction of close
packing [010]. Pink tetrahedra are corner sharing along the [001] direction, and there exist tetrahedral
holes that prevent corner-sharing connections between pink tetrahedra along the [100] direction. These
tetrahedral holes are demarcated by dotted red lines. In going to the wurtzite-like structure, Cu or In
ions must fill the tetrahedral holes indicated in (e). To maintain charge neutrality, two Cu ions must
diffuse out of the Cu 3Se 2 intermediate per In
3+
ion; one Cu must come from the first position of Cu
(blue tetrahedra) and the other from the second position (pink tetrahedra). (f) The structure generated
by removing these tetrahedra from the structure; the red dotted lines represent the tetrahedral holes
that are filled in the transformation to the wurtzite phase, giving a structural motif similar to that shown
in (c). The CIF file for the Cu 3Se 2 phase was obtained from reference 59., 68
Figure 2.13 Powder XRD patterns of the wurtzite-like CuInSe 2 nanocrystals before and after heating to 300 °C in
octadecene for 2.5 h showing that the metastable phase does not undergo a phase transformation to
the thermodynamic chalcopyrite phase., 71
Figure 2.14 (a) TGA curves after heating the wurtzite-like CuInSe 2 nanocrystals to 300 °C. No additional mass
loss was sustained from the material after the first cycle of heating. (b) Powder XRD patterns taken
after each cycle of heating to 300 °C show that the wurtzite-like phase is thermally stable up to this
temperature. (c) TGA curve after heating the wurtzite-like CuInSe 2 nanocrystals to 420 °C. The
material lost ~13% of its weight due to the volatilization of surface ligands from the nanocrystals. (d)
Powder XRD indicates that a nearly complete phase transformation to the thermodynamic chalcopyrite
phase results after one cycle of heating to 420 °C., 72
Figure 2.15 XRD pattern showing a mixture of chalcopyrite and wurtzite phases resulting from a reaction at 300
°C for 1.5 h using Ph 2Se 2. This indicates that the Cu 3Se 2 that normally nucleates when using Ph 2Se 2
were partially converted to Cu 2–xSe intermediates that are more stable at high temperatures. This
mixture of copper selenide phases then reacts to produce mixed wurtzite-like and chalcopyrite phase
CuInSe 2., 73
Figure 2.16 Mixture of copper selenide phases that results when heating Ph 2Se 2 with Cu(oleate) 2 at 220 °C for 15
min., 74
Figure 2.17 (a) XRD pattern of the product resulting from a control reaction between Ph 2Se 2 and Cu(oleate) 2 in
oleylamine at 300 °C, showing that the Cu 2–xSe phase is the predominant phase formed at this
temperature. This supports our hypothesis that at high temperatures the Cu 3Se 2 intermediate converts
to Cu 2–xSe to yield a mixture of wurtzite-like and chalcopyrite CuInSe 2 nanocrystals. (b) UV-vis-NIR
spectrum of the product of the reaction shown in (a). The distinct LSPR feature provides additional
confirmation that the Cu 2–xSe phase is produced when reacting Ph 2Se 2 with Cu(oleate) 2 at 300 °C., 75
Figure 3.1. (a) Powder XRD pattern of orthorhombic AgInSe 2 nanocrystals formed in the presence of oleylamine,
with the results from a Rietveld refinement to the Pna2 1 structure. Tick marks represent individual
reflections of the orthorhombic structure with the difference pattern shown below. λ = 1.5406 Å. (b)
High-resolution TEM micrograph of the orthorhombic AgInSe 2 nanocrystals., 87
Figure 3.2 (a) Rietveld refinements of powder XRD patterns of AgInSe2 in the (a) wurtzite P63mc space group
and in the (b) orthorhombic Pna21 space group. Note that the Pna21 structure can be distinguished by
unique experimentally observed reflections at 20-21° 2θ from the (111) and (020) lattice plane
families, which are absent in a higher symmetry wurtzite structure type., 92
xvii

Figure 3.3 SEM-EDX elemental analysis of orthorhombic AgInSe 2 particles synthesized in oleylamine. After 30
min, the nanocrystals converged close to the expected 1:1:2 ratio of Ag:In:Se at 1:1.04:1.96. The inset
shows how the nanocrystals changed in composition over time, going from metal-rich to more
selenium-rich compositions with time. The 10 and 15 min aliquots demonstrate that the orthorhombic
phase of AgInSe 2 (showing no indications of Ag 2Se at these times by XRD) is compositionally
flexible. Indeed, the we found that the Ag:In:Se ratio could contain as little Se as a 1:1.03:1.37 ratio
while still maintaining the orthorhombic phase (this corresponds to the aliquot taken at 10 min). This
represents a 30% reduction in the amount of Se as compared to the 1:1.04:1.96 ratio measured for the
aliquot taken at 30 min., 93
Figure 3.4. (a) XRD of orthorhombic AgInSe 2 synthesized at 250 °C in oleylamine. The metastable phase persists
at this higher temperature. The mismatch between the reference pattern and the experimental
diffraction pattern may be due preferred orientation of the anisotropic platelets that form under these
conditions, or perhaps from the presence of a chalcopyrite AgInSe 2 impurity. If the latter were the
case, however, a more pronounced shoulder would likely be visible to the left of the peak at 43° 2θ,
as can be distinguished in Figure 3.5. (b) TEM image of the anisotropic platelets that form under these
conditions., 94
Figure 3.5. (a) Annealing powders of the as-prepared orthorhombic AgInSe 2 nanocrystals to 300 °C does not
cause the material to thermally relax to the thermodynamically preferred chalcopyrite structure by
XRD, even after several heating-cooling cycles, indicating that there is a barrier to a phase transition
to the chalcopyrite phase. Note, however, that at these temperatures some of the Ag
+
is reduced to Ag
(marked with *). Powder XRD of the material taken from the TGA crucible after heating to 450 °C
shows that the reduction of Ag
+
to Ag is more pronounced at higher temperatures, but that the
orthorhombic phase still persists. Notably, this progression of XRD patterns was taken from a material
that had been left on the lab bench for 10 months. (b) Heating as-synthesized orthorhombic AgInSe 2
nanocrystals in 1-octadecene at 300 °C for 1 h shows that the orthorhombic phase is still predominant,
although XRD indicates some conversion of orthorhombic to chalcopyrite AgInSe 2, as evidenced by
a growth in the intensity of the peak around 26° 2θ and the asymmetry of the peak at 43° 2θ., 95
Figure 3.6 (a) Aliquot study to elucidate the formation pathway of chalcopyrite AgInSe 2 nanocrystals by powder
XRD. A mixture of binary Ag 2Se phases (tetragonal and orthorhombic) is obtained at early times. This
mixture progresses towards chalcopyrite AgInSe 2 as a function of increasing time, but binary
intermediates are still present even after 15 min. (b) Aliquot study to follow the formation of the
metastable orthorhombic phase of AgInSe 2 by powder XRD reveals that the metastable ternary phase
forms more quickly than chalcopyrite AgInSe 2 when oleylamine is present in large excess (46
equivalents), as no Ag 2Se intermediates are observed by XRD after 10 min. Powder XRD shows that
under these conditions, a similar mixture of orthorhombic and tetragonal Ag 2Se forms at early times.
(c) TEM images of the aliquots corresponding to the diffraction patterns in (b) show that the
nanocrystals evolve over time from isotropic intermediates to anisotropic platelets of orthorhombic
AgInSe 2., 96
Figure 3.7 Powder XRD aliquot studies of a reaction in which Bn 2Se 2 was hot-injected into a flask containing a
solution of only AgNO 3 (with no In(OAc) 3 present). A complex mixture of Ag 2Se polymorphs results.
Although cubic Ag 2Se is the thermodynamically stable polymorph at the reaction temperatures, no
significant phase transitions were observed over the time scale of the reaction, indicating that the other
phases of Ag 2Se present are kinetically resistant towards a phase transition to cubic Ag 2Se under these
conditions., 98
Figure 3.8 (a) Se
2–
sub-lattice of chalcopyrite AgInSe 2; note that the lattice is fcc as it contains an ABC packing
motif. (b) Se
2–
sub-lattice of cubic Ag 2Se; this lattice is body-centered cubic., 99

xviii

Figure 3.9 (a) Hot-injection reactions (highlighted with yellow background) that were allowed to react for longer
times in the presence of excess In
3+
(the initial reactions were performed with 1:1 In:Ag ratios) did not
produce phase-pure chalcopyrite AgInSe 2 by power XRD. Heating-up reactions (highlighted with blue
background) showed better conversion to chalcopyrite AgInSe 2 in the presence of excess In
3+
, with
the 3 h reaction producing nearly phase-pure chalcopyrite AgInSe 2 as shown by a Rietveld refinement
of powder XRD data in (b). All reactions were performed at 250 °C. (c) TEM images corresponding
to chalcopyrite AgInSe 2 for the 3 h heating up method. The rectangular morphologies correspond to
the cubic crystal habit of the chalcopyrite phase., 100
Figure 3.10 Results of all reactions in which TOP was used in attempts to make orthorhombic AgInSe 2. Reaction
A: Oleylamine was replaced with an equal amount of TOP (1 mL). The reaction was heated and the
Bn 2Se 2 was injected at 200 °C. After 2 min, the reaction was stopped due to dissolution of the product;
Ag nanoparticles crashed out of solution. Reaction B: Amount of TOP was reduced to 75 μL total.
The reaction was heated and the Bn 2Se 2 was injected at 200 °C. After 2 min, the reaction was stopped;
Ag 2Se with Ag nanoparticles resulted. Reaction C: Total amount of TOP was 150 μL. The reaction
was heated and the Bn 2Se 2 was injected at 200 °C. After 2 min, the reaction was stopped; Ag 2Se with
Ag nanoparticles resulted. Reaction D: Total amount of TOP was 150 μL. The reaction was heated
and the Bn 2Se 2 was injected at 200 °C. The reaction vessel was rapidly cooled to 100 °C after injection
to slow down the dissolution of Ag 2Se, and left at 100 °C for 30 min in an effort to allow cation
exchange to occur; Ag 2Se with Ag nanoparticles resulted. Reaction E: Total amount of TOP was 500
μL. The reaction was heated and the Bn 2Se 2 was injected at 200 °C. An aliquot was taken after 1 min,
which resulted in Ag 2Se with Ag nanoparticles (E1). The remaining product was allowed to react for
1 additional minute until the material appeared to dissolve, yielding only Ag nanoparticles (E2)., 98
Figure 3.11 (a) Rietveld refinement of powder XRD data and (b) TEM images of orthorhombic AgInSe 2
synthesized in the presence of 1-dodecanethiol. The nanocrystals are 10.1 nm ± 1.0 nm for N = 300
particles. Since 1-dodecanethiol is known to decompose and release sulfur at these reaction
temperatures, it is possible some sulfur is incorporated into the orthorhombic anion sub-lattice.
Quantifying the amount of sulfur in the nanocrystal lattice is non-trivial, as 1-dodecanethiol also
coordinates to the surface of these nanocrystals as a ligand. However, from the c lattice parameter of
the refinement shown in (a), we can interpolate roughly how much sulfur has been incorporated into
the nanocrystal lattice using Vegard’s law and the published lattice parameters of orthorhombic
AgInSe 2 and AgInS 2 (see reference 39). Using this approach, there is roughly 10% sulfur incorporation
into these orthorhombic nanocrystals., 99
Figure 3.12 (a) Aliquots taken directly after injection of Bn 2Se 2 when 1-dodecanethiol is present (1 mL total)
indicate that orthorhombic AgInSe 2 forms very quickly at elevated temperatures (230 °C). (b)
Reducing the amount of 1-dodecanethiol to 120 μL allowed for the observation of orthorhombic Ag 2Se
intermediates at short reaction times., 100
Figure 3.13 (a) HR-TEM of Ag 2Se taken from the 1 min aliquot (b) Line profile of the lattice fringes seen in (a).
The 0.298 nm d-spacing corresponds to the reflection in the XRD observed at 30.5° 2θ., 101
Figure 3.14 (a) Size analysis of dots and platelets as a function of time. The size for the dots is represented by the
diameter, whereas for the platelets, size is represented by the length of the long axis. (b) Population
percentages of dots vs. platelets as a function of time., 101
Figure 3.15 (a) HR-TEM of orthorhombic AgInSe 2 taken from the 30 min aliquot (b) Line profile of the lattice
fringes seen in (a). The 0.348 nm d-spacing corresponds to the reflection in the XRD observed at 25.6°
2θ. (c) HR-TEM of orthorhombic AgInSe 2 taken from the 30 min aliquot. (d) Line profile of the lattice
fringes seen in (c). The 0.320 nm d-spacing corresponds to the reflection in the XRD observed at 27.8°
2θ., 102

xix

Figure 3.16. (a) Se
2–
sub-lattice of orthorhombic Ag 2Se. Se
2–
exists in nearly-planar hexagonal sheets that display
significant in-plane angular distortions. (b) Se
2–
sub-lattice of orthorhombic AgInSe 2. (c) Illustration
of the tetrahedral holes (T h) within the orthorhombic Ag 2Se structure. If this site were occupied with
a cation, the resulting tetrahedron would be corner-sharing with neighboring tetrahedra along the edges
highlighted in yellow. (d) Full structure of orthorhombic Ag 2Se, with the trigonally coordinated Ag
+

sites shown in blue and tetrahedral sites shown in gray. (e) Depiction of orthorhombic Ag 2Se when all
trigonal sites are removed from the structure; the periodic tetrahedral holes within the structure are
illustrated by dashed red lines. This corner-sharing structure is nearly identical to that of orthorhombic
AgInSe 2. (f) Full structure of orthorhombic AgInSe 2 (green atoms = Se, gray atoms/tetrahedra = silver,
pink atoms/tetrahedra = indium)., 103
Figure 3.17 (a) Orthorhombic Ag 2Se as viewed along the [010] direction. The periodic T h holes are shown with
red dashed lines. Note that these vacancies are uninterrupted along the [100] direction. The arrows
represent how a Ag
+
ion would necessarily have to migrate to create the orthorhombic AgInSe 2
structure during a cation exchange process with In
3+
. (b) Orthorhombic AgInSe 2 as viewed along the
[001] direction. Note that Ag
+
and In
3+
sites alternate along the [010] direction. (c) Unit cell of
orthorhombic AgInSe 2. (d) Unit cell of the theoretical structure that would form if the T h holes of
orthorhombic Ag 2Se were systematically filled by incoming In
3+
and no ion-hopping mechanism were
operative. This unit cell is less stable than (c), as demonstrated by ionic site potential and Madelung
energy calculations., 105
Figure 3.18 (a) The 0 K phase diagram of the Ag-In-Se chemical system, color coded by calculated formation
energy. (b) The relative ordering of AgInSe 2 polymorphs, as predicted by calculation., 106
Figure 3.19 (a) Silver-rich region within the pseudo-binary phase diagram of the Ag 2Se-In 2Se 3 phase space for
each respective phase (blue = pseudo-hcp, red = bcc, white = fcc). Notably, there exist lattice
mismatches in going from either phase of Ag 2Se to chalcopyrite AgInSe 2. Such lattice mismatches can
be taken advantage of by leveraging fast cation exchange kinetics on the nanoscale to generate novel
metastable ternary structures. (b) Reaction scheme explaining isolation of metastable AgInSe 2; the
orthorhombic phase of AgInSe 2 is only 10 meV/atom in energy higher than the chalcopyrite phase and
has a Se
2–
sub-lattice analogous to that of Ag 2Se, allowing for fast, coordinating ligand-mediated
conversion to the ternary metastable phase. Panel a: Adapted with permission from reference 43.
Copyright 2001 Elsevier., 108
Figure 4.1 (a) Kesterite structure of Cu 2ZnSnSe 4 (ICSD collection code 189278). (b) Stannite structure of
Cu 2FeSnSe 4 (ICSD collection code 85126). Kesterite and stannite are both I 2-II-IV-VI 2 semiconductor
structure types, and they differ only in the ordering and placement of the I, II, and IV cations. (c)
Structure of eskebornite CuFeSe 2 (ICSD collection code 73376). (d) Structure of chalcopyrite CuFeS 2
(ICSD collection code 2518). (e) Structure of wurtzite ZnS (ICSD collection code 67453). (f) Structure
of wurtzite-like Cu 2FeSiS 4 (ICSD collection code 627355), which has lower space group symmetry
than ZnS due to cation ordering within the hexagonal lattice. (g) Hypothetical chalcopyrite-type
CuFeSe 2 used in our DFT calculations. (h) Hypothetical wurtzite-like (Pna2 1 space group) CuFeSe 2
used in our DFT calculations., 116
Figure 4.2 Powder XRD of Cu 3Se 2 nanocrystals prepared by the reaction between Ph 2Se 2 with Cu(oleate) 2 in
oleylamine for 3 min at 220 °C. Reference stick pattern generated from Cu 3Se 2 CIF from ICSD
collection code 239., 122

xx

Figure 4.3 (a) Powder XRD patterns of reaction aliquots taken during the synthesis of wurtzite-like Cu 2FeSnSe 4
nanocrystals. Prior to injection of Sn and Fe precursors, the intermediate can clearly be indexed to
Cu 3Se 2 (aliquot 1, black pattern). At 3 min after the injection of Sn(ethylhexanoate) 2, a hexagonal
ternary intermediate is observed (aliquot 2, blue pattern), into which Fe diffuses after injection of
Fe(acac) 3 (aliquot 3, green pattern, taken 3 min after injection of Fe(acac) 3). Thereafter, the quaternary
hexagonal intermediate gives way to wurtzite-like Cu 2FeSnSe 4 nanocrystals (aliquots 4-5, yellow and
red patterns, taken 15 and 30 min after injection of Sn(ethylhexanoate) 2, respectively). (b) Rietveld
refinement of the XRD data of the 30 min aliquot (aliquot 5) confirms that a cation-ordered Pmn2 1
unit cell is an appropriate structural model for this wurtzite-like polymorph (χ
2
= 3.458, wR = 5.75%,
a = 8.02 Å, b = 6.91 Å, c = 6.60 Å, α = β = γ = 90°). λ = 1.5406 Å. The refined structure is shown in
the inset. (c) Plot of the elemental compositions of aliquots 1-5 as a function of time, where t = 0
corresponds to the time at which aliquot 1 was taken. The vertical green and black dashed lines
represent the times at which Sn(ethylhexanoate) 2 and Fe(acac) 3 were injected, respectively. All data
points are average atom percentages as determined by SEM-EDS, and error bars represent ± 1σ from
the average at%., 123
Figure 4.4 Rietveld refinement of XRD pattern of 30 min aliquot to the P6 3mc wurtzite structure. λ = 1.5406 Å.
Note that the model fails to account for small reflections that are accounted for in the Pmn2 1
refinement, and that Cu, Fe and Sn are assigned to the same crystallographic site within the structure.,
124
Figure 4.5 Pmn2 1 is related to the P421m space group as the former is a non-isomorphic subgroup of the latter.
Shown here are group-subgroup relationships between P421m, Pmn2 1, and space groups of
intermediate symmetry., 124
Figure 4.6 (a) The (101) plane of Cu 3Se 2. As shown, the d-spacing of this plane represents the distance between
a Se
2–
anion and the mid-point between two in-plane nearest neighbor Se
2–
anions when looking down
the [010] direction. (b) The (210) lattice plane of wurtzite-like Cu 2FeSnSe 4 is analogous to the (101)
of Cu 3Se 2. (c) and (d) reveal that the (111) lattice plane of Cu 3Se 2 is analogous to the (211) of wurtzite-
like Cu 2FeSnSe 4. (e) The (002) is the basal plane of wurtzite-like Cu 2FeSnSe 4, and contains only Cu,
Fe and Sn cations. (f) Lattice fringes corresponding to the (020) plane of wurtzite-like Cu 2FeSnSe 4 are
clearly seen in the high-resolution TEM micrographs of wurtzite-like Cu 2FeSnSe 4 nanocrystals., 125
Figure 4.7 (a)-(e) Raw SEM-EDS data for aliquots 1-5. Each point in Figure 4.3c is an average of four of these
SEM-EDS measurements. (f) SEM-EDS data for the non-aliquot reaction. The powder XRD of this
reaction is shown in the inset., 127
Figure 4.8 (a) UV-vis-NIR absorption spectra of aliquots taken during the synthesis of wurtzite-like Cu 2FeSnSe 4
nanocrystals. Note that there are large surface plasmon resonance features that persist up to 3 min after
injection of Fe(acac) 3 (aliquots 1-3). (b) Inverse logarithmic derivative (ILD) plot (black data points)
of the aliquot 5 UV-vis-NIR spectrum. The dashed red line represents the linear regression that was
used to estimate the optical band gap from the ILD plot using values from 2.0-3.5 eV; the dashed blue
line represents band gap estimation using values from 2.0-4.0 eV. From these, the optical band gap
was determined to lie between 1.48-1.59 eV. The inset shows the UV-vis-NIR spectrum of the aliquot
5 Cu 2FeSnSe 4 nanocrystal suspension in tetrachloroethylene from which the ILD plot was calculated.,
128
Figure 4.9 (a) TEM micrograph of Cu 3Se 2 nanocrystals formed after reacting for 3 min at 220 °C, before Sn or
Fe precursor injections. (b) TEM micrograph of product obtained 3 min after Sn(ethylhexanoate) 2
injection. (c) TEM micrograph of product obtained 3 min after Fe(acac) 3 injection. (d-e) TEM
micrographs of product obtained 15 and 30 min after Sn(ethylhexanoate) 2 injection, respectively. (f)
HR-TEM image of product obtained 30 min after Sn(ethylhexanoate) 2 injection. Lattice fringes from
the (020) planes are visible. (g) Composite image of EDS elemental mapping of Cu, Fe, Sn and Se in
the wurtzite-like Cu 2FeSnSe 4 nanocrystals. (h) Elemental maps of Cu, Fe, Sn, and Se., 130

xxi

Figure 4.10 Relaxed geometric structures and lowest-energy antiferromagnetic configurations for (a) Pmn2 1
Cu 2FeSnSe 4 and (b) I42m Cu 2FeSnSe 4. Experimental magnetic studies of stannite Cu 2FeSnSe 4
confirm that it is antiferromagnetic at low temperatures.
2,3
Comparison of the DFT total energies
indicates that Pmn2 1 Cu 2FeSnSe 4 has a slightly higher energy than I42m Cu 2FeSnSe 4 of 9.4
meV/atom. (c) Calculated phonon dispersion for the Pmn2 1 phase of Cu 2FeSnSe 4 indicates that this is
a dynamically stable structure. The phonon dispersion spectrum is calculated with the Phonopy code
using the finite displacement method and a 2   2  2 supercell., 132
Figure 4.11 Orbital projected density of states (DOS) of (a) Pmn2 1 Cu 2FeSnSe 4 and (b) I42m Cu 2FeSnSe 4. The
atom projected DOS is shown in Figure 4.12., 133
Figure 4.12 Spin-density of states (DOS) calculated with the HSE06 functional for (a) the wurtzite-like Pmn2 1
polymorph of Cu 2FeSnSe 4 and (b) the stannite I42m polymorph of Cu 2FeSnSe 4. Note the difference
in DOS between the two polymorphs near the CBM, where the Pmn2 1 polymorph only has a sparse
manifold of states that can protect hot electrons. Orbital resolved DOS is shown in Figure 4.11.
(c) Band structure around the Γ point calculated with the HSE06 functional for spin-up channel. The
corresponding spin-down channel data are given in Figure 4.13. The Pmn2 1 polymorph of Cu 2FeSnSe 4
has a sharp dispersion along the Z-Γ direction, indicating that its electron is lighter and has a higher
mobility in the z-direction compared to the stannite I42m polymorph., 134
Figure 4.13 Band structure around the Γ point calculated with the HSE06 functional for spin-down channel. The
corresponding result for the spin-up channel is shown in Figure 4.12. The Pmn2 1 polymorph of
Cu 2FeSnSe 4 has a sharp dispersion in the conduction band along the Z-Γ direction, indicating that the
effective mass of the electron is smaller than in I42m Cu 2FeSnSe 4 and that it should have a higher
electron mobility in the z-direction than the stannite I42m polymorph., 135
Figure 4.14 (a) XRD patterns of control aliquot study (1) in which Fe(acac) 3 was injected before
Sn(ethylhexanoate) 2. (b) XRD analysis of the final products of this reaction shows the resulting
material is not phase-pure wurtzite-like Cu 2FeSnSe 4, as the 100% intensity peak coincides with the
100% intensity peak of stannite Cu 2FeSnSe 4, rather than with the 100% intensity peak of wurtzite-like
Cu 2FeSnSe 4., 138
Figure 4.15 (a) XRD patterns of control aliquot study (2) in which Fe(acac) 3 (without Sn(ethylhexanoate) 2) was
injected at any point (with all other variables remaining constant). From this aliquot study, it can be
seen that Cu 3Se 2 nanocrystals nucleate (black pattern) and lead to a hexagonal Cu-Fe-Se intermediate
(blue pattern). However, this ternary intermediate soon gives way to Cu 2–xSe and eskebornite CuFeSe 2
(green pattern) ultimately producing phase-pure eskebornite CuFeSe 2 after 15 min (yellow pattern).
(b) XRD patterns comparing the intermediates generated by injecting Fe (black pattern) or Sn (red
pattern) into Cu 3Se 2 nanocrystals, it is apparent that the mechanisms of Fe and Sn incorporation into
nanocrystals are similar, since structurally similar ternary intermediates form under both conditions.
However, whereas phase-pure wurtzite-like Cu 2FeSnSe 4 forms from the Cu-Sn-Se intermediate when
Sn is injected first, the Cu-Fe-Se intermediate does not yield wurtzite-like CuFeSe 2 in the absence of
Sn. This is strong evidence that eskebornite is too thermodynamically favored to yield wurtzite-like
products., 138
Figure 5.1 (a) TEM micrograph of PVP-capped Ag 2Se nanocrystals. The apparent polycrystalline nature of the
PVP-Ag 2Se nanocrystals is clearly visible. (b) High resolution TEM micrograph exhibiting lattice
fringes with measured d-spacing corresponding to the (110) lattice plane of the anti-PbCl 2-like crystal
structure. The inset in the lower right-hand corner depicts the (110) lattice planes in the anti-PbCl 2-
like crystal structure. (c) Ag and (d) Se elemental distributions in a single PVP-capped Ag 2Se
nanocrystal as determined by TEM-EDX. These elemental maps show that Ag and Se are evenly
distributed throughout the nanocrystal., 153

xxii

Figure 5.2 (a) Rietveld refinement of the proposed anti-PbCl 2-like structure to the experimental powder XRD
pattern of metastable Ag 2Se nanocrystals (λ = 1.5406 Å). The experimental diffraction pattern is
shown with black data points, and the refined model is shown as the blue trace, with the difference
pattern shown below in turquoise. For reference, the calculated powder diffraction pattern of Günter
and Keusch’s “tetragonal” phase is shown in red. The most prominent peak arising from orthorhombic
Ag 2Se is marked by a green asterisk (*), which forms from spontaneous relaxation of the anti-PbCl 2-
like phase. (b) Unit cell of Günter and Keusch’s “tetragonal” phase. (c) Unit cell of the proposed anti-
PbCl 2-like polymorph of Ag 2Se., 154
Figure 5.3 Rietveld refinement of laboratory diffraction powder XRD data of 55-nm oleylamine (OLA)-capped
Ag 2Se nanocrystals (λ = 1.5406 Å). The anti-PbCl 2-like structure provides an excellent fit for this
experimental data., 155
Figure 5.4 Rietveld refinement of synchrotron powder XRD collected on 26-nm Ag 2Se nanocrystals prepared by
the N-heterocyclic carbene method of Lu et al.
26
(λ = 0.143 Å). The anti-PbCl 2-like structure provides
an excellent fit for this experimental data., 156
Figure 5.5 PDFs extracted from variable temperature synchrotron X-ray total scattering data collected at
(a) 25 °C, (b) 120 °C, and (c) again at 25 °C (λ = 0.143 Å). Black circles indicate the PDF and upper
red lines indicate the fit. Lower red lines indicate the difference between the data and the fit., 158
Figure 5.6 Rietveld refinements of synchrotron powder XRD collected on PVP-capped Ag 2Se nanocrystals using
beamline 11-ID-B (λ = 0.143 Å). The anti-PbCl 2-like structure provides an excellent fit for this
experimental data at low temperatures, whereas the cubic structure provides an excellent for Ag 2Se
that forms at high temperatures. While the high-temperature data indicated phase-pure cubic Ag 2Se,
the room-temperature data refined to mixtures of the anti-PbCl 2-like phase (initial weight fraction:
79.1%, final weight fraction: 57.5%), the orthorhombic phase (initial weight fraction: 15.9%, final
weight fraction: 39.1%), and small amounts of elemental Se (initial weight fraction: 5.0%, final weight
fraction: 3.2%)., 163
Figure 5.7 (a) The phonon band structure of the anti-PbCl 2-like Ag 2Se phase. The structure is dynamically stable
since all modes have positive frequencies across the first Brillouin zone. (b) The electronic band
structure of the anti-PbCl 2-like phase computed using the HSE06 hybrid functional
46
showing that it
is a narrow band gap semiconductor. (c) The total energy plotted against the volume per formula unit
for structures obtained through searching (AIRSS) as well as the orthorhombic P2 12 12 1 ( ) and the
anti-PbCl 2-like P2 1/n ( ) phases. The PBEsol exchange-correlation functional is used here. (d) The
P2 unit cell reported by Günter and Keusch. (e) The unit cell in (d) optimized using DFT with the
PBEsol functional. Significant structural changes take place – the adjacent [200] planes shear in the
[001] direction, and the Ag atoms move to different sites., 164
Figure 5.8 Relative energies between phases when computed using different exchange-correlation functionals.
Phases found by AIRSS are colored differently. In particular, PBE, which is known to overestimate
the lattice constants of solids, favors phases with large volumes, and such phases tend to have increased
energy when computed using LDA or PBEsol. Note that the rankings of stabilities between the Günter
and Keusch P2 ( ), P2 12 12 1 ( ), and the P2 1/n anti-PbCl 2-like ( ) phases are identical in all cases.,
166
Figure 6.1 (a) Powder XRD pattern and (c) representative TEM micrograph of NHC-stabilized Cu 3-xP (1). (b)
Powder XRD pattern and (d) representative TEM micrograph of oleylamine-stabilized Cu 3-xP (2). The
stick patterns provided in the powder XRD patterns are for hexagonal Cu 3–xP (PDF# 00-002-1263)., 181
Figure 6.2 (a) UV-vis-NIR spectra of crystalline NHC-stabilized Cu 3-xP (1) and (b) amorphous oleylamine-
stabilized Cu 3-xP (2)., 182
Figure 6.3 Representative HR-TEM image reveals the apparent single-crystalline nature of the nanocrystals 1.
The above lattice fringes with spacing d = 0.20 nm correspond to the (300) planes of the hexagonal
phase of Cu 3-xP, 182
xxiii

Figure 6.4 X-ray photoelectron spectrum confirms the presence of the NHC on the nanocrystal surface, as
indicated by the N 1s peak from the surface-bound NHC on Cu 3-xP (1)., 182
Figure 6.5 High-resolution XPS spectra of (a) Cu 2p and (b) P 2p regions for 1., 183
Figure 6.6. (a) Powder XRD pattern and (b) UV-vis-NIR spectrum of the Cu nanoparticles resulting from heating
up the oleylamine-CuBr mixture to 250 °C without injecting (TMS) 3P. The nanoparticles are
amorphous as they display no reflections in the XRD pattern; however, they have a diagnostic LSPR
feature centered at 700 nm characteristic of Cu nanoparticles., 184
Figure 6.7 TGA traces of (a) oleylamine-stabilized (2) and (b) NHC-stabilized Cu 3-xP (1) nanocrystals., 185
Figure 6.8 (a) Bottom:
1
H NMR spectrum of the NHC-CuBr precursor in CDCl 3. Top:
1
H NMR spectrum of the
NHC-capped Cu 3-xP nanocrystals (1) dispersed in CDCl 3. In comparing these two spectra, it is clear
that the carbene is bound to the nanocrystal surface, as the carbene resonances within the top spectrum
all exhibit significant broadening. This broadening is most clearly shown in the inset, which highlights
the aromatic region of the spectrum containing the benzimidazole ring. (b)
1
H NMR spectrum of the
oleylamine-capped Cu 3-xP nanocrystals (3) dispersed in CDCl 3 after ligand exchange. Notably, there
are no peaks observed in the aromatic region (indicating the absence of carbene ligands, see top inset)
and two broad peaks from 5.30–5.45 ppm are observed corresponding to the alkenyl protons of
oleylamine (bottom inset). Chemical shifts of all spectra were referenced with respect to the solvent
residual peak of CDCl 3 at 7.26 ppm., 186
Figure 6.9 (a) TEM of the Cu 3-xP nanocrystals following ligand exchange. There is no statistically significant
difference in size between the as-synthesized Cu 3-xP nanocrystals (diameter of 6.7  1.1 nm) and the
nanocrystals resulting after ligand exchange (diameter of 6.7  1.5 nm). (b) TGA of 3. A larger mass
loss is associated with greater ligand density of ligands on the surface (3.3 ligands/nm
2
)., 187
Figure 6.10 Polarization curves of 1 and 3 on GCE with current normalized by (a) the geometric surface area of
electrode and (b) electrochemical active surface area. All measurements were performed in N 2-
saturated 0.5 M H 2SO 4 solutions with a scan rate of 5 mV/s., 188
Figure 6.11 EIS responses of 1 (markers) with respective fits (lines) at variable potentials vs. RHE. (a) Nyquist
plots; (b) and (c) Bode plots. All measurements were performed in N 2-saturated 0.5 M H 2SO 4
solutions., 189
Figure 6.12 EIS responses of 3 (markers) with respective fits (lines) at variable potentials vs. RHE. (a) Nyquist
plots; (b) and (c) Bode plots. All measurements were performed in N 2-saturated 0.5 M H 2SO 4
solutions., 189
Figure 6.14 Capacitive current of (a) 1 and (c) 3 at open circuit potential under variable scan rates, and the
corresponding current vs. scan rate plots (b and d) used to calculate C dl values., 190
Figure 6.15 Polarization curves of 1 and 3 with current normalized by the amount of Cu measured by ICP-OES
analysis; loading of 1: 3.02 × 10
-7
mol Cu, loading of 3: 0.71 × 10
-7
mol Cu., 191
Figure 6.16 Tafel plots of 1 and 3 extracted from polarization curves., 192
Figure 6.17 (a) One hour controlled potential electrolysis of 1 at -0.59 V vs. RHE (b) C dl measurements taken
before and after electrolysis. (c) Nyquist plots taken before and after electrolysis at η = 0.44 V., 192
Figure 6.18 (a) One hour controlled potential electrolysis of 3 at -0.59 V vs. RHE (b) C dl measurements taken
before and after electrolysis. (c) Nyquist plots taken before and after electrolysis at η = 0.44 V., 193
Figure 6.19 (a) TEM of the carbene-capped Cu 3-xP nanocrystals (1) after CPE shows that the particles sinter during
electrochemical manipulation. (b) TEM of the ligand-exchanged oleylamine-capped Cu 3-xP
nanocrystals (3) following CPE shows similar behavior., 194
Figure 6.20 Controlled-current electrolysis of 1 at 10 mA/cm
2
in N 2-saturated 0.5M H 2SO 4., 194
xxiv

Figure 6.21 Polarization curves (LSV, 5 mV/s) of 1 in 0.5M H 2SO 4 initially and after 200, 400, 600, 800, and
1000 CV sweeps between 0.1 and -0.6 V vs. RHE with a scan rate of 100 mV/s., 195
Figure 6.22 High resolution XPS spectrum of 1 following 1 h of controlled potential electrolysis. (a) Cu 2p region;
the Cu
+
signature remains while no satellite peaks indicative of Cu
2+
are observed (b) the P 2p region
indicates that the P
3-
is still present after catalysis, although there is a larger oxide peak than what was
observed in the as-prepared material in Figure 6.1b (c) the survey scans of 1 before and after CPE., 195
Figure 6.23 (a) Methylamine and (b) 1,3-(dimethyl)benzimidazol-2-ylidene bound to a model Cu 9P 3 cluster along
with a proton., 196

xxv

Abstract
The crystal structure of a material is an important determinant of its properties. Indeed, all
physicochemical material properties are fundamentally rooted in structure and composition. Given the role
of crystal structures in determining material properties, the prevalence of polymorphism on the nanoscale
is enabling the discovery and design of new materials with distinct properties. This thesis expounds
primarily on the chemistry, properties, and applications of semiconductor nanocrystals that crystallize with
crystal structures distinct from those that are thermodynamically stable in the analogous bulk material
systems. Semiconductor nanocrystals represent an ever-expanding area of materials research and
development due to their highly tunable properties (on the basis of size, shape, composition, crystal
structure, surface functionalization, etc.) that make them apt for use in optoelectronics, solar cells, batteries,
medicine, and a wide array of other applications.
Chapter 1 introduces important concepts related to polymorphism in inorganic materials. Also
highlighted are recent works that demonstrate chemical control of polymorphism in several representative
semiconductor nanocrystal material systems, concluding with examples of emergent properties that arise
from the unique crystal structures adopted by these materials.
Discussed in Chapter 2 are molecular programming and formation mechanism studies of wurtzite-
like CuInSe 2 nanocrystals. This wurtzite-like crystal structure of CuInSe 2 is a polymorph that has only been
observed to exist for nanocrystals of CuInSe 2, and its formation is dependent upon use of the proper
selenium precursors which nucleate a key Cu 3Se 2 nanocrystal intermediate.
Chapter 3 highlights the expansion of the findings of Chapter 2 through studies of a highly related
material, AgInSe 2. Here, it is shown that the formation of different polymorphs of AgInSe 2 can be controlled
by the choice of ligand/solvent in the nanocrystal synthesis. Additionally, formation mechanism studies
reveal that wurtzite-like AgInSe 2 forms via a pathway analogous to that of wurtzite-like CuInSe 2.
Chapter 4 illustrates the use of the chemical principles developed in Chapters 2-3 to predict and
synthesize wurtzite-like Cu 2FeSnSe 4 nanocrystals that have never been observed before this work. UV-vis-
NIR spectra and density functional theory calculations of this novel polymorph indicate that it is an
xxvi

excellent candidate for use as a non-toxic, Earth-abundant absorbing layer in thin-film solar cells.
Additionally, the Cu 2FeSnSe 4 results were used to shed light on the curiosities of the poorly understood
chemistry of CuFeSe 2, which is a ternary analog of Cu 2FeSnSe 4. By comparing these two related material
systems, it was found that Sn plays a critical role in stabilizing the wurtzite-like structure of Cu 2FeSnSe 4;
in the absence of Sn, the chemistry of CuFeSe 2 proceeds down entirely unique reaction pathways that
consistently produce the thermodynamically stable eskebornite phase of CuFeSe 2, rather than a wurtzite-
like CuFeSe 2.
Chapter 5 turns to our studies of a metastable polymorph of Ag 2Se nanocrystals. The crystal
structure of this metastable polymorph of colloidal Ag 2Se nanocrystals remained unsolved until we showed
herein that, on the basis of Rietveld refinements of powder X-ray diffraction data and pair distribution
function analysis, the structure is well-described by an anti-PbCl 2-like structure type. Knowledge of the
crystal structure enabled, for the first time, the calculation of the phonon dispersion curves and the electronic
band structure of this metastable polymorph. Finally, it was found that the theoretical phase space of Ag 2Se
is crowded with many polymorphs that are close in energy, which may explain the preponderance of reports
in the literature of different Ag 2Se polymorphs with distinct crystal structures.
Chapter 6 departs from the storyline of semiconductor nanocrystal polymorphism to focus on the
effects of N-heterocyclic carbene precursors/ligands in the synthesis and electrocatalytic activity of Cu 3-xP
nanocrystals. Here, it is shown that N-heterocyclic carbene copper complexes react via a metathesis reaction
with tris(trimethylsilyl)phospine to yield Cu 3-xP nanocrystals with legacy N-heterocyclic surface ligands.
Furthermore, it was shown that these carbene-capped Cu 3-xP nanocrystals display significantly lower
overpotentials in driving electrocatalytic hydrogen evolution, as compared to Cu 3-xP nanocrystals ligated
with a more traditional surface ligand (oleylamine). Density functional theory calculations indicate that this
lower overpotential is a result of the significant electron donating character of the carbene surface ligands.

