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Interaction of low -energy electrons with beams of sodium clusters, nanoparticles, and fullerenes

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Interaction of low -energy electrons with beams of sodium clusters, nanoparticles, and fullerenes

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Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UM I films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send U M I a complete manuscript and there are missing pages, these w ill be noted. Also, if unauthorized copyright material had to be removed, a note w ill indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact U M I directly to order. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, M l 48106-1346 USA 800-521-0600 R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INTERACTION OF LOW-ENERGY ELECTRONS WITH BEAMS OF SODIUM CLUSTERS, NANOPARTICLES, AND FULLERENES. by Vitaly Golfrid Kasperovich A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA in Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHYSICS) May 2001 R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. U M I Number: 3054760 ____ _ _ < g > UMI UMI Microform 3054760 Copyright 2002 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNIVERSITY OF SOUTHERN CALIFORNIA The Graduate School University Park LOS ANGELES, CALIFORNIA 90089-1695 This dissertation, w ritten b y V i t a l y (£ o lfr * 2 > M a s p e r o v i C H Under the direction o f h~ .z>. D issertation Committee, and approved b y all its members, has been presen ted to an d accepted b y The Graduate School, in p a rtia l fulfillm ent o f requirem ents for th e degree o f DOCTOR OF PHILOSOPHY Dean o f Graduate Studies D ate August 7. 2001 DISSER TA n O N COMMITTEE R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. To my parents, Helena Savostyan and Golfrid Kasperovich. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgments I am thankful to all people who directly or indirectly contributed to this work. I am truly grateful to my graduate advisor, Professor Vitaly V. Kresin, who performed a brilliant mentoring job helping me to become a mature independent researcher. His natural curiosity, professional insight, and humanity always inspired me in my graduate years. I wish to give my thanks to Professors Tu-nan Chang, Gerd Bergmann, Hans Bozler, and Bruce Koel, who devoted their valuable time serving as my qualifying and graduate committee members. I am thankful to my graduate fellows George Tikhonov, Kin Wong, and Sascha Vongehr for help, advice, and support to my research projects. I appreciate talking to Jay and Laura Ray of DeTech and Rick Schaeffer of ABB Extrel who provided me a great deal of assistance in building my particle detector. I want to give my gratitude to staff members of the USC Natural Science Machine Shop - Victor Jordan, Ramon Delgadillo, and Don Wiggins - who performed quality machining for us and were always available for an expert advice. I would like to thank Betty Byers and Dr. Richard Thompson for taking care of my degree progress. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. And finally, I want to give my sincere appreciation to my beloved wife Natalia and, especially, to my charming daughter Anna who helped me to get through the long graduate years, who always were inexhaustible source of inspiration for me, and whose contribution to this thesis is impossible to evaluate. This work was supported by U.S. National Science Foundation. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. V Table of Contents Dedication ii Acknowledgments iii List of Figures and Tables vii Abstract x Chapter 1 Introduction 1 1.1 Clusters: a Link between Molecules and Solids 1 1.2 Clusters of Simple Metals 3 1.3 Motivation and Outline 6 Chapter 2 Inelastic Low-Energy Electron Collisions with Molecular and Metal Clusters: Overview 10 2.1 Molecular Clusters 10 2.2 Fullerenes 14 2.3 Metal Clusters 16 2.4 Electron-Cluster Polarization Interaction 24 Chapter 3 Inelastic Low-Energy Electron Collisions with Sodium Clusters and Nanoparticles: Integral Cross Section Measurement 28 3.1 Experiment 28 3.1.1 Cluster Beam Apparatus 29 3.1.2 Beam Depletion Technique 33 3.1.3 Data Acquisition 34 3.2 Results and Discussion 37 3.2.1 Medium-Sized Clusters 38 3.2.2 Nanoparticles 42 3.2.3 Additional Inelastic Channel 47 3.3 Summary 53 Chapter 4 Negative Ion Formation in Collisions of Slow Electrons with Nan 56 4.1 Experimental Setup 57 4.2 Data Acquisition 60 4.3 Results and Discussion 65 4.4 Summary 68 R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 5 Low-Energy Electron Capture by Free CM Clusters 71 5.1 Experimental Setup 73 5.2 Data Acquisition 76 5.3 Results and Discussion 77 5.4 Summary 81 References 84 Appendix A High Vacuum Mount of the Electron Gun and CEM Detector 93 A. 1 Electron Gun 93 A.2 Channeltron 95 A.2.1 High Vacuum Mount 95 A.2.2 Circuitry 98 Appendix B Cathode Activation Procedure 102 Appendix C Cluster Beam Velocity Measurement 107 C.l Sodium Clusters: Pulse Counting Detection 107 C.2 Fullerenes: Analog Detection 110 Appendix D Beam Depletion Ratio and the Total Cross Section of Inelastic Scattering 113 D. 1 Main Equation 113 D.2 Transverse Thermal Velocity Correction 119 Appendix E Retarding Potential Measurements and Electron Energy Calibration 126 E.l Electron Energy Resolution 126 E.2 Electron Energy Scale Calibration 130 E.3 Richardson-Dushman Equation 133 Appendix F Electron Capture by the Full Image-Charge Potential 136 Appendix G Cluster Escape Probability Calculation 141 Appendix H Data Acquisition and Analysis Programs 147 H. 1 Electron Gun Energy Resolution and Calibration 147 H.2 Cluster Escape Probability Calculation 164 R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures and Tables Fig. 1.1 Fig. 2.1 Fig. 3.1 Fig. 3.2 Fig. 3.3 Fig. 3.4 Fig. 3.5 Fig. 4.1 Experimental mass abundance spectrum Classical trajectories of charged particle motion in an r~* attractive potential Experimental setup used to measure the integral cross section of electron interaction with sodium clusters and nanoparticles Energy dependence of the inelastic electron scattering cross sections for three clusters with closed valence electron shells. Dots: experimental results; dashed line: Langevin capture cross section convoluted with the electron gun energy spread Same as Fig. 3.2 for two open-shell clusters Total depletion cross sections for electron collisions with sodium nanoclusters. The upper panel shows results obtained in the “surface ionization” beam detection mode and the lower panel is for the “UV-ionization mode” (see text). Solid lines: image-charge capture cross sections, Eq. (3.6), convoluted with the electron gun resolution function. Dashed line: best fit of the data using the pure dipole Langevin capture cross section, Eq. (2.4) The result of subtracting the electron attachment contribution from the total inelastic cross section data for (a) sodium clusters and (b) nanoparticles. All the lines in the plots above are smoothing fits designed to guide the eye Section of experimental setup used for negative ion detection (not to scale). A cluster captures an electron in the scattering region of the electron gun and becomes a negative ion. It is extracted by ion optics and accelerated towards a stainless steel conversion dynode, producing positive fragments, which are subsequently detected by the channeltron and result in a TTL pulse registered by a multichannel scaler (MCS) board R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. viii Fig. 4.2 Fig. 4.3 Fig. 4.4 Fig. 5.1 Fig. 5.2 Fig. 5.3 Fig. A.l Fig. A.2 Fig. A.3 Fig. B.l Fig. C.l A typical experimental MCS profile 62 Size dependence of the cluster escape probability px 64 Direct evidence for negative ion formation in collisions of low-energy electrons with neutral sodium clusters Nan. Circles: experimental cross section derived from the anion yield. Line: Langevin electron capture cross section convoluted with the mass abundance spectrum and with the electron gun resolution 66 Experimental setup used to perform depletion measurements on a neutral CM beam 74 Open dots: experimental inelastic cross section of free electron scattering at fullerenes. The solid line in the plot serves to guide the eye. Dashed line: Langevin polarization capture cross section, convoluted with the experimental energy resolution 78 Sticking probability: the probability for an electron, attracted by the polarization field of the cluster, to attach and form long-lived C6 l . The solid line is a smoothing fit serving to guide the eye. 79 High vacuum mount of the electron gun (a) and the channeltron detector (b) 94 Schematic view of the channeltron on a factory mount 98 Two distinct detection modes for negatively charged clusters in our CEM detector 99 Cathode surface temperature calibration chart. Solid squares: pyrometric measurement. Open dots: reading of the mount thermocouple. Line: estimate on the basis of Eq. (B.l) 105 Typical MCS profiles from two choppers shown in Fig. 3.1 108 R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. ix Fig. D. 1 Schematic view of the electron-cluster interaction volume 113 Fig. D.2 Interaction geometry for the electrons with nonvanishing transverse velocities 120 Fig. D.3 The relative correction to the measured cross sections for Na9 5 Q O due to the transverse electron velocity 124 Fig. E.l Retarding potential method 127 Fig. E.2 Electronic differentiation of the retarding field curve 128 Fig. E.3 A typical experimental electron energy profile 129 Fig. E.4 A representative experimental calibration curve 131 Fig. E.5 Expanded view of the low-voltage part of the calibration curve in Fig. E.4 132 Fig. G.l Schematic view of the arrangement used in the escape probability calculation (not to scale). B, = Bu = 0.15 T, Bw = 0.1 T; L, =40 mm, L„ = 5 mm, Lm =A mm; D, = 1 .5 mm, D„ = 7 mm, D,„ = 11 mm 141 Fig. G.2 A fragment of the calculated escape matrix for Ma5 S 145 Table C. 1 Cluster velocities obtained directly from the MCS profiles 110 R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. X Abstract We study the interaction of slow electrons with beams of free sodium clusters: (1) in the size range of 20-200 atoms as produced by a supersonic expansion source, and (2) in the nanometer range (~ 10 000 atoms, 4 nm radius) as produced by a vapor condensation source. The beam depletion technique is employed to obtain the integral inelastic cross section for the electron-cluster scattering. In the low-energy range ( E < 1 eV), the cross sections rise strongly with decreasing energy, in agreement with the “Langevin” mechanism of electron attraction and capture by the polarization field of the cluster. For the smaller clusters, we find good agreement with cross sections calculated on the basis of their electric- dipole polarizabilities. By a direct measurement of cluster anion yield as a function of electron energy, we confirm the action of the Langevin mechanism. For the nanoscale particle beam, we observe extremely large electron attachment cross sections (>104 A2 ). For a quantitative analysis in this size range, it turns out to be necessary to go beyond the usual induced-dipole approximation and to account for the finite particle size by employing the full image-charge potential. It yields an exact analytical expression for the capture cross section and leads to very good agreement with the data. We suggest that electron capture may be a convenient R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. technique for characterizing the sizes of nanoparticles in beams over a wide mass range. At higher energies (up to -5 eV), the total inelastic cross section flattens out, most probably due to collision-induced cluster fragmentation superimposed onto the diminishing anion formation process. This additional channel shows a cross section rising monotonically from a threshold of * 1 eV, going up to -300 A2 at 4 eV for the smaller clusters and -1500 A2 for the nanoscale particles. We argue that cluster fragmentation proceeds directly rather than evaporatively. Electron capture by free fullerenes is also investigated. We confirm the existence of a zero-energy attachment peak. The overall trend of our data follows the behavior of the Langevin capture cross section, indicating that the polarization interaction is important for e~ -C 6 0 scattering as well. The sticking probability is, however, less than unity and depends on the collision energy, reflecting an interplay of the particle symmetry, size, and polarization effects. The observations inspire a number of important further questions regarding the relaxation channels of the captured electrons, the associated time scales, and the detailed behavior of the long- and short-range optical scattering potential. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 Chapter 1 Introduction 1.1 Clusters: a Link between Molecules and Solids For already several decades, scientists all over the world have been attracted by the fascinating and highly promising field of cluster research. What makes cluster science so popular? The answer is not only in the number of potential technical applications that incorporate nanotechnologies but also in the fascinating cluster domain that lies between single atoms and the solid state. Indeed, one wishes to monitor how a certain physical property is changing by adding more and more atoms to the system. And one could be surprised by how dramatic this change turns out to be sometimes. For instance, small mercury clusters reveal dielectric behavior in contrast to bulk mercury which is conductive [BUS’98]. However, it’s not entirely correct to think about a cluster just as of a molecule, because macroscopic concepts appear as well. Specific heat measurements showed recently that for Na* there is a certain temperature at which the particle undergoes “solid-to-liquid” phase transition [SCHM’98]. In fact, temperature as a measure of cluster’s internal energy has become a much discussed and analyzed quantity. We recently developed a method of measuring it for sodium clusters in a beam [BRO’99]. In other words, clusters possess unique physical properties of their own that differ from those of molecules R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 and solids. We would not be exaggerating too much by calling them the “fourth” state of matter in nature. Clusters can be produced in beams (“free clusters”), grown on a substrate, embedded into a dielectric matrix or even into another cluster [BAR’96]. Collected together, they become elementary building blocks for novel artificial materials. For example, [COLE’98] gives detailed overview on different approaches of cluster “superlattices” assembly as well as discusses their physical properties. Being an interdisciplinary field, cluster research profits from a great variety of experimental and theoretical techniques developed in many branches of Physics such as Atomic and Molecular Physics, Condensed Matter Physics, Surface Science, Materials Science, and even Nuclear Physics. In this thesis, the interaction of low-energy electrons with free neutral sodium clusters will be investigated. In addition to its fundamental importance, this process may be relevant in the operation of future nanoelectronic devices. This does not necessarily mean that sodium clusters themselves will become new elementary components in the electronics industry. However, there should exist some general trends in electron-cluster scattering that are common for the interaction of electrons with other systems of reduced dimensionality. The author sincerely hopes that this work will become a useful contribution to the pool of data on metal clusters and R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 nanoparticles. A study of low-energy electrons with CM fullerenes will be also discussed. 1.2 Clusters of Simple Metals Clusters such as the alkali or noble-metal ones are usually referred to as simple metal clusters. The dominant interaction among the atoms of these elements involves weakly bound valence s electrons and the influence of the inner electronic subshells is relatively unimportant for the cluster bonding. In a simple metal cluster, each atom donates its valence electrons to a common electron cloud, so there isn’t a way to ascribe a certain electron to a particular atomic parent. The electrons in this delocalized cloud are nearly free, the positive ions contributing a relatively weak pseudopotential background. The delocalized electrons in a metal cluster are organized into shells [KNI’84, HEE’93]. Particle sizes that correspond to a particular shell closing are especially stable and possess a spherical geometry. For simple metal clusters M n some of these “magic numbers” are n = 8, 20, 40, 58,92. The non-magic, or open-shell, clusters are not spherically symmetric. The particle deforms in order to reduce the electron energy of the uncomplete electronic shell [JAH’37, CLE’85]. Direct or indirect manifestations of the cluster shell structure are found in diverse experimental R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 contexts. For example, in the experimental abundance spectra (see Fig. 1.1) magic cluster sizes are dominant over the nearest neighbors which directly reflects the 0 20 40 60 80 100 120 140 Nan Cluster Size Figure 1.1. Experimental mass abundance spectrum. enhanced stability of the closed-shell clusters. The photoabsorption spectrum of the Na^ [BRE’92, SCHM’99] and Ag*t [TIG’92] ions shows a double-humped profile in correlation with the cluster’s ellipsoidal shape. Signature of the electronic shell structure was also found in ionization potentials, electron affinities, and photoelectron spectra of simple metal clusters [HEE’93, KRE’98]. Experimental polarizability measurements for small sodium clusters clearly show size-dependent R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 behavior with locally reduced values at the 8 and 20 magic numbers [KNI’85, RAY’99]. Similar trend was also observed for deposited Agn clusters [FED’93]. This again points towards the clusters’ discrete electronic shells, commonly referred to as the quantum size effect. It should be noted that alkali metal clusters are highly polarizable [KNI’85, RAY’99]. The origin of this effect can be traced to high mobility of the delocalized electrons. As a result, considerable portion of the electronic cloud spills out above the limits of cluster ionic background [BON’97]. The extend of this tail is almost size-independent and approximately equal to 0.75 A [HEE’93]. C6 0 fullerenes are usually considered as molecular clusters due to the tighter bonding of individual atoms and well defined icosahedral symmetry of the particle. Carbon atom has 4 valence electrons. In the cluster, 3 of them are involved in molecular bonding with nearest neighbors, while the other one becomes essentially delocalized.1 That’s makes the CM molecule somewhat reminiscent of metal clusters. In the former, however, the delocalized electron cloud is essentially restricted to the surface layer. This fact is reflected in the value of cluster’s polarizability a M « 78 A3 [ANT’99, BAL’00], which is comparable to that of Na4. 1 These 180 and 60 electrons are called a and ;r-electrons respectively, which is due to the specific spatial symmetry of the electronic orbitals. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 1.3 Motivation and Outline The enhanced polarizability of alkali-metal clusters leads to the appearance of strong long-range forces in cluster interactions. Examples include the dispersion van der Waals attraction which is manifested, e.g., in elastic scattering of clusters off neutral atoms and molecules [KRE’98a, KRE’98b], the polarization forces arising in cluster collisions with fast ions [GUE’97], and the polarization interaction between fragments in cluster fission [NAH’97]. For instance, the center-of-mass cross sections for Nan -C 6 0 collisions in [KRE’98a] exceed the hard-sphere areas of the collision partners by a factor of -30, indicating that an extremely long-range force is involved. The inelastic scattering of slow electrons with neutral sodium clusters is also governed by the long-range interactions. An early experiment on Nan (n=8, 20, 40) [KRE’94] indicated the presence of large electron scattering cross sections and suggested an interpretation in terms of attachment and fragmentation processes. The inelastic integral cross section exceeded the geometrical cluster cross section by a factor of -2-3 in the 1-6 eV electron energy range. For E < 1 eV, the cross section appeared to rise as the electron energy was decreasing. However, due to the low signal-to-noise quality it remained uncertain whether the cross section truly displayed a strong rise for E -> 0, which would be a signature of electron attachment. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 7 In Chapter 3, we study the interaction of slow electrons with selected free sodium clusters (20, 40, 57, 58, 70) as produced by a supersonic expansion source, and with sodium nanoparticles (-7000-9000 atoms, 4 nm radius) as produced by a vapor condensation source. The beam depletion technique is employed to obtain the integral inelastic cross section for the electron-cluster scattering. In the low-energy range ( E < I eV), the cross sections rise strongly with decreasing energy, in agreement with the “Langevin” mechanism (~ E ~ '/2) of electron attraction and capture by the polarization field of the cluster [LANG’05, VOG’54, LND’76, MCD’89, BON’97]. For the smaller clusters, we find good agreement with cross sections calculated on the basis of the electric-dipole polarizabilities of the former. For a quantitative analysis in the nanosize range, it turns out to be necessary to go beyond the usual induced-dipole approximation and to account for the finite particle size by employing the full image-charge potential. This yields an exact analytical expression for the capture cross section and leads to very good agreement with the data. At higher energies (up to -5 eV), the total inelastic cross section flattens out, most probably due to collision-induced cluster fragmentation superimposed onto the diminishing anion formation process. This additional channel shows a cross section rising monotonically from a threshold of 1-1.5 eV. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. g In Chapter 4, a direct measurement of cluster anion yield as a function of electron energy confirms the action of the Langevin electron capture. The negative cluster ions ( Na~) are detected by a Channel Electron Multiplier through a conversion dynode stage. The theoretical Langevin curve, convoluted with the energy resolution of our electron gun, shows an excellent fit to the experimental data points taken in the 0-3 eV electron energy range. Furthermore, the average conversion probability of Na~ into positive fragments at the stainless steel conversion dynode, biased to +6 kV, is estimated to be ~3%. This appears to be the first measurement of this quantity for a cluster-dynode combination. Chapter 5 contains the beam depletion results for the interaction of low-energy electrons with free C6 0 molecules. The overall electron attachment spectrum displays good agreement with a number of earlier experiments. The total inelastic cross section measurement reveals a steep rise at near zero collision energies, which supports the existence of a strong s - wave electron attachment channel. Being a much stronger bound particle than Nan, CM does not exhibit any appreciable fragmentation pathways of e — Q o scattering at the electron energies investigated ( * 0 - 3 eV). A comparison of our results to the Langevin capture cross section indicates the importance of polarization effects for C6 0 clusters. In summary, the measurement of negative cluster ion yield (Chapter 4) and the beam depletion experiment (Chapter 3) confirm, in two independent ways, the R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 formation of Na~ by the polarization capture mechanism. For CM (Chapter 5), this mechanism appears to be convoluted with strong selection rules based on the high symmetry of the scatterer. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 Chapter 2 Inelastic Low-Energy Electron Collisions with Molecular and Metal Clusters: Overview 2.1 Molecular Clusters Interaction of slow electrons with molecules has received a lot of experimental and theoretical attention in the literature (see, e.g., the recent reviews [SCHE’95, CHU’96, ING’96, ILL’98] and references therein). This process appears to be of a resonant character and proceeds through formation of a temporary negative ion, which subsequently decays in a number of pathways: e~ + AB A +B (a) (AB)’ +e (b) (AB)~ +hv (c) (AB)~+C (d) (2.1) Channels (a) and (b), corresponding to a dissociative attachment (DA) and auto detachment of the temporarily bound electron, are the main reactions for the electron-molecular scattering in the gas phase. Stabilization of ( AB~) by radiative R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 cooling (c) or by energy transfer to a collision partner (d) proceeds usually at much slower rate. In the cluster domain, two more channels should be added to those in (2.1): into internal degrees of freedom (auto- or self-scavenging). As will be shown below, new resonances in the electron attachment cross section can be formed on the basis of these processes. In fact, cluster environment may be considered as a built-in “third body” for every individual molecule in the particle. The reaction pathway (d) now becomes significant and yields new products that are not observed for free molecules under single collision conditions. Solvation effects may also shift and modify resonance features observed in reactions (see Eq. (2.1)) for molecular constituents of a cluster. To be more specific, let’s consider some examples. An 0 [ anion is not observed in collisions of slow electrons with neutral oxygen molecules due to a short lifetime with respect to auto-detachment. For small oxygen clusters, on the other hand, Refs. [KEE’87, STAM’91, ING’96, ILL’98, MAT’99] report a noticeable production of (0 2)~ ions at zero energies, stabilized by evaporative attachment channel (e). Additional peaks at 8.3 eV and 14.5 eV for the same anion are interpreted as a result of self-scavenging (f). Solvated fragment ions (e) i f ) (2.2) Here (A/)x is stabilized by (e) an evaporative attachment or (f) an energy transfer R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 O ' •{01)n display new features at energies different from 6.2 eV, the location of DA resonance to a free 0 2 molecule. Similar zero-energy resonances are also found for negative ions of small water and carbon monoxide clusters [KEE’87, WEB’99] with the only exception that (H2 0 )n anions appear to be stabilized by the self-scavenging process (f). Formation of metastable (C6 F5 / ) ' anions from (C6FS I )n parent clusters is also observed at zero energies [ING’96], although the electron attachment to a single molecule at 0 eV does not yield a long-living product of this type. Cluster environment can be both constructive and destructive regarding processes observed in collisions of electrons with free molecules (all the examples below are taken from [ING’96], unless specially noted). Dissociative attachment channel X~+ C 6 F5 ( X = C l,B r,I) in the e" +C6F5 X scattering is quenched at 0 eV in cluster surroundings as can be seen from the reported solvated ion yields. A very similar effect is discovered for (C //3 / ) ( clusters [WEB’O O ]. Here a vibrational Feshbach2 resonance, observed for dissociative attachment to a single molecule ( / ” + C //3), is already suppressed in production of ( C H J \ / ' anions. On the other hand, the low-energy dissociative attachment cross section is enhanced in (CFJ Cl)n 2 Resonances in electron attachment to excited states of a neutral molecule or cluster are known as Feshbach resonances. In the special case of attachment to vibrationally excited levels of the electronic ground state, these resonances are called vibrational or nuclear-excited Feshbach resonances. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 clusters by one to two orders of magnitude. This enhancement is primarily due to a decrease in the auto-detachment rate. The C F f products of electron attachment to (CFil) n clusters show a Feshbach resonance feature at 6 eV, which is not observed in the dissosiative reaction CFf + / for the molecule. The electron transfer reaction M2 + SF6 -* N2 + SF^ is not operative in the gas phase due to the mismatch between the energy of the donated electrons and the energy window of the electron acceptor. In (jV2 SF6)ti clusters both components are modified in a way that the electron transfer reaction above becomes very effective and can be observed on (SF6)” and ^(jV2)n -(5F6)m J products. The electron attachment in this case proceeds through the self-scavenging channel (f)- A good example of electron auto-scavenging (f) is also reported in [WEB’99a], where a high resolution photoelectron attachment technique is used to examine (N 20 )n clusters. A series of narrow nuclear-excited Feshbach resonances of temporary cluster anions ( N2 0 ) n was observed in the ion yield of solvated dissociation products ( A f2 0 )( / O' . The anion stabilization is interpreted as a two-step process. An electron first vibrationally excites a single N2 0 constituent of the cluster and is subsequently captured as a slow “secondary” electron via a very sharp 0 eV resonance. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 Finally, for some clusters dissociation products are formed through a complex intracluster reaction that may combine several channels presented in the Eqs. (2.1) and (2.2). This is the case for production of NO~ anions from (NO)n clusters [SENN’99]. 2.2 Fullerenes Electron collisions with neutral fiillerene clusters in the gas phase lead to significant production of long-lived QJ ions for collision energies in the range from near 0 eV to over 10 eV. This has been demonstrated by several experimental techniques: bombardment by an electron beam [JAF'94, HUA'95, VOS'95, ELH'97, VAS'97, VOS'Ol], Rydberg electron transfer [HUA'95, FIN'95, WEB'96], and flow in an electron plasma [SMI'96]. A special interest in free-electron capture by C6 0 arose when it was argued [TOS'94] that symmetry considerations, namely the lack of an unoccupied Z.=0 state in the vibronic spectrum of , should forbid the attachment of 5-wave electrons to neutral fullerenes. Therefore, attachment cross section was predicted to show a threshold corresponding to the onset of a p-wave process. Although the proposed theoretical approach was too elementary (it substituted elastic cross sections for the inelastic ones, neglected long-range forces, and disregarded the possibility of angular R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 momentum transfer from/to cluster rotational modes; see the comments in [HUA'95]), first free electron attachment experiments indeed suggested that an activation barrier of -0.2 eV was present [JAF'94, HUA'95, SMI'96]. This was, however, contradicted by Rydberg-electron transfer measurements [HUA'95, FIN'95, WEB'96], other crossed-beam experiments [VOS'95, ELH'97, VAS'97, VOS'Ol], and a critical analysis of earlier data [WEB'96, FAB'01]. Evidently, CM does support a strong electron attachment channel for scattering energies E -> 0. It was remarked in some of the references above that zero energy electron capture may be mediated by the action of the polarization potential. This potential arises when the incoming electron polarizes the cluster and is attracted to the resulting electric moment (see Section 2.4 for more details). For example, Refs. [HUA'95, FIN'95, WEB'96, FAB'01] considered the capture of electrons into image-charge- based bound states or resonances. In this model, the s electron is temporarily caught in a shallow ground state between the long-range polarization field and a hard-core potential wall at distances on the order of the electronic radius of Cfi0 . Stable anions are assumed to be formed by efficient transfer of electron energy to the cluster vibrations (and possibly to the Rydberg core, if present). It's interesting that Ref. [VAS'97] indeed reports the observation of near 0 eV electron attachment of essentially resonant character. The overall contour of the electron attachment spectrum can be briefly summarized as follows: there is a noticeable minimum at 0.3-0.4 eV followed by a R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 monotonic rise to about 1 eV. After that the production rate of has been reported to remain relatively constant up to «6 eV at which point electron autodetachment processes become important [HUA'95, ELH'97, VAS'97, VOS’ Ol]. A certain number of resonance features can be identified in the attachment profile. Their nature and energy location in the spectrum are extensively discussed in Refs. [JAF'94, HUA'95, ELH'97]. Most of them are interpreted as Feshbach and shape3 resonances. The broad minimum around 0.4 eV has been ascribed, to the onset of p-wave attachment [VOS'Ol] or to a superposition of s - and p-channels [WEB'96, FAB'01]. In section 5.3, we describe the C6 0 electron attachment curve measured in our laboratory. 2.3 Metal Clusters Experimental measurement of electron-cluster inelastic scattering cross sections, performed by Kresin et al [KRE’94] (see Section 1.3), stimulated extensive theoretical search for possible channels of electron energy loss. Several research groups subsequently addressed this issue, discussing various inelastic mechanisms: energy transfer to particle-hole or collective excitations (plasmons), emission of radiation, and ionization. 3 Resonances originating from electron attachment into excited electronic states, confined within the centrifugal barrier. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 Light Emission. Two scenarios have been considered theoretically - direct and polarization electron capture. In the former process, an electron loses its energy in a single step and occupies one of the empty bound states of a cluster [SPI’98]. This problem is solved for spherical Nas to first order in the interaction within the framework of time-dependent perturbation theory, including polarization effects. The calculation shows that the major contribution to the total cross section arises from the less bound energy levels near continuum. In the studied energy range (0-2 eV), the direct electron capture contributes very little to the available experimental values for Nat . In the other scenario, an incident electron polarizes the target cluster. The polarization capture mechanism considers the rotation of the induced dipole, which leads to emission of radiation until the orbiting electron is captured [CON’96]. This process is analyzed in the Bom approximation. To circumvent the need for full ab initio calculations, the imaginary part of cluster dynamical polarizability is obtained from experimental data on photoabsorption, automatically omitting exchange- correlation effects in the interaction o f the incident electron with the cluster electron cloud. The real part is then found from the Kramers-Kronig relations. The ratio for polarization versus direct electron capture efficiencies is calculated for collisions of Nalo and Ag„ clusters with medium-energy electrons (~ 1-10 eV). A several-orders- R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 of-magnitude enhancement of the polarization mechanism over single-step light emission is predicted for collision energies in the vicinity of the plasmon resonance. The spectrum of emitted radiation in this “polarization bremsstrahlung” process is analyzed in Ref. [GER’97] for collisions of medium and fast electrons with metal clusters and fullerenes. In this work, the cluster dipole dynamic polarizability is calculated in the plasmon pole approximation. A detailed review of this paper goes beyond the scope of this thesis. Particle-hole and collective excitations. Single particle-hole excitation mechanism of electron energy loss is considered in [SPI’96] for collisions of small metal clusters with slow electrons (up to 5 eV). The inelastic transition amplitudes are calculated in the Bom approximation taking into account the exchange- correlation contribution to electron-cluster interaction potential. This theoretical formalism is applied to the case of e~ - Na% scattering. The total cross section is shown to be dominated by \p -> Id transition. Strong influence of the exchange- correlation and polarization effects on the final result is demonstrated. A possibility of electron energy loss due to the excitation of plasmons of different angular momentum / in metal clusters and fullerenes is theoretically studied in [GER’97a]. The plane-wave Bom approximation is argued to be appropriate for collision energies as low as « 3 eV.4 The multipole moments of the 4 This limit actually appears too low by a factor of 5-10. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 scattering amplitude are expressed in terms of the imaginary part of the cluster dynamic polarizability a(co), which is then estimated in the surface-plasmon-pole approximation. This simplified approach completely disregards polarization and exchange-correlation effects in the electron-cluster interaction, which are essentially non-local in nature. For Nai0, the integral inelastic cross section o f plasmon energy loss is shown to be dominated by a dipole and quadrupole collective excitations in the ~3 to 30 eV collision energy range. Higher angular momentum resonances are expected to be more important for larger clusters and lower collision energies. The calculated cross sections are argued to correlate with the ‘plateau’ region in the experimental data for Na4 0 in Ref. [KRE’94]. The plasmon energy loss mechanism is further analyzed in Ref. [GER’97b]. The theoretical treatment is improved by evaluating the scattering amplitude in the random phase approximation with exchange (RPAE). Yet, the main framework of the approach remains the Bom approximation. Calculated cross sections for Na„(n =20, 40, 58, 92) are systematically different from those obtained in the simplistic plasmon pole approach above. Electron impact ionization and particle-hole excitations, naturally incorporated into RPAE, are blamed for this discrepancy. However, the collective electron modes are shown to provide the major contribution to the calculated cross sections. Polarization interaction of an incoming electron and neutral cluster is still omitted from consideration. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 A new series of computational research is opened with Refs. [IPA’98, CON’99, CON’O O ]. In this essentially ab initio approach, many-electron correlations in electron-cluster inelastic scattering are taken into account within RPAE without any approximation for the partial amplitudes. The polarization interaction between the projectile electron and the cluster electronic system is described using the Dyson equation. Resonance peaks in the total inelastic cross section below and above the surface plasmon resonance frequency co,p are reported. Features with E < cox p are associated with resonance electron attachment into negative ion states of the cluster with simultaneous excitation of a plasmon. Structures with E > o)sp are characterized by the resonance electron attachment to quasi-discrete levels, localized on the cluster, and concurrent plasmon excitation. The quasi-discrete nature of the latter arises primarily from the centrifugal barrier existing for a projectile electron of a given angular momentum, although they are actually located above the vacuum level. These resonance features are discussed to be akin to the shape resonances observed for the electron scattering at molecular clusters and fullerenes (see, e.g., [ING’96]). The model disregards the interaction between the quasi-discrete levels and plasmon excitations. The fact that above calculations fail to reproduce the Langevin electron capture by cluster polarization field (see Section 2.4 and Chapters 3-4) is also noteworthy. The reason may be found in the following. First of all, despite their ab initio R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 character, the computations still leave out a number of significant dynamic and polarization effects. Secondly, this theoretical analysis utilizes the common jellium model that leaves out internal degrees of freedom of the positive background. The cluster is treated as a system of electrons in a self-consistent spherical potential well. This simple approximation has been successful in characterizing electronic shell structure and photoabsorption spectra for simple metal clusters [HEE’93]. On the other hand, it naturally omits from consideration, e.g., cluster fragmentation: a process essentially mediated by the cluster vibronic spectrum. The interaction between electronic and ionic sub-systems of the cluster, furthermore, may be very important in the low-energy electron-cluster scattering dynamics. If the initial stage o f electron attraction is mainly guided by the cloud of delocalized valence electrons (polarization interaction), the actual electron attachment to the cluster (or the cluster fragmentation processes) are likely to involve excitations of the ionic background (see also Section 3.2). Recent experimental work on low-energy electron attachment to small potassium clusters indeed suggested the presence of some structure at energies below and above a)s p for Ks [SENT’O O ]. A strong accent in this paper is made on the independent confirmation of the resonances calculated above. However, this assignment should be considered very tentative in view of the poor statistics of the experimental data. In fact, the statistical variation of the signal has comparable magnitude with the height R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 of assigned resonances. It’s also not absolutely compelling in Ref. [SENT’00] that the electron attachment spectrum for K% is absolutely free from fragmentation from higher cluster sizes. It is a known fact in mass spectrometry that microchannel plate detection efficiency rapidly decreases with particle mass for a given incident energy [GAL’91]. Therefore, an experimental study with increased signal-to-noise resolution and a more sensitive detection technique will provide a more stringent test of the proposed theory. Ionization. Electron energy loss due to impact ionization is briefly discussed in [GER’97b] as a competing inelastic channel to the plasmon excitation mechanism for projectile energies above 10 eV. It is predicted to account for about one-third of the inelastic scattering cross section at collision energies up to 30 eV. Implications of high-energy (e, 2e) electron spectroscopy for metal clusters are also studied in Ref. [KEL’97]. It is shown that such experiments would allow one to investigate the structure analogy between clusters and nuclei. The process of elastic electron-cluster scattering for metallic systems has also been addressed in the literature (see, e.g. [BER’95, GER’97a, IPA’98a]). Na2 is, in a way, the smallest sodium cluster. Dissociative attachment of low- energy electrons to vibrationally excited dimers has been studied in [KEI’99] with high electron energy resolution. Selectively excited Na2(v") are prepared in the vicinity of a repulsive intramolecular orbital of the negative complex Na2. This R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 allows one to conduct a very precise measurement of the DA cross section behavior close to the reaction threshold. High electron energy resolution (A £«2 meV) is achieved by photoionization of sodium monomers, coexistent with Na2 molecules in the supersonic beam. Experimental results in the energy range 0-40 meV are presented for a number of selectively excited vibrational states (11 < v < 22) of the molecule. The threshold behavior of the DA reaction is clearly seen in the data for v" =12. As was already mentioned in the introduction, the signature of electronic shell structure has been found in various properties of simple metal clusters. Recent measurement of the abundance spectrum for dianionic gold clusters [SCHW’99] delivers additional evidence of the power of this phenomenon. Au„', n = 12-28, are formed as a result of electron attachment to Au~ anions, selectively stored in a Penning trap. The experimental abundance spectrum reveals clear even-odd and shell closure features, which are in line with the expectation from electronic structure considerations. For n> 20, a substantial number of singly charged stored clusters can be converted into dianionic species. This opens up a new field of a cluster research. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 2.4 Electron-Cluster Polarization Interaction A target cluster is polarized by an incoming electron. This leads to an electron- cluster polarization interaction. At large enough distance r , we have essentially a point charge e interacting with the induced dipole moment p = a e jr 2, where a is the cluster polarizability. Then the force of electron-cluster attraction is given by F = 2 p -e/r2 = 2ae2 jr 5, since the induced dipole points towards the electron. The corresponding polarization potential is obtained by an elementary integration over the distance r : For a perfectly conducting sphere of radius R , this potential energy represents the leading (dipole) term in the interaction of an electron with its image charge [JAC’75]. Note that a = R3 in this case. The high polarizability of alkali clusters can lead to an efficient attraction and capture of low-energy electrons via the strong polarization field (2.3). A classical analysis of charged particle motion in an r~* attractive potential was first performed by Langevin [LANG’05], who showed that for impact parameters smaller than a certain critical value b0 the projectile spiraled into the center of force (see Fig. 2.1). Assuming that upon close approach a (meta)stable anion is formed, one can associate R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 nbl with the cross section for electron capture. It’s given by the following expression (see also [LND’76, MCD’89, BON’97]): Figure 2.1. Classical trajectories of charged particle motion in an r~* attractive potential. (2.4) where E is the collision energy. Treating electron-cluster scattering quantum- mechanically [VOG’54], one recovers essentially the same result: the integral capture cross section is found to deviate from the classical value by no more than several percent, if the electron energy satisfies the following: R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 [8e2 a m ezE /h4^1 * >1, (2.5) where me is the mass o f electron. For such strongly polarizable systems as alkali clusters, this condition is already met at meV impact energies (e.g., for A /ia,0, the classical capture cross section holds down to * 2 meV). This justifies the use of the term “Langevin capture” even in the sub-eV range where the de Broglie wavelength of the colliding electron exceeds the radius of the cluster. The long-range interaction discussed above is also important when dealing with such reverse processes as thermionic emission or photodetachment of electrons from clusters [KRE’99]. The effect of the polarization interaction (2.3) on the electron emission spectrum is expected to be most pronounced for small kinetic energies of the outgoing electron, i.e. close to the emission threshold. This was recently observed experimentally in the kinetic energy distribution of electrons emitted from laser- heated tungsten cluster anions W~ (n = 4 -11) [PIN’98]. The low-energy part of the emission spectrum is found to be in excellent agreement with the Weisskopf probability distribution for the kinetic energy: where a (£ ) is the attachment cross section, given by (2.4). This expression follows from the principle of detailed balance, according to which the number of electrons leaving and reattaching to the cluster per unit time should be balanced under (2.6) R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 equilibrium conditions. As one can see, the polarization contribution enters Eq. (2.6) through the attachment cross section, which rises steeply at E — > 0. A signature of the polarization interaction has also been found in photoemission spectra of cold Qo [WAN’91]. The energy dependence of the photodetachment cross section in close vicinity to the ionization threshold was found to be in excellent agreement with the theoretical prediction [OMA’65]: where k is the momentum of the outgoing electron expressed in atomic units. The second term in Eq. (2.7) arises from the polarization interaction of the electron with neural CM molecule. (2.7) R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 Chapter 3 Inelastic Low-Energy Electron Collisions with Sodium Clusters and Nanoparticles: Integral Cross Section Measurement 3.1 Experiment Low-energy capture of free electrons by molecules has been studied extensively, but similar experiments on free clusters have been primarily focused on molecular clusters and fullerenes (see Sections 2.1-2.2). Information on metallic systems is extremely limited. An earlier experiment on Nan clusters (« = 8,20,40) [KRE’94] indicated the presence of large electron scattering cross sections and suggested an interpretation in terms of attachment (Langevin electron capture - Section 2.4) and fragmentation processes. However, due to the low signal-to-noise quality it remained uncertain whether the cross sections truly displayed a strong rise for E — > 0, which is a signature of electron attachment. A number of theoretical papers have subsequently addressed the issue of inelastic low and medium energy electron collisions with metal clusters, discussing various energy loss mechanisms: single-electron transitions, excitation of collective oscillations, emission of radiation, and ionization. Unfortunately, no computation so far has been able to reproduce the steep Langevin R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 capture cross section behavior at decreasing electron energies, indicating on either serious omissions in the theory or the irrelevance of the above mechanisms in this collision energy range. A monotonic rise of the anionic yield with decreasing energy has also been observed for small clusters of potassium Kn (/i = 3 — 8) in Ref. [SENT’O O ]. However, due to the uncertainty in the precise geometry of electron- cluster interaction, a quantitative cross section analysis has not been performed. The present experiment addresses medium-sized Nan clusters. We also investigate how the electron-cluster interaction extrapolates into the domain of nanometer-sized particles. As will be shown, the observation of a clear rise of cross sections with decreasing energy, and of a strong increase in cross sections with cluster size provides a distinct signature of polarization effects. The results presented in this chapter have been described in Refs. [KAS’99, KAS’O O , KAS’Ola]. 