Atomic and molecular clusters at ultra-low temperature

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Content ATOMIC AND MOLECULAR CLUSTERS AT ULTRA-LOW TEMPERATURE by Luis F. Gomez 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 2012 Copyright 2012 Luis F. Gomez ii I dedicate this dissertation to Sydney. All those long nights paid off, puppy! iii Table of Contents Dedication ii List of Tables vi List of Figures vii Abstract xv Chapter I: General Introduction 1 1.1. Introduction 1 1.2. Thesis Structure 3 Chapter I Bibliography 6 Chapter II: Experimental Setup 7 2.1. Introduction 7 2.2. Helium droplet concepts 9 2.2.1. Production of helium droplets 9 2.2.2. Helium droplet sizes 11 2.2.3. Capture of foreign atoms and molecules 14 2.2.4. Evaporation of helium following the capture of foreign atoms and 16 molecules 2.2.5. Laser systems 17 2.2.6. Mass spectrometer detection and the depletion technique 18 Chapter II Bibliography 21 Chapter III: Sizes of Large Helium Droplets 22 3.1. Introduction 22 3.2. Experimental 24 3.3. Results 26 3.4. Discussion 34 3.4.1. Average sizes of He droplets 34 3.4.2. Modes of nozzle operation at different temperatures 43 3.4.3. Using mass spectra for determining average droplet sizes 46 in continuous and pulsed expansions 3.5. Conclusion 51 Chapter III Bibliography 53 iv Chapter IV: Surface Deposition and Imaging of Large Ag Clusters 56 Formed in Helium Droplets 4.1. Introduction 56 4.2. Experimental 57 4.3. Results 60 4.4. Discussion 70 4.4.1. Helium droplet collision with surface 71 4.4.2. Soft landing 73 4.4.3. Cluster size distribution 73 4.5. Conclusion 77 Chapter IV Bibliography 78 Chapter V: Photoabsorption of Ag N (N ~ 6-6000) nanoclusters formed in He droplets: 81 A transition from compact to multi-center aggregation 5.1. Introduction 81 5.2. Experimental 82 5.3. Results 83 5.4. Discussion 86 5.5. Conclusion 91 Chapter V Bibliography 92 Chapter VI: Laser-Induced Reconstruction of Ag clusters in Helium droplets 94 6.1. Introduction 94 6.2. Experimental 96 6.3. Results 100 6.4. Discussion 104 6.5. Conclusion 110 Chapter VI Bibliography 112 Chapter VII: Formation of Core-Shell Ag-Ethane Clusters in Helium Droplets 114 7.1. Introduction 114 7.2. Experimental Details 118 7.3. Results 124 7.3.1. Silver-ethane clusters 124 7.3.2.Core-shell Ethane-silver clusters 138 7.4. Discussion 146 7.4.1. IR spectra of adsorbed molecules 146 7.4.2. IR Enhancement 148 7.5. Conclusion 148 Chapter VII Bibliography 150 Chapter VIII: Traces of Vortices in Superfluid Helium Droplets 153 v 8.1. Introduction 153 8.2. Experimental 156 8.3. Results 159 8.4. Discussions 163 8.5. Conclusion 168 Chapter VIII Bibliography 169 Chapter IX: Conclusions and Future Work 172 9.1. Conclusions 172 9.2. Future Work 173 Chapter IX Bibliography 176 Bibliography 177 Appendix 1: TEM Imaging of Ag Clusters Grown in He Droplets 185 Appendix 2: Sizes of Large He Droplets 192 Appendix 3: Traces of Vortices in He Droplets 200 vi List of Tables Table 2.1. 9 Typical chamber pressures at P 0 = 20 bar for T 0 = 300, 11, 7, and 5.5 K. Table 3.1. 32 Nozzle temperature, T 0 ; attenuation coefficients α 4 and α 8 (upper and lower entries) obtained with helium titration; droplet beam velocity, v D ; and average number of He atoms in the droplets, <N He >, according to Eq. 3. 2. Table 1 also contains intensity ratios of peak m = 16 to m = 8 and m = 12. Values of <N He > obtained previously, using deflection techniques of Refs. 17, 28-30 , are shown in the penultimate column. Shaded values of <N He > in the last column are beyond the range of the applied technique as described in the text. All measurements are at nozzle stagnation pressure of P 0 = 20 bar. Table 6.1. 106 Initial He droplet size, He N ; size of the obtained Ag clusters, Ag N ; and absorption cross-sections per Ag atom, σ, at 355 nm and 532 nm excitation. The values obtained with CW excitation at 532 nm are given in parenthesis. vii List of Figures Figure 1.1. 2 4 He phase diagram. Figure 2.1. 8 Schematic of the helium droplet beam vacuum apparatus. NZ: cold nozzle, SK: skimmer, PC1 and PC2: pickup cells, BG: Baratron vacuum gauge, IG1 and IG2: ion gauges, SH1 and SH2: beam shutters, A1 and A2: 6 mm diameter apertures, GV1 and GV2: gate valves, EI: electron impact ionizer, IB: ion bender, QMS: quadrupole mass spectrometer. Figure 2.2. 11 Pressure-temperature phase diagram of 4 He. The dotted, dashed, and solid lines represent isentropes for super-critical, critical, and sub-critical expansions of 4 He at a source pressure of P 0 = 20 bar. Figure 2.3. 14 He N obtained at various nozzle temperatures from continuous expansion of helium, at P 0 =20 bar, through a 5 μm nozzle. Results obtained by our group via measurements with collisional helium gas are shown by filled circles. Results of previous deflection measurements are shown by open stars. 3,7 Right-hand scale shows corresponding liquid droplet diameters obtained using n LHe . Figure 2.4. 16 Probability for capture of k particles by the droplets versus the average number of the captured particles. Figure 2.5. 20 Typical time profile of the mass spectrometer signal at m/z = 8 following the laser pulse at t = 0. Time profile is for laser excitation at 532 nm of Ag 300 cluster in a droplet of He N = 1.8×10 6 . Figure 3.1. 25 Schematic of the He droplet beam vacuum apparatus. NZ: cold nozzle, SK: skimmer, PC1 and PC2: pickup cells, BG: Baratron vacuum gauge, IG1 and IG2: ion gauges, SH1 and SH2: beam shutters, A1 and A2: 6 mm diameter apertures, GV1 and GV2: viii gate valves, EI: electron impact ionizer, IB: ion bender, QMS: quadrupole mass spectrometer. Figure 3.2. 26 Illustration of measurement of He droplet sizes by titration of droplet beam with collisional helium atoms at room temperature. Decrease of He flux into the detection chamber (far right) is measured as a pressure drop, ΔP. Figure 3.3. 28 Intensity of the He droplet beam, produced by continuous expansion of He gas at 20 bar through a 5 µm nozzle, as measured by the partial pressure rise of He in the detection chamber. Nominal reading of the ion gauge (Leybold-Heraeus IM 510 gauge, IE 514 sensor) has been corrected for the sensitivity of the gauge to He gas. Partial pressure rise was obtained as a pressure difference between the beam unblocked and blocked using shutter SH1. Scale on the right-hand side shows flux of He transported by the beam into the detection chamber. Solid line shows 0 1 T dependence normalized to experimental data point at T 0 = 100 K. Figure 3.4. 31 Normalized He flux versus collisional helium gas pressure in the main experimental chamber for droplets obtained at T 0 = 5.7, 6, 7, 9 and 12 K. Filled symbols represent values obtained by measuring the He partial pressure rise in the detection chamber with the mass spectrometer set to m = 4. Open symbols correspond to the measurements of the droplet beam intensity at m = 8. Solid and dashed lines are fits according to Eq. 3.1 for measurements with m = 4 and m = 8, respectively. Figure 3.5. 33 Typical mass spectra of He droplet beams obtained at P 0 = 20 bar and T 0 = 7 (blue trace), 9 (red), and 14.5 K (black). The spectra have been normalized to the same intensity at m = 8. Electron beam energy 100 eV, emission current 4 mA. Contributions from effusive helium gas and rest gas in the detection chamber have been subtracted out. Figure 3.6. 42 He N obtained at various nozzle temperatures from continuous expansion of He, at P 0 = 20 bar, through a 5 µm nozzle. Results obtained via measurements of α 4 with collisional helium and argon gases are shown by filled squares and circles, respectively. Results ix of previous deflection measurements are shown by open triangles 17, 30 and 16, 28-29 stars. Right-hand scale shows corresponding liquid droplet diameters obtained using n LHe . Figure 3.7. 44 Pressure-temperature phase diagram of 4 He. Isentropes (dashed lines) are for 4 He at a stagnation pressure of P 0 = 20 bar from Ref. 23 . Locus of sonic points specifies the states at the orifice for the isentropic expansions. Figure 3.8. 49 Intensity ratios 0.1×I 16 /I 12 (circles) and I 16 /I 8 (triangles) obtained from the mass spectra of the continuous He droplet beams comprised of different droplet sizes. Corresponding nozzle temperatures from Table 3.1 are shown in the upper part of the plot for reference for some of the data points. Average sizes from Ref. 28 are used for N He < 10 4 . Figure 3.9. 50 I 16 /I 8 ratio of He droplet beam obtained from a 1 mm diameter pulsed-valve. Expansion obtained at P 0 = 15 bar for different nominal nozzles temperatures and two repetition rates of 1 Hz and 10 Hz, solid circles and open squares, respectively. For comparison, the results obtained with the 5 µm continuous-nozzle at P 0 = 20 bar from Table 3.1, are shown by triangles. Average droplet sizes are indicated for some of the data points. Figure 4.1. 58 Experimental setup for the surface deposition of metal clusters formed in He droplets. Typical pressure in each vacuum chamber, with the He beam off, is shown. Figure 4.2. 61 TEM images (at 40×10 3 magnification) of Ag N clusters on an amorphous carbon film. Sample s were obtained by exposure to the He droplet beam doped with about 6000 Ag atoms for 0.5 min (a), 2 min (b), 32 min (c), and 120 min (d). For comparison, panel (e) shows clusters formed on the carbon surface upon 32 min exposure to the effusive beam of Ag atoms emanating from the oven, kept at the same temperature as in experiments producing samples in panels (a) – (d). Scale for all images is the same as shown in panel (a). Figure 4.3. 63 Upper panel: Surface density versus deposition time for Ag N clusters of estimated initial size Ag N ~ 6 000. Line connecting x the data points is to guide the eye. Lower panel: Area fraction of the deposited clusters under the same conditions. Insets show a linear fit to the data at short deposition times. Figure 4.4. 66 Size distribution of Ag N deposited on an aC film during 2 minutes (solid squares, 1 000 clusters analyzed) and 32 minutes (open circles, 400 clusters analyzed). Estimated initial average cluster size in both cases is 6 000. Lines connecting data points are to guide the eye. Figure 4.5. 69 Size distribution of Ag N clusters deposited on an aC film for 2 minutes (stars, 200 clusters analyzed) and 16 minutes (circles, 2000 clusters analyzed). Estimated initial average cluster size in both cases is 300. Squares illustrate the cluster size distribution upon exposure to the effusive beam for 32 minutes at the same conditions as in Figure 4.2e. Lines connecting data points are to guide the eye. Figure 5.1. 85 87 Normalized photoabsorption spectra for Ag particles of different average sizes assembled by pick-up in He droplets. Dashed lines in panels (b) and (c) are calculated model cross sections (right-hand scale) and in panel (e) is the fit of the dispersion profile according to the Fano formalism. Top panel (f) shows calculated absorption spectrum of a Ag cluster-cluster aggregate from Ref.[23], see text for details. Figure 5.2. 89 Time between two successive pickup events, t n,n+1 , and time required for recombination of first two picked up Ag atoms, t rec , versus size of He droplets, N He . Corresponding droplet radius, R He , and typical size of Ag N cluster, N Ag , grown within the droplet are also shown on bottom and top axes of plot, respectively. Figure 6.1. 102 Depletion of the M = 8 signal with laser fluence obtained for droplets produced at nozzle temperatures T 0 = 5.5, 6, 7, and 9 K used to grow Ag clusters of 2×10 6 , 4.2×10 4 , 2×10 3 , and 300 atoms, respectively. Pulsed laser excitation is at (a) 532 nm and (b) 355 nm. Figure 6.2. 103 Depletion in M = 8 signal with laser fluence for different Ag cluster sizes measured upon continuous laser excitation at 532 nm. xi Figure 7.1. 117 a) Schematic of the He droplet beam vacuum apparatus. NZ –5 µm diameter nozzle; SK – 1 mm diameter skimmer; PC 1 and PC2 – upstream and downstream pickup cells, respectively; SH – beam shutter; A1 and A2 – 6 mm diameter apertures; GV1 and GV2 – gate valves; EI – electron impact ionizer; IB – ion bender; QMS – quadrupole mass spectrometer. b) Typical depletion dip upon laser excitation at t = 0, as measured at mass M = 8. Weak secondary pulse at about t = 7 ms, shows the effect of laser pulse impinging on the nozzle. Figure 7.2. 125 Infrared spectra of (a) neat Et clusters and (b) core-shell Ag-Et clusters. Panel (a) shows a comparison of the spectra for neat Et clusters obtained with and without the collimating lens. The spectra in (b) are with the collimating lens. The clusters were obtained in He droplets of initial size of He N = 3.3×10 5 (P 0 = 20 bar, T 0 = 9.5 K). The average numbers of the captured Et and Ag particles are indicated for each trace. The original spectra have been smoothed over 20 data points. Figure 7.3. 131 Infrared spectra of neat Et clusters and core-shell Ag-Et clusters. The clusters were obtained in He droplets of initial size He N = (a) 2×10 6 , (b) 5×10 6 , and (c) 10 7 . The average numbers of captured Et and Ag particles are indicated for each trace. The spectra were obtained with collimating lens. The original spectra were smoothed over 20 data points. Some spectra in the panel (c) were also obtained upon attenuation of the laser beam by about a factor of 3 by using a layer of mica. Figure 7.4. 134 (a): Measured values of perpendicular/parallel vs. number of attached Et molecules. For 8 and 7 K, ratios are obtained from the band peak intensities. Data for 9.5 and 9 K are for both integrals and peak intensities, which are in good agreement. b) peak maxima for the ν 8+11 , ν 7 (parallel) and ν 7 (perpendicular) bands, from low to high frequency, respectively. Figure 7.5. 135 Schematic of a close-packed, core-shell Ag-Et cluster. xii Figure 7.6. 136 NEt(1) vs the number of added Et molecules as obtained at T 0 = 9.5, 9, 8, and 7 K, shown by squares, triangles, diamonds and circles, respectively. The horizontal lines show the number of interfacial molecules according to Eq. 7.8. Figure 7.7. 140 Infrared spectra of the clusters obtained upon capture of Et molecules followed by Ag atoms obtained at T 0 = 8 and 7 K, in panels (a) and (b), respectively. The spectra are with collimating lens. The average numbers of the captured Et and Ag particles are indicated in each trace. Figure 7.8. 141 Comparison of the spectra of clusters obtained by doping He droplets of 5×10 6 atoms by about 730 Ag atoms and 900 Et molecules by two different pickup orders as indicated. Doping with Et first, followed by Ag is in black. Doping with Ag, then Et is shown in red. Figure 7.9. 144 I I /I V versus (a) N Ag and (b) N ET for Et captured upstream (PC1) and Ag captured downstream (PC2). Corresponding band maxima for the ν 8+11 , ν 7 (I I ), and ν 7 (I V ) bands are shown in panels (c) and (d). Figure 8.1. 155 Schematic of the experiment. (A) He fluid expands in vacuum and (B) breaks up into rotating droplets. (C) A quantum vortex is formed following evaporative cooling of the droplet to below T λ . (D) The droplet is doped with Ag atoms, which are attracted to the vortex core. (E) The droplet then collides with the carbon surface leaving behind the Ag trace whereas the He evaporates. Figure 8.2. 157 Experimental setup for surface deposition of metal clusters formed in He droplets. Figure 8.3. 161 TEM micrographs obtained upon deposition of Ag-doped droplets of average diameter (A) 100 nm, (B) 300 nm, and (C) 1000 nm and average number of He atoms He N = 10 7 , 3×10 8 , and 1.7×10 10 , respectively. The droplets were attained at a nozzle temperature T 0 = 7, 6 and 5.4 K, respectively. [15] Exposure times to the droplet beam are 120 sec, 4 sec, and 2 sec, respectively. Large dark spot xiii on right side of (C) is artifact likely introduced during sample transfer to the TEM. Figure 8.4. 162 Typical Ag traces obtained in 1000 nm He droplets. The inset to panel (B) shows an enlarged track segment. Figure A1.1. 178 TEM images of Ag N clusters on amorphous carbon film. Magnification is 10×10 3 for panels a, c, and e; for panels b, d, and f a magnification of 40×10 3 was utilized. The samples were obtained by exposing them to the doped droplet beam for 2 min (a, b), 16 min (c, d), and 60 min (e, f). The droplets were obtained at a nozzle temperature T 0 = 9 K for an average size of He N = 1.8×10 6 and doped by Ag until attenuated by ΔP He /P He = 0.63 (a, b), 0.70 (c, d), 0.75 (e, f). According to Eq. 4.1, this gives Ag N ~ 300 atoms. It is seen that the coverage of the samples increases with exposure time. From panel (f), is it seen that at high exposure not only is there a higher density in clusters but the deposits are much larger in size and on the order of about 5 nm. Figure A1.2. 180 TEM images of Ag N clusters deposited on amorphous carbon film taken at 40×10 3 magnification. The samples were obtained by exposing them to the doped droplet beam for 0.5 min (a), 2 min (b), 8 min (c), and 32 min (d). He droplets of average size He N = 2.2×10 7 were obtained at a nozzle temperature T 0 = 7 K. The droplets were then doped with Ag for a droplet beam attenuation of ΔP He /P He = 0.68. At this attenuation Eq. 4.1 gives Ag N ~ 3000 atoms. In panel (d), obtained at an exposure time of t = 32 min it is seen that there is significant coalescence of clusters as previously reported in Chapter 4. At this exposure time, many of the deposits are slightly oblate in shape and as large as approximately 10 nm. Figure A1.3. 181 TEM images obtained at a magnification of 10×10 3 of Ag N clusters on amorphous carbon. The samples were obtained by exposing them to the He droplet beam doped with Ag; exposure times are 4 sec (a) and 2 min (b). The droplets of average initial size He N = 3.08×10 8 were produced at a nozzle temperature T 0 = 6 K, then were doped with Ag atoms until a droplet beam attenuation of ΔP He /P He = 0.80 (a) and 0.66 (b) was reached. At this attenuation xiv Eq 4.1 gives Ag N ~ 4×10 5 atoms. It is seen that many of the deposits, as in panel (a), are elongated spanning several hundred nanometers. This is in contrast to the rounded clusters obtained at T 0 = 9 K and 7 K, shown in Figs. 1 and 2, respectively. Figure A1.4. 182 TEM micrographs of Ag N clusters deposited on amorphous carbon. The micrographs were taken at a magnification of 3×10 3 (panels a, c, and e) and 10×10 3 (panels b, d, and f). The samples were obtained by exposing them to the He droplet beam doped with Ag; exposure times are 2 sec (a), 4 sec (b), 10 sec (c, d), 2 min (e), and 30 min (f). The droplet beam was composed of droplets of average initial size He N = 1.7×10 10 which were produced at a nozzle temperature T 0 = 5.5 K which were doped with Ag atoms until a droplet beam attenuation of ΔP He /P He = 0.70 (a, b), 0.63 (e) was reached. At this attenuation Eq. 4.1 gives Ag N ~ 2×10 6 atoms. It is seen that many of the deposits, as in panel (a), are elongated spanning several hundred nanometers. Figure A2.1. 185 Change of the I 8 signal upon laser pulse at t = 0 as measured at nozzle temperature T 0 = 5.7 K (blue trace) and 8 K (red trace). Onset time is 7.90 and 6.61 ms for T 0 = 5.7 K and 8 K, respectively. Obtained velocities are 173 and 207 m/s for T 0 = 5.7 K and 8 K, respectively. Waveform near t = 0 for T 0 = 8 K is due to electric interference from the laser. Similar waveform is not visible at the scale for T 0 = 5.7 K, as the signal is a factor of about 10 2 larger than for T 0 = 8 K. Figure A2.2. 190 Simulation of the attenuation of the droplet beam versus collisional helium pressure in the main chamber. Black trace is a line with slope equal to − α, as obtained by inverting Eq. A2.10 for a monodisperse beam of droplets of He N = 10 7 . Red trace represents results for such a monodisperse beam but also includes effect of changing cross section. Blue and green traces show results for exponential and log-normal distributions of droplets, respectively, of initial size He N = 10 7 with changing cross- section. Figure A3.1. 194 Experimental setup for surface deposition of metal clusters formed in He droplets. xv Abstract This Dissertation is focused on the study of atomic and molecular clusters in ultra-cold helium nanodroplets. A novel technique for the determination of helium droplet sizes will be discussed, which is based on the attenuation of a beam of helium droplets via collisions with argon and helium scattering gas at room temperature. It is shown that that there exists a new droplet growth regime that can give rise to micrometer-sized droplets of 10 7 –10 11 helium atoms. Helium droplets of this sizes range and smaller are further used to grow Ag clusters. It is shown that the Ag clusters could be surface-deposited onto a carbon film and studied via electron microscopy. This gives the average sizes of the Ag clusters grown in the droplets, their size distributions, and information on the cluster stabilities. In addition, a study of the growth in helium droplets of large Ag clusters via their photoabsorption spectra is reported. The plasmon spectra of the clusters indicate a switch in the cluster growth mechanism from single-centered to multi-centered growth which occurs with increasing droplet size. The latter growth mechanism is shown to result in non-compact, aggregate clusters. The possible reconstruction of such cluster-cluster aggregates upon the absorption of laser radiation is also explored with pulsed and continuous wave laser excitation at 532 and 355 nm. The results are shown to be consistent with a kinetic limit on the energy transfer rate from the excited Ag cluster to the host helium droplet, which is not exceeded in the case of continuous wave excitation. Therefore, upon pulsed laser excitation, the embedded Ag aggregates melt and reconstruct into more compact clusters. xvi The application of the helium droplet technique in building large Ag-ethane core-shell clusters is also reported. The clusters have been studied by infrared spectroscopy of the C-H stretch bands of ethane in the 3 µm range. It is found that the v 7 band of ethane is split into two distinct features which can be used to quantify the number of ethane molecules in and out of contact with Ag. The first experimental observation of vortices in superfluid helium droplets is also reported. This observation was made by introducing Ag atoms, which cluster along the vortex lines, into the droplets. Surface-deposition and imaging of the Ag clusters reveal the presence of elongated track-shaped aggregates, which is consistent with presence of vortices in droplets larger than about 300 nm. 1 Chapter I: General Introduction 1.1. Introduction The two isotopes of helium, 3 He and 4 He, are unique among all elements in that they lack a triple point. Therefore, 3 He and 4 He remain liquid under their saturated vapor pressure, even down to absolute zero temperature, whereas other substances will solidify at low enough temperature. This unusual property of the helium isotopes is the result of the weak van der Waals interactions between the helium atoms as well as their small mass, which results in a large zero point energy of the atoms in their condensed state. It is only under high pressures above approximately 25 bar, as shown in Fig. 1.1, that 4 He can be solidified. Liquid helium has the lowest boiling point among the elements at approximately 4.2 K for 4 He and 3.19 K for 3 He (at 1 atm). 4 He and 3 He liquids, however, show a remarkable difference at low temperature, which is a dramatic manifestation of the role of nuclear spin statistics. At T < 2.2 K, the bosonic (nuclear spin I = 0) 4 He will undergo a phase transition to a superfluid state (HeII in Fig. 1.1), where it displays unique properties such as a negligible viscosity and a very high thermal conductivity, both of which shall prove important in this work. The analogous phase transition occurs for the fermionic (spin I = ½) 3 He isotope at 2.6 mK and originates from paring of Fermions at low temperature. 2 Figure 1.1. 4 He phase diagram. Foreign particles inside bulk liquid helium can be used as probes for studying its microscopic properties. However, the introduction of foreign particles and their study is associated with experimental difficulties since the cohesion energy of the particles largely exceeds the solvation energy and this leads to uncontrolled aggregation for any kind of impurity particles. Nanoscopic droplets of liquid helium can be used capture atoms and molecules. 1-2 This circumvents any problems with their aggregation and pinning to the container walls. Helium droplets can now routinely be produced via well-established molecular beam methods and have been studied in great detail. Helium droplets are capable of reaching an internal temperature of 0.37 K, 3 which is well below the superfluid transition temperature T λ = 2.2 K 4 . 3 Because of their large quantum mechanical delocalization the helium atoms in a superfluid droplet adopt a configuration around the dopant which corresponds to the lowest (ground) quantum mechanical state of the system. Moreover, due to the fact that helium does not absorb light below approximately 21 eV, which corresponds to the 1 1 S – 2 1 P transition, helium droplets represent an ideal matrix over the entire spectral range from the infrared to the vacuum ultraviolet. There are a number of additional experimental merits to the helium droplet technique. The droplet itself may be viewed as a personal cryostat for each individual dopant, powered by the evaporative cooling of the helium atoms from the droplet. This evaporative cooling leads to a freezing out of molecular vibrational states and most of the rotational states, which leads to greatly simplified molecular spectra that are often free from hot bands, for instance. In addition, line broadening of molecules in helium droplets is usually much less pronounced as compared with other solid rare gas matrices. As will be apparent from later chapters, helium droplets can also be used to controllably grow clusters spanning a large size range and clusters up to a micron in length. 1.2. Thesis Structure This thesis summarizes the results of a set of experiments aimed using the helium droplet technique to study large atomic and molecular clusters containing hundreds to millions of particles. The three main focuses in this thesis are: (1) the development of the helium droplet technique as a tool to reliably grow large atomic and molecular clusters; (2) the use of the droplet technique to study the ultra-low temperature mechanisms and 4 kinetics of cluster growth; and (3) its application in the formation of clusters of varying composition, shape, and structure. Of utmost importance in any helium droplet experiment is knowledge of the sizes of droplets produced. To address this, a handy way to determine the droplet sizes, based on the titration of the helium droplet beam with room temperature helium and argon gases, was developed as will be detailed in Chapter 3. The titration experiments are absolute, straightforward, and can be easily implemented in other laboratories. The need for much larger droplets which can be used to grow nanometer-sized clusters further spurred the titration measurements, which showed that there exists a new droplet growth regime that can give rise to micrometer-sized droplets of 10 7 – 10 11 helium atoms. The size-selective production of clusters, their controlled deposition onto substrates, and their stability is of great importance to fundamental studies and in their potential applications. With this in mind, helium droplets were utilized to grow Ag clusters, as will be presented in Chapter 4. We have shown that clusters could be surface-deposited on a carbon film and studied via electron microscopy. This gave the average sizes of the Ag clusters grown in the droplets, their size distributions, and a better understanding of the cluster stabilities. The growth mechanisms of large clusters in superfluid helium droplets remain poorly understood. Here, we study the growth of large Ag clusters in helium droplets via their photoabsorption spectra and is reported in Chapter 5. The plasmon spectra of the clusters indicated a switch in the cluster growth mechanism from single-centered to multi-centered growth with increasing droplet size. Chapter 6 presents the results of 5 experiments focused on the possible reconstruction of the Ag clusters in helium droplets following absorption of intense laser pulses at different wavelengths. The application of the helium droplet technique in building large Ag-ethane clusters is described in Chapter 7. By using the infrared spectroscopy of the C-H stretch bands of ethane in the 3 µm range we were able to study the formation of Ag and ethane into core-shell clusters. In addition, the v 7 band of ethane is split into two distinct features due to molecules on the interface with Ag and molecules away from the interface. We show that, despite the fact that such nanometer-sized core-shell clusters have never been reported, they are stabilized in helium droplets and can be studied quantitatively. Despite the experimental observation of vortices in bulk superfluid helium 5 and calculations 6-7 indicating that they could be stabilized in small helium droplets of just a few hundred atoms, vortices have until now eluded experimental observation in helium droplets. Chapter 8 presents the first experimental observation of vortices in superfluid helium droplets. This observation was made by introducing Ag atoms, which clustered along the vortex lines, into the droplets. Indeed, surface-deposition and imaging of the Ag clusters reveals that vortices are present in droplets larger than about 300 nm. Chapter 9 will conclude the thesis and will be used to discuss the future direction of work described herein. 6 Chapter I Bibliography 1. A. Scheidemann, B. Schilling, J. P. Toennies and J. A. Northby, Physica B 165, 135-136 (1990). 2. A. Scheidemann, J. P. Toennies and J. A. Northby, Physical Review Letters 64 (16), 1899-1902 (1990). 3. M. Hartmann, R. E. Miller, J. P. Toennies and A. Vilesov, Phys. Rev. Lett. 75, 1566-1569 (1995). 4. D. R. Tilley and J. Tilley, Superfluidity and superconductivity. (Institute of Physics Publ., 1990). 5. R. J. Donnelly, Quantized Vortices in Helium II. (Cambridge University Press, Cambridge, 1991). 6. M. Barranco, R. Guardiola, E. S. Hernandez, R. Mayol and M. Pi, J. Low Temp. Phys. 142, 1-81 (2006). 7. F. Dalfovo, R. Mayol, M. Pi and M. Barranco, Physical Review Letters 85 (5), 1028-1031 (2000). 7 Chapter II: General Experimental 2.1. Introduction The helium droplet apparatus is presented schematically in Fig. 2.1. The experimental setup is essentially comprised of four chambers, which are labeled in the figure. In the “source chamber” a beam of droplets is produced. This is done by expanding helium gas at 20 bar into vacuum from a cold nozzle (NZ) (at 5 – 23 K) with a 5 µm aperture. A portion of this expansion is selected by a skimmer (SK). The resulting collimated beam of droplets traverses two differentially-pumped pick-up cells (PC1 and PC2) that are used to introduce atoms and molecules into the droplets by collision. The pick-up cells are located within the “main chamber” which serves as an additional differential pumping stage and increases the interaction length of the helium droplet beam with the counter-propagating laser beam employed during the photoabsorption measurements. Further downstream the doped droplet beam enters the “differential stage” where, during our deposition experiments, it may be collided with substrates placed at approximately 1 m from the helium droplet source. The last “detection chamber” houses the quadrupole mass spectrometer (QMS) which is equipped with an electron-impact ionizer (EI) and is employed for signal detection. The helium droplet source chamber is pumped by a diffusion pump with a nominal pumping speed of 6000 l/s. Each pick-up cell is pumped by turbomolecular pump with a 50 l/s pumping speed. The main chamber is evacuated using by a 8 turbomolecular pump with a pumping speed of 1500 l/s speed. A liquid nitrogen trap was also used in this chamber to reduce the residual water vapor pressure. Finally, 350 l/s and 500 l/s turbopumps were used to pump the “differential stage” and the UHV “detection chamber”, respectively. Some typical pressures in each of the six vacuum chambers are given in Table 2.1 for a helium stagnation pressure P 0 = 20 bar and different nozzle temperatures T 0 = 300, 11, 7, and 5.5 K. Figure 2.1. Schematic of the helium droplet beam vacuum apparatus. NZ: cold nozzle, SK: skimmer, PC1 and PC2: pickup cells, BG: Baratron vacuum gauge, IG1 and IG2: ion gauges, SH1 and SH2: beam shutters, A1 and A2: 6 mm diameter apertures, GV1 and GV2: gate valves, EI: electron impact ionizer, IB: ion bender, QMS: quadrupole mass spectrometer. 9 Source, mbar 1 st Pick-up Cell, mbar 2 nd Pick-up Cell, mbar Main, mbar Differential Stage, mbar Detection, mbar 300 K 1.3×10 -5 2.9×10 -7 4.8×10 -7 3.6×10 -7 6.5×10 -9 5.6×10 -10 11 K 6×10 -5 5.9×10 -7 6.4×10 -7 3.4×10 -7 1.35×10 -8 6.9×10 -9 7 K 1.5×10 -4 2.5×10 -6 2.4×10 -6 1.3×10 -6 3.1×10 -8 2.3×10 -8 5.5 K 9.7×10 -5 6.3×10 -5 2.4×10 -5 6.8×10 -6 9.8×10 -7 1.4×10 -6 Table 2.1. Typical chamber pressures at P 0 = 20 bar for T 0 = 300, 11, 7, and 5.5 K. 2.2. Helium Droplet Concepts 2.2.1. Production of helium droplets Helium droplets are produced here by a supersonic, continuous jet expansion of high-pressure helium gas or fluid into vacuum. The current setup employs a nozzle having a 2 µm channel which opens up to and terminates at a 5 µm diameter aperture. The flow through the aperture can be considered isentropic. The gas starts from a stagnation (slow velocity) state at source pressure P 0 = 20 bar and source temperatures T 0 = 5 – 23 K (which will also be referred to as the “nozzle temperature” throughout). The imposed pressure difference between P 0 and the pressure in the vacuum chamber, P v , which can be taken to be zero for the purposes of this work, accelerates the gas flow in the channel and through the nozzle orifice. 10 The droplets have a velocity in the range of 200 – 500 m/s, which depends on the T 0 and P 0 . 1-2 The relative velocities of the helium droplets in the beams have been measured and are approximately 1 – 3% of the beam velocity, v D . 1 There are three distinct helium expansion regimes 1 leading to droplets of different sizes, as described below. 1. In the sub-critical expansion, which occurs for P 0 = 20 bar at T 0 = 10-23 K, the initial state of the source helium is gas. The helium gas in the jet is cooled adiabatically by a change in state that approaches the gas-liquid coexistence curve from the gas side, i.e. from the right (see solid line trajectories in Fig. 2.2). Typical sizes for helium droplets produced sub-critically are 10 2 – 10 4 helium atoms. 2. In the critical expansion, the expansion trajectory which starts at P 0 = 20 bar and T 0 = 10.2 K cuts through the critical point at P c = 2.2 atm, T c = 5.2 K (see the dashed line trajectory in Fig. 2.2). 3. In the super-critical expansion, which occurs for P 0 = 20 bar at T 0 < 10 K, the initial state of the helium is fluid and the change in state is along an expansion isentrope that crosses the coexistence curve from the liquid side, i.e. from the left. (see dotted line trajectories in Fig. 2.2.) Droplets produced super-critically will range in size from 10 5 to 10 11 helium atoms. 