1

Chapter 1. Polymorphic Metastability in Colloidal Semiconductor Nanocrystals
*Published in ChemNanoMat., 2020, 6, 11, 1567-1588.
1.1 Abstract
Metastable polymorphs of inorganic solids often possess material properties not present in the
corresponding thermodynamic polymorphs, making them targets for the development of new functional
materials. In contrast with isolating metastable bulk materials, syntheses of metastable polymorphs on the
nanoscale are aided by fast non-equilibrium reaction kinetics and the favorable thermodynamic influence
of surface energies, giving rise to greater ease of access to metastable high-temperature polymorphs and, in
some cases, new polymorphs that do not exist in the bulk. The syntheses of metastable semiconductor
nanocrystals are of interest for their potentially unique optoelectronic and physicochemical properties.
However, in many material systems, synthesizing nanocrystalline products away from thermodynamic
equilibrium in a predictable manner remains an outstanding challenge. This chapter outlines direct synthetic
methodologies that have been developed to enable control over the nucleation and growth of metastable
polymorphs of semiconductor nanocrystals by tailoring reaction conditions, precursor kinetics, ligand and
surface effects, and other synthetic levers. The case studies reviewed herein expound on the direct syntheses
of metastable ZnSe, Cu 2SnSe 3, CuInSe 2, Ag 2Se, and AgInSe 2 nanocrystals, and although there remain
numerous examples of metastable nanocrystal syntheses outside of these metal chalcogenide systems, the
concepts discussed are of general utility to the field of metastable nanocrystal syntheses as a whole. Explicit
examples in which new functional properties are afforded by metastable polymorphs of the aforementioned
material systems are presented within the context of applications for solar cells, photonics, and optical
sensing. Finally, the factors that affect the kinetic persistence of metastable nanocrystalline polymorphs are
discussed at length for these material systems.
2

1.2 Introduction
1.2.1 Principles of Metastability
Metastability in colloidal nanocrystals manifests in many ways. Nanocrystal morphologies, sizes,
compositions, and crystal structures can all exhibit different forms of metastability. Due to the diverse
nature of metastability in colloidal nanocrystals, this introduction will be limited to the syntheses,
properties, and applications of metal chalcogenide semiconductor nanocrystals that crystallize in metastable
crystal structures. Before these specific chemistries are highlighted, we will introduce important concepts
and terminology that will be used throughout this thesis by using a canonical example –– the polymorphic
metastability of the diamond allotrope of carbon.
Diamond is one of the two crystalline structures, or polymorphs, that elemental carbon adopts as a
bulk material, and it represents the thermodynamically most stable polymorph of carbon only at pressures
on the order of P > 10
4
atm.
1
Below these pressures, diamond has a free energy higher than the graphite
polymorph of carbon, and therefore it is referred to as metastable with respect to graphite. Here, the term
‘metastable’ indicates only the relative thermodynamic stabilities between these two polymorphs; that is, it
does not describe the timescale over which diamond will spontaneously convert to graphite. As a metastable
polymorph of carbon, diamond is temporally persistent over long time scales due to the large activation
energy barrier (from the required cleavage of sp
3
C-C bonds) that must be overcome for the reconstructive
transformation of diamond into graphite.
2

Humans have had a fascination with diamond dating back to antiquity, and for good reason.
Diamond is an exceptional material – it has the greatest atom density of all terrestrial materials, is the
hardest naturally occurring substance, and it has the highest room-temperature thermal conductivity of any
material.
3
In addition, diamond is optically transparent through a wide range of wavelengths from the
infrared to the ultraviolet region of the electromagnetic spectrum.
3
Graphite, the thermodynamic polymorph
of carbon at low pressures, does not exhibit any of these same properties. The dichotomy between graphite
and diamond exemplifies how the crystal structure of a material dictates its properties and is illustrative of
3

the drastic property differences that can arise between metastable and thermodynamic polymorphs of a
material with a fixed composition.
Syntheses of diamond eluded alchemists and chemists for hundreds of years, although it was not
for lack of effort. Examples of attempted syntheses include those such as that of Scottish chemist James
Ballantyne Hannay, who claimed to have synthesized diamond in 1880 by sealing “bone oil,” lithium, and
paraffin in wrought iron tubes and heating them to “red heat,” after which seventy-seven of his eighty tubes
exploded.
2
In early 1953 American chemist William Eversole, working for the Union Carbide Corporation,
became the first person to veritably synthesize diamond. Interestingly, rather than using high pressures and
high temperatures, Eversole was able to grow small amounts of diamond under kinetically controlled
conditions, with low pressures, through chemical vapor deposition.
4
Only shortly thereafter, in February of
1953, Swedish chemists Erik Lundblad and Halvard Liander of the Swedish industrial company Allmänna
Svenska Eliktriska Aktiebolaget (ASEA) independently synthesized diamond through high-temperature,
high-pressure conditions.
5
However, due to the secrecy of the Union Carbide and ASEA projects, it wasn’t
until 1955 that chemists at the General Electric Company became the first to report a synthesis of diamond
through a high-temperature, high-pressure method.
6a,b
This culmination of centuries of experimentation on
the synthesis of diamond testifies to the difficulty of isolating metastable bulk materials.
Interestingly, polymorphism is pervasive in the chemistries of colloidal nanomaterials– far more
so than in the chemistries of bulk materials. Herein, we discuss the state of the art regarding the direct
syntheses of metastable polymorphs of metal chalcogenide semiconductor nanocrystals, with some of these
polymorphs being previously unknown for the bulk materials. Then, we will highlight properties that these
metastable polymorphs exhibit in comparison to their thermodynamically preferred counterparts, including
examples in which the emergent properties of metastable semiconductor nanocrystals have been leveraged
to improve applications in photonics, optical sensing and imaging, solar cells, and more.
1.2.2 Syntheses of Colloidal Semiconductor Nanocrystals with Metastable Crystal Structures
Metastable materials can have strikingly unique properties that are quite distinct from their thermodynamic
counterparts. Unfortunately, metastable inorganic materials, such as diamond, have historically proven
4

difficult to synthesize.
1,2,4,6
However, polymorphic metastability is much more prevalent on the nanoscale
than for bulk materials. For colloidal nanocrystals, the surface energy (γA, where γ = interfacial excess free
energy and A = interfacial area of the nanocrystal) represents a significant thermodynamic contribution to
the relative stabilities between different crystalline phases.
7–9
This term scales with the surface area to
volume ratio (A/V) and becomes an increasingly more dominant factor for nanocrystals of smaller sizes, or
volumes. These surface energy contributions can compress differences in free energy between polymorphs,
as compared to the bulk, and in some cases can even cause shifts in the ordering of the thermodynamic
stabilities of polymorphs for a given material.
7,8,10–12

Reductions in free energy differences between polymorphs and the fast reaction kinetics of
nanocrystal nucleation and growth make it possible to synthesize colloidal nanocrystals with metastable
crystal structures that in bulk are only accessible at much higher temperatures than those required for the
analogous nanocrystal syntheses.
13
In addition to nanocrystalline analogues of bulk materials, entirely new
crystal phases can also arise on the nanoscale that have no bulk counterparts.
14–24
Therefore, colloidal
nanocrystal chemistry presents both thermodynamic and kinetic advantages in the preparation of metastable
materials, and promises to be fruitful for the discovery of new metastable materials with unique properties.
That said, we generally lack synthetic principles that enable chemists to predictably isolate novel
nanomaterials with metastable crystal structures. Many of the metastable nanomaterials isolated thus far
were done so serendipitously, and ab initio prediction of these phases is difficult, especially when there is
no bulk analogue to suggest that such phases should exist on the nanoscale.
25

Of the synthetic techniques employed to generate metastable polymorphs of semiconductor
nanocrystals, cation exchange is the most well-understood framework to date. In the syntheses of bulk
inorganic solids, high temperatures are generally needed to overcome the sluggish kinetics associated with
solid-solid diffusion, making the isolation of metastable species challenging, as these synthetic conditions
almost invariably favor the formation of thermodynamic products.
26,27
On the nanoscale, however, cation
exchange can readily occur in inorganic nanocrystals. At this length scale, fast reaction kinetics are in part
the result of the inherently high surface area-to-volume ratios of nanomaterials, resulting in drastic
5

reductions of ion diffusion lengths through the solid and a high proportion of defects and vacancies, which
also increase cation exchange rates.
28
Additionally, the organic ligands present in these syntheses facilitate
the exchange of ions at the organic/inorganic interface of nanomaterials.
13,29–31
Cation exchange reactions
are characterized by the complete or partial exchange of cations within a nanostructure in such a way that
the overall particle morphology and the anionic sub-lattice of the nanostructure remain intact.
32–34
While
sulfides and selenides are the most widely studied material systems for cation exchange reactions, this
method has been used to synthesize a broad range of nanocrystalline compounds, many with metastable
crystal structures. Indeed, cation exchange has been applied to the syntheses metal chalcogenides (for
oxides, sulfides, selenides, and tellurides), metal pnictides (for phosphides and antimonides), and metal
fluorides.
35
While cation exchange has proven to be a widely used method for the syntheses of novel
metastable nanomaterials, there is a wide body of cation exchange literature and the topic has already been
reviewed.
29,30,35,36
Therefore, we will focus on the direct syntheses of nanocrystals with metastable crystal
structures and will only discuss cation exchange within the context of mechanisms of direct nanocrystal
syntheses.
Direct methods, such as hot-injection or heating-up procedures, are beneficial in that they do not
require multiple steps and/or post-synthetic modifications to yield the desired material. Even so, direct
syntheses of metastable polymorphs of semiconductor nanocrystals remain an outstanding challenge due to
the necessity of tuning precursor reactivities, which are often solvent-dependent, in addition to optimizing
the time, temperature, and other experimental parameters to yield conditions that result in preferential
nucleation and growth of metastable polymorphs.
35,37–39
In most cases, the effects of these variables (and
their interactions) are complex and therefore still poorly understood.
40,41
In the following section, we review
examples of direct syntheses of semiconductor nanocrystals with metastable crystal structures. While there
are numerous reports of the syntheses of different polymorphs for many material systems, we review the
work that provides insight into the factors that determine control over the crystalline phase of the products.
We will identify advances that have led to increased predictability of reaction products, as well as areas that
warrant further investigation.
6

1.3 Nanocrystal Polymorph Dependence on Reaction Conditions
1.3.1 Phase Control of ZnSe Nanocrystals via Modulation of Rate of Precursor Addition
ZnSe, a wide band gap II-VI semiconductor (bulk band gap, E g = 2.7 eV), is an important phosphor material
that emits in the blue to ultraviolet region of the electromagnetic spectrum, making it useful for applications
in blue light emitting diodes (LEDs) and laser diodes.
42–44
Zunger et al. found that for binary octet
semiconductors, the zinc blende structure is increasingly more stable than the wurtzite structure as the
atomic number of the anion increases, progressing down a group in the periodic table. They coined this
trend as the “anion rule” of wurtzite-zinc blende polymorphism.
45
As predicted by the anion rule, bulk ZnSe
is thermodynamically stable at low temperatures in the cubic zinc blende phase. Above 1411 °C, ZnSe
undergoes a first-order phase transformation to the hexagonal wurtzite structure, which is stable up to the
melting point of 1522 °C.
46
The zinc blende and wurtzite structures are polytypes of each other, meaning
their structures have the same periodicity in two dimensions but differ in periodicity along one
crystallographic direction.
47
This can be seen in Figure 1.1, where the wurtzite structure exhibits ABAB
packing along the c-direction, leading to an eclipsed dihedral conformation, while the zinc blende structure
packs in an ABCABC fashion and produces a staggered dihedral conformation.
45

Polytypism is a common form of polymorphism and results in structures that are often narrowly
separated from one another in terms of their thermodynamic stabilities. For ZnSe, the calculated total energy
difference between these two polytypes reveals that the zinc blende structure is a mere 5.3 meV/atom more
stable than the wurtzite structure (at 0 K);
45
5.3 meV/atom is only 20% of kT at 298 K. This low energy
threshold between these two phases means that, on the nanoscale, formation of either phase can be favored
depending on the synthetic conditions.
In a relatively early example of rational phase control, Cozzoli et al. demonstrated control over the
phase and morphologies of ZnSe nanocrystals by modulating the conditions of nanocrystal nucleation and
7

Figure 1.1 (a) and (b) show the difference in packing along the c-axis for the wurtzite and zinc blende structures,
respectively. (c) and (d) highlight the fact that the wurtzite structure has an eclipsed dihedral conformation while
the zinc blende structure has a staggered dihedral conformation. Adapted with permission from reference 45.
Copyright 1992, American Physical Society.

growth.
9
Here, the direct syntheses of ZnSe nanocrystals were performed by injecting precursor solutions
containing diethyl zinc and trialkylphosphine-selenium adducts into a hot alkyamine solvent. Control over
the phase and morphologies of the resultant nanocrystals was achieved by varying the reaction times,
temperatures, volumes/concentrations, and rates of precursor addition.
A fast injection of the Zn/Se precursor solution promoted nucleation of isotropic ZnSe nanocrystals
in the zinc blende phase (Figure 1.2a). For these reactions, the initial temperature of the alkylamine solvent
was maintained at or above 300 °C. Following injection of the precursor solution, the reaction solution
temperature fell to ~265 °C and was kept at that temperature for the remainder of the reaction. At this lower
temperature, additional precursor solution was injected into the reaction flask dropwise (0.2 mL min
-1
) over
3-5 h to facilitate further growth of the ZnSe nanocrystals, ultimately resulting in relatively monodisperse
zinc blende nanocrystals 3-5 nm in diameter (Figure 1.2b). The hot-injection method enables temporal
separation of the nanocrystal nucleation and growth processes; the initial high temperature of the
alkylamine solvent is sufficient to overcome the activation energy barrier associated with nanocrystal
8

Figure 1.2. (a) Powder X-ray diffraction (XRD) of ZnSe nanocrystals; pattern 1 corresponds to spherical zinc
blende nanocrystals and patterns 2-4 correspond to ZnSe nanorods with aspect ratios of 3, 6, and 8, respectively.
(b) Transmission electron micrographs (TEM) of isotropic zinc blende ZnSe nanocrystals. (c) TEM of ZnSe
nanorods. (d) TEM of ZnSe multipods. All scale bars shown represent 100 nm. Adapted with permission from
reference 9. Copyright 2005, American Chemical Society.

nucleation. The subsequent drop in temperature of the reaction solution that follows injection restricts
further nucleation events, and monomer conversion is steered towards promoting growth of the pre-existing
nuclei, which is a kinetically faster process with a lower activation energy barrier than nucleation.
48

To synthesize anisotropic ZnSe nanocrystals that exhibit the wurtzite structure, the Zn/Se precursor
solution was added to the hot alkylamine solvent at a much lower rate using a syringe pump. It was shown
that the rate of addition, the concentration/total volume of precursor solution, and the temperature of the
receiving flask could all influence nanocrystal phase and morphology. At 345 °C, dropwise addition rates
of the Zn/Se precursor solution ranging from 0.05-0.20 mL min
-1
produced anisotropic wurtzite ZnSe
nanorods (Figure 1.2a,c). Decreasing the temperature of the reaction flask by 15-55 °C while increasing the
injection rate to 0.30-0.40 mL min
-1
resulted in branched ZnSe multipods that contained both wurtzite and
zinc blende domains (Figure 1.2d).
9

To rationalize these results, the authors posit that the chemical potential of the monomers in
solution are vastly different between the hot-injection and dropwise addition methods. For the former, a
high chemical potential is created since monomer supersaturation results as soon as the entirety of the
precursor solution is quickly injected into the reaction flask –– favoring fast, isotropic nucleation and
growth in the zinc blende phase, which does not have a preferred growth axis. In contrast, low monomer
concentration was found to be a critical requirement for the nucleation and growth of wurtzite nanorods.
Under low-concentration conditions, where precursors are added dropwise, monomer supersaturation does
not occur quickly and therefore does not force immediate nucleation and growth of nanocrystals, allowing
the system to reach a quasi-equilibrium between monomers in solution and nanocrystal nuclei before
extensive nanocrystal growth occurs.
The fact that the dropwise method, which favors thermodynamic control rather than kinetic control,
promoted nucleation and growth of wurtzite ZnSe nanorods is particularly interesting, because it indicates
a possible reversal of the thermodynamic stabilities of the zinc blende and wurtzite polytypes under these
conditions. This reversal may be a result of more favorable surfactant stabilization of nanocrystal surfaces
in the wurtzite phase than the zinc blende phase, since the most prevalent facets (and therefore the most
stable facets with the lowest surface energy) of the wurtzite nanorods observed by high-resolution TEM
(HR-TEM) were the nonpolar (100) and (110) facets, which have no equivalent in the zinc blende
structure.
9,49
Indeed, surface ligands have been shown to differentiate the formation of the zinc blende and
wurtzite polytypes in related material systems, such as CdSe nanocrystals.
50

The formation of ZnSe multipods, with both wurtzite and zinc blende domains, resulted primarily
under conditions that strike a balance between thermodynamic and kinetic control. Lower temperatures,
higher precursor volumes or concentrations, and slightly higher rates of precursor addition favor the kinetic
formation of zinc blende nuclei, which could then support anisotropic growth of wurtzite-phase arms from
the polar (111) terminated facets of zinc blende, which is atomically identical to the (001) plane of the
wurtzite structure.
9,51
The main findings of this work underscore the ways in which the kinetics and
thermodynamics of nanocrystal synthesis can be rationally manipulated by changing something as simple
10

as the rate of precursor addition. By simultaneously pulling other synthetic levers, such as temperature and
precursor concentrations, a high degree of control can be achieved to yield ZnSe nanocrystals with
controlled phase and morphology.
1.3.2 Temperature-Dependent Phase Control of Cu 2SnSe 3 Nanocrystals
Copper tin selenides are an attractive class of materials as earth abundant, low toxicity semiconductors for
photovoltaic devices.
52–54
At room temperature, bulk Cu 2SnSe 3 crystallizes with a monoclinic unit cell in
which the cations assume specific positions within the unit cell. This monoclinic structure is derived from
a distorted diamondoid zinc blende structure. At higher temperatures, entropic stabilization favors
randomization of the cations within the unit cell; here, Cu 2SnSe 3 adopts the true zinc blende structure (space
group 𝐹 4
̅
3𝑚 ).
53,55

In 2012, our group discovered that Cu 2SnSe 3 can crystallize in a wurtzite-like structure on the
nanoscale, which is nonexistent on the bulk phase diagram.
22
Expanding upon this discovery, Ryan et al.
demonstrated how phase control could be achieved within this system by leveraging different reaction
temperatures and precursors.
52
In a typical synthesis for wurtzite-like Cu 2SnSe 3 nanocrystals, diphenyl
diselenide (Ph 2Se 2), Cu(oleate) 2, and oleylamine were placed in a flask together and heated. Upon reaching
11

Figure 1.3 (a) Powder XRD patterns and (b,c) TEM and HR-TEM micrographs, respectively, of wurtzite-like
Cu 2SnSe 3 nanocrystals synthesized from a hot-injection method at 240 °C. (d) Powder XRD patterns of zinc blende
Cu 2SnSe 3 nanocrystals synthesized from hot-injection reactions using (i-ii) Ph 2Se 2 and (iii) Se powder. Note that
patterns i-ii contain a small amount of the wurtzite-like phase, marked by an asterisk. (e,f) TEM and HR-TEM
micrographs, respectively, of zinc blende nanocrystals synthesized with Ph 2Se 2. Adapted with permission from
reference 52. Copyright 2014, American Chemical Society.

230 °C, Sn(OAc) 4 in oleylamine was injected and the reaction flask was allowed to recover to a reaction
temperature of 240 °C for 30-60 min. This procedure resulted in fairly monodisperse wurtzite-like
nanocrystals 26 nm in diameter (Figure 1.3a-c).
By increasing the reaction temperature (and temperature of injection) to 300 °C, and using CuCl
and SnCl 2 as metal precursors, nearly phase-pure zinc blende Cu 2SnSe 3 nanocrystals resulted (Figure 1.3d-
f). Under these conditions, a small number of wurtzite-like nanocrystals remained, as evidenced by the
presence of the (100) reflection from the wurtzite-like structure in the powder XRD pattern (Figure 1.3d).
Even so, these experiments demonstrate the drastic influence temperature and precursor selection can have
on phase determination, where near-complete phase control could be achieved by modulating the reaction
12

temperature through a window of 60 °C. Additionally, these results reflect the metastability of the wurtzite-
like phase with respect to the zinc blende phase for this ternary system, as the latter is favored under
thermodynamically controlled conditions (i.e., high temperatures). Interestingly, when Ph 2Se 2 was used as
a chalcogen source, no conditions were found under which Cu 2SnSe 3 could be isolated purely in the zinc
blende phase. To eliminate all traces of the wurtzite-like phase, Ph 2Se 2 was replaced with elemental Se
dissolved in oleylamine. Maintaining the relatively high reaction temperature of 300 °C with Se powder as
the chalcogen source resolved this issue and yielded Cu 2SnSe 3 nanocrystals exclusively in the zinc blende
phase (Figure 1.3d).
Ryan et al. were also able to synthesize Cu 2SnSe 3 polycrystalline tetrapods with domains of both
the zinc blende and wurtzite-like structures in the same nanocrystal. To accomplish this, the synthetic
conditions need to be such that one phase is favored during the nucleation stage and the other during the
growth stage. To synthesize polytypic tetrapods, that is, tetrapods which contain both the zinc blende and
wurtzite-like polytypes within the same nanostructure, the authors altered the original hot-injection
synthesis for wurtzite-like Cu 2SnSe 3 by increasing the temperature of Ph 2Se 2 injection to 290 °C. In doing
so, the initial high temperature of injection is sufficient to favor nucleation of small zinc blende seeds.
However, the subsequent drop (~10 °C) in temperature that occurs following injection causes the kinetic
growth of the wurtzite-like phase to dominate, allowing wurtzite-like arms to terminate four of the (111)
facets of the zinc blende seed nanocrystals (Figure 1.4a).
The authors then demonstrated a complementary method of polytypic nanocrystal growth; that is,
initial nucleation of hexagonal wurtzite-like seeds followed by epitaxial growth of the zinc blende phase.
To do this, a heating-up method was employed whereby Ph 2Se 2, the metal precursors, and oleylamine were
added to a single flask that was then ramped to 310 °C. While ramping, metastable wurtzite-like seeds
nucleate at relatively lower temperatures, but as the temperature continues to rapidly increase, growth of
the zinc blende phase becomes favored, generating linear nanostructures with a central wurtzite domain
sandwiched by zinc blende domains along the tips of the nanocrystals (Figure 1.4b). In these experiments,
13

Figure 1.4 (a) TEM image of polytypic nanocrystalline tetrapods in which the arms are wurtzite-like and the central
seed/core is zinc blende. (b) TEM image of polytypic linear nanocrystals in which the central domain/seed is
wurtzite-like and the tips are zinc blende. Adapted with permission from reference 52. Copyright 2014, American
Chemical Society.

it was found that final reaction temperatures exceeding 300 °C, and the use of CuCl and SnCl 2 chloride
salts, were necessary to yield nanocrystals that uniformly exhibited such polytypism. Lower temperatures
(280 °C), and the use of Ph 2Se 2 and Cu(oleate) 2 with Sn(OAc) 4, produced some heterostructures, but
primarily resulted in phase-pure wurtzite-like nanocrystals, potentially due to the increased reactivity of the
higher-valent Sn(IV) acetate precursor.
This work illustrates how temperature and precursor choice can be modulated to fine-tune the
nucleation and growth kinetics of ternary semiconductor nanocrystals, where isolation of the metastable
wurtzite-like phase can be obtained at relatively low temperatures with fast-reacting precursors.
Thermodynamic control over the system can be achieved by increasing the overall reaction temperature by
only 60 °C and by switching to less-reactive precursors. Manipulating the reaction conditions within the
temperature window where kinetic and thermodynamic control compete can result in control over
nanocrystal polytypism.
1.4 Tuning Precursor Reactivities for Polymorphic Phase Control on the Nanoscale
Since the early 2000s, diorganyl dichalcogenides (R-E-E-R, where R = organic substituent and E = O, S,
Se, Te) have emerged as increasingly useful molecular precursors for the syntheses of metal oxides and
chalcogenides, especially metastable polymorphs of multinary metal chalcogenide nanocrystals.
21,22,24,56–60

14

This has already been introduced in the example of Cu 2SnSe 3 nanocrystals given above. Developing
methods that afford fine control over the kinetics of nanocrystal nucleation and growth is crucial for the
development of rational syntheses of new metastable polymorphs of semiconductor nanocrystals. One
approach that has proven successful in controlling reaction kinetics is leveraging predictable trends in the
reactivities of molecular precursors to affect the rates and/or conditions under which nanocrystal nucleation
and growth occur.
61–63
In this regard, diorganyl dichalcogenides lend themselves to kinetically controlled
syntheses, as their reactivities can be modulated by changing the identity of the organic substituent.
18,64–66

For example, in 2013, Vela et al. demonstrated that by changing the R group within a series of diorganyl
disulfides or diselenides (R-S-S-R or R-Se-Se-R), they could tune the reactivities of these precursors as
chalcogen sources in the preparation of CdS and CdSe nanocrystals, respectively. For each series, bond
dissociation energies of the C-E and E-E bonds (E = S, Se) were calculated by density functional theory
(DFT). While the strength of the E-E bonds was found to be relatively constant, the calculated C-E bond
strengths change more dramatically upon substituting the R group, where precursors that possess large C-
E bond dissociation energies are relatively less reactive compared to precursors with weaker C-E bonds.
Experimentally, the more reactive dichalcogenide precursors yielded isotropic nanocrystals, whereas the
less reactive precursors afforded anisotropic nanocrystals with higher surface areas, which are
morphologically metastable with respect to isotropic nanocrystals with lower surface areas.
64

In the last ten years, dichalcogenide precursors have been employed in the syntheses of ternary
I-III-VI 2 semiconductor nanocrystals.
21,58,67,68
Ternary I-III-VI 2 semiconductor nanocrystals with an
A
+
B
3+
E
2-
2 composition are of interest as relatively non-toxic alternatives to cadmium and lead-containing
semiconductors, with applications in thin film solar cells, light emitting diodes (LEDs), photocatalysis, and
bioimaging.
69
CuInSe 2 is a well-known I-III-VI 2 semiconductor, which, like other I-III-VI 2 semiconductors,
crystallizes in the chalcopyrite structure (space group 𝐼 4
̅
2𝑑 ) at low temperatures.
70
The tetragonal
chalcopyrite structure type is characterized as a supercell of the zinc blende structure in which the anions
pack in a face-centered cubic configuration while the cations fill 50% of the tetrahedral holes in an
alternating fashion (Figure 1.5c).
70–72
At high temperatures, bulk CuInSe 2 assumes the zinc blende structure
15

type up to its melting point, as shown in Figure 1.5b.
73–75
While bulk CuInS 2 behaves similarly in that it
also undergoes a chalcopyrite-to-zinc blende phase transition with increasing temperature, a second high-
temperature phase arises when heating the zinc blende phase beyond 1045 °C; namely, a wurtzite phase of
CuInS 2 (Figure 1.5a, 1.5c), which is stable up to the melting point of 1090 °C.
76,77
Wurtzite CuInS 2 was
also discovered to form on the nanoscale at reaction temperatures much lower than those necessary to
achieve this phase in bulk.
78,79

Figure 1.5 (a) Cu 2S-In 2S 3 pseudo-binary phase diagram. Three phases of CuInS 2 exist in the bulk: the low-
temperature chalcopyrite phase (labeled γ), a higher-temperature zinc blende phase (labeled δ), and the high-
temperature wurtzite phase (labeled ζ). (b) Cu 2Se-In 2Se 3 pseudo-binary phase diagram. Two phases of CuInSe 2
exist in the bulk: the low-temperature chalcopyrite phase (labeled α), and the high-temperature zinc blende phase
(also known as sphalerite, labeled δ). (c) Shown from left to right are the chalcopyrite structure type, the zinc blende
structure type, and the wurtzite structure type for these ternary materials. For the chalcopyrite structure, blue atoms
= Cu
+
, pink atoms = In
3+
, green atoms = S
2-
/Se
2-
. Note that the cations are ordered within the structure. For the zinc
blende and wurtzite structure types, cations randomly occupy the tetrahedral holes, thus blue atoms represent both
Cu
+
and In
3+
in these structures, and green atoms = S
2-
/Se
2-
. Only CuInS 2 exhibits the wurtzite structure in bulk, so
for this structure, yellow atoms = S
2-
. Phase diagrams adapted with permission from reference 74, copyright 2000,
AIP Publishing, and from reference 76, copyright 1980, Elsevier.
16

In 2010, we discovered that CuInSe 2 nanocrystals could be synthesized in a metastable wurtzite-
like crystal structure, analogous to that of wurtzite CuInS 2, by using a Ph 2Se 2 diselenide precursor.
21
Here,
we use the term “wurtzite-like” because these metastable hexagonal phases on the nanoscale often display
long-range cation ordering within the crystal structures, whereas cations in the true wurtzite structure are
not ordered.
80,81
Expanding upon the discovery of this new metastable phase of CuInSe 2, we hypothesized
that trends in dichalcogenide precursor reactivity could be employed to control the reaction kinetics in the
syntheses of CuInSe 2 nanocrystals, providing synthetic pathways for thermodynamically or kinetically
driven mechanisms, thus enabling predictable phase control of this material system simply by changing the
dichalcogenide precursor.
Diselenide precursors with different calculated C-Se bond strengths were used in the synthesis of
the CuInSe 2 nanocrystals. To synthesize the nanocrystals, InCl 3 was hot-injected into a flask containing
Cu(oleate) 2, a diselenide precursor, and oleylamine. Figure 1.6 demonstrates that, when the diselenide
precursors that possess stronger C-Se bond strengths (R = phenyl) were used, the resulting nanocrystals
crystallize in a metastable wurtzite-like phase, whereas precursors with weaker C-Se bonds (R = methyl,
benzyl) yielded the nanocrystals with the thermodynamic chalcopyrite crystal structure.
66
To confirm the
dependence of the nanocrystalline phase on the C-Se bond strength, and not the Se-Se bond strength,
benzeneselenol was employed as a selenium source. This precursor, which has a C-Se bond stronger than
that of Ph 2Se 2 and no Se-Se bond, also produces the wurtzite-like phase, which provides further evidence
that the C-Se bond strength is a primary phase-determining variable.
Ex situ aliquot studies by powder XRD revealed that each ternary polymorph arises from different
distinct phases of binary copper selenide intermediates. Specifically, when using dimethyl or dibenzyl
diselenide, the chalcopyrite phase is generated from an in-situ partial cation exchange reaction between
cubic Cu 2-xSe intermediates and In
3+
in solution. This cation exchange is topotactic; the anion sub-lattice
remains largely unchanged in transitioning from Cu 2-xSe to chalcopyrite CuInSe 2.

17

Figure 1.6 (a) Powder XRD patterns corresponding to CuInSe 2 nanocrystals synthesized with various diorganyl
diselenide precursors. For R = benzyl and methyl, the resulting nanocrystals have the chalcopyrite structure,
whereas for R = phenyl, the nanocrystals crystallize with a metastable wurtzite-like structure. (b) TEM micrographs
of the CuInSe 2 nanocrystals derived from each respective precursor. Adapted with permission from reference 66.
Copyright 2018, American Chemical Society.

In contrast, when Ph 2Se 2 was employed as the chalcogen source, the Cu 3Se 2 phase of copper
selenide was observed as the sole intermediate that ultimately generates the wurtzite-like phase of CuInSe 2.
Interestingly, Cu 3Se 2 is a low-temperature phase of copper selenide that is metastable at the temperatures
of the hot-injection reaction.
82
By inspecting the crystal structure of Cu 3Se 2, we proposed a crystal chemistry
mechanism that rationalizes the conversion of Cu 3Se 2 into wurtzite-like CuInSe 2. Figure 1.7a, b illustrates
the near-isostructural relationship between the pseudo-hexagonal and hexagonal Se
2-
sub-lattices of Cu 3Se 2
and wurtzite-like CuInSe 2, respectively. Thus, we hypothesized that the conversion of Cu 3Se 2 to wurtzite-
like CuInSe 2 is also due to in-situ topotactic partial cation exchange with In
3+
. To generate a wurtzite-like
structure from Cu 3Se 2, the periodic tetrahedral holes within the structure (shown with dotted red lines in
Figure 1.7e) must necessarily be filled by incoming In
3+
atoms, or by Cu
+
atoms that migrate to
accommodate In
3+
in an identical tetrahedral hole elsewhere.
18

Figure 1.7 (a) Pseudo-hexagonal Se
2-
sub-lattice of Cu 3Se 2. (b) Hexagonal Se
2-
sub-lattice of CuInSe 2. (c) Wurtzite-
like structure of CuInSe 2. (d) Side-view of Cu 3Se 2; edge-sharing configurations are highlighted in yellow, teal, and
red. (e) Top-view of Cu 3Se 2; periodic tetrahedral holes within the structure are traced with dotted red lines. (f)
Cu 3Se 2 structure visualized whereby all edge-sharing tetrahedra have been omitted and the periodic vacant
tetrahedral holes in the structure have been traced with dotted red lines. This suggestive depiction of the Cu 3Se 2
structure appears nearly identical to the wurtzite structure shown in (c). In all structures, green = Se
2-
. For the
wurtzite-like structure, blue tetrahedra = Cu
+
/In
3+
. For the Cu 3Se 2 structures, pink and blue tetrahedra represent the
two crystallographically unique copper sites within the crystal structure. Adapted with permission from reference
66. Copyright 2018, American Chemical Society.
To maintain charge balance during the cation exchange, the incoming In
3+
cations must expel the
equivalent of one Cu
+
cation and one Cu
2+
cation, thus generating the CuInSe 2 composition. The most
stable structure resulting from the exchange of two copper cations by an In
3+
cation is that which is
produced by the replacement of unfavorable, edge-sharing motifs in Cu 3Se 2 (highlighted in Figure 1.7d)
with more favorable, corner-sharing motifs in the wurtzite-like structure (Figure 1.7c).
1.5 Ligand and Solvent Effects on Nanocrystal Polymorphism
1.5.1 Surface Stabilization of Metastable Ag 2Se Nanocrystals
Ag 2Se is a narrow-band gap semiconductor that can exhibit phase-dependent superionic Ag
+
conductivity
and giant magnetoresistance.
83–86
In the bulk, Ag 2Se crystallizes in a low-symmetry orthorhombic phase up
to ~135 °C, whereupon it undergoes a first-order phase transition to the superionic conducting body-
19

Figure 1.8 (a) Differential scanning calorimetry curves for trioctylphosphine-stabilized anti-PbCl 2-like Ag 2Se
nanocrystals (bottom curve) and bulk Ag 2Se powder (top curve). (b) Heating and (c) cooling in variable-temperature
powder XRD scans of 8.6 nm trioctylphosphine-stabilized anti-PbCl 2-like Ag 2Se nanocrystals. Adapted with
permission from reference 86. Copyright 2014, American Chemical Society.

centered cubic phase.
87–89
However, for nanocrystals, a third phase of Ag 2Se with ‘tetragonal’ lattice
parameters is also known to form at relatively low temperatures.
15–17,90,91
The crystal structure of this phase
of Ag 2Se was unknown until we showed that it adopts a monoclinic (not tetragonal) anti-PbCl 2-like
structure (see Chapter 5 for the full story of elucidating the structure of this metastable material). While
most of the literature up until now refers to this phase as ‘tetragonal,’ we will herein use the more correct
‘anti-PbCl 2-like’ terminology. This polymorph is temporally and thermally metastable and only isolable
when the crystallite size is confined to the nanoscale.
86
The complex interplay of phases on the nanoscale
make Ag 2Se an intriguing and unique material system in the area of metastable nanocrystals.
The potential for coexistence of the orthorhombic, cubic, and anti-PbCl 2-like phases has led to a
fair degree of confusion within the literature when providing phase assignments for Ag 2Se nanocrystals.
This is largely due to the ease with which the anti-PbCl 2-like phase of Ag 2Se has been mistaken for
orthorhombic Ag 2Se in powder XRD analysis. However, in recent years, synthetic methods have been
developed to cleanly isolate the anti-PbCl 2-like phase of Ag 2Se independently of the other phases.
14,86,90,92

These studies have shown that the method of preparation of the metastable anti-PbCl 2-like phase of Ag 2Se
has profound effects on its properties and persistence.
20

The anti-PbCl 2-like phase has been shown to convert to cubic Ag 2Se upon heating. Cheng et al. and
Norris et al. investigated the effect of the surface ligands on the temperature of this phase transition,
demonstrating that surface stabilization with various n-alkylamines, trialkylphosphines, or polyvinyl
pyrrolidone (PVP) all result in Ag 2Se nanocrystals capable of a reversible and direct anti-PbCl 2-like-to-
cubic Ag 2Se phase transition around 101-109 °C (Figure 1.8).
14,86,92,93
When stabilized with PVP ligands,
anti-PbCl 2-like Ag 2Se was found to be temporally stable for a week or longer at room temperature.
14
In
contrast, it was found that anti-PbCl 2-like Ag 2Se nanocrystals exclusively stabilized with oleylamine
ligands are much less thermally and temporally stable and do not exhibit the anti-PbCl 2-like-to-cubic phase
transition. Upon heating, these nanocrystals undergo an exothermic, irreversible anti-PbCl 2-like-to-
orthorhombic transition within a temperature range of 60-67 °C, and also revert to the orthorhombic phase
of Ag 2Se after 8 h at room temperature.
14
Often, the physicochemical properties of nanomaterials are
dependent on crystallite size. However, in this case, nanocrystal size does not explain the marked instability
of anti-PbCl 2-like Ag 2Se prepared with oleylamine ligands, as the oleylamine-capped nanocrystals used in
this study were of intermediate size (44 nm) compared to nanocrystals that displayed superior thermal and
temporal stability (n-alkylamine or trialkylphosphine-capped nanocrystals were ~10 nm in diameter and
the PVP-capped nanocrystals were ~125 nm in diameter).
14,86
Thus, for the oleylamine-stabilized
nanocrystals, size effects do not account for the low-temperature anti-PbCl 2-like-to-orthorhombic phase
transition.
Understanding the chemistry of the anti-PbCl 2-like Ag 2Se phase requires consideration of multiple
interdependent factors, including the identity of the ligands, nanocrystal size, surface chemistry, and the
influence of defects. As mentioned above, the anti-PbCl 2-like phase is only isolable for nanocrystals. In this
regard, organic ligands are crucial in that they sterically prevent the agglomeration/sintering of the
nanocrystals, enabling the persistence of the metastable phase on the nanoscale. In addition, surface ligands
can selectively stabilize specific crystal facets, thereby influencing overall surface energy of the
nanocrystals. Such ligand binding reduces the overall surface energy of the nanocrystals, and can favor the
formation of a phase that is metastable (or nonexistent) in the bulk.
9,11,94
In seeking to explain the relative
21

instability of the oleylamine-capped anti-PbCl 2-like Ag 2Se, Cheng et al. suggest that perhaps oleylamine
stabilizes the nanocrystal surfaces less than the other ligands that were tested, giving rise to the unique low-
temperature anti-PbCl 2-like-to-orthorhombic phase transition.
14
However, more studies are needed in order
to fully understand why the oleylamine-capped anti-PbCl 2-like Ag 2Se behaves differently than Ag 2Se
stabilized with other ligands.
1.5.2 Ligand-Mediated Phase Control of AgInSe 2 Nanocrystals
AgInSe 2 is a I-III-VI 2 semiconductor with a direct band gap and photoluminescence in the near-infrared
region of the electromagnetic spectrum, making it potentially useful for near-infrared bioimaging.
95–100
As
a I-III-VI 2 semiconductor, AgInSe 2 also crystallizes in the chalcopyrite structure type, as shown in Figure
1.9a, and region 12 of the phase diagram in Figure 1.9c.
101
On the pseudo-binary Ag 2Se-In 2Se 3 bulk phase
diagram, chalcopyrite AgInSe 2 shows a relatively narrow tolerance for compositional deviations from the
1:1:2 ratio of Ag:In:Se. When heated past 963 K, a phase transition occurs in which the occupation of cation
sites within the structure are randomized, leading to formation of a cubic zinc blende structure type with
broader compositional tolerance (region 10 in Figure 1.9c).
102,103
A highly related system, AgInS 2, also
crystallizes in the chalcopyrite structure at low temperatures, but adopts an orthorhombic wurtzite-like
structure (space group 𝑃𝑛𝑎 2
1
, Figure 1.9b) at T > 913 K, as shown in Figure 1.9d;
104–106
this phase has also
been isolated for AgInS 2 nanocrystals.
107
Interestingly, AgInSe 2 nanocrystals also can crystallize in an
analogous orthorhombic structure, despite this phase not being present on the bulk phase diagram for
AgInSe 2.
19,68,100,108–111

22

Figure 1.9 (a) Chalcopyrite structure of AgInSe 2. (b) Orthorhombic wurtzite-like structure of AgInS 2. For both
structures, gray atoms = Ag
+
, pink atoms = In
3+
, green atoms = Se
2-
, and yellow atoms = S
2-
. (c) Pseudo-binary bulk
phase diagram of the Ag 2Se-In 2Se 3 system. AgInSe 2 exists at the 50 mol% composition. Regions 10, 11, and 12
represent AgInSe 2 with the zinc blende structure, zinc blende + chalcopyrite structures, and the chalcopyrite
structure, respectively. The point at 1060 K between regions 1 and 10 lies on the liquidus curve and represents the
melt temperature of AgInSe 2. (d) Pseudo-binary bulk phase diagram of the Ag 2S-In 2S 3 system. Region 5 = liquid +
AgIn 5S 8, region 11 = orthorhombic AgInS 2 + AgIn 5S 8, region 14 = chalcopyrite AgInS 2. Phase diagrams adapted
with permission from reference 102, copyright 2001, Elsevier, and reference 104, copyright 2008, Elsevier.

Recently, we showed that the judicious selection of coordinating ligands enables polymorphic
control in the syntheses of AgInSe 2 nanocrystals.
68
In a general synthesis, the Ag
+
and In
3+
precursors were
dissolved together in a flask in either excess oleylamine or excess oleic acid. Then, the metal-containing
flask was then heated and the Bn 2Se 2 solution was hot-injected into it at the desired temperature. When
oleic acid is included as the coordinating ligand, the resulting AgInSe 2 nanocrystals crystallize in the
thermodynamic chalcopyrite structure (Figure 1.10a), often with some Ag 2Se impurities (vide infra). In
23

Figure 1.10 Powder XRD patterns corresponding to aliquots taken from reactions in which (a) oleic acid was
employed as the coordinating ligand, and (b) oleylamine was employed as the coordinating ligand. (c) TEM
micrographs corresponding to the XRD patterns shown in (b). Adapted with permission from reference 68.
Copyright 2020, American Chemical Society.

contrast, when oleylamine is used as the coordinating ligand, the AgInSe 2 nanocrystals exhibit the
metastable orthorhombic structure (Figure 1.10b).
Ex situ powder XRD analysis of reaction aliquots provided insight into the reaction mechanism; in
both cases, the aliquot taken 1 min after injection of Bn 2Se 2 revealed that binary Ag 2Se intermediates,
namely, a mixture of orthorhombic and anti-PbCl 2-like Ag 2Se, form prior to formation of ternary AgInSe 2
nanocrystals. Although the initial Ag 2Se intermediates appear to be the same for the reactions containing
oleic acid and oleylamine, later time points in the aliquot studies illustrate that these intermediates react in
distinctly different ways, as the oleic acid reaction yields chalcopyrite AgInSe 2 and the oleylamine reaction
yields orthorhombic AgInSe 2.
Although chalcopyrite AgInSe 2 nanocrystals represent the thermodynamic product for these
reactions, generating this phase from binary Ag 2Se intermediates is kinetically slow, as none of the Ag 2Se
24

Figure 1.11 (a) Pseudo-hexagonal Se
2-
sub-lattice of orthorhombic Ag 2Se. (b) Hexagonal Se
2-
sub-lattice of
orthorhombic AgInSe 2. (c) Demarcation of the periodic tetrahedral holes in orthorhombic Ag 2Se. If this site was
occupied with a cation, the resulting tetrahedron would be corner sharing with neighboring tetrahedra along the
edges highlighted in yellow. (d) Side-on view of orthorhombic Ag 2Se, with the two crystallographically unique
Ag
+
sites shown in grey and blue. (e) Orthorhombic Ag 2Se when viewed by omitting all edge-sharing coordination
sites while highlighting periodic tetrahedral holes within the structure with dotted red lines. (f) Orthorhombic
AgInSe 2 structure; grey tetrahedra = Ag
+
sites, pink tetrahedra = In
3+
sites, green atoms = Se
2-
. Adapted with
permission from reference 68. Copyright 2020, American Chemical Society.
intermediates are structurally similar to chalcopyrite. Orthorhombic Ag 2Se has a pseudo-hexagonal Se
2-

sub-lattice (vide infra), whereas cubic Ag 2Se has a body-centered cubic Se
2-
sub-lattice. In contrast,
chalcopyrite AgInSe 2 features a face-centered cubic Se
2-
sub-lattice. Therefore, for any of these Ag 2Se
intermediates to react with In
3+
to yield chalcopyrite AgInSe 2, they must undergo a kinetically slow,
reconstructive transition in which the anionic sub-lattices are disrupted and rearranged to produce a face-
centered cubic structure. We believe it is this kinetic bottleneck that leads to the persistence of minor Ag 2Se
impurities in the synthesis of chalcopyrite AgInSe 2 (Figure 1.10a).
In contrast, we observed that the formation of phase-pure orthorhombic AgInSe 2 occurs quickly,
as shown in Figure 1.10b. Several studies have reported the orthorhombic phase of Ag 2Se as an intermediate
that precedes the metastable orthorhombic phase of AgInSe 2, although these reports did not elaborate on
the mechanism of this transformation or the fate of anti-PbCl 2-like Ag 2Se in these reactions.
108–111
We
25

proposed a mechanism whereby orthorhombic Ag 2Se converts directly to orthorhombic AgInSe 2 by an in-
situ, ligand-mediated topotactic cation exchange process. Figure 1.11 demonstrates the structural
similarities between orthorhombic Ag 2Se and the metastable, orthorhombic phase of AgInSe 2. As can be
seen by comparing Figure 1.11a,b, orthorhombic Ag 2Se possesses a nearly hexagonal Se
2-
sub-lattice
closely related to that found in orthorhombic AgInSe 2. Thus, we posited that a topotactic partial cation
exchange process enables the transformation of the orthorhombic Ag 2Se, which contains edge-sharing Ag
+

polyhedral coordination environments, to orthorhombic AgInSe 2, which is characterized by having a more
stable corner-sharing framework. Incoming In
3+
cations fill the periodic tetrahedral holes (Figure 1.11c,e)
that exist within the orthorhombic Ag 2Se structure, leading to the expulsion of three Ag
+
ions from two
units of Ag 2Se to create the corner-sharing wurtzite-like structure shown in Figure 1.11f. Our proposed
mechanism for this transformation is akin to the mechanism we proposed to explain the formation of
metastable wurtzite-like CuInSe 2 from a copper selenide intermediate.
66
To account for the anti-PbCl 2-like
Ag 2Se intermediate in this mechanism, we hypothesize that anti-PbCl 2-like Ag 2Se converts first to
orthorhombic Ag 2Se, which can then undergo cation exchange to orthorhombic AgInSe 2.
68
Indeed, it is
known that, when ligated with oleylamine, anti-PbCl 2-like Ag 2Se undergoes an irreversible phase transition
to orthorhombic Ag 2Se at 60-67 °C.
14

In the formation of chalcopyrite and orthorhombic AgInSe 2 nanocrystals, the kinetics of the
evolution of the Ag 2Se intermediates depend upon the coordinating ligand present in the reaction mixture;
reactions in which oleic acid is used yield chalcopyrite nanocrystals, while when oleylamine is used,
orthorhombic nanocrystals result. Oleic acid is likely to take the form of oleate, an X-type ligand, which is
a harder base than the neutral, L-type oleylamine ligand, and therefore not well-suited to mediate a fast
topotactic cation exchange reaction by extracting soft Ag
+
cations from orthorhombic Ag 2Se intermediates.
The kinetics of cation exchange reactions are largely dependent on metal-ligand interactions, which can be
described using hard-soft acid base theory.
30
Thus, when oleate is present, the system proceeds down the
slower, thermodynamic pathway characterized by a reconstructive reaction between Ag 2Se intermediates
and In
3+
to yield chalcopyrite AgInSe 2 nanocrystals. In contrast, the softer Lewis basic character of
26

oleylamine matches the soft Ag
+
Lewis acid more appropriately, leading to a more favorable Lewis acid-
base interaction and extraction of Ag
+
from orthorhombic Ag 2Se intermediates, allowing for a kinetically
fast topotactic cation exchange process to outcompete the thermodynamic pathway for formation of
AgInSe 2. Interestingly, quaternary Cu 2ZnSnSe 4 (CZTSe) nanocrystals exhibit a similar polymorphic
dependence on the choice of ligand, demonstrating the generality of these synthetic strategies in preparing
metastable polymorphs on the nanoscale.
24

1.6 The Future of Metastable Nanocrystal Synthesis
While many of the first syntheses of nanomaterials with metastable crystal structures were discovered
serendipitously, strategies are emerging that will galvanize the predictable syntheses of novel metastable
polymorphs on the nanoscale. In addition to the synthetic techniques discussed above, computational
methods have provided invaluable insight into factors that influence the “synthesizability” of metastable
polymorphs. Thermodynamic considerations of phase stability allow prediction and experimental
verification of the most stable polymorphs for material systems under certain conditions. However, any
polymorph other than that defined by the thermodynamic structure for a given set of conditions is
metastable, meaning that there is a seemingly infinite number of potential metastable phases for any
material. Thus, evaluating the probability of the existence and potential for isolation of plausible
polymorphs within a material system is an important, non-trivial task when seeking to synthesize novel
metastable polymorphs.
In 2016, Cedar et al. conducted a data-mining study of DFT-calculated energies for nearly 30,000
inorganic compounds that appear within the Inorganic Crystal Structure Database (ICSD).
112
Of these
compounds, roughly 50% were metastable. To complement the DFT calculations of these experimentally
observed compounds, energy calculations were also carried out for hypothetical structures that were
generated for different material systems by using an algorithm that makes chemically sensible
compositional substitutions in existing crystal structures to create unobserved, but plausible, polymorphs
in silico.
27

Figure 1.12a gives the probability densities of experimentally observed polymorphs (blue curve)
and hypothetical metastable polymorphs (red curve) for binary metal oxides vs the energy of the respective
metastable polymorphs. These curves demonstrate that energy above the thermodynamic ground state
influences the likelihood of the existence of a metastable state. For the experimentally observed
polymorphs, 90% of the metastable polymorphs were observed to be 94 meV/atom or less above the
thermodynamic ground state, while the maximum probability for the energies of hypothetical, unobserved
polymorphs was 150 meV/atom. This supports the intuitive notion that lower-energy metastable
polymorphs are more likely to form than higher-energy polymorphs.
Importantly, energy above the ground state is not the sole predictor for synthesizability of
metastable polymorphs. Figure 1.12c shows that, for these binary metal oxides, numerous hypothetical
polymorphs that have never been experimentally observed have energies that are calculated to be less than
the energies of experimentally observed polymorphs. To explain this phenomenon, Cedar et al. propose a
concept of “remnant stability,” whereby all isolable metastable polymorphs must be, under some set of
thermodynamic conditions, the most stable polymorph. Figure 1.12b illustrates this idea, where the energy
of an unobserved hypothetical metastable phase falls between the experimentally observed α and β phases
for a given set of initial conditions. Manipulations of different thermodynamic parameters (temperature,
pressure, etc.) stabilize the β phase with respect to both the α phase and the hypothetical metastable phase,
allowing for isolation of the β phase under these new conditions. This example shows how, although the
hypothetical metastable phase can have a relatively lower energy than the β phase under the initial
conditions, it cannot be synthesized because it never represents the thermodynamically most stable state
under any set of conditions.
Additionally, it was found that the range of energies of accessible metastable polymorphs tracks
with the cohesive energy of the crystalline solids. For example, the median cohesive energy of
chalcogenides follows the trend of oxides > sulfides > selenides > tellurides. Similarly, the range of energies
of accessible metastable polymorphs above the thermodynamic ground state is greatest for oxides (0 – 100
meV/atom above ground state), followed by sulfides and selenides (0-75 meV/atom above the ground state),
28

and lastly by tellurides (0 – 50 meV/atom above the ground state).
112
When evaluating the feasibility of
isolating hypothetical metastable polymorphs, these findings provide insight as to which structures should
be attainable from a thermodynamic perspective for different chemistries.