3.1.1 Cluster Beam Apparatus The experimental geometry is outlined in Fig. 3.1. The supersonic beam of neutral small and medium-sized clusters is produced by seeded expansion of sodium vapor through a small nozzle [HEE’87]. To generate a beam of nanoparticles, the supersonic source can be exchanged for a vapor condensation gear5 (see Fig. 3.1) which 5 This source will be described in more detail in the thesis of Kin Wong, USC Physics Department. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 M OQNIM a******* UJ o c r 3 O CO < c o z U i a z o o Figure 3.1. Experimental setup used to measure the integral cross section of electron interaction with sodium clusters and nanoparticles. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 is similar in design to the "smoke source" described in Ref. [MCH’89], The beam then passes through a skimmer and, following a 1.5 m long flight path, travels through the collision region of the electron gun and continues towards the detector. There the clusters are photoionized by filtered UV light from an arc lamp, mass selected by a quadrupole mass analyzer (QMA), and registered by a Daly ion counter incorporating a conversion dynode, a scintillator, and a photomultiplier tube [HEE’87]. A typical mass spectrum, obtained in one of the experiments with the supersonic cluster source, is displayed in Fig. 1.1 (Section 1.2). Special remarks should be made regarding the detection of sodium nanoparticles when the condensation source is used. The particle detector in Fig. 3.1 was originally designed to study clusters of up to a few hundred atoms in size. The nanoparticle mass, hence, exceeds our QMA mass capacity by almost two orders of magnitude. Nevertheless, we have found two complementary counting modes which gave a signal proportional to the particle beam intensity. First, we discovered that even with the UV lamp turned off, a signal rate on the order of 103 — 1 O '* counts per second was still observed. We identified it as originating from positive fragments formed upon the impact of large neutral clusters onto the glass window located just downstream of the dynode (see Fig. 3.1). Such processes have been observed for hyperthermal surface scattering of large molecules and molecular clusters (see, e.g., [VOS’88, DAN’89, CHR’92, AND’97]). The second detection mode was derived from the observation that R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 UV illumination of the nanocluster beam produced an even more abundant flux of heavy charged fragments. The QMA could not resolve their masses, but it was able to filter them out of the neutral beam, permitting us to separate these ions from those formed by surface impact. In the following, we will refer to these independent detection modes as "surface-ionization" and "UV-ionization" counting modes. The electron gun, as described before [KRE’91], is based on the design of Ref. [COLN’70]. In the present case, it is mounted on a movable high vacuum manipulator with water cooling (see Appendix A). Electrons are emitted by an indirectly-heated rectangular dispenser cathode6 (Spectra-Mat Inc., Watsonville, CA), extracted by a series of precision-aligned grids and masks, and intersect the cluster beam at a right angle inside an equipotential region bounded by two metal blocks. The length and height of the electron ribbon are / = 25 mm and h = 1.4 mm, respectively, and the entrance of the cluster beam into the collision region is defined by a 1.4 x 1.4 mm2 square aperture. This ensures that the height of the cluster beam in the interaction region is the same as that of the electron beam. To prevent dispersal of the electron beam by space-charge effects, the gun assembly is mounted in a uniform magnetic field (B = 1400gauss) which is directed parallel to the electron beam. Typical electron current densities in the interaction region were in the range of 800 pA/cm2 at energies 6 Details on the cathode activation procedure can be found in Appendix B. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 above 1 eV and up to 200 pA/cm2 at energies below 0.5 eV, corresponding to total impact currents of -80-350 pA. Beam velocities were measured with the help of two identical fast (typically -200 Hz) chopper wheels located =1.25 m apart (see Appendix C for details): the mass spectrometer was set to a particular cluster size and the beam was alternately chopped by wheels 1 and 2. Cluster velocities can be read off directly from the time delay between the arrival of pulses from the two locations. For medium-sized clusters, we found a monotonic decrease from 1100 m/s for Na2 0 to 1015 m/s for Na1 0 with a narrow velocity spread of about 10%, which is a well-known fact in the physics of supersonic molecular beams [SCO’88]. The velocity distribution of nano-sized particles peaks at 230 m/s with a FWHM7 of 20 m/s. It is interesting that the nanocluster beam, while slow, displays a narrow velocity spread similar to that of a supersonic source. 3.1.2 Beam Depletion Technique Electron-cluster scattering, in principle, can be studied by either looking at the individual reaction products or by monitoring the decrease of parent cluster intensity in the original beam. While the former approach usually requires a lot of special 7 Full Width at Half Maximum R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 experimental arrangements, the latter technique is a very natural one. It constitutes the so-called beam depletion method which, however, reflects all the reaction pathways that cause reduction of the cluster counting rate. As the cluster masses are high and the collision energies low, a kinematic estimate shows that elastic electron scattering cannot lead to discernible cluster beam depletion in our apparatus. Thus the cross sections reported here must correspond to inelastic processes: cluster fragmentation and/or electron attachment. In the former case, the relative recoil of the fragments will remove them from the beam, as has been observed earlier in photodepletion spectroscopy [HEE’93]. In the case of electron attachment, the resulting anions will be swept out of the beam by the electron gun’s magnetic field. Even if this Lorentz force were absent, any long-lived anions would be removed from the beam by stray electric fields and by the potential barrier8 present at the entrance to the detection region. 3.1.3 Data Acquisition The electron interaction with medium-sized clusters was monitored by setting the QMA to a chosen mass, pulsing the electron beam on and off at a rate of 4.77 Hz, and observing the concurrent depletion, A N , of the cluster counting rate on a multichannel 8 The detector ion optics is optimized to maximize transmission of positively charged clusters. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 scaler display. The counting rates for individual clusters were in the range of l-5xl04 per second, and the electron-induced depletion ratios AN /N were ~0.2%-l%. The total acquisition time for each collision energy and cluster size was 30-45 minutes. For nanoparticles, the corresponding beam depletion ratio AN/ N ranged from about 20% to 40%, reflecting the huge interaction cross sections. In this case, only a few minutes of acquisition time for every electron energy setting were sufficient to provide experimental data with good statistics. The total effective interaction cross section o tjJ can be found from the following equation [BED’71, COLN’71, Appendix D]: ^ = (31) N v cth Ie l is the electron current, h is the height of the interacting beams (see above), and vc / is the mean cluster beam velocity.9 This relation comes from considering how the electron beam scatters as it passes through the cluster beam. The velocity of the latter can be neglected during the scattering event, since the electrons move much faster. Thus the number of electronic collisions per unit time is proportional to the electron scattering cross section, the electron current, and the cluster beam density. Making use of the rectangular beam geometry and of the fact that the number of electron collisions 9 There is a small error arising from the existence of a transverse thermal velocity for electrons spiraling in the magnetic field (see Appendix D for details). R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 is equal to the number of cluster collisions, one arrives at Eq. (3.1). The reader is referred to Appendix D for further details. The effective cross section in Eq. (3.1) is the intrinsic cross section <x(£) convoluted with the electron energy distribution /(£ - £ „ ) produced by the electron gun [WEB’96, VOS’Ol]: oo J < x ( £ ) / ( £ - £ 0 )< /£ = • 0 -2) f l ( E - E 0)dE 0 where £ 0 represents the nominal electron energy, i.e., the potential applied to the scattering region. A retarding potential technique was used to extract both the electron gun energy spread and the contact potential correction to the nominal electron energy. The measured energy distribution, / ( £ - E0), is well represented by a Gaussian shape with a FWHM of about 0.3 eV for E < 1 eV, and 0.4 eV for higher electron energies. The values for E0 were measured to an accuracy better than 0.1 eV. A detailed description of the energy calibration procedures can be found in Appendix E. For nominal energies less than the FWHM of the electron energy distribution, E0 is no longer a good measure of the average electron collision energy. In this energy range it is more appropriate to introduce an adjusted electron energy (£) as follows [VOS’Ol]: R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 ao fE I ( E - E 0)dE (£) = j4 ------------------, (3-3) j l( E - E 0)dE 0 where the energy spread is given an appropriate cutoff at E = 0. Note that Eq. (3.2) for < r eI(E0) truncates l(E -E 0) at the origin as well. Our calculation showed that (E)» E0 already for nominal energies of 0.5 eV and higher. 3.2 Results and Discussion The results of our measurement are shown in Fig. 3.2-3.4 for selected medium sized sodium clusters and nanoparticles. The inelastic cross sections evidently increase with cluster size. Furthermore, there are two features in the experimental cross section curves, which are common for both studied cluster size ranges. They show a strong upwards trend for collision energies below 1 eV (“rise region”) and remain relatively flat at higher energies (“plateau region”). In the following (Sections 3.2.1-3.2.2), we will first concentrate on the former. It will be shown that this region corresponds to efficient negative ion formation in accordance with the polarization electron capture mechanism, discussed in Section 2.4. We then describe interesting deviations which were encountered in trying to discern the action of the same polarization force in electron attachment to nano-sized R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 clusters. Finally, it will be shown that the near-uniform behavior of the cross section at higher collision energies corresponds to the onset of an additional inelastic channel at »1 eV. We argue that this may be a signature of a direct electron-induced fragmentation process. 3.2.1 Medium-Sized Clusters It is noteworthy that the transition between rise and plateau regions lies exactly in the range of cluster dissociation energies which are also about 1 eV [BRE’89, BOR’O O ]. This means that in the rise region direct electron-impact fragmentation is not possible, and one expects that electron attachment should be the primary process. In fact, one may suppose that the electron capture process will be governed by the strong polarization field. As was stated in Section 2.4, a slow electron approaching a neutral cluster will polarize the latter and be subsequently attracted by the induced dipole field inversely proportional to the fourth power of distance. Electrons approaching the cluster with impact parameters smaller than a certain critical value will spiral into the center of force and be captured. The corresponding cross section is given by Eq. (2.4): const (a /£ )' 2, where E is the energy of the incoming electron and a is the cluster polarizability. We see explicitly that the high polarizability of metal clusters can lead to high electron attachment cross sections. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 9 Na 1000 500 c o Na 1000 o $ 500 (/) < /) O Na 1000 500 0 1 2 3 4 5 Electron energy (eV) Figure 3.2. Energy dependence of the inelastic electron scattering cross sections for three clusters with closed valence electron shells. Dots: experimental results; dashed line: Langevin capture cross section convoluted with the electron gun energy spread. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 In Fig. 3.2, with solid dots we present our experimental data for three clusters with spherical closed electronic shells: Na10, Nai0, and Nass. The dashed lines depict the capture cross sections calculated according to the Langevin formula (2.4) convoluted with the electron gun energy spread as given by Eq. (3.2). For these cluster sizes, we used the experimentally measured polarizabilities taken from Refs. [KNI’85, RAY’99, TIK’01]: a 2 Q = 310A3 , a 4 0 =590 A3 , and a 5 S =820 A3 . It is evident from the figure that the polarization capture mechanism provides an essentially quantitative representation of the low-energy cross section behavior for different cluster sizes. We would like to note that the dashed lines employ no adjustable parameters. As shown above, the very large values of the inelastic cross sections originate from the strength of the long-range polarization potential. We repeated the measurement for two open-shell clusters,1 0 Na5 7 and Na1 0 ( a sl =750A3 [TIK’01], ar7 0 =920A3 [KRE’92]); the results are shown in Fig. 3.3. While the quality o f the data is poorer due to the lower counting rate of these less abundant clusters, the agreement with Eq. (2.4) is still satisfactory (the effects of non-sphericity should be washed out by orientational averaging). This confirms that 1 0 No experimental value yet exists for Na10, so we took a 1 0 from the analytical random-phase approximation (RPA) calculation described in [KRE’92]: this formalism provides results, which are in good agreement with the available data for smaller clusters. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 the Langevin mechanism dominates low-energy electron scattering for a wide range o f cluster sizes. 2000 Na< 1500 1000 CM 500 c o '■§ ® 3000 $ 2500 Na S O 2000 1500 1000 500 Electron Energy (eV) Figure 3.3. Same as Fig. 3.2 for two open-shell clusters. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 3.2.2 Nanoparticles Here we present our results for nano-sized clusters. Fig. 3.4 shows the total depletion cross sections a eff, derived from Eq. (3.1), for electron collisions with sodium particles in the 0-7 eV energy range. The two panels correspond to the different beam detection techniques described in the experimental section: "surface- ionization" and "UV-ionization" counting modes. The cross section values themselves are remarkable. The two sets of data differ slightly in magnitude, which can be understood as follows. The condensation source produces sodium droplets in a certain size range. Since the nanoparticles are not mass selected, our measurements reflect convolutions of the real size dependent cross sections er(n,E) with this mass profile and the sensitivity functions of the ionization modes. The latter, however, are also dependent on the cluster mass and therefore amplify somewhat different portions of the cluster size distribution. The average particle sizes fitted to the two data sets (see below) agree to within 20%, which indicates that our detection techniques are consistent. As was already mentioned, there is no mass resolution in this experiment. Nevertheless, we can hope that efficient electron capture and negative ion production at near-zero energies, observed for smaller clusters, will let us have some insight into the average size of the particles involved. Indeed, the scattering cross section rises R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 Experiment, surface ionization Theory, Na7 8 0 0 Dipole approximation, Na. 16000 '30000 14000 12000 10000 (N ^ 8000 o o (D C O $ 16000 6000 Experiment, UV ionization Theory, Na9 5 0 0 2 ° 14000 12000 10000 8000 6000 0 2 4 6 Electron Energy (eV) Figure 3.4. Total depletion cross sections for electron collisions with sodium nanoclusters. The upper panel shows results obtained in the “surface ionization” beam detection mode and the lower panel is for the “UV-ionization mode” (see text). Solid lines: image*charge capture cross sections, Eq. (3.6), convoluted with the electron gun resolution function. Dashed line: best fit of the data using the pure dipole Langevin capture cross section, Eq. (2.4) R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 sharply as the electron energy goes to zero. Its shape appears similar to that shown in Figs. 3.2-3.3, where Eq. (2.4) gave a very good description of the data. However, our attempt to fit the low-energy data in Fig. 3.4 with such an equation failed completely. We found, in fact, that the curvature of the data cannot be matched by an E 'xn line (see the dashed line in the upper panel). This is also supported by the unreasonably large particle size required by the fit: Na^moo (note that the geometrical cross section of such a cluster would be «14 000 A3 ). Clearly, the usual dipole approximation, used in Section 2.4 to characterize electron-cluster interaction, breaks down for scatterers as large as those encountered here. We realized that it’s necessary to take into account terms higher than the dipole in the expression for the polarization potential. Such terms may become significant due to the large particle size. We need to write down the interaction potential between an electron and a relatively large polarizable particle. It is sensible to make use of the full classical image-charge potential" for the attraction between a point charge and an isolated conducting sphere of radius R [LAND’84]: 1 1 As mentioned in Section 1.2, the surface electron spill-out enhances the dipole polarizability of smaller metal clusters over the value R3 for a conducting sphere of radius R [BON’97]. However, this correction is insignificant for the sizes encountered here: R ~ 40 A (see below). R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. Note that Eq. (2.3) is the leading term in the expansion of this full expression in powers of (/?/r) for r » R . Now we need to calculate the energy-dependent capture cross section for an electron attracted by the field (3.5). This is not easy to achieve quantum- mechanical ly. However, as mentioned in Section 2.4, the complete quantum solution for the dipole potential (2.3) gave a result which coincided with that found from classical mechanics down to very low energies. It is therefore reasonable to expect that the classical capture cross section for V /u ll should be appropriate in the present case too. The way of calculating this cross section is described, e.g., by [LAND’76, KLO’94]. One writes down the effective potential energy Kff (r ) = V ju ll (r) + mb2 vl/2 r2, where the second term is the centrifugal barrier ( b is the electron impact parameter and is the electron velocity far away from the cluster). For a given kinetic energy of collision E = mv2 J 2 , there is a critical impact parameter, b0, below which the electron is not reflected by the V rff and “falls to the center.” The capture cross section is then given by <r(£) = /r& 0 2. This procedure is very simple for a power-law potential such as Eq. (2.3), but it turns out that even for R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 the complete potential in Eq. (3.S) an exact analytical solution can be found (see Appendix F): turns out to be just a sum of the hard-sphere area of the particle and the Langevin cross section, Eq. (2.4). We have fitted our low-energy scattering data1 2 with expression (3.6). As Fig. 3.4 demonstrates, a greatly improved match is obtained with w = 7800 atoms in the surface-ionization detection mode, and « = 9500 atoms in the UV-ionization mode. These values are indeed sufficiently close to each other to support the consistency of the experiment. The corresponding particle radius is R = rx a0 n1 1 3 = 4.2 -4.5 nm (here rt « 4 is the Wigner-Seitz radius of Na and aQ is the Bohr radius). Finally, we would like to point out that in addition to demonstrating strong image-charge attraction between electrons and nanoparticles, this measurement can be used as a tool for calibrating the average nanocluster size. Beams of metal 1 2 In principle, we should have used the complete Beer’s law expression instead of Eq. (3.1) to perform the data analysis for nanoparticle experiment in view of 20% to 40% depletions of the cluster beam (see Appendix D for details). This would make the procedure extremely cumbersome since the cross sections and all corrections would have to be calculated self-consistently. Instead, we made an order-of- magnitude estimate of the fitted particle size change, if one uses complete expression (3.6) where the particle polarizability a is equal to R3 in this case. Interestingly, this R eproduced with perm ission of the copyright owner. Further reproduction prohibited without permission. 47 particles in this size range are of interest for, e.g., film deposition and materials synthesis [MIL’99], thus it is important to be able to characterize them. 3.2.3 Additional Inelastic Channel Before proceeding to the plateau region in Figs. 3.2-3.4, it’s informative to have a quick excursion into Chapter 4, where the measurement of the averaged anion yield A/a" is presented. As shown in Fig. 4.4, our data are again in good agreement with the Langevin capture cross section, Eq. (2.4), averaged over the experimental mass distribution. This independently confirms that the polarization-capture mechanism remains active at least up to an energy of several eV. On the other hand, Figs. 3.2-3.4 show that in the region of 1-1.5 eV the experimental points begin to diverge from the capture cross section line. In other words, it is apparent that another inelastic channel starts contributing to the cluster beam depletion. This is clearly seen if we subtract the electron attachment contribution from the full cross section data. The result is shown in Fig. 3.5(a) for Na1 Q A 0 5 t clusters, and in Fig. 3.5(b) for the Na { 0 , particles. An evident threshold-type process is revealed, with an onset at E,h * 0.8 -1.1 eV for Fig. 3.5(a) and E,h * 1 .3 eV for Fig. 3.5(b), as (D.9) together with the magnetic field correction (D.30). The result is at most a -20% increase in the particle size compared to the values given in the text. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 Na N a ^ N a, 500 400 300 200 CM < 100 c o o 0 C O w 2500 2000 1500 1000 500 Electron Energy (eV) Figure 3.5. The result of subtracting the electron attachment contribution from the total inelastic cross section data for (a) sodium clusters and (b) nanoparticles. All the lines in the plots above are smoothing fits designed to guide the eye. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 determined by a local regression fit. Note that the nano-sized clusters in Fig. 3.5(b) display much larger cross sections but the threshold is close to that for smaller sizes. The precise size dependence of the threshold values is difficult to identify in view of the estimated 10-20% accuracy of the cross section data and the 0.1 eV calibration accuracy of the average electron beam energy.1 3 What mechanism could account for the depletion of cluster beam, depicted in Fig. 3.5? Since it appears on top of electron attachment channel, this could be either an elastic “knockout” of the cluster by an e ', or decomposition (fragmentation). As mentioned earlier, an elastic collision of a few-eV electron with a heavy cluster or nanoparticle would not, however, kinematically be able to deflect the particle as a whole away from the detector entrance within the 50 cm flight path. On the other hand, cluster fragmentation can, in principle, provide enough recoil to result in beam depletion. Electron-induced fragmentation can proceed either directly or evaporatively. The latter implies a uniform distribution of the excitation energy between all the vibrational degrees of freedom (cluster heating) followed by the evaporation of a small fragment (see, e.g., [FR.6’97, HAN’99]). In alkali cluster studies, the 1 3 It’s interesting to note that the cross section behavior of this new inelastic contribution for the medium-sized clusters is well approximated by scaled square roots of the collision energy: const ■ y jE - Elh , as evidenced by the set of curves in Fig. 3.5(a). This kind of energy dependence is typical for reactions with a threshold, R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 evaporative fragmentation follows, e.g., the decay of optically-induced plasmon excitations [HEE’93]. As discussed in Section 2.3, the plasmon electron-energy-loss mechanism, followed by evaporative decay, may also lead to an efficient pathway of electron-cluster inelastic scattering [GER’97a, GER’97b]. However, the excitation of a collective resonance requires a minimum energy transfer of ~3 eV, which is above the thresholds seen in Fig. 3.5. Furthermore, it is rather unlikely that large clusters (and especially nanoparticles) can be heated by the slow electrons from » 400 K [BRO’99, KAS’00] to a temperature high enough to evaporate fast fragments. Finally, there remains the possibility of a direct fragmentation process (the transfer of all or large part of the electron energy to a single atom or small fragment). For alkali clusters, such a low-energy collisional channel has not been studied in detail either theoretically or experimentally.1 4 However, this appears to be a reasonable suggestion for the data in Fig. 3.5. Note, first of all, that the observed thresholds are close to the Na_2 0 _l 0 Q cluster dissociation energies (wO.9-1 eV) [BRE’89, BOR’O O ] and to the heat of vaporization of bulk sodium (0.9 eV) [WEA’87]. Secondly, according to a kinematic estimate, an electron within the experimental energy range can indeed knock out a small fragment with an energy sufficient to remove the recoiling (nano)cluster from the collimated beam. where non-interacting products are formed (see, e.g., [LAND’77]). However, this law usually applies in close proximity to the threshold. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 It would be interesting to understand this mechanism in detail. In the total cross section curves (Figs. 3.2-3.4), the direct fragmentation channel starts to contribute to the Langevin polarization capture process at E > 1 . However, the negative ion yield measurement described in Chapter 4 has revealed only the latter contribution at these collision energies. Hence, the electron-induced fragmentation pathway produces only neutral cluster fragments. This implies, in the classical picture shown in Fig. 2.1, that cluster fragmentation is initiated by an incident electron that is swinging by the cluster rather than spiraling into it. Indeed, the Langevin capture cross section accounts for all of the latter electron-cluster collision events. This leads us to a conclusion that the direct fragmentation channel is, in fact, also of a long-range character, and therefore is likely mediated by the cluster electronic sub-system. Furthermore, following the discussion in Refs. [KRE’91, KRE’94], one may attempt to estimate what characteristic impact parameter is associated with the observed cross sections. It turns out that for, e.g., Na1 0 this parameter exceeds the cluster ion core radius by -60%, which supports our argument. Note, however, that this electronic mechanism is distinct from the evaporative fragmentation process discussed above. Additional experimental and theoretical studies of electron-vibronic coupling in clusters of simple metals are therefore required. 1 4 Direct fragmentation of Na3 .g resulting from an electron-transfer harpooning process, involving similar energies, has been reported in Ref. [GOE’95]. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 Another argument in favor of the direct fragmentation scenario comes from our recent data on electron scattering with CM, taken with the same electron gun and a similar data acquisition procedure (see Chapter 5). A strong electron attachment channel was again observed for E -> 0, but we have not found any signs of an over- 1 eV threshold process: the inelastic cross section continued to decay as the collision energy increased to several eV. (Similar results have been shown in [WEB’96, AGA’99, VOS’Ol].) This is completely consistent with the fact that C6 0 is a much stronger bound molecule than a sodium cluster: its dissociation energy exceeds 8 eV, and may be even as high as 11 eV [HAN’97]. For the larger clusters, it would be also interesting to consider a process intermediate between purely direct and purely evaporative fragmentation. In the field of energetic ion-surface interactions, an incoming particle strikes the bulk surface and generates a local impact zone that becomes heated, melts, and evaporates. Similarly in the electron-cluster scattering case, it may be possible that the electron’s kinetic energy is transferred to a small group of atoms (instead of the entire cluster), causing one or more of them to evaporate. Linking this zone for clusters and nanoparticles on one hand and solid surfaces on the other, the dynamics of such a process and the critical size for its appearance could be investigated. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 3.3 Summary We have measured absolute inelastic cross sections for low-energy electrons (from « 0 to up to 7 eV) interacting with neutral sodium clusters and nanoparticles. The results can be summarized as follows. • The cross sections are found to be quite large: exceeding 1000 A2 for medium-sized and over 104 A2 for nano-sized clusters at £ -> 0 , which is a signature of strong long-range forces involved. • For collision energies below 1 eV, the cross sections rise strongly with decreasing energy, in quantitative agreement with the Langevin mechanism of electron capture by the polarization field. For nanoparticles, it was found necessary to go beyond the usual induced- dipole approximation for the attractive interaction. By taking into account the full electron-particle image charge potential (which yields an exact analytical solution for the capture cross section), we obtained very good agreement with the low-energy behavior of the data. It appears that this may be a convenient technique for calibrating the sizes of nanoparticles in beams over a wide mass range. • In addition to the electron capture, a second strong inelastic channel appears above a threshold of approximately 1 eV. We demonstrated R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 that it can be plausibly assigned to direct fragmentation of the particle by an incoming electron. Such processes have not yet been studied in detail, and we hope that this observation may draw some attention to their importance. It also emphasizes a very interesting problem: direct versus statistical energy transfer to cluster vibrations. Our findings raise a number of basic questions related to electron dynamics near the surface of metal clusters. For example, what is the fate of the electrons that have been captured by the cluster polarization potential? In principle, they may spend some time in a metastable orbit outside the cluster core1 3 and autodetach or, more likely, transfer their energy to other cluster electrons and/or vibrational modes and “fall” into the cluster, following the scenario of either dissociative or evaporative attachment processes; or being auto-scavenged, Eqs. (2.1)-(2.2). Out of these, which are the main relaxation mechanisms (and what are the associated lifetimes) for alkali cluster is still to be researched. The detailed behavior of the total cross sections at energies > 1 eV remains difficult to understand theoretically as far as both electronic and ionic cluster degrees of freedom are concerned. Indeed, as shown in Section 2.3, available theoretical studies are limited: (i) by the utilization of the Bom approximation, which is not 1 5 As speculated in Refs. [FIN'95, WEB'96] for e~ -C M collisions. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 justified in the considered energy range; and (ii) by employing the jellium model, which omits the interaction between electronic and ionic sub-systems of the cluster. To our knowledge, the Langevin electron capture (identified in both the beam depletion cross sections above and direct negative ion Na~ yield data in Chapter 4) has not yet been reproduced in the calculations. This evidently indicates the importance of the detailed cluster ionic structure in low-energy electron scattering dynamics1 6 and the need for a more accurate many-body treatment of interelectron polarization forces. We also have not observed any clear manifestations of theoretically proposed electron energy loss mechanisms (Section 2.3) in our experimental data. This may be in part due to our present experimental accuracy. For example, the resonance features, described in the refined RPAE approach [IPA’98, CON’99, CON’O O ], could be washed out because of the finite collision energy resolution or due to the averaging of the cross section over the experimental mass profile (see Chapter 4 for details). On the other hand, this could also indicate that the effect of these mechanisms on the beam depletion is essentially masked out by the action of the main experimentally observed channels of electron-cluster scattering: electron capture and cluster fragmentation. Some of the predicted energy loss processes, however, could contribute to the latter channels indirectly. This remains a very interesting topic for future experimental work. 1 6 This may also signify some hidden omissions in the theoretical analysis. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 Chapter 4 Negative Ion Formation in Collisions of Slow Electrons with Neutral Na„ In addition to its importance in the fields of spectroscopy and mass spectrometry, low-energy electron attachment has appeared in such diverse contexts as plasma discharges, combustion, excimer laser operation, explosives detection [CHU’96], and DNA radiation damage [BOU’O O ]. Our initial studies of low-energy inelastic electron collisions with small and medium sodium clusters (see Chapter 3 and [KRE’94, KAS’99, KAS’O O ]) have discovered a strong rise of the inelastic integral cross sections as £ — > 0. It was suggested that this behavior was due to efficient negative ion formation. Indeed, as described in Chapter 3, the experimental data in the range < 1 eV are quite well represented by the Langevin expression for electron capture by the polarization field: an incoming slow electron polarizes the neutral cluster and is attracted by the resulting dipole field. For impact parameters below a certain critical value, the electron spirals into the center of force and is captured. For the bigger nanoparticle targets, a quantitative explanation of the data was provided by the full image-charge potential characterizing the electron-particle interaction. A monotonic rise of the K2 ~ _ g yield with decreasing impact energy was also reported in Ref. [SENT’00]. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 However, due to the uncertainty in the precise geometry of electron-cluster interaction, a quantitative cross section analysis was not performed. The beam depletion technique described in Chapter 3 was well suited for measuring absolute cross sections, but could not identify individual reaction products. The evidence for the existence of efficient electron capture was therefore indirect. The experiment presented below was designed to monitor negative ion formation directly, and to verify that the anion yield indeed follows the Langevin mechanism. Our results are also summarized in Ref. [KAS’O O a], 4.1 Experimental Setup The main scheme of the experiment was to pass a collimated supersonic beam of neutral metal clusters through the collision region of an electron gun, extract the resulting negative cluster ions, and to monitor the efficiency of anion formation as a function of electron energy. We exploit the same experimental apparatus which was used for the measurement of e~ - Nan interaction cross sections in Chapter 3, where the reader is referred for further details about the cluster beam and electron gun construction. The arrangement was modified to incorporate a Channel Electron Multiplier (also referred to as a CEM, or a channeltron; Detector Technology, Inc., Palmer, MA) mounted on a movable XYZ-stage and facing the downstream aperture R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 of the electron gun (see Appendix A). The design allowed neutral particles to fly freely through the channeltron and be detected in the manner described in detail previously (photoionized by UV light from an arc lamp, passed through a quadrupole mass analyzer, and detected by an ion counter - see Fig. 3.1). In this way, we could monitor the sodium cluster mass spectrum concurrently with the anion counting. The role of the channeltron was to detect negatively charged particles exiting the scattering region of the electron gun, where electron and cluster beams crossed each other. At the present stage of the experiment we are not able to mass select anions before feeding them into the CEM detector.1 7 Normally, the direct detection efficiency of a commercial channeltron drops as m~'/2, where m is the mass of the incoming particle of a given energy [KUR’79, GAL’91]. To boost the detection efficiency of heavy ions and make it more uniform, a conversion dynode is one of the most commonly used options [HAB’83, FRI’88, GAL’91]. Thus we chose a CEM detector unit containing a build-in conversion dynode with an off-axis channeltron overlooking it, as indicated in Fig. 4.1. The dynode was biased by a high positive voltage of up to 6 kV. The channeltron cone was floated at -2.9 kV and the channel exit was grounded, providing a sufficient voltage gradient across the channel to create a detectable electron avalanche. In this detection mode, an incoming 1 7 This, in fact, is beneficial for the present detection technique. As shown below, the average counting rate in the experiment was about 10 negative ions per second. The mass selection would make this value at least one order of magnitude lower. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 negative ion is attracted by the positively charged conversion dynode, hits it, and breaks up into pieces, some of which are positively charged [STA’80]. The positive fragments are accelerated towards the channeltron entrance by the potential difference of about 9 kV, where secondary electrons are emitted upon impact and an electron avalanche is created. Finally, an all-in-one preamplifier and discriminator unit (Advanced Scientific Instruments Corp., Wheat Ridge, CO) is used to convert the small negative CEM output pulse into a TTL pulse 100 nsec wide. Further details on the CEM circuitry and other particle detection modes can be found in Appendix A. J=L MCS juumul|PREAMP Electron Gun From Supersonic Na„ Source < & - + ■ and Skimmer Chopper 2.9 kV ^ To UV Light, $?-► QMA and Ion Counter onversion +100 V Dynode +5 V + 6 kV Figure 4.1. Section of experimental setup used for negative ion detection (not to scale). A cluster captures an electron in the scattering region o f the electron gun and becomes a negative ion. It is extracted by ion optics and accelerated towards a stainless steel conversion dynode, producing positive fragments, which are subsequently detected by the channeltron and result in a TTL pulse registered by a multichannel scaler (MCS) board. R eproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 This detection technique is beneficial in two ways. First, the negative cone voltage allows the channeltron exit to be grounded, which allows an easy connection to pulse counting electronics. Secondly, the high negative voltage at the CEM cone repels stray electrons that are produced in large quantities at the electron gun cathode. While a stray electron can still hit the conversion dynode, it will only be detected if this hit produces a positive secondary particle, a process much less likely for a given impact energy than the ejection of a secondary electron. The end result is a significant reduction in the level of background noise. 4.2 Data Acquisition The data acquisition mode in our setup can be briefly summarized as follows. The supersonic Nan beam is mechanically chopped at 94 Hz approximately 50 cm away from the source nozzle. After another 1 m of free flight, the clusters enter the scattering region of the electron gun, where some of them form negative ions by capturing low-energy electrons. Since the entire 25 mm-long scattering region is an equipotential volume, the cluster anions leave it with the same translational velocity as the original neutrals in the beam (-1000 m/sec). Elementary ion optics, placed behind the scattering region, focuses the negatively charged clusters into the channeltron. The output pulses of the electron multiplier were collected by a plug-in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 multichannel scaler (MCS) board which was synchronized with the cluster beam chopper. The total counting rate (signal plus noise) was on the order of 3000 counts per second. For each data point, the nominal electron energy was set and calibrated (see below), the energy resolution checked, and then a time-resolved MCS profile was accumulated for approximately 25 minutes. We also monitored the mass population of the original neutral cluster beam by taking mass spectrometer scans before and after each electron energy point. A representative mass spectrum is shown in Fig. 1 . 1 . A typical experimental MCS profile is presented in Fig. 4.2. The scaler starts collecting data immediately after the cluster beam is opened by the chopper wheel. It takes up to 1 ms for the majority of clusters to fly from the chopper to channeltron, which accounts for the delay seen before the signal starts to build up above the noise level. From that moment on, the clusters continuously fly through the electron gun until the chopper blocks the beam again. The washed out boundaries of the signal “bump” is a signature of the intrinsic cluster velocity spread in the supersonic beam. For every accumulated MCS spectrum, the total amount of real signal, AN, was extracted by summing all the channels under the plateau region of the bump and subtracting the noise level for the equivalent number of channels. The estimated accuracy of the extraction is ~10%. In this experiment the signal-to-background ratio Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 ranged from -0.5-3% corresponding to a counting rate of up to 10 negative ions per second. As discussed in Chapter 3, Eq. (3.1) relates the effective integral cross section o tff of the electron-cluster interaction to the measured quantities. At the moment we do not mass resolve negative ions formed in the electron gun scattering region. This implies that expression (3.1) should be modified to convolute the mass-dependent a e j} with the mass spectrum produced by the cluster source (Appendix D): (4.1) 13.0 Original MCS Profile - — Average Level Cluster anions Background 12.0 0 1 2 3 4 5 6 7 8 9 10 Time (ms) Figure 4.2. A typical experimental MCS profile. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 Now N is the total number of clusters of all sizes entering the scattering region during the data acquisition cycle, AN is the total number of detected ions in the same cycle, P is the mass-dependent detection probability for the negative ions in the Channeltron. Indeed, in order to be detected the cluster anion should be able first to escape from the scattering region (probability p,), and then to produce a detected positive fragment (probability p2 ) in a collision with the conversion dynode (see the foregoing section). If we assume that p, and p2 are independent, then {P) = (p,)-(p2). In fact, the probability of the electron auto-detaching on the way to the channeltron should also be considered. However, such a pathway does not appear to be dominant, and will not be included in our estimates. It is, nevertheless, directly related to the general question of relaxation channels for the negative cluster ions and itself makes an interesting subject for a future investigation. A reduced value of p, is primarily due to ion deflection by the strong magnetic field B present in the scattering region (the electron beam is collimated by B = 1400 gauss to prevent its dispersal by space charge repulsion).1 8 Using the equations of charged particle motion in a region of crossed electric and magnetic fields, p, can be estimated quite easily and practically analytically (see details in Appendix G). Fig. 4.3 shows the size dependence of cluster escape probability. In the mass range of interest, the curve can be very well fitted by a scaled square root function. To find Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 (pt), the escape probability is convoluted with the mass spectrum distribution measured during the same acquisition cycle. 0.4 0.3 0.0 Cluster Size Figure 4.3. Size dependence of the cluster escape probability p x. On the other hand, p2 is expected to be a complicated but relatively uniform [STAF’80] function of the ion mass, its velocity, and the condition of the conversion dynode surface. Thus (p2) would vary from one data point to another only if the relative intensities of the opposite ends of the mass spectrum showed a strong shift. However, we verified that the “center of gravity” of the mass spectra remained stable 1 8 It is a beneficial property of the channeltron detector that its normal operation is not drastically altered by magnetic fields of up to 1 Tesla [LIN’99], Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 to within 10%. Hence it is accurate to treat (/?,) as a constant coefficient. As described in the next section, by scaling the theoretical curve to the experimental data points we estimated (p2) ~ 0.03. The cluster beam velocity is another parameter entering Eq. (4.1). In general, in a supersonic beam vc l is a weak function of cluster size. Indeed, it decreases by less than 10% on going from Na2 0 to Na1 0, as shown in Appendix C. Thus we used an average value (vc/) = 1100 m/s in the expression (4.1) instead of performing velocity measurements for every cluster in the mass spectrum. 4.3 Results and Discussion As described before, this experiment was carried out in order to verify directly that cluster beam depletion as a result of collisions with < 1 eV electrons is primarily due to formation of negative cluster ions. The results of our measurements are shown in Fig. 4.4. The experimental data points are related to the value of the maximum cross section in the set (absolute scaling is hampered due to the lack of quantitative information on the dynode conversion probability (p2), defined in the preceding section). Since the latter enters expression (4.1) as an overall scaling factor, this normalization does not affect the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 intrinsic energy dependence of the measured ion yield. The relative accuracy of the data points shown in Fig. 4.4 is estimated to be 10-15 %. • Experiment — Langevin Capture c o <D m 0 8 o 0.6 ■o a> n 0.4 2 a s E o z 0.2 0.0 0.0 0.5 2.0 2.5 3.0 Electron Energy (eV) Figure 4.4. Direct evidence for negative ion formation in collisions of low- energy electrons with neutral sodium clusters Nan. Circles: experimental cross section derived from the anion yield. Line: Langevin electron capture cross section convoluted with the mass abundance spectrum and with the electron gun resolution. The Langevin capture cross section, Eq. (2.4), depends on the cluster size n through the polarizability a : different cluster sizes will have different numerators in the Langevin formula (see also Chapter 3). But the energy denominator will be obviously the same for all particles. Hence if the electron capture mechanism is Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 indeed relevant to our case, the overall shape of the data in Fig. 4.4 should follow an inverse square root dependence on the collision energy: (4* 2> Here / ( « ) is the relative abundance of Nan in the beam, and A is the resulting overall numerator. The solid line in Fig. 4.4 is a least-squares fit of the const •£~'/2 expression to the set of experimental anion yield data. This function was convoluted with the electron gun energy resolution prior to fitting, as defined in Eq. (3.2). There is an impressively good agreement between the shape o f the curve and the experimental points. This result directly confirms that the cross section rise for E -> 0, observed in the beam depletion data - Fig. 3.2-3.4, is a signature of electron capture. Finally, let us estimate the average probability (p2) for cluster anion conversion into positive fragments at the conversion dynode. This can be found from Eq. (4.1) by substituting into it the relevant electron and cluster beam parameters, together with the averaged capture cross section, given by Eq. (4.2). The numerator A in the latter is given, according to Eq. (2.4), by: /f = JT < £ /(„ ),/2 ^ '. (4.3) n To perform the averaging over the experimental mass spectrum, we need to know how the polarizability of a cluster a n depends on its size n . For alkali-metal clusters, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 it can be adequately fitted by the form a n = (/?