11 Figure 2.2. Pressure-temperature phase diagram of 4 He. The dotted, dashed, and solid lines represent isentropes for super-critical, critical, and sub-critical expansions of 4 He at a source pressure of P 0 = 20 bar. 2.2.2. Helium droplet sizes Experiments involving beams of helium droplets rely on knowledge of the average number of helium atoms, He N , comprising the droplets in the beam. This average number is referred to as the “droplet size”. It is a crucial experimental parameter since it dictates the maximal size of cluster that can be grown within the droplet as well as its resulting structure. 12 He N values have been measured for droplets produced sub-critically where He N ≤ 10 4 by the deflection of a continuous beam of helium droplets upon capture of SF 6 molecules from a secondary beam. 3 It was found that the sizes of the helium droplets grown in the sub-critical expansion regime follow a log-normal distribution:   2 2 ln 1 ( ) exp 2 2 N PN          (2.1) The average droplet size, He N , and standard deviation, S, are given as a function of the parameters δ and μ as 2 exp 2 He N       (2.2)   2 exp 1 He SN   (2.3) S has experimentally been shown to be approximately 0.8 of He N . 4 Therefore, the deviation in size is comparable to the average droplet size, He N . Large helium droplets produced super-critically regime have been shown to exhibit an exponential size distribution. At higher temperatures within the super-critical expansion regime, bimodal speed and size distributions have been identified. 1, 5-6 It has been speculated that following the disintegration of the liquid droplets, helium atoms evaporating from the droplets may further feed the monoatomic gas expansion which leads to formation of smaller droplets by recondensation. 13 The sizes of droplets produced super-critically have also been measured. This was done by the deflection of charged droplets in an electric field for the size range10 5 < He N < 10 7 . 7 The sizes of much larger droplets in a continuous droplet beam were recently characterized by our group by titrating the beam with argon and helium atoms at room temperature. 2 We found that droplets produced at the lower T boundary of the supercritical regime could be as large as 10 11 helium atoms. A summary of the droplet sizes at P 0 = 20 bar for nozzle temperatures T 0 = 5.5 – 13 K, as encountered in this work, are shown in Fig. 2.3 below. The corresponding droplet diameters are shown on the right and were obtained according to 1 3 0 R r N  (2.4) in which a spherical droplet shape and bulk density (2.18 × 10 28 m −3 ) is assumed and r 0 = 2.2 Å is the unit radius for 4 He. It is seen from Fig. 2.3, that droplet diameters range from just a few to some thousand nanometers. 14 5 6 7 8 9 10 11 12 13 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 0 10 1 10 2 10 3 Droplet diameter, nm Droplet size, He atoms Nozzle temperature, K Figure 2.3. Average droplet sizes for various nozzle temperatures from continuous expansion of helium, at P 0 =20 bar, through a 5 μm nozzle. Results obtained by our group via measurements with collisional helium gas are shown by filled circles. Results of previous deflection measurements are shown by open stars. 3, 7 Right-hand scale shows corresponding liquid droplet diameters obtained using the density of bulk helium. 2.2.3. Capture of foreign atoms and molecules The process of embedding atoms or molecules into the droplets, which is referred to as the “pick-up”, occurs upon collision of these species with a helium droplet. The pickup cross-section has been shown to be close to the geometrical cross-section of the droplet. 8 15 The pickup of atoms and molecules is accomplished by directing the helium droplet beam through a cell filled with a vapor of the corresponding species. The number of captured particles can be controlled by regulating the pressure of the gas or vapor in the cell, and therefore the number density, n. The pickup process is statistical and Poissonian 8 . That is, the probability to pick up k molecules, P k , in the droplet as it traverse the pickup cell of length L is defined by     exp ! k k nL P n L k        (2.5) Here, σ = πR 2 is the geometrical cross-section of the helium droplet, and R is given by Eq. 2.4 above, The probability distributions for different values k = 0 – 5 are shown in Fig. 2.4. 16 Figure 2.4. Probability for capture of k particles by the droplets versus the average number of the captured particles. 2.2.4. Evaporation of helium following the capture of foreign atoms and molecules The pick-up of atoms and molecules will lead to the loss of helium atoms from the helium droplet by evaporation. This occurs as a result of the dissipation of the energy associated with the impacting particle: the kinetic energy (E kin ) associated with the collision, the particle’s internal energy (E int ), and the binding energy of the particle to the droplet and energy for cluster formation (E bind ). This energy released into the droplet upon pickup, E pick-up , can be expressed as E pick-up = E kin + E int + E bind (2.6) 0 1 2 3 4 5 6 7 8 0.0 0.2 0.4 0.6 0.8 1.0 Probability Atoms/molecules picked up by droplet k=0 k=1 k=2 k=3 k=4 k=5 17 2 int 3 22 s B pick up D bind m kT E v E E      (2.7) where k B is Boltzmann’s constant, T is the temperature of the scattering gas or vapor, m s is the mass of the solute particles, and v D is the velocity of the droplet beam. 2.2.5. Laser systems The laser setup in the experiments of Chapters 6 and 7 consists of a custom built infrared optical parametric oscillator/amplifier (OPO/A) system (LaserVision) pumped by a pulsed Nd:YAG laser (Continuum Inc., PowerLite II 8020). The normal linewidth of the OPO/OPA system output is 0.08 cm -1 and 1 cm -1 with the injection seeder of the Nd:YAG laser on and off, respectively. The output of the OPO/A system can be continuously tuned in the range of 2×10 3 – 14×10 3 cm -1 . The laser setup used in the experiments of Chapter 5 consists of a pulsed optical parametric oscillator (EKSPLA NT342/3/UV). This system can be continuously tuned in the range of 4.5×10 3 – 4.8×10 4 cm -1 (0.5 – 6 eV) with a linewidth of about 10 cm -1 . In both experiments the collimated laser beam was directed counter to the doped droplet beam, for an interaction length of about 1 m. Absolute wavenumbers in the IR were calibrated against the known absorption spectra of reference gas in a photo-acoustic cell. 18 2.2.6. Mass spectrometer detection and the depletion technique In the spectroscopic experiments described in Chapters 5 – 7, a quadrupole mass spectrometer (QMS) has been implemented for signal detection. In this approach, the total flux of the helium droplet beam is detected by the QMS (Extrel MAX300), which is equipped with electron impact ionizer and a multi-channel plate type electron multiplier. The QMS can work in three different operational modes: it can (1) be set on a single mass, (2) scanned over a certain mass range, and (2) be set to detect only ions above a certain m/z ratio by the application of only a DC voltage to the mass filter. During the spectroscopic experiments, a laser pulse is directed through the CaF 2 entrance window at the end of the helium droplet machine coaxially and counter to the droplet beam. This provides optimal overlap between the two beams. Following resonant absorption of a laser photon by the embedded atoms/molecules, the deposited energy leads to the fast (t ≤ 10 -6 s) evaporation of a sizeable fraction of the helium droplet. Absorption of a single IR photon at 2000 cm -1 , for example, corresponds to depositing an energy of ~2800 K into the droplet. Assuming a heat of evaporation of 7 K, this leads to the loss of approximately 400 helium atoms. This reduction in the droplet size results in a decreased cross-section for electron-impact ionization and, therefore, to a transient decrease in the ion current. The helium droplet signal is monitored by sitting on m/z = 8, which corresponds to the dominant splitter ion from droplets. 1 The mass spectrometer signal is monitored before, during, and immediately after the laser pulse. A typical time profile of the mass spectrometer signal following laser excitation is shown in 19 Fig. 2.5. The time profile is then used to obtain the relative depletion of the signal according to 3 Relative depletion = B B II I  (2.8) Here, I B is the average intensity before and after laser excitation (regions I and II) 00 00 ( ) ( ) I II ff I II tt tt B I I II II ff I dt I dt I t t t t         (2.9) And I 3 is given by 0 3 III f III t t I I dt   (2.10) 20 Figure 2.5. Typical time profile of the mass spectrometer signal at m/z = 8 following the laser pulse at t = 0. Time profile is for laser excitation at 532 nm of Ag 300 cluster in a droplet of He N = 1.8×10 6 . 21 Chapter II Bibliography 1. H. Buchenau, E. L. Knuth, J. Northby, J. P. Toennies and C. Winkler, Journal of Chemical Physics 92 (11), 6875-6889 (1990). 2. L. Gomez, E. Loginov, R. Sliter and A. F. Vilesov, J. Chem. Phys. 135, 154201- 154209 (2011). 3. M. Lewerenz, B. Schilling and J. P. Toennies, Chemical Physics Letters 206 (1- 4), 381-387 (1993). 4. J. Harms, J. P. Toennies and F. Dalfovo, Physical Review B 58 (6), 3341-3350 (1998). 5. T. Jiang and J. A. Northby, Physical Review Letters 68 (17), 2620-2623 (1992). 6. H. Buchenau, J. P. Toennies and J. A. Northby, The Journal of Chemical Physics 95 (11), 8134-8148 (1991). 7. U. Henne and J. P. Toennies, The Journal of Chemical Physics 108 (22), 9327- 9338 (1998). 8. M. Lewerenz, B. Schilling and J. P. Toennies, J. Chem. Phys. 102 (20), 8191- 8207 (1995). 22 Chapter III: Sizes of Large He Droplets 3.1. Introduction The He droplet technique has been instrumental in a number of important findings 1-4 . The observation of the rotational spectra of molecules embedded in He droplets has provided for a novel microscopic probe of superfluidity in droplets and its development as a function of droplet size 5-6 . Another very fruitful application of the He droplet technique is in the growth and laser spectroscopic study of atomic and molecular clusters, which is reviewed in Refs. 1-3, 7 . So far, such experiments with He droplets have mainly employed droplets of less than about 10 4 He atoms and, thus, have been focused on relatively small clusters up to about 10 particles. Much larger clusters of thousands of particles can be formed in larger He droplets. Mass spectroscopic studies have reported the formation in large droplets of Ag and Pb clusters up to about 100 atoms 8-10 and Mg clusters 11 of up to several thousand atoms. Ammonia clusters of up to 10 4 molecules have been formed in He droplets and studied via IR spectroscopy 12 . The results of our recent laser spectroscopic study of Ag clusters, Ag N (N = 10 – 10 4 ), suggest a transition from single-center to multi-center aggregation with increasing He droplet size 13 . We have also shown that such metal clusters produced in He droplets can be deposited onto a surface upon impact 14 and imaged by transmission electron microscopy 15 . The average sizes of the deposited clusters were found to be in good agreement with an estimate based on the energy balance of Ag cluster growth in He droplets. 23 The average size of the He droplet, <N He >, is a crucial experimental parameter since it dictates the maximal size of cluster that can be grown within as well as its structure. At present, workers usually rely on <N He > values measured by the deflection of a continuous beam of He droplets upon capture of Xe atoms from a secondary beam and those measured by the deflection of charged droplets in an electric field for <N He > < 10 4 and 10 5 < <N He > < 10 7 , respectively 1, 16-17 . It remains unknown, however, how the results of Refs. 1, 16-17 can be applied to measurements in other laboratories which may employ somewhat different source conditions such as nozzle diameter, temperature, etc. Moreover, the <N He > values obtained in such continuous-nozzle beam expansions are not applicable to the pulsed He droplet beams which were first introduced in our laboratory 18 and have since then been used by other groups 19-22 . In this work, we introduce a technique for the absolute measurement of <N He > > 10 5 , which can be easily replicated in a typical molecular beam apparatus. The technique is based on the attenuation (titration) of a continuous He droplet beam through collisions with argon and helium gas at room temperature. The average sizes determined are in good agreement with the measurements of Refs. 1, 16-17 in the range of <N He > = 10 5 – 10 7 . In addition, the titration measurements have been expanded into the previously unexplored range of much larger droplets of about 10 10 atoms. In this work, we also present our study of the mass spectra of the droplets upon electron impact ionization. The spectra show a large increase in the intensity of the He 4 + signal with increasing He droplet size, as observed previously 23 . This effect is presented as a secondary size standard in the droplet size range of <N He > =10 4 – 10 9 atoms. 24 3.2. Experiment A schematic of the molecular beam apparatus is shown in Fig. 3.1. He droplets are formed by expanding into vacuum high-purity (99.9999%) He gas at a stagnation pressure of P 0 = 20 bar and nozzle temperatures, T 0 , in the range T 0 = 4 – 25 K. As in previous works 13-17, 23-24 , we have employed an electron microscope diaphragm with a 5 µm orifice (Plano A0200P) as the nozzle. According to the manufacturer, the orifice channel has a nominal length of approximately 2 µm. The droplet beam is collimated by a 0.5 mm diameter skimmer and passes through two pickup cells (PC1, PC2) in the main vacuum chamber. Further downstream, the droplet beam traverses a differential pumping stage and finally enters a UHV detection chamber, which hosts a quadrupole mass spectrometer (Extrel MAX300) equipped with an electron impact ionizer. The He droplet velocities, important for obtaining the average droplet sizes as will be shown, were measured by momentarily heating the nozzle with a laser pulse as described in Appendix 2. Helium or argon collisional gas was backfilled into either PC1 or the entire main chamber, as will be discussed in the following. Accordingly, on their way towards the detection chamber, the He droplets experience multiple collisions with helium or argon atoms at room temperature, as illustrated in Fig. 3.2. With each collision the He droplet loses a known number of atoms resulting in an attenuation of the droplet beam. This attenuation was used to deduce the average He droplet size in the beam as will be elaborated upon in Section 3.1. This titration technique is well-suited to large He droplets 25 (N He > 10 5 ) where the scattering of droplets following collision is negligible, and because the droplet capture cross-section can be taken as equal to the geometrical cross-section. Henceforth, as an aid to the reader, helium introduced into the vacuum apparatus through the nozzle into the source chamber will be referred to by chemical symbol (i.e., He) whereas collisional, titrant gas backfilled into the main chamber will be referred to by name (i.e., helium, argon). Figure 3.1. Schematic of the He droplet beam vacuum apparatus. NZ: cold nozzle, SK: skimmer, PC1 and PC2: pickup cells, BG: Baratron vacuum gauge, IG1 and IG2: ion gauges, SH1 and SH2: beam shutters, A1 and A2: 6 mm diameter apertures, GV1 and GV2: gate valves, EI: electron impact ionizer, IB: ion bender, QMS: quadrupole mass spectrometer. 26 Figure 3.2. Illustration of measurement of He droplet sizes by titration of droplet beam with collisional helium atoms at room temperature. Decrease of He flux into the detection chamber (far right) is measured as a pressure drop, ΔP. 3.3. Results At the rear end of the apparatus, in the detection chamber, the droplet beam collides with the wall and evaporates resulting in an increase in the He partial pressure, as illustrated in Fig. 3.2. Figure 3.3 shows the dependence of the He partial pressure in the detection chamber on the nozzle temperature from T 0 = 100 K – 4 K at a constant nozzle stagnation pressure P 0 = 20 bar. The flux of He from the beam into the detection chamber, Φ He , is also shown on the right-hand scale of Fig. 3.3 as was obtained using the nominal pumping speed of the detection chamber of 500 L/s and solid angle of aperture A2, 2.8×10 -5 srad. It is seen that the intensity of the beam increases gradually from T 0 = 27 100 K to 30 K approximately as 0 1 T , which is expected for an ideal gas expansion. At T 0 < 30 K, however, the flux deviates considerably from the ideal gas prediction due to the different modes of He droplet formation, as will be elaborated in Section 4.2. At even lower nozzle temperatures T 0 < 6 K, a remarkable rise in the beam intensity by about a factor of 100 is seen. A similarly sharp rise in the beam intensity at low temperature was observed previously 25-26 . Below nozzle temperatures of about 7 K, the expansion is characterized by a high degree of instability in the flux, which varies by up to a factor of 2 and correlates with the 1.2 Hz mechanical strokes of the cryo-cooler. Therefore, all results in the low temperature range are averages over measurement times of 100 s. This instability is partially due to the vertical movement of the nozzle by about 0.1 mm during the stroke, as measured by telescopic observations along the machine axis. In addition, variations in the nozzle temperature by about ±0.1 K during the cryo-cooler strokes are another source of the instability. 28 Figure 3.3. Intensity of the He droplet beam, produced by continuous expansion of He gas at 20 bar through a 5 µm nozzle, as measured by the partial pressure rise of He in the detection chamber. Nominal reading of the ion gauge (Leybold-Heraeus IM 510 gauge, IE 514 sensor) has been corrected for the sensitivity of the gauge to He gas. Partial pressure rise was obtained as a pressure difference between the beam unblocked and blocked using shutter SH1. Scale on the right-hand side shows flux of He transported by the beam into the detection chamber. Solid line shows 0 1 T dependence normalized to experimental data point at T 0 = 100 K. 29 Figure 3.4 shows typical dependences of the He flux by way of the He droplet beam on the collisional gas pressure, P M , for various nozzle temperatures. The flux has been normalized to its initial value, Φ He (0), obtained prior to the addition of any collision gas. In these experiments, the entire main chamber (including PC1 and PC2) was flooded with collisional helium gas (i.e., M = helium) for a total interaction length L = 66 cm. P M in the main chamber was measured as a pressure rise with an ionization gauge calibrated against a high-sensitivity capacitance diaphragm absolute pressure gauge (MKS Baratron, model 127AA-000.10). Φ He is proportional to the rise in the partial pressure of He in the detection chamber, which was monitored by the mass spectrometer signal at m = 4, I 4 . During the measurements, shutter SH2 was kept in the closed position and allowed for the droplets to be broken up prior to reaching the ionizing region of the mass spectrometer. This technique thereby maintains a direct relation between I 4 and the He content of the beam while eliminating the contribution to the signal from direct droplet ionization. For larger droplets, the efficiency of direct droplet ionization depends on the droplet cross section rather than on the number of He atoms in the droplet. In addition, to eliminate from the signal the contribution from effusive helium from the main chamber, I 4 was measured as a difference between shutter SH1 open and closed. The results in logarithmic-linear scale in Fig. 3.4 show a linear dependence, indicating that the pressure dependences of Φ He can be well fitted by () ln (0) He M M He P P          (3.1) where α is an attenuation coefficient. The values of α were obtained by linear fits to the 30 pressure dependences, some of which are shown in Fig. 3.4, for normalized flux values, Φ He (P M )/ Φ He (0), in the range of 1 – 0.3 (i.e., at or below 70% droplet attenuation). Fitted values of α, normalized by the interaction length L, are listed in Table 3.1 for the different nozzle temperatures tested. Some values represent averages obtained for different experimental runs, which typically deviate by less than about 20%. Figure 3.4 and Table 3.1 show that the α values decrease by about a factor of 200 upon decreasing T 0 from 15 K to 5.4 K, which indicates a large increase in the average droplet size (as will be quantified in Section 4.1). Similar experiments were conducted using collisional argon gas by admitting it into pickup cell PC1 for a smaller interaction length of L = 7.7 cm. As described thus far, the attenuation measurements involved the total flux of He into the detection chamber. This approach for determining the droplet sizes implies that the entire measured flux of He is due to the droplets and, therefore, that the contribution to the flux from He atoms in the beam is small. This, however, is not known a priori. Therefore, measurements were carried out at selected nozzle temperatures in which the ionizer of the mass spectrometer was exposed to the direct He droplet beam with the mass spectrometer set to m = 8. Because the He 2 + signal, I 8 , originates solely from the droplets it is therefore uninfluenced by the atomic contribution. The results obtained with the I 8 signal are shown in Fig. 3.4 by open symbols and the corresponding values of attenuation coefficients obtained, α 8 , are shown in parentheses in the second column of Table 3.1. Attenuation measurements using the I 8 signal were not attempted with collisional argon gas as argon atoms are captured by the droplets. The ionization of 31 argon-doped droplets also yields Ar n + ions. Accordingly, the partitioning of the ion signal is changed with argon doping and interpretation of the attenuation coefficient α 8 is no longer straightforward. Figure 3.4. Normalized He flux versus collisional helium gas pressure in the main experimental chamber for droplets obtained at T 0 = 5.7, 6, 7, 9 and 12 K. Filled symbols represent values obtained by measuring the He partial pressure rise in the detection chamber with the mass spectrometer set to m = 4. Open symbols correspond to the measurements of the droplet beam intensity at m = 8. Solid and dashed lines are fits according to Eq. 1 for measurements with m = 4 and m = 8, respectively. 32 Table 3.1. Nozzle temperature, T 0 ; attenuation coefficients α 4 and α 8 (upper and lower entries) obtained with helium titration; droplet beam velocity, v D ; and average number of He atoms in the droplets, <N He >, according to Eq. 3.2. Table 1 also contains intensity ratios of peak m = 16 to m = 8 and m = 12. Values of <N He > obtained previously, using deflection techniques of Refs. 17, 27-29 , are shown in the penultimate column. Shaded values of <N He > in the last column are beyond the range of the applied technique as described in the text. All measurements are at nozzle stagnation pressure of P 0 = 20 bar. a) measured in this work b) from Ref. 27 c) from Refs. 17, 29 d) from Ref. 28 33 In Fig. 3.5 we show typical mass spectra of the He droplet beams obtained at P 0 = 20 bar and T 0 = 7, 9, and 14.5 K. The spectra were measured at an electron energy U e = 100 eV and emission current I e = 4 mA. The spectra are characterized by a sequence of peaks at every 4 mass units due to He n + cluster ions. It is seen that the intensity of the peak at m = 16 increases markedly with decreasing nozzle temperature, as observed previously 23 . A much smaller intensity variation is observed in the other peaks. Table 3.1 shows the intensity ratios of the mass 16 peak to masses 12 and 8, I 16 /I 12 and I 16 /I 8 , measured with varying T 0 . Figure 3.5. Typical mass spectra of He droplet beams obtained at P 0 = 20 bar and T 0 = 7 (blue trace), 9 (red), and 14.5 K (black). The spectra have been normalized to the same 34 intensity at m = 8. Electron beam energy 100 eV, emission current 4 mA. Contributions from effusive helium gas and rest gas in the detection chamber have been subtracted out. 3.4. Discussion 3.4.1. Average sizes of He droplets Our measurements of the average droplet size rely on the known heat of vaporization of bulk liquid He, E V . We assume that the collision of an atom with a He droplet has a cross section given by π·R 2 , where R=   1/3 1/3 3 0.22 4 He He LHe N N n        (nm) is the radius of the droplet. Then, in the limit of small attenuation, <N He > can be obtained according to 3 2 22 2 31 4 D M M He LHe B D V L v v E NC n k T v E                 (3.2) as described in Appendix 2. Here, n LHe = 2.18×10 28 m -3 is the number density of liquid He 30 , T = 293 K, E M is the energy added to the droplet by the colliding atom of either argon or helium, L is the length of the interaction region, v M is the room temperature velocity of the collisional argon or helium atom of 430 and 1360 m/s, respectively, and v D is the velocity of the He droplet. The attenuation coefficient α is introduced in Eq. 3.1 and is obtained experimentally. The effects of the decreasing droplet collision cross section during the course of titration and the droplet size distribution are addressed in Appendix 2. It is shown that Eq. 3.2 gives an accurate measure of the <N He > over the 35 attenuation range of 1 – 0.3 and that for the exponential droplet size distribution at T 0 < 10 K 17 C = 1. In the case of a log-normal distribution and for droplets produced at T 0 > 10 K 16 , C = 1.3. Assuming full energy exchange, the energy transferred to the droplet upon collision with a helium atom of mass M helium is given by Eq. 3.3. 2 helium 3 22 D He B Mv E k T  (3.3) Argon atoms, on the other hand, are captured by the droplet upon impact; an additional term is therefore associated with the binding energy of the argon atom to the pre-existing argon cluster, E S . 2 argon 3 22 D Ar B S Mv E k T E    (3.4) There is an uncertainty associated with the latter term as the structure of large clusters formed in He droplets is not known a priori. In this work, the bulk sublimation energy, E S , of argon (7680 J/mol) is taken as an estimate 31 . The actual value of E S may be somewhat smaller due to the large fraction of surface atoms in smaller clusters and any possible porosity in larger clusters. The interaction energy of the argon cluster and the liquid He environment is also ignored due to the unknown structure of the cluster. As a result, the values of <N He > via argon titration are inherently less accurate than those obtained by way of titration with helium. Bulk values of E V increase somewhat with temperature from E V = 68.1 to 76.4 J/mol at 0.4 K and 0.8 K, respectively 30 . The characteristic temperature of the droplet 36 can be estimated 32-33 using the known temperature dependence of the vapor pressure 30 and the rate of evaporation from the droplet at an attenuation of 30%, which approximately corresponds to the middle of the attenuation range (0 – 70%) used to obtain the values of α. For the helium (argon) experiments, the temperature of the droplet was estimated to be 0.50 K (0.57 K), 0.59 K (0.67 K), and 0.67 K (0.80 K) for droplets of 10 4 , 10 7 and 10 10 He atoms, respectively. The correction to E V is rather small. For titration with helium gas, we took E V = 73.3 J/mol at T = 0.65 K and for titration with argon we took E V = 75.37 J/mol at T = 0.75 K; these temperatures represent average values over the range of the large He droplets studied, 10 6 – 10 10 . Fig. 3.4 shows that at T 0 = 12 K the attenuation curves obtained with I 4 and I 8 are very similar within the scatter of the data points. These results suggest that He atoms transported by the droplet beam make the predominant contribution to the flux, whereas the contribution of effusive helium is rather minor at this nozzle temperature. On the other hand, as seen in Table 3.1, at T 0 = 14 K α 4 is smaller than α 8 with a larger difference observed at T 0 = 16 K. This likely indicates a substantial atomic contribution to the beam with increasing T 0 . Thus, we conclude that the atomic contribution becomes prevalent with increased T 0 and the I 4 signal ceases to be useful for determining the droplet sizes for T 0 > 13 K. It is seen from Table 1 that the overall tendency of increasing α 4 with T 0 reverses at T 0 >16 K. This result is likely associated with a dominant atomic contribution in the He droplet beam at higher nozzle temperatures, so that at T 0 = 23 K α 4 simply reflects scattering of the beam comprised of He atoms and very small clusters such as He 2 and He 3 , small quantities of which are known to be present in the beam at even higher T 0 37 34 . It is rather unfortunate that the value of α 4 characteristic of atoms and small He clusters is very similar to that obtained at T 0 = 10 K, when He droplets of about 10 5 are being produced. This precludes the use of α 4 for evaluating the abundance of He atoms in the beam. The much smaller values of α 4 obtained at T 0 < 7 K, indeed show that the contribution of atoms to the beam is small at low T 0 . Moreover, prior to the addition of any scattering gas, the high intensity of the beam at low T 0 results in a high base pressure of He in the main chamber of 3×10 -5 and 7×10 -5 mbar at T 0 = 6 and 5.4 K, respectively. At such pressures the intensity of a beam of small droplets obtained at, for example, T 0 = 12 K is attenuated by approximately 80% (see Fig. 3.4). In this way, only larger droplets contribute to the measurements of α 4 at low nozzle temperatures. Previous time-of-flight mass spectrometric measurements have indicated that He atoms in the beam have an approximately 3% faster velocity than droplets, which permits their separation 27 . Accordingly, for P 0 = 20 bar the atomic contribution to the m = 4 signal is apparently dominant at T 0 > 16 K, whereas it is negligible at T 0 < 13 K. At intermediate temperatures both contributions are important, in good agreement with our conclusions. Fig. 3.4 and Table 3.1 show that at T 0 ≤ 10 K the α 8 coefficients measured upon ionization of the droplets are systematically smaller than α 4 , which were obtained from the pressure rise measurements. In very large droplets, the electrons must completely lose their energy in the surface region of the droplet, and the ion signal should be proportional to the droplet’s cross section with I 8 scaling as (N He ) 2/3 . Therefore, in the very large droplets of <N He > > 10 7 the value of α 4 is expected to be about a factor of 1.5 38 larger than α 8 , in agreement with the obtained results in Table 3.1. Therefore, we conclude that the measured values of α 4 can be used to obtain <N- He > in the regime of supercritical expansion at T 0 ≤ 10 K. The values of α 8 , which are easier to acquire experimentally, can also be used to obtain <N He > at T 0 < 8 K after multiplication by a factor of 1.5. From the measured α 4 coefficients listed in Table 3.1, the average number of He atoms in the droplets, listed in the last column of Table 3.1, have been calculated according to Eq. 3.2 at the various nozzle temperatures. Also, shown for comparison are <N He > values obtained previously by way of the deflection techniques of Refs. 17, 27-29 . Figure 3.6 compares the <N He > obtained in this work by titration with helium and argon gases to those from Refs. 17, 27-29 . Indeed, there is very good agreement in the range of T 0 = 7 – 9.5 K. It is also seen that at T 0 < 10 K, both the helium and argon titration results follow the same dependence within the scatter of the data points, lending additional support to the use of Eq. 3. 2. The scattering increases at T 0 < 6 K which may be caused by nozzle instabilities as will be discussed in Section 3.4.2. These results confirm that large He droplets essentially act as isothermal calorimeters during the titrating collisions. It is also seen from Fig. 3.6 that the <N He > obtained via titration above T 0 = 10 K are systematically lower than those previously measured 27 , and that this deviation increases with T 0 . Of course, this may indeed reflect an actual difference in the sizes of the droplets produced in this work and those previously measured. Smaller droplets are more sensitive to difficult-to-control disturbances such as, for example, possible interference from the skimmer. The titration technique is inherently expected, however, 39 to be less reliable for smaller droplets due to a number of effects such as: (i) droplet scattering following collisions with titrant atoms, (ii) the finite width of the liquid He surface, and (iii) the size dependence of E V in small droplets. All of the above would lead to an underestimation of <N He > as is elaborated below. i. At small attenuation, Δ Φ He / Φ He , the average scattering angle, β, of the He droplets following multiple collisions with scattering gas atoms of mass M M , can be approximately obtained as: 2 MB He He V He He D He M M k TNE N M v E       (3.5) for which we have assumed complete momentum transfer upon collision. At Δ Φ He / Φ He = 0.3, for the two droplet sizes N He = 10 4 and 10 3 , we obtain β ≈ 2×10 -3 and 6×10 -3 , respectively. This is comparable to or larger than the collimation angle of the beam of about θ/2= 4×10 -3 , defined by the 3 mm orifice in PC2 (40 cm from the nozzle). Therefore, scattering will contribute to a decrease in the beam intensity and lead to an underestimation of the droplet sizes at N He < 10 5 . The effect of scattering by argon atoms is more pronounced than by helium atoms, which contributes to the smaller values of <N He > obtained with argon for T 0 > 10 K, as shown in Fig. 3.6. ii. The surface of the He droplet is not sharp but has a significant width of about 0.6 – 0.8 nm, where the density drops from 90% to 10% of the bulk value 35 . Calculations 35 have indicated that the scattering cross-section is largely determined by the outer regions of the droplet with substantial scattering from regions of density as low as 1%. Measurements of the integral cross-section for scattering of He droplets by argon atoms 40 indicate an effective density of about 0.5 and 0.7 of n LHe in He droplets of 10 3 and 10 4 atoms, respectively 35 . Therefore, using the bulk liquid He value n LHe in Eq. 3.2 will lead to an underestimation of the droplet sizes. iii. Small droplets have a large fraction of surface atoms and, thus, a smaller binding energy than for bulk liquid by about   1/3 37.4 He N   J/mol 33 . Therefore, using bulk values of E v will result in an underestimation of <N He >. The effects of (i) – (iii) should be taken into account. However, this would require a simulation of the beam broadening as well as more knowledge of the scattering of atoms at the surface of the He droplets. Some estimate of the accuracy of the titration technique can be obtained from the amount of data scattering between measurements in this work for different experimental runs as well as between argon and helium titrants. Another point of reference is to compare the results with previous measurements 17, 27-29 using deflection techniques. Here, we conservatively estimate that the values of <N He > > 10 5 obtained in this work are accurate to within about a factor of 2. For very large droplets of <N He > > 10 8 , the largest source of error is the day to day variation in the measured <N He > which may amount up to about a factor of 2 at T 0 < 6K. These variations may result from instabilities of the nozzle beam expansion at these conditions, indicating that the <N He > measurements should preferably be done contemporaneously. The accuracy of the obtained <N He > values at T 0 = 9 – 10 K can also be influenced by the bimodal distribution of droplet sizes in this temperature range as found previously 17, 29 . Finally, the deviation between the <N He > obtained in different laboratories may be caused by deviation of the actual nozzle 41 diameters from their nominal value of about 20% as well as by inaccuracies in determining the nozzle temperature. 