Figure 1.12 (a) Probability density of metastable binary metal oxide polymorphs vs the polymorph energies above
the ground state. The blue curve represents the trend for experimentally observed polymorphs, while the red curve
represents the trend for hypothetical, unobserved metastable polymorphs. (b) Graph demonstrating the requirement
of “remnant stability” for the syntheses of metastable polymorphs. (c) Plot of the calculated energies of
experimentally observed polymorphs (blue points) and unobserved polymorphs (red points) for different binary
metal oxides. Note that for each material, there exist hypothetical polymorphs that fall energetically between
experimentally observed polymorphs, proving that energy above the ground state is not the only factor in
determining synthesizability of metastable polymorphs. Reprinted from reference 112. 2016 © The Authors, some
rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a
Creative Commons Attribution Non-Commercial License 4.0 (CC BY-NC).
29

The stipulation of remnant stability limits the number of possible isolable polymorphs and suggests
that by expanding our knowledge of the thermodynamic stabilities of material systems under variable
conditions, we can identify which metastable polymorphs should be attainable. While insightful, it is
difficult to extend this principle to the nanoscale due to the aforementioned complexity of parameters that
influence thermodynamic stabilities of nanomaterials, including surface energy, morphology, defects,
surface ligand interactions, size effects, composition, etc. Recently, we proposed a conceptual framework
that utilizes thermodynamic bulk phase diagrams to target material systems that may yield novel metastable
polymorphs on the nanoscale.
68
This framework was developed after noting emerging patterns in our studies
of the mechanisms of formation for metastable wurtzite-like CuInSe 2 and AgInSe 2 nanocrystals; in both
cases, the metastable ternary wurtzite-like phases form as In
3+
reacts with binary selenide intermediates
(Cu 3Se 2 or orthorhombic Ag 2Se, respectively) that possess pseudo-hexagonal Se
2-
sub-lattices and are
metastable at the reaction temperatures (vide supra).
66,68
Kinetically fast topotactic cation exchange
reactions preserve the hexagonal structures of the intermediates and generate the metastable hexagonal
ternary nanocrystals. While the chalcopyrite phase is the thermodynamically stable polymorph for both
CuInSe 2 and AgInSe 2, producing this phase from Cu 3Se 2 or orthorhombic Ag 2Se is kinetically slow due to
the activation energy barrier associated with reorganizing the Se
2-
sub-lattices of the intermediates from
nearly hexagonal frameworks to face-centered cubic frameworks. As depicted in Figure 1.13, these “lattice
mismatches” between binary and ternary material systems allow kinetic pathways to prevail over
thermodynamic pathways, and lead to the formation of ternary metastable materials.

30

Figure 1.13 (a) Simplified pseudo-binary Ag 2Se-In 2Se 3 phase diagram. Lattice mismatches between phases are
color-coded, where red = body-centered cubic Se
2-
sub-lattice, blue = pseudo-hexagonal Se
2-
sub-lattice, and white
= face-centered cubic Se
2-
sub-lattice. (b) Reaction scheme demonstrating how the lattice mismatch between
orthorhombic Ag 2Se and chalcopyrite AgInSe 2 prevents the thermodynamic pathway from operating, allowing the
system to follow the kinetically faster pathway to yield metastable orthorhombic AgInSe 2. Adapted with permission
from reference 68, copyright 2020, American Chemical Society, and reference 102, copyright 2001, Elsevier.

In seeking to synthesize new metastable polymorphs on the nanoscale, chemists should consult
pseudo-binary or ternary phase diagrams to design syntheses that exploit the kinetic advantages afforded
by such lattice mismatches. This approach, when combined with DFT calculations that shed light on the
relative thermodynamic stabilities of predicted metastable phases, should provide chemists with a method
of predictably synthesizing novel metastable polymorphs on the nanoscale. Additionally, although not
covered in this chapter, machine learning tools are becoming more widely used in materials research in
general, and promise to further expand our reach into the realm of new metastable nanomaterials
syntheses.
113–116

1.7 Properties and Applications of Semiconductor Nanocrystals with Metastable Crystal Structures
Interest in metastable materials is driven by their potential to manifest new functional properties. However,
in addition to physical properties, the kinetic persistence of metastable materials is an important metric in
31

determining the utility of metastable materials for technological applications. For instance, the metastable
halide perovskite-phase of CsPbI 3 represents a noteworthy example in which the physical properties of the
material are highly desirable for applications in solar cells and LEDs, but its commercial use will be limited
by the relatively fast relaxation to the “nonfunctional” thermodynamically stable orthorhombic
phase.
94,117,118
For the purposes of this chapter, discussion of the applications, properties, and persistence of
metastable polymorphic nanomaterials will be limited to the materials discussed in 1.3-1.5. While these
materials have potential applications ranging from infrared emitters for biological imaging,
100,110
to solar
cells,
119,120
and non-linear optics,
111
we will highlight work in this section that explicitly demonstrates new
functional properties brought about by metastable crystal structures. That said, the field of metastable
polymorphic nanomaterials has thus far primarily focused on the syntheses of metastable nanomaterials,
and much still remains to be discovered regarding the properties of many of these novel systems.
1.7.1 Optical Properties and Electrochemiluminescence Applications of Wurtzite ZnSe
Nanocrystals
Metastable wurtzite zinc selenide nanocrystals exhibit several notably different optical properties compared
to the zinc blende polymorph. For example, emission from zinc blende ZnSe nanowires is polarized parallel
to the direction of the nanowire, while polarized photoluminescence occurs perpendicular to the c-axis of
wurtzite ZnSe nanowires.
121
This property makes wurtzite ZnSe useful for single-photon emitters. When
excited with light, electron-hole pairs within the wurtzite nanowires form transient dipoles perpendicular
to long axis of the nanowire (c-axis); such orthogonal dipoles are necessary to achieve the highest possible
rates of photon emission, whereas in zinc blende ZnSe, the transient excitonic dipoles form parallel to the
direction of the nanowire, which reduces photon extraction efficiencies.
121,122
In addition to photonics, the
wurtzite phase may be preferable to the zinc blende phase for electrochemiluminescence applications.
123

Electrochemiluminescence (ECL) is the process whereby species generated at electrode surfaces react to
yield electronic excited states that luminesce. ECL is a highly sensitive technique that can be used to detect
chemical and biological analytes in solution.
124

32

Figure 1.14 (a) Depiction of the defect-free ABAB stacking in wurtzite ZnSe. The alternating direction of the Zn-
Se bond is indicated by red and green arrows. (b) Aberration-corrected high-angle annular-dark-field (HAADF)
image of wurtzite ZnSe nanocrystals containing symmetry-breaking defects. In the upper left corner, a structural
model is superimposed upon the image. The bottom right corner is a simulated HAADF representation of the
experimental data. (c) Model representing the atomic structure found in (b); note that the translational symmetry of
the direction of the Zn-Se bond is broken here, as compared to in (a). Adapted with permission from reference 123,
copyright 2016, American Chemical Society.

In their studies of ZnSe as a material for ECL applications, Dai et al. found that wurtzite ZnSe nanocrystals
possess defective segments that break the translational symmetry of the crystal, as illustrated by aberration-
corrected high-angle annular-dark-field (HAADF) images of wurtzite ZnSe nanocrystals in Figure 1.14.
Such symmetry-breaking defects induce local charge imbalances within the material, and result in novel
optical properties.
123,125
Zinc blende ZnSe nanocrystals also displayed symmetry-breaking defects, although
electron holography experiments revealed that the net local charges in defective segments of ZnSe
nanocrystals were greater in the wurtzite phase than in the zinc blende phase.
123

To test the application of these nanocrystals as ECL sensors, electrodes modified with ZnSe were
fabricated and subject to reductive potentials in the presence of aqueous K 2S 2O 8 as a co-reactant. Under
these conditions, S 2O 8
2-
reduces to form equivalents of SO 4
●-
, a powerful oxidant. It is speculated the
33

Figure 1.15 (a) ECL mechanism that elucidates interactions between SO 4
●-
and negatively charged ZnSe. (b) Plot
of ECL signal intensity as a function of the net charge of defect regions in different forms of ZnSe, as measured by
electron holography. Note that wurtzite ZnSe has the highest charge and also the greatest ECL intensity. (c)
Potential-dependent ECL intensity for wurtzite ZnSe, zinc blende ZnSe, bulk ZnSe, and the bare glassy-carbon
electrode. (d) The ECL signal (blue curve) is significantly red shifted from the intrinsic photoluminescence (black
curve) of wurtzite ZnSe nanocrystals, suggesting ECL originates from an intra-gap surface trap state. Adapted with
permission from reference 123, copyright 2016, American Chemical Society.
symmetry-breaking defects result in electron injection into the conduction band of ZnSe in negatively
charged defect regions of the ZnSe nanocrystals. These negatively charged domains are oxidized by SO 4
●-
, producing SO 4
2-
and a charge-neutral excited state of ZnSe that can then undergo radiative relaxation. This
proposed ECL mechanism is depicted in Figure 1.15a. Importantly, the greater excess of charge in wurtzite
ZnSe defect segments was found to enhance probability of electron-hole recombination in wurtzite ZnSe,
translating into more intense electrochemiluminescence from these nanocrystals as compared to zinc blende
ZnSe nanocrystals or bulk zinc blende ZnSe (Figure 1.15b,c). ECL is notably red-shifted from the intrinsic
photoluminescence of the ZnSe nanocrystals, suggesting that ECL originates from relaxation of electrons
34

in intra-gap surface trap states (Figure 1.15d).
123
These results show that the defect chemistry can differ
between polymorphs, and that defects play a role in influencing the properties of the metastable
nanomaterials.
1.7.2 Metastable Wurtzite-Like CuInSe 2 Nanocrystals
As mentioned in 1.4, CuInSe 2 is an excellent candidate for application in thin-film photovoltaics due to its
relatively low toxicity and direct band gap of ~1.0 eV.
126
Lau et al. sought to explore the properties of the
metastable wurtzite-like phase of CuInSe 2 through a first-principles DFT study.
127
The wurtzite-like phase
in this study was characterized by an ordering of the Cu
+
and In
3+
sites within a hexagonally close-packed
framework of Se
2-
; such ordering has been experimentally verified for wurtzite-like CuInSe 2 nanocrystals.
80

The valence band maximum (VBM) of the chalcopyrite CuInSe 2 has antibonding character arising from
interactions between Cu d-states and Se p-states.
128
The Cu d-electrons are relatively localized and
contribute little to the density of states near the Fermi energy, as shown in Figure 1.16a. In contrast, greater
hybridization of Cu d-states with In and Se p-states reduces the localization of Cu d-electrons in wurtzite-
like CuInSe 2 and results greater density of states near the Fermi energy (Figure 1.16a), which should
theoretically enhance electronic excitation and transport in CuInSe 2.
127

Moreover, the calculated electronic band structure of the wurtzite-like phase suggests that this
phase may be a more efficient absorber of the solar spectrum than the chalcopyrite phase. Figure 1.16b,c
indicates that, while both polymorphs have narrow, direct band gaps, light absorption in the wurtzite-like
phase should be enhanced compared to the chalcopyrite phase due to a near-direct transition from the VBM
to the minimum of the Fermi+1 conduction band. In the chalcopyrite phase, this excitation is an indirect,
phonon-assisted transition, making it less probable than in the wurtzite-like phase. Figure 1.16d illustrates
35

Figure 1.16 (a) Calculated density of states for Cu d-states for wurtzite-like (top) and chalcopyrite (bottom)
CuInSe 2. The Fermi energy is set to zero. (b) Calculated band structure for wurtzite-like CuInSe 2. (c) Calculated
band structure for chalcopyrite CuInSe 2. (d) Simulated electronic absorption profiles for wurtzite-like and
chalcopyrite CuInSe 2; note that the wurtzite-like phase is expected to display comparable or superior absorption to
the chalcopyrite phase from 920 – 613 nm (1.35 – 2.0 eV) of the electromagnetic spectrum. Adapted with
permission from reference 127, copyright 2012, Royal Society of Chemistry.

that the calculated electronic absorption for wurtzite-like CuInSe 2 is greater than that of the chalcopyrite
phase through the range of the electromagnetic spectrum most relevant for solar cells.
127
In addition to the
favorable electronic band structure of wurtzite-like CuInSe 2, wurtzite and wurtzite-like phases are often
more compositionally flexible than other polymorphs of I-III-VI 2 semiconductors (see Figures 1.5, 1.9),
which opens opportunities for fine tuning of the composition-dependent band gaps of these materials.
129

Such strategies have been successfully employed for band gap engineering in similar material systems.
36

Indeed, by synthetically tuning the S:Se ratio in wurtzite-like CuZnSn(S 1-xSe x) 4 nanocrystals, the band gap
can be linearly tuned from 1.0 to 1.5 eV, which is a wider range than afforded through the same
compositional tuning within the thermodynamically preferred kesterite polymorph of CuZnSn(S 1-xSe x) 4.
59,60

1.7.3 Persistence of Wurtzite-like CuInSe 2 Nanocrystals
Lau et al. calculated that the wurtzite-like phase of CuInSe 2 is metastable with respect to the chalcopyrite
polymorph by a mere 5-9 meV/atom (at 0 K), and that there exists a large activation energy barrier to
convert between these two phases.
127
Indeed, we experimentally verified the temporal and thermal stability
of the wurtzite-like phase in CuInSe 2 nanocrystals.
66
Post-synthetically heating wurtzite-like CuInSe 2
nanocrystals to 300 °C in solution failed to induce a phase transition to the thermodynamically stable
chalcopyrite phase. Similar results were found when the nanocrystals in powder form were exposed to
multiple heating-cooling cycles to 300 °C. Only when the nanocrystals were heated past the temperature
(420 °C) at which the oleylamine ligands volatilize from surface of the nanocrystals did we observe a phase
transition to the chalcopyrite phase. This thermal stability is remarkable for a metastable nanocrystalline
polymorph, especially considering that the temperature of solid-solid phase transitions are often
substantially reduced on the nanoscale.
130–132
These experiments, and the fact that we observed wurtzite-
like phase CuInSe 2 nanocrystals to show no sign of relaxation to the chalcopyrite phase after one year,
66

support calculations that predict the wurtzite-like polymorph to be a highly persistent, deep local minimum
within the energetic landscape of polymorphic CuInSe 2. This profound kinetic trapping of the metastable
phase may be common to many material systems capable of crystallizing with wurtzite-like structure types;
we experimentally showed that a similar wurtzite-like phase of AgInSe 2 nanocrystals displayed comparable
temporal and thermal persistence to that of wurtzite-like CuInSe 2,
66
and Ryan et al. found the wurtzite-like
phase of CuZnSnS 4 nanocrystals to be persistent up to ~380 °C.
133

1.7.4 Metastable Ag 2Se Nanocrystals
As discussed in 1.5.1, Ag 2Se has two polymorphs in bulk, namely the low- and high-temperature
orthorhombic and cubic phases, respectively, and an additional metastable anti-PbCl 2-like polymorph that
37

only forms on the nanoscale. Physicochemical property differences often exist between polymorphic
materials. For example, the orthorhombic-to-cubic phase transition in Ag 2Se is accompanied by changes to
the electronic structure of Ag 2Se. At low temperatures, orthorhombic Ag 2Se is a low-band gap
semiconductor. Upon transitioning to cubic Ag 2Se, the material becomes both electronically metallic and a
superionic conductor in which mobile Ag
+
ions are capable of collective motion within the body-centered
cubic framework of Se
2-
anions.
134–138

While an exhaustive assessment of all applications of Ag 2Se is beyond the scope of this chapter,
the unique properties of different polymorphs of Ag 2Se, and the ability to control phase transitions between
polymorphs on the nanoscale, makes this material system attractive for thermoelectrics,
136
electrical
switches and digital memory storage,
86,139–141
infrared optoelectronic devices,
142
and catalysts for metal
chalcogenide nanowire synthesis.
93
The existence of the high-temperature cubic phase and the metastable
low-temperature anti-PbCl 2-like phase gives rise to two types of polymorphic metastability at low
temperatures, where Ag 2Se can exist in either one of these phases and still be metastable with respect to
orthorhombic Ag 2Se. Presented herein are two examples in which metastable cubic and anti-PbCl 2-like
Ag 2Se have been exploited for their characteristic properties to introduce new functionalities in nanocrystal
syntheses and optoelectronics, respectively.
Thermodynamically, the cubic phase of Ag 2Se is stable above T > 135 °C.
87–89
However, this
superionic conducting phase can be kinetically trapped at lower temperatures, and has even been observed
at room temperature.
139
Yang et al. demonstrated that cubic Ag 2Se can be used to catalyze the low-
temperature growth of ZnSe nanowires, enabling nanowire synthesis at temperatures as low as 100 °C, a
lower temperature than any previously reported temperatures for the syntheses of crystalline ZnSe
nanowires.
93
In their syntheses, nearly equimolar amounts of the zinc and selenium precursors were
dissolved and then heated in the presence of a small amount of AgNO 3 (roughly 2% of the equivalents of
zinc) to produce the Ag 2Se-catalyzed ZnSe nanowires.
Here, the cubic phase plays a pivotal role in the proposed “solution-solid-solid” mechanism of
catalyzed nanowire growth: First, the extreme mobility of Ag
+
and the prevalence of vacancies in cubic
38

Ag 2Se favor incorporation of other cations, like Zn
2+
, into the nanocrystals, leading to an intermediate Ag-
Zn-Se solid solution. However, since the solubility of ZnSe in Ag 2Se at low temperatures is small, the solid
solution quickly becomes supersaturated with Zn
2+
, facilitating a phase-segregating process in which ZnSe
precipitates from Ag 2Se, effectively regenerating the catalyst. Once a Ag 2Se-ZnSe solid-solid interface is
established, diffusion of cations (both Ag
+
into ZnSe and Zn
2+
into Ag 2Se) across the interface encourages
further growth of ZnSe at the interface as more Zn
2+
is incorporated from solution into vacancies created as
a consequence of cation migration. Yang et al. hypothesize that it is this migration of cations through the
solid-solid interface that drives anisotropic growth of ZnSe. The Ag 2Se-catalyzed mechanism of ZnSe
nanowire growth is depicted in Figure 1.17a, along with TEM micrographs and energy-dispersive
spectroscopy elemental mapping of the nanocrystals in Figure 1.17b,c. They found this method of catalysis
with cubic Ag 2Se could be extended to the low-temperature synthesis of crystalline CdSe nanowires, and
that superionic Ag 2S and Cu 2S nanocrystals are capable of catalyzing nanowire growth as well.
93

Figure 1.17 (a) Scheme illustrating the proposed solution-solid-solid mechanism of cubic Ag 2Se-catalyzed ZnSe
nanowire growth. (b) TEM micrograph of ZnSe nanowires grown via Ag 2Se catalysis. Note that the nanowires are
capped with Ag 2Se tips. (c) Scanning TEM micrograph and energy-dispersive spectroscopy elemental mapping of
ZnSe nanowires capped with the Ag 2Se tip. Adapted with permission from reference 93, copyright 2013, American
Chemical Society.
39

1.7.5 Optoelectronic Properties of Anti-PbCl 2-Like Ag 2Se Nanocrystals
In contrast to the metallic, superionic conducting cubic phase, the metastable anti-PbCl 2-like phase of Ag 2Se
is a narrow band gap semiconductor. However, due to the fact it only arises on the nanoscale, relatively
little is known about the anti-PbCl 2-like phase of Ag 2Se in comparison to the orthorhombic or cubic phases
(see Chapter 5 on our recent findings regarding the crystalline and electronic structure of anti-PbCl 2-like
Ag 2Se). In the first detailed study of the optical properties of anti-PbCl 2-like Ag 2Se nanocrystals, Norris et
al. showed that this material shows promise for use as emitters or detectors of the mid-infrared region of
the electromagnetic spectrum.
142
Importantly, Ag 2Se is less toxic than other materials, such as HgTe or
HgCdTe, that are employed in mid-infrared optoelectronics.
143

By synthesizing anti-PbCl 2-like Ag 2Se nanocrystals of different sizes (2.7 – 10.4 nm in diameter),
Norris et al. were able to systematically tune the optical band gap of the material. Indeed, they calculated
the Bohr exciton radius of this phase to be roughly 2.9 nm, indicating that any nanocrystals under 5.8 nm
in diameter should exhibit strong quantum confinement, as shown in Figure 1.18c. While such confinement-
induced band gap tunability is ubiquitous in nanocrystal chemistry, anti-PbCl 2-like Ag 2Se nanocrystals
afford the unique feature of tunability of absorption in the mid-infrared, exhibiting some of the longest
wavelength absorption peaks reported for colloidal nanocrystals, up to 6.5 μm (Figure 1.18a,b).
142

Figure 1.18 (a) Mid-infrared absorption spectra for anti-PbCl 2-like Ag 2Se nanocrystals of different sizes. The large
peak at 0.35 eV corresponds to a solvent absorption peak. (b) Plot of the lowest transition energies for anti-PbCl 2-
like Ag 2Se nanocrystals as a function of nanocrystal diameter. (c) Lowest transition energies vs 1/nanocrystal
radius. The red curve represents the predicted lowest transition energies as a function of 1/radius as calculated
through effective mass theory. This relationship is linear when plotted lowest transition energies versus 1/radius
2

(inset). Adapted with permission from reference 142, copyright 2012, Royal Society of Chemistry.
40

Within the strong confinement regime, there exists a linear relationship between the lowest energy
transition of the nanocrystals and 1/nanocrystal radius
2
, as pictured in the inset of Figure 1.18c. The
effective bulk band gap of anti-PbCl 2-like Ag 2Se is calculated by solving for the y-intercept of the line of
best fit of the transition energy vs 1/radius
2
, where the y-intercept represents a crystal with an infinite radius.
This treatment produces a value of 0.064 eV for the bulk band gap of anti-PbCl 2-like Ag 2Se. Although bulk
anti-PbCl 2-like Ag 2Se has never been observed, the minimum experimental band gap observed is roughly
0.07 eV, which fits well with the results of this calculation.
144
Notably, this band gap is less than that of the
stable semiconducting orthorhombic phase of Ag 2Se, which has a bulk band gap of 0.15 – 0.18 eV,
suggesting that the anti-PbCl 2-like polymorph extends functionality of this material system deeper into the
infrared region of the electromagnetic spectrum.
142
Finally, Norris et al. also demonstrated that these anti-
PbCl 2-like Ag 2Se nanocrystals fluoresce in the infrared, making them useful for applications as mid-infrared
optoelectronic detectors and emitters.
142

1.7.6 Core-Shell Effects on the High-Temperature Stability of Anti-PbCl 2-Like Ag 2Se Nanocrystals
The effects of surface ligands on the temporal and thermal persistence of the metastable anti-PbCl 2-like
phase of Ag 2Se has been discussed in 1.5.1, underscoring that this phase, under certain conditions, can last
for a week or longer and can undergo a phase transition to the high-temperature cubic phase of Ag 2Se
around ~100 °C. Relevant to the application of Ag 2Se as a material for phase-dependent electrical
switching, Norris et al. found that the temperature of the anti-PbCl 2-like-to-cubic phase transition can be
increased significantly by installing a shell around anti-PbCl 2-like Ag 2Se nanocrystal cores.
86
In fact, if
there is a significant mismatch in lattice parameters between the core and shell materials, the shell can
induce pressures on the order of a few gigapascals on the core.
145
In the case of anti-PbCl 2-like Ag 2Se, it
was found that the phase transition temperature could be controlled by depositing shells with a lesser lattice
mismatch (ZnS, 8.5%) or a greater lattice mismatch (CdS, 17%), as well as by controlling the number of
layers of deposited core material. Intriguingly, a 50 °C increase was observed for the anti-PbCl 2-like-to-
cubic phase transition when depositing a shell of CdS around the Ag 2Se cores. Similarly, by growing
variable thickness shells of ZnS around anti-PbCl 2-like Ag 2Se nanocrystals, the phase transition
41

temperature could be tuned by 30-65 °C.
86
Since cubic Ag 2Se is a metallic superionic conductor, it is useful
for electrical switching applications to have such fine control over the temperature at which this phase
transition occurs.
1.8 Conclusions
The direct syntheses of metastable polymorphic nanocrystals are developing from a science reliant on
empirical findings to a field equipped with synthetic strategies that allow desired polymorphs to be targeted.
In this chapter, the highlighted methodologies for polymorphic control on the nanoscale included
modulation of reaction conditions (temperature, time, concentration, etc.), kinetic control via prudent
selection of molecular precursors, ligand effects, and surface chemistry considerations. While these
methodologies show broad utility in preparing metastable nanomaterials, they are by no means the only
methods of obtaining nanocrystals with metastable crystal structures. Other methods not discussed here,
such as those that exploit the hysteresis of pressure-induced phase transitions, have also led to isolation of
persistent metastable polymorphs.
146

Recent data mining research of thousands of inorganic compounds suggests that, in order to be
isolable, metastable polymorphs must be thermodynamically favored under some set of conditions, and that
their persistence away from thermodynamic equilibrium is evidence of “remnant” thermodynamic
stability.
112
This concept is useful in that it places limits on the number of possible metastable polymorphs
for a material, reducing the otherwise potentially infinite metastable phase space to a more tractable, albeit,
still vast, thermodynamically defined phase space. In this vein, understanding polymorphic metastability
from the perspective of thermodynamics compels us to gain a more quantitative knowledge of
thermodynamic phase relations on the nanoscale, and how those relations depend on variables such as
temperature, surface energy, ligands, composition, etc. If this can be achieved, new metastable
nanomaterials might be predictably synthesized by manipulating thermodynamic reaction parameters to
target desired polymorphs. However, obtaining quantitative thermodynamic information across
multivariate phase spaces on the nanoscale is a Herculean task, due to the myriad variables and complexities
of nanoscale material systems. Therefore, the continued development of kinetic frameworks and other
42

methods towards the rational syntheses of metastable polymorphs will likely remain the most practical for
discovering new metastable materials. Although not covered in this chapter, chemists continue to push the
boundaries of cation exchange as a highly fruitful method of obtaining new polymorphs. In addition,
outlined in this chapter are examples that demonstrate how bulk thermodynamic phase diagrams can be
used to predict the kinetic isolation of metastable polymorphs on the nanoscale. In the near future, machine
learning tools promise use in the design of syntheses for metastable nanomaterials.
Metastable polymorphs of semiconductor nanocrystals often manifest distinct physical, chemical,
and optoelectronic properties from their thermodynamic congeners. Continued exploration into the
syntheses and properties of metastable phase spaces is needed and should be motivated by their potential
to afford functional materials for photonics, optical sensing and imaging, solar cells, LEDs, thermoelectrics,
and other applications. The selected material case studies in this chapter highlight explicit examples in
which metastable polymorphs yield new functional properties that open doors to enhanced device
performances or completely novel applications that could not be achieved without access to these
metastable phases. The study of the properties and technological applications of metastable polymorphic
nanomaterials is a broad field in its own right and deserves a more in-depth review than is possible here.
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51

Chapter 2. Utilizing Diselenide Precursors towards the Rationally Controlled Synthesis of
Metastable CuInSe2 Nanocrystals

*Published in Chem. Mater. 2018, 30, 5704-5713.

2.1 Abstract
Within the past decade, there has been an emergence of reports regarding the synthetic isolation of
multinary metal chalcogenide nanocrystals that persist under ambient conditions with metastable crystal
structures; however, many of the direct syntheses remain largely serendipitous with respect to the conditions
needed to achieve the metastable product. Towards the development of more rational design principles that
enable the predictable isolation of metastable nanocrystals, we demonstrate a molecular programming
approach for the synthesis of CuInSe 2 nanocrystals utilizing diorganyl diselenide precursors of the structure
R-Se-Se-R. Specifically, we show that the kinetics of diselenide precursor conversion are dependent upon
C–Se and Se–Se bond dissociation energies, and that the strength of the C–Se bond is the phase-directing
variable. When employing dibenzyl and dimethyl diselenide precursors with relatively weaker C–Se bonds,
the resulting nanocrystals form in the thermodynamically stable chalcopyrite phase of CuInSe 2. However,
precursors like diphenyl diselenide that possess stronger C–Se bonds alter the reaction kinetics so as to steer
the reaction towards formation of the metastable wurtzite-like phase. These two phases form via distinct
copper selenide intermediates, with chalcopyrite forming through Cu 2–xSe and the wurtzite-like phase
forming through Cu 3Se 2 intermediates, and it was found that the ultimate wurtzite-like phase displays
remarkable resistance to relaxation to the chalcopyrite phase. This molecular programming approach should
be applicable towards the isolation of other metastable phases of metal chalcogenide nanocrystals.
2.2 Introduction
Chemical systems under thermodynamic equilibrium will spontaneously undergo a minimization of their
free energy by converging to the lowest energy state or structure possible for a given set of thermodynamic
parameters (e.g., temperature, pressure). Higher energy species may be kinetically stabilized if the
activation barrier associated with conversion to the ground state is significant enough to prevent the system
from achieving its thermodynamic minimum. In such cases, the kinetically trapped species are referred to
52

as ‘metastable,’ as they persist despite their thermodynamic instability. Examples of kinetic stabilization of
metastable species pervade the natural world; the diamond allotrope of carbon is a classic example.
1
In
crystalline solids, metastability arises for materials that exhibit energetic differences between polymorphs,
compositions, and crystallite size.
2,3
As is often the case, metastable materials can display drastically
different properties than their more thermodynamically stable counterparts;
2,4–6
however, traditional high-
temperature solid-state techniques do not provide sufficient synthetic control to predictably yield metastable
products. Such methods typically rely on supplying the reaction vessel with an excess of heat in order to
overcome the kinetic barriers of solid state diffusion, which usually drives the formation of the most
thermodynamically stable products.
7,8
Solution-phase colloidal nanocrystal syntheses, on the other hand,
can afford more kinetic control, providing new pathways to explore metastable materials.
Metastability can be inherent to colloidal nanocrystals since these materials possess higher surface-
to-volume ratios than their bulk counterparts.
9
The increasing contribution from surface energy to the
overall lattice energy with decreasing particle size sometimes allows phases that typically form only at high
temperatures to be stabilized at significantly lower temperatures at the nanoscale.
10,11
Cation exchange
reactions represent a common kinetically controlled technique employed for the synthesis of metastable
nanocrystals. For example, syntheses of metastable CoS,
12
MnS,
13
ZnSe,
14
and Cu 2–xSe
15
nanocrystals via
cation exchange have been reported. While cation exchange has proven to be a versatile method to isolate
metastable nanocrystals, it may not always be feasible to perform post-synthetic modifications of a parent
nanocrystal platform to yield a given metastable product.
There also exist numerous examples of syntheses of metastable nanocrystals via direct solution-
phase chemistry.
16–18
We, and others, have reported the syntheses of metastable semiconductor nanocrystals
such as CuInSe 2,
19,20
Cu 2SnSe 3,
21
CuInS 2,
22,23
CuIn xGa 1–xS 2,
24
and Cu 2ZnSnS 4;
25,26
however, these reports
have been mainly happenstantial with respect to the isolation of metastable phases of the resulting
nanocrystal products. While these discoveries nicely illustrate the potential of using solution-phase
chemistry to directly access metastable phases, they do not provide robust synthetic design principles that
53

enable predictable syntheses of metastable phases. Thus, there remains a need for rational methodologies
that may be employed towards the fabrication of metastable colloidal nanocrystals.
In this vein, chemists have turned to a “molecular programming” approach by which the properties
of nanomaterials can be rationally controlled through careful selection of molecular precursors that follow
predictable trends in reactivity.
27-31
Diorganyl dichalcogenides (R-E-E-R, where E = S, Se, Te and R =
alkyl, allyl, benzyl, phenyl) have emerged over the past decade as versatile precursors for the controlled
synthesis of metal chalcogenide nanocrystals.
32
In part, the utility of this family of precursors stems from
their predictable reactivity as a function of the C–E and E–E bond strengths, as first proposed by Vela and
co-workers.
33
Most notably, they posited that the C–E bond strength is highly dependent upon the identity
of the organic functional group of the dichalcogenide, which they used, in turn, to control the morphology
of CdS and CdSe nanocrystals. Recent work supports the importance of considering the C–S and S–S bond
strengths when using diorganyl disulfides in the solution-phase synthesis of iron sulfide, which
demonstrated that the resulting composition of iron sulfide is tunable from sulfur-rich pyrite (FeS 2) to more
iron-rich compositions, such as greigite (Fe 3S 4) and pyrrhotite (Fe 7S 8), as a function of the C–S bond
strength.
34

Herein, we show how diorganyl dichalcogenides can be used to rationally control the phase of
ternary CuInSe 2 semiconductor nanocrystals using a molecular programming approach. Specifically, the
judicious choice of R 2Se 2 (i.e., R = benzyl (Bn), methyl (Me), phenyl (Ph)) precursor enables kinetic control
over nanocrystal formation such that either the thermodynamic chalcopyrite phase or a metastable,
hexagonal wurtzite-like phase may be selectively synthesized. Among the different classes of
semiconductor nanocrystals, the ternary I-III-VI 2 family, with an A
+
B
3+
E
2–
2 composition, has garnered a
great deal of attention for use in photovoltaics, light-emitting diodes, and nonlinear optical devices.
24
The
most common crystal structure of I-III-VI 2 semiconductors is chalcopyrite; the tetrahedral structure of
chalcopyrites can be considered a superlattice structure of zinc blende in which the A
+
and B
3+
ions are
ordered in the cation sublattice sites. This is the thermodynamically preferred structure for bulk CuInSe 2.
A random distribution of the cations leads to the zinc blende phase.
24
We reported the first example of a
54

wurtzite-like phase for CuInSe 2 nanocrystals, which was a previously unknown phase for the bulk
material.
19
Subsequent ab initio calculations on this wurtzite-like phase of CuInSe 2 revealed it to possess
advantageous electronic and optical properties over the chalcopyrite phase, such as increased optical density
under near-infrared and visible light.
35
The molecular programming approach demonstrated herein can be
used to rationally enact selectivity within the CuInSe 2 phase space for colloidal nanocrystals.
2.3 Experimental
2.3.1 Materials and General Procedures
Copper(II) dichloride dihydrate (CuCl 2∙2H 2O, Sigma Aldrich), sodium oleate (Na(oleate), >97%, TCI
America), indium(III) trichloride (InCl 3, 98%, Sigma Aldrich), diphenyl diselenide (Ph 2Se 2, 98%, Sigma
Aldrich), dibenzyl diselenide (Bn 2Se 2, 98%, Alfa Aesar), dimethyl diselenide (Me 2Se 2, 96%, Sigma
Aldrich), benzeneselenol (PhSeH, 97%, Sigma Aldrich), oleylamine (70%, Sigma Aldrich). Oleylamine
was degassed under vacuum at 90 °C for 4 h and then overnight at room temperature prior to use. Reactions
were conducted under a nitrogen atmosphere by using standard Schlenk techniques. All reactions employed
J-KEM temperature controllers with in-situ thermocouples in order to control and monitor the temperature
of the reaction vessel.
2.3.2 Synthesis of Cu(II) oleate
An adapted literature approach was used.
20
Na(oleate) (3.0 g, 9.85 mmol) and CuCl 2∙2H 2O (0.84 g, 4.93
mmol) were placed in a round bottom flask. A solution containing 10 mL ethanol, 8 mL water, and 17 mL
of hexanes was added to the flask and heated to 70 °C. After 25 min, an additional 10 mL of hexanes was
added to the solution and the flask was kept at 70 °C for 4 h. The resulting product collected in the hexanes
layer and was washed three times with 30 mL of water in a separatory funnel. The hexanes layer was
collected, and all volatiles were removed to yield the blue-green Cu(oleate) 2 product.
2.3.3 Synthesis of CuInSe 2 Nanocrystals
We adapted the synthesis of the CuInSe 2 nanocrystals from Wang et al., as their synthetic method produces
nanocrystals with more uniform morphologies.
20
Cu(oleate) 2 (0.16 g, 0.25 mmol) and R 2Se 2 (0.25 mmol; R
55

= Bn or Ph) were loaded into a 3-neck round bottom flask under air. Anhydrous InCl 3 (0.055 g, 0.25 mmol
when using Ph 2Se 2; 0.066 g, 0.30 mmol when using Bn 2Se 2) was loaded into a 2-neck flask under a nitrogen
atmosphere. Oleylamine was injected into the 2-neck (4 mL) and 3-neck (8 mL) flasks under a nitrogen
atmosphere. Both flasks were then brought to 70 °C and degassed for 30 min under vacuum. Then, the
temperature of the flasks was raised to 120 °C and 140 °C for the 2-neck and 3-neck flasks, respectively,
and degassed for an additional 30 min. The temperature of the 3-neck flask was then set to 255 °C.
Nanocrystal nucleation was evident prior to injection of the InCl 3 precursor as the reaction mixture turned
black. The oleylamine solution of InCl 3 was injected into the 3-neck flask once the reaction mixture reached
230 °C. The reaction was then permitted to heat to 255 °C, at which point it was left to react for 1.5 h. The
reaction was thermally quenched by placing it in a room-temperature water bath. The resulting nanocrystal
suspension was split equally between two centrifuge tubes that were filled to 40 mL with ethanol, sonicated
for 10 min, and centrifuged at 6000 rpm for 2 min. This washing procedure was repeated twice with 10 mL
of hexanes used to re-disperse the nanocrystals and 30 mL of ethanol as the antisolvent. The nanocrystals
were then either dispersed in toluene for spectroscopic analyses or dispersed in hexanes and dried down to
a powder for X-ray diffraction and thermal analysis.
2.3.4 Synthesis of CuInSe 2 Nanocrystals using Me 2Se 2
For syntheses involving Me 2Se 2 (b.p. 155-157 °C), the InCl 3 and Cu(oleate) 2 precursors were heated in 8
mL of oleylamine and 4 mL of oleylamine containing an equimolar amount of Me 2Se 2 was injected at 230
°C. Room temperature water was used for the condenser attached to the 3-neck flask in order to prevent
Me 2Se 2 precursor volatilization.
2.3.5 Synthesis of Copper Selenide Nanocrystals
Cu(oleate) 2 (0.16 g, 0.25 mmol) and R 2Se 2 (0.25 mmol, R = Bn or Ph) were placed in a 3-neck round bottom
flask and dissolved in 12 mL of oleylamine under nitrogen. The flask was then heated to 70 °C and degassed
for 30 min under vacuum. Then, the temperature was raised to 140 °C and degassed for an additional 30
min. Then 3-neck flask was ramped to 220 °C under nitrogen at 5-6 °C min
–1
and held at that temperature
56

for the desired reaction duration. The reaction was then thermally quenched by placing it in a room-
temperature water bath and worked up as previously described.
2.3.6 Characterization
Powder X-ray diffraction (XRD) measurements were made using a Rigaku Ultima IV Powder X-ray
diffractometer using Cu Kα radiation (λ = 1.54 Å). Powder samples were prepared on a zero-diffraction
silicon substrate. For the aliquot studies of Figure 2.3, diffraction patterns were taken on a Rigaku Miniflex
600 powder X-ray diffractometer. Aliquots of the nanocrystal suspensions in hexanes were prepared for
XRD by drop-casting the suspension onto a glass substrate. UV-vis-NIR absorption spectroscopy was
performed on nanocrystal suspensions in toluene in a 150-mm integrating sphere using a Perkin-Elmer
Lambda 950 UV-vis-NIR spectrometer and a 1-cm path length quartz cuvette. Transmission electron
microscopy (TEM) was performed on dropcast samples supported on holey carbon-coated copper TEM
grids (Ted Pella, Inc.). The grids were placed in a vacuum oven overnight at 60 °C for removal of volatile
organics. TEM imaging was performed on a JEOL JEM-2100 microscope at an operating voltage of 200
kV, equipped with a Gatan Orius CCD camera. Thermogravimetric analysis (TGA) was performed using a
Netzsch STA449c with a heating rate of 5 °C min
–1
using an approximate sample size of 10 mg in an
alumina crucible. Fourier Transform Infrared Spectroscopy (FT-IR) was performed using a Bruker Vertex
80 FTIR Spectrometer; solid samples were prepared within a matrix of KBr.
2.3.7 Density Functional Theory (DFT)
Bond dissociation energies were calculated as enthalpies of homolytic cleavage for the bonds of interest.
All bond dissociation energy calculations were carried out at the DFT level using Q-Chem
36
through the
USC Center for High Performance Computing. First, geometry optimizations were performed with the 6-
31G(d) basis set and the Boese-Martin for Kinetics (BMK) functional. Then, single-point energy
calculations of the optimized structures were performed using the 6-311G(d,p) extended basis set with the
BMK functional.
57

2.4 Results and Discussion
We posited that varying the R group of R 2Se 2 precursors should allow us to tune the kinetics of nanocrystal
formation, and possibly the resulting nanocrystal phase. To test this hypothesis, we employed a synthesis
adapted from Wang et al. to synthesize colloidal CuInSe 2 nanocrystals. In short, an oleylamine solution of
InCl 3 was injected into a hot oleylamine solution of Cu(oleate) 2 and the R 2Se 2 precursor, and then the
reaction was heated to 255 °C for 1.5 h. Here, oleylamine serves a trifold purpose, acting as the solvent, a
reducing agent for the Cu(oleate) 2 precursor, and as a ligand that coordinates to the surface of the resulting
nanocrystals (Figure 2.1).
37,38
These experimental conditions were held constant unless otherwise noted,
with the exception of Me 2Se 2 which was hot injected into an oleylamine solution of Cu(oleate) 2 and InCl 3
because of the volatility of Me 2Se 2. The ceramic yield of CuInSe 2 nanocrystals resulting from reaction with
Bn 2Se 2 was 62 ± 1.5% and 62 ± 1.6% with Ph 2Se 2, as assessed by organic content-corrected
thermogravimetric analysis. With a starting diselenide:Cu molar ratio of 1:1, this result suggests that both
selenium atoms from the diselenide precursor are available for nanocrystal growth and the diselenide,
therefore, the diselenide precursor does not act as a limiting reagent. Upon work up, the as-prepared
nanocrystals were dispersible in toluene and hexanes, and maintained colloidal stability for >6 months.

Figure 2.1 (a) FT-IR spectra of Cu 2-xSe and Cu 3Se 2 intermediates that were isolated from aliquot studies during the
synthesis of chalcopyrite and wurtzite-like CuInSe 2, respectively. Both indicate that oleylamine ligands are bound
to the surface of these intermediates as the spectra display IR bands characteristic of oleylamine (2800-3000 cm
-1

ν C-H, 1520 – 1700 cm
-1
δ N-H, 1460 cm
-1
δ C-H, 1384 cm
-1
ν C-N). (b) Normalized TGA curves of intermediate Cu 2-xSe
and Cu 3Se 2 nanocrystals that were obtained from aliquots in the synthesis of chalcopyrite and wurtzite-like CuInSe 2,
respectively. The two curves have qualitatively similar profiles and both exhibit distinct mass loss events near 350
°C, which is the boiling point of oleylamine. This further supports that oleylamine is the ligand bound to these
intermediates.
58

When considering the mechanism of nanocrystal formation for syntheses employing diorganyl
diselenides, it is clear that both the C–Se bonds and the Se–Se bond of the diselenide precursor must be
cleaved in order to liberate Se
2–
and incorporate it into the nanocrystal. Consequently, the rate of nanocrystal
formation must depend upon the kinetics of dichalcogenide precursor conversion. It follows that the kinetics
of nanocrystal formation may then be tunable by modulating the bond strengths (or relative reactivities) of
these precursors as a function of the R group substituent.
The results of these colloidal nanocrystal syntheses with Ph 2Se 2 and Bn 2Se 2, as characterized by
powder X-ray diffraction (XRD) and transmission electron microscopy (TEM), are provided in Figure 2.2.
Consistent with our previous results (although under significantly different synthetic conditions),
19
the
reaction with Ph 2Se 2 gives the hexagonal, wurtzite-like phase of CuInSe 2 nanocrystals, with lattice
parameters of a = 4.08 Å and c = 6.72 Å that are in agreement with the literature.
19
Interestingly, the reaction
with Bn 2Se 2 yields the thermodynamic chalcopyrite phase of CuInSe 2 nanocrystals, with lattice parameters
of a = 5.79 Å and c = 11.56 Å that are also consistent with the literature.
39-41
To confirm that this trend
could be explained by invoking differences in precursor conversion kinetics, we sought to compare the
relative C–Se and Se–Se bond dissociation energies (BDEs) between the diselenide precursors. Density
functional theory (DFT) was employed to calculate the enthalpies of homolytic bond cleavage of the C–Se
and Se–Se bonds for each precursor. It was found that the C–Se bonds vary more significantly in strength
than do the Se–Se bonds for these diselenide precursors, with a net difference of 22 kcal mol
-1
separating
the stronger (BDE = 65 kcal mol
–1
) and weaker (BDE = 43 kcal mol
–1
) C–Se bonds in Ph 2Se 2 and Bn 2Se 2,
respectively. In comparison, the net difference in BDEs for the Se–Se bonds is 11 kcal mol
-1
, with the
Ph 2Se 2 precursor possessing a weaker Se–Se bond (BDE = 42 kcal mol
–1
; see Table 2.1 for the full listing
of Se-Se bond strengths). To better understand the effects of the C–Se and Se–Se bonds in phase
determination in the CuInSe 2 nanocrystal synthesis, a third diselenide (i.e., Me 2Se 2) was investigated, which
was also found to yield chalcopyrite nanocrystals (Figure 2.2). The Me 2Se 2 precursor possesses an
intermediate calculated C–Se BDE = 57 kcal mol
–1
and a Se–Se BDE = 54 kcal mol
–1
. When comparing
these BDEs to
59

Figure 2.2 (a) Powder X-ray diffraction patterns of CuInSe 2 nanocrystals derived from the corresponding diselenide
precursors shown at right. The C–Se bond dissociation energies that were calculated by DFT are given below each
precursor.

(b) Transmission electron micrographs of the nanocrystals that result from syntheses using the four different
selenium precursors.