„+<5)3, where R „ =rx a0 nip is the cluster core radius (r, = 3.96 is the Wigner-Seitz parameter for sodium and a0 is the Bohr radius) and 8 ~ 0.75 A is the valence electron spill-out parameter [HEE’93]. Using Eq. (4.3), together with an estimate that the detection efficiency of the supersonic beam by the mass spectrometer unit is about 30%, we found that the average dynode conversion probability (p2) is approximately equal to 0.03: on average only 3% of cluster anions incident on the dynode are detected by the CEM.1 9 This is, indeed, a realistic value [STAF’80, SCHA’00]. 4.4 Summary In summary, we have studied the interaction of a beam of low-energy electrons with free neutral sodium clusters. The efficient formation of negatively charged Na~ ions in the 0-3 eV collision energy range has been observed directly, confirming an earlier hypothesis. The energy dependence of the experimental mass-averaged anion 1 9 We operated the conversion dynode at maximum voltage (+ 6 kV) allowable by the CEM design. For an experiment with a mass selection of cluster anions, one would require considerably higher detection efficiency to be able to register all the negative ions, formed in the electron-cluster collisions. This can be achieved by, e.g., spacing the conversion dynode stage from the channeltron in a way similar to the design in Ref. [FRI’88], which allows voltages of up to 40 kV being applied to the dynode. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 yield is found to be in excellent agreement with the Langevin mechanism of electron capture in the cluster polarization field. Further experimental and theoretical studies regarding the negative ion formation dynamics and relaxation channels should be undertaken. For molecular clusters, electron attachment appears to proceed through an intermediate resonant excited state (see Chapter 2), which subsequently decays via a number of pathways. It is interesting whether a similar intermediate state is formed in electron-metal cluster collisions, what its lifetime is, and how it decays. Do the metal clusters undergo fast direct fragmentation (“dissociative attachment” [KEI’99]), heat up and evaporate (“evaporative attachment” [MAT’99]), or are relatively long-lived (“auto scavenging” [WEB’99])? Or does the attracted electron merely stay in a remote “orbit” and quickly auto-detach? It is likely that the answer depends on the cluster size and the collision energy range, and therefore encompasses a number of dynamical processes. As already discussed at the end of Chapter 3, there exist a possibility of a direct electron “fall into the cluster”. Various electron energy loss mechanism has been examined theoretically, by which the energy was redistributed into the vibrational, collective, or particle-hole excitations of the cluster [SPI’96, GER’97a, GER’97b], or lost by radiation [CON’96, SPI’98]. However, perhaps due to the oversimplified approach (the Bom approximation) and to ignoring the internal structure of the cluster core, these calculations have failed to re-produce the Langevin mechanism of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 the polarization electron capture. It appears that the low-energy electron dynamics at the cluster surface is essentially defined by the complicated interplay between the electronic and ionic sub-systems of the metal particle. These issues will be the matter of further experiments in our lab. In the first place, it would be beneficial to achieve mass selectivity of the cluster anions formed in the electron gun. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 Chapter 5 Low-Energy Electron Capture by Free C6 0 Clusters Electron collisions with neutral fullerene molecules in the gas phase lead to significant production of long-lived C 6 ~ 0 ions for collision energies from near 0 eV to over 10 eV. This has been established by several experimental techniques: bombardment by an electron beam [JAF'94, HUA'95, VOS'95, ELH'97, VAS'97, VOS'Ol], Rydberg electron transfer [HUA'95, FIN'95, WEB'96], and flow in an electron plasma [SMI'96]. Despite the theoretically predicted lack of an unoccupied L=0 state in the vibronic spectrum of C6 ~ 0 [TOS'94], the molecule does support a strong electron attachment channel for E — > 0 (see Chapter 2 for details). In Refs. [HUA'95, FIN'95, WEB'96, FAB'01], it was rationalized that, in principle, slow electrons could be captured into the image-charge-based bound states or resonances, mediated by the cluster polarization field. It’s noteworthy that the resonant electron attachment to CM at near 0 eV is indeed reported in Ref. [VAS'97]. This argument is further supported by the photoelectron spectra of C^ [WAN’91], where the prominent action of polarization forces has been identified in the shape of the spectrum near threshold. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 Evidently, the long-range polarization field plays a key role in the dynamics of low- energy electron scattering at fullerenes. A related question has been studied in Chapters 3 and 4 for alkali-metal clusters and nanoparticles. It was found that in the energy range from zero up to a few eV, the anion formation cross section is in very good agreement with the Langevin capture formula (2.4). The fullerenes are considerably less polarizable compared to alkali clusters ( a C u « 78 A3 [ANT’99, BAL’O O ]). However, Eq. (2.4) should be relevant for CM too. Indeed, for fullerenes condition (2.5) holds down to the energies of -10 meV. It is important to keep in mind that the Langevin formula provides only the probability of electron spiraling into the cluster. The full attachment cross section must also include the probability of the excess energy dissipation to bring the electron-cluster system into a stable anionic state. Our measurements have shown that for alkali clusters this sticking probability is very close to unity. This is most likely due to their essentially molten state under our experimental conditions [SCHM’98]. The fullerenes, on the other hand, possess a well-defined symmetry of the ionic core which can impose certain selection rules on the coupling of the incoming electron to the ionic vibrations. As a result, as we will see, for CM the Langevin formalism defines only the overall trend of the cross section curve. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 Below, we report our measurement of the e~ - C M capture cross section using a cluster beam depletion technique similar to that described in Chapter 3. We obtain absolute cross section values in 0 to 3 eV energy range and demonstrate clear evidence for strong enhancement of the attachment for E -> 0. These results can also be found in Ref. [KAS’01], 5.1 Experimental Setup An outline of the apparatus2 0 is shown in Fig. 5.1. The copper source is loaded with about 1 gram of 99.5% pure fullerene powder (MER Corporation, Tucson, AZ) and baked out for several hours prior to the experiment. A beam of free fullerenes is created by effusive expansion of C6 0 vapor, saturated at 580°C, through a small nozzle channel (diameter 0.5 mm, length 3 mm, T „ „ . =690°C). Then, the beam passes through a divider hole (length 3.5 cm, diameter 2.5 mm) and enters the scattering and detection chamber. We use exactly the same electron gun as in the alkali clusters experiment (Chapter 3). It is located about 20 cm downstream from the cluster source. Fullerene anions formed within the scattering region of the gun are swept out of the original beam by the strong magnetic field and are therefore not 2 0 The beam chambers and vacuum system have been designed and assembled by George Tikhonov, USC Physics Department (2000). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 dl/\IV"3dd 2Jd3ddOHO Ill ■ z 1 o III 1 z : t m t g III ■ L U U rnl 1 — » _j L U ! > ddddOHO I Figure S.l. Experimental setup used to perform depletion measurements on a neutral CM beam. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 detected (the cyclotron radius is estimated to be ~5 mm). The collision energies used here are approximately a factor of 4 below the dissociation threshold [HAN’97], so electron attachment is the only possible depletion mechanism. The remaining neutral component of the cluster beam follows another 30 cm free flight towards the detector. The detector utilizes the rods and electron bombardment ionizer of a commercial quadrupole analyzer (Ametek, Pittsburgh, PA). However, the Cm mass far exceeds the range of this quadrupole, and therefore we operated it as an ion guide powered by a homebuilt RF generator. In order to distinguish between the real C6 0 signal and the background gas, we employed a lock-in detection technique. The beam of neutral fullerenes was mechanically chopped at a rate of 86 Hz. The analog output of the detector’s Faraday cup, boosted by a current-to-voltage preamplifier (Model 181, EG&G PARC, Princeton, NJ), was fed into a lock-in amplifier (SRS, Sunnyvale, CA) together with a chopper reference signal (see Fig. 5.1). The lock-in output at the reference frequency is proportional to the intensity of the CM beam. Typical lock-in reading for a preamplifier setting of 10‘ 9 A/V was 2-3 mV, corresponding to a Faraday cup current of a few picoamperes. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 5.2 Data Acquisition As mentioned above, a beam depletion technique was used to extract the integral e~ - C 6 o cross sections (Chapter 3). The electron beam is chopped at a rate of 0.25 Hz, which is considerably less than the cluster beam chopping frequency. Therefore, it does not interfere with the lock-in reading of the intensity of the neutral C6 0 beam arriving at the detector. During each electron-on or -off interval, this lock-in reading, V, is continuously measured and the results are stored in computer memory. A beam depletion ratio is then defined as AN /N = (F _ ^ - F _ m)/ f \ ^ . For every electron energy, we accumulated data for approximately 30 minutes to achieve good convergence of the cumulative AN/N. The depletion ratios were ~ (1 -5 )x 10"3 with an estimated accuracy of 10-15%. These magnitudes are comparable to those in the earlier e~ - Na„ scattering experiment. A recipe for calculating the effective interaction cross sections a cff from the depletion ratios AN/N is given in Chapter 3. The energy calibration and resolution measurements has also been described before. In short, the energy spread of the electron gun is well represented by a Gaussian shape with a FWHM « 0.3 eV for collision energies below 1 eV, and approximately 0.4 eV for the higher values. The absolute energy scale is calibrated to an accuracy of about 0.1 eV (see also Eq. (3.3) and discussion in the text). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 Cluster beam velocity was measured by the following method [SCHD’O O ]. The periodic signal detected by the lock-in is not in phase with the chopper reference pulse because it takes a certain time for the clusters to travel from the chopper wheel to the detector. This phase delay, is easily converted into the cluster flight time. To increase accuracy, it is beneficial to place choppers in two different locations along the beam and to record the phase delay for each one. Then the cluster flight time between the chopper wheels is proportional to the phase difference A< p 2 - A< p x , and the cluster velocity is given by vC m = 2 k f Q L/(A<p2 - A< p { ), where f 0 is the beam chopping rate and L is the distance between the choppers (see Appendix C). This technique gave vc . = 210 ±20 m/sec for the source conditions listed above.2 1 5.3 Results and Discussion In Fig. 5.2, open circles represent the effective cross sections obtained on the basis of Eq. (3.1). The solid line in the plot is a smoothing fit drawn as a guide to the eye. The data display a strong rise for decreasing electron energies, indicating the presence of a strong attachment channel. 2 1 The velocity error comes mainly from the unknown shape of the cluster velocity distribution. Our detector unit is particle density sensitive, which means that the measured velocity is slightly different from the mean velocity of clusters passing through the scattering region of our electron gun [SCO’88]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 1000 “ o Experiment — Langevin C apture 8 0 0 - CM ° s I 6 0 0 - tS < 1 ) C O 4 0 0 - (O CO 2 o 2 0 0 - 0.0 1.0 1.5 2.0 0.5 2.5 Electron Energy (eV) Figure 5.2. Open dots: experimental inelastic cross section of free electron scattering at fullerenes. The solid line in the plot serves to guide the eye. Dashed line: Langevin polarization capture cross section, convoluted with the experimental energy resolution. The dashed curve is the Langevin cross section, Eq. (2.4), calculated using the experimental polarizability aC m * 78 A3 [ANT’99, BAL’00] and convoluted with the electron gun energy spread as described in Chapter 3. The experimental data have a general correlation with the Langevin trend for E > 1 eV and for £-> 0. To provide a quantitative basis for this correlation, consider the electron capture as a two-stage process. The first, long-range, stage is governed by the polarization interaction and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 the Langevin curve is a measure of how efficiently the electrons are “drawn to the center” by the cluster’s polarization field. The full Q j formation cross section, however, also reflects how efficiently these trapped electrons “stick” to the fullerenes. We can therefore define a “sticking probability” P via ^c a p tu re ^L angevin ^ ' (5.1) 0.8 - (o 0 .6 - o o O ) .E 0.4“ Oo 0.2 - 0.0 1.0 0.0 0.5 2.0 1.5 2.5 Electron Energy (eV) Figure 5.3. Sticking probability: the probability for an electron, attracted by the polarization field of the cluster, to attach and form long-lived . The solid line is a smoothing fit serving to guide the eye. This is analogous, e.g., to the definition of “survival probability” in the study of electron-molecule dissociative attachment [ING’96]. By taking the ratio of the experimental cross sections to the Langevin value we obtain the result in Fig. 5.3. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 The structure of this curve and the fact that it lies below unity may be interpreted as consequences of attachment selection rules imposed by the high symmetry of the fullerene. It is also interesting that for an electron gun with a perfect energy resolution profile 7 ( £ - £ 0) — ► I0 S (E -E 0), the sticking probability P would be directly proportional to the rate coefficient for anion formation: eti cC *(£„) = \< Jc a r lu r r (v)vf(v-vQ )dv oc j(7c a p lllK (E)EinI ( E - E 0)dE o o » ( 5 . 2 ) W o ^capture ( ^0 ) X & capture ( ^0 ) ^ ( ^0 ) where v is the electron velocity. Most of the published electron attachment results rely on measurements of the negative ion yield versus electron energy. Such an approach gives only relative cross sections unless a separate measurement of the fullerene flux is performed. Furthermore, the strong decrease of electron current at low energies, typical for electron guns, can considerably distort the attachment cross section behavior in this energy range. This may account for the underestimation of the low-energy peak for £ -> 0 in Refs. [HUA’95, ELH’97]. Vostrikov et al. [VOS’95, VOS’Ol] were the first to report integral formation cross sections with a strong low-energy rise. Our results extend to a factor-of-two lower collision energies and, therefore, reflect much higher attachment cross sections. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 The overall contour of our data is in satisfactory agreement with the results of other groups. There is a broad minimum at 0.3-0.4 eV followed by a monotonic rise to about 1 eV. After that the production rate of remains relatively uniform up to «6 eV at which point electron auto-detachment processes become important [HUA'95, ELH'97, VAS'97, VOS'Ol]. The feature around 0.2 eV has been interpreted as either a nuclear-exited Feschbach resonance [JAF'94] or a shape resonance [HUA'95]; it is also present in the data of Refs. [VOS’95, VOS’Ol]. The minimum around 0.4 eV has been ascribed to the onset ofp-wave attachment [VOS’Ol] or to a superposition of s- and p-channels2 2 [WEB'96, FAB'01]. However, identifying the onset regions of different partial-wave contributions is very tentative in view of the evident importance of the long-range polarization field. 5.4 Summary We have performed beam depletion measurements of absolute cross sections for the capture of free low-energy electrons by neutral CM in a crossed-beam configuration. The main results can be summarized as follows. 2 2 Although the E 1 / 2 dependence of Eq. (2.4) happens to look the same as for inelastic s-wave scattering, it is not restricted to the lowest partial wave. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 • Attachment cross section exhibits a strong rise with decreasing energy. • The general trend of our data is correlated with the Langevin theory of electron capture by the polarization field of fullerene particles. This indicates the importance of long-range forces in the interaction of clusters with electrons and ions. • The detailed structure of the cross section curve may be understood on the basis of attachment selection rules (imposed by the high symmetry of CM) and a superposition of different partial wave contributions. This structure manifests itself very clearly via the sticking probability P, i.e., the probability that an electron, drawn to the fullerene surface by the polarization field of the latter, will attach and form a stable anion. Further studies of the dynamics of low-energy electron attachment to fullerenes are required due to several reasons. What are the relevant partial waves (and corresponding thresholds) dominating electron attachment process in the energy range between zero and several eV? What is the precise role of symmetries and Jahn- Teller distortions? Are there any intermediate resonance states and what are their relaxation pathways and time scales? These questions are important for an understanding of fundamental characteristics of fullerenes, of fullerene-electron and fullerene-ion interactions, and of the properties of fullerene-based materials (e.g., Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 conduction electron scattering and electron-phonon coupling in the doped fullerides, etc.) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 References [AGA’99] A.A.Agarkov, V.A.Galichin, S.V.Drozdov, D.Yu.Dubov, and A.A.Vostrikov, Proc. XXIV Intern. Conf. on Phenomena in Ionized Gases (ICPIG), Warsaw, 1999, vol. 4. [AND’97] P.U.Andersson and J.B.C.Pettersson, Z. Phys. D 41, 57 (1997). [ANT’99] R.Antoine, Ph.Dugourd, D.Rayane, E.Benichou. M.Broyer, F.Chandezon, and C.Guet, J. Chem. Phys. 110,9771 (1999). [BAR’96] A.Bartelt, J.D.Close, F.Federmann, N.Quaas, and J.P.Toennies, Phys. Rev. Lett. 77,3525 (1996). [BAL’00] A.Ballard, K.Bonin, and J.Louderback, J. Chem. Phys. 113, 5732 (2000). [BED’71] B.Bederson and LJ.KiefFer, Rev. Mod. Phys. 43,601 (1971). [BER’95] M.Bemath, O.Dragun, M.R.Spinella, and H.Massmann, Z. Phys. D 33, 71 (1995). [BON’97] K.D.Bonin and V.V.Kresin, Electric-Dipole Polarizabilities o f Atoms, Molecules and Clusters (World Scientific, Singapore, 1997). [BOR’O O ] J.Borggreen, K.Hansen, F.Chandezon, T.Dossing, M.Elhajal, and O.Echt, Phys. Rev. A 62,013202 (2000). [BOU’O O ] B.Boudai'ffa, P.Cloutier, D.Hunting, M.A.Huels, and L.Sanche, in Science 287,1658 (2000). [BRE’89] C.Brechignac, Ph.Cahuzac, J.Leygnier and J.Weiner, J. Chem. Phys. 90, 1492 (1989). [BRE’92] C.Brechignac, Ph.Cahuzac, F.Carlier, M. de Frutos, and J.Leygnier, Chem. Phys. Lett. 189, 28 (1992). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 [BRO’99] [BUS’98] [CHR’92] [CHU’96] [CLE’85] [COLE’98] [COLN’68] [COLN’70] [COLN’71] [CON’96] [CON’99] [CON’O O ] [CRO’79] [CRO’80] [DAN’89] P.Brockhaus, K.Wong, K. Hansen, V.Kasperovich, G.Tikhonov, and V.V.Kresin, Phys. Rev. A 59,495 (1999). R.Busani, M.Folkers, O.Cheshnovsky, Phys. Rev. Lett. 81, 3836 (1998). W.Christen, K.-L.Kompa, H.Schroder, and H.Sttilpnagel, B.Bunsenges. Phys. Chem. 96, 1197 (1992). A.Chutjian, A.Garscadden, and J.M.Wadehra, Phys. Rep. 264, 6 (1996). K.Clemenger, Phys. Rev. B 32, 1359 (1985). C.P.Collier, T.Vossmeyer, J.R.Heath, Ann. Rev. Phys. Chem. 49, 371 (1998). R.E.Collins, Ph.D. Thesis, New York University, New York, 1968. R.E.Collins, B.B.Aubrey, P.N.Eisner, and RJ.Celotta, Rev. Sci. Instrum. 41,1403(1970). R.E.Collins, B.Bederson, and M.Goldstein, Phys. Rev. A 3, 1976 (1971). J.-P.Connerade and A.V.Solov’yov, J. Phys. B 29, 365 (1996). J.-P.Connerade, L.G.Gerchikov, A.N.Ipatov and A.V.Solov'yov, J. Phys. B 32, 877 (1999). J.-P.Connerade, L.G.Gerchikov, A.N.Ipatov, and S.Sentiirk, J. Phys. B 33, 5109 (2000). J.L.Cronin, Spectra-Mat Incorporated, Practical Aspects o f Modern Dispenser Cathodes (Watsonville, CA, 1979). J.L.Cronin, Spectra-Mat Incorporated, Modern Dispenser Cathodes (Watsonville, CA, 1980). A.Danon and A.Amirav, J. Phys. Chem. 93, 5549 (1989). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 [ELH’97] [FAB’Ol] [FED’93] [FIN’95] [FRI’88] [FRO’97] [GAL’91] [GER’97] [GER’97a] [GER’97b] [GOE’95] [GUE’97] [HAB’83] [HAN’97] [HAN’99] O.Elhamidi, J.Pommier and, R.Abouaf, J. Phys. B 30,4633 (1997). I.I.Fabrikant and H.Hotop, Phys. Rev. A 63,022706 (2001). S.Fedrigo, W.Harbich, J.Belyaev, and J.Buttet, Chem. Phys. Lett 211, 166(1993). C.D.Finch, R.A.Popple, P.Nordlander, and F.B.Dunning, Chem. Phys. Lett. 244,345 (1995). P.G.Friedman, KJ.Bertsche, M.C.Michel, D.E.Morris, R.A.Muller, and P.P.Tans, Rev. Sci. Instrum. 59, 98 (1988). P.Frobrich, Ann. Physik 6,403 (1997). Galileo Electro-Optics Corporation, Channeltron Electron Multiplier Handbook for Mass Spectrometry Applications (Sturbridge, MA, 1991). L.G.Gerchikov and A.V.Solov’yov, Z. Phys. D 42,279 (1997). L.G.Gerchikov, A.V.Solov’yov, J.-P.Connerade, and W.Greiner J. Phys. B 30,4133 (1997). L.G.Gerchikov, A.N.Ipatov, and A.V.Solov’yov, J. Phys. B 30, 5939 (1997). A.Goerke, G.Leipelt, H.Palm, C.P.Schulz, and I.V.Hertel, Z. Phys. D 32,311 (1995). C.Guet, X.Biquard, P.Blaise, S.A.Blundell, M.Gross, B.A.Huber, D.Jalabert, M.Maurel, L.Plagne, and J.C.Rocco, Z. Phys. D 40, 317 (1997). H.Haberland and M.Winterer, Rev. Sci. Instrum. 54, 764 (1983). K.Hansen and O.Echt, Phys. Rev. Lett. 78,2337 (1997). K.Hansen and U.Naher, Phys. Rev. A 60,1240 (1999). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 [HEE’87] [HEE’93] [HOR’89] [HUA’95] [ILL’98] [ING’96] [IPA’98] pPA’98a] [JAC’75] [JAF’94] [JAH’37] [KAS’99] [KAS’O O ] [KAS’O O a] W.A. de Heer, W.D.Knight, M.Y.Chou and M.L.Cohen, in Solid State Physics, vol.40, ed. by H.Ehrenreich and D.Tumbull (Academic, New York, 1987). W.A. de Heer, Rev. Mod. Phys. 65,611 (1993). P.Horowitz and W.Hill, The Art o f Electronics (Cambridge University Press, Cambridge, 1989). J.Huang, H.S.Carman, Jr., and R.N.Compton, J. Phys. Chem. 99, 1719(1995). E.Illenberger and B.M.Smimov, Usp. Fiz. Nauk 168, 731 (1998) [Phys. Usp. 41,651 (1998)]. O.Ingolfsson, F.Weik, and E.Illenberger, Int. J. Mass Spectrom. Ion Processes 155,1 (1996). A.Ipatov, J.-P.Connerade, L.G.Gerchikov, and A.V.Solov'yov, J. Phys. B 31, L27 (1998). A.N.Ipatov, V.K.Ivanov, B.D.Agap'ev, and W.Ekardt, J. Phys. B 31, 925 (1998). J.D.Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975). T.Jaflke, E.Illenberger, M.Lezius, S.Matejcik, D.Smith, and T.D.Mark, Chem. Phys. Lett. 226,213 (1994). H.AJahn, and E.Teller, Proc. R. Soc. London Ser. A 161,220 (1937). V.Kasperovich, G.Tikhonov, K.Wong, P.Brokhaus, and V.V.Kresin, Phys. Rev. A 60, 3071 (1999). V.Kasperovich, K.Wong, G.Tikhonov, and V.V.Kresin, Phys. Rev. Lett. 85,2729 (2000). V.Kasperovich, G.Tikhonov, K.Wong, and V.V.Kresin, Phys. Rev. A 62,063201 (2000). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 [KAS’Ol] [KAS’Ola] [KEE’87] [KEI’99] [KEL’97] [KLO’94] [KNI’84] [KNI’85] [KRE’91] [KRE’92] [KRE’94] [KRE’98] [KRE’98a] [KRE’98b] V.Kasperovich, G.Tikhonov, and V.V.Kresin, Chem. Phys. Lett. 337, 55 (2001). V.Kasperovich, K.Wong, G.Tikhonov, and V.V.Kresin, XX Intern. Symp. on Small Particles and Inorganic Clusters (ISSPIC), Atlanta, 2000; submitted to Eur. Phys. J. D, November (2000). R.G.Keesee, A.W.Castleman, Jr., and T.D.Mark, in Swarm Studies and Inelastic Electron-Molecule Collisions, edited by L.C.Pitchford, B.V.McCoy, A.Chutjian, and S.Trajmar (Springer, New York, 1987). M.Keil, T.Kolling, K.Bergmann, and W.Meyer, Eur. Phys. J. D 7, 55- 64 (1999). S.Keller, E.Engel, H.Ast, and R.M.Dreizler, J. Phys. B 30, L703 (1997). C.E.Klots, J. Chem. Phys. 100, 1035 (1994). W.D.Knight, K.Clemenger, W.A. de Heer, W.A.Saunders, M.Y.Chou, and M.L.Cohen, Phys. Rev. Lett. 52,2141 (1984). W.D.Knight, K.Clemenger, W.A. de Heer, and W.A.Saunders, Phys. Rev. B 31, 2539 (1985). V.V.Kresin, Ph.D. Thesis, University of California, Berkeley, 1991. V.V.Kresin, Phys. Rep. 220,1 (1992). V.V.Kresin, A.Scheidemann, and W.D.Knight, in Electron Collisions with Molecules, Clusters, and Surfaces, ed. by H.Ehrhardt and L.A.Morgan (Plenum, New York, 1994). V.V.Kresin and W.D.Knight, in Pair Correlations in Many-Fermion Systems, ed. by V.Z.Kresin (Plenum Press, New York, 1998). V.V.Kresin, V.Kasperovich, G.Tikhonov, and K.Wong, Phys. Rev. A 57, 383 (1998). V.V.Kresin, G.Tikhonov, V.Kasperovich, K.Wong, and P.Brockhaus, J. Chem. Phys. 108,6660 (1998). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 9 [KRE’99] [KUR’79] [LAND’76] [LAND’77] [LAND’84] [LANG’05] [LIN’99] [MAT’99] [MCD’89] [MCH’89] [MIL’99] [NAH’97] [OMA’65] [PIN’98] V.V.Kresin and C.Guet, Philos. Mag. B 79, 1401 (1999). E.A.Kurz, Am. Lab. 11,67 (1979). L.D.Landau and E.M.Lifshitz, Mechanics, 3rd ed. (Pergamon, Oxford, 1976), Sec. 18. L.D.Landau and E.M.Lifshitz, Quantum Mechanics, 3rd ed. (Pergamon, Oxford, 1977), Sec. 147. L.D.Landau, E.M.Lifshitz, and L.P.Pitaevskii, Electrodynamics o f Continuous Media, 2nd ed. (Pergamon, Oxford, 1984), Sec. 3. P.Langevin, Ann. Chim. Phys. 5,245 (1905). B.Lincoln, Galileo Electro-Optics Corporation, private communication. S.Matejcik, P.Stampfli, A.Stamatovic, P.Scheier, and T.D.Mark, J. Chem. Phys. Ill, 3548 (1999). E.W.McDaniel, Atomic Collisions: Electron and Photon Projectiles (Wiley, New York, 1989). K.M.McHugh, H.W.Sarkas, J.G.Eaton, C.R.Westgate, and K.H.Bowen, Z. Phys. D. 12,3 (1989). P.Milani and S.Iannotta, Cluster Beam Synthesis o f Nanostructured Materials (Springer, Berlin, 1999). U.Naher, S.Bjomholm, S.Frauendorf, F.Garcias, and C.Guet, Phys. Rep. 285,245 (1997). T.F.O’Malley, Phys. Rev. 137 A, 1668 (1965). J.C.Pinare, B.Baguenard, C.Bordas, and M.Broyer, Phys. Rev. Lett. 81,2225(1998). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 [RAY’99] [SCHA’00] [SCHD’O O ] [SCHE’95] [SCHM’98] [SCHM’99] [SCHW’99] [SCO’88] [SENN’99] [SENT’O O ] [SMI’96] [SPA'48] [SPI'96] [SPI'98] [STAF'80] D.Rayane, A.R.Allouche, E.Benichou, R.Antoine, M.Aubert-Frecon, Ph.Dugourd, M.Broyer, C.Ristori, F.Chandezon, B.A.Huber, and C.Guet, Eur. Phys. J. D 9,243 (1999). R.Schaeffer, ABB Extrel, private communication. A.A.Scheidemann, private communication. M.K.Scheller, R.N.Compton, and L.S.Cederbaum, Science 270, 1160 (1995). M.Schmidt, R.Kusche, B. von IssendorfF, and H.Haberland, Nature 393,238(1998). M.Schmidt, C.Ellert, W.Kronmiiller, and H.Haberland, Phys. Rev. B 59, 10970 (1999). L.Schweikhard, A.Herlert, S.Kriickeberg, M.Vogel, and C.Walther, Philos. Mag. B 79, 1343 (1999). Atomic and Molecular Beam Methods, ed. by G.Scoles, Vol. I (Oxford, New York, 1988). G.Senn, D.Muigg, G.Denifl, A.Stamatovic, P.Scheier, and T.D.Mark, Eur. Phys. J.D 9 , 159(1999). S.Sentiirk, J.-P.Connerade, D.D.Burgess, and N.J.Mason, J. Phys. B 33, 2763 (2000). D.Smith and P.Spanel, J. Phys. B 29, 5199 (1996). K.R.Spangenberg, Vacuum Tubes (McGraw-Hill, New York, 1948). M.R.Spinella, M.Bemath, and O.Dragun, and H.Massmann Phys. Rev. A 54,2197 (1996). M.R.Spinella, M.Bemath, and O.Dragun, Phys. Rev. A 58, 2985 (1998). G.C.StafFord, Environ. Health Perspect. 36,85 (1980). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 [STAM’91] [TAN’95] [TIG’92] [TIK’Ol] [TIK’**] [TOS’94] [VAS’97] [VOG’54] [VOL’88] [yOS’88] [VOS’95] [VOS’Ol] [WAN’91] [WEA’87] A.S.Stamatovic and T.D.Maerk, Rapid Commun. Mass Spectrom. 5, 51 (1991). B.K.Tanner, Introduction to the Physics o f Electrons in Solids (Cambridge University Press, Cambridge, 1995). J.Tiggesbaumker, L.Roller, H.O.Lutz, and K.H.Meiwes-Broer, Chem. Phys. Lett. 190,42 (1992). G.Tikhonov, K.Wong, V.Kasperovich, and V.V.Kresin, to be published. G.Tikhonov, Ph.D. Thesis, University of Southern California, in preparation. E.Tosatti and N.Manini, Chem. Phys. Lett. 223, 61 (1994). Y.V.Vasil’ev, R.F.Tuktarov, and V.A.Mazunov, Rapid Commun. Mass Spectrom. 11,757 (1997). E.Vogt and G.H.Wannier, Phys. Rev. 95, 1190 (1954). M.Vollmer, K.Selby, V.Kresin, J.Masui, M.Kruger, and W.D.Knight, Rev. Sci. Instrum. 59, 1965 (1988). A.A.Vostrikov, D.Yu.Dubov, and M.R.Predtechenskii, Sov. Phys. Tech. Phys. 33, 1153 (1988). A.A.Vostrikov, D.Yu.Dubov, and A.A.Agarkov, Pis’ma Zh. Tekh. Fiz. 21, 55 (1995) [Tech. Phys. Lett. 21, 517 (1995)]. A.A.Vostrikov, A.A.Agarkov, and D.Yu.Dubov, High Temp. 39, 22 (2001). L.-S.Wang, J.Conceicao, C.Jin, and R.E.Smalley, Chem. Phys. Lett. 182,5(1991). CRC Handbook o f Chemistry and Physics, ed. by R.C.Weast, 67th ed. (CRC Press, Boca Raton, 1987). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 [WEB’96] J.M.Weber, M.-W.Ruf, and H.Hotop, Z. Phys. D 37, 351 (1996). [WEB’99] J.M.Weber, E.Leber, M.-W.Ruf, and H.Hotop, Eur. Phys. J. D 7, 587 (1999). [WEB’99a] J.M.Weber, E.Leber, M.-W.Ruf, and H.Hotop, Phys. Rev. Lett. 82, 516(1999). [WEB’O O ] J.M.Weber, I.I.Fabrikant, E.Leber, M.-W.Ruf, and H.Hotop, Eur. Phys. J. D 11,247 (2000). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 Appendix A High Vacuum Mount o f the Electron Gun and C EM Detector A.l Electron Gun In our experiments, we use essentially the same electron gun that has been described in Ref. [KRE’91, KRE’94]. To have more flexibility in positioning, the gun is mounted on a movable high vacuum feedthrough, which allows a vertical travel of about 5 cm (see Fig. A.la). The two stainless steel rods serve as guiding rails to prevent any axial twisting of the electron gun assembly. In this configuration, the alignment procedure can be performed in the following way. One puts a light source behind the skimmer and looks through the telescope aligned with the cluster beam (Fig. 3.1). The position of the electron gun is optimized until the skimmer’s hole appears vertically in the center of the scattering region aperture. During the experiment, the alignment quality may be verified by looking for the maximum counting rate for clusters passing the scattering region. If necessary, the optimization procedure can be repeated for the horizontal direction: small misalignments can be compensated by moving the experimental chamber, connected to the beam apparatus with two flexible bellows. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) Front V ie w Side V ie w (b) 94 C O T3 tLU tm c o as Figure A.I. detector (b). High vacuum mount of the electron gun (a) and the channeltron Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Channeltron 05 9 5 The main drawback of this movable design is a reduced cooling rate of the electron gun assembly. In the earlier setup, the heat emitted by the cathode was efficiently dissipated in the iron base plates, directly connected to the top of the scattering chamber. This problem was solved by connecting two water-cooled brass blocks along the base plates.2 3 Water was delivered by a pair of flexible stainless steel tubings. We have to admit that this cooling system was a source of constant headache in the experiments since it had a tendency to leak. To reduce the risk of demagnetizing, the permanent magnets used for the electron beam collimation were screened from the direct heat by a pair of aluminum shields. A.2 Channeltron A.2.1 High Vacuum Mount Sitting next to the electron gun in Fig. A.lb is the Channeltron detector mount. Its particular design was greatly affected by the lack of available free space in the scattering chamber. The channeltron mounting plate is connected to a pair of stainless steel rods through a long aluminum arm. One of them bears a guiding function while the other is, in fact, the shaft of a high vacuum feedthrough that 2 3 The contact quality can be improved by sandwiching a thin copper foil between the blocks and plates. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 provides a vertical (Z) displacement of the system. Specially designed stainless steel “pants” securely hold the rods in place to prevent mutual twisting. The entire gadget is suspended from a homebuilt XY-stage, which allows about 12 mm linear travel in each direction. The CEM detector operation requires a high voltage to be delivered to the channeltron. This is realized via a set of tinned copper wires attached to a 4-pin high voltage feedthrough entering the scattering chamber from a side. These wires are coated by a number of fine ceramic beads to reduce the risk of a shortcut between them and to the ground. The electric feedthrough has a voltage rating of up to 10 kV for each pin. The channeltron output (anode) is terminated by a regular 50Q BNC cable via a high voltage capacitor. This dc decoupling is required to protect the pulse counting electronics from the constant high voltage applied to the anode. The signal leaves the scattering chamber through a high vacuum male-to-male BNC connector. Note the orientation of the conversion dynode and the multiplier glass cone in Fig. A.lb. This is done to minimize the effect of the focusing magnetic field (see Chapter 3) on the ion detection process. We found that the value of this field can be as high as 1 kG at close approach to the electron gun. However, it is mainly confined in the horizontal plane and directed normally to the cluster beam flight pass. The Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 negative ions2 4 bom in the collision region are detected via the conversion dynode stage as described in Chapter 4. Upon impact the particle breaks into pieces and positive fragments are guided by the electric field towards the multiplier cone. To make the effect of the magnetic field minimal, the electric and magnetic fields are made parallel to each other (Fig. A.lb). Now, the magnetic field tends to curl the charged fragments over the E -lines providing extra focusing for those particles that have non vanishing velocity components along the dynode surface. As mentioned in Chapter 4, this detection scheme significantly improves the signal-to-noise ratio by reducing the detection probability for stray electrons. The background noise level was decreased even more when we installed a thin molybdenum plate with a small hole (07mm) behind the scattering region (Fig. A.lb). Its purpose is to hide the electron emitting cathode from a direct view of the channeltron detector. The plate is attached to the electron gun iron base plates and electrically isolated from them by thin layers of mica. During the experiments a small extracting voltage of approximately 5 V was applied to this molybdenum plate to guide the negative cluster ions exiting the scattering region into the channeltron detector. 2 4 The influence of the magnetic field on the trajectories of these negative ions is taken into account explicitly in calculation of the escape probability in Appendix G. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 8 A.2.2 Circuitry A schematic view of our channeltron2 5 (Detector Technology 402-25-HG, Palmer, MA) on a factory mount is shown in Fig. A.2. This unit is designed to operate in a pulse counting mode (typical gains of 107 to 10* at 2-3 kV applied across the multiplier), which is consistent with the weak ion signals detected in our experiment (nominally, the channeltron can resolve up to 50 millions incident particles per second). The device manual recommends ambient pressure level for the safe operation to be better than 10"* torr. 73mm 44mm 38mm <—25 mm 27mm 11mm DIA Figure A.2. Schematic view of the channeltron on a factory mount. 2 5 The multiplier we used is a modified 402A-H model incorporating a 25 mm size cone with a grid over it. This gives the origin to the additional information in the part number. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 In our design, the voltages supplied to the channeltron play a dual role. On one hand, they create a potential difference of about 2-3 kV across the channel to generate appropriate electron avalanche. Indeed, in the pulse counting regime, the multiplier should register every single particle entering the detector. On the other hand, these voltages preaccelerate the entering anions, which originally have energies of several eV. This preacceleration is very important in our case since cluster ions are relatively heavy particles [GAL’91]. +5 kV +3 kV 1 nF Channeltron 50 Q Pulse C o u n ting E le ctro n ics Conversion Dynode -100 V - 3 kV 1 nF Channeltron son Pulse C o u n tin g E le ctro n ics Conversion Dynode +6 kV Figure A.3. Two distinct detection modes for negatively charged clusters in our CEM detector. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 Summarized in Fig. A.3 are two distinct negative ion detection modes on the basis of our channeltron multiplier.2 6 In Fig. A.3a, negative ions are fed straight into the channeltron, the conversion dynode performing only a deflection function. There are several drawbacks to this regime. First of all, in order to accelerate the incoming particle, the multiplier cone should be biased to high positive voltage of 2-3 kV, which makes it necessary to raise the CEM anode potential to even higher values: 4- 5 kV. Practically, this is not very convenient since the latter should be connected to the highly sensitive pulse counting electronics. A commonly used solution for this complication is dc decoupling via a high voltage capacitor:2 7 it blocks the strong dc component while tiny ac pulses are free to pass. However, the possibility to demolish the counting electronics is not entirely eliminated. Indeed, if due to some failure the power supply connected to the CEM anode momentarily goes to the ground level, all the energy stored inside the capacitor (Fig. A.3a) is released into the counting circuit in the form of a short, high-amplitude pulse causing severe damage to the equipment.2 8 Secondly, the detection mode in Fig. A.3a does not discriminate against 2 6 The resistance in the figure is two 1 Mfi resistors (Kobra precision high voltage resistors) connected in series. 2 7 Such an option is realized in our design on the basis of a 1000 pF ceramic disk capacitor rated to 15 kV (Murata Electronics DHR22ZM102M15K, Lake Forest, CA). 2 8 We did experience such an episode, which cost us a repair of the preamplifier unit. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101 stray electrons which are abundant in our experimental configuration. This is a very adverse effect in view of the low counting rate from the negative cluster ions. Finally, when connecting separate power supplies across the channel, one may find that the applied voltages sometimes do not coincide with the dial settings. This can be easily understood by drawing the circuit diagram of the connection replacing the channeltron by the equivalent resistor of -100-200 MQ and including the input resistances of the power supplies. In selected models, the latter could be as high as 100 MQ. The circuit in Fig. A.3b, on the other hand, is deprived of all these shortcomings. The ions are accelerated by a stand-alone conversion dynode stage to high energies of up to 6 keV. This mode allows good detection efficiency in the first place and, simultaneously, screens copious background electrons. Indeed, the high negative potential of the channeltron cone prevents stray electrons from passing into the multiplier. They, nevertheless, can be detected through the conversion dynode by sputtering a positive particle from the surface, but this is a much less probable process than the emission of secondaries in Fig. A.3a. Since the cone is highly negative, the CEM anode can be grounded, which removes the necessity to decouple the counting electronics and all the problems related to that. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 Appendix B Cathode Activation Procedure Electrons in our gun are generated by a tungsten-base dispenser cathode [CRO’80]. In this type of emitters, the porous W matrix acts as a reservoir for Ba, which serves as an electron emitting material. The latter is originally stored in oxidized sate, BaO. At the operating temperature, barium becomes free via a certain chemical reaction, diffuses to the surface, and forms a low work-function layer that produces electrons through the thermionic emission. We utilize the well-known 3-1- 1-80 type. This means that our cathode contains 80% W, and 3-1-1 stands for 3BaO:CaO:Al2 0 3 which indicates the chemical composition of the impregnant. The dispenser cathodes are more contamination tolerant and have better emission characteristics than traditional oxide units. The emitters are supplied by Spectra-Mat, Inc. (Watsonville, CA) in a custom shape kindly shared by Professor L. Vuskovic (Old Dominion University). According to the supplier’s technical bulletin, the dispenser cathode should not be exposed to atmospheric conditions for more than 48 hours. The barium-calcium- aluminate is very hydroscopic [CRO’79]. It will readily absorb moisture converting the oxides into carbonates which results in volume expansion and discharge of the impregnant from the pores of the tungsten matrix {blooming). When the shipping Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 ampoule is broken, it is recommended to transfer the emitter into a vacuum o f 10'3 torr or better reasonably soon. Typically, it took us up to one hour to completely install the electron gun with the cathode into the setup. In general, the cathode activation procedure is very simple. One slowly ramps up the temperature (the heater power) until the electron emission is observed. There are several aspects to pay attention to. • The pressure in the chamber should never go above 10"6 torr during the activation process. If this happens, the heater power should be reduced until the pressure recovers. Otherwise, the heater may become poisoned. • When the power is applied to the cathode for the first time, the unit will outgas a lot. Usually ramping the heater current in 0.1 A increments for every 10-15 minutes is a sufficiently slow rate to keep the pressure in the chamber at the safe level. This may take hours. • If the heater power is increased too fast so the moisture cannot escape, then hydroxides and carbonates may be formed. This not only reduces the emission capabilities but also causes blistering and cracking of the emitting surface. To prevent this, the cathode must “bake” at 200-400°C long enough to allow complete outgassing of the water vapor. • The electron emission is the best indicator of the activation. It starts usually at about 1000°C. However, the activation rate may vary and is a direct function of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 the cathode age, poisoning level, and temperature. Typically, older emitters should be heated up more to reach the required level o f emission. The cathode temperature should never exceed 1200°C, a limit imposed by the safe operation conditions of the cathode heater. During the experiments, the cathode was usually operated at the following conditions: Ic a lh = 5 - 6 A and V c a lh = 15 - 20 V. • A cooled dispenser cathode can be exposed to air again, however it will be exceptionally sensitive to humidity and contamination. The cathode can be subsequently reactivated following the guidelines above. Note that the outgassing time may become considerably shorter. Monitoring the pressure in the chamber, one may ramp the heater current by, e.g., 0.2-0.3 A every 5-10 minutes. Temperature of the surface is one of the key parameters during the activation process. It turned out, however, that the reading of a thermocouple attached to the cathode bottom was a few hundreds degrees below the actual surface temperature, as verified by a pyrometric measurement (Fig. B.l). Nevertheless, the cathode temperature can be reasonably estimated from the following relation:2 9 T ^ (‘C ) = ^P -T ,-273, (B.l) where R(T) is the value of the cathode heater resistance for a certain power input and is the resistance at room temperature T 0. The reference value can be Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 measured directly before installing the cathode in the electron gun. The value for R(T) can be obtained from the following simple routine. While ramping the current Ic a th > read the voltage V C ( l l h applied to the cathode heater when the temperature of the system is stabilized (usually 10-15 minutes after the power input change). The ratio V c a th / 1 c m h is equal to R(T) + Rm KS, where Rw in, is the known resistance of wires connecting the heater to the power source. 1000 ^ 800 2 600 © 400 200 - 2.5 3.0 2.0 Resistance (Q) Figure B.l. Cathode surface temperature calibration chart. Solid squares: pyrometric measurement. Open dots: reading of the mount thermocouple. Line: estimate on the basis of Eq. (B.l). 2 9 It is based on the linear increase of the resistance of the cathode heater with temperature. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 The solid line in Fig. B.l is calculated from Eq. (B.l) using values of V calh and Ic a lh taken during a pyrometric surface temperature measurement (solid squares). Obviously, the change in the ohmic resistance of the heater can be used to calibrate the cathode surface temperature scale. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 Appendix C Cluster Beam Velocity Measurement C.l Sodium Clusters: Pulse Counting Detection Our cluster velocity measurement is very similar in spirit to the laser-induced beam depletion method described in detail in [VOL’88]. The cluster beam is repeatedly blocked and opened by a mechanical chopper which is a rotating metal wheel with two holes in it (Fig. 3.1). This makes the cluster counting rate oscillate with the same periodicity. However, there is a clear phase shift between the reference and cluster signal associated with the delayed appearance of clusters at the detector. Indeed, when the chopper wheel opens the beam, it takes a certain time t for the majority of clusters to reach the detection region because of their finite velocity. This flight time can be monitored and measured by recording the signal intensity versus time passed since the beam is opened. Our PC is equipped with a plug-in multichannel scaler (MCS) board which allows a time resolution down to 10//sec. A typical experimental MCS profile is shown in Fig. C.l. Note that the cluster signal rises and falls gradually which is a signature of the intrinsic velocity spread in the beam. To avoid detector time delay errors, it’s beneficial to place choppers in two Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 V ) ■ 4 -t c 3 0.8 (0 CM < D C O o: 0.6 .c o> .£ 0.4 c O 0.2 0.0 0.0 0.5 5 2.0 2.5 3.0 3.5 4.0 Time (ms) Figure C.l. Typical MCS profiles from two choppers shown in Fig. 3.1 different locations along the beam and compare the MCS profiles for each of them (Fig. C.l). The exact shape of the cluster velocity distribution can be precisely and automatically extracted from this measurements [TIK.’**]. However, there is no velocity selection in our experiment, so Eq. (3.1) contains the average velocity of clusters vc l in the beam. And the latter quantity can be directly estimated from the chopped signal behavior. For each MCS profile, one finds the time moment when the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 9 cluster counting rate gains about 50% of its full strength3 0 (see times /, and t2 in Fig. C.l). The time difference At = t2- t l is approximately equal to the average cluster flight time between the chopper wheels.3 1 Then vc / can be evaluated as L /A t, where L is the distance between the chopper wheels ( L «1.25 m in our setup). It turns out that this simple procedure gives cluster velocities which are in better than 1% agreement with values obtained from the sophisticated procedure described in [TIK’**]. Selected results of our measurements are given in Table C.l. Every velocity value in this table is averaged over several data acquisition cycles with varied direction of rotation of the chopper wheels. Our results are in good agreement with earlier photo-depletion measurement,3 2 Ref. [KRE’91]. The data for medium-sized clusters were recorded at the following conditions of the supersonic source: Tm urct=605 °C, 7^„/ ( . = 760 °C, and PA r =6.5 bars. The average rate for 3 0 One should be careful when choosing the right signal “bump”. For too low time resolution setting, more than one full signal-on signal-off period may appear in the MCS profile. Sometimes, one can even see the bump from the previous on-off session. This complication is easily eliminated by changing the MCS time scale: the right signal pulse should change its location accordingly with respect to the origin. 