42 Figure 3.6. <N He > obtained at various nozzle temperatures from continuous expansion of He, at P 0 = 20 bar, through a 5 µm nozzle. Results obtained via measurements of α 4 with collisional helium and argon gases are shown by filled squares and circles, respectively. Results of previous deflection measurements are shown by open triangles 17, 29 and 16, 27-28 stars. Right-hand scale shows corresponding liquid droplet diameters obtained using n LHe . 43 3.4.2. Modes of nozzle operation at different temperatures The temperature dependences of the He flux and droplet sizes, shown in Fig. 3.3 and Fig. 3.6, respectively, give information on the different regimes of droplet formation in the nozzle beam expansion. Fig. 3.3 shows that the beam intensity increases gradually from T 0 = 100 K to 30 K approximately as 0 1 T , which is expected for an ideal gas expansion. The intensity drops below T 0 ≈ 30 K until about 20 K, which is likely associated with the scattering of He atoms in the beam during droplet formation, as evidenced by the appearance of He N + (N ≥ 3) peaks in the mass spectrum below T 0 ≈ 22 K. From T 0 = 18 K – 10 K, the intensity of the beam rises gradually due to an increasing degree of droplet formation. Whereas He atoms have a broader angular distribution, droplets tend to remain on axis resulting in a larger downstream flux into the detection chamber. At T 0 = 17 – 10 K the average droplet size increases gradually from <N He > = 10 3 to about 5×10 4 . In this so-called subcritical regime, the expansion isentropes cross the gas-liquid phase separation line from the gas side 23-24 , i.e., droplets are produced by aggregation of atoms. This is shown in Fig. 3.7, which is the pressure-temperature phase diagram for 4 He at a stagnation pressure of P 0 = 20 bar with isentropes from Ref. 23 . According to Fig. 3.7, the expansion isentrope which starts at P 0 = 20 atm and T 0 = 10 K comes very close to the critical point: T C = 5.2 K, P C = 2.28 atm. In the supercritical regime, at T 0 < 10 K, the expansion isentropes cross the gas-liquid phase separation line from the liquid side, i.e., droplets are formed by fragmentation of the fluid. The locations of the sonic points show that this fragmentation occurs downstream 44 from the nozzle orifice for temperatures down to about 6 K. Upon decrease of the nozzle temperature from 10 K to 8 K, <N He > increases by a factor of about 10 2 , as seen in Fig. 3.6. Upon further decrease of temperature from 8 to 6.5 K both the droplet size and flux increase, but at a much slower rate. At T 0 = 7 K, the flux remains only about a factor of 2 larger than that predicted for an ideal gas expansion (see solid curve in Fig. 3) which indicates a similar degree of collimation in the beam. Figure 3.7. Pressure-temperature phase diagram of 4 He. Isentropes (dashed lines) are for 4 He at a stagnation pressure of P 0 = 20 bar from Ref. 23 . Locus of sonic points specifies the states at the orifice for the isentropic expansions. 45 At temperatures below 6 K, there is a sudden increase in droplet size by a factor of 10 3 and an increase in the flux by about a factor of 100, compared to that at T 0 = 7 K, which indicates a new regime of nozzle operation. According to Fig. 3.7, the expansion starting at 6 K becomes sonic at the orifice. At lower T 0 < 6 K the expansion crosses the phase separation line before it reaches the exit of the nozzle. The fluid separates into large droplets and a dense gas which continues to expand along the nozzle channel. The formation of droplets inside the nozzle is consistent with the high degree of collimation of the beam under these conditions. The temperature dependence of the He droplet velocities provides additional evidence for the formation of an unstable jet at T 0 < 6 K. Table 3.1 shows that the He droplet velocities drop sharply from 195 m/s at 6.5 K to 175 m/s at 6 K and remain constant at lower temperatures. Inspection of the isentropes for T 0 < 6K in Fig. 3.7, shows that during the expansion the pressure drops from 20 bar to less than 1 bar with the He remaining fluid, i.e., before the phase separation. Therefore, the velocities of the He droplets in this regime can be approximated by the Bernoulli equation for fluid flow through a thin orifice, Eq. 3.6. 0 2 Bern P v   (3.6) During the expansion, the density of the He fluid changes from about ρ =153 kg/m 3 at 20 bar, 5.7 K to about 119 kg/m 3 at the phase separation line, 4.5 K 30, 36 . Taking an average density of ρ =136 kg/m 3 and backing pressure P 0 = 2·10 6 Pa, a velocity of v Bern = 171 m/s is obtained which is in good agreement with the measured value of v D = 173 m/s. The 46 validity of the Bernoulli equation for the determination of the velocity of a liquid He jet at even lower nozzle temperatures T 0 ≤ 4.2 K was proved previously in Ref. 37 . Upon decrease of T 0 , to below about 5 K the time required for phase separation becomes comparable with the expansion time through the nozzle, and He emanates as a liquid jet into vacuum, where it cools via evaporation. Indeed, at T 0 < 5 K a sharp liquid jet is formed which one could observe with the naked eye or with a microscope. The sharp jet, as we have observed, misses the skimmer orifice leading to the diminished flux at T 0 < 5 K in Fig. 3. Figure 3.7 shows that the expansion isentrope, which starts at T = 5 K, P 0 = 20 bar crosses the gas-liquid phase separation line at about 4 K. Previous studies 24 have indicated that the liquid He jet remains stable at temperatures lower than about 3.7 K in agreement with the present results. At some distance from the nozzle, the jet breaks up into large droplets of about 8 µm in diameter (N He ≈ 5×10 13 ) due to Rayleigh instability 26, 37 . Finally, in the temperature range T 0 = 5 – 6 K, the nozzle expansion is expected to be unstable, as any small change of temperature and pressure will effect a large variation in the position of the sonic point, any beam collimation, and, therefore, of the measured <N He >. This is in agreement with the observed fluctuations in the flux by about a factor of 2, fluctuations which are in phase with the strokes of the closed-cycle refrigerator. 3.4.3. Using mass spectra for determining average droplet sizes in continuous and pulsed expansions Table 3.1 and Fig. 3.8 show the intensity ratios of the mass peaks m = 16 to m = 8 47 and 12, I 16 /I 8 and I 16 /I 12 , measured at various T 0 corresponding to droplets of different average sizes <N He >. It is seen that there is only a small change in the relative intensity of the He 4 + signal in the range of T 0 = 19 – 11K corresponding to <N He > = 10 3 –10 4 . Upon further decrease of the nozzle temperature from 19 K to 6 K (<N He > ~ 10 9 ) the ratios I 16 /I 12 and I 16 /I 8 increase by about a factor of 15 and 30, respectively, and then remain approximately constant at lower temperatures. Therefore, the values of I 16 /I 12 and I 16 /I 8 can be effectively used as measures of the He droplet size in the range of 10 4 – 10 9 . It should be noted, however, that the transmission of the quadrupole mass filter depends on the m/e ratio and the electron optics settings. Therefore, I 16 /I 12 and I 16 /I 8 can also be used in order to gauge the importance of such effects. Mass spectroscopic monitoring of the average droplet sizes is especially useful in the case of pulsed He droplet beams. The average droplet size in the pulsed expansion may depend on such factors as the mechanical nozzle assembly, pulse duration, and repetition rate. Therefore, some method of intrinsically monitoring the droplet sizes such as through the ratio I 16 /I 8 , for example, would be very helpful. Figure 3.9 shows the results of measurements of the I 16 /I 8 ratio for a beam of He droplets obtained by way of a 1 mm diameter pulsed-valve 18 at a He gas stagnation pressure of P 0 = 15 bar. This ratio was measured at different nominal nozzle temperatures for the two repetition rates of 1 Hz and 10 Hz indicated by solid circles and open squares, respectively. From Fig. 3.9 it is seen that the I 16 /I 8 ratio obtained for the pulsed nozzle expansion increases gradually from about 0.05 to 0.35 with decreasing nozzle temperature from 20 K to 10 K. From the results of Fig. 3.8, it follows that the <N He > 48 correspondingly changes from about 5×10 4 to 10 7 . Similar droplet sizes in the continuous beam expansion are obtained at lower nozzle temperatures ranging from 10 to 7 K. No signs of saturation in the measured values of the I 16 /I 8 ratio are seen for the pulsed nozzle expansion; therefore even larger droplets are expected to be formed below 10 K, which is, however, not an attainable temperature with the present pulsed-nozzle setup. In order to achieve such a low nozzle temperature the current temperature gradient between the cooling stage and the nozzle must be suppressed, which in the present work was about 6 K. We have used a commercial Series 99 (General Dynamics Valves, Inc.) pulsed-nozzle manufactured of stainless steel which has low heat conductivity. A recent paper 22 reports of droplets as large as 10 12 atoms under comparable experimental conditions. It would be interesting to compare the I 16 /I 8 ratios obtained in Ref. 22 with those obtained in this work for the continuous beam expansion shown in Fig. 3.7 to validate the droplet sizes. 49 Figure 3.8. Intensity ratios 0.1×I 16 /I 12 (circles) and I 16 /I 8 (triangles) obtained from the mass spectra of the continuous He droplet beams comprised of different droplet sizes. Corresponding nozzle temperatures from Table 1 are shown in the upper part of the plot for reference for some of the data points. Average sizes from Ref. 27 are used for N He < 10 4 and sizes obtained in this work for larger droplets. 50 Figure 3.9. I 16 /I 8 ratio of He droplet beam obtained from a 1 mm diameter pulsed-valve. Expansion obtained at P 0 = 15 bar for different nominal nozzles temperatures and two repetition rates of 1 Hz and 10 Hz, solid circles and open squares, respectively. For comparison, the results obtained with the 5 µm continuous-nozzle at P 0 = 20 bar from Table 3.1, are shown by triangles. Average droplet sizes are indicated for some of the data points. 51 The increase in large droplets of the relative intensity at m = 16 due to He 4 + has been attributed to the creation of multiple metastable He 2 * exciplexes within the same droplet upon electron impact 38 . Recombination of two He 2 * particles on the surface of the droplet produces He 4 + ions which are ejected 38 . Upon entering liquid He, an electron loses its energy and can produce a number of ions and excited He atoms, the latter of which result in the formation of He 2 * exciplexes. The energy loss in each inelastic scattering event ranges from about 25 eV for ionization to about 21 eV for production of the lowest He* excited state. The mean free path of 100 eV electrons in liquid He can be estimated from the total inelastic collision cross section for collisions with He atoms 39-40 and n LHe. to be 10, 11, 14 and 184 nm at electron energies of E = 100 eV, 75 eV, 50 eV, and 25 eV, respectively. The ratio of the yields of ionization and excitation remains approximately constant at about 3:1 at E > 40 eV. However at small energies of less than about 25 eV ionization is practically diminished and inelastic collisions produce He*, which is required to obtain He 4 + ions. Therefore, the relative intensity of I 16 is expected to continue increasing until the He droplets reach a diameter of about 300 nm (N He ~ 3×10 8 ) in good agreement with our experimental observations. 3.5. Conclusions We have demonstrated that the average He droplet sizes in a continuous droplet beam could be obtained by titration of the beam through collisions with argon and helium atoms. In addition to the observed quantitative agreement with previous measurements in 52 the size range <N He > = 10 5 – 10 7 , the titration measurements have provided average sizes in the previously uncharted size range of very large droplets of 10 7 – 10 10 He atoms. These results confirm that during titration large He droplets essentially act as isothermal calorimeters. A rapid increase in the droplet size and beam flux at very low nozzle temperatures T 0 < 6 K was observed and is consistent with a new regime of nozzle operation. In this operation regime, droplets are formed within the nozzle interior before reaching the sonic point resulting in a highly collimated beam of very large He droplets of <N He > = 10 8 – 10 10 . Finally, the mass spectra of the droplet beam upon electron impact ionization have also been obtained. It has been shown that the large increase in the intensity of the He 4 + signal in the spectra with increasing droplet size can be used as a secondary size standard in the droplet size range of N He =10 4 – 10 9 atoms. 53 Chapter III Bibliography 1. J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. 43, 2622-2648 (2004). 2. M. Y. Choi, G. E. Douberly, T. M. Falconer, W. K. Lewis, C. M. Lindsay, J. M. Merritt, P. L. Stiles and R. E. Miller, Int. Rev. Phys. Chem. 25, 15-75 (2006). 3. J. Tiggesbäumker and F. Stienkemeier, Phys. Chem. Chem. Phys. 34, 4748-4770 (2007). 4. C. Callegari, K. K. Lehmann, R. Schmied and G. Scoles, J. Chem. Phys. 115, 10090-10110 (2001). 5. S. Grebenev, J. P. 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Stone, Y. K. Kim and J. P. Desclaux, Journal of Research of the National Institute of Standards and Technology 107 (4), 327-337 (2002). 56 Chapter IV: Surface Deposition and Imaging of Large Ag Clusters Formed in He Droplets 4.1. Introduction The He droplet technique has proven pivotal in a number of important findings 1-3 . The observation of rotational spectra of molecules embedded in He droplets has provided for a novel microscopic probe of superfluidity in He droplets and its development as a function of droplet size 4-5 . Another very fruitful application of the He droplet technique is in the growth and study of atomic and molecular clusters. Successful coupling of the He droplet technique with laser spectroscopy in the infrared and visible spectral regions in the study of the structure and dynamics of small molecular and atomic clusters in He droplets is reviewed in Refs. 1-3, 6-7 . Moreover, He droplets offer straightforward control over the cluster size and allow the formation of multi-component clusters, such as metal- molecule clusters. So far, many cluster experiments with He droplets have employed droplets of less than about 10 4 atoms resulting in small clusters of no more than about 10 particles. However, previous works indicate that large He droplets can be used to form large atomic or molecular clusters 2 . In particular, the formation of silver and lead clusters of up to about 100 atoms 8-10 and magnesium clusters 11 of up to several thousands of atoms in He droplets has been proven by mass spectroscopic experiments. We showed that ammonia clusters containing up to 10 4 molecules can be formed in He droplets and studied via infrared spectroscopy 12 . The results of our recent laser spectroscopic study of silver clusters, Ag N (N ~ 10 – 10 4 ), suggest a transition from single-center to multi-center 57 aggregation in going from small to large He droplets 13 . Thus aggregation in liquid He can also be used to form unique metal samples of nano-granular structure. Our recent work indicates that metal clusters produced in He droplets can be deposited on a surface upon impact 14 . Supported metal nanoclusters have large potential in heterogeneous catalysis 15 , plasmonics 16-17 and single molecule spectroscopy 18 . Of fundamental importance in these areas are the production of size-selected clusters, their controlled deposition onto different substrates, and the stability of such arrays of clusters 19 . In this work, Ag N clusters formed in He droplets have been deposited on an amorphous carbon (aC) film and studied via transmission electron microscope (TEM) imaging. We will first briefly describe the experimental setup. Secondly, we report on the TEM imaging of Ag N clusters with estimated average sizes <N Ag > ~ 300 and 6 000 deposited on aC films at various deposition times and on their size distributions and fluxes. Lastly, we discuss the cluster size distributions as well as the mechanism of surface deposition for such clusters grown in He droplets. 4.2. Experimental The schematic of the molecular beam apparatus is shown in Figure 4.1. Helium nanodroplets with an average size of <N He > = 4·10 7 and 2.4·10 6 are formed by expanding high purity (99.9999%) He gas at a pressure of 20 bars into vacuum through a 5 µm diameter nozzle at temperatures of T 0 = 7 and 9 K, respectively 3 . The beam is collimated by a 0.5 mm diameter skimmer and passes through a 6 cm long differentially-pumped pickup cell at 26 cm from the He droplet source. The pick-up cell contains a resistively 58 heated alumina oven filled with metallic Ag. Further downstream the doped droplet beam enters the deposition chamber where it collides with substrates placed 93 cm from the He droplet source. The substrates are 3 mm diameter standard TEM supports (Ted Pella 01820). They consist of an amorphous carbon film, 15-25 nm thick, mounted on a 300 mesh copper grid coated on the underside by a 30-60 nm thick Formvar film. Typically, a set of 6 samples mounted onto the linear motion manipulator were kept under 10 -8 mbar high vacuum for approximately 24 hours before deposition experiments. The samples were then removed from vacuum and TEM imaging was carried out within 12 hours following deposition. The imaging was conducted on a JEOL JEM-2100 using an electron beam energy of 200 keV. The TEM images were analyzed with the ImageJ image processing package 20 . Figure 4.1. Experimental setup for the surface deposition of metal clusters formed in He droplets. Typical pressure in each vacuum chamber, with the He beam off, is shown. 59 The average number of Ag atoms captured per He droplet, <N Ag >, has been estimated using the attenuation of the He droplet beam, as described in detail elsewhere 14 . The flux of He atoms transported by the droplets is monitored as a rise in the partial pressure of He, P He , in the UHV analysis chamber downstream from the deposition chamber which was typically in the range of 10 -8 – 10 -7 mbar. Upon repeated capture of Ag atoms the average size of the droplets decreases by evaporation of He atoms, which is monitored by a decrease in the pressure rise, ΔP He . The dominant contribution to the energy release upon capture comes from the binding energy of the Ag atoms to the pre- existing Ag N cluster, and thus <N Ag > can be obtained as: He He He Ag He Ag P N E N PE         (4.1) where E He is the 0.6 meV 21 binding energy of He atoms to the droplet, <N He > is the initial average size of the He droplet, and E Ag ≈ 3 eV is the energy associated with the addition of one Ag atom 22 . Maximum flux of silver transported by the He droplet beam is achieved through a balance between doping as many Ag atoms into the droplets while retaining as many carrier droplets as possible. It is known that smaller droplets are extinguished at smaller pickup pressures than larger ones. For a given pickup pressure of silver, a range of smaller He droplets in the size distribution will be fully evaporated and the released Ag N clusters will be scattered away from the beam axis. Scattering of the free clusters is more efficient, due to their smaller mass, as compared with the clusters embedded in He droplets. Thus, most of the studied clusters must be carried by the He droplets. At the typical doping conditions there are essentially no bare He droplets in the beam. In this 60 work, Ag N clusters were obtained using an approximately constant attenuation of the He droplet beam of ΔP He /P He = 0.7, which gives the maximum flux of embedded atoms 14 . At the two average droplet sizes employed, <N He > = 2.4·10 6 and 4·10 7 , Eq. 4.1 gives <N Ag > ≈ 300 and 6 000, respectively. 4.3. Results Figure 4.2 shows TEM images of samples exposed to the He droplet beam produced at T 0 = 7 K doped with Ag clusters of <N Ag > ~ 6000 atoms, as estimated from Eq. 4.1, for 0.5 min, 2 min, 32 min and 120 min in panels (a), (b), (c) and (d), respectively. It is seen that the coverage of the samples increases with exposure and at the highest coverage in panels (c) and (d) some clusters are elongated in shape. Such clusters likely result from aggregation of deposited clusters. Figure 4.2e shows the results of a control experiment in which the sample was exposed for approximately 32 min to an effusive beam of Ag atoms from the oven, which was set to the same temperature as in Figures 4.2a–d, i.e. with the He droplet beam off. Sample (e) reveals a high density of small clusters of <N Ag > ≈ 200 formed by aggregation of Ag atoms on the surface. We have observed that such small clusters are not stable under the illumination of the TEM electron beam as they disappear after about 5 min of imaging at a current density of 100 nA/cm 2 . Apparently, the electron beam imparts the clusters with sufficient temperature such that they either drift out of the field of view or evaporate completely. Previous high resolution studies have indicated a change in the structure of the clusters upon electron beam irradiation 23-24 . This sets a limit on the small cluster sizes which can 61 be imaged in this work at <N Ag > ≈ 200. It can be estimated that the contribution of the effusive beam is negligible at short exposure times such as 0.5 min, as in panel (a). At longer exposure time, single atoms originating from the effusive beam must combine with large clusters deposited via He droplets or combine into small clusters such as in panel (e). Figure 4.2. TEM images (at 40·10 3 magnification) of Ag N clusters on an amorphous carbon film. Samples were obtained by exposure to the He droplet beam doped with about 6000 Ag atoms for 0.5 min (a), 2 min (b), 32 min (c), and 120 min (d). For comparison, panel (e) shows clusters formed on the carbon surface upon 32 min exposure to the effusive beam of Ag atoms emanating from the oven, kept at the same temperature as in experiments producing samples in panels (a) – (d). Scale for all images is the same as shown in panel (a). 62 For each of the four deposition times shown in Figure 4.2, a large number of images were recorded to obtain the surface coverage and density of the deposited clusters. The obtained surface coverage and density for each of these is shown in the lower and upper panels of Figure 3, respectively. It is apparent from the insets in Figure 4.3 that at short deposition time the number of clusters as well as the surface coverage rise almost linearly with time; these, however, become less than linear at longer deposition time, which indicates coalescence of the clusters. The field of view of the electron microscope is of the order of 1 µm 2 , which is much smaller than the diameter of the He droplet beam of about 6 mm at the substrate location. Therefore we do not expect any inhomogeneity of the cluster flux or size distribution over the micrographs. Our results indicate that clusters deposited over a short exposure time of less than about 2 min remain intact and reflect the primary distribution of the deposited clusters. 63 0 1 2 3 0 20 40 60 80 100 120 0 5 10 15 0 2 0 0.1 0.2 0 2 0 0.5 Cluster density x10 -11 [cluster/cm 2 ] Deposition time [min] Area Fraction x10 2 Figure 4.3. Upper panel: Surface density versus deposition time for Ag N clusters of estimated initial size <N Ag > ~ 6 000. Line connecting the data points is to guide the eye. Lower panel: Area fraction of the deposited clusters under the same conditions. Insets show a linear fit to the data at short deposition times. 64 For an imaged cluster of surface area S, we can calculate the number of Ag atoms, N Ag , contained within as: 13 22 4 3 Ag N S n    , (4.2) where n = 5.85·10 22 cm -3 is the number density of bulk silver. Here, we assume a spherical shape of the deposited clusters. Small clusters, as in this work, must be nearly spherical because the Ag-Ag N binding energy of ≈ 3 eV 22 is stronger than that of the Ag- carbon surface of ≈ 1 eV 25 . Based on the results in Figure 3, new samples with deposition times of 2 min and 32 min were prepared for analysis of the cluster size distribution. The samples were imaged at a magnification of 40·10 3 . Approximately 1 000 clusters were detected over 50 images taken of different areas of the 2 min sample. Each image was obtained within less than a minute to minimize any possible distortion of the size distribution induced by the TEM electron beam. The obtained size distributions are shown in Figure 4.4 by filled squares and open circles for the 2 min and 32 min samples, respectively. The mean cluster size obtained according to Eq. 4.2 from the 2 min samples was <N Ag > = 6 400 with a root mean square deviation ΔN Ag = 5 000. In comparison, the distribution of the clusters obtained at the longer deposition time of 32 min, where clusters with N Ag > 15 000 are abundant, is shifted towards larger sizes. As a result, the mean cluster size at 32 min deposition is almost a factor of two larger with <N Ag > = 11 800 and ΔN Ag = 11 400. This must be a result of aggregation of the clusters at high surface density, in agreement with the results in Figure 4.3. 65 From the surface density of the clusters at short deposition time, such as in Figure 4.2b, the silver deposition flux was obtained to be 7·10 11 clusters/(sr·s) or 8·10 7 clusters/(cm 2 ·s). The corresponding atomic flux is 4.4·10 15 atoms/(sr·s) or 5·10 11 atoms/(cm 2 ·s). The cluster flux is a factor of two smaller than the flux of undoped He droplets of 1.6·10 12 droplets/(sr·s) estimated from the pressure rise in the UHV analysis chamber and average He droplet size. The rate of cluster formation from the effusive beam with a mean cluster size of <N Ag > ≈ 200 atoms, such as in Figure 4.2e, was obtained to be 4.7·10 7 clusters/(cm 2 ·s). This corresponds to an effusive atomic Ag flux of 9·10 9 atoms/(cm 2 ·s), which is a factor of 100 smaller compared to that transported in He droplets. This comparison shows that Ag N clusters in He droplets are the primary source of the deposited clusters in Figure 4.2a–d, whereas the effusive beam is relatively weak. 66 0 1x10 4 2x10 4 3x10 4 4x10 4 5x10 4 0 0.2 0.4 0.6 0.8 1.0 32 min <N Ag >=11 800 2 min <N Ag >=6 400 Normalized counts N Ag Figure 4.4. Size distribution of Ag N deposited on an aC film during 2 minutes (solid squares, 1 000 clusters analyzed) and 32 minutes (open circles, 400 clusters analyzed). Estimated initial average cluster size in both cases is 6 000. Lines connecting data points are to guide the eye. 67 Additional experiments were carried out at an increased He droplet source temperature of 9 K to deposit smaller Ag N clusters, estimated at about 300 atoms from eq 1, via He droplets consisting of about 2.4·10 6 atoms. Figure 4.5 shows the size distributions obtained after 2 minutes and 16 minutes of deposition, indicated by stars and open circles, respectively. The mean size of the deposited clusters produced in He droplets was obtained to be <N Ag > = 600, ΔN Ag = 600 for deposition over 2 min and <N Ag > = 800, ΔN Ag = 700 for deposition over 16 min. Thus the obtained sizes are about a factor of two larger than estimated. On the other hand, the distributions of the deposited clusters peak at N Ag ≈ 400 in better agreement with the estimate. The average cluster size at longer deposition time is only somewhat larger indicating that the deposition flux for 16 min is still low enough to avoid substantial cluster aggregation (area fraction is less than 1%). In addition, the appearance of the rather long tail at larger sizes (up to N Ag = 6 000, not shown in Figure 4.5) in the distribution for 16 min may indicate that smaller clusters remain mobile upon deposition and some of them coalesce even at low coverage. From the cluster counts in Figure 4.5, the deposition flux was obtained to be 5·10 12 clusters/(sr·s) or 5.6·10 8 clusters/(cm 2 ·s). The corresponding atomic flux is 3·10 15 atoms/(sr·s) or 3.4·10 11 atoms/(cm 2 ·s). The Ag N cluster flux is about a factor of three smaller than the estimated flux of undoped He droplets of 1.7·10 13 droplets/(sr∙s). The obtained value, however, is in very good agreement with the previously measured deposition flux of Ag atoms, under similar experimental conditions 14 employing a quartz crystal microbalance, of 3.2·10 15 atoms/(sr·s). 68 The distribution of clusters, shown in Figure 4.2e, resulting from the effusive beam (without He droplets) over an exposure of 32 min is shown in Figure 4.5 by solid squares. It is seen that clusters obtained from the effusive beam are smaller, with a distribution peaking at NAg ≈ 200. The distribution may be somewhat biased towards larger sizes as we are not able to reliably detect clusters of less than NAg ≈ 200 or of diameter smaller than about 2 nm due to low contrast in the TEM images, as well as cluster evaporation under the electron beam illumination. 69 0 1000 2000 3000 0.0 0.2 0.4 0.6 0.8 1.0 2 min <N Ag >=600 16 min <N Ag >=800 Effusive beam <N Ag >=200 Normalized counts N Ag Figure 4.5. Size distribution of Ag N clusters deposited on an aC film for 2 minutes (stars, 200 clusters analyzed) and 16 minutes (circles, 2 000 clusters analyzed). Estimated initial average cluster size in both cases is 300. Squares illustrate the cluster size distribution upon exposure to the effusive beam for 32 minutes at the same conditions as in Figure 4.2e. Lines connecting data points are to guide the eye. 70 4.4. Discussion The ratio of the flux of deposited Ag N clusters to that of He droplets in the beam gives the deposition yield of the clusters. Our results show that the flux of Ag N clusters determined from the TEM images is about a factor of two to three smaller than the flux of He droplets. This may indicate a somewhat smaller than unity sticking probability for the clusters in He droplets. On the other hand, a difference of this magnitude may be due to uncertainties in the estimates. For example, the initial He droplet sizes in this work may differ from that in previous measurements 3, 26 due to the use of a different nozzle plate and some slight inaccuracy in the actual nozzle temperature. In addition, according to Ref. 27 , there is a considerable and unknown fraction of small droplets in the beam which adds uncertainty to the estimates based on average droplet size. Moreover, the measurements of the droplet size distribution via deflection of droplets having an attached electron in Ref. 28 , which we rely on, cannot be used to study droplets of less than about 10 5 , since such droplets do not bind an electron. Therefore, we conclude that the sticking probability of Ag N clusters in He droplets colliding with the aC surface is large but cannot be determined with high accuracy at present. In comparison, in our previous work 14 , where the Ag flux was measured by a microbalance, both cluster flux and the droplet flux were equal within experimental error: 7.5·10 12 clusters/(sr·s) and 7·10 12 droplet/(sr·s), respectively. 71 4.4.1. Helium droplet collision with surface The cold He droplets eventually disintegrate following collision with the warm surface, releasing the embedded Ag N clusters. The surface collision of microscopic droplets (e.g., water, ethanol, etc.) has been thoroughly investigated via fast photography as well as theoretical calculations; see for example reviews in Refs. 29-30 and references therein. The experimental conditions used in this work such as nanometer-sized He droplets, nano-scale substrate roughness, and high vacuum conditions differ substantially from those in the reviews. However, for estimation purposes, we consider the results obtained for such macroscopic droplets. It is well known that the outcome of a collision such as rebounding, spreading, or splashing depends on the collision speed v, density within the droplet ρ, droplet diameter D, and surface tension of the liquid σ, as well as on properties of the substrate. The initial phase of a collision of an incompressible drop depends on the magnitude of the Weber number, We, given by Eq. 4.3. 2 vD We    (4.3) It is seen that We is proportional to the ratio of kinetic energy to the surface energy. Bouncing of drops is observed at small Weber number, We < 10, and depends on wetting of the surface by the drop liquid. Usually, splashing occurs when We exceeds a certain critical value of about We = 100; see for example Ref. 31 . In this work, He droplets have an impact velocity of about 200 m/s, the helium density at 0.4 K is 145 kg/m 3 , 32 and the surface tension is 3.54·10 -4 N/m 32 ; thus the magnitude of We is estimated to be 1600. In addition, collisions with surfaces at 72 temperatures above the critical temperature of the liquid are influenced by heat transfer and the fast evaporation of the droplet liquid. In the present experiments, the substrate temperature of about 300 K is substantially higher than the critical temperature of liquid helium, 5.2 K. Experiments with classical droplets (water and organic liquids) having values of We ≈ 2 000 – 10 000 were reported by Pan et al. 33 . Manzello and Yang 34 have studied collisions at surface temperatures above the critical point of the drop liquid and We = 700 - 750. In both studies, fast imaging of the surface impact of mm-sized water droplets shows considerable spread of the droplet during the impact leading to the formation of a liquid disc of diameter up to about ten times larger than the initial droplet. If the same scenario is valid for He droplets of 100 nm diameter, as employed in this work, containing Ag N clusters as in Figure 4.2, the resulting thickness of the liquid disc will be around 1 nm which is smaller than the diameter of the embedded Ag 6000 cluster of about 6 nm. Of course, fracture of the disc may occur at some point when its height becomes comparable to the distance between He atoms in the liquid of about 0.4 nm as follows from the number density of liquid He of 21.8 nm -3 . 32 Thus we expect that during the impact the dopant Ag N cluster will come in direct contact with the aC surface and remain attached to it, while the He droplet disintegrates. This scenario is in agreement with the observed high yield of the deposited clusters. During the expansion along the surface of the colliding droplet its rim can attain a high velocity comparable to the velocity of sound in liquid He of about 240 m/s 32 . Therefore, the embedded clusters may also be dragged along the surface before attachment. This He-assisted mobility of the clusters on the surface may contribute to enhanced combination of the clusters. At 73 present, it remains unclear whether heat transfer from the surface will be important during the short time of the expansion phase following collision which lasts for about 0.5 ns. 4.4.2. Soft landing The Ag N clusters in He droplets collide with the aC at the velocity of the droplet beam which is known to be about 200 and 300 m/s for the larger and smaller droplets 35 used in this work, respectively. Within the assumption that the kinetic energy of the clusters is determined by the velocity of the carrier droplets, the kinetic energy per impacting Ag atom in the large clusters is about 0.034 eV. This is much less than one tenth the binding energy of a single Ag atom to the cluster of about 3 eV and to the surface which is about 1 eV for amorphous carbon 25 . Thus He droplet deposition is well within the so called “soft landing” regime 19 ; accordingly, the cluster and the surface remain intact upon collision. The estimated collision energy is less than the lowest yet reported in the literature of 0.05 eV for Sb N ions, <N> = 90 – 2 200, impacting aC 36 . 