Table 2.1 Bond dissociation energies calculated for different selenium precursors. Geometry optimizations were
performed using the 6-31G(d) basis set and the BMK functional. Then, single-point energy calculations were carried
out with the 6-311G(d,p) basis set and the BMK functional. Thiophenol was used was a control calculation to gauge
the accuracy of these estimates. The experimentally determined bond C–S dissociation energy of thiophenol is 86.5 ±
2 kcal/mol.
Precursor C –Se bond (kcal/mol) Se –Se (kcal/mol)
PhSeH 77.57 N/A
Ph 2Se 71.06 N/A
Ph 2Se 2 64.65 42.10
Me 2Se 2 57.18 54.06
Bn 2Se 2 43.09 53.31
PhSH (control) 87.50 N/A

Ph 2Se 2, which yields wurtzite-like nanocrystals, the difference in BDEs for the Se–Se bonds remains nearly
constant at 12 kcal mol
–1
, but the difference in BDEs for the C–Se bonds is reduced to 8 kcal mol
–1
.
These results suggest that employing diselenide precursors with weaker C–Se bonds than those of
Ph 2Se 2 results in the formation of the thermodynamic, chalcopyrite phase. To confirm that kinetic control
of CuInSe 2 nanocrystal formation depends on the strength of the C–Se, and not the Se–Se bond, two control
60

experiments were conducted under otherwise identical synthetic conditions in which benzeneselenol
(PhSeH) and diphenyl selenide (Ph 2Se) were employed as two selenium precursors lacking Se–Se bonds.
As in the case of Ph 2Se 2, both of these precursors have strong calculated C–Se bonds (BDE = 78 kcal mol
-1

for PhSeH and 71 kcal mol
–1
for Ph 2Se), meaning both could impart similar kinetic effects on phase
determination. As demonstrated in Figure 2.2, the reaction with benzeneselenol indeed yields the wurtzite-
like phase, as expected. In contrast, Ph 2Se did not yield any isolable crystalline product, likely because two
strong C–Se bonds must be broken to liberate each equivalent of selenium and this does not readily occur
before the volatilization of the precursor (Ph 2Se b.p. 115-117 °C), even when injecting Ph 2Se into a hot
solution containing Cu(oleate) 2 and InCl 3.
2.4.1 CuInSe2 Formation Pathways
To further probe the mechanisms of chalcopyrite and wurtzite-like phase determination for these CuInSe 2
nanocrystals, studies were performed in which aliquots of the reaction mixture were removed at specific
time intervals following the hot injection of the InCl 3 solution. Phase progressions of the nanocrystalline
products were obtained by taking powder XRD patterns of each aliquot. As seen in Figure 2.3, both phases
of CuInSe 2 are the result of reactions of copper selenide nanocrystal intermediates with In
3+
ions in solution
to yield either the chalcopyrite or wurtzite-like CuInSe 2 nanocrystals. Copper selenide intermediates have
been observed before in syntheses of CuInSe 2 nanocrystals,
20,40
and have also been used as precursors in
the preparation of CuInSe 2 nanocrystals via cation exchange reactions.
42,43
In our syntheses, the nucleation
of copper selenide nanocrystal intermediates is clearly evidenced by a change in the color of the reaction
solution prior to InCl 3 injection. These visual cues differ when employing either Ph 2Se 2 or Bn 2Se 2 as
selenium precursors, which is indicative of their distinct influences on the reaction kinetics. In both cases,
the starting oleylamine solution containing the diselenide precursor and Cu(oleate) 2 is a vibrant blue at low
temperatures. When heating to the desired reaction temperature while using Ph 2Se 2, the solution changes
from blue to a translucent yellow color at temperatures between 140-180 °C. Between 180-190 °C, the
solution becomes opaque and assumes a light-brown hue. At 200 °C, the solution begins to turn black,
61

Figure 2.3 (a,b) Phase progression of chalcopyrite CuInSe 2 nanocrystals when using the Bn 2Se 2 precursor, as
monitored by XRD. Times correspond to the time after injection of InCl 3. A clear progression can be seen from these
copper selenide intermediates to the final chalcopyrite CuInSe 2 product. After 3 min, Cu 2–xSe and CuSe intermediates
are both observed. (c,d) Phase progression of the wurtzite-like CuInSe 2 nanocrystals when using the Ph 2Se 2 precursor,
as monitored by XRD. After 3 min, the umangite Cu 3Se 2 phase is the primary intermediate.

Figure 2.4 XRD patterns of aliquots taken from the reaction between Bn 2Se 2 and Cu(oleate) 2 heated in oleylamine
to 220 °C in the absence of InCl 3. Aliquots of the reaction solution were removed as the flask was heated and after
the reaction flask reached 220 °C. The aliquot at 2 min reveals that some crystalline products begin to form at
relatively low temperatures.

62

Figure 2.5 XRD pattern of the product resulting from a control reaction between Bn 2Se 2 and Cu(oleate) 2 at 220 °C
in the absence of InCl 3. The same Cu 2–xSe and CuSe intermediates were observed as those in Figure 2.3a,b.

indicating the nucleation of copper selenide nanocrystals. In contrast, when heating a solution containing
Bn 2Se 2 as the selenium precursor, the solution changes directly from blue to opaque black at temperatures
just above 140 °C and yields crystalline copper selenide intermediates at temperatures as low as 160 °C
(Figure 2.4), indicative of a lower-energy barrier to nanocrystal nucleation for this precursor.
Figure 2.3a shows the XRD pattern of an aliquot taken 3 min after the hot injection of InCl 3 into a
reaction containing Bn 2Se 2. This pattern can be indexed to several phases of copper selenide, including
intermediates of the Cu 2–xSe berzelianite structure and the hexagonal klockmannite phase of CuSe. These
two phases of copper selenide represent the most thermodynamically stable species at high temperatures
under copper-rich (Cu 2-xSe) or slightly more copper-deficient conditions (CuSe), as per the bulk Cu–Se
binary phase diagram.
44
To confirm that these phases correctly represent the reactive copper selenide
intermediates, a control experiment in which Bn 2Se 2 and Cu(oleate) 2 were heated in oleylamine in the
absence of InCl 3 led to the formation of berzelianite Cu 2–xSe and klockmannite CuSe nanocrystals (Figure
2.5), which is consistent with the intermediates observed in Figure 2.3a,b.
The early disappearance of the CuSe phase in Figure 2.3b indicates that CuSe is converted either
to CuInSe 2 directly, or to the Cu 2–xSe phase which, in turn, yields chalcopyrite CuInSe 2 upon the diffusion
of In
3+
into the copper selenide crystal lattice. The direct synthesis of chalcopyrite CuInSe 2 via the
63

combination of CuSe and InSe precursors has been reported,
45
but since no crystallographic evidence of
InSe formation is observed in Figure 2.3a,b this mechanism is ruled out. Because Cu 2-xSe was observed to
persist for longer than CuSe as the last remaining intermediate prior to the ultimate formation of CuInSe 2,
we hypothesized that the CuSe in solution converts to Cu 2–xSe, which subsequently forms chalcopyrite
CuInSe 2. To test this hypothesis, a control experiment was performed in which aliquots were removed at
specific time intervals from a solution in which Bn 2Se 2 and Cu(oleate) 2 precursors were heated together in
oleylamine under the same conditions as those employed in the aliquot study of Figure 2.3. However, this
control revealed that after the initial nucleation of a mixture of Cu 2-xSe and CuSe nanocrystals, CuSe
persisted and did not convert to Cu 2-xSe over time (Figure 2.6). This finding indicates that the consumption
of Cu 2-xSe in the formation of CuInSe 2 with In
3+
is required to drive the transformation of CuSe to Cu 2–xSe
in-situ. Indeed, the diffusion of In
3+
into Cu 2-xSe to form CuInSe 2 necessarily expels 1-x Cu atoms from the
crystal lattice into solution. These 1-x Cu atoms may then recombine with CuSe nanocrystals to generate
Cu 2-xSe. This hypothesis is consistent with the fact that Cu 2–xSe is more thermodynamically stable than
klockmannite CuSe under Cu-rich conditions, and as observed in Figure 2.3b, the Cu 2–xSe intermediate
persists after the disappearance CuSe.

Figure 2.6 XRD patterns of aliquots taken from a control reaction between Bn 2Se 2 and Cu(oleate) 2 at 220 °C in the
absence of InCl 3. CuSe does not convert to Cu 2–xSe in the absence of In
3+
in solution.

64

The aliquot studies of Figure 2.3 were performed at a lower temperature (220 °C) than the
conditions employed to synthesize phase-pure CuInSe 2 nanocrystals in order to better trace the transient
intermediates that yield either chalcopyrite or wurtzite-like CuInSe 2. The analogous aliquot studies at the
reaction temperature of 255 °C were performed for both Bn 2Se 2 and Ph 2Se 2 to confirm that the intermediates
identified from Figure 2.3 were the same as those present at higher temperatures (Figure 2.7). While Figure
2.7 shows that the klockmannite CuSe phase was not observed prior to formation of chalcopyrite CuInSe 2
(due to fast conversion at 255 °C), the Cu 2-xSe intermediate was still present at early reaction times. Cu 2-xSe
is a highly p-doped semiconductor and displays localized surface plasmon resonance (LSPR) signatures in
the near-infrared region of the spectrum when x > 0.
50–52
UV-vis-NIR spectra were taken for aliquots of this
reaction employing Bn 2Se 2, and the spectra provide additional confirmation of the presence of Cu 2–xSe
intermediates by the broad LSPR feature centered between 1100 and 1600 nm (Figure 2.8).

Figure 2.7 (a) XRD patterns of aliquots taken under the same conditions as the reaction shown in Figure 2.3a,b
except performed at a final reaction temperature of 255 °C. The same Cu 2–xSe intermediate is observed at early
times, which is consistent with our hypothesis that Cu 2–xSe is the reactive intermediate that produces chalcopyrite
CuInSe 2. (b) XRD patterns of aliquots taken under the same conditions as the reaction shown in Figure 2.3c,d
except performed at a final reaction temperature of 255 °C. The same Cu 3Se 2 intermediate was observed, consistent
with our hypothesis that Cu 3Se 2 is the reactive intermediate that produces wurtzite-like CuInSe 2.

65

Figure 2.8 UV-vis-NIR absorption spectra of the aliquots of the reaction shown at left in Figure 2.7; at early times,
Cu 2–xSe intermediates are present and display a significant localized surface plasmon resonance (LSPR) feature in
the near infrared. As Cu 2–xSe is consumed to yield CuInSe 2, this feature disappears as the aliquots at later times
display an absorption spectrum characteristic of chalcopyrite CuInSe 2 nanocrystals.

Figure 2.9 XRD pattern of the product resulting from a reaction with Me 2Se 2; full conversion to chalcopyrite
CuInSe 2 is not observed under these conditions (held at a low temperature, 220 °C for 20 min) as indicated by the
presence of the Cu 2–xSe intermediates.

As the reaction proceeded to form chalcopyrite CuInSe 2, the LSPR feature decreased in intensity until
giving way to the absorption spectrum of chalcopyrite CuInSe 2 that displays broad absorption through the
visible region with a characteristic band gap of ~1.0 eV.
53,54
Consistent with the assignment of Cu 2–xSe as
the intermediate that results in CuInSe 2 formation, the chalcopyrite CuInSe 2 nanocrystals derived from
Me 2Se 2 also pass through this Cu 2–xSe intermediate (Figure 2.9).
66

In addition to the evidence provided by aliquot studies, the highly similar structures of antifluorite
Cu 2-xSe and chalcopyrite CuInSe 2 suggest that this phase transformation should occur readily. The
chalcopyrite structure can be described as a supercell of the zinc blende structure comprised of a Se
2–
fcc
lattice in which 50% of the tetrahedral holes are filled by bands of Cu
+
and In
3+
that alternate along the
[100] and [001] directions (Figure 2.10). While the Cu 2–xSe structure depends upon copper stoichiometry
at lower temperatures, the anionic sub-lattice of Se
2–
in Cu 2–xSe is fcc at temperatures above 130 °C for all
values of x.
46
The high-temperature (433 K) lattice constant of antifluorite-type Cu 2Se has been reported to
be a = 5.787 Å.
46
For comparison, the lattice parameter of the Se
2–
sub-lattice in chalcopyrite CuInSe 2 is a
= 5.792 Å at 433 K,
47
which represents an expansion of the Cu 2Se lattice by only 0.078%. Previous work
has shown that the soft Cu
+
ions from the relatively copper-rich Cu 2–xSe phase has made this phase a useful
starting material for nanoscale cation exchange experiments as Cu
+
easily diffuses out of the structure to be
replaced by harder Lewis acids.
15,55
The near exact match of the Se
2–
sub-lattices between Cu 2–xSe and
CuInSe 2, the mobility of Cu
+
ions through the structure,
56,57
and easy In
3+
diffusion into the structure
facilitate the transformation of Cu 2-xSe to chalcopyrite CuInSe 2.

Figure 2.10 Illustration of the phase transformation of the cubic antifluorite-type Cu 2–xSe structure to the tetragonal
chalcopyrite CuInSe 2 structure upon exchange of Cu for In cations (Cu = blue, In = pink, Se = green). The fcc Se sub-
lattice is effectively unchanged in this transformation; the high-temperature lattice constant (433 K) for Cu 2Se is 5.787
Å, which would require an expansion of only 0.078% to match the lattice constant of the chalcopyrite Se sub-lattice
lattice parameter of 5.792 Å at 433 K.
46,47
CIF files for the Cu 2-xSe and chalcopyrite CuInSe 2 phases were taken from
references 48,49.
67

The wurtzite-like CuInSe 2 nanocrystals from the reaction with Ph 2Se 2 form through a different
intermediate, namely, the Cu 3Se 2 umangite phase of copper selenide (Figure 2.3c,d). As a control to verify
that Cu 3Se 2 is the reactive intermediate that precedes wurtzite-like CuInSe 2, Ph 2Se 2 was heated in
oleylamine with Cu(oleate) 2 to generate Cu 3Se 2, as illustrated in Figure 2.11. Cu 3Se 2 possesses a tetragonal
crystal structure
58,59
that contains two crystallographically unique copper sites (referred herein as “first-
position” and “second position” copper atoms, labeled in blue and pink, respectively, in Figure 2.12d,e)
and a single crystallographically distinct Se
2–
site. Although formally the stoichiometry of umangite would
necessitate mixed oxidation states of copper to balance two Se
2–
anions, X-ray photoelectron spectroscopy
(XPS) measurements of umangite have revealed that copper is monovalent and the oxidation state of
selenium is -3/2.
60
However, XPS indicates that the oxidation states of Cu, In, and Se are +1, +2, and -2,
respectively, in chalcopyrite and wurtzite-like CuInSe 2.
20,61
In going from Cu 3Se 2 to CuInSe 2, selenium
must undergo a reduction to the -2 oxidation state with a concomitant decrease in the copper content as In
3+

diffuses into the structure. To aid in thinking about this transformation, employing the formal Cu oxidation
states of +1 and +2 in Cu 3Se 2 is a useful bookkeeping tool, even if these oxidation states do not accurately
represent the electronic structure of Cu 3Se 2; to produce two Se
2–
anions that originated from the -3/2
oxidation state, one copper atom must be oxidized to Cu
2+
for every two selenium atoms. In this way,
umangite can be thought of as Cu
+
2Cu
2+
Se
2–
2. Upon diffusion of In
3+
, the equivalent of one Cu
+
and one
Cu
2+
ion must diffuse out of the material to maintain charge neutrality and produce the correct Cu
+
In
3+
Se
2-
2
stoichiometry.

68

Figure 2.11 XRD pattern of the product resulting from a control reaction between Ph 2Se 2 and Cu(oleate) 2 at 220 °C
for 3 min in the absence of InCl 3. The same Cu 3Se 2 phase was produced, consistent with the observations in Figure
2.3c,d and Figure 2.7.

Figure 2.12 (a) Se sub-lattice of Cu 3Se 2. Each Se atom has six nearest neighbors that are nearly in plane. These planes
of Se alternate in an ABAB fashion along the [010] direction. (b) Se sub-lattice of wurtzite-like CuInSe 2. Close packing
occurs along the [001] direction. By XRD, the experimental d-spacing for the (002) planes in our wurtzite-like CuInSe 2
nanocrystals is 3.343(2) Å, which requires a 4.44% expansion of the interplanar Se•••Se distance within umangite as
obtained from the crystal structure of Cu 3Se 2. (c) Wurtzite-like structure of CuInSe 2; it was assumed that Cu and In
cations are randomly distributed throughout the tetrahedral sites in the structure, so the blue tetrahedra represent both
Cu and In positions. (d) Side view of the Cu 3Se 2 structure along the [001] direction. Note that the first Cu position
(blue) shares four edges (highlighted in yellow) with second Cu position (pink). Each pink tetrahedron shares two
edges (highlighted in red) with a blue tetrahedron and one edge (highlighted in teal) with an adjacent pink tetrahedron.
(e) Top view of Cu 3Se 2 looking down the direction of close packing [010]. Pink tetrahedra are corner sharing along
the [001] direction, and there exist tetrahedral holes that prevent corner-sharing connections between pink tetrahedra
along the [100] direction. These tetrahedral holes are demarcated by dotted red lines. In going to the wurtzite-like
structure, Cu or In ions must fill the tetrahedral holes indicated in (e). To maintain charge neutrality, two Cu ions must
diffuse out of the Cu 3Se 2 intermediate per In
3+
ion; one Cu must come from the first position of Cu (blue tetrahedra)
and the other from the second position (pink tetrahedra). (f) The structure generated by removing these tetrahedra
from the structure; the red dotted lines represent the tetrahedral holes that are filled in the transformation to the wurtzite
phase, giving a structural motif similar to that shown in (c). The CIF file for the Cu 3Se 2 phase was obtained from
reference 59.
69

The conversion of Cu 3Se 2 to wurtzite-like CuInSe 2 nanocrystals represents a larger structural
transformation from the intermediate to the final product than does the Cu 2–xSe to chalcopyrite CuInSe 2
conversion. The wurtzite-like CuInSe 2 structure may be considered as a hexagonally close-packed
framework of Se
2–
anions throughout which the Cu
+
and In
3+
cations fill 50% of the tetrahedral holes,
creating a network of corner-sharing selenium-terminated tetrahedra, as illustrated in Figure 2.12c. This
hexagonal close packing mandates that each Se
2–
has six in-plane nearest neighbors (Figure 2.12b). To
envision the structural similarities between the wurtzite-like phase of CuInSe 2 and Cu 3Se 2, it is noted that
the Se
2–
sub-lattice within the Cu 3Se 2 structure maintains a quasi-planar hexagonal framework of Se
2–

anions that stack in an alternating ABAB fashion (Figure 2.12a). The interplanar distance between these
anion layers is 3.201 Å, which is close to the 3.343 Å d-spacing for the (002) planes of wurtzite-like CuInSe 2
nanocrystals, as experimentally measured by XRD. Thus, to assume the structure of the wurtzite-like Se
2–

sub-lattice, the Cu 3Se 2 Se
2–
sub-lattice needs to expand by 4.44% in the interplanar direction while assuming
a higher degree of planarity within each Se
2–
sheet.
Knowing that the structure of the anionic sub-lattice of Cu 3Se 2 can be viewed as a slight distortion
of the wurtzite- like anionic sub-lattice, we now turn to understand how the structure as a whole changes
upon In
3+
incorporation to give way to the wurtzite-like product. Within the umangite structure, the two
distinct copper sites in Cu 3Se 2 form two types of Se-terminated tetrahedra – the first copper site (blue
tetrahedra in Figure 2.12d,e) is a distorted tetrahedron that shares four edges with adjacent second-position
copper tetrahedra (pink tetrahedra in Figure 2.12d,e). The second copper site can be thought of a copper
atom at the center of a tetrahedron that shares an edge with the vicinal second-position copper tetrahedron,
and two edges with the adjacent first-position copper tetrahedron. These edge-sharing configurations are
depicted best in Figure 2.12d; because the wurtzite-like structure is composed entirely of corner-sharing
tetrahedra, diffusion of In
3+
into Cu 3Se 2 must disrupt this edge-sharing motif to yield a framework of only
corner-sharing tetrahedra. The perspective illustrated in Figure 2.12e highlights the existence of tetrahedral
holes in the umangite structure that, if filled, would yield the necessary corner-sharing structure within the
(010) plane. As previously mentioned, the diffusion of every In
3+
ion into the umangite intermediate causes
70

the removal of two copper ions (one Cu
+
and one Cu
2+
). Occupation of the tetrahedral holes highlighted in
Figure 2.12e would cause the vicinal first-position copper sites to diffuse out of the structure to prevent the
formation of an unstable face-sharing configuration. In addition, occupation of this tetrahedral hole should
also expel one of the second-position copper atoms that would otherwise assume an unstable edge-sharing
motif with the newly-formed indium-centered tetrahedron.
62
Removal of these two copper atoms per In
3+

cation in the structure leads to the structure shown in Figure 2.12f, where the tetrahedral holes indicated by
dashed lines would be filled either by the incoming In
3+
ions or Cu
+
ions that shift to those sites, thus
enabling In
3+
incorporation at another corner-sharing tetrahedral site in the structure. In summary, we can
understand this phase transformation by considering a distortion of the Cu 3Se 2 sub-lattice to the wurtzite-
like Se
2–
sub-lattice and by assessing which holes are filled upon In
3+
incorporation and how that affects
each copper site in umangite. The distinct berzelianite and umangite intermediates and the aforementioned
discrepancy in the temperatures at which these copper selenides nucleate when using Bn 2Se 2 and Ph 2Se 2
suggest that the stronger C–Se bond of Ph 2Se 2 contributes to an elevation of the activation energy barrier
associated with formation of Cu 2–xSe intermediates and steers the reaction toward formation of wurtzite-
like CuInSe 2 via a metastable Cu 3Se 2 intermediate.
2.4.2 Assessing the Persistence of the Wurtzite-Like Phase
Since the wurtzite-like phase is a metastable phase at room temperature with respect to the bulk material,
we wanted to test its structural persistence and ascertain whether or not a phase transition to the chalcopyrite
structure could be achieved by thermal activation. After synthesis and work-up, the wurtzite-like CuInSe 2
nanocrystals remain in this phase at room temperature for greater than 1 year. As a preliminary experiment,
a powder sample of the wurtzite-like CuInSe 2 nanocrystals was dispersed in 1-octadecene, a high boiling,
non-coordinating solvent, and heated to 300 °C for 2.5 h. Powder XRD measurements of the nanocrystals
were taken before and after this treatment; the results show that heating the wurtzite-like nanocrystals in
solution did not induce a phase change to chalcopyrite (Figure 2.13).

71

Figure 2.13 Powder XRD patterns of the wurtzite-like CuInSe 2 nanocrystals before and after heating to 300 °C in
octadecene for 2.5 h showing that the metastable phase does not undergo a phase transformation to the
thermodynamic chalcopyrite phase.

The analogous experiment was then carried out with wurtzite-like nanocrystals in the solid state. The
nanocrystals were heated under nitrogen to 300 °C at 5 °C min
–1
and experienced a ~3.5 wt.% loss due to
loss of residual organics, as demonstrated by the thermogravimetric analysis (TGA) trace provided in Figure
2.14a. After heating the nanocrystals to 300 °C, holding at that temperature for 10 min, and cooling them
back to room temperature, XRD revealed that no phase change occurred. This heating-cooling cycle was
repeated two additional times, and XRD analysis of the nanocrystals shows that the wurtzite-like phase
remains persistent upon heating and cooling, as shown in Figure 2.14b. Moreover, Scherrer analysis of the
corresponding XRD patterns suggests that the grain size of the nanocrystals (i.e., 17 nm) does not change
during these heating-cooling cycles. In contrast, upon heating the wurtzite-like nanocrystals to 420 °C, a
greater fraction of the surface ligands was removed (representing ~13 wt.% loss by TGA, Figure 2.14c),
which resulted in a phase transformation from the metastable wurtzite-like phase to predominately the
thermodynamically stable chalcopyrite phase, as illustrated in Figure 2.14d.
72

Figure 2.14 (a) TGA curves after heating the wurtzite-like CuInSe 2 nanocrystals to 300 °C. No additional mass loss
was sustained from the material after the first cycle of heating. (b) Powder XRD patterns taken after each cycle of
heating to 300 °C show that the wurtzite-like phase is thermally stable up to this temperature. (c) TGA curve after
heating the wurtzite-like CuInSe 2 nanocrystals to 420 °C. The material lost ~13% of its weight due to the volatilization
of surface ligands from the nanocrystals. (d) Powder XRD indicates that a nearly complete phase transformation to
the thermodynamic chalcopyrite phase results after one cycle of heating to 420 °C.

Interestingly, while we observed that a post-synthetic transformation from the wurtzite-like phase to the
chalcopyrite phase does not occur at 300 °C either in solution or in the solid state, we discovered that a
mixture of these phases results when the nanocrystals are synthesized at 300 °C with Ph 2Se 2 (Figure 2.15).
Since this mixture cannot be obtained from a direct wurtzite-like-to-chalcopyrite phase transformation at
this temperature, it must be the result of the chemistry of the copper selenide nanocrystal intermediates.
Since Cu 2–xSe is thermodynamically favored above 123 °C while Cu 3Se 2 is metastable at elevated
temperatures,
44
the mechanisms to produce wurtzite-like or chalcopyrite CuInSe 2 must be competing at
higher reaction temperatures, as dictated by the extent of a phase transformation from the intermediate
Cu 3Se 2 phase to the Cu 2–xSe phase. Such a transformation for copper selenide is known to occur at elevated
temperatures,
63
and a mixture of phases of CuInSe 2 can be explained by an incomplete transformation of
73

Cu 3Se 2 to Cu 2–xSe, where the resultant Cu 2-xSe yields chalcopyrite and the remaining Cu 3Se 2 form wurtzite-
like CuInSe 2 nanocrystals. Several control experiments were performed that support this conclusion: (1)
When Ph 2Se 2 and Cu(oleate) 2 were heated in oleylamine at low temperatures for short times (3 min), pure
Cu 3Se 2 resulted as shown in Figure 2.11. In the typical synthesis of wurtzite-like CuInSe 2, InCl 3 is injected
at 230 °C and the temperature is then increased to 255 °C for the duration of the reaction. These reaction
conditions allow for diffusion of In
3+
into Cu 3Se 2 before a phase transformation from umangite to Cu 2–xSe
can occur. (2) However, if Ph 2Se 2 and Cu(oleate) 2 are heated together at low temperatures for longer times
(15 min), then a partial phase transformation from Cu 3Se 2 to the CuSe and Cu 2-xSe phases results (Figure
2.16).

Figure 2.15 XRD pattern showing a mixture of chalcopyrite and wurtzite phases resulting from a reaction at 300 °C
for 1.5 h using Ph 2Se 2. This indicates that the Cu 3Se 2 that normally nucleates when using Ph 2Se 2 were partially
converted to Cu 2–xSe intermediates that are more stable at high temperatures. This mixture of copper selenide phases
then reacts to produce mixed wurtzite-like and chalcopyrite phase CuInSe 2.

74

Figure 2.16 Mixture of copper selenide phases that results when heating Ph 2Se 2 with Cu(oleate) 2 at 220
°C for 15 min.

This demonstrates that Cu 3Se 2 is a kinetic, metastable intermediate, and that timely injection of
InCl 3 is necessary to obtain phase-pure wurtzite-like CuInSe 2 from the Cu 3Se 2 intermediate nanocrystals
before they convert to the more thermodynamically stable high-temperature berzelianite and klockmannite
phases. The formation of a mixture of chalcopyrite and wurtzite-like CuInSe 2 nanocrystals when using
Ph 2Se 2 at an elevated reaction temperature of 300 °C indicates that the indium incorporation into the Cu 3Se 2
is a diffusion-limited process that does not give quantitative yields of wurtzite-like CuInSe 2 within minutes
of InCl 3 injection, likely due to the complicated nature of the umangite-to-wurtzite-like phase
transformation. The sustained heating of the reaction vessel is important to drive the formation of CuInSe 2,
and when this heating step is performed at higher temperatures, the rate of conversion of Cu 3Se 2 to CuSe
or Cu 2-xSe becomes kinetically competitive with the rate of the phase transformation from Cu 3Se 2 to
wurtzite-like CuInSe 2. (3) As a final control experiment, it was found that when Ph 2Se 2 was reacted with
Cu(oleate) 2 at 300 °C, the thermodynamically stable Cu 2–xSe phase resulted, as observed by XRD and UV-
vis-NIR analysis (Figure 2.17). Thus, when isolating metastable materials, it is important not only to
consider the persistence of the metastable state, but also the various thermodynamic minima that may exist
for intermediate compositions that give way to the “final” metastable or thermodynamic products.

75

Figure 2.17 (a) XRD pattern of the product resulting from a control reaction between Ph 2Se 2 and Cu(oleate) 2 in
oleylamine at 300 °C, showing that the Cu 2–xSe phase is the predominant phase formed at this temperature. This
supports our hypothesis that at high temperatures the Cu 3Se 2 intermediate converts to Cu 2–xSe to yield a mixture of
wurtzite-like and chalcopyrite CuInSe 2 nanocrystals. (b) UV-vis-NIR spectrum of the product of the reaction shown
in (a). The distinct LSPR feature provides additional confirmation that the Cu 2–xSe phase is produced when reacting
Ph 2Se 2 with Cu(oleate) 2 at 300 °C.

2.5 Conclusions
In conclusion, we demonstrated a molecular programming approach using diorganyl diselenides that
predictably allows for control over the resulting phase of colloidal CuInSe 2 nanocrystals as a function of
the C–Se bond strength. It was found that the chalcopyrite phase forms from precursors with weaker C–Se
bonds via a fast nucleating Cu 2–xSe nanocrystal intermediate, while the metastable wurtzite-like phase forms
from precursors with stronger C–Se bonds through a slow nucleating umangite Cu 3Se 2 phase. By comparing
the Se
2–
sub-lattices to those of the final CuInSe 2 phases, and by considering the mobility/extraction of
copper from these intermediate structures, a structural rationalization for phase determination was
developed. The wurtzite-like phase of CuInSe 2 nanocrystals was found to be kinetically persistent for many
months at room temperature, and up to at least 300 °C upon multiple heating and cooling cycles, but
transitions to the chalcopyrite phase upon decomposition and loss of the surface ligands at 420 °C.
Therefore, even though the wurtzite-like phase is a high-temperature phase of CuIn(S,Se) 2 in the bulk phase
diagram, it can be kinetically accessed on the nanoscale at relatively low temperatures, and remain
persistent in its bulk metastable phase.
There are multiple examples of diorganyl dichalcogenide precursors being used to serendipitously
access metastable hexagonal phases of multinary chalcogenide nanocrystals, including CuInS 2,
64

76

Cu 2ZnSnSe 4,
65
Cu 2ZnSnS 4–xSe x,
66,67
and Cu 2SnSe 3
21
instead of their thermodynamically preferred tetragonal
or monoclinic phases. The molecular programming approach presented here offers the possibility of being
able to rationally access these metastable hexagonal phases as a function of dichalcogenide C–Se or C–S
bond strengths, moving beyond the traditional model of size-reducing bulk thermodynamic phases.
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Chapter 3. Ligand-Mediated Phase Control in Colloidal AgInSe2 Nanocrystals

*Published in Chem. Mater. 2020, 32, 2935-2945.

3.1 Abstract
Synthetic studies of colloidal nanoparticles that crystallize in metastable structures represent an emerging
area of interest in the development of novel functional materials, as metastable nanomaterials may exhibit
unique properties when compared to their counterparts that crystallize in thermodynamically preferred
structures. Herein, we demonstrate how phase control of colloidal AgInSe 2 nanocrystals can be achieved
by performing reactions in the presence, or absence, of coordinating ligands that can act as cation exchange
mediators (i.e., oleylamine or 1-dodecanethiol). These coordinating ligands play a crucial role in formation
of metastable AgInSe 2 nanocrystals, as they mediate in-situ topotactic conversion of an orthorhombic Ag 2Se
intermediate to a metastable orthorhombic phase of AgInSe 2. We provide a detailed mechanistic crystal
chemistry description of this process to structurally elucidate how the orthorhombic phase of AgInSe 2
forms. Density functional theory calculations suggest that the metastable orthorhombic phase of AgInSe 2
is metastable by a small margin, at 10 meV/atom above the thermodynamic ground state. In the absence of
oleylamine or 1-dodecanethiol, Ag 2Se nanocrystal intermediates convert through kinetically slow, non-
topotactic conversion processes to yield the thermodynamically preferred chalcopyrite structure of
AgInSe 2. On the basis of these discoveries, we offer new insight into the prediction of novel metastable
multinary nanocrystal phases that do not exist on bulk phase diagrams.
3.2 Introduction
Metastability, broadly defined, is the kinetic persistence of a system that exists in a higher free energy state
than the thermodynamically most stable state for a given set of conditions. The application of metastable
materials are ubiquitous, and include examples from diamond wafers for semiconductor applications to the
use of technetium-99m as a radiotracer in gamma ray imaging.
1,2
All nanomaterials are inherently
metastable with respect to their bulk material counterparts as a result of their high surface energies and
large surface area-to-volume ratios.
3,4

82

In addition to the useful properties afforded by size effects for colloidal nanocrystal analogs of
thermodynamically stable bulk materials of that same crystal phase, the thermodynamic scales of phase
equilibria on the nanoscale are often compressed, allowing relatively low-temperature syntheses of
crystalline polymorphs that only exist at much higher temperatures and/or pressures in the bulk.
5–8

Furthermore, entirely new crystal phases can arise on the nanoscale that have no known counterparts in
bulk.
9–13
Because the physical properties of a material are linked to its crystal structure, the ability to isolate
new or difficult-to-access metastable structures on the nanoscale holds promise for the discovery of novel
functional materials with properties different from, and possibly superior to, the properties of more
thermodynamically stable materials.
14–18
To synthetically target such materials, it is important to consider
that a metastable state is only isolable if, under some set of conditions, that state represents a thermodynamic
minimum.
5
In other words, if a state is never the thermodynamically most stable state under any set of
conditions, it is not synthesizable.
The synthetic chemistry of colloidal nanocrystals that persist in metastable states with respect to
their bulk analogs remains a science largely dependent on empirical findings, rather than on bottom-up
design principles. This is partially a result of the myriad variables that can contribute to phase determination,
such as nanocrystal size,
8
surface area-to-volume ratio,
19
surface functionalization,
14
crystal defects,
9
etc.
These confounding variables make it difficult to draw direct analogies between the thermodynamic phase
diagrams of bulk materials and corresponding stabilities at the nanoscale,
20–22
thus making the predictable
syntheses of metastable colloidal nanocrystals an outstanding challenge.
23

Diorganyl dichalcogenides (R-E-E-R, where E = S, Se, Te, and R = Ph, Me, Bz, etc.) are proven
molecular precursors for the preparation of colloidal metal chalcogenide nanocrystals, and in particular, for
the preparation of metastable phases of these nanocrystals, including wurtzite or wurtzite-like phases of
CuInS 2, Cu 2SnSe 3, Cu 2ZnSnS 4, and Cu 2–xSe.
24–27
We were the first to report a previously unknown wurtzite-
like phase of CuInSe 2 from a synthesis utilizing a diselenide precursor, which was shown to be critical in
phase determination of the resulting nanocrystals. We subsequently determined that the functional groups
on the diselenide precursor could be leveraged to molecularly program different polymorphs of the resulting
83

colloidal CuInSe 2 nanocrystals depending on the C–Se precursor bond strength.
24
Herein, we explore a
related ternary chalcogenide, AgInSe 2, that is of interest for applications in near-infrared luminescence and
as a solar absorber for thin film photovoltaics.
28–33
Like CuInSe 2, AgInSe 2 belongs to the family of I-III-VI 2
semiconductors that adopt a thermodynamically preferred chalcopyrite structure in bulk. Possessing an
A
+
B
3+
E
2–
2 composition, the diamondoid structure of chalcopyrite can be thought of as a supercell of zinc
blende, where the A
+
and B
3+
cations are ordered in the cation sub-lattice and the Se
2–
sub-lattice adopts a
cubic close packed structure. In the case of AgInSe 2, a metastable orthorhombic phase is also known to
exist only on the nanoscale, where the Se
2–
sub-lattice adopts a hexagonally close-packed structure.
Isostructural with the high-temperature orthorhombic phase of bulk AgInS 2, the In
3+
and Ag
+
cations in this
metastable phase of AgInSe 2 are ordered and alternate along the [001] crystallographic direction.
34

While dichalcogenides have been utilized to access a wide range of metastable colloidal nanocrystal
phases, as previously mentioned, it has also been observed that the presence or absence of coordinating
ligands influences phase determination in these reactions.
14,35–37
Herein, we elucidate the role of
coordinating ligands in the phase determination of AgInSe 2 nanocrystals synthesized using dibenzyl
diselenide as the selenium precursor. This mechanism is notably different from previously proposed
mechanisms for the formation of metastable orthorhombic AgInSe 2 nanocrystals.
38–40
Finally, we propose
a general conceptual framework that explains the isolation of previously empirically discovered metastable
polymorphs on the nanoscale and may aid in future rational discoveries of metastable materials that do not
exist on bulk phase diagrams.
3.3 Experimental
3.3.1 Materials and General Procedures
Silver(I) nitrate (AgNO 3, Alfa Aesar, 99.9%), indium(III) acetate (In(OAc) 3, Alfa Aesar, 99.99%), dibenzyl
diselenide (Bn 2Se 2, Alfa Aesar, 95%), 1-dodecanethiol (Alfa Aesar, 98%), 1-octadecene (ODE, Sigma-
Aldrich, 90%), oleic acid (Alfa Aesar, 90%), trioctylphosphine (TOP, Sigma-Aldrich, 90%) and oleylamine
(70%, Sigma−Aldrich) were all used as received, with no further purification. All solvents were degassed
84

prior to use for 4 h at 105 °C and then overnight at room temperature. Reactions were conducted under a
nitrogen atmosphere using standard Schlenk techniques. All reactions employed J-KEM temperature
controllers with in-situ thermocouples in order to control and monitor the temperature of the reaction vessel.
3.3.2 Synthesis of Orthorhombic AgInSe 2 Nanocrystals
In a typical synthesis, Bn 2Se 2 (170.2 mg, 0.5 mmol) was added to a two-neck round-bottom flask. To this,
1 mL of ODE and 1 mL of oleylamine were added. The flask was then degassed at 100 °C for 1 h. Then,
the solution was heated to 200 °C for 1 h to yield a clear, orange solution that was then cooled to 70 °C.
AgNO 3 (33.9 mg, 0.2 mmol) and In(OAc) 3 (58.4 mg, 0.2 mmol) were loaded into a 25 mL three-neck
round-bottom flask. 8 mL of ODE, 1 mL of oleylamine, and 100 μL of oleic acid were then added to the
three-neck flask, and the solution was degassed for 1 h at room temperature, making sure not to expose the
flask to light. The metal-containing flask was then ramped to 90 °C at which point the Bn 2Se 2 solution was
injected, nucleating Ag 2Se nanocrystals. The flask was then ramped to 230 °C at 10 °C/min under nitrogen
and held there for a total of 30 min from the time of injection. Aliquots were removed from the reaction
flask at intermediate time points.
3.3.3 Synthesis of Chalcopyrite AgInSe 2 Nanocrystals
In the syntheses of chalcopyrite AgInSe 2 nanocrystals, all of the oleylamine was replaced with an equal
volume of oleic acid, keeping the volumes of ODE constant. AgNO 3 (33.9 mg, 0.2 mmol) and In(OAc) 3
(58.4 mg, 0.2 mmol) were loaded into a 25 mL three-neck round-bottom flask, while Bn 2Se 2 (68.0 mg, 0.2
mmol) was added to a two-neck round-bottom flask. After adding the solvents, the flasks were degassed at
100 °C for 1 h. The metal precursor-containing flask was then ramped to 230 °C at 10 °C/min under
nitrogen. Upon reaching 230 °C, the Bn 2Se 2 solution was injected into the metal precursor-containing flask,
resulting in nucleation of nanocrystals. Aliquots of the reaction were taken at intermediate time points.
3.3.4 Nanocrystal Workup
As aliquots were removed from the reaction flask, they were directly injected into 15 mL centrifuge tubes
containing ethanol. These centrifuge tubes were then filled to volume with ethanol and were bath sonicated
85

for 10 min, and centrifuged for 3 min. The supernatant was decanted and the product was redispersed in 2
mL of hexanes in each centrifuge tube and filled to volume with ethanol. This washing procedure was
repeated once more to yield particles for XRD analysis.
3.3.5 Electrostatic Site Potential and Madelung Energy Calculations
The orthorhombic AgInSe 2 CIF served as a template to create the CIF of the theoretical structure that would
result if the vacancies in the orthorhombic Ag 2Se structure were directly filled by In
3+
(we derived the CIF
of orthorhombic AgInSe 2 itself from a CIF of the isostructural AgInS 2, corrected for lattice parameters, unit
cell volume and composition. The collection code for the AgInS 2 CIF in the ICSD is 51618). Because the
space group of this theoretical structure was not known, the space group was defined as P1 in the CIF and
the Cartesian coordinates of each atom in the structure were explicitly defined.
The VESTA software allows users to calculate electrostatic site potentials and Madelung energies based on
user inputs. For all calculations, user inputs for radius = 1 Å and for region = 4 Å
-1
. The output for Madelung
energy calculations is in terms of energy per mole of asymmetric units; because the CIF of the theoretical
structure explicitly defined the coordinates of each atom without the use of symmetry operators, the
asymmetric unit was the entire unit cell. The unit cell is formally Ag 4In 4Se 8, so to get the Madelung energy
on a per mole basis, the final output was divided by four.
3.3.6 Characterization
Powder X-ray diffraction (XRD) measurements were performed on a Rigaku Ultima IV powder X-ray
diffractometer using Cu Kα radiation (λ = 1.5406 Å). Samples were analyzed on a zero-diffraction silicon
substrate. Transmission electron microscopy (TEM) micrographs were obtained from dropcast samples
supported on holey carbon-coated copper TEM grids (Ted Pella, Inc.). Grids were placed in a vacuum oven
overnight at 60 °C for removal of volatile organics. A JEOL JEM-2100 microscope with a Gatan Orius
charge-coupled device (CCD) camera was used to take TEM images at an operating voltage of 200 kV.
Thermogravimetric analysis (TGA) was performed on a TGA Q50 instrument with a heating rate of 10
°C/min with an approximate sample size of 10 mg in an alumina crucible. SEM-EDX elemental analysis
86

was performed using a JEOL JSM-7001F microscope with an operating voltage of 7 kV and a working
distance of 15 mm. Samples were prepared by drop casting nanocrystal suspensions dispersed in hexanes
onto copper plates that were heated until the deposited material was dry.
3.3.7 Density Functional Theory (DFT)
Formation energy calculations were performed on the orthorhombic Pna2 1 polymorph using the Vienna
Ab-initio Simulation Package (VASP), plane-augmented wave pseudopotentials and a k-point density of
64 points per Å
-3
, consistent with Materials Project standard settings to ensure the energies would be directly
comparable to existing Materials Project calculations.
41,42
The atomic positions and crystal lattice were
allowed to relax, resulting in lattice parameters of a = 7.48 Å, b = 8.76 Å and c =7.14 Å. These calculations
were performed using the PBE exchange-correlation functional, and so lattice parameters are expected to
be slightly over-estimated compared to experiment.
3.4 Results and Discussion
In a typical reaction, AgNO 3 and In(OAc) 3 were dissolved together in a mixture of 1-octadecene (ODE),
oleylamine, and oleic acid. In a separate flask, the dibenzyl diselenide (Bn 2Se 2) selenium source was
dissolved in oleylamine and ODE. The metal precursor solution was then heated to 90 °C, at which point
the solution containing the diselenide was injected into the flask (note: higher temperatures of injection
cannot be achieved in oleylamine as the AgNO 3 reduces to Ag nanoparticles at temperatures greater than
~100 °C in this solvent mixture). The flask was then rapidly ramped to 230 °C and held at that temperature

87

Figure 3.1. (a) Powder XRD pattern of orthorhombic AgInSe 2 nanocrystals formed in the presence of oleylamine,
with the results from a Rietveld refinement to the Pna2 1 structure. Tick marks represent individual reflections of
the orthorhombic structure with the difference pattern shown below. λ = 1.5406 Å. (b) High-resolution TEM
micrograph of the orthorhombic AgInSe 2 nanocrystals.

for the desired reaction time. Under these reaction conditions, we observed the formation of colloidally
stable, AgInSe 2 nanocrystals that crystallize in the orthorhombic Pna2 1 space group, which is a metastable
phase of AgInSe 2 known to form only on the nanoscale (Figure 3.1).
34,43
The powder X-ray diffraction
(XRD) pattern of the phase-pure orthorhombic nanocrystals is given in Figure 3.1a. Rietveld refinement of
the XRD pattern using the Pna2 1 space group returns lattice parameters of a = 7.305(4), b = 8.513(3), and
c = 6.991(1) Å, with a unit cell volume of V = 434.8(1) Å
3
. These values are in close agreement with the
previously reported experimental values for orthorhombic AgInSe 2 (i.e., a = 7.33 Å, b = 8.52 Å, and c =
7.02 Å; V = 438 Å
3
).
39
This orthorhombic phase is similar to the wurtzite structure type, with the notable
distinction between them being the ordering of Ag
+
and In
3+
in the orthorhombic structure. Discerning
wurtzite from wurtzite-like structures can be difficult and has been a point of interest within studies of
metastable ternary chalcogenide materials.
15,33,44
In this case, orthorhombic AgInSe 2 in the Pna2 1 space
group exhibits distinct reflections (at 20-21° 2θ) from the (111) and (020) lattice planes, which are absent
in a higher symmetry wurtzite structure type (space group P6 3mc, see Figure 3.2).
88

Figure 3.2 (a) Rietveld refinements of powder XRD patterns of AgInSe2 in the (a) wurtzite P63mc space group and
in the (b) orthorhombic Pna21 space group. Note that the Pna21 structure can be distinguished by unique
experimentally observed reflections at 20-21° 2θ from the (111) and (020) lattice plane families, which are absent in
a higher symmetry wurtzite structure type.

The Rietveld refinement and the observation of low-angle reflections in Figure 3.2 lead us to conclude that
the metastable AgInSe 2 nanocrystals likely assume a wurtzite-like structure that maintains Ag
+
and In
3+

ordering within the crystalline lattice. When allowed to react for 30 min, the elemental composition of the
metastable AgInSe 2 nanocrystals converged close to the expected 1:1:2 ratio of Ag:In:Se, with a
composition measured by SEM-EDX of 1:1.04:1.96 (Figure 3.3). Interestingly, at earlier reaction times,
the orthorhombic phase still observed, but at more metal-rich compositions, indicating that this phase has
a broad composition tolerance (Figure 3.3), similar to the high-temperature wurtzite phase in the Cu-In-S
system.
45
Indeed, we found that the Ag:In:Se ratio could contain as little Se as a 1:1.03:1.37 ratio while still
maintaining the orthorhombic phase (corresponding to an aliquot taken at 10 min). This represents a 30%
reduction in the amount of Se as compared to the 1:1.04:1.96 ratio measured for the aliquot taken at 30 min.

89

Figure 3.3 SEM-EDX elemental analysis of orthorhombic AgInSe 2 particles synthesized in oleylamine. After 30 min,
the nanocrystals converged close to the expected 1:1:2 ratio of Ag:In:Se at 1:1.04:1.96. The inset shows how the
nanocrystals changed in composition over time, going from metal-rich to more selenium-rich compositions with time.
The 10 and 15 min aliquots demonstrate that the orthorhombic phase of AgInSe 2 (showing no indications of Ag 2Se at
these times by XRD) is compositionally flexible. Indeed, the we found that the Ag:In:Se ratio could contain as little
Se as a 1:1.03:1.37 ratio while still maintaining the orthorhombic phase (this corresponds to the aliquot taken at 10
min). This represents a 30% reduction in the amount of Se as compared to the 1:1.04:1.96 ratio measured for the
aliquot taken at 30 min.