4.4.3. Cluster size distribution The size distribution of the Ag N clusters is a convolution of both the pick-up probabilities and the He droplet size distribution in the beam. In the supercritical expansion regime, as used in this work, the droplet size decays approximately exponentially towards larger sizes, having a mean square deviation comparable to the mean size: ΔN He /<N He > ≈ 1. 26 Thus the width of the distribution of the neat He droplet 74 sizes is comparable to that for deposited Ag clusters, where we found ΔN Ag /<N Ag > ≈ 0.8. Therefore we conclude that the width of the cluster size distribution is mainly defined by the size distribution of the hosting He droplets. There must also be some bias in our experiment towards larger droplets which carry large clusters. Smaller Ag N clusters are formed in smaller He droplets from the distribution; such droplets are not only more effectively evaporated in collisions with Ag atoms but also scattered more. Both of these effects combine as a bias towards larger clusters. The final size distribution, shape, and morphology of the deposited clusters are defined by the interplay between the dynamics of the doped He droplet impact 29-30 , the nature of the substrate surface, cluster aggregation 37-39 , secondary processes 40 , and the TEM imaging procedure itself 23-24 . As discussed earlier, Ag N clusters may experience some considerable translation along the surface during the droplet impact prior to adsorption, contributing to the mobility of the clusters on the surface and increasing the possibility of cluster aggregation. This depends on, for instance, the deposition rate 37-39 and the kinetic energy of the impacting clusters 41 . Once deposited, adsorption is facilitated by the known high density of surface defects of aC that serve as adsorption sites for deposited metal clusters 37 . The long term mobility of the clusters depends on the nature of these adsorption sites. Clusters will either remain pinned to some strong adsorption site or diffuse over the substrate until they find a suitable adsorption site or combine with another Ag N cluster. In fact, clusters on an atomically flat surface are known to remain mobile and can agglomerate by diffusion to form larger metal islands which are fractals under certain conditions 39 . The linear dependence of the surface 75 coverage at short deposition time in the present experiments shows that aggregation of clusters is not important at surface densities of less than about 1.6·10 10 clusters/cm 2 . However, this becomes important at higher surface densities. The largest surface density of clusters in Figure 4.3 corresponds well to the saturation cluster density of around 5·10 11 clusters/cm 2 measured for various metal clusters (In, Bi, Au, Ag) on aC films 37-38, 40, 42 . The obtained mean cluster size of <N Ag > = 6 400 in Figure 4.4 is in good agreement with the estimate based on the binding energy of atoms in Ag N clusters and the initial average size of the He droplets. Thus we conclude that clusters remain intact upon deposition and that aggregation of the clusters is not important at low coverage, such as in Figure 4.2a-b. Despite this conclusion, clusters may experience some reconstruction upon attachment to the surface at room temperature. Recently, we have studied the structure of Ag N clusters formed in He droplets (in situ) via optical spectroscopy 13 . We have found that in smaller clusters, such as the N Ag ~ 600 clusters studied in this work, the spectra are dominated by a surface plasmon resonance near 3.8 eV consistent with absorption by individual compact metallic particles. However, larger clusters, such as the N Ag ~ 6400 clusters studied in this work, reveal unexpectedly strong broad absorption at low frequency extending down to ≈0.5 eV. This suggests a transition from single-center to multi-center formation, in agreement with estimates of cluster growth kinetics in large He droplets. Accordingly, a number of small clusters , which later coalesce into an aggregate inside the hosting He droplet, are formed during pickup. These small clusters may retain their individuality because the energy barrier associated 76 with reconstruction into a close packed cluster is insurmountable at 0.4 K in He droplets. However, upon deposition onto a surface at room temperature cluster aggregates must coalesce into compact particles. The coalescence must be facilitated by the long residency of the clusters on the surface of half a day prior to TEM imaging, including several hours at ambient conditions, as well as by exposure to the electron beam during the imaging procedure. This conjecture is supported by the results of Ref. 39 , which show that small (N < 1 000) Ag N clusters deposited on an aC surface aggregate and coalesce within a few hours. The average cluster size of smaller clusters, <N Ag > = 600 in Figure 4.5, is a factor of two larger than that estimated from eq 1, which may indicate some aggregation of the clusters. It may also be the result of low contrast in the TEM images of small clusters, such that the obtained distribution is biased towards larger sizes. In fact, it has been previously observed that Au clusters of less than 1 nm diameter could not be detected immediately after deposition due to low contrast in the TEM images 38, 43 . Popescu et al. 40 reported the detection of Au clusters of 0.3 nm diameter only after 7 days exposure to ambient atmospheric conditions, which may indicate the importance of some secondary processes resulting in increased contrast in the TEM images of small clusters. The electron beam itself, requisite for TEM imaging, is also known to induce evaporation of small deposited Ag N clusters. This would also explain the inability to reliably image clusters of less than about 200 atoms in the present work. Finally, the accuracy of the estimates according to Eq. 4.1 heavily rely on the average He droplet sizes from Refs. 3, 26 . The He droplet sizes obtained at the nominal nozzle temperature of 9 K in this work 77 strongly depend on the actual nozzle temperature; any slight variation in the actual nozzle temperature would lead to droplets of initial average size different from those reported in Refs. 3, 26 . Therefore, the Ag N clusters assembled within will likewise exhibit a strong size-dependence on the actual nozzle temperature adding to any uncertainty in the estimates. Therefore, the disagreement factor of about two between the estimated and measured cluster sizes is not unexpected. 4.5. Conclusions We have demonstrated that metal clusters formed in He droplets can be successfully extracted by deposition onto an amorphous carbon film. The mean size of the deposited Ag N clusters is within about a factor of two in agreement with the estimated initial cluster size, which is based on the binding energy of the clusters and initial He droplet size. This shows that such clusters remain intact upon deposition and TEM imaging. This study opens up new opportunities for routinely synthesizing in He droplets diverse metal and metal-molecule clusters spanning a wide range of cluster sizes and compositions and for studying their deposition on different substrates. 78 Chapter IV References 1. M. 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In particular, their strong optical resonances, the possibility of localization of excitations in composite materials, and the corresponding enhancement and modification of electromagnetic resonances underpin the study of plasmonics, surface-enhanced Raman scattering, optical sensing, solar light harvesting, plasmon enhanced nanocatalysis, etc. As a consequence, there is interest in understanding and developing cluster growth and aggregation processes and in characterizing the resulting optical properties 2 . It is desirable to extend studies of composite materials to smaller, sub-nanometer sized grains. Granular composites of this type cannot be easily produced at the relatively high temperatures encountered in colloidal chemistry or molecular beam deposition, because of the ready coalescence of sub-nm clusters. This calls for building truly nano- composite materials at very low temperature. Liquid He is a unique medium for aggregation as it facilitates fast thermalization of particles while allowing freedom of mobility and agglomeration 3-4 . In this work, we study the electronic excitation spectra of Ag N clusters grown in superfluid He droplets, covering a wide range of droplet sizes (N He ~10 4 -10 7 ), cluster sizes (N Ag ~6-6000), and wavelengths (IR to UV). The main finding is that, whereas the spectra 82 of Ag N clusters with up to hundreds of atoms are dominated by an intense resonance close to the well-known surface plasmon frequency of Ag nanoparticles, larger particles exhibit a novel feature: strong, broad absorption extending all the way into the IR region. This suggests that assembly of large nano-composites in He droplets produces open structures, in contrast with the close-packing growth of the smaller clusters. An estimate of cluster growth kinetics supports a transition from single-center to multi-center growth with increasing droplet size, resulting in non-compact aggregates. Moreover, the emergence of a characteristic dispersion profile in the spectra of large clusters supports the coexistence of localized and delocalized electronic excitations in composite systems, as predicted theoretically 5 . 5.2. Experimental The beam apparatus is described in detail elsewhere 6 . Expansion of He gas at 20 bars through a 5 µm diameter nozzle at T 0 =10, 9.5, 9, 8, and 7 K yields droplets of initial average size of N He ≈2.1 10 4 , 2.7 10 5 , 2.4 10 6 , 1.4 10 7 , and 4 10 7 , respectively 3-4 . The droplets capture Ag atoms while passing through a heated alumina oven. Further downstream, they are detected by a quadrupole mass spectrometer (QMS) hosted in a separate UHV chamber. The average number of captured Ag atoms, N Ag , was estimated via attenuation of the droplet beam, as described in Ref. 6 . The flux of He atoms transported by the droplets is monitored by the partial pressure of He in the QMS chamber, P He . Upon capture of Ag atoms the average droplet size decreases by an amount ΔN He , as reflected by a decrease in the partial pressure, ΔP He : He He He He // N N P P    . In 83 this work He He / 0.7 PP  6 was used in order to maximize the flux of picked-up atoms and hence the signal-to-noise ratio in the recorded spectra. Therefore N Ag can be obtained as   Ag He He Ag N N E E  6 , where E He =0.6 meV is the binding energy of He atoms to the droplet and E Ag is the energy associated with the addition of one Ag atom, i.e., the binding energy of an Ag atom to a pre-existing Ag cluster. For the present accuracy, it is adequate to use E Ag ≈2 eV for N Ag up to several tens of atoms, which is the measured average binding energy of clusters in this size range 7 , and the bulk cohesive energy E Ag 3 eV 8 for particles with N Ag 10 2 . 5.3. Results The Ag N clusters have a broad size distribution, which is a convolution of pick-up probabilities and the He droplet size distribution in the beam, the latter of width comparable to the average size 9 . We carried out transmission electron microscope (TEM) imaging of Ag N clusters, obtained under the same experimental conditions as in Fig. 1(e), deposited on amorphous carbon films. These measurements have shown that the clusters have an average size of <N Ag > = 6400 with a mean square deviation ΔN Ag = 5000 10 . Similar agreement between the estimate and TEM measurements was also found for the clusters in Fig. 1(c). For the clusters with N Ag  10 2 , the uncertainty in average size is amplified by size variations in the binding energies 7 and by the fact that TEM measurements become impractical due to low contrast. 84 The absorption spectra of Ag N clusters in the range of 0.5 – 6 eV were obtained by beam depletion spectroscopy using a pulsed optical parametric oscillator (EKSPLA NT342/3/UV). The collimated laser beam was directed counter to the doped droplet beam, for an interaction length of about 1 m. During the 7 ns laser pulse a Ag N cluster absorbs multiple photons. We assume that excitation of the clusters proceeds in a “multistep” manner, i.e., that the interval between successive absorption events is longer than the relaxation time of the excitation 11 . This is consistent with the ~10 fs decay time of plasmons in Ag nanoparticles 12 . Fast relaxation of the absorbed energy results in evaporation of a sizable fraction of the host He droplet, which is monitored by the QMS as a transient fractional depletion of the 2 He  signal 3-4 . This depletion ratio is approximately proportional to the number of He atoms evaporated from the droplet and thereby to the energy released. The photoabsorption spectra discussed below have all been obtained in the linear depletion regime with an attenuated laser beam. The measured absorption spectra are shown as solid lines in Fig. 5.1 (a)-(e). The spectra of the smaller clusters have a pronounced peak in the near-UV part and a prominent rise at higher energies. The peak’s maximum shifts towards lower energies with increasing cluster size: 3.8 eV, 3.7 eV and 3.6 eV in clusters of nominal sizes <N Ag >~6, 60, and 300, respectively, approaching the 3.5 eV dipolar surface plasma resonance (SPR) frequency of Ag spheres 1 . 85 Figure 5.1. Normalized photoabsorption spectra for Ag particles of different average sizes assembled by pick-up in He droplets. Dashed lines in panels (b) and (c) are calculated model cross sections (right-hand scale) and in panel (e) is the fit of the dispersion profile according to the Fano formalism. Top panel (f) shows calculated absorption spectrum of a Ag cluster-cluster aggregate from Ref. 13 , see text for details. 86 5.4. Discussion Previous studies of small Ag N clusters in He droplets reported a sharp, ≈50 meV, peak at ≈4 eV 14 in the resonant two-photon ionization spectra of Ag 8 . This is distinct from the absorption spectra of size-selected Ag N=8-39 clusters in cryo-matrices 15 , which exhibit broad structures concentrated between 3 eV and 4.5 eV. The small Ag N cluster data in Fig. 5.1 are consistent with the latter, with the spectra in Fig. 1 representing a convolution of different sizes. Size effects in the photoabsorption of noble-metal clusters have been discussed within a model where the cluster structure is approximated by a core with a bulk-like dielectric function, and a surface layer of width a in which only Drude-type s-electron screening is present 16-17 . This arises from the reduced overlap of s- and d-electron wavefunctions at the surface 18 . In addition, the wavefunctions of the outer electrons “spill out” beyond the surface by a length δ. The dashed lines in Fig. 5.1 (b,c) show the result of fitting the spectra with a spherical core-shell model 19-20 . The clusters with <N Ag >~60 and 300 are well described with the parameter choices a=0.5 Å and δ=0.2 Å and a resonance damping factor of 20%. This is close to the parameters selected in Ref. 19 for free cluster ions 17, 21 : a≈1.3 Å, and δ≈0 for Ag N  , δ≈1.2 Å for Ag N  . The relatively small spill-out parameter δ for the present neutral Ag N clusters likely derives from the exchange repulsion between the s-electrons of the metal and the He matrix. The calculations also account for the broad absorption at energies >5 eV, which arises from the interaction of electron excitation modes of the core and the outer region 19-20 . 87 The pattern changes for larger clusters and qualitatively new features develop: (i) an intense band spanning the red and near-IR spectral ranges and (ii) a characteristic, dispersion-like profile of the excitation at 3.5–4.5 eV close to the SPR frequency. The weakening of the UV-VIS spectrum correlates with the appearance of the IR band, as the total area under the per-atom curves in Fig. 1(a)-(e) remains unchanged within the accuracy of the experiment. The low-frequency band is unexpected, since extensive studies of individual Ag nanoclusters in molecular beams, on surfaces, and in colloids did not show such absorption 1 . On the other hand, certain colloidal cluster-cluster aggregates (CCAs) of nanoparticles strongly absorb in the red 1, 22-23 . The changes in the spectra in Fig. 1(a-e) show qualitative similarities with those obtained upon aggregation of larger Ag particles (R = 5-25 nm) in colloids 22-23 . Initially, the spectrum is dominated by a plasmon peak of isolated Ag particles, which in solution has a maximum at about 3 eV. Upon extensive aggregation the intensity of the resonance decreases and the spectrum acquires a broad wing of approximately constant intensity extending down to the lowest studied excitation energy of about 1.5 eV 22-23 . The spectrum of the CCAs is determined by the strong electromagnetic interaction between the plasmon resonances of individual particles. Model calculations show that CCAs often have a fractal structure 13 , in qualitative agreement with TEM images in colloidal aggregates 23 . Fig. 5.1(f) shows an example of the calculated absorption spectrum of a CCA consisting of 100 Ag particles, each 5 nm in diameter 13 . The spectra were calculated in the dipole approximation with renormalization of the distance between particles by a factor of about 0.8. The renormalization constant is 88 an empirical parameter required because pure dipole-dipole theory underestimates the interaction for small interparticle distances. It is seen that the calculated spectrum extends to lower frequencies near 1 eV similarly to the experimental spectrum. Thus, the spectrum in Fig. 5.1(e), measured upon doping He droplets with about 6000 Ag atoms, is consistent with the CCA spectra. To gain insight into the formation of clusters in He droplets we compare the time between two successive Ag pickup events, t n,n+1, with the time required for recombination of the first two Ag atoms inside the He matrix, t rec . The former can be obtained as the ratio of the time of flight of He droplets through the pickup cell (the velocity of the beam is ≈200-300 m/s 4 ) to the number of captured Ag atoms. The latter time can be estimated as He /v rec r tV   , where He V is the volume of the droplet, r  = 30 Å 2 is the recombination cross-section of Ag atoms (using the van der Waals radius of Ag), and v ≈10 m/s is the estimated velocity of Ag atoms in the droplet assuming fast thermalization as supported by Ref. 24 . Fig. 2 shows the results for t rec and t n,n+1 , as well as the droplet parameters employed in this work. The experiment is seen to span two different modes of cluster formation. In small droplets t rec is much faster than t n,n+1 , which results in single-center cluster growth. On the other hand, in very large droplets Ag atoms are added at a much faster rate than the time required for recombination, which must result in the formation of multiple smaller clusters (whose precise size is unknown at present). At longer times these coagulate into a composite. The values of t n,n+1 and t rec are of the same order of magnitude for N He ~10 6 , corresponding to hosting N Ag ~100 atoms. Therefore this droplet 89 size defines the lower threshold for multi-center recombination. Upon coagulation, small clusters may retain their individuality as the energy barrier associated with reconstruction into a close packed cluster is insurmountable at about 0.4 K in He droplets. 4 The appearance of the IR band for N Ag greater than several hundred atoms (Fig. 5.1) is in good agreement with this estimated threshold for the onset of multi-center growth. Figure 5.2. Time between two successive pickup events, t n,n+1 , and time required for recombination of first two picked up Ag atoms, t rec , versus size of He droplets, N He . Corresponding droplet radius, R He , and typical size of Ag N cluster, N Ag , grown within the droplet are also shown on bottom and top axes of plot, respectively. 90 We now address feature (ii), the dispersion profile in the range of 3.5–4.5 eV, which develops in Fig. 5.1(d) and is fully apparent in Fig. 5.1(e). Its shape resembles that of a Fano-resonance 25-26 , which generically originates from the interaction between the narrow and broad spectra of a quantum oscillator. The dashed curve in Fig. 1(e) shows the fit of the experimental spectrum to a Fano profile,       2 2 2 00 / 2 / / 2 q               , in the vicinity of the resonance. The fit parameters are: resonance energy ν 0 = 3.85 eV; width Γ = 0.30 eV; asymmetry q = -1.38. In order to account for the changing intensity of the continuous background over the resonance we have added to the fit a linear function increasing towards higher energies. The value of ν 0 is close to the frequency of the plasmon resonance in isolated small Ag N clusters, see Fig. 5.1(a). However, this resonance in Fig. 5.1(e) should not be identified with isolated clusters, because of the formation of CCAs. The coupling strength, V, between the narrow and broad states is V = 0.22 eV as obtained from the width parameter Γ=2π|V| 2 25 . The asymmetry parameter q reflects the transition probabilities of the resonance and the broad spectrum. The appearance of the rather narrow resonance in CCAs is surprising in view of their expected inhomogeneity. Nevertheless, it has been predicted 5 that in disordered nano-systems, such as cluster assemblies and semi-continuous metal films, there is a coexistence of localized (due to the inhomogeneity of the clusters) and delocalized modes. Recent measurements of near-field statistics 27 and fluctuations of the local density of states 28 in percolated metal films provided support for such mode coexistence. 91 However, there has been no direct spectroscopic confirmation. We propose that the Fano-type feature may be assigned to the interaction of the localized and delocalized modes as expected theoretically 26 . The spectrum in Fig. 5.1(e) also shows that both modes are luminous in a 3D sample having sub-nm graininess. Calculations indicate large differences between the spectra of fractal CCAs and compact, non-fractal aggregates 22, 29 . The latter were predicted to have a similar spread of the density of states as in CCAs, but with luminous modes concentrated in a narrow spectral range close to the plasmon resonance in isolated clusters. This was rationalized in terms of certain propensity rules due to the overall spherical shape of the compact aggregates. At present the structure of the cluster aggregates formed inside the He droplets remains unknown, thus caution should be exercised in applying theoretical spectra obtained for some distinct aggregation models. It is conceivable, for example, that the clusters obtained in He droplets may be more loosely packed (having voids) but non-fractal, thus showing a coexistence of narrow and broad modes. 5.5. Conclusions In the future, detailed surface deposition experiments and X-ray scattering measurements may determine the structure of the discovered aggregates. It will be interesting to extend this work to even larger as well as to multi-component clusters, and to investigate the application of such aggregates to surface-enhanced molecular spectroscopy at ultra-low temperatures. 92 Chapter V Bibliography 1. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters. (Springer, New York, 1998). 2. K. D. Sattler, in Handbook of Nanophysics, edited by K. D. Sattler (CRC Press, Boca Raton, 2010), Vol. 2 and 6. 3. J. Tiggesbäumker and F. Stienkemeier, Phys. Chem. Chem. Phys. 9 (34), 4748- 4770 (2007). 4. J. P. Toennies and A. F. Vilesov, Angew. Chem.-Int. Ed. 43 (20), 2622-2648 (2004). 5. M. I. Stockman, S. V. Faleev and D. J. Bergman, Phys. Rev. Lett. 87 (16), 167401 (2001). 6. V. Mozhayskiy, M. N. Slipchenko, V. K. Adamchuk and A. F. Vilesov, J. Chem. Phys. 127 (9), 094701 (2007). 7. S. Krückeberg, G. Dietrich, K. Lutzenkirchen, L. Schweikhard, C. Walther and J. Ziegler, J. Chem. Phys. 110 (15), 7216-7227 (1999). 8. B. M. Smirnov, Reference Data on Atomic Physics and Atomic Processes. (Springer, Berlin, 2008). 9. U. Henne and J. P. Toennies, J. Chem. Phys. 108 (22), 9327-9338 (1998). 10. E. Loginov, L. F. Gomez and A. F. Vilesov, J. Phys. Chem. A 115, 7199-7204 (2011). 11. C. Bréchignac, P. Cahuzac, N. Kebaili, J. Leygnier and A. Sarfati, Phys. Rev. Lett. 68 (26), 3916-3919 (1992). 12. J. Bosbach, C. Hendrich, F. Stietz, T. Vartanyan and F. Trager, Phys. Rev. Lett. 89 (25), 257404 (2002). 13. V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov and I. L. Isaev, Phys. Rev. B 70 (5), 054202 (2004). 14. T. Diederich, J. Tiggesbäumker and K. H. Meiwes-Broer, J. Chem. Phys. 116 (8), 3263-3269 (2002). 93 15. M. Harb, F. Rabilloud, D. Simon, A. Rydlo, S. Lecoultre, F. Conus, V. Rodrigues and C. Felix, J. Chem. Phys. 129 (19), 194108 (2008). 16. E. Cottancin, G. Celep, J. Lerme, M. Pellarin, J. R. Huntzinger, J. L. Vialle and M. Broyer, Theor. Chem. Acc. 116 (4-5), 514-523 (2006). 17. J. Tiggesbäumker, L. Köller, K. H. Meiwes-Broer and A. Liebsch, Phys. Rev. A 48 (3), R1749-R1752 (1993). 18. V. V. Kresin, Phys. Rev. B 51 (3), 1844-1899 (1995). 19. V. Kasperovich and V. V. Kresin, Philos. Mag. B 78 (4), 385-396 (1998). (In Fig.2 ε 1 and ε 2 were accidentally interchanged). 20. J. Lermé, Euro. Phys. J. D 10 (2), 265-277 (2000). 21. J. Tiggesbäumker, L. Köller and K. H. Meiwes-Broer, Chem. Phys. Lett. 260 (3-4), 428-432 (1996). 22. V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim and R. L. Armstrong, Phys. Rev. B 53 (5), 2425-2436 (1996). 23. S. V. Karpov, V. S. Gerasimov, I. L. Isaev and V. A. Markel, J. Chem. Phys. 125 (11), 111101 (2006). 24. S. Grebenev, M. Hartmann, M. Havenith, B. Sartakov, J. P. Toennies and A. F. Vilesov, J. Chem. Phys. 112 (10), 4485-4495 (2000). 25. U. Fano, Phys. Rev. 1 (6), 1866-& (1961). 26. B. Luk'yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen and C. T. Chong, Nature Mat. 9 (9), 707-715 (2010). 27. K. Seal, D. A. Genov, A. K. Sarychev, H. Noh, V. M. Shalaev, Z. C. Ying, X. Zhang and H. Cao, Phys. Rev. Lett. 97 (20), 206103 (2006). 28. V. Krachmalnicoff, E. Castanie, Y. De Wilde and R. Carminati, Phys. Rev. Lett. 105 (18), 183901 (2010). 29. Z. Naeimi and M. Miri, Phys. Rev. B 80 (22), 224202 (2009). 94 Chapter VI: Laser-Induced Reconstruction of Ag clusters in He droplets 6.1. Introduction Helium droplets are unique hosts for the assembly and interrogation of diverse molecular and atomic clusters. 1-6 Helium remains fluid down to absolute zero temperature and is superfluid at temperatures below T λ = 2.18 K. Therefore, particles captured by the droplets move freely within until they meet and combine. The excess energy is transferred to the He bath and eventually removed through evaporative cooling, which maintains the droplets at the low temperature of 0.38 K. 7 Helium droplets were found to be a useful matrix for isolating single molecules and clusters. Early works were devoted to the spectroscopic study of small clusters which were often found to have equilibrium structure. It was also obtained that He droplets may facilitate the formation of unusual, metastable clusters such as linear chains of HCN molecules. 8 In a recent study of the spectra of Mg clusters in He droplets, it was hypothesized that the Mg atoms form metastable weakly bound complexes where individual Mg atoms are separated by a He layer resembling a “bubble foam”. 9 Previously, impurity gels formed in bulk liquid He were ascribed an unusual structure in which He snowballs around the impurities hindered their combination, but were latter reassigned to porous aggregates of clusters. 10 It follows that liquid He as a solvent offers an interesting perspective on chemistry at ultra-low temperatures and opens up the potential for obtaining some novel materials. 95 Therefore, it is of great interest to study the kinetics and mechanisms behind the combination of particles in superfluids and the structure of the resulting clusters. Recently, we have expanded our studies of aggregation to very large He droplets consisting of 10 6 - 10 10 atoms with diameters of about 0.1 - 1 µm. 11 For all intents and purposes such droplets can be viewed as small specimens of bulk superfluid He. Such droplets remain superfluid throughout the experiments and are therefore ideal hosts for studying the combination of multiple atomic or molecular particles entering the droplet. Furthermore, droplets of this size can facilitate the formation of correspondingly large Ag clusters of up to 10 6 atoms. 12 Recently, we reported on the photoabsorption spectra of Ag clusters, ranging in size, N Ag , from N Ag = 6 – 6000, in He droplets. 13 The spectra of the smaller clusters, N Ag < 100, showed a pronounced surface plasma resonance peak near 3.5 eV, similar to that of Ag clusters obtained through colloidal chemistry. For Ag clusters larger than about N Ag ~ 300, there was an increase in the infrared absorption with a concomitant decrease in the UV absorption. These changes were consistent with a shift in the growth mechanism from single- to multiple-centered growth following the increase in the droplet size. Accordingly, in the larger droplets multiple small clusters were formed which subsequently combined into cluster-cluster aggregates or some other non-compact structure, which was facilitated by the low temperature in the droplets. Large Ag clusters were also deposited on a surface at room temperature and imaged via electron microscopy. 14 Finally, we found that the Ag deposits obtained from very large He droplets of N He = 10 10 were elongated and track-like in shape with an average length 96 comparable to the host droplet diameter. 11 Therefore, we concluded that such large droplets contained quantum vortices, which served as aggregation centers. The impurity particles clustered along the vortex lines as previously demonstrated in bulk liquid He using H 2 and Au clusters (see 15-16 and references therein). While studying the spectra of Ag clusters in He droplets 13 , we observed some pronounced laser power saturation effects. However, the irregularly shaped laser beam from the optical parametric oscillator used in Ref. 13 precluded a quantitative study of this effect. Laser power saturation of the He droplet depletion signal may indicate reconstruction of the Ag clusters in the droplets upon pulsed laser irradiation. Such an effect may be exploited to learn about the details of energy exchange between the excited nano-clusters and the surrounding superfluid He environment. In this work, we study the laser power dependence of the depletion signal following the irradiation of the Ag clusters in the droplets by the second and third harmonics of a pulsed Nd:YAG laser at 532 and 355 nm, respectively, which have nearly Gaussian beam profiles. Photons at 532 nm excite the broad absorption peak characteristic of large Ag clusters, whereas 355 nm is close to the maximum of the plasmon resonance. Similar measurements were also conducted using a continuous wave (CW) laser operating at 532 nm. 6.2. Experimental A schematic of the molecular beam apparatus is shown in Figure 2.1. Helium nanodroplets of average size He N = 3×10 5 – 2×10 10 are formed by expanding high purity (99.9999%) He gas at a pressure of 20 bar into vacuum through a 5 µm diameter 97 nozzle at temperatures of T 0 = 9.5 – 5.5 K, respectively. 11 The droplet beam is collimated by a 0.5 mm diameter skimmer. The droplets capture Ag atoms while passing through a heated alumina oven filled with metallic Ag. The average number of Ag atoms captured per He droplet, Ag N , has been estimated using the attenuation of the droplet beam, as described in detail elsewhere. 14 The flux of He atoms transported by the droplets is monitored as a rise in the partial pressure of He, P He , in the UHV analysis chamber. P He was typically in the range of 10 -8 – 10 -7 mbar. Upon repeated capture of Ag atoms the average size of the droplets decreases by evaporation of He atoms and is monitored as a pressure drop, ΔP He , in the terminal chamber. Ag N can be obtained according to: He He He Ag He Ag PN E N PE   (6.1) where E He is the 0.60 meV binding energy of He atoms to the droplet, He N is the average size of the He droplet before being doped with Ag, and E Ag ≈ 2.8 eV is the energy released upon the capture of one Ag atom. E Ag is a sum of the binding energy of the Ag atoms to the pre-existing embedded cluster plus the thermal energy of Ag atoms in the pickup cell of about 0.15 eV. The binding energy per Ag atom in clusters is smaller than cohesion energy of Ag atoms in the bulk, E coh = 2.96 eV 17 , by about 0.3 eV for compact Ag 100 clusters and 0.6 eV for Ag 10 . 18 As the atomic structure of the Ag clusters obtained in liquid He remains unknown, our estimates assume aggregates in liquid He that are comprised of dense clusters of about 100 Ag atoms. Here, the Ag clusters were obtained by employing a constant attenuation, A, of the He droplet beam of 98 A = ΔP He / P He = 0.7 (i.e. 0.7 of the droplet was lost via evaporation upon doping with Ag atoms). Therefore, despite their different sizes, the doped droplets contain the same average number of He atoms, about 2000, per each Ag atom in the cluster. For the five droplet sizes employed He N = 2×10 10 , 3×10 8 , 1×10 7 , 2×10 6 , and 3×10 5 obtained at T 0 = 5.5, 6, 7, 9, and 9.5 K, respectively, Eq. 6.1 gives Ag N = 2×10 6 , 4×10 4 , 2×10 3 , 2.5×10 2 , and 46, respectively. The intensity of the He droplet beam was measured 110 cm downstream from the pickup cell by a quadrupole mass spectrometer which was equipped with an electron beam ionizer. The signal at mass M = 8 au, I 8 , due to He 2 + splitter ions was used as a monitor of the intensity of the droplet beam. The laser beam propagates anti-collinear to the droplet beam. The laser pulse energy was measured by a calibrated pyroelectric detector, which could be placed on the beam axis, inside the vacuum apparatus about half way between the pickup cell and the mass spectrometer. The average fluence, F, was then obtained by normalizing the energy, by the area of the 6 mm orifice in front of the detector. Following the absorption of multiple photons by the Ag clusters and the concomitant heating of the droplet, a large number of He atoms evaporate from the droplet which results in a decrease in I 8 . The typical shape of the depletion dip upon the pulsed excitation is shown in Fig. 2.5. The signal lasts for about 5 ms, which is the time of flight of the droplets from the pickup cell to the ionizer of the mass spectrometer 110 cm downstream. The decrease in the mass spectrometer signal was used to obtain the fractional depletion, D, of the original signal according to i f i I I I D 8 8 8   where the 99 superscripts i and f refer to the signal before and during the laser pulse, respectively. In the case of the CW laser measurements, the laser output was chopped electronically at 50 Hz, and the depletion signal was obtained using a lock-in amplifier which was multiplied by a factor of 2. We employed a pulsed Powerlite 8020 Nd:YAG laser (7 ns nominal pulse width, 20 Hz repetition rate) with second and third harmonic stages to give output at 532 and 355 nm, respectively. The pulse energy was varied by changing the Q-switch delay of the Nd:YAG amplifier. A CW laser from Shanghai Dreamlasers (model SLD 532-500T) was used to continuously produce 500 mW at 532 nm. Its output was attenuated by a set of neutral filters. Both the pulsed and CW laser beams had a diameter of approximately 6 mm at the entrance to the vacuum apparatus. This facilitated good overlap with the He droplet beam which expanded from about 1 mm at the pickup cell to about 6 mm at the orifice leading to the ionizing region of the mass spectrometer. 100 6.3. Results Fig. 6.1(a) shows the fractional depletion, D, of the signal versus average laser fluence, F, measured with the pulsed laser at 532 nm for embedded Ag clusters of different sizes. In the smallest clusters of about Ag N = 300, D rises approximately linearly up to F ≈ 25 mJ/cm 2 . At higher F the signal reaches a constant level at D ≈ 0.20. For Ag N = 2×10 3 , D again rises linearly up to a few mJ/cm 2 , and becomes independent of F above approximately 10 mJ/cm 2 . The slope of the linear part at small F is larger in the Ag 1300 clusters, which indicates a greater absorption cross-section per Ag atom than for the smaller Ag 300 clusters, as will be discussed in the Discussion section below. In the largest clusters of approximately 4.2×10 4 and 2×10 6 Ag atoms, the signal rises sharply at F < 2 mJ/cm 2 and then continues to grow at a slower rate until finally reaching D ≈ 0.12 for F = 40 mJ/cm 2 . In contrast to the smaller clusters, in the largest clusters the signal does not reach a clear saturation even at the highest F values employed. Fig. 6.1(b) shows similar measurements of D, but with the pulsed laser at 355 nm. At low F < 2 mJ/cm 2 all four cluster sizes show similar dependences. At higher F the dependence becomes sub-linear, reaching a value of D = 0.8 for the largest clusters, 2×10 6 and 4.2×10 4 Ag atoms, at F ≈ 15 mJ/cm 2 . For the smaller Ag 1300 clusters, D ≈ 0.55 is somewhat less. For the smallest Ag 250 clusters, D shows a sharp change in slope at F ≈ 2 mJ/cm 2 and rises more slowly at higher values of F. Figure 6.2 shows the D vs. F dependences using CW excitation at 532 nm for five different cluster sizes indicated in the inset. In comparison to the results obtained with 101 pulsed excitation, the dependence of D is approximately linear in all cases through the range of laser fluences measured and shows only small signs of sub-linear behavior at the highest fluences. However, the slope of the linear part of the curves decreases by about a factor of 10 in going from cluster size Ag N = 2×10 3 to 50. 102 0 10 20 30 40 50 0.00 0.05 0.10 0.15 0.20 N Ag = 2x10 6 , 5.5 K N Ag = 4x10 4 , 6 K N Ag = 2x10 3 , 7 K N Ag = 250, 9 K Depletion at 532 nm, Pulsed Depletion Fluence, mJ/cm 2 (a) 0 5 10 15 20 25 0.0 0.2 0.4 0.6 0.8 N Ag = 2x10 6 , 5.5 K N Ag = 4x10 4 , 6 K N Ag = 2x10 3 , 7 K N Ag = 250, 9 K Depletion Fluence, mJ/cm 2 Depletion at 355 nm, Pulsed (b) Figure 6.1. Depletion of the M = 8 signal with laser fluence obtained for droplets produced at nozzle temperatures T 0 = 5.5, 6, 7, and 9 K used to grow Ag clusters of 2×10 6 , 4.2×10 4 , 2×10 3 , and 300 atoms, respectively. Pulsed laser excitation is at (a) 532 nm and (b) 355 nm. 103 -200 0 200 400 600 800 1000 1200 1400 1600 1800 0.0 0.1 0.2 0.3 0.4 N Ag = 2x10 6 , 5.5 K N Ag = 4x10 4 , 6 K N Ag = 2x10 3 , 7 K N Ag = 250, 9 K N Ag = 46, 9.5 K Depletion Fluence, mW/cm 2 Continuous Laser Depletion Figure 6.2. Depletion in M = 8 signal with laser fluence for different Ag cluster sizes measured upon continuous laser excitation at 532 nm. 104 6.4. Discussion The pulsed and CW laser experiments differ by about 6 orders of magnitude in excitation rate of the embedded Ag clusters. Whereas the pulsed excitation occurs over about 7 ns, in the case of the CW laser excitation the clusters absorb light during the time-of-flight of about 5 ms from the pickup cell to the ionizer of the mass spectrometer. It is known that the dephasing lifetime of the plasmon excitations in the Ag clusters is of the order of 10 fs 19 , and that the electron-electron and electron-phonon relaxation times are of the order of 1 ps 20-21 , i.e. much shorter than either of the two excitation times. At the highest CW laser fluence of 1600 mW/cm 2 in Fig. 6.2, the clusters accumulate a dose of radiation of about 9 mJ/cm 2 during their time-of-flight of 5.5 ms, as for clusters produced at T 0 = 7 K. This dose corresponds to about a quarter of the maximum fluence used in the pulsed excitation shown in Fig. 6.1(a) for which the depletion reaches a saturation level at about D = 0.14 for T 0 = 7 K. In comparison, a much larger level of D = 0.60 is reached in the case of CW irradiation where the signal shows only small signs of deviations from linearity. The large difference between the pulsed and CW excitation in the relative depletion of the signal following irradiation by the same number of photons indicates a kinetic limitation on the level of absorption that can be reached in the pulsed excitation with 532 nm. On the other hand, pulsed excitation at 355 nm leads to much higher values of D as is seen from Fig. 6.1(b). Fig. 6.1(b) shows that at the highest F of about 20 mJ/cm 2 , D = 0.4, 0.5, 0.8, and 0.8 for Ag clusters made at T 0 = 9, 7, 6, and 5.5 K. In addition, at T 0 = 9 K, D also shows some abrupt change in slope at F = 3 mJ/cm 2 . 105 Figures 6.1 and 6.2 show that at low laser fluence, D is proportional to F. The corresponding values of the slope, S [cm 2 /J], can be used to obtain the per atom absorption cross-sections of the Ag clusters, σ [cm 2 ], according to Eq. 6.2 below. 2 (1 ) [ / ] 1.5 Ag A S depl cm J E A        (6.2) The factor of 1.5 comes from the assumed N He 2/3 dependence of the electron-impact ionization cross-section in large He droplets; the factor is unity in the case of a N He dependence. Our results 11 indicate that the ionization efficiency changes from I 8 ≈ N 2/3 in large droplets, N He > 10 7 , to I 8 ≈ N in small droplets, N He < 10 4 , which can lead to a 20% overestimation of the σ values for measurements at T 0 = 9 and 9.5 K. In the case of the CW excitation the slopes, in cm 2 /W, obtained from Fig. 6.2 are divided by the irradiation time t = L/v D , where v D is the velocity of the droplet beam 11 , listed in Table 6.1, and L = 1.10 m is the distance from the pickup cell to the ionizer of the mass spectrometer. The absorption cross-sections obtained in this work are summarized in Table 6.1. The values obtained with the CW excitation at 532 nm are shown in parenthesis. 106 Table 6.1. Initial He droplet size, He N ; size of the obtained Ag clusters, Ag N ; and absorption cross-sections per Ag atom, σ, at 355 nm and 532 nm excitation. The values obtained with CW excitation at 532 nm are given in parenthesis. a) It was not possible to obtain slopes for pulsed excitation, due to an insufficient number of data points at low F and a large fluctuation of the I 8 base line at low T 0 resulting in a large scattering in the data points. T 0, K He N , 11 Ag N v, m/s, 11 S (355), cm 2 /J σ (355), A 2 , pulsed S (532) cm 2 /J (cm 2 /W) σ (532), A 2 . pulsed (CW) 5.5 1.7 × 10 10 2.4 × 10 6 173 170 0.50 -- a (0.16) -- (0.072) 6 3.1 × 10 8 4.3 × 10 4 175 170 0.50 -- a (0.25) -- (0.11) 7 1× 10 7 2 × 10 3 200 120 0.35 37 (0.31) 0.11 (0.16) 9 1.8 × 10 6 250 223 250 0.72 12 (0.093) 0.035 (0.054) 9.5 3.3 × 10 5 46 236 --- --- --- (0.036) --- (0.022) 107 Our previous measurements 13 show that the spectrum of the Ag clusters obtained at T 0 = 9 K is dominated by a plasmon resonance at about 3.5 eV which indicates the formation of predominantly spherical, compact clusters. The absorption cross-section obtained σ(Ag 250 , 355 nm) = 0.72 A 2 compares well with the known values for spherical Ag clusters close to the plasmon resonance frequency. For example, σ = 0.45 A 2 has been obtained for (Ag 70±5 ) + clusters in a beam at the maximum absorption of about 3.7 eV. 22 The theoretical absorption cross-section for Ag 2000 clusters at the maximum of the plasmon band, 3.5 eV, was found to be about 0.4 A 2 . 13 Here, we note that the absolute values of σ obtained in this work should have a rather large uncertainty of up to a factor of 2 primarily due to the unknown effective value of F along the droplet beam. The accuracy could be improved by measuring the laser beam profile and obtaining overlap integrals with the droplet beam which was not attempted, however, in this work. Table 6.1 shows that σ(Ag 2000 , 355 nm) is about a factor of 2 smaller than σ(Ag 250 , 355 nm). This is consistent with our previous 11 finding of an intense infrared band in the former clusters which effects a decrease in the intensity at the plasmon frequency. It is seen that the σ(355) increases again in the largest Ag N = 4.3×10 4 and 2×10 6 clusters. The cluster size dependence of the σ(532) follows an opposite trend and is greatest for Ag N = 2×10 3 clusters. This behavior is expected if the infrared band borrows intensity from the plasmon resonance band as is the case for cluster-cluster aggregates. It is also seen that the values of σ(532) obtained with CW excitation are approximately a factor of 1.5 larger those obtained via pulsed excitation for T 0 = 7 K and 9 K, for which σ values exist. Some deviation of the results is not unexpected in view of 108 the different shapes of the CW and pulsed laser beams which were not be quantified in this work. The ratio R of cross-sections at 532 nm to 355 nm, R = σ(532)/σ(355), was found to be 0.3 and 0.05 for measurements at 7 K and 9 K, respectively. Calculations give R = 0.02 and 0.03 for clusters having 6000 and 60 Ag atoms, respectively. Therefore, in smaller clusters the ratio approaches the prediction for spherical clusters, whereas in larger clusters σ(532) is a factor of 10 larger than expected. This is again consistent with the spectrum of cluster-cluster aggregates, which shows extensive infrared absorption due to the interaction between the plasmon modes of the clusters. The different laser power dependences of the signal upon excitation at 532 and 355 nm may indicate reconstruction of the Ag clusters upon pulsed laser irradiation. Cluster-cluster aggregates, for instance, may reconstruct into compact clusters, which have a weak absorption at 532 nm. This will result in bleaching upon excitation, consistent with the observed saturation of the signal upon pulsed 532 nm excitation. On the other hand, little bleaching is expected at 355 nm close to plasmon maximum in agreement with the results in Fig. 6.1(b). The level of depletion D can be used to obtain the energy absorbed, E abs , per atom according to Eq. 6.3. (1 ) 1.5 Ag abs He He E A E D E AE       (6.3) The saturation level of the signal for excitation of Ag 2000 at 532 nm, D = 0.14, was used to estimate the energy threshold for reconstruction of the clusters as 0.26 eV per Ag atom. This energy is comparable with ΔE coh of about 0.3 eV in Ag 100 clusters, which will 109 be released upon formation of the larger clusters. Therefore, a sizable portion of the depletion signal at 532 nm may originate from the energy gain associated with the reconstruction itself, which renders an estimate of the reconstruction threshold energy less certain. Nevertheless an instantaneous absorption of 0.2 eV per Ag atom will raise the temperature of the clusters to about 1500 K, which is above the melting temperature of bulk Ag at 1233 K. The different behavior following CW excitation at 532 nm indicates that the absorbed energy is dissipated into the He bath without noticeable reconstruction of the clusters, which is due to the slower rate of excitation by a factor of 10 6 than the pulsed excitation. Although superfluid He is characterized by an exceptionally large heat conductivity, this is most applicable for small amounts of transferred heat. Heat transfer from a solid to superfluid He is also known to be inefficient due to the large mismatch in the velocity of sound, which is known as Kapitza resistance. 23 Above certain values of the heat per area in W/cm 2 24 , a bubble of He gas will be formed which effectively insulates the hot body from the liquid He environment. This effect was dramatically manifested in early experiments in which a tungsten filament could be heated white inside a vessel filled with superfluid He. 25 In the pulsed experiments with compact Ag 1000 clusters having surface area of about 32 nm 2 the energy release during the 7 ns pulse of about 250 eV (D = 0.14) corresponds to a surface energy flux of about 2×10 4 W/cm 2 , which is much above the threshold for the bubble formation. On the other hand, during the CW excitation the heat flux is estimated to be only about 2×10 -2 W/cm 2 , i.e., below the bubble formation threshold. Therefore, following absorption of CW radiation 110 by the Ag cluster the heat will be effectively transferred to the He bath and the clusters will remain at low temperature. 6.5. Conclusions We have observed saturation of the depletion signal of Ag clusters in He droplets upon pulsed laser excitation at 532 nm at sufficiently high laser fluence. The same effect, however, was not observed for CW laser excitation at the same wavelength and similar laser fluences. This is consistent with a kinetic limit on the energy transfer rate from the excited Ag cluster to the host He droplet, which is not exceeded in the case of CW excitation. Estimates of the Ag cluster temperature have shown that in the absence of energy transfer the cluster can reach temperatures of about 1500 K during the laser pulse, which is well above the melting point of Ag. Therefore, it is likely that the embedded Ag clusters, upon pulsed laser excitation, melt and reconstruct into more compact clusters. In addition, by measuring the dependence of the depletion signal on the laser fluence, cluster absorption cross-sections were obtained for the various cluster sizes. The cross-sections were found to be in line with our previous assignment of compact clusters for N Ag ~ 250 and cluster-cluster aggregates N Ag ~ 2000. In the future, the heat transfer rate between the excited Ag cluster and the host He droplet could be measured by analyzing of the fast initial drop of the M = 8 signal upon laser excitation. In addition, the saturation effect could be explored further by employing double resonance experiments in which a pump pulse could be used to initiate the 111 reconstruction of the Ag cluster followed by a probe pulse to measure the absorption spectrum. 112 Chapter VI Bibliography 1. J. P. Toennies and A. F. Vilesov, Ann. Rev. Phys. Chem. 49, 1-41 (1998). 2. J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. 43, 2622-2648 (2004). 3. C. Callegari, K. K. Lehmann, R. Schmied and G. Scoles, J. Chem. Phys. 115, 10090-10110 (2001). 4. M. Y. Choi, G. E. Douberly, T. M. Falconer, W. K. Lewis, C. M. Lindsay, J. M. Merritt, P. L. Stiles and R. E. Miller, Int. Rev. Phys. Chem. 25, 15-75 (2006). 5. F. Stienkemeier and K. K. Lehmann, Journal of Physics B-Atomic Molecular and Optical Physics 39 (8), R127-R166 (2006). 6. J. Tiggesbaumker and F. Stienkemeier, Physical Chemistry Chemical Physics 9 (34), 4748-4770 (2007). 7. M. Hartmann, R. E. Miller, J. P. Toennies and A. Vilesov, Phys. Rev. Lett. 75, 1566-1569 (1995). 8. K. Nauta and R. E. Miller, Science 283 (5409), 1895-1897 (1999). 9. A. Przystawik, S. Gode, T. Doppner, J. Tiggesbaumker and K. H. Meiwes-Broer, Physical Review A 78 (2), 021202 (2008). 10. E. B. Gordon, Low Temperature Physics 30 (10), 756-762 (2004). 11. L. F. Gomez, E. Loginov, R. Sliter and A. F. Vilesov, J. Chem. Phys. 135, 154201-154209 (2011). 12. L. Gomez, E. Loginov and A. F. Vilesov, Phys. Rev. Lett. 108, 155302 (2012). 13. E. Loginov, L. F. Gomez, N. Chiang, A. Halder, N. Guggemos, V. V. Kresin and A. F. Vilesov, Phys. Rev. Lett. 106, 233401-233404 (2011). 14. E. Loginov, L. F. Gomez and A. F. Vilesov, J. Phys. Chem. A 115, 7199-7204 (2011). 15. M. S. Paoletti, R. B. Fiorito, K. R. Sreenivasan and D. P. Lathrop, Journal of the Physical Society of Japan 77 (11), 111007-111001-111007 (2008). 16. V. Lebedev, P. Moroshkin, B. Grobety, E. Gordon and A. Weis, Journal of Low Temperature Physics 165 (3-4), 166-176 (2011). 113 17. C. Kittel, Introduction to Solid State Physics. (Willey, New York, 1966). 18. F. Baletto, R. Ferrando, A. Fortunelli, F. Montalenti and C. Mottet, Journal of Chemical Physics 116 (9), 3856-3863 (2002). 19. J. Bosbach, C. Hendrich, F. Stietz, T. Vartanyan and F. Trager, Physical Review Letters 89 (25), 257404 (2002). 20. C. Voisin, N. Del Fatti, D. Christofilos and F. Vallee, Journal of Physical Chemistry B 105 (12), 2264-2280 (2001). 21. M. Maillard, M. P. Pileni, S. Link and M. A. El-Sayed, Journal of Physical Chemistry B 108 (17), 5230-5234 (2004). 22. J. Tiggesbäumker, L. Koller, K. H. Meiwesbroer and A. Liebsch, Physical Review A 48 (3), R1749-R1752 (1993). 23. G. L. Pollack, Reviews of Modern Physics 41 (1), 48-& (1969). 24. J. S. Vinson, F. J. Agee, R. J. Manning and F. L. Hereford, Physical Review 168 (1), 180-& (1968). 25. G. E. Spangler and F. L. Hereford, Physical Review Letters 20 (22), 1229-& (1968). 114 Chapter VII: Formation of Core-Shell Ag-Ethane Clusters in He Droplets 7.1. Introduction Superfluid He droplets provide a unique medium for the growth of atomic and molecular clusters. 1-4 5 Atoms embedded into the He droplets rapidly thermalize to the low temperature of T = 0.38 K 2-4, 6-8 and eventually coagulate. The maximum size of the clusters formed is proportional to the average size of the He droplets. Therefore, in order to obtain large, nanometer-sized clusters 9-10 , He droplets consisting of at least 10 6 – 10 7 He atoms are required and are obtained through a so-called “supercritical”, low- temperature expansion. 11 12 13 Large metal clusters produced in He droplets can be deposited onto a surface upon impact 9 and imaged by transmission electron microscopy 10 . The kinetics and formation mechanisms of large clusters in superfluid solvents remain poorly understood. Recently, we studied the formation of Ag clusters of up to a few thousand atoms in He droplets via optical laser spectroscopy. We found that small silver clusters (N Ag ≈ 100) have a plasmon resonance at about 3.7 eV, similar to that obtained previously for dense spherical clusters at higher temperatures. On the other hand, larger Ag clusters of N Ag > 1000 formed in He droplets of N He ≈ 10 7 atoms have an unusually broad spectrum extending into the infrared spectral range. 14 The dramatic change in the spectra indicates that the larger clusters have a lower density such as in cluster-cluster aggregates or are not spherical. The infrared absorption of silver clusters may also originate from elongated clusters, which have transversal and longitudinal modes with the latter being shifted towards low frequency. Indeed, very recent experiments show that 115 deposited Ag clusters obtained in even droplets of N He > 10 8 atoms are elongated in shape, which was ascribed to the aggregation along quantum vortices in the superfluid He droplets 15 , and can therefore possess low-frequency longitudinal modes. In this work, we continue our study of the growth of large clusters in He droplets and extend it to the formation of clusters consisting of Ag and ethane. He droplets are ideal hosts for the assembly of such metal-molecule clusters by doping with two sequential pickup cells. It is likely that the particles added upstream will make a core covered by the shell of the particles added downstream. In this work, the formation of core-shell clusters consisting of Ag atoms and ethane molecules (Et) has been studied via infrared spectroscopy of C-H stretching bands of Et in the 3 µm range. We found that the perpendicular ν 7 band of Et has two distinct features due to molecules on the interface with silver cluster and more distant molecules which are not in direct contact with the Ag atoms. The intensity ratio of the two bands is used to corroborate the structure of the composite clusters. Ag has a factor of about 10 larger molar enthalpy of evaporation as compared with Et. Therefore, if Ag atoms are captured in the upstream pickup cell, Ag core-Et shell clusters are formed which are also thermodynamically stable. On the other hand, the reverse Et core-Ag shell structure is energetically unfavorable, because of the large fraction of the surface atoms in the silver shell. We show that such reversed Et core-Ag shell clusters can nevertheless be stabilized in He droplets. The results of similar studies with methane, ethylene, and acetylene molecules will be reported elsewhere. 116 He droplets can be viewed as calorimeters with a temperature that is fixed by the fast evaporative cooling 13 of the He atoms. The absorbed energy associated with the pickup of a particle by a He droplet is proportionally related to the decrease in the droplet’s size via the known evaporation enthalpy of liquid He, 5 cm- 1 . This evaporative cooling property is a particularly appealing aspect of beams of large droplets for which the scattering following the capture of a large number of particles is negligible. Therefore throughout this paper we use calorimetry in He droplets in order to obtain the number of captured Ag and Et particles as well as the absorbed IR laser energy per Et molecule. We found that Et absorbs a sizeable amount of energy of up to about 1500 cm - 1 per molecule in neat Et and core-shell Ag-Et clusters. The observed laser power saturation indicates the excitation of nearly all molecules in the clusters which shows that the vibrational cooling of the clusters in He droplets is much slower than the laser pulse duration of 7 ns. 117 Figure 7.1. a) Schematic of the He droplet beam vacuum apparatus. NZ –5 µm diameter nozzle; SK – 1 mm diameter skimmer; PC 1 and PC2 – upstream and downstream pickup cells, respectively; SH – beam shutter; A1 and A2 – 6 mm diameter apertures; GV1 and GV2 – gate valves; EI – electron impact ionizer; IB – ion bender; QMS – quadrupole mass spectrometer. b) Typical depletion dip upon laser excitation at t = 0, as measured at mass M = 8. Weak secondary pulse at about t = 7 ms, shows the effect of laser pulse impinging on the nozzle. -10 -5 0 5 10 15 2.0 2.5 3.0 3.5 I 8 , arb. un. Time, ms b) 118 7.2. Experimental The schematic of the vacuum He droplet beam apparatus is shown in Figure 7.1(a). He nanodroplets are formed in the source chamber by expanding high purity (99.9999%) He gas at a pressure of 20 bar into vacuum through a nozzle (NZ) of 5 µm nominal diameter. Droplets having an average size of <N He > = 1.0·10 7 , 5.3·10 6 , 1.8·10 6 and 3.3·10 5 are obtained at nozzle temperatures T 0 = 7, 8, 9 and 9.5 K, respectively. The sizes of the He droplets that are given were measured recently by the droplet attenuation technique. 13 The somewhat larger sizes quoted in our previous works 10, 14 were based on deflection measurements. 12 It should be noted that our measurements of the droplet sizes 13 via the attenuation technique were measured more recently and with a different nozzle orifice than the measurements described in this work. Therefore, the average droplet sizes (and number of particles in the clusters grown within) are probably only accurate to within a factor of 2 as discussed in Ref. 13 Approximately 10 mm downstream, the He droplets pass through a skimmer (SK) into the main high vacuum chamber which contains two identical 6-cm-long differentially-pumped pickup cells (PC1 and PC2). In this work either the upstream (PC1) or the downstream (PC2) cell hosts a resistively heated oven filled with metallic silver. The temperature inside the oven can be increased up to about 1200 °C, as obtained by direct thermocouple measurements. The operating vapor pressure of silver in the oven is estimated to be around 10 -3 mbar and is adjusted by the regulated power supply of the filament. Ethane gas (99.96%, Matheson Gas Products) was admitted into 119 either PC1 or PC2 via a leak valve (MDC, MLV-21) for pressures in the range of 10 -4 – 10 -3 mbar. The doped He droplets pass through an additional differential pumping stage and enter into the ultra high vacuum chamber housing a quadrupole mass-spectrometer (QMS) (Extrel, MAX 300), which is equipped with an electron beam ionizer (EI) and 90° ion bender (IB). In this work the mass filter was set to M = 8 (He 2 + ), which is known to be the dominant splitter ion upon electron impact ionization of large He droplets 16-17 . The addition of Et molecules or Ag atoms to the droplet causes an attenuation in the transport of He atoms by the beam given by A = ΔP He /P He , where P He is the partial pressure of He in the detection chamber due to the beam and ΔP He is the change in the partial pressure of He following the pickup. 9 10 13 The number of captured particles in the upstream pickup cell (PC1) can be obtained from the attenuation of the beam intensity, A 1 , which consists of droplets of initial average size, N He , as: 11 He He M M EN NA E   (7.1) where E He = 6.1 cm -1 is the evaporation enthalpy of He atoms at T = 0.65 K 18 , as estimated during the pickup. 13 E M is the energy associated with the pickup of a single particle, M, which is due to its kinetic and internal energy as well as the cohesion energy released during cluster formation. The kinetic energy with respect to a He droplet and internal energy of the particle approximately equals the enthalpy difference H 0 (300 K)- H 0 (0 K), which for ethane is calculated to be 990 cm -1 . 19 Ag atoms have a kinetic energy contribution of only about 1200 cm -1 and a cohesion energy of in the bulk of 120 E coh (Ag) = 2.96 eV=2.4*10 4 cm -1 20 . For ethane we take E coh (Et) = 1230 cm -1 , which equals the evaporation enthalpy of liquid ethane at T = 184 K. This implies, that ethane clusters in He are glassy, with a pair distribution similar to that in the liquid. This conjecture is supported by a recent study of micrometer-sized ethane clusters which indicated the formation of liquid clusters at T = 78 K, which is well below freezing temperature at about 90 K. The subsequent freezing and transition from phase I to phase II was on the time scale of hundreds of seconds. 21-22 At the lower temperatures necessary for the bulk crystalline phase II, the binding is larger by the enthalpy of fusion and enthalpy of phase I to phase II transition of 230 and 190 cm -1 , respectively. 23 The cohesive energy is smaller in clusters due to large fraction of the surface particles and approximately scales with the number of the particles in the cluster, n, as E coh (n) ≈ E coh (∞)(1-0.8*n -1/3 ) as obtained for liquid rare gas and silver clusters. 24 Considering that the clusters encountered in this work consist of about 100 – 1000 particles, we take E coh in clusters as15% less than in the bulk; in effect, we take E coh = 20300 cm -1 and 1050 cm - 1 , for silver and ethane, respectively. In addition, E coh could be even smaller due to the possibility of non-compact aggregate structures 14 formed in liquid He; this effect cannot be quantified in lieu of any knowledge on the microscopic structure of the clusters. The energy quotient in Eq. 7.1 is the inverse number of evaporated He atoms per one added particle of M, which is estimated at 3500 and 330 for Ag atoms and Et molecules, respectively. In this work, relatively large levels of attenuation, A Ag = 0.4-0.8, of the He droplet beam by Ag atoms were employed and were obtained from direct measurements of ΔP He . 121 For Et, however, due to its smaller E coh (Et) a much smaller A is obtained for a given number of embedded particles than in the case of Ag. In the case of ethane, A could thus not be accurately obtained from the direct ΔP He measurements. Therefore known dependence of A vs ethane pickup pressure, P Et , 13 was used: (1 exp( ( ) ) Et He Et A N P      (7.2) Here α is an attenuation coefficient determined at each nozzle temperature at high level of attenuation. In the case of when ethane was added in the downstream pickup cell (PC2) at pressure P 2Et the value of α should be scaled as (N He ) -1/3 to take into account the decrease of the average droplet size upon capture of Ag atoms in the upstream pickup cell (PC1). Therefore, the attenuation of the beam and the number of the Et molecules added in the downstream pickup cell are obtained with Eq. 7.3 and 7.4, respectively. 22 1/3 1 () 1 exp[ ] (1 ) He ET Et Ag N AP A       (7.3) 12 2 (1 ) He Ag ET He ET ET E A A N N E     (7.4) where A 1Ag is the attenuation of the He droplet beam due to addition of Ag atoms in the upstream pickup cell. A similar expression was used to obtain N 2Ag ; A 2Ag was always obtained from direct measurements of the beam attenuation. In a typical experiment with core-shell Ag-Et clusters, the temperature of the oven in PC1 was increased until the He droplet beam was attenuated by about A 1 = 70%, leading to formation of the Ag cluster containing N Ag ≈ 1000 atoms. Then, Et was added in PC2 causing an additional 30% attenuation of the beam and leading to the capture of 122 about 1400 ethane molecules. The reduced size of the droplets following the addition of Ag and Et to form the core-shell clusters amounts to about 1·10 6 He atoms, i.e., approximately 80% less than the initial size. Nevertheless, the radius of the remaining He droplet is still about a factor of 10 larger than that of the embedded Ag-Et cluster; the number of the He atoms in the droplet is about a factor of 10 3 larger than the number of particles comprising the cluster. The infrared spectra of the clusters were obtained using a pulsed optical parametric oscillator-amplifier (LaserVision, pulse width 7 ns, pulse energy 5 mJ, repetition rate 20 Hz, spectral resolution 2 cm -1 ). Absolute frequencies were calibrated against the gas spectrum of methane in a photoacoustic cell and are expected to be accurate to within about 2 cm -1 . The infrared laser beam with a diameter of about 5 mm propagated anti-collinear to the droplet beam. The laser pulse energy remained constant throughout the scans to within about 20%. The laser fluence could be estimated to be about 10 mJ/cm 2 . In most of the described experiments, the divergent OPO laser beam collimated with a 1 m lens placed in front of the entrance window to the vacuum apparatus, which led to an increased fluence by about a factor of 5. The laser fluence remained constant during experimental runs conducted within the same day; the results for runs within the same day are presented in the figures. The fluency could, however, vary by up to a factor of about 3 between runs conducted on different days due to the slow deterioration of the laser output and inaccuracies in the laser beam and collimating lens adjustments. 123 Following the absorption of multiple photons by the ethane molecules in the clusters and the concomitant heating of the droplet, a large number of He atoms will evaporate from the droplet which results in a transient depletion of the mass spectrometer signal, I 8 , as shown in Fig. 7.1(b). The depletion lasts for approximately 6 ms which is the time-of-flight of the droplets from the pickup cell to the ionizer of the mass spectrometer, which is 110 cm downstream from the pickup cell. The shape of the signal reflects changing of the effective laser fluency along the flight length. The tail of the dip corresponds to clusters excited close to the pickup cell at the center of the droplet beam. Such clusters interact with the central part of the laser beam, which has higher fluency, thus larger depletion at the tail of the dip. On the other hand, the initial part of the pulse originates from the even overlap of the droplet and laser beams, each of about 6 mm in diameter, close to ionizer of the mass spectrometer, therefore averaged fluency is smaller giving rise to smaller level of the depletion signal. We obtain the fractional depletion, D, of the signal as i f i I I I D 8 8 8   where the superscripts i and f refer to the average signal before the laser pulse and during the depletion dip, respectively. The D values obtained in this work were typically less than about 0.2. The intensities of the spectra reported in this work are given in units of absorbed energy per ethane molecule in the clusters. The total energy absorbed by the cluster can be obtained from D as: D E N A A He He        ) 1 ( ) 1 ( 2 1  . Then, using Eqs. 7.1 and 7.4 the absorbed energy per ethane molecule is obtained as: 124 12 1 1 ( 1) (1 ) C Ag ET Et E A E D A         (7.5) 2 2 1 ( 1) C ET Et E E D A       (7.6) for Et added in the upstream and downstream pickup cells, respectively. It is seen that the absorbed energy per ethane molecule is independent of the droplet sizes and their corresponding uncertainty. The factor of β=1.5 takes into account the dependence of the ionization cross-section on the droplet size which in large droplets scales as N He 2/3 . Our recent measurements of the attenuation coefficients for He indicate a somewhat faster scaling which can be approximated with N He 1/β , with the average value of β = 1.25 for the droplet sizes studied in this work. 13 Therefore, the values obtained for E 1C and E 2C may be overestimated by about 20%. 7.3. Results 7.3.1. Silver-ethane clusters Figure 7.2 shows typical spectra of (a) neat Et and (b) Ag-Et clusters in the range of the C-H stretch vibrations which were obtained in He droplets of initial size 3.3×10 5 atoms (T 0 = 9.5 K). The average number of Ag atoms and Et molecules in the clusters are indicated in the figure. 125 2800 2850 2900 2950 3000 0 500 1000 1500 2000        Energy adsorbed per ethane molecule, cm -1 wavenumber, cm -1 20 pts AAv smooth of "Ag0Et226, 9.5 K, no lens, 151921" 20 pts AAv smooth of "Ag0Et226, 9.5 K, lens, 160708"   a) 2800 2850 2900 2950 3000 0 500 1000 1500 2000        Energy adsorbed per ethane molecule, cm -1 wavenumber, cm -1 20 pts AAv smooth of "Ag0Et226, 9.5 K, lens, 160708" 20 pts AAv smooth of "Ag50Et18, 9.5 K, lens, 163633" 20 pts AAv smooth of "Ag50Et34, 9. 5 K, lens, 184933"   b) V I Figure 7.2. Infrared spectra of (a) neat Et clusters and (b) core-shell Ag-Et clusters. Panel (a) shows a comparison of the spectra for neat Et clusters obtained with and without the collimating lens. The spectra in (b) are with the collimating lens. The 126 clusters were obtained in He droplets of initial size of N He = 3.3×10 5 (P 0 = 20 bar, T 0 = 9.5 K). The average numbers of the captured Et and Ag particles are indicated for each trace. The original spectra have been smoothed over 20 data points. Fig. 7.2(a) shows the spectra of the neat Et clusters of about 225 molecules obtained at high and low laser fluence, i.e. with and without the collimating lens. The clusters were obtained in He droplets of N He = 3.3 10 5 . The spectra show three peaks at approximately 2882, 2945 and 2975 cm -1 , which are assigned to ν 5 (//), ν 8+11 (//), and ν 7 ( ┴ ) bands of Et molecules in the clusters, respectively. The assignment is based on the close proximity of the peaks to the origins of the corresponding bands in free Et molecules at 2895.7, 2953.8, and 2985.4 cm -1 , respectively. 