Formation of the metastable orthorhombic phase of AgInSe 2 using Bn 2Se 2 was a surprising result,
as it differs from what we observed when employing Bn 2Se 2 in the synthesis of CuInSe 2 nanocrystals; there,
diselenide precursors possessing relatively weak C–Se bonds, including Bn 2Se 2, gave the
thermodynamically preferred chalcopyrite phase of CuInSe 2.
24
Thus, we anticipated that Bn 2Se 2 might
similarly produce the thermodynamically preferred chalcopyrite phase of AgInSe 2, yet this turned out not
to be the case. This indicates that the mechanism of formation of this metastable phase when using Bn 2Se 2
is distinct from that which was previously observed for the formation of CuInSe 2.
Although Bn 2Se 2 leads to the metastable orthorhombic phase of AgInSe 2, we surmised that
increasing the reaction temperature might yield the thermodynamic phase of AgInSe 2. The initial reactions
with Bn 2Se 2 to give orthorhombic AgInSe 2 nanocrystals were performed at 230 °C. Increasing reaction
90

Figure 3.4. (a) XRD of orthorhombic AgInSe 2 synthesized at 250 °C in oleylamine. The metastable phase persists at
this higher temperature. The mismatch between the reference pattern and the experimental diffraction pattern may be
due preferred orientation of the anisotropic platelets that form under these conditions, or perhaps from the presence of
a chalcopyrite AgInSe 2 impurity. If the latter were the case, however, a more pronounced shoulder would likely be
visible to the left of the peak at 43° 2θ, as can be distinguished in Figure 3.5. (b) TEM image of the anisotropic
platelets that form under these conditions.

temperatures to 250 °C still resulted in formation of metastable orthorhombic AgInSe 2 (Figure 3.4).
Annealing powders of the metastable AgInSe 2 nanocrystals to 300 °C in the solid state also does not cause
the material to thermally relax to the chalcopyrite phase, even after several heating/cooling cycles (Figure
3.5). Moreover, after leaving the as-prepared orthorhombic AgInSe 2 nanocrystals for over a year on the lab
bench under ambient conditions, they maintain their metastable orthorhombic structure. Heating the as-
synthesized orthorhombic AgInSe 2 nanocrystals at 300 °C for 1 h as a colloidal suspension in ODE also
leaves the metastable phase mostly intact, although some conversion to the chalcopyrite phase was
observed, indicating that this metastable phase is more thermally resistant to relaxation as a solid-state
powder at high temperatures than as a colloid in solution (Figure 3.5b). Empirically, the orthorhombic phase
of these AgInSe 2 nanocrystals appears to be a local minimum in the energetic landscape of this material
system that has a high barrier to reorganization to the thermodynamically preferred phase, and thus the
orthorhombic phase remains kinetically persistent.
To explore the potential roles of the coordinating species (i.e., oleylamine and oleic acid) in phase
determination, they were systematically omitted from the reactions. When oleic acid is omitted from the
reaction by replacing it with an equal volume of oleylamine, under otherwise identical conditions, the
reaction still returns orthorhombic AgInSe 2. This suggests that oleic acid does not play a major
91

Figure 3.5. (a) Annealing powders of the as-prepared orthorhombic AgInSe 2 nanocrystals to 300 °C does not cause
the material to thermally relax to the thermodynamically preferred chalcopyrite structure by XRD, even after several
heating-cooling cycles, indicating that there is a barrier to a phase transition to the chalcopyrite phase. Note, however,
that at these temperatures some of the Ag
+
is reduced to Ag (marked with *). Powder XRD of the material taken from
the TGA crucible after heating to 450 °C shows that the reduction of Ag
+
to Ag is more pronounced at higher
temperatures, but that the orthorhombic phase still persists. Notably, this progression of XRD patterns was taken from
a material that had been left on the lab bench for 10 months. (b) Heating as-synthesized orthorhombic AgInSe 2
nanocrystals in 1-octadecene at 300 °C for 1 h shows that the orthorhombic phase is still predominant, although XRD
indicates some conversion of orthorhombic to chalcopyrite AgInSe 2, as evidenced by a growth in the intensity of the
peak around 26° 2θ and the asymmetry of the peak at 43° 2θ.

role in phase determination in the presence of oleylamine. Conversely, when oleylamine is replaced by an
equal volume of oleic acid, we found that the analogous hot-injection reaction with Bn 2Se 2 performed at
230 °C yields chalcopyrite AgInSe 2 with minor Ag 2Se impurities (Figure 3.6a). This result illustrates that
oleylamine plays a critical role in phase determination in this reaction.

92

Figure 3.6 (a) Aliquot study to elucidate the formation pathway of chalcopyrite AgInSe 2 nanocrystals by powder
XRD. A mixture of binary Ag 2Se phases (tetragonal and orthorhombic) is obtained at early times. This mixture
progresses towards chalcopyrite AgInSe 2 as a function of increasing time, but binary intermediates are still present
even after 15 min. (b) Aliquot study to follow the formation of the metastable orthorhombic phase of AgInSe 2 by
powder XRD reveals that the metastable ternary phase forms more quickly than chalcopyrite AgInSe 2 when
oleylamine is present in large excess (46 equivalents), as no Ag 2Se intermediates are observed by XRD after 10 min.
Powder XRD shows that under these conditions, a similar mixture of orthorhombic and tetragonal Ag 2Se forms at
early times. (c) TEM images of the aliquots corresponding to the diffraction patterns in (b) show that the nanocrystals
evolve over time from isotropic intermediates to anisotropic platelets of orthorhombic AgInSe 2.

3.4.1 Formation of Chalcopyrite AgInSe 2
To probe the formation of chalcopyrite AgInSe 2, a study was performed without oleylamine in which
aliquots were removed at certain time points after the injection of Bn 2Se 2. Powder XRD patterns of
nanocrystal products isolated from each aliquot show Ag 2Se intermediates at early times that, over the span
of 15 min, convert into chalcopyrite AgInSe 2 upon reaction with In
3+
in solution (Figure 3.6a). Bulk Ag 2Se
exhibits two stable polymorphs –– namely, a low-temperature orthorhombic phase and a high temperature
(T > 130 °C) cubic phase.
9,46
However, an additional metastable tetragonal polymorph is known to form
within polycrystalline thin films and for Ag 2Se nanocrystals.
9–13
To the best of our knowledge, the crystal
structure of this tetragonal phase of Ag 2Se has not yet been unambiguously determined, in large part due to
its instability as a bulk material under any known conditions. Even so, Wang et al. conducted a thorough
investigation of the phase transitions that occur between the tetragonal, orthorhombic, and cubic phases of
93

Ag 2Se nanocrystals by variable-temperature powder XRD measurements.
9
For their system, they reported
that the tetragonal phase can undergo different phase transitions, depending on the identity of the surface
ligands. When stabilized with oleylamine, tetragonal Ag 2Se converts to the orthorhombic phase at 60-67
°C, which can then convert at higher temperatures (135-139 °C) to cubic Ag 2Se. When stabilized with
polyvinyl pyrrolidone, tetragonal Ag 2Se undergoes a direct transition to the cubic phase of Ag 2Se at 104-
109 °C.
Figure 3.6a illustrates that 1 min after injecting Bn 2Se 2 into the metal precursor solution in the
absence of oleylamine, both the tetragonal and orthorhombic phases of Ag 2Se are present. Phase
quantification of each respective polymorph is difficult due to the high degree of overlap of the powder
XRD patterns of these phases and the fact that the structure of the tetragonal polymorph has not yet been
solved. Both the orthorhombic and the tetragonal phases of Ag 2Se are likely metastable at the reaction
temperature of the aliquot study, and they are both capable of undergoing direct phase transitions to form
cubic Ag 2Se at elevated temperatures, which led us to believe that perhaps the cubic phase of Ag 2Se is the
binary intermediate that ultimately gives rise to chalcopyrite AgInSe 2. However, a control experiment in
which Bn 2Se 2 was hot-injected into a flask containing only AgNO 3 (i.e., with no In(OAc) 3 precursor)
revealed that these Ag 2Se phases do not undergo phase transitions to the cubic phase of Ag 2Se after 30 min
(Figure 3.7) under the same conditions used for the aliquot study shown in Figure 3.6a, suggesting that each
of the intermediate Ag 2Se phases must be capable of directly converting to chalcopyrite AgInSe 2 in the
presence of In
3+
cations.

94

Figure 3.7 Powder XRD aliquot studies of a reaction in which Bn 2Se 2 was hot-injected into a flask containing a
solution of only AgNO 3 (with no In(OAc) 3 present). A complex mixture of Ag 2Se polymorphs results. Although
cubic Ag 2Se is the thermodynamically stable polymorph at the reaction temperatures, no significant phase
transitions were observed over the time scale of the reaction, indicating that the other phases of Ag 2Se present are
kinetically resistant towards a phase transition to cubic Ag 2Se under these conditions.

This observation is supported by the fact that on the bulk Ag 2Se-In 2Se 3 pseudo-binary phase diagram of
AgInSe 2, both cubic and orthorhombic Ag 2Se can convert to chalcopyrite AgInSe 2 with increasing In
3+

content.
43
On the nanoscale, conversion of Ag 2Se to AgInSe 2 can be thought of as a reaction in which two
equivalents of Ag 2Se combine with one equivalent of In
3+
to yield AgInSe 2 with the expulsion of three Ag
+

ions. Neither orthorhombic nor cubic Ag 2Se have cubic close-packed Se
2–
anion sub-lattices (i.e., cubic
Ag 2Se is body-centered cubic and orthorhombic Ag 2Se is nearly hexagonally close-packed, vide infra),
whereas the Se
2–
sub-lattice of chalcopyrite AgInSe 2 is cubic close-packed (see Figure 3.8). Thus, to
generate chalcopyrite AgInSe 2 nanocrystals from Ag 2Se intermediates, a reconstructive transition via non-
topotactic cation exchange must occur in which the Se
2–
sub-lattice reorganizes to a cubic close-packed
structure.
While this reorganization to the chalcopyrite structure is thermodynamically favored, it is
necessarily kinetically slow. For that reason, the hot-injection syntheses without oleylamine always resulted
in products comprised of chalcopyrite AgInSe 2 with some binary Ag 2Se impurities, even when reactions
were carried out in the presence of excess In(OAc) 3 and for extended periods of time (Figure 3.9). To
95

Figure 3.8 (a) Se
2–
sub-lattice of chalcopyrite AgInSe 2; note that the lattice is fcc as it contains an ABC packing
motif. (b) Se
2–
sub-lattice of cubic Ag 2Se; this lattice is body-centered cubic.

improve the phase purity of the chalcopyrite AgInSe 2 products, a heating up procedure can be employed,
whereby all reagents were combined in a flask with oleic acid and ODE and heated to the desired reaction
temperature. This method proved to be more effective in converting the Ag 2Se intermediates to a product
containing almost exclusively chalcopyrite AgInSe 2 (Figure 3.9).

96

Figure 3.9 (a) Hot-injection reactions (highlighted with yellow background) that were allowed to react for longer
times in the presence of excess In
3+
(the initial reactions were performed with 1:1 In:Ag ratios) did not produce phase-
pure chalcopyrite AgInSe 2 by power XRD. Heating-up reactions (highlighted with blue background) showed better
conversion to chalcopyrite AgInSe 2 in the presence of excess In
3+
, with the 3 h reaction producing nearly phase-pure
chalcopyrite AgInSe 2 as shown by a Rietveld refinement of powder XRD data in (b). All reactions were performed at
250 °C. (c) TEM images corresponding to chalcopyrite AgInSe 2 for the 3 h heating up method. The rectangular
morphologies correspond to the cubic crystal habit of the chalcopyrite phase.

3.4.2 Formation of Orthorhombic AgInSe 2 and the Role of Cation Exchange-Mediating Ligands
The formation of orthorhombic AgInSe 2 nanocrystals in the presence of oleylamine suggests that
oleylamine changes the mechanism of formation for the ternary material. To better understand the
mechanism of formation of orthorhombic AgInSe 2 nanocrystals when oleylamine is present, we performed
an additional aliquot study to track the formation of the metastable ternary phase. Interestingly, the
intermediates observed by XRD 1 min after injection of the Bn 2Se 2 are nearly identical to those observed
at early times in the absence of oleylamine (Figure 3.6a); namely, a mixture of orthorhombic and tetragonal
Ag 2Se are observed. It should be noted that similar powder XRD patterns of Ag 2Se intermediates have been
reported in prior studies of orthorhombic AgInSe 2,
38–40,47
although these reports have largely dismissed the
presence of the tetragonal phase in their discussions of the data, assigning the intermediate as purely
orthorhombic Ag 2Se or providing no phase assignment at all. While our studies herein suggest that
97

orthorhombic Ag 2Se is indeed the intermediate that leads to formation of orthorhombic AgInSe 2 (vide
infra), the work of Wang et al. sheds light on the potential fate of the tetragonal phase in these reactions.
They showed that, when stabilized with oleylamine surface ligands, the metastable tetragonal phase of
Ag 2Se undergoes a phase transition to orthorhombic Ag 2Se at relatively low temperatures.
9
Thus, when
reacting with In
3+
in solution in the presence of oleylamine, orthorhombic Ag 2Se converts directly to
orthorhombic AgInSe 2, whereas tetragonal Ag 2Se has the ability to undergo a phase transition to
orthorhombic Ag 2Se and then convert to orthorhombic AgInSe 2.
In contrast to the long-lived binary Ag 2Se intermediates observed in the aliquot study with no
oleylamine (Figure 3.6a), the analogous aliquot study in the presence of oleylamine reveals fast conversion
of Ag 2Se intermediates to the metastable orthorhombic AgInSe 2 product, as no Ag 2Se intermediates remain
after 10 min (Figure 3.6b). This illustrates that, under these conditions, Ag 2Se quickly and quantitatively
converts to the orthorhombic phase of AgInSe 2 in the presence of oleylamine. This fast conversion
elucidates the role of oleylamine in the reaction; as a softer Lewis base than oleate, oleylamine is capable
of mediating cation exchange from Ag 2Se that is otherwise kinetically sluggish to react in the presence of
In
3+
cations, presumably due to the difficulty of extracting Ag
+
from the structure, which is necessary for
In
3+
diffusion. Indeed, unlike the cubic phase of Ag 2Se, the orthorhombic phase is not a superionic Ag
+
ion
conductor, with an ionic conductivity of only ~10
–4
S/cm,
48
meaning that this phase should not be able to
undergo facile cation exchange in the absence of a mediating ligand.
While others
38–40,47
have observed the presence of orthorhombic Ag 2Se prior to the formation of
orthorhombic AgInSe 2, this transformation is not well understood in the literature. Abazović et al.
speculated that the formation of the metastable phase of AgInSe 2 is in some way related to how ligands
bind to the surfaces of the ternary nanocrystal nuclei, thus directing the phase towards orthorhombic
AgInSe 2.
38
We propose a more nuanced mechanism of formation for orthorhombic AgInSe 2 whereby a
ligand-mediated topotactic cation exchange converts orthorhombic Ag 2Se to orthorhombic AgInSe 2.
To confirm the dependence of orthorhombic AgInSe 2 formation on the presence of a cation
exchange-mediating base, we sought to synthesize this phase using other soft bases, such as
98

Figure 3.10 Results of all reactions in which TOP was used in attempts to make orthorhombic AgInSe 2. Reaction A:
Oleylamine was replaced with an equal amount of TOP (1 mL). The reaction was heated and the Bn 2Se 2 was injected
at 200 °C. After 2 min, the reaction was stopped due to dissolution of the product; Ag nanoparticles crashed out of
solution. Reaction B: Amount of TOP was reduced to 75 μL total. The reaction was heated and the Bn 2Se 2 was
injected at 200 °C. After 2 min, the reaction was stopped; Ag 2Se with Ag nanoparticles resulted. Reaction C: Total
amount of TOP was 150 μL. The reaction was heated and the Bn 2Se 2 was injected at 200 °C. After 2 min, the reaction
was stopped; Ag 2Se with Ag nanoparticles resulted. Reaction D: Total amount of TOP was 150 μL. The reaction was
heated and the Bn 2Se 2 was injected at 200 °C. The reaction vessel was rapidly cooled to 100 °C after injection to slow
down the dissolution of Ag 2Se, and left at 100 °C for 30 min in an effort to allow cation exchange to occur; Ag 2Se
with Ag nanoparticles resulted. Reaction E: Total amount of TOP was 500 μL. The reaction was heated and the
Bn 2Se 2 was injected at 200 °C. An aliquot was taken after 1 min, which resulted in Ag 2Se with Ag nanoparticles (E1).
The remaining product was allowed to react for 1 additional minute until the material appeared to dissolve, yielding
only Ag nanoparticles (E2).

trioctylphosphine (TOP) or 1-dodecanethiol. Preliminary reactions with TOP yielded orthorhombic Ag 2Se
products at short reaction times (Figure 3.10), which indicated that perhaps longer reaction times would
allow conversion of this intermediate to orthorhombic AgInSe 2. However, allowing the reaction to run for
longer times led to the dissolution of the Ag 2Se intermediate and produced Ag nanoparticles as the only
solid product from the reaction (Figure 3.10). Varying reaction times, temperatures, and the amount of TOP
in subsequent reactions produced similar results (Figure 3.10), with no evidence of AgInSe 2 formation. This
result is in line with the findings of Han et al., which showed that TOP can extract Ag
+
, among other cations,
from metal chalcogenide nanocrystals and reduce them to their zerovalent state. Indeed, they showed that
this occurs when reacting TOP with both Ag 2S and AgInS 2 nanocrystals.
49
Furthermore, TOP is also known
to extract S
2–
and Se
2–
from metal chalcogenide nanostructures,
50,51
all of which explains the
99

Figure 3.11 (a) Rietveld refinement of powder XRD data and (b) TEM images of orthorhombic AgInSe 2 synthesized
in the presence of 1-dodecanethiol. The nanocrystals are 10.1 nm ± 1.0 nm for N = 300 particles. Since 1-dodecanethiol
is known to decompose and release sulfur at these reaction temperatures, it is possible some sulfur is incorporated into
the orthorhombic anion sub-lattice. Quantifying the amount of sulfur in the nanocrystal lattice is non-trivial, as 1-
dodecanethiol also coordinates to the surface of these nanocrystals as a ligand. However, from the c lattice parameter
of the refinement shown in (a), we can interpolate roughly how much sulfur has been incorporated into the nanocrystal
lattice using Vegard’s law and the published lattice parameters of orthorhombic AgInSe 2 and AgInS 2 (see reference
39). Using this approach, there is roughly 10% sulfur incorporation into these orthorhombic nanocrystals.

observed instability of the binary Ag 2Se intermediate in our attempts to synthesize orthorhombic AgInSe 2
with TOP as a cation exchange mediator.
While TOP proved ineffective, we were able to use 1-dodecanethiol as a replacement for
oleylamine to synthesize phase-pure orthorhombic AgInSe 2 nanocrystals (Figure 3.11a). Removing
oleylamine from the reaction mixture allowed us to employ higher temperatures of injection (230 °C) since
AgNO 3 does not reduce to Ag nanoparticles at such a low temperature in this solvent mixture. Aliquot
studies under these conditions show that conversion to orthorhombic AgInSe 2 occurs on a very short time
scale (Figure 3.12a). To observe the intermediates, the amount of 1-dodecanethiol was reduced from the
original 58 equivalents (relative to the metal precursors) to 5 equivalents (Figure 3.12b). Notably, Figure
3.12b indicates that the predominant intermediate observed under low-1-dodecanethiol conditions is the
orthorhombic phase of Ag 2Se, which further supports the assignment of orthorhombic Ag 2Se as the
intermediate that leads to orthorhombic AgInSe 2.
Interestingly, in addition to conversion from orthorhombic Ag 2Se to orthorhombic AgInSe 2 in the
presence of oleylamine, Figure 3.6c demonstrates that the ternary nanocrystals themselves undergo
100

Figure 3.12 (a) Aliquots taken directly after injection of Bn 2Se 2 when 1-dodecanethiol is present (1 mL total) indicate
that orthorhombic AgInSe 2 forms very quickly at elevated temperatures (230 °C). (b) Reducing the amount of 1-
dodecanethiol to 120 μL allowed for the observation of orthorhombic Ag 2Se intermediates at short reaction times.

morphological changes whereby isotropic dots grow into anisotropic platelets over time. TEM and high-
resolution TEM (HR-TEM) analysis of the aliquots shown in Figure 3.6b,c illustrates that at early reaction
times, spherical Ag 2Se seeds nucleate (diameter = 9.0 ± 2.1 nm). Lattice fringes can be observed via HR-
TEM of the Ag 2Se nanocrystals formed after 1 min (Figure 3.13). The measured d-spacing (0.298 nm)
corresponds to the reflection at 30.5° 2θ in the powder XRD pattern of the intermediate (Figure 3.6b), which
is associated with a reflection from the tetragonal phase of Ag 2Se and the (102) plane of orthorhombic
Ag 2Se. Through partial cation exchange reactions, these Ag 2Se seeds convert to spherical AgInSe 2
nanocrystals. Indeed, after 10 min, XRD indicates that the orthorhombic AgInSe 2 is phase-pure, with 65%
of the nanocrystals exhibiting a spherical morphology by TEM and with no statistically significant change
in particle diameter of these dots (8.6 ± 1.4 nm) from the original Ag 2Se seed nanocrystals (Figure 3.14a).
Measuring the ratio of dots to platelets by TEM from the 10, 20, and 30 min aliquots indicates that the dots
give rise over time to the anisotropic platelet morphologies that comprise 35%, 55%, and 73% of the
nanocrystals in these aliquots, respectively (Figure 3.14b). The increase in platelet population is
concomitant with a complementary reduction of the population of spherical dots. HR-TEM of the
orthorhombic AgInSe 2 nanocrystals show that the platelets are highly crystalline; lattice fringes with d-
spacings of 0.348 nm and 0.320 nm are clearly visible (Figure 3.15) and correspond to the (002) and the
(121) lattice planes of orthorhombic AgInSe 2. These lattice planes are associated with reflections in the
XRD pattern at 25.6 and 27.8° 2θ, respectively. Partial cation exchange followed by seeded growth
101

Figure 3.13 (a) HR-TEM of Ag 2Se taken from the 1 min aliquot (b) Line profile of the lattice fringes seen
in (a). The 0.298 nm d-spacing corresponds to the reflection in the XRD observed at 30.5° 2θ.

Figure 3.14 (a) Size analysis of dots and platelets as a function of time. The size for the dots is represented
by the diameter, whereas for the platelets, size is represented by the length of the long axis. (b) Population
percentages of dots vs. platelets as a function of time.

is a mechanism that is known for multinary metal chalcogenide nanocrystals, where the growth following
cation exchange is driven by direct conversion of monomers in solution to the multinary material without
going through the binary phase of the original seed nanocrystals.
52
This appears to be the mode of growth
for these orthorhombic AgInSe 2 nanocrystals, as no Ag 2Se is observed by XRD or TEM as the spherical
AgInSe 2 dots mature into anisotropic platelets. We found that the average length of the long axis of the
platelets increased from 18.8 ± 5.6 nm at 10 min, to 22.4 ± 6.2 nm at 20 min, to 23.3 ± 6.3 nm at 30 min
(Figure 3.14a).

102

Figure 3.15 (a) HR-TEM of orthorhombic AgInSe 2 taken from the 30 min aliquot (b) Line profile of the lattice fringes
seen in (a). The 0.348 nm d-spacing corresponds to the reflection in the XRD observed at 25.6° 2θ. (c) HR-TEM of
orthorhombic AgInSe 2 taken from the 30 min aliquot. (d) Line profile of the lattice fringes seen in (c). The 0.320 nm
d-spacing corresponds to the reflection in the XRD observed at 27.8° 2θ.

3.4.3 Crystal Chemistry of the Orthorhombic Ag 2Se to Orthorhombic AgInSe 2 Conversion and
Computational Results
In addition to our experimental evidence of the conversion of orthorhombic Ag 2Se to orthorhombic
AgInSe 2, structural comparisons of orthorhombic Ag 2Se to orthorhombic AgInSe 2 reveal similarities
between these two crystal structures and elucidate how the process of cation exchange transforms the former
into the latter. Upon examining the Se
2–
sub-lattice of orthorhombic Ag 2Se, it is apparent that there exists a
nearly hexagonally close-packed network of Se
2–
anions in the [010] direction (Figure 3.16a). These
hexagonal sheets of Se
2–
are nearly planar, although the in-plane Se-Se angles are distorted from the 120°
in-plane angles within the hexagonal lattice of orthorhombic AgInSe 2 (Figure 3.16a, b). The interplanar d-
spacing between Se
2–
sheets along the [010] direction in orthorhombic Ag 2Se is 3.56 Å, whereas the d-
103

Figure 3.16. (a) Se
2–
sub-lattice of orthorhombic Ag 2Se. Se
2–
exists in nearly-planar hexagonal sheets that display
significant in-plane angular distortions. (b) Se
2–
sub-lattice of orthorhombic AgInSe 2. (c) Illustration of the tetrahedral
holes (T h) within the orthorhombic Ag 2Se structure. If this site were occupied with a cation, the resulting tetrahedron
would be corner-sharing with neighboring tetrahedra along the edges highlighted in yellow. (d) Full structure of
orthorhombic Ag 2Se, with the trigonally coordinated Ag
+
sites shown in blue and tetrahedral sites shown in gray. (e)
Depiction of orthorhombic Ag 2Se when all trigonal sites are removed from the structure; the periodic tetrahedral holes
within the structure are illustrated by dashed red lines. This corner-sharing structure is nearly identical to that of
orthorhombic AgInSe 2. (f) Full structure of orthorhombic AgInSe 2 (green atoms = Se, gray atoms/tetrahedra = silver,
pink atoms/tetrahedra = indium).

spacing along the [001] direction of close packing in AgInSe 2 is slightly less, at 3.51 Å. Moreover, the
average Se-Se distance within a hexagonal sheet of Se is 4.53 Å for orthorhombic Ag 2Se and 4.24 Å for
orthorhombic AgInSe 2. Topotactic cation exchange from orthorhombic Ag 2Se to orthorhombic AgInSe 2
should naturally allow for this slight lattice contraction, considering the ionic radius of four-coordinate Ag
+

is 129 pm and that of four-coordinate In
3+
is 94 pm. Overall, the Se
2–
sub-lattice of orthorhombic Ag 2Se
resembles that of AgInSe 2, since only slight changes are needed to take the former to the latter.
Considering that the Se
2–
sub-lattices are so similar, the redistribution of cations upon cation
exchange with In
3+
comprises a more significant structural transformation in going from orthorhombic
Ag 2Se to orthorhombic AgInSe 2. The asymmetric unit of orthorhombic Ag 2Se has one crystallographically
unique Se
2–
site and two unique Ag
+
sites.
46,53
Of the two Ag
+
sites, one site resides within a tetrahedral
104

hole. These tetrahedra share edges with two adjacent, symmetrically equivalent tetrahedra along the [100]
direction. The other Ag
+
site exists in a trigonal planar coordination geometry (Figure 3.16d).
The orthorhombic structure of AgInSe 2 is a wurtzite-like structure in that the Se
2–
sub-lattice is
hexagonally close-packed and all cations reside in corner-sharing tetrahedral coordination environments.
Thus, to form this structure from orthorhombic Ag 2Se, cation exchange needs to occur in a manner that
disrupts the edge-sharing and trigonal planar coordination geometries to yield the requisite corner-sharing
tetrahedron motif. To achieve such a transformation, the periodic tetrahedral holes that exist within the
structure of orthorhombic Ag 2Se (Figure 3.16c, e) need to be filled by either incoming In
3+
ions or by
neighboring Ag
+
ions that, when migrating, would then leave corner-sharing tetrahedral holes that In
3+

could fill. Figure 3.16e demonstrates how removing the edge-sharing tetrahedra and trigonal planar
coordination environments from the orthorhombic Ag 2Se structure, and placing cations within the periodic
tetrahedral holes, leads to the wurtzite-like structure of orthorhombic AgInSe 2. Occupation of the
tetrahedral holes in orthorhombic Ag 2Se would lead to unstable, edge-sharing configurations with both the
proximal Ag
+
tetrahedra and trigonal planar sites (Figure 3.16c). Every In
3+
ion incorporated into the
structure necessarily must expel three Ag
+
ions to maintain charge neutrality. Therefore, it is useful to
visualize a transformation wherein each In
3+
atom displaces one Ag
+
atom from a neighboring tetrahedral
coordination site and two Ag
+
atoms from trigonal planar coordination sites, creating more stable corner-
sharing configurations via the displacement of edge-sharing motifs within the structure.
While the mechanism described above illustrates how the corner-sharing network of tetrahedra in
orthorhombic AgInSe 2 can be derived from orthorhombic Ag 2Se, it does not explicitly explain how or why
the specific ordering of cations in orthorhombic AgInSe 2 arises through this transformation. In fact, the
tetrahedral holes within orthorhombic Ag 2Se are periodic such that along the [100] direction, they form a
linear channel of vacancies (Figure 3.17a). If all In
3+
cations were to occupy these vacancies, the resulting
ternary structure would contain linear chains of Ag
+
and In
3+
in the [010] direction, where the cations within
each chain would be identical (Figure 3.17d). However, this arrangement of cations is not present within

105

Figure 3.17 (a) Orthorhombic Ag 2Se as viewed along the [010] direction. The periodic T h holes are shown with red
dashed lines. Note that these vacancies are uninterrupted along the [100] direction. The arrows represent how a Ag
+

ion would necessarily have to migrate to create the orthorhombic AgInSe 2 structure during a cation exchange process
with In
3+
. (b) Orthorhombic AgInSe 2 as viewed along the [001] direction. Note that Ag
+
and In
3+
sites alternate along
the [010] direction. (c) Unit cell of orthorhombic AgInSe 2. (d) Unit cell of the theoretical structure that would form if
the T h holes of orthorhombic Ag 2Se were systematically filled by incoming In
3+
and no ion-hopping mechanism were
operative. This unit cell is less stable than (c), as demonstrated by ionic site potential and Madelung energy
calculations.

the orthorhombic structure of AgInSe 2, rather, the cationic sites along the [010] direction alternate between
Ag
+
and In
3+
(Figure 3.17b). This indicates that an ion hopping process is operative during cation exchange
such that Ag
+
ions migrate to accommodate incoming In
3+
. By comparing the calculated electrostatic site
potentials and Madelung energy of the orthorhombic AgInSe 2 structure to the site potentials and Madelung
energy of the structure that would result by simply filling the periodic holes within orthorhombic Ag 2Se,
we found that there is an electrostatic driving force that causes this shuffling of Ag
+
during cation exchange;
in the theoretical ternary structure, derived directly from orthorhombic Ag 2Se with no ion hopping, the
calculated In
3+
site potential is greater (-1.54 e/Å) than that for the In
3+
site in orthorhombic AgInSe 2

(-1.67
e/Å), which is an indication that electrostatic repulsion between neighboring In
3+
ions is more significant
in this theoretical arrangement than in the orthorhombic structure of AgInSe 2. This finding is also supported
by the Madelung energy calculations, which represents the attractive electrostatic component to the lattice
energy of an ionic solid.
54
The Madelung energy of the theoretical ternary structure is higher in energy
(-7.38 MJ/mol) than that of the experimentally observed orthorhombic AgInSe 2 structure (-7.60 MJ/mol).
The Materials Project database contains thermodynamic information calculated on six polymorphs
on AgInSe 2, two of which are experimentally known (𝐼 4
̅
2𝑑 , 𝑅 3
̅
𝑚 ), and four of which are theoretical
106

Figure 3.18 (a) The 0 K phase diagram of the Ag-In-Se chemical system, color coded by calculated formation
energy. (b) The relative ordering of AgInSe 2 polymorphs, as predicted by calculation.

structures (R3m, I4 1/amd, Fdd2, P4/mmm) calculated by DFT. Of these, the tetragonal 𝐼 4
̅
2𝑑 polymorph is
predicted to be stable, with the trigonal 𝑅 3
̅
𝑚 polymorph exhibiting a degree of metastability at 0.1 eV/atom
above the 0 K convex hull (Figure 3.18). Typically, materials with a predicted metastability in the range of
~0.1 eV/atom are considered in principle synthesizable under appropriate conditions, although this is highly
dependent on chemical composition.
55

To supplement these calculations, an additional calculation was performed on the orthorhombic
Pna2 1 polymorph of AgInSe 2. The Pna2 1 polymorph was found to have a formation energy of -0.412
eV/atom, which is 10 meV/atom above the predicted stable chalcopyrite phase of AgInSe 2. Figure 3.18
combines this result with existing Materials Project data calculated using the phase diagram analysis
capability of the pymatgen package.
56
This low lying metastability is not unprecedented; in fact, many
metastable metal selenide materials are less than 25 meV/atom above the thermodynamic ground state (for
example, the high-temperature zinc blende phase of CuInSe 2 is a mere 20 meV higher in enthalpy than
chalcopyrite CuInSe 2),
57
and the median energy above the ground state for metastable ternary polymorphs
irrespective of composition is 6.9 meV/atom.
5
Thus, while the orthorhombic structure is metastable, it is
only higher in energy than the chalcopyrite structure by a small margin, which may explain why it is
isolable.
107

3.4.4 Predicting the Syntheses of Novel Metastable Polymorphs on the Nanoscale
Predictable syntheses of metastable materials at large remain a challenge. From this work, and our previous
work on phase control of CuInSe 2 nanocrystals,
24
we note an interesting pattern emerging. In both cases,
the metastable ternary chalcogenide nanocrystals form via topotactic cation exchange from low-temperature
structures of binary selenides, which are metastable at the relatively high temperatures of their respective
nanocrystal syntheses.
Notably, for both copper and silver selenides, the low-temperature (Cu 3Se 2 and orthorhombic
Ag 2Se) and high-temperature (Cu 2–xSe and cubic Ag 2Se) phases differ significantly in their Se
2–
sub-lattices,
with the low-temperature phases of each being pseudo-hexagonal and the high-temperature phases
assuming face-centered and body-centered cubic Se
2–
sub-lattices, respectively. As mentioned above, the
chalcopyrite structure type possesses a face-centered cubic Se
2–
sub-lattice. Therefore, isolating metastable
ternaries in these cases relies on the conversion of binary selenides that possess Se
2–
sub-lattices that do not
form in bulk for the ternary materials. In the formation of both metastable polymorphs of AgInSe 2 and
CuInSe 2, kinetically fast topotactic cation exchange mechanisms provide the means of preserving the
distinct hexagonal Se
2–
sub-lattices upon reaction within In
3+
. These mechanisms outcompete processes that
would otherwise lead to the thermodynamically preferred crystal structures, and instead lead to metastable
ternary structures that do not exist on their respective bulk phase diagrams for the ternary selenides.
More generally, a promising area to explore in the rational discovery of new metastable
nanomaterials may be within material systems that exhibit sub-lattice mismatches between the binary and
ternary anionic sub-lattices, where the binary polymorphs with distinct anionic sub-lattices could generate
new metastable ternary structures by reacting with a third element in such a way that the anionic sub-lattice
is preserved. In effect, lattice mismatches between anionic sub-lattices can act as effective kinetic barriers
that restrict quick access to thermodynamic structures, allowing for the isolation of metastable polymorphs
on the nanoscale, exemplified by Figure 3.19. Inspecting pseudo-binary phase diagrams for ternary material
systems, and the phase diagrams of the binaries that could lead to ternary materials, is insightful
108

Figure 3.19 (a) Silver-rich region within the pseudo-binary phase diagram of the Ag 2Se-In 2Se 3 phase space for each
respective phase (blue = pseudo-hcp, red = bcc, white = fcc). Notably, there exist lattice mismatches in going from
either phase of Ag 2Se to chalcopyrite AgInSe 2. Such lattice mismatches can be taken advantage of by leveraging fast
cation exchange kinetics on the nanoscale to generate novel metastable ternary structures. (b) Reaction scheme
explaining isolation of metastable AgInSe 2; the orthorhombic phase of AgInSe 2 is only 10 meV/atom in energy higher
than the chalcopyrite phase and has a Se
2–
sub-lattice analogous to that of Ag 2Se, allowing for fast, coordinating
ligand-mediated conversion to the ternary metastable phase. Panel a: Adapted with permission from reference 43.
Copyright 2001 Elsevier.

and can act as a guide when searching for lattice mismatches to exploit for new metastable nanomaterial
syntheses.
To check that this conceptual framework holds true for more than just CuInSe 2 and AgInSe 2, we
inspected the pseudo-binary phase diagram of the Cu 2Se-SnSe 2 system; here, with increasing Sn
4+
content,
cubic Cu 2Se (66.7% Cu, 33.3% Se, stable above ~130 °C) converts to a cubic, sphalerite phase of
Cu 2SnSe 3.
58
However, the low-temperature Cu 3Se 2 phase (60% Cu, 40% Se) has a pseudo-hexagonal
anionic sub-lattice
24
and it maintains a Cu:Se ratio within the boundaries of the two-phase Cu 2Se-SnSe 2
region. Therefore, we expect a kinetically fast reaction of Cu 3Se 2 with Sn
4+
to produce a metastable,
hexagonal phase of Cu 2SnSe 3 since there exists a sub-lattice mismatch in going from Cu 3Se 2 to the
thermodynamically preferred sphalerite phase of Cu 2SnSe 3. Indeed, such a metastable hexagonal phase
exists that was previously unknown in bulk, as we first reported the isolation of wurtzite-like Cu 2SnSe 3
nanocrystals in 2012.
59
This further illustrates the utility of leveraging sub-lattice mismatches to generate
novel metastable materials.
109

We hypothesize that this conceptual framework can also be extended to the predictable isolation of
metastable phases not present on bulk phase diagrams for quaternary materials. To support this hypothesis,
we turned to the Cu 2ZnSnS 4 literature. Cu 2ZnSnS 4 is a quaternary material that possesses a face-centered
cubic anionic sub-lattice and crystallizes with a kesterite structure type,
60,61
analogous to the diamondoid
chalcopyrite structure type for ternary materials. The quasi-ternary Cu 2S-ZnS-SnS 2 phase diagram shows
that, in bulk, the introduction of ZnS and SnS 2 into Cu 2S results in the conversion of a Cu 2S polymorph
(digenite, a high-temperature phase stable up to 1130 °C) with a face-centered cubic anionic sub-lattice to
kesterite Cu 2ZnSnS 4.
62,63
However, wurtzite-like Cu 2ZnSnS 4 nanocrystals have been synthesized,
64,65

despite the fact that this phase does not exist in bulk. Phenomenologically, this wurtzite-like phase must be
the result of kinetically fast reactions with a low-temperature phase of Cu 2-xS (such as djurelite or
roxbyite)
23,63
that does not possess an fcc anionic sub-lattice. Thus, the predictive power of this conceptual
framework can be proven by using it to explain empirically discovered metastable ternary and quaternary
nanomaterials. In summary, coupling the identification of material systems that exhibit lattice mismatches
between potential kinetic intermediates and the thermodynamically expected products with computations
that reveal the energetics of the predicted metastable phases could provide a useful new methodology for
the rational discovery of metastable nanomaterials that have never been observed before on bulk phase
diagrams.
3.5 Conclusions
In conclusion, this work sheds light on the mechanism of phase determination in AgInSe 2 nanocrystals.
More specifically, oleylamine and 1-dodecanethiol can mediate a fast cation exchange from orthorhombic
Ag 2Se to form a metastable phase of orthorhombic AgInSe 2. Without the use of these Lewis bases as
exchange mediators, this orthorhombic Ag 2Se intermediate cannot undergo cation exchange due to its low
intrinsic ionic mobility. For reactions that occur in the absence of soft coordinating bases, Ag 2Se
intermediates form and then convert to the thermodynamic chalcopyrite structure of AgInSe 2 via kinetically
slow non-topotactic conversion processes. In addition to elucidating the conversion of orthorhombic Ag 2Se
to the metastable orthorhombic phase of AgInSe 2, we discovered that the isolation of the latter likely also
110

correlates with the fact that it is only marginally metastable at 10 meV/atom above the ground state. Finally,
we provide a new conceptual framework to predict metastable polymorphs that do not form in bulk; using
phase diagrams, it is possible to identify sub-lattice mismatches that exist between kinetic intermediates
that form quickly in nanocrystal syntheses and the thermodynamically most stable polymorphs for
multinary materials. Fast conversion of intermediates with distinct sub-lattices can generate new metastable
structures of multinary nanomaterials not present on bulk phase diagrams. In predicting these new phases,
convex hull calculations can provide an idea of whether or not such metastable materials should be isolable
from a thermodynamic perspective.
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114

Chapter 4. Discovery of a Wurtzite-like Cu2FeSnSe4 Semiconductor Nanocrystal
Polymorph and Implications for Related CuFeSe2 Materials

4.1 Abstract
I 2-II-IV-VI 4 and I-III-VI 2 semiconductor nanocrystals have found applications in photovoltaics and other
optoelectronic technologies because of their low toxicity and efficient light absorption into the near-
infrared. Herein, we report the discovery of a metastable wurtzite-like polymorph of Cu 2FeSnSe 4, a member
of the I 2-II-IV-VI 4 family of semiconductors containing only Earth-abundant metals. Density functional
theory calculations on this metastable polymorph of Cu 2FeSnSe 4 indicate that it may be a superior
semiconductor for solar energy and optoelectronics applications compared to the thermodynamically
preferred stannite polymorph, since the former displays a sharper dispersion of energy levels near the
conduction band minimum that can enhance electron mobility and suppress hot electron cooling. The
experimental optical band gap was measured by the inverse logarithmic derivative method to be direct, in
agreement with theory, and in the range of 1.48-1.59 eV. Mechanistic studies reveal that this metastable
phase derives from intermediate Cu 3Se 2 nanocrystals that serve as a structural template for the final
hexagonal wurtzite-like product. We compare the chemistry of wurtzite-like Cu 2FeSnSe 4 to the related
CuFeSe 2 material system. Our experimental and computational comparisons between Cu 2FeSnSe 4 and
CuFeSe 2 shed light on both the unique crystal chemistry of CuFeSe 2 that prevents it from forming wurtzite-
like polymorphs, and the essential role of Sn in stabilizing the metastable structure of Cu 2FeSnSe 4. This
work provides insight into the importance of elemental composition when designing syntheses for
metastable materials.
4.2 Introduction
Crystalline silicon, which possesses the diamond structure type, currently dominates the solar energy
landscape, commanding as much as 90% of the market share of solar cell materials.
1,2
This is in part due to
the natural abundance of Si, its stability and low toxicity, and recent advancements in Si processing.
2

However, the indirect nature of the 1.1 eV band gap of crystalline Si drastically limits its ability to
efficiently absorb sunlight, since the electronic transition across the optical band gap is a low-probability,
115

phonon-assisted process.
3,4
There are numerous classes of multinary semiconductors that, like Si, also
crystallize with diamond-like structures, including III-V and II-VI zinc blende materials, I-III-VI 2
chalcopyrites, and I 2-II-IV-VI 4 kesterites and stannites.
5
Many of these multinary compounds are of interest
for photovoltaic applications, as the majority are direct band gap materials that absorb visible light more
efficiently than crystalline Si, allowing their implementation in thin film solar cells.
6,7
Whereas some III-V
and II-VI semiconductors contain toxic As or Cd, I-III-VI 2 and I 2-II-IV-VI 4 are promising as less-toxic
materials.
8–10

Quaternary I 2-II-IV-VI 4 (A 2
+
B
2+
C
4+
E 4
2–
) semiconductors crystallize with face-centered cubic anion
sub-lattices that possess specific orderings of cations throughout tetrahedral coordination sites in the
structure, effectively creating tetragonal superlattices of the zinc blende structure.
11
Two common I 2-II-IV-
VI 4 structure types, kesterite (e.g., Cu 2ZnSn(S,Se) 4, Figure 4.1a) and stannite (e.g., Cu 2FeSn(S,Se) 4, Figure
4.1b) differ only by the ordering of the A
+
, B
2+
, and C
4+
cations throughout the structure.
11
Such I 2-II-IV-
VI 4 compounds are quite compositionally versatile, where kesterite forms for A
+
= Cu
+
, Ag
+
; B
2+
= Zn
2+
,
Cd
2+
, Hg
2+
; C
4+
= Si
4+
, Ge
4+
, Sn
4+
; and E
2–
= S
2–
, Se
2–
, Te
2–
.
12
Stannites are known to form for A
+
= Cu
+
; B
2+

= Mn
2+
, Fe
2+
, Co
2+
, Ni
2+
; C
4+
= Si
4+
, Ge
4+
, Sn
4+
; and E
2–
= S
2–
, Se
2–
.
13–17
The tremendous compositional
diversity of these materials makes them apt for research and development of tunable optoelectronic and
magnetic devices.
15
Indeed, Cu 2FeSnS 4 dye-sensitized solar cells have achieved 8.0% power conversion
efficiency,
18
and thin film solar cells of Cu 2ZnSn(S xSe 1–x) 4 have reached 12.6% power conversion
efficiency.
19
A similar material, Cu 2FeSnSe 4, has received less attention than its Zn congener, despite also
holding promise as an efficient solar absorber due to its favorable direct band gap, the Earth abundance of
Cu and Fe (whereas Zn is a more critical element),
20
and high absorption coefficients through the visible
region.
21–24

Discoveries in the last decade have also revealed structural diversity within this class of materials,
where I 2-II-IV-VI 4 semiconductors can adopt metastable wurtzite-like crystal structures on the
nanoscale.
13,25–29
We will refer to these phases as “wurtzite-like” since such phases feature hexagonal close
116

Figure 4.1 (a) Kesterite structure of Cu 2ZnSnSe 4 (ICSD collection code 189278). (b) Stannite structure of
Cu 2FeSnSe 4 (ICSD collection code 85126). Kesterite and stannite are both I 2-II-IV-VI 2 semiconductor structure
types, and they differ only in the ordering and placement of the I, II, and IV cations. (c) Structure of eskebornite
CuFeSe 2 (ICSD collection code 73376). (d) Structure of chalcopyrite CuFeS 2 (ICSD collection code 2518). (e)
Structure of wurtzite ZnS (ICSD collection code 67453). (f) Structure of wurtzite-like Cu 2FeSiS 4 (ICSD collection
code 627355), which has lower space group symmetry than ZnS due to cation ordering within the hexagonal lattice.
(g) Hypothetical chalcopyrite-type CuFeSe 2 used in our DFT calculations. (h) Hypothetical wurtzite-like (Pna2 1
space group) CuFeSe 2 used in our DFT calculations.

packing but often maintain ordered cation sub-lattices, which lower the crystallographic symmetry away
from the wurtzite P6 3mc space group (Figure 4.1e,f).
13,15,30
For some materials, metastable wurtzite or
wurtzite-like phases are present at high temperatures on bulk phase diagrams, whereas for others such
phases are crystal structures that only exist on the nanoscale.
25

Since the structure of a material directly influences its properties, the emergence of metastable
polymorphs may open the door to new functional materials and afford new ways of tuning material
properties that complement compositional tuning.
31,32
For example, band gap engineering by tuning the
S:Se ratio in Cu 2ZnSn(S xSe 1–x) 4 nanocrystals yields a larger range of experimentally accessible band gaps
in the wurtzite-like phase (0.5 eV of tunability) than tuning through the same compositional range in the
117

kesterite phase.
35,36
Furthermore, wurtzite-like phases exhibit exceptional compositional tolerance with
respect to cation ratios, which affords further tunability. Zhang et al. showed that in wurtzite-like
Cu 2ZnSnS 4 nanocrystals, the Cu/(Zn+Sn) ratio can be tuned from 0.5–1.2, with the wurtzite-like crystal
structure remaining intact throughout this entire compositional range.
37

While materials in metastable crystal structures can afford unique and useful properties,
synthesizing metastable materials necessarily requires kinetic control of the chemistry away from
thermodynamic equilibrium, which is not always easy to achieve. For example, we found that the crystalline
phase of CuInSe 2 can be controlled by employing different diorganyl diselenide (R-Se-Se-R) precursors in
the syntheses of these nanocrystals.
39
Precursors that possess strong R-Se bonds (R = phenyl) yield the
metastable wurtzite-like phase of CuInSe 2. In contrast, employing precursors with weaker R-Se bonds (R
= methyl, benzyl) results in the thermodynamically stable chalcopyrite phase.
We report herein a synthesis of a wurtzite-like polymorph of the I 2-II-IV-VI 2 semiconductor
Cu 2FeSnSe 4, characterize its structure, morphology, and electronic absorption properties, and investigate
its mechanism of formation. Density functional theory (DFT) calculations indicate that this polymorph may
improve upon the performance of Cu 2FeSnSe 4-based photovoltaics, as the wurtzite-like polymorph features
a sharp energy dispersion near the conduction band minimum (CBM), which may translate into higher
electron mobility and longer hot electron lifetimes. Mechanistic studies suggest that Sn is key to stabilizing
the wurtzite-like structure; a wurtzite-like compound does not form when only Cu, Fe and Se are present,
which indicates that a wurtzite-like polymorph of CuFeSe 2, which remains a curiosity in the field of
metastable I-III-VI 2 nanomaterials, may be untenable under standard synthetic conditions.
4.3 Experimental
4.3.1 Materials and General Procedures
Copper(II) dichloride dihydrate (CuCl 2·2H 2O, Sigma-Aldrich), sodium oleate (>97%, TCI America),
diphenyl diselenide (Ph 2Se 2, 98%, Sigma-Aldrich), iron(III) tris(acetylacetonate) (Fe(acac) 3, Sigma-
Aldrich), tin(II) ethylhexanoate (Sn(ethylhexanoate) 2, Sigma-Aldrich), and oleylamine (70%, Sigma-
118

Aldrich) were obtained as indicated. Oleylamine was degassed under vacuum at 90 °C for 4 h and then
overnight at room temperature prior to use. Reactions were conducted under a nitrogen atmosphere by using
standard Schlenk techniques. All reactions employed J-KEM temperature controllers with in situ
thermocouples in order to control and monitor the temperature of the reaction vessel. Cu(oleate) 2 was
synthesized according to a published procedure.
39

4.3.2 Aliquot Studies of Wurtzite-Like Cu 2FeSnSe 4 Nanocrystals
The Ph 2Se 2 (0.109 g, 0.35 mmol) and Cu(oleate) 2 (0.219 g, 0.35 mmol) precursors were loaded into a three-
neck flask, followed by the addition of 8 mL of oleylamine. Sn(ethylhexanoate) 2 (97 μL, 0.30 mmol) and
Fe(acac) 3 (0.088 g, 0.25 mmol) were loaded into separate two-neck flasks followed by addition of 2 mL of
oleylamine into each flask. All flasks were then degassed under vacuum for 30 min at 100 °C. Next, the
three-neck flask was heated and held at 220 °C for 3 min to nucleate Cu 3Se 2 nanocrystals. A 2 mL aliquot
of the reaction mixture was removed in order to observe the Cu 3Se 2 intermediate. Then, the
Sn(ethylhexanoate) 2 solution was injected, and the temperature of the reaction flask was set to 250 °C. The
reaction was allowed to react for 3 min after injection of Sn(ethylhexanoate) 2 before removal of a second 2
mL aliquot. Then, the Fe(acac) 3 solution was injected; 3 min after injection of Fe(acac) 3, a third 2 mL
aliquot was removed. The last two 2 mL aliquots were removed 15 and 30 min after the injection of
Sn(ethylhexanoate) 2 (Scheme 4.1). When removed from the reaction mixture, all aliquots were quenched
by direct injection into centrifuge tubes containing ~10 mL room temperature ethanol. Additional ethanol
was added to the centrifuge tubes to bring the volume of the solution to a total of 15 mL, and the centrifuge
tubes were then briefly vortexed and centrifuged. The supernatant was decanted, the nanocrystals were
redispersed by sonicating in 5 mL of hexanes and were then washed again in a similar manner after
additional of 10 mL of ethanol. After this second wash, the nanocrystals were redispersed in hexanes by
sonication, at which point they were suitable for characterization by poweder X-ray diffraction (XRD),
transmission electron microscopy (TEM), and scanning electron microscopy-energy dispersive X-ray
spectroscopy (SEM-EDS). For UV-vis-NIR spectroscopy, the nanocrystals were redispersed in
tetrachloroethylene.
119

Scheme 4.1 Timeline to the aliquot study of the synthesis of Cu 2FeSnSe 4.
4.3.3 Direct Synthesis of Wurtzite-Like Cu 2FeSnSe 4 Nanocrystals
To directly synthesize the wurtzite-like Cu 2FeSnSe 4 nanocrystals without taking aliquots, Ph 2Se 2 (0.078 g,
0.25 mmol) and Cu(oleate) 2 (0.117 g, 0.1875 mmol) and Sn(ethylhexanoate) 2 (20.25 μL, 0.0625 mmol)
were loaded into a three-neck flask, followed by the addition of 6 mL of oleylamine. Fe(acac) 3 (0.0221 g,
0.0625 mmol) was loaded into a separate two-neck flask followed by addition of 2 mL of oleylamine. Both
flasks were then degassed under vacuum for 30 min at 100 °C. The three-neck flask was then heated and
held at 220 °C for 3 min, at which point the Fe(acac) 3 solution was injected into the three-neck flask and
the temperature was set to 250 °C. Upon reaching 250 °C, the flask was allowed to react for 30 min. The
flask was cooled in a room temperature water bath, and the reaction mixture was split evenly into two 40
mL centrifuge which were filled to volume with ethanol. The centrifuge tubes were briefly vortexed and
centrifuged, and the supernatant was decanted. The product was redispersed by addition of 5 mL of hexanes
120

to each centrifuge tube, which were then filled to volume with ethanol, and centrifuged again. The washed
product was then redispersed in hexanes prior to subsequent characterization.
4.3.4 Characterization
Powder XRD data was obtained on a Rigaku Ultima IV powder X-ray diffractometer with Cu Kα radiation
(λ = 1.5406 Å). Samples were analyzed on zero-diffraction silicon substrates. TEM micrographs were
obtained from dropcast samples supported on holey carbon-coated copper TEM grids (Ted Pella, Inc.).
Grids were dried in a vacuum oven overnight at 60 °C for the removal of volatile organics. A JEOL JEM-
2100F microscope with a Gatan Orius charge coupled device camera was used to take TEM images at an
operating voltage of 200 kV. TEM energy dispersive spectroscopy (TEM-EDS) data was acquired using an
accelerating voltage of 200 kV and a probe current of 300 pA; the probe size was ca. 1.5 nm. SEM−EDS
elemental analysis was performed using a JEOL JSM-7001F microscope with an operating voltage of 17
kV. Samples were prepared by drop casting nanocrystal suspensions dispersed in hexanes onto silicon
substrates that were heated until the deposited material was dry. UV-vis-NIR absorption spectroscopy was
performed for nanocrystal suspensions in tetrachloroethylene in a 1 cm path length quartz cuvette placed
within a 150 mm integrating sphere on a PerkinElmer Lambda 950 UV−vis−NIR spectrometer. Rietveld
refinements were performed in GSAS.
43
The profile parameters U, V, W, X, and Y were refined to account
for the broad peak shapes of the nanocrystals in the XRD patterns. Six cosine Fourier series variables were
used to fit background contributions. The lattice parameters, atomic positions, thermal displacement
parameters, fractional occupancies, and spherical harmonics contributions were also refined.
4.3.5 Density Functional Theory Calculations
DFT calculations were performed using the Vienna Ab Initio Simulation Package (VASP).
44
The electron-
nuclei interactions were described using the projector augmented wave method.
45
A 450 eV energy cutoff
was used in all calculations. The antiferromagnetic Cu 2FeSnSe 4 structure was represented using a 2  2 
2 supercell, which has 128 atoms. 3  3  3 and 4  4  2 Monkhorst-Pack k-point meshes were used to
sample the Brillouin zone for the Pmn2 1 and 𝐼 4
̅
2𝑚 phases of Cu 2FeSnSe 4, respectively. The PBE exchange-
121

correlation functional was employed in geometry optimization and the search of the most stable
antiferromagnetic structure.
46
As well known, the PBE functional can strongly underestimate the band gap
due to the self-interaction error, and the band gap problem can be severe if transition metals are involved.
To get a more accurate electronic structure, the HSE06 hybrid functional with a reduced 2  2  2 Γ-centered
k-point mesh was used to further evaluate the energy and electronic structure.
47

4.4 Results and Discussion
In designing a synthetic route to wurtzite-like Cu 2FeSnSe 4, we chose Ph 2Se 2 as a selenium source as it
preferentially nucleates the requisite Cu 3Se 2 intermediate in oleylamine that can give rise to wurtzite-like
products.
39
Oleylamine is used as the solvent/ligand of choice, as it is known to act as a reducing agent at
elevated temperatures while also behaving as a surface ligand for the resulting nanocrystals.
48
In our typical
hot-injection aliquot studies (Scheme 4.1), Ph 2Se 2 and Cu(oleate) 2 were combined in a flask with
oleylamine and heated to 220 °C to nucleate Cu 3Se 2 nanocrystals. After 3 min at 220 °C, an aliquot of the
reaction mixture was removed in order to confirm the Cu 3Se 2 intermediate. Then, Sn(ethylhexanoate) 2 (one
molar equivalent relative to Cu remaining in the reaction mixture following the removal of the first aliquot)
in oleylamine was injected and the temperature of the reaction flask was set to 250 °C. The reaction was
allowed to react for 3 min before removal of a second aliquot followed by injection of Fe(acac) 3 (one molar
equivalent relative to the total amount of Cu and Sn remaining in the reaction mixture following the removal
of the second aliquot). The reaction was allowed to proceed for a total of 30 min after the initial injection
of Sn(ethylhexanoate) 2, where further aliquots were removed from the reaction mixture as time progressed.
In this way, the reaction was monitored stepwise before and after the injection of the Sn and Fe precursors.
We should note that, for the sake of a convenient non-aliquot synthesis of wurtzite-like Cu 2FeSnSe 4
nanocrystals, we combined the Cu(oleate) 2, Ph 2Se 2 and Sn(ethylhexanoate) 2 precursors in oleylamine,
heated them to 220 °C for 3 min and then injected Fe(acac) 3 with subsequent heating at 250 °C for 30 min
to yield the same nanocrystal product (see Experimental for details). The wurtzite-like Cu 2FeSnSe 4
122

nanocrystals are stable in air at room temperature and were not observed to relax to the thermodynamic
stannite phase after 7 months.
Powder X-ray diffraction (XRD) of the reaction aliquots reveal that the Cu 3Se 2 intermediate is
present prior to injection of the Sn or Fe precursors (Figure 4.2), as expected when using the Ph 2Se 2
precursor.
39
Notably, reflections uniquely assignable to Cu 3Se 2 disappear soon after injection of
Sn(ethylhexanoate) 2, indicating that Sn diffuses quickly into the scaffold provided by Cu 3Se 2 to create a
distinct hexagonal, ternary intermediate (vide infra for composition data). Subsequent injection of Fe(acac) 3
leads to Fe incorporation into this intermediate. Aliquots taken 15-30 min after the Sn(ethylhexanoate) 2
injection reveal a phase-pure wurtzite-like Cu 2FeSnSe 4 product (Figure 4.3a). This aliquot study confirms
our initial hypothesis insofar as we were able to derive a quaternary hexagonal polymorph by leveraging
the Ph 2Se 2 precursor chemistry and the binary Cu 3Se 2 intermediate with a nearly hexagonal Se sub-lattice.
Many of the multinary wurtzite-like phases possess ordered cation sub-lattices; indeed, quaternary
compounds such as Cu 2FeSiS 4, Cu 2FePbSe 4, and Cu 2FeSiTe 4 are known to crystallize in wurtzite-like
structures with the orthorhombic space group Pmn2 1.
13
To assess possible structures for this new

Figure 4.2 Powder XRD of Cu 3Se 2 nanocrystals prepared by the reaction between Ph 2Se 2 with Cu(oleate) 2 in
oleylamine for 3 min at 220 °C. Reference stick pattern generated from Cu 3Se 2 CIF from ICSD collection code
239.

123

Figure 4.3 (a) Powder XRD patterns of reaction aliquots taken during the synthesis of wurtzite-like Cu 2FeSnSe 4
nanocrystals. Prior to injection of Sn and Fe precursors, the intermediate can clearly be indexed to Cu 3Se 2 (aliquot
1, black pattern). At 3 min after the injection of Sn(ethylhexanoate) 2, a hexagonal ternary intermediate is observed
(aliquot 2, blue pattern), into which Fe diffuses after injection of Fe(acac) 3 (aliquot 3, green pattern, taken 3 min
after injection of Fe(acac) 3). Thereafter, the quaternary hexagonal intermediate gives way to wurtzite-like
Cu 2FeSnSe 4 nanocrystals (aliquots 4-5, yellow and red patterns, taken 15 and 30 min after injection of
Sn(ethylhexanoate) 2, respectively). (b) Rietveld refinement of the XRD data of the 30 min aliquot (aliquot 5)
confirms that a cation-ordered Pmn2 1 unit cell is an appropriate structural model for this wurtzite-like polymorph
(χ
2
= 3.458, wR = 5.75%, a = 8.02 Å, b = 6.91 Å, c = 6.60 Å, α = β = γ = 90°).  = 1.5406 Å. The refined structure
is shown in the inset. (c) Plot of the elemental compositions of aliquots 1-5 as a function of time, where t = 0
corresponds to the time at which aliquot 1 was taken. The vertical green and black dashed lines represent the times
at which Sn(ethylhexanoate) 2 and Fe(acac) 3 were injected, respectively. All data points are average atom
percentages as determined by SEM-EDS, and error bars represent ± 1  from the average at%.

Cu 2FeSnSe 4 polymorph, we performed a pair of Rietveld refinements of the XRD data from the 30 min
aliquot. In our first refinement, we assumed this polymorph had a true wurtzite structure (space group
P6 3mc) in which Cu, Fe and Sn are randomly distributed over a single Wycoff position in the crystal
structure. This treatment returned a reduced χ
2
of 4.18 and a wR of 7.19% (Figure 4.4). In our second
refinement, we fit the XRD data to a theoretical cation-ordered structure derived from an analogous Pmn2 1
wurtzite-like structure of Cu 2FeSiS 4.
43
This refinement (Figure 4.3b) yielded a significantly better
124

Figure 4.4 Rietveld refinement of XRD pattern of 30 min aliquot to the P6 3mc wurtzite structure. l = 1.5406 Å.
Note that the model fails to account for small reflections that are accounted for in the Pmn2 1 refinement, and that
Cu, Fe and Sn are assigned to the same crystallographic site within the structure.

Figure 4.5 Pmn2 1 is related to the 𝑃 4
̅
2
1
𝑚 space group as the former is a non-isomorphic subgroup of the latter.
Shown here are group-subgroup relationships between 𝑃 4
̅
2
1
𝑚 , Pmn2 1, and space groups of intermediate symmetry.

fit with a reduced χ
2
of 3.46 and a wR of 5.75%, suggesting that such ordering of Cu, Fe and Sn manifests
in the cation sub-lattice of this polymorph. Indeed, the Pmn2 1 structural model accounts for low-intensity
reflections that are not captured with the P6 3mc structural model, most notably visible at 34-37° 2θ.
Symmetry considerations also support the assignment of the Pmn2 1 space group to this polymorph. The
125

Figure 4.6 (a) The (101) plane of Cu 3Se 2. As shown, the d-spacing of this plane represents the distance between a
Se
2–
anion and the mid-point between two in-plane nearest neighbor Se
2–
anions when looking down the [010]
direction. (b) The (210) lattice plane of wurtzite-like Cu 2FeSnSe 4 is analogous to the (101) of Cu 3Se 2. (c) and (d)
reveal that the (111) lattice plane of Cu 3Se 2 is analogous to the (211) of wurtzite-like Cu 2FeSnSe 4. (e) The (002) is
the basal plane of wurtzite-like Cu 2FeSnSe 4, and contains only Cu, Fe and Sn cations. (f) Lattice fringes
corresponding to the (020) plane of wurtzite-like Cu 2FeSnSe 4 are clearly seen in the high-resolution TEM
micrographs of wurtzite-like Cu 2FeSnSe 4 nanocrystals.

binary Cu 3Se 2 intermediate crystallizes with the 𝑃 4
̅
2
1
𝑚 space group. Upon incorporation of Sn and Fe, the
space group symmetry is reduced, but not lost; Pmn2 1 is a non-isomorphic sub-group of 𝑃 4
̅
2
1
𝑚 of index 8
(see Figure 4.5),
44
which confirms that there is a crystallographic symmetry relationship between the binary
intermediate and the quaternary wurtzite-like product.
This symmetry relationship can be observed in the XRD data by analyzing the evolution of peaks
in Figure 4.3a. As the reaction progresses, the 100% intensity peak shifts from 25° (i.e., the (101) reflection
of Cu 3Se 2) to 25.7° 2θ (i.e., the (210) reflection of Cu 2FeSnSe 4). These reflections correspond to analogous
planes of atoms in the Cu 3Se 2 and Cu 2FeSnSe 4 structures. More specifically, inspection of the (101) and
(210) planes in Cu 3Se 2 and wurtzite-like Cu 2FeSnSe 4, respectively, reveals that these lattice planes represent
126

the d-spacing between a Se
2–
anion and the mid-point between two in-plane nearest neighbor Se
2–
anions
when looking down the direction of close packing (Figure 4.6a,b). Similarly, the reflections at ~29° 2θ for
Cu 3Se 2 and Cu 2FeSnSe 4 also arise from crystallographically analogous planes of Se atoms (Figure 4.6c,d).
These findings are useful in that they help characterize and assign reflections in the intermediate phases
between Cu 3Se 2 and Cu 2FeSnSe 4; the persistence of such peaks in the intermediate structure suggests that
the Se
2–
sub-lattice is quite rigid throughout this transformation and undergoes only a slight contraction as
Cu is exchanged for Fe and Sn cations. The middle reflection of the wurtzite-like pattern at ~27° 2θ arises
slowly and is not observed until 15 min after injection of Sn(ethylhexanoate) 2 (aliquot 4). This reflection
can be assigned to the (002) plane, a plane that contains exclusively Cu, Fe and Sn cations and no Se (Figure
4.6e). From this analysis, we can conclude that the intermediate phases have ordered Se
2–
sub-lattices, but
disordered cation sub-lattices. The emergence of the (002) peak at ~27° 2θ arises only when an ordered
cation sub-lattice is established within the material.
The ensemble elemental compositions of the aliquots were tracked via SEM-EDS (Figure 4.3c,
Figure 4.7). Prior to injection of the Sn and Fe, Cu 3Se 2 was observed close to the nominal stoichiometry
(aliquot 1, Cu 3.3Se 1.7), which is in agreement with the structural assignment of this phase by XRD. After
injection of Sn(ethylhexanoate) 2, the at% of Cu dropped by 20%, concomitant with incorporation of Sn into
the material, while the at% of Se dropped by only 3%. The large reduction in Cu content suggests that Sn
partially exchanges for Cu, while the Se at% is merely diluted as the total metal content increases. This
ternary intermediate (which, as mentioned above, retains the hexagonal Se
2–
sub-lattice) has an average
composition of Cu 2.0Sn 1.0Se 1.4, and an overall metal:Se ratio of 2.15. After taking aliquot 2, Fe(acac) 3 was
injected and allowed to react for 3 min prior to removal of aliquot 3. Aliquot 3 revealed that injection of
Fe(acac) 3 led to further reductions in the at% of Cu and Se, while the at% of Sn remained relatively
unchanged. Here, the average composition of the quaternary hexagonal intermediate was found to be metal-
rich, at Cu 1.6Fe 1.5Sn 1.2Se 1.0 with an overall metal:Se ratio of 4.28. Aliquot 4 was taken 15 min after injection
of Sn(ethylhexanoate) 2, at which point the nanocrystals appear to have the wurtzite-like structure by XRD,
although the material is still metal-rich at an average composition of Cu 1.7Fe 1.2Sn 1.0Se 2.5 (overall metal:Se
127

Figure 4.7 (a)-(e) Raw SEM-EDS data for aliquots 1-5. Each point in Figure 4.3c is an average of four of these
SEM-EDS measurements. (f) SEM-EDS data for the non-aliquot reaction. The powder XRD of this reaction is
shown in the inset.

ratio = 1.56). Interestingly, while the Se at% fell in the times immediately following injections of Sn and
Fe precursors, it rebounded in aliquots 4 and 5, going from 18.9 at% in aliquot 3 to a higher at% in aliquot
4 (39.0%), all the way to within in a standard deviation of the expected Se content in aliquot 5 (42.9%, with
the expected Se at% of 50% for Cu 2FeSnSe 4). The average composition of the wurtzite-like product from
aliquot 5 was Cu 1.9Fe 1.0Sn 1.0Se 2.9, with an overall metal:Se ratio = 1.33. Interestingly, this compositional
128

Figure 4.8 (a) UV-vis-NIR absorption spectra of aliquots taken during the synthesis of wurtzite-like Cu 2FeSnSe 4
nanocrystals. Note that there are large surface plasmon resonance features that persist up to 3 min after injection of
Fe(acac) 3 (aliquots 1-3). (b) Inverse logarithmic derivative (ILD) plot (black data points) of the aliquot 5 UV-vis-NIR
spectrum. The dashed red line represents the linear regression that was used to estimate the optical band gap from the
ILD plot using values from 2.0-3.5 eV; the dashed blue line represents band gap estimation using values from 2.0-4.0
eV. From these, the optical band gap was determined to lie between 1.48-1.59 eV. The inset shows the UV-vis-NIR
spectrum of the aliquot 5 Cu 2FeSnSe 4 nanocrystal suspension in tetrachloroethylene from which the ILD plot was
calculated.

progression illustrates that the wurtzite-like phase is stable as a slightly metal-rich material, and that the
ratios of Cu, Fe, and Sn can vary without large structural changes. Such compositional flexibility has been
observed for other wurtzite-like materials,
35,45–48
and could be useful for tailoring the chemical and
optoelectronic properties of this material.
UV-vis-NIR spectroscopy of the same aliquot series supports our proposed mechanism of
formation for this Cu 2FeSnSe 4 material (Figure 4.8a). Prior to injection of Sn(ethylhexanoate) 2 and
Fe(acac) 3, the absorption spectrum is consistent with Cu 3Se 2 nanocrystals, with the onset of NIR absorption
beginning in the red region of the visible spectrum (i.e., dilute suspensions of these nanocrystals appear
blue-green). It is well known that copper chalcogenide nanocrystals can display strong surface plasmon
responses in the NIR.
49
Interestingly, the spectrum of the aliquot taken 3 min after injection of
Sn(ethylhexanoate) 2 also exhibits a significant absorption band in the NIR, indicative of plasmonic behavior
of this intermediate ternary hexagonal phase. This plasmonic absorption is red shifted further into the NIR
compared to the spectrum of Cu 3Se 2, which is in accordance with the exchange of Cu for Sn in the
nanocrystals, as plasmons of copper tin selenide nanocrystals have been observed to red shift deeper into
129

the NIR as the Sn content rises.
50
After injection of Fe(acac) 3, and as the nanocrystals ripen, the plasmon
resonance disappears by the 15 min aliquot, yielding absorption spectra more characteristic of a non-
plasmonic semiconductor.
To estimate the optical band gap of this material, we employed the inverse logarithmic derivative
(ILD) method, which is derived from the Tauc method and was first proposed by Jarosińksi et al.
51
The
ILD method has been shown to allow for accurate measurements of semiconductor band gaps using
absorbance data as inputs. This method has advantages over other commonly used methods, such as the
Tauc or McLean methods, in that the type of electronic transition (i.e., direct or indirect) does not need to
be known a priori and that extrapolation from the linear region of the ILD plot allows for determination of
the optical band gap within a relatively narrow range of possible values (see 4.6 for ILD calculations).
Applying this method, we determined that our wurtzite-like Cu 2FeSnSe 4 nanocrystals have an optical band
gap in the range of 1.48-1.59 eV, depending on the range of values used in the least squares fit to the linear
region of the ILD plot (Figure 4.8b).
The reciprocal of the slope of the line of best fit from the ILD linear regression is equal to the
exponential factor m in the Tauc equation (see 4.6), which yields information about the nature of electronic
transitions in the material. For bulk direct band gap semiconductors, the exponential factor m = 0.5, and
one would expect an ILD linear regression to have a slope of 2. Importantly, however, Conibeer et al.
showed that for direct band gap semiconductor nanocrystals, the exponential factor m exhibits a size
dependence due to the relaxation of momentum selection rules for optical transitions in small nanocrystals,
where for spherical nanocrystals 500 nm in diameter or less, 0.5 ≤ m ≤ 1, with m increasing in value as the
nanocrystal diameter decreases.
52
For the wurtzite-like Cu 2FeSnSe 4 nanocrystals, m was found to be 0.86 ≤
m ≤ 0.96, depending on the range of values used in the least squares fit. These m values are only slightly
larger than those that Conibeer et al. calculated for spherical nanocrystals of similar diameters; deviations
from perfectly spherical morphologies in the wurtzite-like Cu 2FeSnSe 4 nanocrystals likely cause moderate
inflation of the experimental m values as compared to those calculated by Conibeer et al. From the

130

Figure 4.9 (a) TEM micrograph of Cu 3Se 2 nanocrystals formed after reacting for 3 min at 220 °C, before Sn or Fe
precursor injections. (b) TEM micrograph of product obtained 3 min after Sn(ethylhexanoate) 2 injection. (c) TEM
micrograph of product obtained 3 min after Fe(acac) 3 injection. (d-e) TEM micrographs of product obtained 15 and
30 min after Sn(ethylhexanoate) 2 injection, respectively. (f) HR-TEM image of product obtained 30 min after
Sn(ethylhexanoate) 2 injection. Lattice fringes from the (020) planes are visible. (g) Composite image of EDS elemental
mapping of Cu, Fe, Sn and Se in the wurtzite-like Cu 2FeSnSe 4 nanocrystals. (h) Elemental maps of Cu, Fe, Sn, and
Se.

experimental m values, we deduce that the wurtzite-like polymorph of Cu 2FeSnSe 4 nanocrystals is
adequately described as a direct band gap semiconductor.
The formation of Cu 2FeSnSe 4 nanocrystals was also monitored by TEM as the reaction progressed.
Well-defined, quasi-spherical nanocrystals of Cu 3Se 2 (average diameter 12.3 ± 2.3 nm, for N = 300
nanocrystals) are observed just prior to injection of Sn(ethylhexanoate) 2 (Figure 4.9a). Shortly after
injection of Sn(ethylhexanoate) 2, intermediate copper tin selenide nanocrystals form via exchange of Cu
for Sn (Figure 4.9b). Injection of Fe(acac) 3 results in Fe incorporation into the hexagonal intermediate
(Figure 4.9c) that ultimately gives way to phase-pure (average diameter 19.6 ± 3.0 nm, for N = 300
nanocrystals) wurtzite-like Cu 2FeSnSe 4 (Figure 4.93d-f). The fact that nanocrystals in this aliquot study are
morphologically similar in shape throughout the reaction supports our conclusion from the XRD data that
the anion sub-lattice remains intact throughout this transformation, and that the progression of peaks seen
131

in the XRD is largely a result of shifting cation composition and ordering within the nanocrystals. The
increase in nanocrystal size indicates that Cu 3Se 2 serves as a template onto which the wurtzite-like
nanocrystals grow as Sn, Fe, and additional Se incorporate along the course of the reaction. Lattice fringes
of the final wurtzite-like product are observed through high-resolution TEM and suggest apparent single
crystalline particles. The measured d-spacing (0.35 nm) corresponds to the (020) plane (Figure 4.6f) that
contributes to the 100% intensity peak observed in the XRD pattern at 25.7° 2θ. The wurtzite-like product
30 min after Sn injection was analyzed for elemental ratios via TEM-EDS (Figure 4.9g, h). The elemental
maps reveal that Cu, Fe, Sn and Se are evenly distributed throughout the nanocrystals, and that the examined
nanocrystals are compositionally close (Cu 2.00Fe 0.86Sn 0.96Se 4.19) to the expected Cu 2FeSnSe 4 stoichiometry.
4.4.1 Electronic Structure Calculations for Wurtzite-Like and Stannite Cu 2FeSnSe 4 Polymorphs
DFT calculations indicate that the Pmn2 1 polymorph of Cu 2FeSnSe 4 is dynamically stable and is
slightly metastable at 9.4 meV/atom above the energy of the lowest energy stannite structure of Cu 2FeSnSe 4
(Figure 4.10). The calculations predict that both wurtzite-like and stannite polymorphs of Cu 2FeSnSe 4 favor
antiferromagnetic structures (Figure 4.10), which is corroborated by experimental data indicating
antiferromagnetism in stannite Cu 2FeSnSe 4 at low temperatures.
53,54
As a direct band gap semiconductor
composed of Earth abundant metals, wurtzite-like Cu 2FeSnSe 4 could be important for low-cost thin film
solar cells. Indeed, a number of works have already been published that identify the thermodynamically
preferred stannite 𝐼 4
̅
2𝑚 polymorph of Cu 2FeSnSe 4 as a promising, low-toxicity solar absorber.
21,23,24,55,56

To compare the optoelectronic properties of the stannite 𝐼 4
̅
2𝑚 polymorph of Cu 2FeSnSe 4 to the
wurtzite-like Pmn2 1 polymorph, we calculated the spin-density of states for both polymorphs in their most
stable antiferromagnetic configuration using the HSE06 functional (Figure 4.12 and Figures 4.10-8). For
both polymorphs, the valence band edges are composed primarily of Cu-d and Se-p orbitals. The largest
contributions to the conduction band edges originate from Se-p and Sn-s orbitals for stannite 𝐼 4
̅
2𝑚
polymorph, while the wurtzite-like Pmn2 1 polymorph has a strong hybridization from Se-s, Se-p, and Sn-s
states (Figure 4.11). Interestingly, while both polymorphs have low density of states (DOS) near the
132

conduction band minimum (CBM), it is significantly lower for the wurtzite-like Pmn2 1 polymorph. Taking
into account the significant computation cost of HSE06 DOS with dense sampling of the Brillouin zone,
we further calculated the HSE06 band structure (Figure 4.12c). Given that the most stable antiferromagnetic
phase of both polymorphs is predicted to have a direct band gap at the Γ point, we present two key k-point
paths near the Γ point. The Pmn2 1 polymorph features a sharp dispersion of the CBM around the Γ point,
which rationalizes the lower DOS near the CBM. The Pmn2 1 polymorph may be preferable over the 𝐼 4
̅
2𝑚
polymorph in solar cell applictions, since the sparse manifolds of states near the CBM in the former can
increase the lifetime of hot electrons.

Figure 4.10 Relaxed geometric structures and lowest-energy antiferromagnetic configurations for (a) Pmn2 1
Cu 2FeSnSe 4 and (b) 𝐼 4
̅
2𝑚 Cu 2FeSnSe 4. Experimental magnetic studies of stannite Cu 2FeSnSe 4 confirm that it is
antiferromagnetic at low temperatures.
2,3
Comparison of the DFT total energies indicates that Pmn2 1 Cu 2FeSnSe 4
has a slightly higher energy than 𝐼 4
̅
2𝑚 Cu 2FeSnSe 4 of 9.4 meV/atom. (c) Calculated phonon dispersion for the
Pmn2 1 phase of Cu 2FeSnSe 4 indicates that this is a dynamically stable structure. The phonon dispersion spectrum
is calculated with the Phonopy code using the finite displacement method and a 2   2  2 supercell.

133

Figure 4.11 Orbital projected density of states (DOS) of (a) Pmn2 1 Cu 2FeSnSe 4 and (b) 𝐼 4
̅
2𝑚 Cu 2FeSnSe 4. The
atom projected DOS is shown in Figure 4.12.
134

Figure 4.12 Spin-density of states (DOS) calculated with the HSE06 functional for (a) the wurtzite-like Pmn2 1
polymorph of Cu 2FeSnSe 4 and (b) the stannite 𝐼 4
̅
2𝑚 polymorph of Cu 2FeSnSe 4. Note the difference in DOS
between the two polymorphs near the CBM, where the Pmn2 1 polymorph only has a sparse manifold of states that
can protect hot electrons. Orbital resolved DOS is shown in Figure 4.11. (c) Band structure around the Γ point
calculated with the HSE06 functional for spin-up channel. The corresponding spin-down channel data are given in
Figure 4.13. The Pmn2 1 polymorph of Cu 2FeSnSe 4 has a sharp dispersion along the Z-Γ direction, indicating that
its electron is lighter and has a higher mobility in the z-direction compared to the stannite 𝐼 4
̅
2𝑚 polymorph.

Wurtzite-like CuInSe 2 is found to have a similar dispersion of the CBM deriving from In and Se s-orbitals,
57

and was also predicted to be a superior solar absorber compared to the thermodynamically preferred
chalcopyrite phase of CuInSe 2. The sharper dispersion of the CBM along the Z-Γ direction indicates the
Pmn2 1 polymorph of Cu 2FeSnSe 4 has a smaller electron mass and higher electron mobility in the z-
direction. The band gaps of Cu 2FeSnSe 4, as determined by the DOS and band structure calculations are
0.66 eV and 0.75 eV for the 𝐼 4
̅
2𝑚 and the Pmn2 1 polymorphs, respectively. These values are likely
underestimated by the calculations due to strong electron correlation in these materials. Note the low DOS
associated with the lowest energy excitation into the CBM may prevent its experimental identification. The
135

gap between the valence band maximum and CBM+1 is 1.15 eV, showing better agreement with the
experiment (Figure 4.8b).

Figure 4.13 Band structure around the Γ point calculated with the HSE06 functional for spin-down channel. The
corresponding result for the spin-up channel is shown in Figure 4.12. The Pmn2 1 polymorph of Cu 2FeSnSe 4 has a
sharp dispersion in the conduction band along the Z-Γ direction, indicating that the effective mass of the electron is
smaller than in 𝐼 4
̅
2𝑚 Cu 2FeSnSe 4 and that it should have a higher electron mobility in the z-direction than the stannite
𝐼 4
̅
2𝑚 polymorph.
136

4.4.2 Learning from Wurtzite-Like Cu 2FeSnSe 4: Implications for Unknown Wurtzite-Like CuFeSe 2
and the Stabilizing Effect of Tin
From a growing number of reports, it is clear that metastable wurtzite-like polymorphs are
accessible for a range of diamond-like semiconductors on the nanoscale. For example, wurtzite-like I-III-
VI 2 polymorphs have been reported for nanocrystals of CuFeS 2,
58,59
CuGaS 2,
60,61
CuGaSe 2,
62
CuInS 2,
48,63

CuInSe 2,
64
CuIn 1–xGa xS 2,
60,65
CuIn 1–xGa xSe 2,
62
AgGaS 2,
66
AgGaSe 2,
67
AgInS 2,
68,69
and AgInSe 2.
70
In
discovering wurtzite-like Cu 2FeSnSe 4, we seek to compare this chemistry to that of a related I-III-VI 2
compound (i.e., CuFeSe 2) and ultimately determine whether the synthetic conditions used herein could be
applied to the synthesis of wurtzite-like CuFeSe 2, which is unknown.
CuFeSe 2 does not appear in the aforementioned list of experimentally observed wurtzite-like phases
of I-III-VI 2 semiconductors. To underscore the curiosity of this absence, note that within this list of observed
wurtzite-like I-III-VI 2 materials, seven contain Cu, five contain Se (three of which contain both Se and Cu),
and one contains both Cu and Fe. Additionally, this list reveals that for a given experimentally observed
wurtzite-like I-III-S 2, the analogous wurtzite-like I-III-Se 2 semiconductors have also been isolated, with
CuFeSe 2 standing out as the only exception.
Another intriguing peculiarity of CuFeSe 2 is that while the vast majority of I-III-VI 2
semiconductors adopt the chalcopyrite structure type (the ternary analog to kesterite and stannite structure
types, Figure 4.1d) as the ground state structure,
71
the thermodynamically most stable structure of CuFeSe 2
is not chalcopyrite, but rather eskebornite (Figure 4.1c).
72–75
The eskebornite structure is related to
chalcopyrite as both feature face-centered cubic anion sub-lattices and tetragonal unit cells. However,
whereas chalcopyrite is a framework of Se
2–
-terminated corner-sharing Cu and Fe tetrahedra, the
eskebornite structure features edge-sharing Cu and Fe tetrahedra (Figure 4.1c).
73,74
The edge-sharing
configurations in eskebornite allow for nearly 1 Å reductions in the Cu-Cu and Cu-Fe distances as compared
to CuFeS 2, giving rise to metal-metal interactions and metallic properties of CuFeSe 2.
73–75

Pursuant to the discovery of an analgous wurtzite-like phase of CuFeSe 2, we were determined to
explore this synthetic space more thoroughly. However, after testing numerous reaction conditions,
137

precursors, and synthetic methods (i.e., hot-injection, heating up, cation exchange methods), we were
unable to isolate a wurtzite-like CuFeSe 2 polymorph. Instead, all resulting products were some mixture of
binary copper selenides and/or eskebornite CuFeSe 2. These results are in agreement with the CuFeSe 2
literature; indeed, it appears that others have tried to synthesize wurtzite-like CuFeSe 2, as a recent synthesis
of eskebornite CuFeSe 2 nanocrystals was reported using Ph 2Se 2 in oleylamine under nearly identical
conditions known to produce wurtzite-like CuInSe 2 nanocrystals.
36,76,77
Thus, it appears that wurtzite-like
CuFeSe 2 cannot be isolated under conditions typically used to obtain such metastable polymorphs. In
drawing this conclusion, it seems that the presence of Sn stabilizes the wurtzite-like structure in the Pmn2 1
Cu 2FeSnSe 4 polymorph. To explain this, we hypothesize that Sn incorporation into the lattice prevents the
formation of the otherwise favorable Cu-Cu and Cu-Fe interactions that dictate the edge-sharing crystal
chemistry of eskebornite CuFeSe 2.
To test our hypothesis regarding the necessity of Sn in stabilizing the wurtzite-like structure in
Cu 2FeSnSe 4, we performed two control experiments derived from our original aliquot study of Cu 2FeSnSe 4.
(1) Cu 3Se 2 nanocrystals were nucleated and stepwise injected with Fe(acac) 3 first, followed by injection of
Sn(ethylhexanoate) 2 second, taking aliquots between injections, and then letting the mixture react for 30
min after the initial Fe injection. This is the reverse order of precursor injections used in the initial synthesis.
(2) The Sn precursor injection was omitted altogether. The results of controls (1) and (2) reveal that injection
of Fe(acac) 3 into a solution containing Cu 3Se 2 nanocrystals leads directly to Cu-Fe-Se hexagonal
intermediates that display XRD patterns (Figure 4.14, Figure 4.15) similar to the hexagonal Cu-Sn-Se and
Cu-Fe-Sn-Se intermediates observed in Figure 4.3a. This result suggests that the mechanisms of Fe and Sn
diffusion/cation exchange into Cu 3Se 2 are similar. The crystal chemistry beyond this initial diffusion step,
however, depends on whether or not Sn is introduced.
If no Sn is present, as in (2), the ternary hexagonal intermediate observed at early times does not
yield wurtzite-like products, but rather converts to intermediate Cu 2–xSe and eskebornite, which then
produces phase-pure eskebornite CuFeSe 2 after 15 min (Figure 4.15). This is strong evidence that wurtzite-
like phases of CuFeSe 2 are not isolable under typical synthetic conditions, since the Cu-Fe-Se intermediate
138

Figure 4.14 (a) XRD patterns of control aliquot study (1) in which Fe(acac) 3 was injected before
Sn(ethylhexanoate) 2. (b) XRD analysis of the final products of this reaction shows the resulting material is not
phase-pure wurtzite-like Cu 2FeSnSe 4, as the 100% intensity peak coincides with the 100% intensity peak of stannite
Cu 2FeSnSe 4, rather than with the 100% intensity peak of wurtzite-like Cu 2FeSnSe 4.

Figure 4.15 (a) XRD patterns of control aliquot study (2) in which Fe(acac) 3 (without Sn(ethylhexanoate) 2) was
injected at any point (with all other variables remaining constant). From this aliquot study, it can be seen that Cu 3Se 2
nanocrystals nucleate (black pattern) and lead to a hexagonal Cu-Fe-Se intermediate (blue pattern). However, this
ternary intermediate soon gives way to Cu 2–xSe and eskebornite CuFeSe 2 (green pattern) ultimately producing
phase-pure eskebornite CuFeSe 2 after 15 min (yellow pattern). (b) XRD patterns comparing the intermediates
generated by injecting Fe (black pattern) or Sn (red pattern) into Cu 3Se 2 nanocrystals, it is apparent that the
mechanisms of Fe and Sn incorporation into nanocrystals are similar, since structurally similar ternary
intermediates form under both conditions. However, whereas phase-pure wurtzite-like Cu 2FeSnSe 4 forms from the
Cu-Sn-Se intermediate when Sn is injected first, the Cu-Fe-Se intermediate does not yield wurtzite-like CuFeSe 2
in the absence of Sn. This is strong evidence that eskebornite is too thermodynamically favored to yield wurtzite-
like products.
observed here is crystallographically similar to the intermediate that produces wurtzite-like Cu 2FeSnSe 4,
yet it ultimately gives way to the thermodynamic eskebornite phase of CuFeSe 2.
If Sn is injected shortly after Fe, as in control (1), a mixture of wurtzite-like Cu 2FeSnSe 4 and
eskebornite products occur, as well as what appears to be SnSe (Figure 4.14). Here, the hexagonal Cu-Fe-
Se intermediate initially forms, but likely starts partially to convert into the Cu 2–xSe and eskebornite
CuFeSe 2 products seen in (2) before Sn is injected. Upon Sn injection, Cu 2–xSe and eskebornite CuFeSe 2
139

intermediates can react with Sn to yield face-centered cubic Sn-containing products, including stannite
Cu 2FeSnSe 4, while any remaining hexagonal Cu-Fe-Se intermediates react with Sn to yield wurtzite-like
Cu 2FeSnSe 4. These control experiments underscore that Sn incorporation is required before Fe in order to
yield phase-pure wurtzite-like product, as Sn prevents the material from reverting to an edge-sharing, cubic
structure. Indeed, in our synthesis of wurtzite-like Cu 2FeSnSe 4, Sn(ethylhexanoate) 2 is injected first, and
Fe cannot disrupt the hexagonal lattice and drive the reaction towards eskebornite CuFeSe 2 or stannite
Cu 2FeSnSe 4 since the hexagonal Cu-Sn-Se intermediate has already formed.
To explain why CuFeSe 2 prefers the eskebornite phase over corner-sharing polymorphs like
chalcopyrite or wurtzite-like structures, we performed DFT calculations to assess the energy differences (at
0 K) between the stable eskebornite phase of CuFeSe 2 and hypothetical chalcopyrite (space group 𝐼 4
̅
2𝑑 ,
Figure 4.1g) and wurtzite-like (space group Pna2 1, Figure 4.1h) polymorphs of CuFeSe 2. Our calculations
indicate that the eskebornite polymorph is 3.9 meV/atom lower in energy than the chalcopyrite polymorph,
and 14.4 meV/atom lower in energy than the wurtzite-like polymorph. Because the Se
2–
sub-lattices of
eskebornite and chalcopyrite are effectively identical, the 3.9 meV/atom difference in energy between their
respective structures may be attributed to the different distributions of Cu and Fe in the two structures.
While this 3.9 meV/atom energy difference is not large, there would likely only be a small activation energy
barrier, if any, associated with reorganizing Cu and Fe to make eskebornite from a metastable chalcopyrite
CuFeSe 2 polymorph, since the Se
2–
sub-lattice would not need to shift. Indeed, it is well-known that Cu is
quite mobile within copper selenide materials,
78
which prompted us to conclude that the combination of a
slight driving force and a low activation energy barrier is what favors formation of eskebornite CuFeSe 2
and preempts formation of a metastable chalcopyrite CuFeSe 2 polymorph.
Although the 14.4 meV/atom energy difference between a hypothetical wurtzite-like polymorph
and eskebornite CuFeSe 2 does not appear particularly large, it is nearly four times the chalcopyrite-
eskebornite energy difference and is larger than the calculated energy differences between metastable
wurtzite-like phases and the thermodynamic ground states of related metal selenides. For example, wurtzite
or wurtzite-like phases of ZnSe, CuInSe 2, and AgInSe 2 have been calculated to be 5-10 meV/atom above
140

their zinc blende or chalcopyrite ground states,
45,57,79
and we calculated wurtzite-like Cu 2FeSnSe 4 to be 9.4
meV/atom above the stable stannite polymorph. Thus, in this context, it can be seen that the energy
difference between hypothetical wurtzite-like CuFeSe 2 and the eskebornite ground state is 5-10 meV/atom
greater than the wurtzite-ground state energy differences for other structurally related metal selenides.
That said, energy above the ground state is not the only factor that determines whether a metastable
polymorph is isolable. Ceder et al. showed that for different metal oxides, numerous theoretical polymorphs
are calculated to be closer in energy to the thermodynamic ground state structures than known, observed
metastable polymorphs. To explain this, they suggest that in order to be isolable, a polymorph must be the
thermodynamically most stable polymorph under some set of conditions (pressure, temperature, high/low
surface-to-volume ratios, etc.); if a theoretical polymorph never represents the lowest energy structure under
any set of conditions, it will not be isolable, even if it is only marginally higher in energy than the lowest
energy state.
80
In this case, wurtzite-like CuFeSe 2 is 5-10 meV/atom higher in energy compared to the
typical energies above the ground state for metastable wurtzite-like metal selenides, which prevents this
phase from being energetically competitive with the stable eskebornite phase under any of the conditions
typically used to isolate these nanocrystals.
Notably, the 3.9 meV/atom reduction in energy afforded by forming the eskebornite phase rather
than chalcopyrite is close in magnitude to the ~5 meV/atom excess in energy above the ground state
calculated for the wurtzite-like CuFeSe 2 polymorph. From this perspective, we may consider the high
energy difference between wurtzite-like CuFeSe 2 and its ground state to be a result of an unusually low-
energy ground state, rather than an unusually high-energy wurtzite-like polymorph. In fact, the energy
difference between the theoretical chalcopyrite and wurtzite-like CuFeSe 2 polymorphs is 10.5 meV/atom,
which is on the high end of calculated energies above the ground state for isolable metastable wurtzite-like
metal selenides.
45,57,79

We hypothesized that the lower energy of the eskebornite phase may be due to the driving force of
establishing Cu-Cu and Cu-Fe interactions that have been proposed in the literature as the source of
metallicity in CuFeSe 2.
73–75
To test this hypothesis, we performed Bader analyses on eskebornite as well as
141

the theoretical chalcopyrite and wurtzite-like CuFeSe 2 polymorphs. We found that the electron density on
Cu and Fe is greater in eskebornite than in either of the two hypothetical polymorphs, while the electron
density on Se is reduced for eskebornite as compared to the wurtzite-like or chalcopyrite polymorphs (Table
4.1), which provides evidence for the presence of Cu-Cu and Cu-Fe interactions, and agrees with the
reported metallic nature of eskebornite CuFeSe 2.
73–75
These findings support our hypothesis that for
Cu 2FeSnSe 4, the wurtzite-like polymorph is accessible since Sn incorporation into the structure prevents
formation of an edge-sharing structure facilitating Cu-Cu and Cu-Fe interactions. Indeed, in our refined
wurtzite-like Cu 2FeSnSe 4 structure, the minimum Cu-Cu and Cu-Fe distances are 3.84 Å and 4.02 Å,
respectively, which are much larger than the corresponding minimum Cu-Cu (2.76 Å) and Cu-Fe (2.77 Å)
distances in eskebornite CuFeSe 2. Thus, Sn plays a crucial role in stabilizing the metastable wurtzite-like
polymorph of Cu 2FeSnSe 4, serving as an insightful example of how the elemental composition of a material
can be leveraged to control crystal chemistry.