25 The bands of Et in clusters are shifted towards low frequency by about 10 cm -1 and have a FWHM of about 8 cm -1 due to the intermolecular interactions in the cluster. In comparison ν 7 = 2971 cm -1 was observed in solid ethane 26 which is at about 4 cm -1 lower frequency than in the clusters and is consistent with a lower molecular coordination in the clusters. It is apparent from the figure that upon collimation of the laser beam, the intensities of the ν 5 and ν 8+11 bands increase by about a factor of 5, while the intensity of the ν 7 band only increases by about a factor of 2.5 and assumes a larger width of about 11 cm -1 . This is indicative of laser power saturation of the stronger ν 7 band. At the band maximum each ethane molecule of the cluster absorbs about 1700 cm -1 . This is close to the expected saturation level which equals to about 2000 cm -1 per molecule, taking into account the degeneracy g = 2 of the 127 upper e u -state of the ν 7 band. The observed saturation indicates that the lifetime of the vibrational excitation in the ethane clusters is longer that the duration of the laser pulse of about 7 ns. Fig. 7.2(b) shows the spectra obtained upon capture of about 50 Ag atoms in PC1 followed by capture of about 18 and 34 Et molecules in PC2 as measured with the collimating lens. The spectrum of neat Et 226 clusters is also shown for comparison. It is seen, that the ν 7 band in Ag-Et clusters has low and high frequency components, which are labeled I and V in the figure, respectively. The frequency of the I and V peaks were found to be 2962 and 2975 cm -1 in Ag 50 Et 34 , and shifted by about 1.5 cm -1 towards higher frequency than for the smaller Ag 50 Et 18 cluster. In a composite cluster the Ag atoms form a core whose surface is covered by Et molecules captured downstream. At smaller number of the added Et molecules, the surface of the Ag core will be only partially covered by Et. Under these conditions, the low frequency I component of the ν 7 band dominates and was therefore assigned to Et molecules on the interface with the Ag core. The ν 7 band of the interface molecules has an additional low frequency shift, due to interaction with Ag atoms. The small shift in frequency for the interfacial Et molecules with respect to that of free Et of about 22 cm -1 suggests that the molecules are physisorbed. The higher frequency V peak is assigned to the ethane molecules not in immediate contact with the Ag atoms and residing in the next solvation shell. The frequencies of the I and V bands decrease somewhat with increasing number of attached Et molecules and are somewhat higher than that in the neat Et clusters. This effect is likely due to increased coordination of Et molecules in larger clusters. 128 In comparison to the ν 7 perpendicular band the weaker ν 5 and ν 8+11 parallel bands do not show any splitting. At small N Et = 20 no ν 5 and ν 8+11 bands are evident, whereas at higher N Et = 50, some new weak peaks appear at about 2885 and 2947 cm -1 close to the frequency of the ν 5 and ν 8+11 bands in neat Et clusters. We therefore assigned these peaks to the ν 5 and ν 8+11 bands of Et molecules in the second solvation shell. In accord with this assignment, the ν 5 and ν 8+11 bands of the Et molecules at the interface with the Ag cluster have low intensity. Figure 7.3(a) shows an example of the spectra obtained in larger He droplets of N He = 2·10 6 (T 0 = 9 K), for clusters containing approximately 270 Ag atoms. The spectra of Ag 270 Et m clusters are in agreement with those in Fig. 3 in obtained smaller He droplets and show a similar splitting into I and V bands. The total integrated intensity of the ν 7 band of the Ag 270 ET 59 and Ag 270 ET 217 clusters is the same within 10%, which indicates that the infrared absorption cross section of Et molecules in the first shell is similar to that in more distant shells. The intensity ratio of the V and I peaks, I V /I I , can therefore be used in order to obtain the fraction of Et molecules at the interface with the Ag cluster. The integral over the ν 7 band in the presence of Ag clusters is found to be about 20% smaller than that of neat Et clusters. We consider this agreement satisfactory, considering that the spectra with and without Ag were obtained on different days and with the collimating lens and laser slightly re-adjusted. Figure 7.3(b) shows an example of the spectra obtained in larger He droplets of N He = 5·10 6 (T 0 = 8 K), containing about 850 Ag atoms. Again, the spectra of the ν 7 band show a similar splitting and trend upon increase of the number of the added Et 129 molecules. However, it is seen that the spectra contain some strong continuum that is present even in the absence of the added Et molecules and is, therefore, assigned to the absorption of the Ag clusters. A similar continuum was previously observed in the visible and near infrared part of the spectrum 14 for Ag clusters; it was ascribed to formation of Ag cluster-cluster aggregates in large He droplets and extends into the mid infrared range of about 3000 cm -1 . The continuum causes a large level of noise in the spectrum, so that measurements at low N Et become tedious. Again the integrated intensity of the ν 7 band remains approximately the same with different number of added N Et . The spectrum with largest number of Et molecules, Ag 850 Et 900 is very similar to that of neat ethane clusters, except for the weak I component of the ν 7 band. This cluster has an approximately similar number of Ag atoms and Et molecules, which allows for an estimation of the cross-section due to Ag cluster absorption around 3000 cm -1 to be about 0.002 A 2 per Ag atom. Here, we used known absorption cross-section in the maximum of ethane ν 7 , which has a band of 10 cm -1 width, of 0.02 A 2 , and the measured intensity ratio of the ν 7 band and the continuum of about 10. The two peaks of the ν 7 band are still observed in the largest clusters obtained at T 0 =7 K, although the intensity of the Ag continuum becomes comparable to the ν 7 band and the quality of the measurements deteriorates. Therefore, we attempted a limited number of measurements for different clusters sizes, for which some results are shown in Fig. 7.3(c) at two different N Et . The two traces for each cluster correspond to full laser fluence and a factor of about 3 attenuation. It is seen that the bands at higher laser fluence have some pronounced wings extending towards low wavenunbers. This may 130 indicate coupling of the vibrations with plasmon modes of the Ag cluster; however, no attempt to study of this effect was made. 131 2850 2900 2950 3000 0 500 1000 1500 2000 Absorbed energy per ethane molecule, cm -1 Wavenumber, cm -1 20 pts AAv smooth of "Ag0Et1254, 9 K, lens, 101606" 20 pts AAv smooth of "Ag270Et59, 9 K, lens, 194402" 20 pts AAv smooth of "Ag270Et214, 9 K, lens, 205706" (a) 2850 2900 2950 3000 0 500 1000 1500 2000 Absorbed energy per ethane molecule, cm -1 Wavenumber,cm -1 20 pts AAv smooth of "Ag780Et903, 8 K, lens, 101225" 20 pts AAv smooth of "Ag860Et394, 8 K, lens, 124849" 20 pts AAv smooth of "Ag860Et129, 8 K, lens, 110754" 20 pts AAv smooth of "Ag900Et221, 8 K, 122627" (b) 132 2900 2920 2940 2960 2980 3000 3020 0 200 400 600 800 1000 1200 1400 Energy absorbed per ethane molecule, cm -1 wavenumber, cm -1 10 pts AAv smooth of "Ag1300Et1091, no mica, 7 K, 164012" 10 pts AAv smooth of "Ag1300Et1091, with mica, 7 K, 173224" 10 pts AAv smooth of "Ag1300Et686, no mica, 7 K, 192153" 10 pts AAv smooth of "Ag1300Et686, with mica, 7 K, 183209" (c) Figure 7.3. Infrared spectra of neat Et clusters and core-shell Ag-Et clusters. The clusters were obtained in He droplets of initial size N He = (a) 2·10 6 , (b) 5 10 6 , and (c) 10 7 . The average numbers of captured Et and Ag particles are indicated for each trace. The spectra were obtained with collimating lens. The original spectra were smoothed over 20 data points. Some spectra in the panel (c) were also obtained upon attenuation of the laser beam by about a factor of 3 by using a layer of mica. 133 In order to study the growth of the Et shell over the core Ag cluster a number of spectra were obtained in the vicinity of the ν 7 band for different numbers of added Ag atoms and Et molecules. We found that the spectra could be well-fitted by Gaussian shapes, which give the integrated peak intensities, positions, and widths. The intensity ratios I V /I I and peak positions as a function of the N Et molecules are shown in Fig. 7.4(a) and (b), respectively. Four sets of measurements in He droplets obtained at T 0 = 9.5, 9, 8, and 7 K containing 53, 164, 733 and 1311 Ag atoms are shown by filled circles, squares, triangles, and diamonds, respectively. It is seen that the measured ratios depend linearly on the number of Et molecules, which is consistent with a complete filling of the first shell of molecules around the Ag core. 134 0 1000 2000 3000 4000 5000 0 2 4 6 8 10 N1=20 N1=67 N1=392 9.5 K Iv/Ii 9.5 Iv/Ii max 9 K Iv/Ii 9 Iv/Ii max 8 Iv/Ii max 7 Iv/Ii max Iv/Ii NEt N1=788 a) 0 1000 2000 3000 4000 5000 2930 2940 2950 2960 2970 2980 2990 9.5 K 9.5 K 9.5 K 9K 9K 9K 8K 8K 8K 7K 7K 7K Wavenumber, cm -1 N ET b) Figure 7.4. (a): Measured values of I V /I I vs. number of attached Et molecules. For 8 and 7 K, ratios are obtained from the band peak intensities. Data for 9.5 and 9 K are for both integrals and peak intensities, which are in good agreement. b) peak maxima for the ν 8+11 , ν 7 (I I ) and ν 7 (I V ) bands, from low to high frequency, respectively. 135 In order to facilitate the discussion, we compare the measured I V /I I ratios with the predictions of a model which assumes a simple arrangement of a close-packed spherical Ag cluster that is covered by dense layers of Et molecules, as shown in Fig. 7.5. R Ag R Ag +r Ethane N Ethane (1) N Ethane (2) Fig. 7.5. Schematic of the close-packed, core-shell Ag-Et cluster. According to this model the radius of a core cluster of N Ag particles is calculated as: 1 3 M M M R r N  (7.7) 136 where r M is the Wigner-Seits radius of the particles 1/3 3 () 4 M M r n   . Here, r Ag = 0.16 nm and r Et = 0.25 nm, as obtained from the corresponding bulk number densities, n M . 27-28 . The number of particles in the n th shell around the core cluster is obtained as       2 2 4 2 1 Ag ethane Et ethane R n r Nn r   (7.8) 500 1000 1500 2000 2500 3000 3500 4000 100 200 300 400 500 600 700 9.5 K Ns int Ns 9.5 K max Ns 9K int Ns 9K Max Ns 8K max 7K N I N ET 45 80 180 250 Figure 7.6. N Et (1) vs the number of added Et molecules as obtained at T 0 = 9.5, 9, 8, and 7 K, shown by squares, triangles, diamonds and circles, respectively. The horizontal lines show the number of interfacial molecules according to Eq. 7.8. 137 Figure 7.6 shows the measured values of N Et (1) for clusters obtained at different T 0 and compares them with the numbers obtained according to Eq. 7.8. Experimental values of N Et (1) were obtained under the assumption that I I and I V are proportional to the number of Et molecules at the interface and removed from the interface, respectively, according to Eq. 7.9 below. (1) 1 Et Et I V N N I I   (7.9) It is seen from the figure that N Et (1) first increases linearly at low N Et , then reaches a plateau which corresponds to the filling of the first solvation shell around the Ag cluster. At T 0 = 9 K the N Et (1) ≈ 60 is in reasonable agreement and somewhat lower than 80 as obtained from Eq. 7.8. The somewhat smaller value is not unexpected as the ethane molecules are attached to the surface of the Ag clusters at T < 1 K and are likely immobilized. Therefore, some loose packing is expected in the first shell. On the other hand, the measurements at T 0 = 8 and 7 K give N Et (1) = 250 and 500, respectively, which are larger than the 180 and 250, respectively, obtained from Eq. 7.8. This may be the result of inaccuracies in the determination via beam attenuation of the number of the Ag atoms and Et molecules picked up, although it is unclear why this deviation sets in abruptly. The onset of the deviation correlates with the onset of the IR absorbtion of the Ag clusters and may result from the smaller density and respectively larger surface area of the large Ag clusters as discussed in Ref. 14 . This would lead to a greater number of interface Et molecules than expected according to Eq. 7.8. The dependence of N Et (1) on 138 N ET at T 0 = 8 and 7 K has an initial slope of about 1/3, i.e., less than the expected value of 1 for the attachment of single Et molecules. This may indicate that the Et molecules may form small clusters before attachment to the Ag core. 7.3.2.Core-shell Ethane-silver clusters Figure 7.7(a) shows the spectra of the ν 7 band of clusters obtained upon addition into He droplets produced at T 0 = 8 K of about 860 Et molecules in the upstream pickup cell (PC1) and a varying number of Ag atoms in the downstream pickup cell (PC2). The spectra show a splitting of the ν 7 band into two components at about 2962 and 2972 cm -1 with widths of about 8 cm -1 (FWHM) which we, once again, assign to Et molecules in contact with Ag and in the volume of the Et cluster, i.e., I and V, respectively. Upon increase of N Ag the intensity of the I band increases, whereas that of the V band decreases, indicating a corresponding increase in the fraction of the interfacial ethane molecules. This behavior is consistent with clusters composed of an Et core and a shell of Ag. The fraction of Et molecules on the surface of a dense, spherical cluster containing 860 molecules can be estimated from the liquid drop model to be about 40%. This is in agreement with about I V /I I ≈ 2 intensity ratios in the spectra obtained upon addition of about 738 Ag atoms. The number of the Ag atoms in the first shell around the compact Et 860 cluster is estimated, from Eq. 7.8 with the subscripts interchanged for Ag and Et, to be about 1000. This is similar to that in Fig. 7.7, indicating the formation of one monolayer shell of Ag atoms around the Et core cluster. In the case of the smallest N Ag = 139 441, we found I V /I I ≈ 5, in agreement with the expected smaller number of interfacial Et molecules, which are surrounded by an incomplete shell of Ag atoms. 140 2920 2940 2960 2980 3000 0 200 400 600 Adsorbed energy per ethane molecule, cm -1 Wavenumber, cm -1 Et860Ag738, lens, 8 K, 163542 Et860Ag441, lens, 8 K, 171937 Et860Ag594, lens, 8 K, 143415 a) 2920 2940 2960 2980 3000 0 200 400 600 800 Absorbed energy per ethane molecule, cm -1 Wavenumber, cm -1 Et718Ag1639, with lens, 7 K, 182824 Et768Ag771, with lens, 7 K, 154731 b) Figure 7.7. Infrared spectra of the clusters obtained upon capture of Et molecules followed by Ag atoms obtained at T 0 = 8 and 7 K, in panels (a) and (b), respectively. The spectra are with collimating lens. The average numbers of the captured Et and Ag particles are indicated in each trace. 141 2900 2920 2940 2960 2980 3000 3020 0 200 400 600 800 1000 Absorbed Energy per Ethane molecule, cm -1 Wavenumber, cm -1 Et860Ag738, lens, 8 K, 163542 Ag730Et932, 8 K, lens, 142225 Figure 7.8. Comparison of the spectra of clusters obtained by doping He droplets of 5 10 6 atoms by about 730 Ag atoms and 900 Et molecules by two different pickup orders as indicated. Doping with Et first, followed by Ag is in black. Doping with Ag, then Et is shown in red. 142 The maximum number of Ag atoms that could be added to a He droplet is limited by the heat capacity of the droplet; thus, the larger Ag clusters shown in Fig. 7.7(b) were obtained in the correspondingly larger He droplets obtained at T 0 = 7 K. The spectra shown in Figs. 7.7(a) and (b) are for two EtAg clusters that have approximately the same size Et core. It is seen that the intensities of the I and V bands become comparable upon the addition of approximately 1600 Ag atoms. Figure 7.8 shows a comparison of the spectra obtained for two clusters both containing the approximately N Ag ≈ 730 and N ET ≈900 which differ, however, in the order of pickup of Et and Ag. It is seen in both spectra that the I and V peaks have similar a width of about 9 cm -1 . The positions of the I peaks in the spectra of both clusters are very similar, i.e. 2961 and 2960 cm -1 . On the other hand, the V peak of the core-shell Et-Ag clusters is at 2972 cm -1 compared to 2975 cm -1 in the Ag-Et clusters. The lower frequency of the V band in the Et-Ag clusters is in agreement with the picture of Et molecules being completely surrounded within the Et core, whereas in the case of Ag-ET clusters the Et molecules on the surface of the composite clusters have a higher C-H stretch frequency which contributes to the overall higher V band frequency. Due to smaller spacing of the I and V bands in the spectra of the Et-Ag clusters, the two bands appear somewhat less resolved compared to those measured for Ag-Et clusters. The ratio of the integrated band intensities I I /I V of the two spectra in Fig. 7.8 was found to be 2.0 and 3.5 in Et-Ag and Ag-Et clusters, respectively. The larger value of I I /I V is expected in the case of Ag-Et because of the larger fraction of surface molecules in contact with Ag atoms. Therefore, we conclude that the core-shell Et-Ag structure of 143 the clusters is stabilized at low temperature in He droplets. Remarkably, no continuum due to the absorption of Ag was observed which underscores the different arrangement of Ag atoms in the Et-Ag clusters. 144 400 600 800 1000 1200 1400 1600 0 1 2 3 4 5 6 8 K IV/Ii 8K max 7 K IV/Ii 7 K max IV/Ii N(Ag) NEt = 800 Nvol/Nsurf=1.3 N1Ag = 980 a) 0 500 1000 1500 2000 0.0 0.5 1.0 1.5 2.0 2.5 b) NAg=700 N1Ag=1750 incomplete shell 8 K IV/Ii 8K max Nvol/Nsurf I V /I I NET NAg=880 N1Ag=640 complete shell 145 400 600 800 1000 1200 1400 1600 1800 2930 2940 2950 2960 2970 2980 8 K 8K 8K 7 K 7 K 7 K Wavenumber, cm -1 NAg c) 0 500 1000 1500 2000 2930 2935 2940 2945 2950 2955 2960 2965 2970 2975 2980 8K 8K 8K Wavenumber, cm -1 NET d) Figure 7.9. I I /I V versus (a) N Ag and (b) N ET for Et captured upstream (PC1) and Ag captured downstream (PC2). Corresponding band maxima for the ν 8+11 , ν 7 (I I ), and ν 7 (I V ) bands are shown in panels (c) and (d). 146 7.4. Discussion 7.4.1. IR spectra of adsorbed molecules Previous studies 29-30 of the adsorption of ethane (as well as ethylene and acetylene) molecules on surfaces of coinage metals have shown that the molecules are physisorbed with their C-C bonds nearly parallel to the metal surface. Molecules in the second layer and further away, on the other hand, are more randomly oriented with respect to the surface. We assume in this work that the same is true for molecules adsorbed on the surface of the Ag clusters. The observation of two peaks in the infrared spectra, the I and V peaks, in this work is in good agreement with previous studies of the molecular films on metal surfaces. 31 32-33 34 For example, the IR spectra of ethane and ethylene molecules deposited on Cu films at 50 K have been studied via infrared spectroscopy in Ref. 35 . Both smooth and rough Cu surfaces were studied and obtained via atomic Cu deposition at 300 K and 50 K, respectively; both surfaces resulted in very similar infrared spectra of Et. At submonolayer Et coverage of the Cu surface the frequency of the perpendicular ν 7 (e u ) band was found at approximately 2960 cm -1 , which is very close to the value found here of 2962 cm -1 (from Fig. 3(b) above) for Et molecules on Ag clusters. The ν 7 (e u ) vibration is doubly degenerate, with a transition dipole moment perpendicular to the C-C axis. At higher coverage of Et on the Cu surface, an additional band at about 2977 cm -1 was observed whose intensity was found to be proportional to the Et coverage. The band at 2977 cm -1 was assigned to Et molecules in the second layer and further away, similar to the band observed here at 2980 cm -1 for Ag- Et clusters. At the highest exposure of 4.8 L the intensity of the 2977 cm -1 band was 147 found to be about a factor of four higher as compared with the 2965 cm -1 band. This fact shows that the intensity ratio of the interface and volume bands can indeed be used for determination of the fraction of the molecules on the interface. It was also shown in that in distinction to the perpendicular ν 7 (e u ) band the parallel ν 5 (a 2u ) band of Et molecules was not detectable at sub-monolayer coverage. 35 In the case of the ν 5 (a 2u ) vibration the vibrational transition dipole moment is along the C-C axis molecular axis of ethane. At higher coverage, the ν 5 band is seen at 2883 cm -1 which very close to its frequency of 2880 cm -1 in the bulk solid. Similar results have been reported for ethylene molecules, where the parallel ν 11 and ν 9 bands have only been detected at higher coverage beyond the first monolayer. 35 It is known that the usual selection rules in the infrared spectra should be modified for when the molecules are adsorbed on a metal surface which is on account of the interaction of the electromagnetic field with the metal. Because the direction of the electric field is perpendicular to the metal surface, only the molecular vibrational modes of transition dipole moment perpendicular to the metal surface can be excited. Theoretical calculations obtained similar but somewhat relaxed selection rules for molecules attached to spherical metal particles of diameters as small as 2 nm 29-30 . These considerations explain the presence of the ν 7 perpendicular band and the simultaneous absence of the ν 5 and ν 8+11 parallel bands in the spectra of the adsorbed Et molecules in the first layer on Ag clusters assuming a preferred orientation of the adsorbed molecules as parallel to the surface. Ethane molecules in the second and subsequent layers are expected to have a random angular distribution and, thus, the selection rules implied by 148 the metal surface are relaxed. It also shows that Ag clusters as small as 100 atoms are metallic, in agreement with the previous observation of a plasmon resonance excitation in small clusters. 14 7.4.2. IR Enhancement The linear dependence of I I /I Tot suggests absorption probability remains the same for molecules at different distances from the surface of metal cluster. Overall, the depletion signal is comparable to that in neat ethane clusters at the same laser pulse energy. Therefore, our experiments do not indicate any noticeable enhancement of the IR absorption for the molecules adsorbed on the Ag clusters. This may be expected for small Ag clusters whose plasmon resonance is far from the IR frequencies. However in Ag clusters obtained at 7 K there is a noticeable absorption of Ag cluster at 3 microns. 7.5. Conclusions We studied the utility of large helium droplets of 10 6 -10 7 atoms for the growth of composite clusters consisting of a silver core and a shell of ethane molecules (and vice- versa). The clusters were assembled by doping He droplets with up to 10 3 silver atoms and ethane molecules in two sequential pickup cells and studied via infrared spectroscopy in the C-H stretch region. We found that the ν 7 band of ethane molecules on the interface with the silver atoms has a low frequency shift of approximately 15 cm -1 with respect to that of more distant ethane molecules away from the interface. The intensity ratio of the two bands was used for evaluation of the core-shell cluster structure. In addition, it was 149 observed that the clusters obtained by doping He droplets first with Ag atoms followed by ethane molecules have a silver core which is covered by a shell of ethane molecules. On the other hand, the results indicate that clusters obtained by adding silver atoms to the preformed ethane core have a metal shell, which is stabilized at low temperature in He droplets. 150 Chapter VII Bibliography 1. J. P. Toennies and A. F. Vilesov, Ann. Rev. Phys. Chem. 49, 1-41 (1998). 2. J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. 43, 2622-2648 (2004). 3. M. Y. Choi, G. E. Douberly, T. M. Falconer, W. K. Lewis, C. M. Lindsay, J. M. Merritt, P. L. Stiles and R. E. Miller, Int. Rev. Phys. Chem. 25, 15-75 (2006). 4. F. Stienkemeier and K. K. Lehmann, J. Phys. B 39, R127-R166 (2006). 5. M. Hartmann, R. E. Miller, J. P. Toennies and A. Vilesov, Phys. Rev. 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Tysoe, Surface Science 486 (1-2), 9-23 (2001). 35. A. Priebe, A. Pucci and A. Otto, J. Phys. Chem. B 110 (4), 1673-1679 (2006). 153 Chapter VIII: Traces of Vortices in Superfluid Helium Droplets 8.1. Introduction First observed in 4 He, quantum vortices are one of the most dramatic hallmarks of superfluidity. 1-3 In contrast to a normal fluid, which will rotate as a solid body when its container moves at low angular velocity, a superfluid will remain at rest. However, above a certain critical angular velocity the thermodynamically stable state of a superfluid includes one or more quantum vortices. Such a vortex can be characterized by a macroscopic wave function and quantized velocity circulation in units of h M   , where h is Planck’s constant and M is the mass of the 4 He atom. 2-3 Recently, the study of vorticity was extended to finite systems such as Bose-Einstein condensates (BECs) confined to traps. 3-4 The transfer of energy and angular momentum in finite systems between quantized vortices and surface excitations is of particular interest as it defines the nucleation dynamics, shape, and stability of the involved vortices. 3-4 In comparison to confined BECs, 4 He droplets are self-contained and present a case for the strongly interacting superfluid. Moreover, the diameter of a vortex core which is approximately 0.2 nm in superfluid He 2 is small relative to the droplet size, suggesting a three dimensionality of the vortices in droplets. Vorticity in He droplets has therefore attracted considerable interest. 5-8 Early attempts at observing vortices in mm-sized He droplets include experiments with magnetic levitation. 9 A critical angular velocity necessary for the formation of 154 vortices in droplets has been estimated. 10 Calculations predict that vortices in superfluid He droplets are curved in shape and that there exists a substantial barrier in free energy to their formation. 11 It was also shown that curved vortices must be stable in nanometer- sized droplets because of their smaller energy per angular momentum relative to evaporation or the possible accepting modes of the droplet such as surface ripplons. 6 According to calculations 7, 12 , the vortices can be stabilized in droplets consisting of just a few hundred He atoms by pinning foreign particles to the vortex lines. The trapping of electrons and ions was instrumental in early observations of vortex rings in bulk liquid He. 13 Therefore, the possibility of trapping probe atoms and molecules along vortices in He droplets was considered 5, 14 . However, thus far all spectroscopic observations in He droplets can be explained without invoking vorticity. 5-8 Vortices in bulk superfluid He, as well as in BECs, are often produced by the application of a rotating perturbation 2-4 . Such an approach is difficult to apply to the droplets in a fast-moving beam; the droplets themselves must carry sufficient energy and angular momentum for a vortex to exist. It was therefore concluded that vortices are not produced efficiently in a typical beam experiment involving the capture of impurities or during the growth of the droplets from a gas expansion. 6 In this work, we circumvented these limitations by producing He droplets containing vortices via fragmentation of a cryogenic He fluid. 15 The vortices were traced by introducing Ag atoms into the droplets, which clustered along the vortex lines as previously demonstrated in bulk liquid He using H 2 and Au clusters (see 16-17 and references therein). 155 Experiments in beams of He droplets have been reviewed previously. 8, 18-19 A schematic of the experiment is shown in Fig. 8.1. Helium droplets are produced by expansion of He, at 20 bar and a temperature T 0 = 5.4 – 7 K, into vacuum through a nozzle of diameter D = 5 μm. The droplets cool rapidly via evaporation and reach a temperature of 0.37 K 20 , which is well below the superfluid transition temperature T λ = 2.17 K 2-3 . Further downstream the droplets capture 10 3 – 10 6 Ag atoms in an oven. 21 The droplets are then collided against a thin carbon film substrate at room temperature. 21 Upon impact, the droplets evaporate leaving the Ag traces on the surface, which are subsequently imaged via a transmission electron microscope (TEM). More details are provided in the Appendix 3. Figure 8.1. Schematic of the experiment. (A) He fluid expands in vacuum and (B) breaks up into rotating droplets. (C) A quantum vortex is formed following evaporative cooling of the droplet to below T λ . (D) The droplet is doped with Ag atoms, which are 156 attracted to the vortex core. (E) The droplet then collides with the carbon surface leaving behind the Ag trace whereas the He evaporates. 8.2. Experimental A schematic of the molecular beam apparatus, described previously 21 , is shown in Fig. 8.1. Helium nanodroplets are formed by expanding high purity (99.9999%) He gas, at cryogenic temperatures and a pressure of 20 bar through a nozzle of 5 µm nominal diameter and a nominal channel length of 2 µm (Plano A0200P), into vacuum 15, 19 . In this work nozzle temperatures of T 0 = 7, 6 and 5.4 K were used resulting in droplets of average size, <N He >, of approximately 10 7 , 3×10 8 and 1.6×10 10 atoms, respectively. 15 The droplet size distribution in the beam is nearly exponential 22 and, thus, the probability for a droplet of size N is given by: ( ) exp He N PN N      (8.1) The central part of the expansion is separated by a 0.5 mm diameter skimmer and the resulting droplet beam captures Ag atoms in a resistively heated alumina oven 26 cm from the He droplet source. 21 Further downstream, the doped droplet beam enters the deposition chamber where it collides with substrates placed 93 cm from the He droplet source. The substrates are 3 mm diameter standard TEM supports (Ted Pella 01820) consisting of an amorphous carbon film, 15-25 nm thick, mounted on a 300 mesh copper grid that is coated on the underside by a 30-60 nm thick Formvar film. Typically, a set of 157 six samples mounted onto a linear motion positioner were kept under 10 -8 mbar high vacuum for approximately 24 hours before the deposition experiments. The samples were then removed from vacuum and TEM imaging was carried out within 6 hours following deposition. The imaging was conducted on a JEOL JEM-2100 electron microscope at an electron beam energy of 200 keV. Experiments indicate that the structure of the track-shaped deposits is well- preserved during the transfer of the samples and TEM imaging. Some of the tracks have been illuminated for as long as approximately 10 minutes by the 200 kV electron beam of the TEM without any noticeable change in appearance. The micrograph of Fig. 8.3 C was obtained during the re-imaging of the sample following its exposure to ambient conditions for about one month. It is seen that the tracks of Fig. 8.3 C have the same generic shape as those imaged immediately following their deposition (such as in Fig. 8.3, A and B) which indicates that there is no substantial diffusion of the Ag beads on the surface. The beads in Fig. 8.3 C appear more rounded which may indicate some slow reconstruction of the beads at ambient conditions. 158 Figure 8.2. Experimental setup for surface deposition of metal clusters formed in He droplets. The degree of Ag doping of the droplets is controlled by varying the temperature of the oven which is filled with metallic Ag and, thus, the vapor pressure of the Ag atoms within. The average number of Ag atoms captured per He droplet, <N Ag >, has been estimated using the attenuation of the droplet beam 21 23 . The flux of He atoms transported by the droplets is monitored as a rise in the partial pressure of He, P He , in the UHV analysis chamber downstream from the deposition chamber. Upon repeated capture of Ag atoms, the average size of the droplets decreases by evaporation of He atoms, which is monitored by a decrease in the partial pressure of He, ΔP He . The dominant contribution to the energy released upon Ag atom capture is from the binding energy of the Ag atoms during the formation of Ag N clusters. Thus, <N Ag > can be obtained as: He He He Ag He Ag PN E N PE   (8.2) 159 where E He is the 0.6 meV 24 binding energy of He atoms to the droplet, <N He > is the initial average size of the He droplet, and E Ag ≈ 3 eV is the energy associated with the addition of one Ag atom 25 . In this work, He droplets were doped with Ag atoms until about 70% of the He content was evaporated for a reduction in diameter of approximately 30%. At the three average droplet sizes employed, <N He > = 10 7 , 3×10 8 , and 1.6×10 10 , Eq. 2 gives <N Ag > ≈ 1.4×10 3 , 4×10 4 , and 2×10 6 , respectively. The temperature of the helium droplets, as they traverse the oven, increases above their temperature of T = 0.38 K in vacuum 20 due to the energy release associated with the pickup of Ag atoms. The temperature of the droplets inside the oven can be estimated 15, 24, 26 using the known temperature-dependence of the vapor pressure of helium 27 and the rate of evaporation of helium atoms from the droplet during the time of flight of about 200 μs. Estimates show that for all experiments in this work the droplet temperature in the oven does not exceed 1 K and, thus, remains well below the superfluid transition temperature of 2.17 K. 8.3. Results Figure 8.2, A – C shows some typical TEM micrographs of the Ag aggregates (black traces) grown in He droplets with average diameters of 100, 300, and 1000 nm, respectively. 15 The micrographs reveal that the shapes of the obtained Ag traces change remarkably with increased He droplet size. The aggregates obtained in the smallest droplets are round in shape (Fig. 8.2A), whereas those obtained in the larger droplets are track-like (Fig. 8.2, B and C). The number of tracks observed in the micrographs is in 160 agreement with the measured flux of the He droplets 15 . Moreover, the tracks in Fig. 8.2, B and C are well-separated by empty regions in the micrographs. Therefore, we conclude that each track results from the impact of a single, doped He droplet. As control experiments, the samples were exposed to an effusive beam of Ag atoms emanating from the oven, in the absence of He droplets, which was kept at the same temperature as in Fig. 8.2C. At a deposition time of 2 s, as in Fig. 8.2C, no deposits could be detected in the TEM images. At a much longer exposure time of 30 min a high density of evenly distributed round clusters smaller than about 2 nm in diameter was observed. Therefore we conclude that diffusion of Ag atoms and clusters on the substrate surface cannot cause the observed elongated tracks. Some representative tracks are shown at higher magnification in Fig. 8.3. Each of the tracks consists of tens of segments having a cross section of about 10 nm, as shown in the inset to Fig. 8.3B. Analysis of about 100 images such as in Fig. 8.3 A, B gives the length of the tracks to be (540 ± 220) nm, which is comparable to the average diameter of the droplets of about 700 nm after being doped by Ag. The scatter is consistent with the mean square deviation of the droplet diameter of approximately 35% and with the multitude of track shapes. The number of Ag atoms in a track of this average length was estimated assuming a bulk density and a cylindrical track shape to be about 10 6 in agreement with the number of captured Ag atoms. 161 Figure 8.3. TEM micrographs obtained upon deposition of Ag-doped droplets of average diameter (A) 100 nm, (B) 300 nm, and (C) 1000 nm and average number of He atoms <N He > = 10 7 , 3×10 8 , and 1.7×10 10 , respectively. The droplets were attained at a nozzle temperature T 0 = 7, 6 and 5.4 K, respectively. 15 Exposure times to the droplet beam are 120 sec, 4 sec, and 2 sec, respectively. Large dark spot on right side of (C) is artifact likely introduced during sample transfer to the TEM. 162 Figure 8.4. Typical Ag traces obtained in 1000 nm He droplets. The inset to panel (B) shows an enlarged track segment. 163 8.4. Discussion In an isotropic droplet, the recombination of Ag atoms will likely result in fractal aggregates 28 , as are often encountered in colloidal chemistry. In order for the aggregates to assume track shapes of length comparable to droplet diameter a long-range guiding force, such as the force of attraction of foreign particles to the core of a vortex line in a superfluid 7 , is required. An impurity particle does not partake in the circulation of the superfluid, so trapping of a particle in the vortex core leads to a reduction in the kinetic energy of the superfluid by about 5 K, as calculated for Xe atoms. 12 The binding of Ag atoms and small Ag clusters formed inside the He droplets 29 to the vortex core and subsequent aggregation of the trapped particles leads to the formation of the observed elongated aggregates. A similar mechanism has been well-documented in bulk superfluid He 16-17 . Therefore, we conclude that aggregation in vortices provides the most likely explanation of the observed elongated aggregates. In contrast, the formation of much shorter, linear molecular clusters such as (HCN) 7 in small He droplets of less than 10 nm diameter (N He <10 4 ) has been attributed to the strong dipole-dipole interaction of the HCN molecules. 30 This mechanism, however, is not applicable to the atoms and metal clusters used in this work which are devoid of a permanent dipole moment. Furthermore, van der Waals interactions between the recombining particles are short range (of the order of three diameters for spherical particles) 31 and strongest for aggregates with large surface contact (such as the T-shaped configuration of three particles), so they are not expected to facilitate the formation of long tracks. 164 The prevalence of the track-shaped deposits indicates that vortices are present in droplets larger than about 300 nm and that they survive the 1.5 ms flight time from nozzle to Ag oven. The appearance of the vortices in the large droplets correlates with the different regimes of the nozzle beam expansion. Our recent work 15 indicates that droplet formation occurs within the nozzle for T 0 < 6.5 K (as in Fig. 8.2, B and C). At T 0 = 7 K (Fig. 8.2 A), the fluid breaks up into droplets beyond the nozzle which may not be favorable for the formation of vortices. The density of Ag is approximately a factor of 80 larger than that of liquid He and its binding energy is 5000 times larger; it is therefore likely that during the impact of the doped He droplet the Ag inclusions move nearly ballistically toward the surface whereas the He evaporates. In this way, the TEM images (Fig. 8.3) represent two-dimensional projections of the vortex traces as they exist in the He droplets. The most common deposit shape, with an occurrence of about 40%, is tracked and curved (Fig 8.3, A – B) which must result from single curved vortices, as predicted theoretically. 11 In many instances the tracks have short (Fig. 8.3, A – B) or longer branches (Fig. 8.3, C – D). Such longer branches may indicate the presence of multiple vortices within the same droplet. Fig. 8.3E resembles the projection of two braided traces which is consistent with two gyrating parallel vortices. A small number of traces have loops (Fig. 8.3, F and G) which may indicate the presence of both vortex lines and vortex rings in the same droplet. Finally, Fig. 8.3H resembles a tangle of vortices. The state of the He fluid during the expansion is defined by its isentropes. Accordingly, an expansion starting at T 0 = 5.4 K, P 0 = 20 bar, as in Fig. 8.2C and in Fig. 165 8.3, will reach the phase separation line inside the nozzle where the fluid will break up into droplets at T ≈ 4.1 K, P ≈ 0.9 bar. 15, 32 Thus, the droplets are initially composed of normal fluid. The temperature of the droplets at a distance S from the nozzle of diameter D can be estimated from the He saturated vapor density 27 and the local number density, n, of the He gas which follows 2 0 2 D nn S  . Here, n 0 is the number density of the He gas at phase separation. According to our estimate, the temperature of the droplets approaches T λ at S = 0.02 mm after 10 -7 s of expansion assuming a droplet velocity υ D = 173 m/s 15 . At S = 0.2 mm and after 10 -6 s, the temperature falls to ≈1 K corresponding to a superfluid with a normal fluid fraction of only about 7×10 -3 27 . Subsequently, the droplets cool even further by evaporation to 0.37 K. 20 The spontaneous formation of vortices during the rapid superfluid transition in bulk liquid He has caught the attention of many as a model of the creation of cosmic strings during the early expansion of the Universe. 33 In this work, however, the rotating droplets may originate from asymmetries in the flow through the nozzle channel. Once the droplet becomes superfluid, solid body rotation is no longer feasible and the rotation takes the form of a vortex. 6 11 Estimates show that a normal fluid droplet of 1000 nm diameter rotating at an equatorial velocity of about 0.2 m/s has sufficient rotational energy and angular momentum for the creation of a rectilinear vortex. Such a rotational velocity is feasible for a droplet moving at υ D ≈ 173 m/s through a narrow D = 5 μm diameter nozzle. In addition, the corresponding angular velocity of about 4×10 5 rad/s would remain well below the stability limit of the droplet at about 10 7 rad/s. 34 166 Our expansion is characterized by a Reynolds number D e D R     ≈ 4×10 4 , which is higher than the typical threshold for turbulence at about 3×10 3 . Here ν ≈ 2.5×10 -8 m 2 /s is the kinematic viscosity of normal fluid He 27 . Therefore, the interaction of the fast moving He fluid with the walls of the nozzle can generate classical vortices 35 which become trapped in the droplets upon fragmentation. In a normal fluid, a vortex has a solid body rotating core of diameter d which will increase with time, τ, according to   16 2 d  . 36 Therefore the lifetimes of vortices in normal fluid droplets of diameter 100 and 1000 nm are estimated at τ ≈ 2.5×10 -8 and 2.5×10 -6 s, respectively. It follows that, although the lifetime of classical vortices in the smaller droplets is too short, vortices will persist in the larger droplets at T λ and can contribute to quantum vortex formation. If the angular momentum of a superfluid droplet, L D , is equal to ħ·N He then a single rectilinear vortex is formed; a smaller value of L D corresponds to the formation of a curved vortex 6 . If the droplet possesses a larger angular momentum, however, the resulting quantum vortex will be formed in a non-stationary state and will eventually decay into a collection of unit circulation vortices of different shapes and orientation. Some of the branched vortices as well as the other intriguing shapes shown in Fig. 3 may indeed originate from the evolution of such non-stationary states during the time-of-flight of the droplets. Also interesting, our results allow for an estimation of the mean square vorticity, ω, in the expansion according to L   35 where L is the length of quantum vortex lines per unit volume. Assuming that each of the 300 nm diameter droplets contains a 167 single vortex spanning the droplet diameter one obtains ω ≈ 10 6 s -1 . This is a factor of approximately 10 3 larger than typically observed in turbulent bulk superfluid He. 35 We comment now on the possible origins of the segmentation of the Ag traces. It was shown that 10 µm H 2 clusters attached to vortices in bulk superfluid He are uniformly spaced along the vortex core 16 and hypothesized that clusters attached to a vortex repel each other through a mechanism which remains to be understood. In contrast, the deposits obtained in this work often contain intact, elongated Ag segments (Fig. 8.3, A – B) indicating that the traces may actually be continuous inside the droplets. From the droplet velocity, the kinetic energy of the surface impact is estimated at about 0.02 eV per Ag atom, which is much less than the binding energy of Ag atoms in solid of about 3 eV. Therefore, the aggregates should remain largely intact although the impact may fracture the traces into segments. Any subsequent reconstruction is expected to be more pronounced in smaller Ag clusters and may affect our ability to detect vortices in the small 100 nm diameter droplets. In the future, measurements should be expanded to imaging by means of X-ray diffraction inside the droplets in order to attain the structure of the traces as well as to assess the smallest size droplet which can carry a vortex. Very recently, the formation of bundles of metallic nano-filaments upon the ablation of metals in bulk liquid He by a focused pulsed laser beam was reported. 17 The observation of similar nano-filaments in both superfluid and normal He indicates that their formation occurs on a short time scale close to the hot environment of the ablation spot, by trapping and coalescence of the particles in turbulent eddies in the ablation area. 17 Subsequently, the nano-filaments and small spherical particles aggregate into cm-long 168 bundles along the vortex lines in superfluid He, whereas in the normal fluid He the fragments are spread uniformly. The very different experimental conditions of Ref. 17 and this work render the results difficult to compare. In this work, the Ag atoms enter the droplets which remain at T < T λ throughout. On the other hand, the violent ablation process in Ref. 17 provides for poorly characterized initial conditions. In this respect, the levitation of superfluid droplets in high vacuum 9 followed by their controllable doping with atoms may provide an ideal system for studying vortex-guided aggregation in macroscopic samples of superfluid He. 8.5. Conclusion In conclusion, our results indicate that superfluid He droplets of diameters larger than 300 nm, produced upon fragmentation of a free fluid-jet, contain single and multiple vortices. The vortices may originate from the solid body rotation of the normal fluid droplets or from classical vortices in the expanding fluid that are entrapped by the droplets upon fragmentation. After entering vacuum, the droplets cool down and become superfluid within less than 1 µs where classical vortices and rotations may give rise to quantum vortices. In addition, we have observed some rather unusual deposit shapes that indicate the formation during the rapid superfluid transition of non-stationary vortex states. 169 Chapter VIII Bibliography 1. R. P. Feynman, in Progress in low temperature physics, edited by C. J. Gorter (North-Holland Publishing Company, Amsterdam, 1955), Vol. 1, pp. 1-53. 2. R. J. Donnelly, Quantized Vortices in Helium II. (Cambridge University Press, Cambridge, 1991). 3. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation. (Clarendon Press, Oxford, 2003). 4. A. L. Fetter, Reviews of Modern Physics 81 (2), 647-691 (2009). 5. J. D. Close, F. Federmann, K. Hoffmann and N. Quaas, Journal of Low Temperature Physics 111 (3-4), 661-676 (1998). 6. K. K. Lehmann and R. Schmied, Phys. Rev. B 68 (22), 224520 (2003). 7. M. Barranco, R. Guardiola, E. S. Hernandez, R. Mayol and M. Pi, J. Low Temp. Phys. 142, 1-81 (2006). 8. F. Stienkemeier and K. K. Lehmann, J. Phys. B 39, R127-R166 (2006). 9. M. A. Weilert, D. L. Whitaker, H. J. Maris and G. M. Seidel, Journal of Low Temperature Physics 106 (1-2), 101-131 (1997). 10. L. Pitaevskii and S. Stringari, Zeitschrift Fur Physik D-Atoms Molecules and Clusters 16 (4), 299-301 (1990). 11. G. H. Bauer, R. J. Donnelly and W. F. Vinen, Journal of Low Temperature Physics 98 (1-2), 47-65 (1995). 12. F. Dalfovo, R. Mayol, M. Pi and M. Barranco, Physical Review Letters 85 (5), 1028-1031 (2000). 13. G. W. Rayfield and F. Reif, Phys. Rev. 136, A1194-A1208 (1964). 14. F. Ancilotto, M. Barranco and M. Pi, Phys. Rev. Lett. 91, 105301-105301-105304 (2003). 15. L. F. Gomez, E. Loginov, R. Sliter and A. F. Vilesov, J. Chem. Phys. 135, 154201 (2011). 170 16. M. S. Paoletti, R. B. Fiorito, K. R. Sreenivasan and D. P. Lathrop, Journal of the Physical Society of Japan 77 (11), 111007-111001-111007 (2008). 17. V. Lebedev, P. Moroshkin, B. Grobety, E. Gordon and A. Weis, Journal of Low Temperature Physics 165 (3-4), 166-176 (2011). 18. C. Callegari, K. K. Lehmann, R. Schmied and G. Scoles, J. Chem. Phys. 115, 10090-10110 (2001). 19. J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. 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Loginov, L. F. Gomez, N. Chiang, A. Halder, N. Guggemos, V. V. Kresin and A. F. Vilesov, Phys. Rev. Lett. 106, 233401-233404 (2011). 30. K. Nauta and R. E. Miller, Science 283 (5409), 1895-1897 (1999). 171 31. J. N. Israelachvili, Intermolecular and surface forces, 3 ed. (Academic Press, San Diego, Oxford, Amsterdam, 2011). 32. H. Buchenau, E. L. Knuth, J. Northby, J. P. Toennies and C. Winkler, Journal of Chemical Physics 92 (11), 6875-6889 (1990). 33. W. H. Zurek, Nature 317 (6037), 505-508 (1985). 34. R. A. Brown and L. E. Scriven, Proc. R. Soc. A 371 (1746), 331-357 (1980). 35. R. J. Donnelly, in Quantized vortex dynamics and superfluid turbulence, edited by C. F. Barenghi, R. J. Donnelly and W. F. Vinen (Springer, Berlin, 2001), pp. 17- 35. 36. J.-Z. Wu, H.-Y. Ma and M.-D. Zhou, Vorticity and Vortex Dynamics. (Springer, Berlin, Heidelberg, 2006). 172 Chapter IX: Conclusions and Future Work 9.1. Conclusions This thesis summarizes the results of a set of experiments aimed at using the helium droplet technique to assemble and study large atomic and molecular clusters containing hundreds to millions of particles. By introducing a novel titration method, it was shown that large helium droplets of up to 10 11 helium atoms and diameters of up to 1 µm could be attained. Such large droplets were shown to be produced via the break-up of a jet of helium fluid within the nozzle. Furthermore, the helium droplet technique was used to produce Ag clusters by the pickup of Ag atoms from a hot oven. The Ag clusters were, in addition, deposited on substrates and images via electron microscopy in order to attain the cluster sizes and size distributions. The formation mechanisms and kinetics of Ag cluster growth were explored by measuring the photoabsorption spectra of the Ag clusters in helium droplets. The spectra reveal that while smaller (N Ag < 300) clusters are likely compact in structure and results from single-centered cluster growth, the larger “clusters” (N Ag ~2000) are most likely cluster-cluster aggregates which come about by the aggregation of smaller clusters formed in various locations within the host helium droplet. The reconstruction of the Ag clusters of various sizes in helium droplets upon excitation by pulsed and cw laser beams at 532 and 355 nm was reported. The results were shown to be consistent with a kinetic limit on the energy transfer rate from the 173 excited Ag cluster to the host helium droplet, which was not exceeded in the case of cw excitation. The first experimental observation of vortices in superfluid helium droplets was also reported. This observation was made by introducing Ag atoms, which clustered along the vortex lines, into the droplets. Surface-deposition and imaging of the Ag clusters revealed the presence of track-shaped aggregates indicating that vortices are present in droplets larger than about 300 nm. Lastly, it was also shown that the helium droplet technique could be used to in build large metal-molecule, Ag-ethane clusters. By using the infrared spectroscopy of the C-H stretch bands of ethane it was shown that core-shell Ag-ethane clusters could be grown. In addition, it was found that the v 7 band of ethane is split into two distinct features which could be used to quantify the number of ethane molecules in and out of contact with Ag. 9.2 Future Work In spite of the fact that vortices are ubiquitous in nature, relatively little is known about vorticity in free finite systems. Vortices in viscous droplets are unstable and decay into forms of rigid body rotation. Therefore studies in viscosity-free superfluid helium droplets are of special significance. The existence of quantum vortices in He droplets has long been a matter of debate and a direct proof for their appearance has not been shown. 1 . In Chapter 8, we showed that Ag clusters formed in He droplets of about 100 nm diameter resulted in randomly distributed, round cluster imprints as expected for an 174 isotropic dopant distribution in the droplet. However, the use of much larger He droplets of about <N He >≈10 10 gave rise to tracks (see Fig. 8.3) with widths of about 7 nm and an average length of about 1 µm. We ascribe the formation of these tracks to the self- assembly of the clusters along single quantum vortices, which effectively serve as condensation centers. 2 However, surface deposition of the Ag clusters at a velocity of ≈170 m/s and subsequent exposure to air during transfer of the samples to perform TEM causes some physical and chemical modification of the Ag samples, which may change shapes of the deposits to some unknown extent. Therefore, it would be interesting to image the quantum vortices inside the superfluid helium droplets. This could be accomplished by way of x-ray diffraction of atomic/cluster tracers in the droplets. To this end, Xe atoms, which will be attracted to the vortex cores can serve as tracers. Using gaseous Xe as tracers instead of Ag simplifies the experiment significantly. Moreover, an about 20 times smaller cohesion energy of Xe versus Ag permits embedding a correspondingly larger number of Xe atoms and thus a larger signal. Recent experiments by Bostedt and co-workers at the Linac Coherent Light Source (LCLS) have demonstrated imaging of Xe nano-clusters consisting of ≈10 5 Xe atoms at a photon energy of 1.5 keV. X-ray diffraction experiments can be used to directly probe the abundance, size distribution, and in particular the shape of the vortices. The unique single-shot imaging capability of the LCLS, for example, will be the key to derive the shapes of single vortices, which are directly related to the angular momentum stored in the droplets and cannot be measured by any other means. For such experiments, the droplet size 175 distribution can be characterized by imaging neat He droplets prior to the experiments on Xe-doped droplets. The systematic variation of droplet sizes will provide direct access to the minimum droplet sizes that are required to support single and multiple vortex formation. Experiments with different levels of Xe doping will gauge the influence of the doping on the vortices. Observation of multiple vortices in the same droplet will give information on their mutual interaction, which is considered an important process in quantum turbulence. 176 Chapter IX References: 1. K. K. Lehmann and R. Schmied, Phys. Rev. B 68 (22), 224520 (2003). 2. G. P. Bewley, D. P. Lathrop and K. R. 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Further downstream, the doped droplets entered the deposition chamber and collided against substrates placed at ~93 cm from the He droplet source. The substrates were 3 mm diameter standard TEM grids (Ted Pella 01820). Typically, the samples were kept under 10 -8 mbar vacuum for approximately 24 hours before the deposition experiments. The samples were then removed from vacuum and imaging was carried out within 12 hours following deposition. The imaging was conducted on a JEOL JEM-2100 at an electron beam energy of 200 keV. 186 Figure A1.1. TEM images of Ag N clusters on amorphous carbon film. Magnification is 10×10 3 for panels a, c, and e; for panels b, d, and f a magnification of 40×10 3 was utilized. The samples were obtained by exposing them to the doped droplet beam for 2 min (a, b), 16 min (c, d), and 60 min (e, f). The droplets were obtained at a nozzle 187 temperature T 0 = 9 K for an average size of He N = 1.8×10 6 and doped by Ag until attenuated by ΔP He /P He = 0.63 (a, b), 0.70 (c, d), 0.75 (e, f). According to Eq. 4.1, this gives <N Ag > ~ 300 atoms. It is seen that the coverage of the samples increases with exposure time. From panel (f), is it seen that at high exposure not only is there a higher density in clusters but the deposits are much larger in size and on the order of about 5 nm. 188 Figure A1.2. TEM images of Ag N clusters deposited on amorphous carbon film taken at 40×10 3 magnification. The samples were obtained by exposing them to the doped droplet beam for 0.5 min (a), 2 min (b), 8 min (c), and 32 min (d). He droplets of average size He N = 2.2×10 7 were obtained at a nozzle temperature T 0 = 7 K. The droplets were then doped with Ag for a droplet beam attenuation of ΔP He /P He = 0.68. At this attenuation Eq. 4.1 gives <N Ag > ~ 3000 atoms. In panel (d), obtained at an exposure time of t = 32 min it is seen that there is significant coalescence of clusters as previously reported in Chapter 4. At this exposure time, many of the deposits are slightly oblate in shape and as large as approximately 10 nm. 189 Figure A1.3. TEM images obtained at a magnification of 10×10 3 of Ag N clusters on amorphous carbon. The samples were obtained by exposing them to the He droplet beam doped with Ag; exposure times are 4 sec (a) and 2 min (b). The droplets of average initial size He N = 3.08×10 8 were produced at a nozzle temperature T 0 = 6 K, then were doped with Ag atoms until a droplet beam attenuation of ΔP He /P He = 0.80 (a) and 0.66 (b) was reached. At this attenuation Eq 4.1 gives <N Ag > ~ 4×10 5 atoms. It is seen that many of the deposits, as in panel (a), are elongated spanning several hundred nanometers. This is in contrast to the rounded clusters obtained at T 0 = 9 K and 7 K, shown in Figs. 1 and 2, respectively. 190 Figure A1.4. TEM micrographs of Ag N clusters deposited on amorphous carbon. The micrographs were taken at a magnification of 3×10 3 (panels a, c, and e) and 10×10 3 (panels b, d, and f). The samples were obtained by exposing them to the He droplet beam doped with Ag; exposure times are 2 sec (a), 4 sec (b), 10 sec (c, d), 2 min (e), and 30 min (f). The droplet beam was composed of droplets of average initial size He N = 191 1.7×10 10 which were produced at a nozzle temperature T 0 = 5.5 K which were doped with Ag atoms until a droplet beam attenuation of ΔP He /P He = 0.70 (a, b), 0.63 (e) was reached. At this attenuation Eq. 4.1 gives <N Ag > ~ 2×10 6 atoms. It is seen that many of the deposits, as in panel (a), are elongated spanning several hundred nanometers. 192 Appendix 2: Sizes of Large He Droplets 1. He droplet velocities In this work, He droplet velocities were obtained for the range of nozzle temperatures T 0 = 5 – 9.5 K. During the measurements, the unfocused output of a pulsed Nd:YAG laser (Continuum, Powerlite Series 8020; beam diameter 5 mm, wavelength 532 nm, pulse energy 6 mJ, pulse width 7 ns) has been directed counter to the droplet beam such that the laser pulses traveled through the skimmer from behind and finally terminated on the nozzle surface. Each laser pulse has been observed to lead to a transient decrease (“dip”) in the ion current with the mass spectrometer set to m = 8, I 8 . The impinging laser pulse causes a momentary increase of the nozzle temperature, which results in a transient decrease in the beam intensity. Figure A2.1 shows the time dependence of the I 8 signal upon laser irradiation at t = 0 for the two representative nozzle temperatures T 0 = 5.7 K and 8 K. The onset time, taken at the half minimum of the falling edge of the signal dip, represents the time necessary for He droplets at the front of the concatenation of the attenuated beam to reach the ionizing region of the mass spectrometer. The droplet velocities were then obtained as the ratio of the nozzle-to- ionizer distance (137 cm) to the onset time. The intensity of the laser-induced dip decreases with nozzle temperature and could not be measured in the regime of subcritical expansion, T 0 > 10 K, at the laser pulse energy employed. Any higher laser pulse energy or focusing was not attempted, however, as it risks damage to the nozzle. 193 Figure A2.1. Change of the I 8 signal upon laser pulse at t = 0 as measured at nozzle temperature T 0 = 5.7 K (blue trace) and 8 K (red trace). Onset time is 7.90 and 6.61 ms for T 0 = 5.7 K and 8 K, respectively. Obtained velocities are 173 and 207 m/s for T 0 = 5.7 K and 8 K, respectively. Waveform near t = 0 for T 0 = 8 K is due to electric interference from the laser. Similar waveform is not visible at the scale for T 0 = 5.7 K, as the signal is a factor of about 10 2 larger than for T 0 = 8 K. 194 2. Droplet size measurements via attenuation of the beam For a given nozzle temperature, T 0 , the fractional depletion, f, of the He atom flux transported by the droplets was measured with pressure of collisional argon or helium gas in the chamber, P M . At low pressure, the slope of this dependence, α, is defined in S1. M f P   (A2.1) Taking the size of the droplets to be N He , the number of He atoms evaporated from the droplet, N evaporated , during its travel through the collision chamber filled with gas M at pressure P M is given by: evaporated He M N N P     (A2.2) The number of collisions a droplet experiences as it traverses the chamber is related to the droplet radius R D , the length of the collision chamber L, and the number density of the collisional gas n M , according to the following equation. 2 collision D M N R L n      (A2.3) The factor γ relates the droplet, ν D , and collisional gas velocities, ν M , and scales the number of collisions accordingly. 22 2 DM D vv v    (A2.4) The collisional gas number density, is given by M M B P n kT  (A2.5) 195 where k B is Boltzmann’s constant and T is the temperature of the collisional gas. The droplet radius is given by 1/3 3 4 He D LHe N R n      (A2.6) where n LHe is the number density of liquid helium. Therefore, after substitution into Eq. A2.3 of expressions for R D , n M , and γ we obtain 2/3 22 2 3 4 He M D M collision LHe B D N P v v NL n k T v           . (A2.7) We can also calculate the number of He atoms evaporated from the droplet during its traversal of the collision chamber according to Eq. A2.8 below. M evaporated collisions V E NN E     , (A2.8) where E M is the energy associated with collision, and E V is the energy required to remove one He atom from the droplet. This can be rewritten as 2/3 22 2 3 4 He M D M M evaporated LHe B D V N P v v E NL n k T v E            (A2.9) by invoking Eq. S7. Equating Eqs. A2.2 and A2.9, then solving for N He gives an expression for the droplet size. 3 2 22 31 4 D M M He LHe B D V L v v E N n k T v E                (A2.10) 196 3. The effects of the decreasing droplet size during scattering and the droplet size distribution Eq. A2.10 assumes a monodisperse distribution of droplets and ignores the effect of the decreasing droplet size in the course of multiple collisions. In order to study the validity of these approximations, we modeled the He droplet titration process as the droplet travels through the collision chamber filled with helium. The results are compared with the experimental dependence of () ln (0) He M M He P P          (A2.11) with the value of α, obtained by inverting Eq. A2.10 for the droplet size N He = 10 7 , as shown by the black line in Fig. A2.2. During the course of the simulations, the droplet was allowed to travel a distance given by the corresponding mean free path at a helium pressure of P M . Then, the He droplet was taken to collide with an atom of helium resulting in the loss of 52 He atoms by evaporation. Upon collision, a new, reduced droplet cross-section and a corresponding mean free path were calculated. This process was repeated until the droplet completely traversed the collision chamber of length L = 66 cm or was extinguished. The red curve in Fig. A2.2 shows the results of such a simulation for monodisperse He droplets of initial size 10 7 atoms. It is seen that once the droplet attenuation is taken into account, the effect of the changing cross section is to bend the curve towards faster attenuation. The blue curve shows the results of simulations when both the effects of decreasing cross-section and the droplet size distribution were taken 197 into account. An exponential droplet size distribution was applied as found experimentally 1 for the supercritical expansion regime:   1 He N N He P N e N   (A2.12) where, <N He > = 10 7 . It is seen that the effect of the droplet size distribution effectively counters that of changing cross-section and bends the curve back upward. In addition, the average slope for the simulation shown by the blue curve over the range of attenuation of 1 – 0.3, as applied in our measurements, was found to be the same as that obtained from inversion of Eq. A2.10, which is shown by the black line in Fig. A2.2. This shows that Eq. A2.10 essentially gives the average droplet size if the measurements are performed within the specified attenuation range. The results of similar simulations for the log-normal droplet size distribution (ΔN He = 0.8 <N He >) 2 , as in a subcritical expansion at T 0 >10 K, are shown in Fig. S2 by the green trace. Accordingly, Eq. A2.10 underestimates the size and should be multiplied by a factor of C = 1.3. 198 Figure A2.2. Simulation of the attenuation of the droplet beam versus collisional helium pressure in the main chamber. Black trace is a line with slope equal to − α, as obtained by inverting Eq. A2.10 for a monodisperse beam of droplets of N He = 10 7 . Red trace represents results for such a monodisperse beam but also includes effect of changing cross section. Blue and green traces show results for exponential and log-normal distributions of droplets, respectively, of initial size <N He >= 10 7 with changing cross- section. 199 References 1. U. Henne and J. P. Toennies, J. Chem. Phys. 108, 9327 (1998). 2. B. Schilling, MPI, Ph. D. Thesis, Göttingen University, 1993. 200 Appendix 3 : Traces of Vortices in He Droplets A schematic of the molecular beam apparatus, described previously 1 , is shown in Fig. A3.1. Helium nanodroplets are formed by expanding high purity (99.9999%) He, at cryogenic temperatures and a pressure of 20 bar through a nozzle of 5 µm nominal diameter and a nominal channel length of 2 µm (Plano A0200P), into vacuum 2-3 . In this work nozzle temperatures of T 0 = 7, 6 and 5.4 K were used resulting in droplets of average size, He N , of approximately 10 7 , 3×10 8 and 1.7×10 10 atoms, respectively. 3 The droplet size distribution in the beam is nearly exponential 4 and, thus, the probability for a droplet of size N is given by: ( ) exp He N PN N      (A3.1) The liquid drop diameter of the droplet can be obtained as 0.44 (N He ) 1/3 (nm). 5 According to Eq. A3.1, the mean square deviation in droplet diameters in the beam is approximately 35%. The central part of the expansion is separated by a 0.5 mm diameter skimmer and the resulting droplet beam captures Ag atoms in a resistively heated alumina oven 26 cm from the He droplet source. 1 Further downstream, the doped droplet beam enters the deposition chamber where it collides with substrates placed 93 cm from the He droplet source. The substrates are 3 mm diameter standard TEM supports (Ted Pella 01820) consisting of an amorphous carbon film, 15-25 nm thick, mounted on a 300 mesh copper 201 grid that is coated on the underside by a 30-60 nm thick Formvar film. Typically, a set of six samples mounted onto a linear motion positioner were kept under 10 -8 mbar high vacuum for approximately 24 hours before the deposition experiments. After deposition, the samples were removed from vacuum and TEM imaging was carried out within 6 hours. The imaging was conducted on a JEOL JEM-2100 electron microscope at an electron beam energy of 200 keV. Experiments indicate that the structure of the track-shaped deposits is well- preserved during the transfer of the samples and TEM imaging. Some of the tracks have been illuminated for as long as approximately 10 minutes by the 200 kV electron beam of the TEM without any noticeable change in appearance. The micrograph of Fig. A3.3C was obtained during the re-imaging of the sample following its exposure to ambient conditions for about one month. It is seen that the tracks of Fig. A3.3C have the same generic shape as those imaged immediately following their deposition (such as in Fig. A3.3, A and B) which indicates that there is no substantial diffusion of the Ag beads on the surface. The beads in Fig. A3.3C appear more rounded which may indicate some slow reconstruction at ambient conditions. 202 Figure A3.1. Experimental setup for surface deposition of metal clusters formed in He droplets. The degree of Ag doping of the droplets is controlled by varying the temperature of the oven which is filled with metallic Ag and, thus, the vapor pressure of the Ag atoms within. The average number of Ag atoms captured per He droplet, <N Ag >, can be estimated using the attenuation of the droplet beam 1 6 . The flux of He atoms transported via the droplets is monitored as a rise in the partial pressure of He, P He , in the UHV analysis chamber downstream from the deposition chamber. Upon repeated capture of Ag atoms, the average size of the droplets decreases by evaporation of He atoms, which is monitored by a decrease in the partial pressure of He, ΔP He . The dominant contribution to the energy released upon Ag atom capture is from the binding energy of the Ag atoms during the formation of Ag N clusters. Thus, Ag N can be estimated as: 203 He He He Ag He Ag PN E N PE   (A3.2) where E He is the 0.6 meV 5 binding energy of He atoms to the droplet, He N is the initial average size of the He droplet, and E Ag ≈ 3 eV is the energy associated with the addition of one Ag atom 7 . In this work, He droplets were doped with Ag atoms until about 70% of their He content was evaporated for a reduction in diameter of approximately 30%. At the three average droplet sizes employed, He N = 10 7 , 3×10 8 , and 1.7×10 10 , Eq. 2 gives Ag N ≈ 1.4×10 3 , 4×10 4 , and 2×10 6 , respectively. The temperature of the helium droplets, as they traverse the oven, increases above their temperature of T = 0.38 K in vacuum 8 due to the energy release associated with the pickup of Ag atoms. The temperature of the droplets inside the oven can be estimated 3, 5, 9 using the known temperature-dependence of the vapor pressure of helium 10 and the rate of evaporation of helium atoms from the droplet during the time of flight of about 200 μs. Estimates show that for all experiments in this work the droplet temperature in the oven does not exceed 1 K and, thus, remains well below the superfluid transition temperature of 2.17 K. 204 References 1. E. Loginov, L. F. Gomez and A. F. Vilesov, J. Phys. Chem. A 115, 7199-7204 (2011). 2. J. P. Toennies and A. F. Vilesov, Angew. Chem. Int. Ed. 43, 2622-2648 (2004). 3. L. F. Gomez, E. Loginov, R. Sliter and A. F. Vilesov, J. Chem. Phys. 135, 154201 (2011). 4. U. Henne and J. P. Toennies, The Journal of Chemical Physics 108 (22), 9327- 9338 (1998). 5. D. M. Brink and S. Stringari, Zeitschrift Fur Physik D-Atoms Molecules and Clusters 15 (3), 257-263 (1990). 6. V. Mozhayskiy, M. Slipchenko, V. K. Adamchuk and A. F. Vilesov, J. Chem. Phys. 127, 094701-094701-094706 (2007). 7. B. M. Smirnov, Reference Data on Atomic Physics and Atomic Processes. (Springer, Berlin, Heidelberg, 2008). 8. M. Hartmann, R. E. Miller, J. P. Toennies and A. Vilesov, Phys. Rev. Lett. 75, 1566-1569 (1995). 9. M. Hartmann, N. Pörtner, B. Sartakov, J. P. Toennies and A. F. Vilesov, J. Chem. Phys. 110 (11), 5109-5123 (1999). 10. R. J. Donnelly and C. F. Barenghi, Journal of Physical and Chemical Reference Data 27 (6), 1217-1274 (1998).