Table 4.1 Bader charges of the Cu, Fe, and Se atoms in the different phases of CuFeSe 2.
Eskebornite Wurtzite-Like Chalcopyrite
Atom Average Electron Count Atom Average Electron Count Atom Average Electron Count
Cu 10.66 Cu 10.60 Cu 10.60
Fe 7.25 Fe 7.20 Fe 7.21
Se 6.54 Se 6.60 Se 6.59

4.5 Conclusions
We report a metastable wurtzite-like polymorph of Cu 2FeSnSe 4, which forms upon Sn and Fe incorporation
into a binary Cu 3Se 2 intermediate. The experimentally determined optical band gap of these Cu 2FeSnSe 4
nanocrystals is direct and lies between 1.48-1.59 eV. Wurtzite-like polymorphs are often compositionally
flexible, and so it may be possible in future work to compositionally engineer the range of accessible band
gaps in this material by varying the metal ratios and/or by alloying with other chalcogens, making this
material system a potential candidate for implementation into photovoltaics and other optoelectronic
devices. DFT calculations suggest that this metastable phase may have a beneficial electronic structure over
142

the thermodynamic stannite phase of Cu 2FeSnSe 4 for photovoltaic applications, as the former has a sharp
energy dispersion near the CBM, indicating a higher electron mobility and longer-lived hot electrons.
We address the similarities and differences between the chemistry of this wurtzite-like polymorph
and the related CuFeSe 2 material system. Notably, a wurtzite-like polymorph has not been reported for
CuFeSe 2, despite the fact that many seemingly similar I-III-VI 2 semiconductors, including CuFeS 2, have
been found to crystallize with wurtzite-like structures on the nanoscale. In this vein, we find that Sn
incorporation into Cu 2FeSnSe 4 is absolutely essential in order to stabilize the wurtzite-like structure; in the
absence of Sn, the chemistry invariably yields the thermodynamically preferred eskebornite CuFeSe 2 phase.
We hypothesize that Sn plays a role in stabilizing the wurtzite-like structure in Cu 2FeSnSe 4 by preventing
Cu-Cu and Cu-Fe interactions that would otherwise dominate the crystal chemistry and drive the formation
of eskebornite CuFeSe 2. This finding provides insight into why there is a gap in the literature regarding
reports of wurtzite-like CuFeSe 2 and provides a way to think about the role of different elemental species
when designing syntheses for metastable compounds.
4.6 Determination of band gap from inverse logarithmic derivative (ILD) method:
The ILD method has been shown to allow for accurate measurements of semiconductor band gaps using
absorbance data or absorption coefficients as inputs. This method has an advantage over other commonly
used methods in that the type of electronic transition (direct or indirect) does not need to be known a priori
in order to calculate the electronic band gap. The derivation is as follows:

Taking the natural log of the Tauc eq 1 yields eq 3, where α is the absorbance value or absorption coefficient,
h is Planck’s constant, ν is the frequency of light, a is a constant, E g is the intrinsic band gap, and m is a
constant with different assigned values depending on the dispersion of the valence and conduction bands.
For direct band gaps m = 1/2, and for indirect band gaps, m = 2.

𝛼 ℎ𝜈 = 𝑎 (ℎ𝜈 − 𝐸 𝑔 )
𝑚
(1)
143

ln(𝛼 ℎ𝜈 ) = ln(𝑎 (ℎ𝜈 − 𝐸 𝑔 )
𝑚 )
(2)
ln(𝛼 ℎ𝜈 ) = ln(𝑎 ) + 𝑚𝑙𝑛 (ℎ𝜈 − 𝐸 𝑔 )
(3)

Taking the derivative of eq 3 with respect to the independent variable hν gives eq 5:

𝑑 (ln(𝛼 ℎ𝜈 ))
𝑑 ℎ𝜈 =
𝑑 (ln(𝑎 ) + 𝑚𝑙𝑛 (ℎ𝜈 − 𝐸 𝑔 ))
𝑑 ℎ𝜈
(4)
𝑑 (ln(𝛼 ℎ𝜈 ))
𝑑 ℎ𝜈 =
𝑚 ℎ𝜈 − 𝐸 𝑔
(5)

Taking the inverse of eq 5,

𝑑 ℎ𝜈 𝑑 (ln(𝛼 ℎ𝜈 ))
=
1
𝑚 (ℎ𝜈 − 𝐸 𝑔 ) ≈
∆ℎ𝜈 ∆(ln(𝛼 ℎ𝜈 ))

(6)

Distributing 1/m in eq 6 yields eq 7. Eq 7 shows that a plot of hv versus the ratio of the change in hv divided
by the change in the natural log of αhv produces a linear plot with a slope of 1/m and an x-intercept of E g.
Thus, both the values of m and E g can be found through this manipulation without any prior knowledge of
the electronic structure of the material.
1

∆ℎ𝜈 ∆(ln(𝛼 ℎ𝜈 ))
=
1
𝑚 ℎ𝜈 −
1
𝑚 𝐸 𝑔
(7)

We found for wurtzite-like Cu 2FeSnSe 4 nanocrystals, that the calculated value of m fell between 0.86 and
0.96, depending on the linear region selected for least squares analysis.

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149

Chapter 5. Crystal Structure of Colloidally Prepared Metastable Ag2Se Nanocrystals

*Published in Nano Lett. 2021, https://doi.org/10.1021/acs.nanolett.1c02045.

5.1 Abstract
Structural polymorphism is known for many bulk materials; however, on the nanoscale metastable
polymorphs tend to form more readily than in the bulk, and with more structural variety. One such
metastable polymorph observed for colloidal Ag 2Se nanocrystals has traditionally been referred to as the
“tetragonal” phase of Ag 2Se. While there are reports on the chemistry and properties of this metastable
polymorph, its crystal structure, and therefore electronic structure, has yet to be determined. We report that
an anti-PbCl 2-like structure type (space group P2 1/n) more accurately describes the powder X-ray
diffraction and X-ray total scattering patterns of colloidal Ag 2Se nanocrystals prepared by several different
methods. Density functional theory (DFT) calculations indicate that this anti-PbCl 2-like Ag 2Se polymorph
is a dynamically stable, narrow-band gap semiconductor. The anti-PbCl 2-like structure of Ag 2Se is a low-
lying metastable polymorph at 5-25 meV/atom above ground state, depending on the exchange-correlation
functional used.
5.2 Introduction
Polymorphism, or the ability of fixed compositions of matter to crystallize in two or more different crystal
structures, is common in solid-state chemistry. The stability of different polymorphs is determined by their
relative free energies under a given set of conditions (temperature, pressure, etc.).
1
While thermodynamics
determine the relative free energies of polymorphs,
2
the kinetics of phase transitions dictate the time scales
of the conversion of higher energy polymorphs to more stable polymorphs for a given set of conditions.
Thus, if the activation energy of a phase transition is sufficiently large, it is possible for a polymorph to be
observed far from the conditions where it is thermodynamically preferred, making it kinetically trapped or
‘metastable.’
The increased surface energy and decreased lattice energy of nanocrystals leads to reduced
activation energies for solid-solid phase transitions in nanocrystals relative to the same transitions in their
150

bulk material analogs.
3–5
These differences enable the syntheses of certain nanocrystal phases at much lower
temperatures than the analogous syntheses of bulk crystals. Additionally, differences in free energy between
polymorphs change due to, in large part, the role of surface energy in determining thermodynamic stabilities
of nanocrystals.
6–10

Surface energetics play such a large role that they can favor the formation of polymorphs that are
not observed in the corresponding bulk materials;
10–12
this phenomenon has been observed in the binary
chalcogenide Ag 2Se. In the bulk, Ag 2Se crystallizes with an orthorhombic crystal structure (P2 12 12 1 space
group) at temperatures up to ~133 °C (1 atm), at which point it undergoes a phase transition to a body-
centered cubic structure (𝐼𝑚 3
̅
𝑚 space group), which is stable until the melt at 897 °C.
13,14
While the
orthorhombic and cubic phases are also observed on the nanoscale, other distinct polymorphs have been
observed within colloidal Ag 2Se nanocrystals and thin films with sub-micron thicknesses.
15–20
Günter and
Keusch tabulated a number of findings of Ag 2Se in unknown crystal structures;
15
they proposed a
monoclinic, “pseudo-tetragonal” unit cell with P2 space group symmetry to describe the crystal structure
of nanometer-thickness thin films of Ag 2Se. Since this report, numerous papers have referenced Günter and
Keusch’s “pseudo-tetragonal” unit cell when assigning a phase to metastable colloidal Ag 2Se nanocrystals
that, by powder X-ray diffraction (XRD), appear to adopt a crystal structure that is qualitatively distinct
from both the known orthorhombic and cubic phases of Ag 2Se.
12,16,21–27
Most of these publications use the
crystal system established by Günter and Keusch; that is, they refer to the metastable Ag 2Se nanocrystals
as having a “pseudo-tetragonal” or “tetragonal” unit cell. However, there are no prior refinements of powder
XRD data of these metastable Ag 2Se nanocrystals to the unit cell described by Günter and Keusch. Rather,
the diffraction data has only been qualitatively compared to the d-spacings and lattice parameters reported
by Günter and Keusch.
12,15,16,24

This is perhaps unsurprising, as solving the crystal structure for a colloidal nanocrystal is quite
difficult – single crystal structure determination is rare and Scherrer broadening complicates the analysis
of powder diffraction data collected on nanocrystals with low-symmetry crystal structures in which
reflections tend to overlap. Additionally, in the case of metastable Ag 2Se nanocrystals, attaining phase-pure
151

samples can be difficult, as orthorhombic Ag 2Se easily forms along with the metastable phase, and/or the
metastable phase can undergo some degree of phase relaxation to the orthorhombic polymorph after
synthesis.
16,22
That said, structural knowledge of nanocrystals is critically important, as different
polymorphs possess unique properties.
28
In the case of Ag 2Se, substantial changes in physical properties
accompany solid-solid phase transitions.
29
For example, the orthorhombic phase of Ag 2Se is known to be a
narrow-band gap semiconductor in the bulk (E g = 0.15 eV), and orthorhombic Ag 2Se nanocrystals are
promising for near-infrared detection and imaging applications and as topological insulators.
30–33
In
contrast, the high-temperature cubic phase is electrically and ionically conductive, with highly mobile Ag
+

cations that move through a rigid body-centered Se
2–
sub-lattice.
23,34,35
These properties of cubic Ag 2Se are
desirable for solid-state electrolytes,
29,36,37
and the differences in electrical and thermal conductivity
between orthorhombic and cubic Ag 2Se have been used to optimize thermoelectric responses at
temperatures near the boundary of the orthorhombic-to-cubic phase transition.
38
Significantly less is known
about “tetragonal” phase of Ag 2Se nanocrystals, in part because the crystal structure remains unresolved.
However, Sahu et al. determined that the infrared absorption of metastable “tetragonal” Ag 2Se nanocrystals
is broadly tunable through the near- to mid-infrared region as a result of size-dependent quantum
confinement.
21
Furthermore, it has been shown that the phase transitions of “tetragonal” Ag 2Se nanocrystals
are dependent on the identity of the surface ligands bound to the colloidal Ag 2Se nanocrystals.
10,16,22,39,40

Given that the crystal structure determines material properties, obtaining the structure solution to
the unresolved metastable phase of Ag 2Se nanocrystals is crucial to advance our understanding of its
optoelectronic properties. Herein, we find that the metastable phase of Ag 2Se, previously assigned as
“tetragonal,” is actually isostructural with the anti-PbCl 2-like structure type adopted by Ag 2S at ambient
temperature and pressure, which crystallizes in the monoclinic space group P2 1/n.
41
Thus, previous
assignments of the “tetragonal” unit cell are incorrect in the context of describing the crystal structure of
colloidal metastable Ag 2Se nanocrystals. We perform additional structural characterizations of our
nanocrystals throughout the same temperature-dependent phase transitions reported by Sahu et al.
22
and
Wang et al.
16
in order to investigate the nanocrystals' crystal chemistry and to further confirm that our P2 1/n
152

phase undergoes the same structural transitions reported for "tetragonal" nanocrystals. Density functional
theory (DFT) calculations reveal that this anti-PbCl 2-like Ag 2Se is dynamically stable and is predicted to
be a narrow-band gap semiconductor, consistent with experiments.
5.3 Nanocrystal Preparation
Colloidal Ag 2Se nanocrystals in the metastable “tetragonal” phase were prepared by the method of Wang
et al.
16
In brief, the nanocrystals were prepared via solvothermal synthesis in DMF by combining AgNO 3,
SeO 2, oleic acid, and polyvinyl pyrrolidone (PVP) and heating to 200 °C for 9-12 h in a Parr bomb. This
solvothermal method was chosen because the resulting PVP-capped Ag 2Se nanocrystals persist in the
metastable “tetragonal” phase longer (i.e., days), and produce larger nanocrystals to minimize Scherrer
broadening, than other preparative methods.
16,22,26

Transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDX)
elemental mapping reveal that the resulting Ag 2Se nanocrystals are consistent with those previously
reported for the PVP-enabled solvothermal method (Figure 5.1).
16
TEM images of the Ag 2Se nanocrystals
show that the nanocrystals are fairly large, with an average diameter of 143  33 nm ( /𝑑 ̅
= 23%, Figure
5.1a). Elemental analysis was performed using TEM-EDX, the results of which show that Ag and Se are
distributed evenly throughout the particles and that the nanocrystals are close to the ideal stoichiometry,
with an average composition of Ag 2.1Se 1.0 (Figure 5.1c,d).
153

Figure 5.1 (a) TEM micrograph of PVP-capped Ag 2Se nanocrystals. The apparent polycrystalline nature of the
PVP-Ag 2Se nanocrystals is clearly visible. (b) High resolution TEM micrograph exhibiting lattice fringes with
measured d-spacing corresponding to the (110) lattice plane of the anti-PbCl 2-like crystal structure. The inset in the
lower right-hand corner depicts the (110) lattice planes in the anti-PbCl 2-like crystal structure. (c) Ag and (d) Se
elemental distributions in a single PVP-capped Ag 2Se nanocrystal as determined by TEM-EDX. These elemental
maps show that Ag and Se are evenly distributed throughout the nanocrystal.

5.4 Structure Determination
Laboratory powder XRD data collected on the Ag 2Se nanocrystals are provided in Figure 5.2a, and are in
qualitative agreement with prior reports of this metastable phase.
16,22,40
This data was obtained immediately
after the nanocrystal synthesis. A simulated powder XRD pattern of the theoretical “tetragonal” structure
154

reported by Günter and Keusch is shown in red. While there are a few peaks in the XRD pattern that
correspond to reflections in the simulated “tetragonal” pattern, it is clear that the “tetragonal” pattern does
not account for most of the experimentally observed reflections. All attempts to perform Rietveld
refinements of the “tetragonal” structure against the experimental XRD data diverged to unphysical values.
Alternatively, a Rietveld refinement with a good quality-of-fit was obtained starting with the structure type
of a closely related material; namely, anti-PbCl 2-like Ag 2S,
41
which is shown in blue (Figure 5.2a). This
structure accounts for nearly all reflections in the powder XRD pattern of the Ag 2Se nanocrystals, although
a small fraction (weight fraction < 1%) of the orthorhombic P2 12 12 1 Ag 2Se structure accounts for some
residual low-intensity reflections. For this two-phase refinement, a Rw of 4.32% was achieved. Refined
values of the anti-PbCl 2-like Ag 2Se phase (a = 4.2960(8) Å; b = 6.9982(6) Å; c = 8.1977(27) Å; β =
101.278(7)°) are given in Table 5.1.

Figure 5.2 (a) Rietveld refinement of the proposed anti-PbCl 2-like structure to the experimental powder XRD
pattern of metastable Ag 2Se nanocrystals (λ = 1.5406 Å). The experimental diffraction pattern is shown with
black data points, and the refined model is shown as the blue trace, with the difference pattern shown below in
turquoise. For reference, the calculated powder diffraction pattern of Günter and Keusch’s “tetragonal” phase is
shown in red. The most prominent peak arising from orthorhombic Ag 2Se is marked by a green asterisk (*),
which forms from spontaneous relaxation of the anti-PbCl 2-like phase. (b) Unit cell of Günter and Keusch’s
“tetragonal” phase. (c) Unit cell of the proposed anti-PbCl 2-like polymorph of Ag 2Se.
155

Table 5.1 Refined values of the anti-PbCl 2-like Ag 2Se phase for PVP-capped nanocrystals. Parameters correspond to
the Rietveld refinement shown in Figure 5.2a.
Space group P2 1/n, Rietveld refinement Rw = 4.32%
a = 4.2960(8) Å; b = 6.9982(6) Å; c = 8.1977(27) Å;  = 101.278(7)°; V = 241.70(6) Å
3

atom x y z U iso
Ag1 0.7386(16) 0.0249(9) 0.3420(9) 0.1303(29)
Ag2 0.2362(15) 0.3588(9) 0.4459(7) 0.1115(24)
Se 0.3284(14) 0.2460(11) 0.1425(7) 0.0676(22)

The anti-PbCl 2-like structure also provided satisfactory refinements to powder XRD data collected on
nanocrystals prepared by alternate oleylamine- and N-heterocyclic carbene-enabled syntheses,
16,26
as shown
in Figures 5.3, 5.4. In addition, TEM micrographs show that the PVP-capped Ag 2Se nanocrystals are
polycrystalline (Figure 5.1a) and high-resolution TEM reveals lattice fringes visible near the edges of the
particles that have measured d-spacings of 0.37 nm, corresponding to the (110) lattice planes of the anti-
PbCl 2-like structure (Figure 5.1b). Thus, it appears that the average structure of the metastable Ag 2Se
nanocrystals can be adequately described as anti-PbCl 2-like.

Figure 5.3 Rietveld refinement of laboratory diffraction powder XRD data of 55-nm oleylamine (OLA)-capped
Ag 2Se nanocrystals (λ = 1.5406 Å). The anti-PbCl 2-like structure provides an excellent fit for this experimental
data.

156

Figure 5.4 Rietveld refinement of synchrotron powder XRD collected on 26-nm Ag 2Se nanocrystals prepared by the
N-heterocyclic carbene method of Lu et al.
26
(λ = 0.143 Å). The anti-PbCl 2-like structure provides an excellent fit for
this experimental data.

The anti-PbCl 2-like structure is monoclinic with space group P2 1/n. Whereas the “tetragonal”
structure of Ag 2Se shown in Figure 5.2b is a slightly distorted face-centered cubic-lattice of Se
2–
anions
containing interstitial Ag
+
cations, the anti-PbCl 2-like structure shown in Figure 5.2c features distorted
edge-sharing AgSe 4 tetrahedra. There are four formula units of Ag 2Se within the anti-PbCl 2-like unit cell.
The Se
2-
anions arrange in nearly planar sheets that propagate along the 2 1 screw axis in the [010] direction,
and the Ag
+
cations reside between these sheets. The observation of the anti-PbCl 2-like structure of Ag 2S
in Ag 2Se nanocrystals is consistent with other reports of metal selenide nanocrystals that adopt metastable
crystal structures not found in the bulk, but are isostructural with known polymorphs that form in the bulk
for analogous metal sulfides.
10,42
In the text below, the phase previously referred to as “tetragonal” will now
be referred to as anti-PbCl 2-like.
Given the limitations of diffraction studies on colloidal nanocrystals, a dual-space approach that
combines Rietveld and pair distribution function (PDF) analysis of X-ray total scattering data is often
useful.
43–45
The PDF is a histogram of atom-atom distances that represent the local atomic (Å-scale)
structure of a material. The PDFs given in Figure 5.5 were extracted from variable temperature synchrotron
X-ray total scattering data collected on the same sample of Ag 2Se nanocrystals at T = 25 °C, 120 °C, and
157

then cooled to 25 °C again. Crystallographic parameters of the phases in each of the PDF fits are given in
Table 5.2. While the maximum temperature T = 120 °C is below the temperature of the orthorhombic-to-
cubic phase transition in the bulk, it is above the “pseudo-tetragonal”-to-cubic phase transition for the Ag 2Se
nanocrystals prepared by the PVP-enabled solvothermal method, as reported by Sahu et al.
22
Due to the 2:1
atomic ratio of Ag to Se, and the relative X-ray atomic scattering factor (Z) of Ag relative to Se, the Ag-Ag
interatomic distances contribute the most intensity to the PDF, followed by Ag-Se distances and, finally,
Se-Se distances. The PDFs were fit between 5 Å < r < 20 Å. The lower limit of the range was selected to
exclude Fourier ripples and to avoid modelling unphysical Ag-Ag distances generated by closely spaced,
fractionally occupied Ag sites in cubic Ag 2Se.
158

Figure 5.5 PDFs extracted from variable temperature synchrotron X-ray total scattering data collected at
(a) 25 °C, (b) 120 °C, and (c) again at 25 °C (λ = 0.143 Å). Black circles indicate the PDF and upper red lines
indicate the fit. Lower red lines indicate the difference between the data and the fit.
159

Table 5.2 Crystallographic parameters of the predominant Ag 2Se phase for PVP-capped nanocrystals from each of
the PDF fits at different temperatures.
T = 25 °C, Space group P2 1/n, Rw = 5.75%
a = 4.32 Å; b = 6.98 Å; c = 8.19 Å;  = 100.9°; V = 241.9 Å
3

atom x y z U iso
Se 0.326 0.253 0.146 0.0300
Ag1 0.733 0.017 0.348 0.0281
Ag2 0.230 0.349 0.449 0.00639
T = 120 °C, Space group Im3
̅
m, Rw = 17.4%
a = 4.98 Å
atom x y z U iso
Se 0.0 0.0 0.0 0.0392
Ag1 0.5 0.5 0.5 0.00802
Ag2 0.25 0.5 0.0 0.0396
Ag3 0.410 0.410 0.0 0.266
T = 25 °C (upon cooling), Space group P2 1/n, Rw = 5.4%
a = 4.31 Å; b = 6.97 Å; c = 8.19 Å;  = 100.9°; V = 238.2 Å
3

atom x y z U iso
Se 0.302 0.260 0.149 0.026
Ag1 0.725 0.021 0.355 0.020
Ag2 0.239 0.328 0.453 0.026

The differences between the PDFs for T = 25 and 120 °C are readily apparent. In particular, distinct
features at G(r) = 9.7, 12.1, and 13.5 Å that are clearly present at 25 °C are not apparent at 120 °C. This
loss of features is consistent with a phase transition from a lower-symmetry to a higher-symmetry crystal
160

structure. The high-temperature cubic structure features highly mobile Ag
+
cations, which are expected to
generate broadened features corresponding to Ag-Ag and Ag-Se distances in the PDF of Ag 2Se. A very
good fit to the PDF of the initial measurement at T = 25 °C was obtained using a model in which the majority
phase was anti-PbCl 2-like Ag 2Se. The best fit to the data, shown in Figure 5.5a, occurred when a fraction
of orthorhombic Ag 2Se and a small fraction of elemental Se were included. The relative weight fractions in
the model for anti-PbCl 2-like Ag 2Se, orthorhombic Ag 2Se, and elemental Se were 80.2%, 16.2%, and 3.7%,
respectively. The presence of some orthorhombic Ag 2Se is expected and consistent with reports that
metastable PVP-capped Ag 2Se nanocrystals relax to the orthorhombic structure at room temperature on a
timescale of days to weeks; given the ~1 week between the synthesis and the analysis of Ag 2Se nanocrystals
on the beamline, partial relaxation of the anti-PbCl 2-like phase was therefore inevitable and expected. The
small fraction of elemental Se is likely left over from reduced SeO 2 precursor in the solvothermal synthesis.
The statistical quality-of-fit for this three-phase model is R w = 5.8%.
The PDF for the nanocrystals at T = 120 °C, shown in Figure 5.5b, is well-described by the high-
temperature cubic structure of Ag 2Se, with R w = 17.4%. The cubic Ag 2Se structure contains three
crystallographically distinct Ag sites, each of which is partially occupied. Allowing each of these
occupancies to refine freely led to a Ag/Se ratio of 1.78:1. This apparently Ag-deficient stoichiometry is
likely due to some of the Ag
+
ions in the ionically conducting cubic Ag 2Se phase being broadly distributed
between crystallographic sites and not populating any distinct atom-atom distances. When elemental Se
was included in these fits, the weight fraction refined towards a negligibly small value.
Figure 5.5c shows the PDF of the same PVP-capped Ag 2Se nanocrystals after they were returned
to room temperature. Once again, the three-phase model with anti-PbCl 2-like Ag 2Se, orthorhombic Ag 2Se,
and elemental Se provides a close description of the PDF with R w = 5.4%. For this PDF, the weight fraction
of the orthorhombic phase refined to 41.9% and the elemental Se fraction refined to 5.7%. This result shows
that the anti-PbCl 2-like-to-cubic phase transition is at least partially reversible for these PVP-capped Ag 2Se
nanocrystals, a result which is analogous to the qualitative reversibility Sahu et al. demonstrated for smaller
"tetragonal" Ag 2Se nanocrystals. However, Sahu et al. also showed that this metastable phase is
161

increasingly unstable for larger Ag 2Se nanocrystals.
22
Similarly, Wang et al. showed that large (~125 nm)
oleylamine-capped metastable Ag 2Se nanocrystals irreversibly convert to the orthorhombic phase upon
heating.
16
In our case, the partial conversion of anti-PbCl 2-like Ag 2Se to the orthorhombic phase likely
occurs due a fraction of the nanocrystals undergoing a cubic-to-orthorhombic phase transition upon cooling,
rather than reverting to the metastable anti-PbCl 2-like phase at lower temperatures. Thus, our findings of
the partial-reversibility of this phase transition, along with partial conversion to the stable orthorhombic
phase, are consistent with the reported temperature-dependent behavior of this metastable material.
Concurrent with the collection of synchrotron X-ray total scattering data, synchrotron powder XRD
data were also collected on the same samples at each temperature. Rietveld refinements were performed to
those data and the results are shown in Figure 5.6 and refined crystallographic parameters are reported in
Table 5.3. In these refinements a good quality-of-fit was obtained with the same combinations of phases at
each temperature as in the PDF fits, suggesting good agreement between the local and average structures.

162

Table 5.3 Crystallographic parameters of the predominant Ag 2Se phase for PVP-capped nanocrystals from each of
the Rietveld refinement fits at different temperatures using beamline 11-ID-B.
T = 25 °C, Space group P2 1/n, Rietveld refinement Rw = 3.56%
a = 4.29 Å; b = 7.00 Å; c = 8.19 Å;  = 101.3°; V = 241.5 Å
3

atom x y z U iso
Se 0.329 0.250 0.141 0.0550
Ag1 0.739 0.022 0.346 0.0479
Ag2 0.240 0.352 0.447 0.0165
T = 120 °C, Space group Im3
̅
m, Rietveld refinement Rw = 1.36%
a = 4.98 Å
atom x y z U iso
Se 0.0 0.0 0.0 0.0635
Ag1 0.5 0.5 0.5 0.1240
Ag2 0.25 0.5 0.0 0.0180
Ag3 0.416 0.416 0.0 0.0322
T = 25 °C (upon cooling), Space group P2 1/n, Rietveld refinement Rw = 3.02%
a = 4.29 Å; b = 7.00 Å; c = 8.19 Å;  = 101.2°; V = 241.4 Å
3

atom x y z U iso
Se1 0.328 0.250 0.140 0.0150
Ag1 0.739 0.022 0.345 0.0529
Ag2 0.240 0.352 0.447 0.0456

163

Figure 5.6 Rietveld refinements of synchrotron powder XRD collected on PVP-capped Ag 2Se nanocrystals using
beamline 11-ID-B (λ = 0.143 Å). The anti-PbCl 2-like structure provides an excellent fit for this experimental data at
low temperatures, whereas the cubic structure provides an excellent for Ag 2Se that forms at high temperatures. While
the high-temperature data indicated phase-pure cubic Ag 2Se, the room-temperature data refined to mixtures of the
anti-PbCl 2-like phase (initial weight fraction: 79.1%, final weight fraction: 57.5%), the orthorhombic phase (initial
weight fraction: 15.9%, final weight fraction: 39.1%), and small amounts of elemental Se (initial weight fraction:
5.0%, final weight fraction: 3.2%).
164

5.5 Density Functional Theory
The phase space of Ag 2Se was explored computationally using ab-initio random structure searching
(AIRSS). In addition to the experimental orthorhombic P2 12 12 1 phase, a large number of other polymorphs
emerged (Figure 5.7c). This crowded Ag 2Se energy landscape is consistent with the experimental
observations of a complex phase space on the nanoscale.
15

Figure 5.7 (a) The phonon band structure of the anti-PbCl 2-like Ag 2Se phase. The structure is dynamically stable
since all modes have positive frequencies across the first Brillouin zone. (b) The electronic band structure of the
anti-PbCl 2-like phase computed using the HSE06 hybrid functional
46
showing that it is a narrow band gap
semiconductor. (c) The total energy plotted against the volume per formula unit for structures obtained through
searching (AIRSS) as well as the orthorhombic P2 12 12 1 ( ) and the anti-PbCl 2-like P2 1/n ( ) phases. The PBEsol
exchange-correlation functional is used here. (d) The P2 unit cell reported by Günter and Keusch. (e) The unit cell
in (d) optimized using DFT with the PBEsol functional. Significant structural changes take place – the adjacent
[200] planes shear in the [001] direction, and the Ag atoms move to different sites.

165

Intriguingly, the DFT calculations suggest the existence of Ag 2Se structures with lower energies
than the empirically stable, low-temperature orthorhombic phase. Notably, the energetics among different
phases appear to depend on the exchange-correlation functionals. In particular, the PBE exchange-
correlation functional, which often overestimates the lattice constant of solids, biases towards structures
that are less dense (e.g., those with large volumes per formula unit). On the other hand, the PBEsol
functional appears to give more reliable energy rankings, although there are still two phases predicted to be
more stable than the orthorhombic P2 12 12 1 phase. It is possible that the orthorhombic P2 12 12 1 phase is not
predicted to be the most energetically stable structure due to the neglect of entropic stabilization in our
calculations.
The anti-PbCl 2-like phase was also found through ab-initio random structure searching when
limiting the possible polymorphs of Ag 2Se to the P2 1/n space group. Here, the anti-PbCl 2-like phase was
~20 meV/atom higher than the orthorhombic polymorph using the PBEsol functional, and many other
theoretical polymorphs were predicted to lie between these two phases. We recomputed the energies of
selected low-energy phases using the LDA and PBE functionals, as well as the hybrid functional HSE06.
The anti-PbCl 2-like phase is found to be consistently higher in energy than the stable orthorhombic
polymorph, although the difference varies between 5 meV/atom and 25 meV/atom, as shown in Figure 5.8.

166

Figure 5.8 Relative energies between phases when computed using different exchange-correlation functionals. Phases
found by AIRSS are colored differently. In particular, PBE, which is known to overestimate the lattice constants of
solids, favors phases with large volumes, and such phases tend to have increased energy when computed using LDA
or PBEsol. Note that the rankings of stabilities between the Günter and Keusch P2 ( ), P2 12 12 1 ( ), and the P2 1/n
anti-PbCl 2-like ( ) phases are identical in all cases.

The calculated electronic structure of the anti-PbCl 2-like phase shows that it is a semiconductor
with a narrow gap ~0.13 eV at the Γ-point, as shown in Figure 5.7b. We found that the orthorhombic
polymorph also has a narrow gap, at ~0.05 eV, consistent with previous DFT work.
47
The band gap openings
only take place with HSE06 function, as both polymorphs have no band gap if the PBEsol functional is
used instead. These band gaps are quite close to experimentally determined optical band gap measurements
for these two polymorphs of Ag 2Se.
21,48
The phonon band structure can be used to reveal the dynamical
stability of a structure, as any distortions that reduce the total energy would manifest in phonon modes with
imaginary frequencies (often plotted as negative values). Our phonon calculations find no such imaginary
(negative) frequencies in the band structure of the anti-PbCl 2-like phase, as shown in Figure 5.7a. This
confirms that the structure is indeed dynamically stable.
Interestingly, the P2 unit cell reported by Günter and Keusch appears to be far from a local
minimum on the potential energy surface; significant structural rearrangements occur during geometry
relaxation calculations (Figure 5.7d,e), and the relaxed structure is still ~20 meV/atom higher in energy
167

than the anti-PbCl 2-like phase. Although the instability of Günter and Keusch’s P2 phase means that it is
unlikely to exist in a bulk form, strain involved in thin films could play an important role for stabilization
of this polymorph, but it cannot be sustained with increasing thickness.
5.6 Experimental
5.6.1 PVP Solvothermal Synthesis of Ag 2Se Nanocrystals
PVP-capped Ag 2Se nanocrystals were prepared by modifications of the method of Wang et al.
16
Particles
prepared for lab diffraction were made by adding 0.344 g PVP (MW = 55,000), 0.030 g of SeO 2, and 0.034
g of AgNO 3 dissolved in 10 mL of dimethyl formamide (DMF) with stirring. Oleic acid (5 mL) was
subsequently added and the solution was sealed in a 40 mL Teflon-lined pressure reactor. The contents
were heated in a furnace for 9-12 h at 200 °C. For immediate lab diffraction, the resulting nanocrystal
suspensions in DMF were equally split between two 45 mL centrifuge tubes, filled to volume with ethanol,
and centrifuged. The products were then re-dispersed in 5 mL hexanes in each centrifuge tube, vortex
mixed, and washed with an additional 20 mL of ethanol followed by centrifugation. The products were then
re-dispersed in hexanes and dropcast for immediate characterization. For synchrotron analysis, the particles
were made using an identical procedure, but with a smaller molecular weight PVP (MW = 10,000, 0.25 g).
Reaction products were purified by four cycles of washing with ethanol and centrifugation, after which they
were dried at 45 °C under vacuum. Individual samples were screened for phase-purity using laboratory X-
ray diffraction. Multiple samples of Ag 2Se nanocrystals were then combined to achieve a quantity sufficient
for synchrotron X-ray total scattering experiments (~30 mg).
5.6.2 Oleylamine Synthesis of Ag 2Se Nanocrystals
Oleylamine-capped Ag 2Se nanocrystals were prepared by a modification of the method of Wang et al.
16

SeO 2 (0.030 g) was loaded into a three-neck round bottom flask. AgNO 3 (0.034 g) was added to a separate
two-neck round bottom flask. 6 mL and 2 mL of oleylamine were added to the three-neck and two neck-
flasks, respectively. The three-neck flask was degassed for 1 h under vacuum at 70 °C. Less aggressive
degassing was implemented for the two-neck flask since AgNO 3 is prone to reduction by oleylamine at
168

relatively low temperatures; the two-neck flask was degassed at room temperature for 30 min at room
temperature and at 65 °C for 30 min, allowing full dissolution of the AgNO 3. The two-neck flask was
covered with foil to prevent light exposure. Both flasks were then filled with nitrogen, and the three-neck
flask was ramped to 180 °C and kept at that temperature for 5 min. Then, the Ag-oleylamine solution was
injected into the three-neck flask containing Se, and the reaction was allowed to recover to 180 °C, at which
point the reaction was left for 1 h. Once cool, the product was split into two 15 mL centrifuge tubes, each
of which was filled to volume with toluene and centrifuged for 5 min. The supernatant was decanted, and
Ag 2Se product was re-dispersed in hexanes and dropcast for immediate powder XRD analysis. While only
washing the particles once produced a larger background in the diffraction pattern, we found that more
aggressive washing accelerates relaxation of Ag 2Se to the orthorhombic phase and makes obtaining a phase-
pure product difficult.
5.6.3 NHC Synthesis of Ag 2Se Nanocrystals
N-heterocyclic carbene-capped Ag 2Se nanocrystals were prepared as detailed by Lu et al.
26

5.6.4 Characterization
Laboratory powder X-Ray diffraction patterns were taken on a Rigaku Miniflex 600 powder X-ray
diffractometer with a Cu Kα radiation source (λ = 1.5406 Å). Nanocrystal suspensions in hexanes were
drop-cast onto a silicon zero diffraction substrate, dried, and immediately placed in the diffractometer for
analysis.
Samples for synchrotron X-ray total scattering were ground in an agate mortar and pestle and
loaded into Kapton tubes that were sealed with epoxy. X-ray total scattering data were collected using the
11-ID-B beamline at the Advanced Photon Source with a photon wavelength of λ = 0.143 Å. A CeO 2
standard was used to calibrate sample-detector distance and data was collected on an empty Kapton tube in
order to perform background subtraction. A hot air blower was used to regulate sample temperature during
data collection. Data were collected at 25 °C, then 120 °C, and subsequently at 25 °C upon cooling again.
A reduced scattering structure function, S(Q), with the appropriate corrections for instrumental parameters,
169

scattering by Kapton, multiple scattering, sample absorption, X-ray polarization, and Compton scattering,
was obtained from the data using the program PDFgetX3. A pair distribution function (PDF), G(r), was
obtained by direct Fourier transformation of S(Q) with a 0 Å
–1
< Q < 27 Å
–1
. PDFs were analyzed using the
program PDFGUI. The parameter Q damp was fixed at 0.075 and the parameters for scale and the linear
atomic correlation factor were allowed to refine.
All Rietveld refinements were performed using the program GSAS-II. Instrument parameters U, V,
W, X, and Y were allowed to refine. Preferred orientation was accounted for by refinement of four spherical
harmonics variables. Diffuse background scattering was fit with fixed points and a shifted Chebychev
function with 6 parameters for laboratory powder XRD data and 36 parameters for synchrotron XRD data.
Transmission electron microscopy (TEM) micrographs were taken for drop-cast dispersions of
Ag 2Se nanocrystals supported on holey carbon-coated copper grids (Ted Pella, Inc.). Grids were dried in a
vacuum oven overnight at room temperature for the removal of volatile organics. A JEOL JEM-2100F
microscope with a Gatan Orius charge coupled device camera was used to take TEM images at an operating
voltage of 200 kV. TEM energy dispersive spectroscopy (TEM-EDX) data was acquired using an
accelerating voltage of 80 kV. Using scanning transmission electron microscopy, the probe current was 400
pA, and the probe size approximately 1.5 nm.
5.6.5 Density Functional Theory Calculations
Ab initio random structure searching (AIRSS)
49,50
was used to explore the configuration space of Ag 2Se.
Plane wave density functional calculations are performed using CASTEP
51
for searching with PBE,
52

PBEsol
53
functionals and on-the-fly generated core-corrected pseudopotentials. A plane-wave cutoff energy
of 340 eV is used and the reciprocal space is sampled with Monkhorst-Park grid with spacing 0.07 2π Å
–1
.
Additional DFT calculations for final energies and band structures are performed using the VASP
54,55

package with the PBE_54 PAW dataset and a plane wave cutoff energy of 550 eV. The reciprocal space is
sampled with a Gamma-centered Monkhorst-Park grid with 0.04 2π Å
–1
spacing. Finite-displacement
phonon calculations are performed using the Phonopy
56
package and VASP using the PBEsol functional.
The hybrid HSE06 functional
46
is used for the band structure calculations. We found that the inclusion of
170

spin orbit coupling only gives rise to minor changes in the electronic band structure, hence they are only
included in calculations concerning the size of the band gap. The AiiDA framework
57,58
is used to automate
the DFT calculation workflows and persevere their provenance. Electronic and phonon band structure
diagrams were generated using the sumo package.
59

5.7 Conclusions
To conclude, we have shown that the metastable polymorph of colloidal Ag 2Se nanocrystals, commonly
referred to as the “tetragonal” phase, more accurately adopts an anti-PbCl 2-like structure. DFT calculations
reveal that this polymorph is a true local minimum within the energy-structure landscape of Ag 2Se.
Electronic structure calculations indicate that anti-PbCl 2-like Ag 2Se is a narrow-band gap semiconductor.
In addition, we find that this phase space is crowded with theoretical, relatively low-energy polymorphs,
which may explain the preponderance of reports of different Ag 2Se polymorphs on the nanoscale.
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174

Chapter 6. Synthesis and Electrocatalytic HER Studies of Carbene-Ligated Cu3-xP
Nanocrystals

*Published in ACS Appl. Mater. Interfaces 2020, 12, 14, 16394–16401.

6.1 Abstract
N-heterocyclic carbenes (NHCs) are an important class of ligands capable of making strong carbon-metal
bonds. Recently, there has been a growing interest in the study of carbene-ligated nanocrystals, primarily
coinage metal nanocrystals, which have found applications as catalysts for numerous reactions. The general
ability of NHC ligands to positively affect the catalytic properties of other types of nanocrystal catalysts
remains unknown. Herein, we present the first carbene-stabilized Cu 3–xP nanocrystals. Inquiries into the
mechanism of formation of NHC-ligated Cu 3-xP nanocrystals suggest that crystalline Cu 3–xP forms directly
as a result of a high-temperature metathesis reaction between a tris(trimethylsilyl)phosphine precursor and
an NHC-CuBr precursor, the latter of which behaves as a source of both carbene ligand and Cu
+
. To study
the effect of the NHC surface ligands on catalytic performance, we tested the electrocatalytic hydrogen
evolving ability of the NHC-ligated Cu 3–xP nanocrystals and found they possess superior activity to
analogous oleylamine-ligated Cu 3–xP nanocrystals. Density functional theory calculations suggest that the
NHC ligands minimize unfavorable electrostatic interactions between the copper phosphide surface and H
+

during the first step of the hydrogen evolution reaction, which likely contributes to the superior performance
of NHC-ligated Cu 3–xP catalysts as compared to oleylamine-ligated Cu 3–xP catalysts.
6.2 Introduction
N-Heterocyclic carbene (NHC) ligands have significant value as a result of their structural diversity,
chemical stability, and strong electron donation that leads to a high coordinating ability with metals.
1
While
NHCs are now commonly employed as neutral L-type ligands for molecular complexes, they are also
gaining increasing utility as ligands to support the steric stabilization of nanocrystals.
2–7
And just as NHC
ligands are widely utilized in molecular complexes for homogeneous catalysis as a result of their steric and
electronic properties,
8
supporting NHC ligands are becoming of interest for heterogeneous nanocrystal
catalysts. It has been demonstrated that NHC ligands have the ability to enhance nanocrystal catalyst
175

stability and increase nanocrystal catalyst activity and/or selectivity.
9–12
NHC-stabilized nanocrystals have
been shown to display catalytic activity toward, for example, hydrogenations and semihydrogenations,
9,12–
14
lactonization,
10
asymmetric arylations,
15
Buchwald-Hartwig aminations,
16
and cross-coupling reactions.
15

NHC-stabilized nanocrystals have also been shown to be competent electrocatalysts for CO 2 reduction.
11,17
For example, Cao et al. investigated the use of NHC-stabilized Au nanocrystals as electrocatalysts for the
reduction of CO 2 to CO. Interestingly, the Au nanocrystal catalyst with surface-bound carbene ligands
exhibited a higher Faradaic efficiency for CO 2 reduction to CO than did bare (or ligand-less) Au
nanoparticles; it was further shown that the NHC affected the mechanistic pathway of catalysis.
17

Despite the proven benefits of applying NHC ligands to nanocrystal catalysts, they have thus far
only been supported on metal nanocrystal catalysts (e.g., Ru, Au, Pt, Pd, Cu).
9–18
Therefore, the potential
utility of NHC ligands as supporting ligands for other types of nanocrystal catalysts is currently unknown.
Certain metal phosphide nanocrystals have emerged as an important class of catalysts for reactions such as
hydrodesulfurization,
19–21
hydrodeoxygenation,
22
and the hydrogen evolution reaction (HER).
23
Along these
lines, self-doped copper phosphide (Cu 3 xP) nanocrystals have been shown to be efficient Janus catalysts
for overall electrochemical water splitting.
24,25
Synthetic methods for the preparation of colloidal Cu 3 xP
nanocrystals remain underdeveloped, however. Early reports utilized trioctylphosphine (TOP) to
phosphidize zero-valent Cu nanocrystals under relatively high-temperature conditions (320 °C).
26
More
recently, reactive phosphines, such as tris(trimethylsilyl)phosphine ((TMS) 3P), have been introduced as the
phosphide source, which helped to lower reaction temperatures to 120 °C.
27,28

Herein, we present a direct synthetic route to NHC-stabilized Cu 3-xP nanocrystals to explore the
effect of the carbene ligand when using the resulting nanocrystals as HER electrocatalysts. The direct
synthesis of NHC-stabilized Cu 3-xP nanocrystals circumvents the need for a post-synthetic ligand exchange
for the installation of carbenes on the nanocrystal surface. To the best of our knowledge, this is the first
example of a metal phosphide nanocrystal supported by a carbene ligand. The NHC-stabilized Cu 3-xP
nanocrystal synthesis, characterization, and electrocatalytic HER studies will be discussed in detail, and
176

density functional theory (DFT) calculations were carried out to elucidate the electronic effects of NHC
ligands on catalysis.
6.3 Experimental
6.3.1 Materials and General Procedures
Reagents and solvents were purchased from commercial sources and used as received, unless otherwise
noted. Benzimidazole (C 7H 6N 2, 99%), 1-bromotetradecane (C 14H 29Br), copper( ) oxide (99.9%), potassium
carbonate (K 2CO 3, anhydrous, 99%), and 1,4-dioxane were purchased from Alfa Aesar. Copper(I) bromide
(98%) was purchased from Strem Chemicals. 1-octadecene (ODE, technical grade, 90%), oleylamine
(technical grade, 70%), tris(trimethylsilyl)phosphine ((TMS) 3P, 95%) and a phosphorus ICP standard (1000
ppm in 2% aqueous nitric acid) were purchased from Sigma-Aldrich. The copper ICP standard (1000 ppm
in 2% aqueous nitric acid) was purchased from Perkin Elmer. Reactions involving air- or moisture-sensitive
compounds were conducted under a nitrogen atmosphere by using standard Schlenk techniques. 1-
Octadecene and oleylamine were degassed for 4 h at 105 °C and then overnight at room temperature prior
to use.
6.3.2 Preparation of (TMS) 3P Stock Solution
Caution! (TMS) 3P is a pyrophoric material that must be handled with care. In a N 2 glove box, an ampule
containing 1 g of liquid (TMS) 3P was opened and the contents were added to a Schlenk flask containing 40
mL ODE (dried as mentioned above) to make a 0.1 M stock solution that was used for all subsequent
reactions.
6.3.3 Synthesis of NHC-Stabilized Cu 3-xP Nanocrystals
In a typical Cu 3xP nanocrystal synthesis, a solution of NHC-CuBr (195 mg, 0.300 mmol) in 6 mL ODE
was prepared. The mixture was subjected to vacuum and held for 1 h at 115 ˚C to remove any adventitious
water. NHC-CuBr was completely dissolved in ODE after 1 h of stirring at 115 ˚C. Subsequently, the
temperature was raised to 250 ˚C and 0.5 mL of the 0.1 M (TMS) 3P stock solution was rapidly added into
the NHC-CuBr solution. The solution immediately became black and turbid upon phosphine addition. After
177

2 min, the reaction was quenched by removing the heat and placing the flask in a room temperature water
bath. To remove 1-octadecene and any unreacted precursors and by-products, the Cu 3xP nanocrystals were
washed by splitting the crude reaction mixture into two 40-mL centrifuge tubes that were then filled to
volume with acetone. The centrifuge tubes were sonicated for 10 min and centrifuged for 5 min at 6000
rpm. For long-term colloidal stability, particles were washed only once with acetone and redispersed in
toluene or tetrachloroethylene (TCE). For electrochemical studies, an additional partial wash was
performed in which the product of one centrifuge tube was redispersed in 5 mL of hexanes, washed with
an additional 10 mL of acetone in the same manner as described above, and finally redispersed in 5 mL of
hexanes. This hexanes suspension could then be dropcast directly onto a glassy carbon electrode for
catalysis studies.
6.3.4 Characterization
UV-vis-NIR spectroscopy was carried out on a Perkin-Elmer Lamba 950 spectrophotometer equipped with
a 150-mm integrating sphere, using a quartz cuvette for liquid samples. Spectra were taken in
tetrachloroethylene to reduce solvent contributions to the spectrum in the NIR region. Powder X-ray
diffraction (XRD) data was collected using a Rigaku Ultima IV diffractometer in parallel beam geometry
(2-mm beam width) using Cu Ka radiation (λ = 1.54 Å). Samples were prepared by drop casting the
nanocrystals onto zero-diffraction, single crystal Si substrates. X-ray photoelectron spectra (XPS) were
obtained using a Kratos Axis Ultra X-ray photoelectron spectrometer with an analyzer lens in hybrid mode.
High-resolution scans were performed using a monochromatic aluminum anode with an operating current
of 6 mA and voltage of 10 kV using a step size of 0.1 eV, a pass energy of 40 eV, and a pressure range
between 1 3  10
–8
Torr. The binding energies for all spectra were referenced to the C 1s core level at 284.8
eV. Transmission electron microscopy (TEM) analysis was performed on a JEOL JEM-2100 microscope
at an operating voltage of 200 kV equipped with a Gatan Orius CCD camera. Samples for TEM analysis
were prepared from dilute purified nanocrystal suspensions drop cast from hexanes dispersions onto 400
mesh carbon-coated copper grids (Ted Pella, Inc.). Thermogravimetric analysis (TGA) was performed on
178

a TGA Q50 instrument with a heating rate of 10 °C·min
−1
. 8-10 mg samples were used for all TGA studies,
and samples were measured by TGA after one full wash and one partial wash, identical to the workup used
for catalytic studies. More details on the ligand density calculations determined by TGA are provided in in
section 6.6. Fourier transform infrared spectroscopy (FT-IR) was performed on a Bruker Vertex 80 FT-IR
spectrometer. Samples were prepared as a powder within a matrix of KBr. Inductively-coupled plasma
optical emission spectroscopy (ICP-OES) was performed on an iCap 7400 ICP. All samples were digested
with 2 mL of concentrated nitric acid and subsequently diluted to 25 mL with Millipore water in a
volumetric flask. Phosphorus and copper ICP standards were prepared at different concentrations (0.1 ppm,
0.8 ppm, 2 ppm, 4 ppm, 10 ppm) to construct a five-point calibration curve from which the sample
concentrations of Cu and P could be determined. NMR spectra were taken on a Varian VNMRS600 in
CDCl 3.
6.3.5 Electrochemical Methods
Electrochemistry experiments were carried out using a VersaSTAT 3 potentiostat in a three-electrode
configuration electrochemical cell under an inert N 2 atmosphere. A rotating disk electrode (RDE, glassy
carbon insert, 0.196 cm
2
surface area) was used as the working electrode. The glassy carbon surface was
polished with 0.05 μm Al 2O 3 polish powder and sonicated in Millipore water prior to use. A graphite rod,
purchased from Graphite Machining, Inc. (Grade NAC-500 Purified, < 10 ppm ash level), was used as the
counter electrode. The reference electrode, placed in a separate compartment and connected by a porous
Teflon tip, was based on an aqueous Ag/AgCl/1.0 M KCl electrode (purchased from CH Instrument, Inc.).
All potentials reported in this paper were converted to the reversible hydrogen electrode (RHE) by adding
a value of (0.235 + 0.059 × pH) V. 0.5 M H 2SO 4 aqueous solution was used as the electrolyte and was
purged with nitrogen thoroughly prior to electrochemical testing. Cyclic voltammograms for double layer
capacitance (C dl) measurements were taken over a 100 mV potential window centered around the open
circuit potential (OCP) at scan rates of 10, 20, 30, 40, 50, and 60 mV/s. The capacitance current obtained
from the current difference (Δi = i a – i c) at OCP was plotted against the scan rate. The slope is twice the
value of the double layer capacitance. Controlled potential electrolysis (CPE) measurements to determine
179

long-term stability and Faradaic efficiency were conducted in a sealed two-chambered H cell where the
first chamber held the working and reference electrodes in 40 mL of 0.5 M H 2SO 4 aqueous solution and the
second chamber held the counter electrode in 25 mL of 0.5 M H 2SO 4 aqueous solution. The two chambers
were both under N 2 and separated by a fine porosity glass frit. CPE experiments were performed with a
glassy carbon plate electrode (6 cm × 1 cm × 0.3 cm; Tokai Carbon USA) as the working electrode and a
graphite rod as the counter electrode. The reference electrode was a Ag/AgCl/1.0 M KCl (aq.) electrode
separated from the solution by a porous Teflon tip. Using a gas-tight syringe, 2 mL of gas was withdrawn
from the headspace of the H cell and injected into a gas chromatography instrument (Shimadzu GC-2010-
Plus) equipped with a BID detector and a Restek ShinCarbon ST Micropacked column. To determine the
Faradaic efficiency, the theoretical H 2 amount based on total charge flowed was compared with the GC-
detected H 2 produced from CPE. Electrochemical impedance spectroscopy (EIS) measurements were
carried out at different overpotentials in the frequency range of 100 kHz – 1 Hz with 10 mV sinusoidal
perturbations. Experimental EIS data were analyzed and fitted with the ZSimpWin software using a two-
time constant parallel model. All of the polarization curves presented herein were corrected for iR loss
according to the following equation:
E corr = E mea – iR s
where E corr is the iR-corrected potential, E mea is the experimentally measured potential, and R s is the solution
resistance extracted from the fitted EIS data.
6.3.6 Density Functional Theory
Density functional theory (DFT) calculations at the B97/def2-SVP level of theory
29,30
were performed using
the ab initio quantum chemistry software Q-Chem
31
to probe the electronic effects of L-type NHC and
alkylamine ligands on proton binding to a Cu 3P catalyst.
180

6.4 Results and Discussion
6.4.1 Synthesis and Characterization
We previously reported that a metathesis reaction between bromo[1,3-(ditetradecyl)benzimidazol-2-
ylidene]metal(I) (NHC-MBr, M = Ag, Cu) complexes and bis(trialkylsilyl) chalcogenides ((R 3Si) 2E, where
E = S, Se) under ambient conditions yields monodisperse M 2E nanocrystals, where the NHC ligands bearing
long-chain alkyl substituents remain coordinated to the nanocrystal surface and provide excellent colloidal
stability.
7
Here, we extended the use of the same NHC-CuBr precursor to the preparation of Cu 3 xP
nanocrystals by reaction with (TMS) 3P. Initial attempts to synthesize Cu 3xP nanocrystals at room
temperature resulted in an amorphous product, as revealed by powder X-ray diffraction (XRD). Therefore,
the reaction temperature was raised to 250 °C and (TMS) 3P was rapidly injected into a solution of NHC-
CuBr in the high-boiling, non-coordinating solvent 1-octadecene. This resulted in the direct formation of
Cu 3xP nanocrystals.
The as-synthesized Cu 3 xP nanocrystals (1) were confirmed by powder XRD to be phase-pure
hexagonal Cu 3xP, with lattice parameters determined by a Le Bail fit of a = 6.9376(14) Å and c =
7.1462(26) Å, which agree with literature values (PDF no. 00-002-1263, Figure 6.1a). The UV-vis-NIR
absorption spectrum displays a characteristic LSPR band at ~1360 nm for the resulting nanocrystals (Figure
6.2), as expected due to copper vacancies in the structure.
27,28
Inductively coupled plasma optical emission
spectroscopy (ICP-OES) analysis of the as-synthesized product confirms a substoichiometric average
composition of Cu 2.30P, consistent with the copper-poor composition of Cu 3–xP, which is known to allow a
wide range of compositions from 0.1 < x < 0.7.
32
Figure 6.1c illustrates a representative transmission
electron microscopy (TEM) image of the quasi-spherical Cu 3xP nanocrystals. The nanocrystals have a
mean diameter of 6.7  1.1 nm (N = 300 counts), and high-resolution TEM (HR-TEM) reveals their apparent

181

Figure 6.1 (a) Powder XRD pattern and (c) representative TEM micrograph of NHC-stabilized Cu 3-xP (1). (b)
Powder XRD pattern and (d) representative TEM micrograph of oleylamine-stabilized Cu 3-xP (2). The stick patterns
provided in the powder XRD patterns are for hexagonal Cu 3–xP (PDF# 00-002-1263).

single-crystalline nature with a lattice spacing of d = 0.20 nm corresponding to the (300) planes of the
expected hexagonal phase (Figure 6.3).
Suspensions of 1 are colloidally stable under inert atmosphere, which can be ascribed to steric
stabilization from legacy surface-bound NHC ligands, as evidenced by the presence of a N 1s peak from
the NHC in the X-ray photoelectron spectrum (XPS) of the isolated nanocrystals (Figure 6.4), with further
support from solution
1
H NMR spectroscopy (vide infra).The high-resolution XPS spectrum of the Cu 2p
region confirms the presence of Cu
+
in the Cu 3 xP nanocrystals with peaks centered at the expected binding
energies of Cu 2p 1/2 at 952.4 eV and 2p 3/2 at 932.6 eV, and excludes any significant amount of Cu
2+
, in
which case two Cu
2+
satellite peaks at 942 eV and 962 eV would be observed (Figure 6.5a).
25,33

Additionally, the high-resolution XPS spectrum of the P 2p region shows characteristic binding energies
for P
3–
(2p 1/2 at 129.2 eV, 2p 3/2 at 128.4 eV), with a small amount of oxidized P species (i.e., PO x) observed
at a binding energy of 132.5 eV (Figure 6.5b), which is within the range of reported binding energies for
oxidized P species for copper phosphide.
24, 25, 33-35
The oxidative stability of the Cu 3 xP nanocrystals is in
agreement with previously observed results.
28

To further investigate the synthetic role of the NHC ligand, a control reaction was carried out in
which the NHC-CuBr complex was replaced by CuBr in the presence of stoichiometric oleylamine, keeping
the Cu:ligand molar ratio at 1:1.
182

Figure 6.2 (a) UV-vis-NIR spectra of crystalline NHC-stabilized Cu 3-xP (1) and (b) amorphous oleylamine-
stabilized Cu 3-xP (2).

Figure 6.3 Representative HR-TEM image reveals the apparent single-crystalline nature of the nanocrystals 1. The
above lattice fringes with spacing d = 0.20 nm correspond to the (300) planes of the hexagonal phase of Cu 3-xP.

Figure 6.4 X-ray photoelectron spectrum confirms the presence of the NHC on the nanocrystal surface, as indicated
by the N 1s peak from the surface-bound NHC on Cu 3-xP (1).
183

Figure 6.5 High-resolution XPS spectra of (a) Cu 2p and (b) P 2p regions for 1.

The reaction was otherwise performed identically. Interestingly, this control experiment yielded nearly
amorphous copper phosphide nanoparticles (2) (Figure 6.1b, d), which also display a broad plasmon
resonance feature in the NIR (Figure 6.2). Elemental analysis by ICP-OES of 2 reveals an average
composition of Cu 1.96P, deviating from the range of reported compositions for crystalline Cu 3–xP.
Transmission electron micrographs of the oleylamine-stabilized particles give a similar mean diameter of
5.5  1.0 nm (N = 300 counts).
This control experiment provides two insights. First, it demonstrates that copper phosphide
nanoparticles (albeit quasi-amorphous) can be synthesized using oleylamine as a ligand as long as it is not
used in excess (i.e., Liu et al. observe the reduction of Cu
+
to Cu nanocrystals without phosphidation by
(TMS) 3P when oleylamine is used as a solvent in the absence of TOP
28
). Second, it indicates that the NHC
ligand plays a significant role in directing the crystallinity of the resulting product. Carbene-influenced
nanocrystal growth is not wholly unprecedented; there exists evidence that nanoparticles synthesized in
imidazolium-based ionic liquids nucleate and grow in the presence of carbene ligands formed in-situ by
deprotonation of the imidazolium cation.
36–38
In that vein, we previously observed that when imidazolium-
based ionic liquids are used to synthesize nickel phosphide nanocrystals, phase-pure Ni 2P forms, as
compared to a mixture of phases that results from a different reaction pathway when using octadecene
instead of the ionic liquid under otherwise identical conditions.
39

184

Figure 6.6. (a) Powder XRD pattern and (b) UV-vis-NIR spectrum of the Cu nanoparticles resulting from heating up
the oleylamine-CuBr mixture to 250 °C without injecting (TMS) 3P. The nanoparticles are amorphous as they display
no reflections in the XRD pattern; however, they have a diagnostic LSPR feature centered at 700 nm characteristic of
Cu nanoparticles.

To explain the disparate degrees of crystallinity observed for 1 and 2, we noted that these two
reactions visibly differ in the process of nucleation –– while heating the oleylamine-CuBr mixture to the
250 ˚C reaction temperature, the solution transitions from a light-yellow color of dissolved oleylamine-
CuBr at low temperatures to a dark blue-black color at temperatures greater than ~215 ˚C. Upon injection
of the (TMS) 3P precursor at 250 ˚C, the reaction mixture immediately turns black and becomes turbid,
indicating the formation of Cu 3-xP. We hypothesized that the color changes that precede the injection of
(TMS) 3P could be indicative of Cu nanoparticle formation induced by the reduction of Cu
+
by oleylamine.
To test this hypothesis, we performed a control experiment in the absence of any phosphorus source, in
which we heated the oleylamine-CuBr mixture to 250 ˚C and then quickly cooled the reaction mixture to
room temperature. The electronic absorption spectrum of the product reveals a single, broad peak in the
visible region centered at 700 nm (Figure 6.6), attributable to LSPR absorption of Cu nanoparticles.
40–42

Powder XRD of the product confirms it is amorphous in nature (Figure 6.6). This result sheds light on the
mechanism of formation of 2; injection of the very reactive (TMS) 3P precursor phosphidizes amorphous
Cu nanoparticles and, despite the high temperature injection, leads to a persistent quasi-amorphous phase
of Cu 3-xP. It is known that amorphous materials are often stabilized when containing glass-forming elements
185

Figure 6.7 TGA traces of (a) oleylamine-stabilized (2) and (b) NHC-stabilized Cu 3-xP (1) nanocrystals.

including B, C, Si or P, which may explain why structural reorganization to crystalline copper phosphide
is not observed.
43

In contrast, no such cascade of color changes occurs prior to injection of (TMS) 3P in the presence
of the NHC ligand, indicating that copper nanoparticles do not form as intermediates. This difference is
likely due to the robust Cu–C bond within the NHC-CuBr precursor (i.e., Boehme and Frenking calculated
via DFT that the bond dissociation energy of the Cu–C bond of a CuCl complex of imidazole-2-ylidene
falls between 67-73 kcal/mol),
44
and the absence of the primary amine reducing agent. Therefore, rather
than proceeding through phosphidation of an amorphous Cu nanoparticle intermediate, the carbene
precursor produces crystalline Cu 3-xP directly through a metathesis reaction between NHC-CuBr and
(TMS) 3P to produce crystalline Cu 3-xP and TMS-Br. Thus, the NHC ligand serves dual purposes, namely,
it affords colloidal stability to the resulting nanocrystals and it circumvents the formation of zero-valent Cu
intermediates, allowing crystalline Cu 3-xP to be accessed directly. Thus, in general, using metal-carbene
precursors to make metal pnictide or metal chalcogenide nanocrystals may prove to be beneficial for
chemistries that are susceptible to proceeding through undesirable zero-valent intermediates.
The carbene ligand used herein binds tightly to the nanocrystal surface but is more bulky than
oleylamine.
3
To determine the density of ligands on the surface of 1 and 2, thermogravimetric analysis
(TGA) was performed on isolated powders of both samples (Figure 6.7). The ligand density was determined
to be ~1.0 ligands/nm
2
for 1 and ~2.5 ligands/nm
2
for 2 (see ligand density calculations below for

186

Figure 6.8 (a) Bottom:
1
H NMR spectrum of the NHC-CuBr precursor in CDCl 3. Top:
1
H NMR spectrum of the NHC-
capped Cu 3-xP nanocrystals (1) dispersed in CDCl 3. In comparing these two spectra, it is clear that the carbene is bound
to the nanocrystal surface, as the carbene resonances within the top spectrum all exhibit significant broadening. This
broadening is most clearly shown in the inset, which highlights the aromatic region of the spectrum containing the
benzimidazole ring. (b)
1
H NMR spectrum of the oleylamine-capped Cu 3-xP nanocrystals (3) dispersed in CDCl 3 after
ligand exchange. Notably, there are no peaks observed in the aromatic region (indicating the absence of carbene
ligands, see top inset) and two broad peaks from 5.30–5.45 ppm are observed corresponding to the alkenyl protons of
oleylamine (bottom inset). Chemical shifts of all spectra were referenced with respect to the solvent residual peak of
CDCl 3 at 7.26 ppm.

calculation details). This finding demonstrates that, despite being a stronger binding L-type ligand, the
steric bulk of the carbene prevents 1 from having a higher ligand density than 2.
Due to the utility of Cu 3xP electrocatalysts for water splitting,
24,25,45
we aimed to test these carbene-
stabilized Cu 3 xP nanocrystals for HER to evaluate both their potential as electrocatalysts and the effect the
NHC ligand has on catalysis. To evaluate the effect of the carbene on catalysis, we sought to compare the
HER activity of carbene-stabilized Cu 3-xP nanocrystals to oleylamine-stabilized Cu 3-xP nanocrystals.
However, since 2 differs both in the identity of the supporting ligand and the degree of crystallinity of the
nanocrystals, a straightforward comparison of the HER activity of 1 and 2 cannot be cleanly made.
Therefore, we synthesized crystalline, carbene-stabilized Cu 3-xP nanocrystals and then performed a post-
synthetic ligand exchange under forcing conditions by dispersing 1 in an excess of oleylamine at 85 °C for
2 h.
The
1
H NMR spectrum of 1 prior to the ligand exchange clearly indicates the binding of the carbene
to the nanocrystal surface, as the signature resonances of the NHC ligand are significantly broadened
compared to the NHC-CuBr precursor (Figure 6.8a).
187

Figure 6.9 (a) TEM of the Cu 3-xP nanocrystals following ligand exchange. There is no statistically significant
difference in size between the as-synthesized Cu 3-xP nanocrystals (diameter of 6.7  1.1 nm) and the nanocrystals
resulting after ligand exchange (diameter of 6.7  1.5 nm). (b) TGA of 3. A larger mass loss is associated with
greater ligand density of ligands on the surface (3.3 ligands/nm
2
).

The
1
H NMR spectrum of the ligand-exchanged Cu 3-xP nanocrystals (3) indicates that ligand exchange is
quantitative under these conditions, as no sign of the signature benzimidazole resonances remains in the
aromatic region. Furthermore, the two peaks in the range of 5.26–5.46 ppm are diagnostic of a dynamic
equilibrium of bound/free oleylamine on the surface of the nanocrystal (Figure 6.8b).
46,47
Interestingly,
while oleylamine binding is a dynamic process on the NMR timescale, no resonances associated with a free
carbene are observed in the
1
H NMR spectrum of 1, reiterating that the carbene binds more tightly to the
nanocrystal surface than oleylamine.
TGA analysis of 3 returns a higher ligand density than that of 1 or 2, at 3.3 ligands/nm
2
, which is
not surprising considering the ligand exchange step was performed with a large excess of oleylamine,
whereas the preparations of 1 and 2 maintained Cu:ligand ratios of 1:1. Importantly, the nanocrystals
maintain their crystallinity after ligand exchange and show no statistically significant change in nanocrystal
size, as verified by TEM analysis (Figure 6.9).
188

6.4.2 Electrocatalytic HER Studies
To investigate the electrocatalytic HER activity of 1 and 3, detailed electrochemical measurements were
performed in a three-electrode setup with N 2-saturated 0.5 M H 2SO 4 aqueous electrolyte. 1 and 3 were
deposited onto glassy carbon electrodes by directly drop-casting the respective hexane suspensions without

Figure 6.10 Polarization curves of 1 and 3 on GCE with current normalized by (a) the geometric surface area of
electrode and (b) electrochemical active surface area. All measurements were performed in N 2-saturated 0.5 M H 2SO 4
solutions with a scan rate of 5 mV/s.

Table 6.1 Overview of the HER performance of 1 and 3
Catalyst 1 3
Onset (V vs. RHE) -0.34 -0.65
𝜂 10 𝑚𝐴 /𝑐𝑚
2 (V) 0.45 0.86
Tafel slope (mV/dec) 85 228
R ct ( ) 19.7 (η = 0.44 V)
951 (η = 0.54
V)
ECSA (cm
2
)
a
3.59 0.71
Faradaic efficiency (%) 81.3 ± 0.5 72.1 ± 0.1
a
ECSA = C dl/C s, C s = 0.035 mF/cm
2
.
48,49
189

further modifications. In general, 1 exhibits better overall HER activity than 3 (Figure 6.10 and Table 6.1);
that is, the overpotential to reach 10 mA/cm
2
current density is 0.45 V for 1 and 0.86 V for 3, and 1 shows
a much lower Tafel slope of 85 mV/dec as compared to the 228 mV/dec for 3. The superior activity of 1 is
correlated with a lower charge transport resistance (R ct), as revealed by the electrochemical impedance
spectroscopy (EIS). Figures 6.11 and 6.12 show the EIS responses of 1 and 3, which are described by a
two-time constant parallel model (Figure 6.13). In both cases, the R ct value decreases at larger
overpotentials (Table 6.2), as expected for an enhanced HER rate with increased catalytic driving force,
and 1 exhibits lower R ct values in comparison to 3. For instance, at an overpotential of 0.44 V, the R ct of 1
is only 19.7 , whereas the R ct of 3 is 951  at an overpotential of 0.55 V. The lower R ct and Tafel slope
of 1 suggest that the HER kinetics are much more favored on the surface of 1 than 3.

Figure 6.11 EIS responses of 1 (markers) with respective fits (lines) at variable potentials vs. RHE. (a) Nyquist plots;
(b) and (c) Bode plots. All measurements were performed in N 2-saturated 0.5 M H 2SO 4 solutions.

Figure 6.12 EIS responses of 3 (markers) with respective fits (lines) at variable potentials vs. RHE. (a) Nyquist plots;
(b) and (c) Bode plots. All measurements were performed in N 2-saturated 0.5 M H 2SO 4 solutions.

190

Figure 6.13 The two-time constant parallel equivalent circuit used to fit the EIS response of the HER on the catalyst-
modified electrode.

Figure 6.14 Capacitive current of (a) 1 and (c) 3 at open circuit potential under variable scan rates, and the
corresponding current vs. scan rate plots (b and d) used to calculate C dl values.

Table 6.2 R ct values of 1 extracted from EIS at variable potentials
Potential (V) vs. RHE -0.24 -0.34 -0.44
R s ( ) 9.24 9.62 9.55
R ct of 1 ( ) 1785 122.6 19.74

191

Double layer capacitance (C dl) measurements were performed to obtain the electrochemical active
surface area (ECSA) of the catalyst-modified electrodes. As shown in Figure 6.14, 1 displays a much higher
C dl (125.6 μF) than 3 (25.0 μF), indicating a larger ECSA. This is consistent with the fact that the surface
ligand density of 3 is higher than 1, as mentioned previously. To achieve a more equitable comparison
between the two electrocatalysts, we normalized the catalytic current by the ECSA, instead of the geometric
surface area of the electrode (0.196 cm
2
). As shown in Figure 6.10b, upon normalization by ECSA, the
superior activity of 1 is maintained – there is still a 0.33 V overpotential difference at 3 mA/cm
2
ECSA that is
not accounted for by the ECSA alone. Therefore, 1 displays higher HER activity than 3 not only because
of its larger number of active sites, but also due to the higher intrinsic activity of individual sites.
Normalizing the current density by the loading of the catalyst yielded similar results where 1 showed higher
activity (Figure 6.15).
The superior HER activity of 1 suggests that the carbene ligands afford several benefits over
oleylamine ligands for catalysis. First, the lower surface ligand coverage of 1 not only helps to expose more
catalytically active sites, but also make the interfacial electron transfer between the electrode and the
electrolyte more efficient. This is evidenced by a lower solution resistance (R s) of 1 as compared to 3 (Table
6.2, 6.3), which is affected by the electrical resistance of the catalyst layer. Second, it is also possible that
the NHC ligands have a beneficial electronic effect at the nanocrystal surface that helps to enhance the
catalytic activity. Cao and coworkers previously reported on the enhanced electrocatalytic CO 2 reduction

Figure 6.15 Polarization curves of 1 and 3 with current normalized by the amount of Cu measured by ICP-OES
analysis; loading of 1: 3.02 × 10
-7
mol Cu, loading of 3: 0.71 × 10
-7
mol Cu.
192

Figure 6.16 Tafel plots of 1 and 3 extracted from polarization curves.

Table 6.3 R ct values of 3 extracted from EIS at variable potentials
Potential (V) vs. RHE -0.54 -0.64 -0.74
R s ( ) 25.8 26.1 26.1
R ct of 3 ( ) 951.1 142.7 38.6

activity of a NHC-functionalized Au nanoparticle catalyst.
17
Based on the different Tafel slopes of the
carbene-functionalized Au nanoparticles (72 mV/dec) and the parent Au nanoparticles (138 mV/dec), they
concluded that the strong σ-donation electronic effect from the carbenes alters the electron density at the
gold surface, which induces a shift in the rate-determining step for CO 2 reduction. We observe a similar
phenomenon here, where 1 exhibits a lower Tafel slope in comparison to 3 (85 mV/dec vs. 228 mV/dec,
Figure 6.16). From this, we can deduce that for 1, the rate- determining step is likely the Heyrovsky or Tafel

Figure 6.17 (a) One hour controlled potential electrolysis of 1 at -0.59 V vs. RHE (b) C dl measurements taken before
and after electrolysis. (c) Nyquist plots taken before and after electrolysis at η = 0.44 V.
193

Figure 6.18 (a) One hour controlled potential electrolysis of 3 at -0.59 V vs. RHE (b) C dl measurements taken before
and after electrolysis. (c) Nyquist plots taken before and after electrolysis at η = 0.44 V.

Table 6.4 Comparison of the characteristic values of 1 and 3 before and after electrolysis
Material FE (%)
R ct, 0.44V ( ) ECSA (cm
2
)
Before CPE After CPE Before CPE After CPE
1 81.3 ± 0.5 14.3 7.5 46.4 6.8
3 72.1 ± 0.1 241 11.3 1.9 1.6

step, whereas for 3, the rate-determining step is likely the Volmer step.
50
However, it is noteworthy that the
as-measured Tafel slopes might contain contributions from other sources that are not related to HER
kinetics, such as the uncompensated resistance originating from the charge transfer between the electrode
substrate and the catalyst.
51
Even so, such uncompensated contributions likely would not account for the
large difference in the measured Tafel slopes of 1 and 3, maintaining that the rate-determining step of HER
is different for these two catalysts.
Controlled potential electrolysis (CPE) experiments were performed to investigate the long-term
stabilities of the materials as well as their Faradaic efficiency (FE) for hydrogen production for catalysts 1
and 3 (Figure 6.17, 6.18). For 1, the current response remains relatively steady over the course of 1 h under
an applied potential of -0.59 V vs. RHE (Figure 6.17a), with slight fluctuations caused by the evolution of
bubbles on the electrode surface. However, when comparing the C dl and EIS responses before and after
CPE, it is found that the ECSA of the catalyst was reduced from 46.4 cm
2
to 6.8 cm
2
which was
accompanied by a decrease in R ct from 14.3  to 7.5  (Figure 6.17, Table 6.4).
194

Figure 6.19 (a) TEM of the carbene-capped Cu 3-xP nanocrystals (1) after CPE shows that the particles sinter during
electrochemical manipulation. (b) TEM of the ligand-exchanged oleylamine-capped Cu 3-xP nanocrystals (3)
following CPE shows similar behavior.

Figure 6.20 Controlled-current electrolysis of 1 at 10 mA/cm
2
in N 2-saturated 0.5M H 2SO 4.
195

Figure 6.21 Polarization curves (LSV, 5 mV/s) of 1 in 0.5M H 2SO 4 initially and after 200, 400, 600, 800, and 1000
CV sweeps between 0.1 and -0.6 V vs. RHE with a scan rate of 100 mV/s.

Figure 6.22 High resolution XPS spectrum of 1 following 1 h of controlled potential electrolysis. (a) Cu 2p region;
the Cu
+
signature remains while no satellite peaks indicative of Cu
2+
are observed (b) the P 2p region indicates that
the P
3-
is still present after catalysis, although there is a larger oxide peak than what was observed in the as-prepared
material in Figure 6.1b (c) the survey scans of 1 before and after CPE.

The FE for hydrogen production is 81.3 ± 0.5% for 1, calculated by comparing the total charge passed and
the amount of H 2 produced over the period of 1 h. The change in ECSA and R ct during electrolysis and the
less-than-unity FE is potentially a consequence of partial surface ligand desorption, a phenomenon that has
been observed for other electrocatalytic nanomaterials.
52,53
Indeed, the TEM image of the post-electrolysis
1 reveals sintering of the nanoparticles (Figure 6.19a), a consequence of the surface ligand loss. The stability
of 1 was further evaluated by long-term controlled current electrolysis and CV cycling experiments (Figure
196

6.20, 6.21), and in both cases 1 displayed good stability. Furthermore, XPS of the material left on the
electrode following CPE indicates that the Cu 3-xP remains intact, as shown by the persistence of the Cu
+

and P
3-
signals, with a slight increase in the oxidation of P being the only sign of degradation by XPS
(Figure 6.22).On the other hand, the FE of 3 is only 72.1 ± 0.1%. The R ct value is massively reduced after
electrolysis (from 241  to 11.3 ), along with a minimal decrease in the ECSA (from 1.9 cm
2
to 1.6 cm
2
).
Similarly, these behaviors are attributed to the loss of surface ligands, but to a larger extent in comparison
to 1. Since the oleylamine ligands have a higher surface ligand density and do not bind as tightly as the
carbene ligands, a greater loss of the oleylamine ligands is expected, which leads to a lower FE. TEM
images of the ligand-exchanged nanocrystals (3) following CPE also reveals sintering (Figure 6.19b). While
recent studies of metal phosphide nanocrystal HER catalysts lack reports of Faradaic efficiencies,
24,54
we
believe another potential source of Faradaic losses for these catalysts may originate from the reduction of
surface oxidized species that form upon exposure to air. Indeed, XPS of 1 indicates the presence of PO x
species on the nanocrystal surface prior to catalysis (Figure 6.5b).

Figure 6.23 (a) Methylamine and (b) 1,3-(dimethyl)benzimidazol-2-ylidene bound to a model Cu 9P 3 cluster along
with a proton.

6.4.3 Density Functional Theory Calculations
Density functional theory (DFT) calculations were performed to probe the electronic effects of NHC and
alkylamine ligands on proton binding to a Cu 3P catalyst. A model Cu 9P 3 cluster with one surface ligand
197

(either 1,3-(dimethyl)benzimidazol-2-ylidene or methylamine, see Figure 6.23) bound to a copper atom was
used to represent catalysts 1 and 3, respectively. The energies of proton binding to an adjacent surface site
on these clusters were then calculated and the physical origins of catalyst-proton interactions were

Table 6.5 Energy decomposition analysis results of proton binding to the ligated Cu 9P 3 clusters.

Cu-bound proton P-bound proton
(kJ/mol) Amine NHC Difference Amine NHC Difference
Electrostatics 82.5 64.8 17.7 46.6 8.7 37.8
Pauli repulsion 0.0 0.3 -0.3 -0.1 0.2 -0.3
Polarization -578.4 -584.2 5.8 -579.0 -571.1 -7.9
Charge transfer -560.5 -564.5 4.0 -487.2 -489.8 2.6
H-binding energy 0.0 -29.7 29.7 44.4 16.2 28.2

examined using the second generation absolutely localized molecular orbital energy decomposition analysis
(ALMO-EDA, referred to as EDA in this text).
55–57

Binding energies reveal that the proton prefers to bind at Cu-Cu bridge sites rather than P centers.
When comparing the proton binding energies for NHC- and amine-ligated clusters, it was found that proton
binding to the NHC-ligated cluster was favored by 29.7 kJ/mol (7.1 kcal/mol). EDA showed that cluster-
proton interactions are dominated by charge transfer and polarization terms, with smaller, repulsive
contributions from electrostatics (see Table 6.5). While charge transfer and polarization contributions are
largely similar, electrostatic contributions are smaller for the NHC-ligated cluster than the amine-ligated
cluster. This phenomenon likely arises as a consequence of stronger σ-donation from the NHC ligand to the
Cu
+
center, which results in diminished electrostatic repulsion between Cu
+
and the proton.
The calculations suggest that the weaker electrostatic repulsions lead to more favorable proton
binding for NHC-bound clusters. During catalysis, more favorable proton binding should speed up the rate
of the Volmer step for NHC-ligated nanocrystals. This result aligns well with our experimental Tafel
198

analysis wherein 1 exhibits a low Tafel slope, indicating that the Volmer step is fast and is not likely the
rate-determining step. In contrast, 3 displays a higher Tafel slope characteristic of a slow, rate-determining
Volmer step. Therefore, the nature of the L-type ligand on the surface of our Cu 3–xP nanocrystal catalysts
could indeed be contributing an electronic influence on catalytic activity and the rate-determining step.
6.5 Conclusions
In conclusion, we report a new synthesis that directly produces crystalline, NHC-stabilized Cu 3-xP
nanocrystals. This represents the first example of a carbene-stabilized metal phosphide nanocrystal. The
NHC-stabilized Cu 3-xP nanocrystals exhibit better HER activity compared to their oleylamine-capped
counterparts with respect to the onset of catalysis, Tafel slope, and overpotential to reach 10 mA/cm
2
current
density. DFT calculations suggest that the NHC ligands change the electronics of the copper phosphide
catalyst surface by reducing unfavorable electrostatics, which may contribute to the superior catalytic
performance of the NHC-ligated Cu 3-xP catalyst. Future studies should focus on leveraging the high
synthetic tunability of the NHC surface ligands to confer better stability or improved activity. Specifically,
the design of NHC ligands with variable electronic properties could be used to modulate their effect on
electrocatalysis.
6.6 Ligand Density Calculations
Sample calculation:

Initial mass of sample
(corrected for residual
solvent content) (mg)
Sample mass after TGA
Composition : Molecular
Weight (g mol
-1
)
NHC-capped
Cu 3-xP
10.307 9.165 mg (89%) Cu 2.30P : 177.13

Average nanocrystal
diameter (nm)
Average nanocrystal
surface area (nm
2
)
Average nanocrystal volume
(nm
3
)
NHC-capped
Cu 3-xP
6.7 141 157

Mass losses were determined by TGA. The composition of the nanocrystalline materials were found
through ICP-OES. The average diameter of the two nanocrystal samples were obtained through TEM.
199

Assuming a spherical nanocrystal shape, the average surface areas and volumes were calculated. The
molecular weight of the ligand is the molecular weight of the NHC-CuBr precursor minus CuBr and a
proton (510.895 g mol
-1
).
𝑇𝑜𝑡𝑎𝑙 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑟𝑏𝑒𝑛𝑒 𝑙𝑖𝑔𝑎𝑛𝑑 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒 = (100% − 89%) ∗ 10.307 𝑚𝑔
= 1.14 𝑚𝑔 𝑙𝑖𝑔𝑎𝑛𝑑 (2.23 ∗ 10
−6
𝑚𝑜𝑙 )
# 𝑐𝑎𝑟𝑏𝑒𝑛𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒 = 2.23 ∗ 10
−6
𝑚𝑜𝑙 ∗ 𝑁 𝐴 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑚𝑜 𝑙 −1
= 1.34 ∗ 10
18
𝑐𝑎𝑟𝑏𝑒𝑛𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠

To find the ligand density, we need to know the number of carbene ligands per unit surface area. Therefore,
we can divide the total number of carbene molecules in the sample by the total surface area of the sample.
To find the total surface area of the sample, it was assumed that the unit cell volume of Cu 2.30P is similar to
Cu 3P, which is known to have a unit cell volume of 0.2996 nm
3
. Using this value and the calculated
nanocrystal volume, the total number of unit cells per nanocrystal can be found:
# 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙𝑠 𝑝𝑒𝑟 𝑛𝑎𝑛𝑜𝑐𝑟𝑦𝑠𝑡𝑎𝑙 =
𝑉 𝑛𝑎𝑛𝑜𝑐𝑟𝑦𝑠𝑡𝑎𝑙 𝑉 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 = 525 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙𝑠 𝑝𝑒𝑟 𝑛𝑎𝑛𝑜𝑐𝑟𝑦𝑠𝑡𝑎𝑙

Formally, each unit cell of copper phosphide is Cu 18P 6. However, by ICP-OES, the experimentally
determined Cu:P ratio was 2.3:1 for the carbene-capped nanocrystals, which translates to a formula per unit
cell of Cu 13.8P 6. Knowing the mass per unit cell and the number of unit cells per nanocrystal, the mass per
nanocrystal was found. From this, and the mass of copper phosphide left after TGA, the total number of
nanocrystals in the sample was found. The total surface area of the sample was found by multiplying the
surface area per nanocrystal by the total number of nanocrystals in the sample.
𝑚𝑎𝑠𝑠 𝑝𝑒𝑟 𝑛𝑎𝑛𝑜𝑐𝑟𝑦𝑠𝑡𝑎𝑙 = 525 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙𝑠 ∗ 𝑤𝑒𝑖𝑔 ℎ𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 = 9.28 ∗ 10
−19
𝑔
𝑡𝑜𝑡𝑎𝑙 # 𝑛𝑎𝑛𝑜𝑐𝑟𝑦𝑠𝑡𝑎𝑙𝑠 =
9.165 ∗ 10
−3
𝑔 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒 𝑎𝑓𝑡𝑒𝑟 𝑇𝐺𝐴 9.28 ∗ 10
−19
𝑔 𝑛𝑎𝑛𝑜𝑐𝑟𝑦𝑠𝑡𝑎 𝑙 −1
= 9.88 ∗ 10
15
𝑛𝑎𝑛𝑜𝑐𝑟𝑦𝑠𝑡𝑎𝑙𝑠
𝑡𝑜𝑡𝑎𝑙 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒 = 9.88 ∗ 10
15
𝑛𝑎𝑛𝑜𝑐𝑟𝑦𝑠𝑡𝑎𝑙𝑠 ∗ 141 𝑛 𝑚 2
𝑛𝑎𝑛𝑜𝑐𝑟𝑦𝑠𝑡𝑎 𝑙 −1
= 1.39 ∗ 10
18
𝑛 𝑚 2

𝑙𝑖𝑔𝑎𝑛𝑑 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
1.34 ∗ 10
18
𝑐𝑎𝑟𝑏𝑒𝑛𝑒 𝑚𝑜𝑙 𝑒𝑐𝑢𝑙𝑒𝑠 1.39 ∗ 10
18
𝑛 𝑚 2
= 0.97 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑛 𝑚 −2

These calculations rely on the densities of the materials (mass per unit cell). For the quasi-amorphous
oleylamine-capped copper phosphide, we assumed the oleylamine-capped particles had unit cells of the
same volume as the carbene-capped nanocrystals. Following the same procedure, calculations for the
200

amorphous oleylamine-capped particles (2) yield a ligand density of 2.5 ligands nm
-2
, and 3.3 ligands nm
-2

for the crystalline Cu 3-xP nanocrystals after ligand exchange (3).

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Abstract (if available)

Abstract The crystal structure of a material is an important determinant of its properties. Indeed, all physicochemical material properties are fundamentally rooted in structure and composition. Given the role of crystal structures in determining material properties, the prevalence of polymorphism on the nanoscale is enabling the discovery and design of new materials with distinct properties. This thesis expounds primarily on the chemistry, properties, and applications of semiconductor nanocrystals that crystallize with crystal structures distinct from those that are thermodynamically stable in the analogous bulk material systems. Semiconductor nanocrystals represent an ever-expanding area of materials research and development due to their highly tunable properties (on the basis of size, shape, composition, crystal structure, surface functionalization, etc.) that make them apt for use in optoelectronics, solar cells, batteries, medicine, and a wide array of other applications. ❧ Chapter 1 introduces important concepts related to polymorphism in inorganic materials. Also highlighted are recent works that demonstrate chemical control of polymorphism in several representative semiconductor nanocrystal material systems, concluding with examples of emergent properties that arise from the unique crystal structures adopted by these materials. ❧ Discussed in Chapter 2 are molecular programming and formation mechanism studies of wurtzite-like CuInSe₂ nanocrystals. This wurtzite-like crystal structure of CuInSe₂ is a polymorph that has only been observed to exist for nanocrystals of CuInSe₂, and its formation is dependent upon use of the proper selenium precursors which nucleate a key Cu₃Se₂ nanocrystal intermediate. ❧ Chapter 3 highlights the expansion of the findings of Chapter 2 through studies of a highly related material, AgInSe₂. Here, it is shown that the formation of different polymorphs of AgInSe₂ can be controlled by the choice of ligand/solvent in the nanocrystal synthesis. Additionally, formation mechanism studies reveal that wurtzite-like AgInSe₂ forms via a pathway analogous to that of wurtzite-like CuInSe₂. ❧ Chapter 4 illustrates the use of the chemical principles developed in Chapters 2-3 to predict and synthesize wurtzite-like Cu₂FeSnSe₄ nanocrystals that have never been observed before this work. UV-vis-NIR spectra and density functional theory calculations of this novel polymorph indicate that it is an excellent candidate for use as a non-toxic, Earth-abundant absorbing layer in thin-film solar cells. Additionally, the Cu₂FeSnSe₄ results were used to shed light on the curiosities of the poorly understood chemistry of CuFeSe₂, which is a ternary analog of Cu₂FeSnSe₄. By comparing these two related material systems, it was found that Sn plays a critical role in stabilizing the wurtzite-like structure of Cu₂FeSnSe₂; in the absence of Sn, the chemistry of CuFeSe₂ proceeds down entirely unique reaction pathways that consistently produce the thermodynamically stable eskebornite phase of CuFeSe₂, rather than a wurtzite-like CuFeSe₂. ❧ Chapter 5 turns to our studies of a metastable polymorph of Ag₂Se nanocrystals. The crystal structure of this metastable polymorph of colloidal Ag₂Se nanocrystals remained unsolved until we showed herein that, on the basis of Rietveld refinements of powder X-ray diffraction data and pair distribution function analysis, the structure is well-described by an anti-PbCl₂-like structure type. Knowledge of the crystal structure enabled, for the first time, the calculation of the phonon dispersion curves and the electronic band structure of this metastable polymorph. Finally, it was found that the theoretical phase space of Ag₂Se is crowded with many polymorphs that are close in energy, which may explain the preponderance of reports in the literature of different Ag₂Se polymorphs with distinct crystal structures. ❧ Chapter 6 departs from the storyline of semiconductor nanocrystal polymorphism to focus on the effects of N-heterocyclic carbene precursors/ligands in the synthesis and electrocatalytic activity of Cu₃₋ₓP nanocrystals. Here, it is shown that N-heterocyclic carbene copper complexes react via a metathesis reaction with tris(trimethylsilyl)phosphine to yield Cu₃₋ₓP nanocrystals with legacy N-heterocyclic surface ligands. Furthermore, it was shown that these carbene-capped Cu₃₋ₓP nanocrystals display significantly lower overpotentials in driving electrocatalytic hydrogen evolution, as compared to Cu₃₋ₓP nanocrystals ligated with a more traditional surface ligand (oleylamine). Density functional theory calculations indicate that this lower overpotential is a result of the significant electron donating character of the carbene surface ligands.

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Creator Tappan, Bryce Arend (author)

Core Title The chemistry of polymorphism in semiconductor nanocrystals

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Degree Conferral Date 2021-12

Publication Date 09/28/2021

Defense Date 08/06/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag chemistry,metastability,nanocrystals,OAI-PMH Harvest,polymorphism,semiconductor,solar cells

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Brutchey, Richard (committee chair), Feakins, Sarah (committee member), Melot, Brent (committee member)

Creator Email tappan@usc.edu,tappanbr@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC15965159

Unique identifier UC15965159

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Rights Tappan, Bryce Arend

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Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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