Asset Metadata

Creator Gomez, Luis F. (author)

Core Title Atomic and molecular clusters at ultra-low temperature

Contributor Electronically uploaded by the author (provenance)

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Publication Date 11/16/2012

Defense Date 11/02/2012

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

Tag clusters,core-shell clusters,droplets,helium,helium droplets,helium nanodroplets,helium-4,nanoclusters,nanodroplets,OAI-PMH Harvest,plasmons,quantum vortices,quantum vorticity,silver clusters,silver nanoclusters,spectroscopy,superfluid,superfluid helium,superfluidity,surface plasmons,surface-deposition,TEM,TEM imaging,vortices

Language English

Advisor Vilesov, Andrey F. (committee chair), Kresin, Vitaly V. (committee member), Reisler, Hanna (committee member)

Creator Email luisfgomezinla@yahoo.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-111812

Unique identifier UC11290429

Identifier usctheses-c3-111812 (legacy record id)

Legacy Identifier etd-GomezLuisF-1297.pdf

Dmrecord 111812

Document Type Dissertation

Rights Gomez, Luis F.

Type texts

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

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Abstract (if available)

Abstract This Dissertation is focused on the study of atomic and molecular clusters in ultra-cold helium nanodroplets. A novel technique for the determination of helium droplet sizes will be discussed, which is based on the attenuation of a beam of helium droplets via collisions with argon and helium scattering gas at room temperature. It is shown that that there exists a new droplet growth regime that can give rise to micrometer-sized droplets of 10⁷–10¹¹ helium atoms. Helium droplets of this sizes range and smaller are further used to grow Ag clusters. It is shown that the Ag clusters could be surface-deposited onto a carbon film and studied via electron microscopy. This gives the average sizes of the Ag clusters grown in the droplets, their size distributions, and information on the cluster stabilities. ❧ In addition, a study of the growth in helium droplets of large Ag clusters via their photoabsorption spectra is reported. The plasmon spectra of the clusters indicate a switch in the cluster growth mechanism from single-centered to multi-centered growth which occurs with increasing droplet size. The latter growth mechanism is shown to result in non-compact, aggregate clusters. ❧ The possible reconstruction of such cluster-cluster aggregates upon the absorption of laser radiation is also explored with pulsed and continuous wave laser excitation at 532 and 355 nm. The results are shown to be consistent with a kinetic limit on the energy transfer rate from the excited Ag cluster to the host helium droplet, which is not exceeded in the case of continuous wave excitation. Therefore, upon pulsed laser excitation, the embedded Ag aggregates melt and reconstruct into more compact clusters. ❧ The application of the helium droplet technique in building large Ag-ethane core-shell clusters is also reported. The clusters have been studied by infrared spectroscopy of the C-H stretch bands of ethane in the 3 µm range. It is found that the nu7 band of ethane is split into two distinct features which can be used to quantify the number of ethane molecules in and out of contact with Ag. ❧ The first experimental observation of vortices in superfluid helium droplets is also reported. This observation was made by introducing Ag atoms, which cluster along the vortex lines, into the droplets. Surface-deposition and imaging of the Ag clusters reveal the presence of elongated track-shaped aggregates, which is consistent with presence of vortices in droplets larger than about 300 nm.