3 1 The deconvoluted velocity profile appears slightly asymmetric as will be shown in [TIK’**]. This means that the average velocity in the beam is a little bit off the profile’s maximum. 3 2 The average cluster beam velocity may be influenced by several factors, such as stagnation pressure, source conditions, and the nozzle shape. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 nanoparticles produced in the condensation source was measured at: T o v e n =380°C, T n o zd e = 100 °C, and PH e = 1 .8 torr. Cluster Size Cluster velocity calculated directly from MCS profiles (m/sec) Average velocity measurement by the method of [TIK’**] (m/sec) Relative Difference (% ) Naw 10971 15 109813 0.1 10331 15 103912 0.6 NaS 7 1022120 102713 0.5 Najg 1022 1 20 102612 0.4 Na7 0 1016130 102012 0.4 Na„ (n~l0,000) 22713 229.110.3 0.9 Table C. 1. Cluster velocities obtained directly from the MCS profiles. C.2 Fullerenes: Analog Detection The velocity measurement for frillerenes is very similar in spirit to the procedure described above. The CM beam is repeatedly blocked, and the velocity estimate is obtained from the delayed appearance of the cluster signal at the detector comparing Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I ll to the chopper reference pulse. This accrued signal phase shift A < p was measured concurrently to the cluster beam intensity by the lock-in amplifier (see Chapter 5 for details). It is easily converted into the cluster flight time. Indeed, A<p-< u 0 / = 2jcf0-t, where /„ is the chopping frequency and / is the flight time from the chopper wheel to the detector. The average cluster velocity vc is, therefore, equal to l/t where / is the known flight pass. As mentioned above, it’s beneficial to place choppers in two different location along the beam to eliminate any detector time delay that may underestimate the velocity measured. Then the cluster flight time between the chopper wheels is proportional to the phase difference AO = A< p 2 - A< p x, and the cluster velocity is given by: vc (C.1) c“ AO where L is the distance between the choppers. Using technique above, we found vc = 210 ±20 m/sec for the following source conditions: T m m =580°C and T m zdt =690°C. This result is the average for several different chopping frequencies in the range from 90 to 200 Hz. The main uncertainty source in this estimate is the unknown shape of the cluster beam velocity distribution. Our detector utilizes an electron ionizer which produces ion counting rate that is proportional to the cluster beam density. Therefore, the average particle Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 speed measured at the detector is slightly different from the mean velocity of clusters flying through the scattering region of the electron gun [SCO’88]. The example of particle flow through a thin-wall orifice shows that this difference is on the order of 10% [SCO’88]. So we assumed this to be a reasonable estimate for our source. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 Appendix D Beam Depletion Ratio and the Total Cross Section o f Inelastic Scattering D.l Main Equation As discussed in Chapter 3, the absolute cross sections of the inelastic electron- cluster interaction are calculated from the measured depletion of the cluster beam. Here we show how these quantities are related to each other. In the following, we will disregard the cluster displacement in the interaction volume during the scattering event, since incident electrons are moving much faster. Indeed, even for E = 0.01 eV, which is inaccessibly low energy for our technique, the electron velocity is almost two orders of magnitude higher than the average cluster speed (-1000 m/sec). The schematic representation of the interaction volume is given in Fig. D.l. Front View Side View 1 1 r Nan------► * td y dx A I Figure D. 1. Schematic view of the electron-cluster interaction volume. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 The integral cross section of the electron-cluster inelastic scattering is defined as: where Je represents electron current density and Ne - the number of inelastically beam of electrons of current density Jt is incident on a stationary target (cluster), Consider the interacting beams inside small volume hdxdy as shown in Fig. D.l. Then, the reduction of the electron current density over the span dy is given by: where nc l is the density of clusters in the scattering region.3 4 Using the cross section definition, Eq. (D.2) can be transformed into: Integrating (D.3) over y , one finds the total attenuation of the electron current density in the volume h2 d x(see Fig. D.l): 3 3 While it is a very general definition, the cross section in our measurement represents only those channels of electron-cluster inelastic scattering that result in an appreciable cluster beam depletion. So, Ne in our case is the number of inelastically scattered electrons per unit time which reduce the cluster flux. 3 4 In (D.2), {hdxdy)nc , is the number of scatterers in the volume. (D.l) scattered electrons per unit time.3 3 This definition should be understood as follows: a and Ne parameter gives the number of inelastic scattering events per unit time. (D.2) d J e = -J e{y)<jnc ,dy. (D.3) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 A7e = y °( \ - e-andh), (D.4) where J° is the electron current density before entering the scattering region. In our experiments, crndh is expected to be much smaller than unity (the cluster beam density is very low), so we can expand the exponent in Eq. (D.4) in powers of this parameter: A Je » J°(Tnclh . (D.5) In principle, the cluster density in (D.5) is not constant over the interaction volume. Indeed, if there is a substantial depletion of the cluster beam, the cluster flux will vary with x (Fig. D.l), and this change will be reflected in the behavior of the cluster density nd (x) according to:3 5 = (D.6) Vcl where Jd(x) is the cluster current density, and vc / is the beam velocity. An inelastic collision event equally depletes the electron and cluster beams: AJe (hdx) = dJcl(h2). (D.7) Combining Eqs. (D.5)-(D.7), we find: 3J w • . - r.> , / \ . 5 d X . Indeed in Fig. D.l, Jd {x)h2— is the number of clusters inside the volume Vc/ h2dx. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 d J c, _ ( T j ^ d x ( D 8 ) JA x ) v , Integrating this equation over the scattering volume, Fig. D.l, gives the total reduction of the cluster current density A Jd , in a form analogous to Beer’s law for gas scattering: A \T A I l - e •' = l - e (D.9) N d J cl where ld is the electron number current, and ANcl/N c l is the experimentally determined relative depletion of the cluster counting rate. If the latter is relatively small, we can treat rtc , (x) in (D.5) as a constant, and repeating all the steps above, one arrives to: (D.10) Nd vc l h which is, in fact, the leading term in the expansion of exponent in Eq. (D.9). In the following, we will show how expression (D.10) should be changed for experimental techniques, which are handicapped in terms of energy, velocity, and/or mass resolution.3 6 3 6 In principal, this also can be done for Eq. (D.9). However, the corrections discussed below would have to be calculated self-consistently and numerically. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 For experiments with limited electron energy resolution , ANcl arises from the interaction of clusters with electron beam which has a certain energy profile /(£-£„): tWd = f a ( E ) d E = -Z * -'fo (E )l(E -E ,)J E , (D.U) " Vcl " 0 where Anc , is a portion of cluster flux which was scattered by the electrons in the narrow collision energy range (E, E+dE). It is convenient to introduce the effective cross section <x^(£0), which is the convolution of the intrinsic cross section cr(£) with the electron energy spread3 7 [WEB’96, VOS’Ol]: ao |< r ( £ ) /( £ - £ 0)d£ <?'ff(Eo) = S L ^ --------------------• (D.l 2) f l ( E - E 0)dE 0 From Eqs. (D.l 1) and (D.l2), we find: (D.13) N „ ” vdh' ao where Ie l = j l ( E - E 0)dE is the cumulative number of electrons with all energies: 0 the number current measured experimentally. 3 7 This is merely the averaging of cr(£ ) over the electron energy distribution. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 118 Furthermore, if we do not perform velocity selection of clusters entering the scattering volume, the experimental value for A Ncl is effectively summed over the cluster velocity profile: co - c o / \ *Nd = \Anc l (v)dv = aeg , (D. 14) 0 " 0 v where nd (y)dv is the portion of the cluster flux that has velocities in the range from v to v+ dv . Since electrons are moving much faster than clusters, < J eg should not strongly depend on the cluster velocity, and can be treated as constant factor in Eq. ao (D.14). Remembering that Nc l = jn c/ (v)dv, one finds from (D.l4): 0 AN,., I, / I (D-I5> where: p ^ - d v = ■ 2 — ------ (D.l 6) which averages v_ l over the beam velocity profile. Note that in Eq. (D .l5), we replaced this exact expression by (v )'. This is considered to be a good approximation in view of the narrow spread of cluster velocities (about 10% [TIK’**]) and the 10%-20% overall accuracy of our measurements. In this form, Eq. (D.1S) was used to calculate the inelastic cross sections in Chapter 3. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 Finally, if there is no mass resolution in the experiment, it is very easy to show that Eq. (D .l5) will be modified to:3 8 where (...) means averaging over the cluster mass spectrum. Eq. (D.l7) was used to perform the data analysis for the ion yield measurement in Chapter 4. D.2 Transverse Thermal Velocity Correction As mentioned before, we use magnetic field in the electron gun design to reduce the space-charge dispersal of the electron ribbon. The magnetic field lines are perpendicular to the cluster beam flight pass to guide the electrons into the interaction volume. This would not be reflected in the form of Eqs. (D.9)-(D.10), if the electrons were emitted exclusively in the direction orthogonal to the cathode surface. However, there is a certain angular distribution for the electron emission due to the parallel thermal velocity component v(, which becomes significant for electron energies of about 0.1 eV ( Tn ifa ce ~ 1000°C). 3 8 Just follow the same steps as for the velocity averaging. (D.l 7) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 Side View tdy •* Figure D.2. Interaction geometry for the electrons with nonvanishing transverse velocities. In the following, we assume that the number of electrons having velocities between v , and ^ + dv^ is given by the two-dimensional Maxwell velocity distribution: v ^ iiT j (D.l 8) oo where Ic = is the total number current, an knT = 0.1 eV. Such electrons o take a longer trip through the scattering region, and their total travel distance3 9 is (Fig. D.2): 3 9 Note that the total travel time through the interaction volume is not affected by v,. The electron trajectory in the magnetic field is a spiral which, if unfolded, makes up a straight pass forming the angle 0 with the direction of normal incidence. Indeed, the magnetic force changes only the direction of v, while keeping the magnitudes of v± and v, constant. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121 h'= — T a \ ’ <DI9) cos(0 ) where 0 is the angle of emission defined as: co s(0 ) = - = ^ = . (D.20) V v: + v n This changes: (D.2).o: (D.21) haxcos{0) cos(0 ) where, hdxcos{0) is the cross sectional area of the electron strip entering the elementary volume hdxdy (see Fig. D.2); (D.5) to: a j » (D.22) cos(0 ) and(D.7)to: &Je (hdxcos(0)) = d Jc l(h2}, (D.23) so Eq. (D.8) appears intact resulting in the familiar expression: M vn) . " 1 -e r- , (D.24) K, where And (vN ) is the cluster beam depletion caused by electrons with transverse velocities in the (v,, v , +<fv,) range. There is a difference, though, since the number current Ie is now defined as the electron flux through the angled area hi (Fig. D.2): Ie = J° ■ hico s(0 ). As a result, Eq. (D.9) is modified to: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 122 - M i l ) ! N (D.25) i v c/ As before, we will consider only the linear term in this expression. The amount of cluster beam depletion A Nd observed in the experiment is made up of all velocity contributions Anc l (vM ) in accordance with Eq. (D.25): n J V " v . h l cos(0\ " x ,h ' K C /,. o w s(0 ) vclh \c o s ( 0 ) /^ or A Ncl_ <r Nd \cos(0)/^ vclh ' where (cr/cos(0)}^ is given by (see also Eq. (D.20)): / ^ \ ~ ] < t(v h )Vv' + v i i ■ /^(vn)^i (D.26) V X 0 [cos(6 > )/,i (D.27) For medium-sized clusters, the interaction with electrons at low energies is well characterized by the Langevin capture cross section a ,(E ) = const- E~'1 2 (see Chapter 3). Let’s plug this expression in (D.27) remembering that E = const{v\ + V j j 2) : Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 123 1 “ r const Hi t VvW cos(0)/^ a \ _ H o yf] vi + v , i ii const = < rL{vL). (D.28) / /, ( v ii) ^ i o It turns out that, because of the specific energy dependence of the Langevin cross section, the results of our measurements are not affected by the transverse thermal velocities of electrons. For E >1 eV ( vx » v,), the magnetic field correction is much less important than in the near-zero energy range and, therefore, is not considered here. For nanoparticles, the situation is different since the interaction cross section contains the energy-independent term: <r(£) = x R 1 + < j l(E ) , so (D.27) will look as follow: As discussed in Chapter 3, the average nanoparticle size was determined by fitting resolution-corrected cr(E) to the experimental data set. In principle, one also needs to correct it as shown in Eq. (D.29). However, to obtain an order-of-magnitude estimate of the magnetic field correction, we can take already available sizes4 0 from 4 0 The fitting procedure in Chapter 3 has been performed ignoring the transverse thermal velocities of electrons. 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 124 Chapter 3 and use them in Eq. (D.29). In this way, the relative correction due to the transverse electron velocity is defined as follows: xR 2 / I 2 2 \ \ xR 2 A c t (T 0 cr,(v±)+ xR 2 a L (vL) + x R 2 The results of our calculations for A fa9 5 0 0 (assuming kB TM lfa c e = 0.1 eV) are shown in Fig. D.3. Obviously, the effect of the magnetic field on our measurement is increasing as E — > 0. It’s straightforward now to apply this correction to the experimental data a m e m u K d : _ ^m eaxund / r x 1 \ V c o rrra c J “ / V . A / v • ( D . 3 1 ) (l + A tr/(T0) 10 8 6 4 2 0 0.0 0.5 1.5 1.0 Electron energy (eV) Figure D.3. The relative correction to the measured cross sections for Na9 S O O due to the transverse electron velocity. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 125 We fitted this new set of data with cr(£) = tcR1 +cr/ (£ ) expression again and discovered that the actual particle size was overestimated by 6%. This corresponds to the particle radius change of 2%. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 126 Appendix E Retarding Potential Measurements and Electron Energy Calibration E.l Electron Energy Resolution Our electron energy distribution measurement is realized on the basis of the retarding potential technique. Consider an electron current created at the cathode with some energy spread / ( £ - £ „ ) which is collected at the metal anode (Fig. E.l). If the cathode is grounded, the voltage applied to the anode V A is a measure of the electron potential energy.4 1 As shown in Fig. E.l, the amount of detected current is a step-like function of V A. Indeed, if the anode potential is set to be too negative, then no signal is observed since the electrons do not have enough kinetic energy to overcome the potential barrier of the collector. When V A is slowly decreased (made more and more positive), more energetic electrons in / (£ - £0) are able to reach the anode resulting in a certain value of current. The latter will grow with the anode potential until all of the electrons are detected, so no change in the signal is observed for V A>0. Clearly, the monotonic rise of the retarding curve is a signature of the intrinsic electron energy spread, and is given by: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 127 '(K .)= 1 ‘ I(E -E ,)d E , (E.l) 'K , where / ( £ - £ „ ) is number of electrons having energies between E and E+dE, and E0 is the central energy for a symmetric profile. The energy distribution is easily deconvoluted from (E.l) by differentiating it over anode voltage: ? ! ^ K l ( e V A- E ') . (E.2) <*V A Cathode Anode Figure E. 1. Retarding potential method. Differentiation may be performed either graphically from the retarding field curve, or more conveniently, electronically using the circuit illustrated in Fig. E.2. In this circuit a weak ac modulation voltage is added to the slowly ramped dc anode 4 1 We ignore the cathode-anode contact potential correction at this point to emphasize the main idea of the method. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 128 potential. The ac voltage developed across the sensing resistor R is proportional to di/dV, if the modulation voltage is sufficiently small [COLN’68, HOR’89]. To Lock-In Amplifier Figure E.2. Electronic differentiation of the retarding field curve. In practice, a computer-controlled digital-to-analog converter (Keithley 500, Cleveland, OH) stepped up the dc voltage applied to the virtual ground of a function generator (Hewlett-Packard 3325B, Everett, WA), which was set to output a small amplitude square wave signal (typically 3-5 mV, 157 Hz). Then, the mixed output of the generator was applied to the anode through a 1 kO sensing resistor.4 2 The potential drop across the latter was measured by a lock-in amplifier (SRS 530, Sunnyvale, CA). The analog output of the lock-in was read by the analog-to-digital Cathode Anode AC Ramped DC Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 129 converter (Keithley 500), and di/dV data were stored in the computer file together with the corresponding values of the anode voltage. At the same time, this software allowed us to visualize the recorded curve for the immediate check of the electron gun resolution (see Appendix H for the program code and details). A typical experimental di/dV plot is shown in Fig. E.3. The measured energy spread was found to rang from 0.25-0.3 eV for the anode current of 100-200 pA to 0.3-0.4 eV for currents of up to 400 pA at the electron energies of ~1 eV, which is in agreement with values in the original gun design, Ref. [COLN’70]. C O 1 0.8 3 0.6 _< 1 < °A ■ a 0.2 0.0 -0.5 -0.3 -0.1 0.1 0.3 0.5 Anode V oltage (V) Figure E.3. A typical experimental electron energy profile. 4 2 This value is chosen not to alter the dc voltage applied to the anode. Typical current in this circuit was < 10 pA, so expected voltage reduction is less than 0.01 V, which does not exceed our energy scale calibration precision. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 130 E.2 Electron Energy Scale Calibration If the electron emitter is at the ground potential, the voltage applied to the scattering region Km determines the kinetic energy of the incident electron beam. The electron energy defined in this way should be corrected for the work function difference between the scattering region and the cathode (contact potential correction), AfVslt_ c = fVS R - W c : The latter is sensitive to the cathode age and its poisoning level, so we have to be able to measure this difference at the run conditions. While the original calibration technique [COLN’70] is very complicated,4 3 there exist a different procedure to determine AWS R _ C. It was observed in Ref. [KRE’91] that the current appearing at the anode is described by the Richardson-Dushman thermionic emission formula [SPA’48]: 4 3 One has to take a series of retarding potential curves di/dV (Section E.l) at decreasing scattering region voltage. Technically, this is quite difficult to realize since the anode current becomes exponentially low. E — e K s r ^ ^srt-r ■ (E.3) (E.4) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 131 The physics behind this equation is simple: only those thermal electrons which have enough energy to overcome the potential barrier between the cathode and scattering region are detected at the anode (see Section E.3 for details). We used Eq. (E.4) in our analysis. 200 'Z 150 c I O 100 ffl T3 O C < 0.0 -0.5 0.5 2.0 2.5 Scattering Region Voltage (V) Figure E.4. A representative experimental calibration curve. The technical side of the calibration process was to measure the iA[VSR ) dependence. Varied scattering region voltage was generated by the digital-to-analog converter (Keithley 500) operated by a computer program (see Appendix H), and the anode current was read by a digital multimeter (Keithley 197, Cleveland, OH) interfaced to the PC through the GPIB connection. A representative calibration curve Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132 is shown in Fig. E.4. The AW ^,_C correction was found from the linear regression fit to the low-voltage part of the data as illustrated in Fig. E.5. The measured contact potential difference typically varied from about 0.3 eV to 0.5 eV which was directly related to the cathode age and the condition of the emitting surface. The overall calibration error in this method did not exceed 0.1 eV. • 2 3 -4 5 -6 - 1.0 -0.8 - 0.2 - 0.6 -0.4 0.0 Scattering Region Voltage (V) Figure E.5. Expanded view of the low-voltage part of the calibration curve in Fig. E.4. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 133 E.3 Richardson-Dushman Equation In accordance with the Fermi-Dirac distribution, a certain fraction of electrons has enough energy to escape from the metal surface. If the latter coincides with the yz-plane, the current density of electrons having x -component greater than vx0, with i/n*v;0 =E f +W, (E.5) is given by [TAN’95]: J = f evxn(vx)dvx , (E.6) • * V o where m is the electron effective mass, E,, is the Fermi energy, W is the work function, and n(vx)dvx is the number density of electrons with a ; -component in the range (vx, vx +dvx). The number density of electrons with velocities in the (vx,Vj + dvx)(vy,vy - + - dvv)(v., v. +dv.) range is given by: 2 n(vx, v , v.)dvxdv dv. = f ' — I 2nh J dvxdvvdv. e * * r +1 (E.7) where n(vx, v , v.)dvxdv dv. = (spin factor)x(number of states)x(occupancy). Then: 4 4 A free particle in a box of unit volume has one allowed energy state per (2;r/i)3 cube in the momentum space. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 134 n(vx)dvx =2 f • \ 3 m 2 7Th) dv- L dv> L dv--vrT' k ‘ T + 1 (E.8) Since E should exceed EF by at least a value of the work function W (see (E.5)), and usually W » k BT for metal surfaces, the exponent in (E.8) is much greater than unity. With this and E = ^ m ( v \ + v2 y + v*) (E.8) becomes: n(vx)dvx = 2 f • \ 3 Ef mv\ m — ---- 2 nh e‘-Te i v dv, £ e “ •rA , £ e . (E.9) Using £ < ! - “ ' * = , (E.9) can be simplified as follows: n(vx)dvx = 2 -5L.1Y 2 Tuh J \ m J (E.10) Finally, combining (E.6) and (E.10): J = f ,2 \ F , em kaT 2x1 hi \ y ek * T f vxe 2i* Tdvx = f .9 \ em knT 2n h 2fc3 y e k 'T e 2*.r f * 2 , rr\ ) 1 ( -2, ~ em k„T [ 2 F )tB r _ em k„T using (E.5) .2 fc3 2it h \ \ w 'k.T 2x1 hi v y (E.l 1) . _ , em k„T , If we define A =-7 -* —, then: 2x h w J r d = AT e (E.l 2) which is the famous Dushman-Richardson equation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 135 In order to apply (E.12) to our electron gun, condition (E.5) should be replaced by the scattering region retarding potential ( (~e)VS R + WS R > W c\ Vc = 0): = ys.+ff'a . (E.13) Repeating all the steps above, (E.12) is transformed into:4 5 C V SR -W SK + W c-W c J = AT2 e kJ = AT2 e k* r f -IV,- \ AT2 e k "r V ~ J r d 'e kBr > (E.l4) where JR D is the total current density, Eq. (E.12), reaching the anode when the electron beam is not blocked at the scattering region ((-e)VS R + W S R < fV c). 4 5 A space charge correction due to the electron cloud above the emitter (if significant) would merely redefine the work function in Eq. (E.12): W = W + (-e) V s p c h > W . And, correspondingly, AW S R _ C = W S R - W c in (E. 14). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 136 Appendix F Electron Capture by the Full Image-Charge Potential The full classical image-charge potential for the attraction between a point charge and an isolated conducting sphere of radius R is given by [LAND’84]: F- W = - 2# F ) - (R I) The procedure is to consider the electron motion in the effective potential [LAND’76]: K /r(r) = v m (r)+ !2rl ’ (F-2) where, in the centrifugal term, b is the electron impact parameter and vM is the electron velocity far away from the particle. For a given kinetic energy of collision E = m vl/2 , there is a critical impact parameter, bQ , below which the electron is not reflected by the and “falls to the center.” The capture cross section is then given by cr(E) = zbg. Step 1 For a given collision energy E and an impact parameter b , let’s find the distance r0, at which the effective potential energy has maximum: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 137 dV. 'B dr = 0 -> e2Ri (2r1- R 1)-m b 1 vl[ri - 2 r 2R2 + RA) = Q or (mb2 vl )r4 -(2 R2 mb2 vl + 2 e2R3)r2 + mbW^R4 +e2 R5 = 0. There are two distinct solutions to this quadratic equation: (F.3) mb2 vl +e2R±y]e2Rmb2 vl +e*R2 mb2 v2 (F-4) the one with negative sign in the numerator being unphysical (the maximum should be found outside the sphere, i.e., r0 > R ). It’s convenient to change the variables to: e2R = x and mb2v2 m = 2Eb2 =y, so (F.4) becomes:4 6 rQ 2=R2 x + y + yfx2 +xy (F.5) Step 2 By plugging r0 into the expression for Kjr , we find the height of the centrifugal barrier for given values of E and b : 46 It’s very easy to prove that V eff has a maximum at r0 defined by (F.5). We have to find the second derivative of the effective potential over the distance and evaluate it at r0. After some algebra, one discovers that 'B S r2 < 0 . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 138 Using ^ = M ' o ) = xR2 2/b2 2r0 2( r - - R 2) 2r2 y — t xR2 r o - R ro - R 2 = R2 — y this becomes: xR2 y \ y + l v° = ■ 'ff 2 R2 I f 1 + ^ + 1 [ y + x + yfe 1 2R x + x ^ + 1 + J ^ + 1 y 2 R2 x 1 + I f - I f " 2 R2x " I f (F.6) Step 3 Finally, we can obtain the expression for the critical parameter b0 by setting V e t = E (an electron just sliding over the top of the centrifugal barrier): l + j ^ + i 2R xE \ x R -l; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 3 9 squaring: x 2Rz£x R^/lEx X 2R2Ex RJEx ' or finally y = 2R2E + 2y[2RjEx. (F.7) Recalling that x = e2R and y = 2Eb2, Eq. (F.7) takes the following form: 2Eb2 = 2R2E + 2y/2Ry [Ee2R; bo = R2 + J ~ ~ — • (F.8) For impact parameters less than b0, the electron is not reflected by V e jJ and spirals into the particle center. The corresponding capture cross section is then taken to be: / r\ l ’ 0 2 l27r2 e2Ri n2 1 2 n 2 e2 a o (E ) = 7 ib -0 =7cR +yj — = xR 2+y j — - — , (F.9) where a = R3 is the polarizability of the conducting sphere [JAC’75], It is remarkable that for such a complicated potential as Eq. (F.l) the capture cross sections turns out to be merely the sum of the hard-sphere area of the particle and the Langevin cross section, Eq. (2.4): = ,+&,.{£)■ (F.10) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 140 This result was also found by Klots in Ref. [KLO’94]. He used the same recipe to proceed from (F.2) to (F.10), however, the algebra was different from that given above. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141 Appendix G Cluster Escape Probability Calculation A cluster anion of a charge (-e ) is bom inside the equipotential volume (Region I in Fig. G.l) having the original beam velocity v 0 and experiencing the magnetic force due to the collimating magnetic field B . In Regions II and III. the particle trajectory is influenced by both magnetic and electric fields which are orthogonal to each other. Therefore, it’s essential for our calculation to know the exact form of ion trajectory in the crossed field configuration. Side View +5V +100 v +0.5 V B, B n - © ^ y° = -- Q --------- ® -------------- © — Q--© -- Q - x -n © -------- © B it _ Scattering Region i t T Conversion Dynode L it L iu Region I Region II Region III Figure G.l. Schematic view of the arrangement used in the escape probability calculation (not to scale). B, = B„ =0.15 T, B,„ =0.1 T; L, =40 mm, Ln =5 mm, Lm = 4 mm; D, = 15 mm, D„ = 7 mm, D,„ = 11 mm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 142 In the coordinate system indicated in Fig. G.l., B (0 ,0 ,5 ) and £ (-£ ,0 ,0 ). The total force acting on the particle is given by: £ = - e ^ £ + vx 5j, (G.l) where the first and the second terms are the electric and magnetic forces respectively. The cross product in (G. 1) is equal to: v x B = i j k x y z 0 0 B = i ( y B ) - j (xB), (G.2) where / , j , and k are unit vectors along the coordinate axes. Combining Eqs. (G.l) and (G.2): F = i e (E -y B )-je (x B ), (G.3) and using the second Newton’s law F = m(x,y,z), one arrives at the following system of coupled differential equations: £ . x = co\ y 1 B y = o)x (G.4) 2 = 0 , where eo = eB/m is the cyclotron frequency, at which the particle would revolve in the absence of the electric field. This system is easily solved by, e.g., differentiating the first line and plugging the result into the second one to eliminate y : Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 143 x + qj2x = 0 => x +g)2x = const, (G.5) which is the familiar equation for the harmonic oscillator. After some algebra, one finds for the coordinates: x{t) = Cx cos(cot) + C2 sin(<yf) + C3 E t y(t) = Cx sin(eot)-C2 cos(o)t) + — + C4 (G.6) B z(t) = C5 t+C6, and for the velocities: x(/) = -C, <ysin(<y/) + C2 <ycos(a)/) £ y{t) = Cx ocos(<yf)+C 2 <ysin((y/)H— (G-7) B z(t) = C5 where C,_ 6 are constants defined by the initial conditions. Now, let’s apply results (G.6) and (G.7) to the negative ion motion in Fig. G.l. As mentioned before, the particles are bom with the original beam velocity v0(vo,0 ,0) at some location inside the interaction volume ^ (jc ^y ^ O ).4 7 Thus for Region I. we have: 4 7 To simplify calculations, we assume that all the ions are formed in the z = 0 plane which is supported by the fact that the cluster beam is by factor of 5 narrower than the radius of the smallest aperture in Fig. G. 1. This makes C5 = C6 = 0. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 144 (G.8) The ion trajectory inside the Region II is defined by the same set of equations with the initial conditions taken when the particle is exiting Region I, Coefficients (G.8) through (G.10) completely define the pass of an ion from the interaction volume to the conversion dynode. The cluster escape probability was calculated by a computer program which is given in Appendix H. We put a 10 x 100 grid over the interaction volume creating 1000 random places for the ion birth. The trajectory analysis above was applied to each of these spots. The particle was considered to be lost, if it either was not able to leave the scattering region or missed one of the apertures shown in Fig. G.l. In this case, the corresponding spot in the interaction volume was assigned a value o f 0. Otherwise, this location received a value of 1. A representative escape “matrix” is n, (*i ('«#). ° ) md ?0(*/ ). y, ). o ): And, similarly, for Region III: r - ya Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 145 shown in Fig. G.2. Then, the escape probability was defined by summing all these numbers4 8 and dividing the total by 1000. o o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Figure G.2. A fragment of the calculated escape matrix for Na5S. 4 8 The convergence of the result was checked by varying the elementary flight time increment. In principle, we also should have verified that the probability converged by varying the number of ion birth places. However, such a precise calculation was not an issue in the experiment. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 146 Fig. 4.3 illustrates the variation of the escape probability with cluster size. Obviously, heavier particles have a greater chance to reach the detector since the magnetic field deviates them less than the lighter ones. The calculated dependence is very well represented by the scaled square root function: 0.0351 • -JN. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 147 Appendix H Data Acquisition and Analysis Programs H.l Electron Gun Energy Resolution and Calibration The electron energy resolution and calibration can be probed by launching the gun.exe file and following the menu options. One can choose to acquire (r) the energy resolution profile and (c) calibration curve, or to visualize (v) any of those previously taken. The gun.exe is generated by compiling the following set of files for the DOS platform (the Keithley 500 software requires the DOS mode):4 9 gun.c /* creates main menu */ resol.c /* acquires resolution profile */ calib.c /* takes calibration curve */ r_video.c /* shows saved resolution profile */ c_video.c /* shows saved calibration curve */ setana.c /* sets a selected analog output of the DAC, Keithley 500, to a chosen value */ 4 9 Originally, the Symantec C++ 7.5 compiler was used. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 148 readana.c /* reads a selected analog input of the ADC, Keithley 500 */ plot.C /* makes a dot on the graphical screen */ clear.c /* removes everything from the text screen */ decl.h gpib.dll m cib.lib /* the last three components create GPIB interfacing between the program and the DMM, Keithley 197, in the DOS environment */. The complete text for some of these routines is given below. # i n c l u d e < s t d i o . h > t i n c l u d e < d o s . h > v o i d r e s o l ( f l o a t * , f l o a t * , f l o a t * , f l o a t * , i n t * , f l o a t * , f l o a t * ) ; v o i d c a l i b ( d o u b l e * , d o u b l e * ) ; v o i d c l e a r ( ) ; v o i d r _ v i d e o ( f l o a t * , f l o a t * ) ; v o i d c _ v i d e o ( d o u b l e * , d o u b l e * ) ; v o i d m a i n ( ) { i n t a i n , k ; u n i o n R E G S i n , o u t ; f l o a t 1 1 , h i , a t , d w , D C [ 5 1 0 ] , D I S T [ 5 1 0 ] ; d o u b l e S R V [ 1 5 0 ] , M 4 R [ 1 5 0 ] ; c h a r k e y [ 2 ] ; l l = - 2 . 4 ; h l = 2 . 4 ; d v f = 0 . 5 ; s t = 2 0 . 0 ; a i n = 0 ; / * F o l d e r s " / r e s o l " a n d " / c a l i b " w i l l n o t b e c r e a t e d a u t o m a t i c a l l y . Y o u h a v e t o d o i t m a n u a l l y o t h e r w i s e t h e d a t a f i l e s w i l l b e l o s t * / p r i n t f ( " \ n M a k e s u r e y o u h a v e ' / r e a o l ' a n d ' / c a l i b ' f o l d e r s i n t h e c u r r e n t d i r e c t o r y ! \ n " ) ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 149 p r i n t f ( " \ n P r e s s a n y k e y t o c o n t i n u e . . . " ) ; g e t c h ( ) ; d o { c l e a r ( ) ; p r i n t f ( " \ n \ n ( R e s o l u t i o n ) : p r e s s \ " r \ " , ( C a l i b r a t i o n ) : p r e s s \ " c \ " , ( V i d e o ) : p r e s s \ " v \ " , " ) ; p r i n t f ( " \ n \ n ( E x i t ) : p r e s s \ " e \ " . \ n " ) ; p r i n t f ( " \ n \ n : " ) ; s c a n f ( " % s " , k e y ) ; s w i t c h ( k e y [ 0 ] ) { c a s e ' c ' : c l e a r ( ) ; c a l i b ( S R V , M I R ) ; b r e a k ; c a s e ' r ' : c l e a r ( ) ; r e s o l ( £ 1 1 , £ h l , f i s t , f i d w , f i a i n , D C , D I S T ) ; b r e a k ; c a s e ' v ' : c l e a r ( ) ; p r i n t f ( " \ n \ n C a l i b r a t i o n C u r v e s : p r e s s \ " c \ " , R e s o l u t i o n C u r v e s : p r e s s \ " r \ " . " ) ; p r i n t f ( " \ n \ n : " ) ; s c a n f ( " % s " , k e y ) ; s w i t c h ( k e y [ 0 ] ) { c a s e ' c ' : c _ v i d e o ( S R V , M M R ) ; b r e a k ; c a s e ' r ' : r _ v i d e o ( D C , D I S T ) ; b r e a k ; ) b r e a k ; c a s e ' e ' : e x i t ( l ) ; b r e a k ; > ) w h i l e d ) ; > ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ resol.c *********** + i i n c l u d e < d o s . h > ♦ i n c l u d e < s t d i o . h > ♦ i n c l u d e < t i m e . h > ♦ i n c l u d e < s t r i n g . h > ♦ d e f i n e K E I T H L E Y S E G O x c f f O Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 150 v o i d c l e a r ( ) ; v o i d r e s o l ( f l o a t * l i p , f l o a t * h i p , f l o a t * s t p , f l o a t * d w p , i n t * a i n p , f l o a t * D C , f l o a t * D I S T ) ( c l o c k _ t d e l a y , m o m e n t ; i n t i , i m a x , k , N , a o u t , i n c , c ; f l o a t x , y , f t m p , m i n , m a x ; u n i o n R E G S i n , o u t ; c h a r n a m e [ 2 0 ] , c o n d [ 3 ] , p a t h [ 3 0 ] , n o t e s [ 1 0 0 ] ; F I L E * d i s t , * t e s t ; x = y = m a x = m i n = 0 . 0 ; k = 0 ; / * A t t h i s p o i n t , t h e p r o g r a m r e q u e s t s t h e s t a r t i n g a n d e n d i n g p o i n t s o f a s c a n , t h e v o l t a g e i n c r e m e n t , t h e t i m e d e l a y b e f o r e t h e l o c k - i n o u t p u t i s r e a d , a n d t h e K e i t h l e y a n a l o g i n p u t t o w h i c h t h e l a t t e r i s c o n n e c t e d * / p r i n t f ( " \ n \ n \ n A n o d e V o l t a g e L o w L i m i t ( - 2 . 4 . . . 2 . 4 V ) . " ) ; p r i n t f ( " \ n P r e s s ' E n t e r ' t o a c c e p t [ % . 2 f ] V o r a n y o t h e r f o r a n e w o n e . " , * l l p ) ; i f ( g e t c h ( ) ! = 1 3 ) ( p r i n t f ( " \ n \ n E n t e r t h e n e w v a l u e h e r e : " ) ; s c a n f ( " % f " , S f t m p ) ; i f ( ( f t m p < - 2 . 4 ) | | ( f t m p > 2 . 4 ) ) * l l p = - 2 . 4 ; e l s e * l l p = f t m p ; } c l e a r ( ) ; p r i n t f ( " \ n \ n \ t \ t \ t . . . % . 2 f V v a l u e w a s s e t " , * l l p ) ; p r i n t f ( " \ n \ n \ n A n o d e V o l t a g e H i g h L i m i t ( L o w L i m i t . . . 2 . 4 V ) . " ) ; d o { p r i n t f ( " \ n P r e s s ' E n t e r ' t o a c c e p t [ % . 2 f ] V o r a n y o t h e r f o r a n e w o n e . " , * h l p ) ; i f ( g e t c h ( ) ! = 1 3 ) { p r i n t f ( " \ n \ n E n t e r t h e n e w v a l u e h e r e : " ) ; s c a n f ( " % f " , & f t m p ) ; i f ( ( f t m p < - 2 . 4 ) | | ( f t m p > 2 . 4 ) ) * h l p = 2 . 4 ; i f ( f t m p < = * l l p ) p r i n t f ( " \ n \ n Y o u r H i g h L i m i t i s b e l o w L o w L i m i t . T r y a g a i n . . . " ) ; e l s e { * h l p = f t m p ; b r e a k ; > > e l s e b r e a k ; ) w h i l e d ) ; c l e a r ( ) ; p r i n t f ( " \ n \ n \ t \ t \ t . . . % . 2 f V v a l u e w a s s e t " , * h l p ) ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. p r i n t f ( " \ n \ n \ n A n o d e V o l t a g e I n c r e m e n t ( > 1 0 m V ) . " ) ; d o { p r i n t f ( " \ n P r e s s ' E n t e r ' t o a c c e p t [ % . l f ] m V o r a n y o t h e r f o r n e w o n e . " , * s t p ) ; i f ( g e t c h ( ) ! = 1 3 ) { p r i n t f ( " \ n \ n E n t e r t h e n e w v a l u e h e r e : " ) ; s c a n f ( " % f " , f i f t m p ) ; i f ( ( f t m p < 0 . 0 ) I I ( f t m p > 5 0 0 0 . 0 ) ) * s t p = 2 0 . 0 ; i f ( f t m p < = 1 0 . 0 ) p r i n t f ( " \ n \ n Y o u r V o l t a g e I n c r e m e n t i s b e l o w l i m i t . T r y a g a i n . . . " ) ; e l s e ( * s t p = f t m p ; b r e a k ; ) } e l s e b r e a k ; } w h i l e d ) ; c l e a r ( ) ; p r i n t f ( " \ n \ n \ t \ t \ t . . . % . l f m V v a l u e w a s s e t " , * s t p ) ; p r i n t f ( " \ n \ n \ n L o c k - i n D w e l l T i m e . " ) ; p r i n t f ( " \ n P r e s s ' E n t e r ' t o a c c e p t [ % . 3 f ] s e c o r a n y o t h e r f o r a n e w o n e . " , * d w p ) ; i f ( g e t c h O ! * 1 3 ) { p r i n t f ( " \ n \ n E n t e r t h e n e w v a l u e h e r e : " ) ; s c a n f ( " % f " , S f t m p ) ; i f ( f t m p < 0 . 0 ) * d w p = 0 . 5 ; e l s e * d w p = f t m p ; } c l e a r ( ) ; p r i n t f ( " \ n \ n \ t \ t \ t . . . % . 3 f s e c v a l u e w a s s e t " , * d w p ) ; p r i n t f ( " \ n \ n \ n A n a l o g O U T m u s t b e 2 ( - 2 . 5 V . . . + 2 . 5 V ) " ) ; p r i n t f ( " \ n \ n P r e s s a n y k e y t o c o n t i n u e . . . " ) ; g e t c h ( ) ; a o u t = 2 ; c l e a r ( ) ; p r i n t f ( " \ n \ n \ n A n a l o g I N . " ) ; p r i n t f ( " \ n P r e s s ' E n t e r ' t o a c c e p t [ % d ] o r a n y o t h e r f o r a n e w o n e . " , * a i n p ) ; i f ( g e t c h O > - 1 3 ) ( p r i n t f ( " \ n \ n E n t e r t h e n e w v a l u e h e r e : " ) ; s c a n f ( " % d ” , a i n p ) ; > p r i n t f ( " \ n \ n \ t \ t \ t . . . % d v a l u e w a s s e t " , * a i n p ) ; c l e a r ( ) ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 152 / * T h e S T R O B E f e a t u r e ( s e e K e i t h l e y 5 0 0 m a n u a l ) i s e n a b l e d * / p o k e b ( K E I T H L E Y j S E G , 0 x 9 d , 0 x 4 0 ) ; p r i n t f ( " \ n \ n \ n E L E C T R O N E N E R G Y C A L I B R A T I O N P R O G R A M : U S C , J u n e 1 9 9 8 \ n \ n " ) ; p r i n t f ( " C u r r e n t e n e r g y s t e p : % . l f m V \ n L L : % . 2 f V \ n H L : % . 2 f V \ n D w e l l t i m e : % . 3 f s e c \ n \ n " , * s t p , * l l p , * h l p , * d w p ) ; p r i n t f ( " S E T A N A L O G O U T : % d \ n \ n R E A D A N A L O G I N : % d \ n \ n " , a o u t , ♦ a i n p ) ; / * T h e s t a r t i n g v a l u e f o r K e i t h l e y D A C i s d e f i n e d . S e e a l s o t h e r e m a r k i n t h e m a i n p a r t b e l o w a b o u t t h e c o n v e r s i o n f o r m u l a * / i = ( i n t ) ( ( * l l p + 2 . 4 8 5 ) * 4 0 9 6 . 0 / 4 . 9 9 6 ) ; / * T h e e n d i n g v a l u e f o r K e i t h l e y D A C i s d e f i n e d * / i m a x = ( i n t ) ( ( * h l p + 2 . 4 8 5 ) * 4 0 9 6 . 0 / 4 . 9 9 6 ) ; / * T h e d i g i t a l i n c r e m e n t f o r K e i t h l e y D A C i s d e f i n e d * / i n c = ( i n t ) ( * s t p * 4 . 0 9 6 / 4 . 9 9 6 ) ; / * M a i n p a r t * / / * T h e a n o d e v o l t a g e i s s c a n n e d b e t w e e n t h e u s e r - d e f i n e d v a l u e s w i t h t h e g i v e n i n c r e m e n t * / d o { p r i n t f ( " I t e r a t i o n n u m b e r i s : % d " , k ) ; / * T h e a n o d e v o l t a g e i s s e t . N o t e t h e c o n v e r s i o n f o r m u l a b e l o w . I d e a l l y , i t w o u l d l o o k l i k e 5 * i / 4 0 9 6 - 2 . 5 . H o w e v e r , t h e K e i t h l e y ( - 2 . 5 , 2 . 5 ) a n a l o g o u t p u t s e t s s l i g h t l y d i f f e r e n t v a l u e s f o r i = 0 a n d i = 4 0 9 5 . * / s e t a n a ( a o u t , i ) ; * ( D C + k ) = ( 4 . 9 9 6 * ( d o u b l e ) i / 4 0 9 6 . 0 ) - 2 . 4 8 5 ; p r i n t f ( " D C v o l t a g e v a l u e i s : % . 3 f " , * ( D C + k ) ) ; / * T h e u s e r - c o n t r o l l e d t i m e d e l a y i s s e t * / m a m e n t s c l o c k ( ) ; d o d e l a y « c l o c k ( ) ; w h i l e ( ( f l o a t ) d e l a y / C L O C K S _ P E R _ S E C < ( f l o a t ) m o m e n t / C L O C K S _ P E R _ S E C + * d w p ) ; / * T h e l o c k - i n o u t p u t i s r e a d * / * ( D I S T + k ) * ( f l o a t ) r e a d a n a ( * a i n p ) * 1 0 . 0 / 4 0 9 6 . 0 ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 153 p r i n t f ( " S i g n a l i s : % . 3 f \ r " , * ( D I S T + k ) ) ; i * i + i n c ; k + + ; N * k ; } w h i l e ( i < = i m a x ) ; p r i n t f ( " \ n \ n N o t e s : " ) ; g e t s ( n o t e s ) ; /* T h e d a t a a r e s a v e d i n a u s e r - d e f i n e d f i l e l o c a t e d i n t h e . / r e s o l f o l d e r * / d o { p r i n t f ( " \ n \ n E n t e r d a t a f i l e n a m e h e r e : " ) ; s c a n f ( " % s " , n a m e ) ; p a t h [ 0 ] = ' . ’ ; p a t h [ 1 ] = ' / ' ; p a t h [ 2 ] = ' r ' ; p a t h [ 3 ] = ' e ' ; p a t h [ 4 ] = ' s ' ; p a t h [ 5 ] = ’ o ' ; p a t h [ 6 ] = ' l ' ; p a t h [ 7 ] = ' / ’ ; p a t h [ 8 ] = ' \ 0 ' ; s t r e a t ( p a t h , n a m e ) ; t e a t = f o p e n ( p a t h , " r " ) ; i f ( t e s t ! * 0 ) { p r i n t f ( " \ n \ n F i l e \ ” % s \ " a l r e a d y e x i s t s . O v e r w r i t e ? ( y / n ) " , n a m e ) ; s c a n f ( " % s " , c o n d ) ; i f ( c o n d [ 0 ] = ' y ' ) b r e s U c ; ) e l s e b r e a k ; ) w h i l e ( 1 ) ; d i s t = f o p e n ( p a t h , " w " ) ; f p r i n t f ( d i s t , " % s \ n " , n o t e s ) ; f p r i n t f ( d i s t , " A n o d e V o l t a g e ( V ) , L o c k - i n S i g n a l ( V ) \ n " ) ; f o r ( k = 0 ; k < N ; k + + ) f p r i n t f ( d i s t , " % . 3 f , % . 3 f \ n " , * ( D C + k ) , * ( D I S T + k ) ) ; f c l o s e ( d i s t ) ; p r i n t f ( " \ n \ n \ t \ t \ t % s h a s b e e n c r e a t e d \ n " , n a m e ) ; g e t c h ( ) ; / * T h e 3 2 0 x 2 0 0 c o l o r g r a p h i c s m o d e i s s e t * / i n . h . a l = 4 ; i n . h . a h = 0 ; ( v o i d ) i n t 8 6 ( 0 x 1 0 , & i n , f i o u t ) ; / * T h e c o l o r p a l e t t e i s s e t * / i n . h . b l = 1 6 ; i n . h . a h * ! ! ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 154 ( v o i d ) i n t 8 6 ( 0 x 1 0 , 4 i n , £ o u t ) ; f o r ( k = 0 ; k < N ; k + + ) i f ( * ( D C + k ) < m i n ) m i n = * ( D C + k ) ; f o r ( k * 0 ; k < N ; k + + ) i f ( * ( D C + k ) > m a x ) m a x = * ( D C + k ) ; / * T h e d a t a i a p l o t t e d * / f o r ( k = 0 ; k < M ; k + + ) { x = 1 0 . 0 + 3 0 0 . 0 + ( * ( D C + k ) - m i n ) / ( m a x - m i n ) ; y » 1 9 9 . 0 * ( * ( D I S T + k ) / 1 0 . 0 ) ; p l o t ( ( i n t ) x , 1 9 9 - ( i n t ) y , l ) ; ) g e t c h ( ) ; > # i n c l u d e < t i m e . h > # i n c l u d e < s t d i o . h > # i n c l u d e < d o a . h > # i n c l u d e < m a t h . h > i i n c l u d e " d e c l . h ” # d e f i n e K E I T H L E Y _ S E G O x c f f O v o i d r e p o r t _ e r r o r ( i n t , c h a r * ) ; v o i d c l e a r ( ) ; v o i d c a l i b ( d o u b l e * S R V , d o u b l e * M 4 R ) { i n t d m m , i , m , k , N ; c h a r r e a d i n g [ 3 0 ] , c o n v [ 3 0 ] , s p r , p w [ 1 0 ] , n a m e [ 2 0 ] , c o n d [ 3 ] , p a t h [ 3 0 ] , n o t e s [ 1 0 0 ] ; d o u b l e t m p , x , y , m i n , m a x , p e e k ; u n i o n R E G S i n , o u t ; c l o c k _ t d e l a y , m o m e n t ; F I L E * d a t a , * t e a t ; k = N = 0 ; x = y = m i n = = m a x = 0 . 0 ; p r i n t f ( " \ n \ n \ n S e t \ " D C , A , a n d 2 m A a c a l e \ " a t t h e M u l t i m e t e r f r o n t p a n e l " ) ; p r i n t f ( " \ n P r e a a a n y k e y w h e n d o n e . . . " ) ; g e t c h ( ) ; / * K e i t h l e y d i g i t a l m u l t i m e t e r i a i n i t i a l i z e d . T h e d e v i c e p r i m a r y G P I B a d d r e s s ( 2 0 ) c a n f o u n d o n i t s r e a r p a n e l * / i f ( ( d m m - i b d e v ( 0 , 2 0 , 0 , T I O s , 1 , 0 ) ) < 0 ) r e p o r t _ e r r o r ( d m m , " C o u l d n o t o p e n D M 4 ” ) ; / * T h e d e v i c e i a c l e a r e d * / i b c l r ( d m m ) ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 155 / * T h e D M 4 d a t a f o r m a t w i t h o u t p r e f i x i s s e t ( s e e K e i t h l e y 1 9 7 m a n u a l ) * / i b w r t ( d m m , " G 1 X " , 3 L ) ; / * T h e S T R O B E f e a t u r e ( s e e K e i t h l e y 5 0 0 m a n u a l ) i s e n a b l e d * / p o k e b ( K E I T H L E Y _ S E G , 0 x 9 d , 0 x 4 0 ) ; p r i n t f ( " \ n \ n " ) ; / * M a i n p a r t * / / * T h e s c a t t e r i n g r e g i o n v o l t a g e i s v a r i e d f r o m - 1 V t o 0 . 5 V * / f o r ( i = 1 2 2 8 ; i < 2 8 6 8 ; i + = 2 0 ) { p r i n t f ( " I t e r a t i o n # i s : % d ; " , k ) ; / * T h e s c a t t e r i n g r e g i o n v o l t a g e i s s e t . * / s e t a n a ( 2 , i ) ; * ( S R V + k ) = ( 4 . 9 9 6 * ( d o u b l e ) i / 4 0 9 6 . 0 ) - 2 . 4 8 5 ; p r i n t f ( " S R i s s e t t o : % . 3 f V ; " , * ( S R V + k ) ) ; / * T h e 7 0 0 m s t i m e d e l a y i s s e t * / m o m e n t = c l o c k ( ) ; d o d e l a y = c l o c k ( ) ; w h i l e ( ( f l o a t ) d e l a y / C L O C K S _ P E R _ S E C < ( f l o a t ) m o m e n t / C L O C K S _ P E R _ S E C + 0 . 7 ) ; / * T h e D M 4 i s t r i g g e r e d * / i b t r g ( d m m ) ; / * A s e r i a l p o l l o f D M 4 i s c o n d u c t e d . I f b i t 6 o f spr i s s e t , t h e d e v i c e i s r e q u e s t i n g s e r v i c e * / i b r s p ( d m m , & s p r ) ; d o { } w h i l e ( s p r & 6 4 — 0 ) ; / * T h e d a t a a r e r e a d f r o m t h e D M 4 . T h e r e c e i v e d s t r i n g i s t e r m i n a t e d b y a n u l l c h a r a c t e r * / i b r d ( d m m , r e a d i n g , 2 0 L ) ; i f ( i b s t a £ E R R ) r e p o r t _ e r r o r ( d m m , " C o u l d n o t r e a d d a t a f r o m m u l t i m e t e r " ) ; r e a d i n g [ i b c n t ] = ' \ 0 ' ; / * T h e d a t a m a n t i s s a i s s e p a r a t e d * / Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 156 f o r ( m — 0 ; m < 8 ; m + + ) c o n v [ m ] — r e a d i n g [ m ] ; c o n v [ m + 1 ] = ' \ 0 ' ; / * T h e d a t a e x p o n e n t i s s e p a r a t e d * / f o r ( m - 0 ; m < 2 ; m + + ) p w [ m ] - r e a d i n g [ 9 + m ] ; p w [ m ] = ' \ 0 ' ; / * T h e d a t a i s c o n v e r t e d i n t o a d o u b l e f o r m a t + / * ( M 4 R + k ) = 1 0 0 0 0 0 0 . 0 * a t o f ( c o n v ) * p o w ( 1 0 . 0 , a t o f ( p w ) ) ; p r i n t f ( " M u l t i m e t e r r e a d s : % . 3 f u A \ r " , * ( J * 4 R + k ) ) ; k + + ; } c l e a r ( ) ; / * T h e s c a n n i n g s t e p i s i n c r e a s e d a n d t h e p r o c e d u r e a b o v e r e p e a t e d . T h e s c a t t e r i n g r e g i o n v o l t a g e i s s c a n n e d f r o m 0 . 5 V t o 2 . 5 V * / p r i n t f ( " \ n \ n \ n T h e V o l t a g e S t e p h a s b e e n i n c r e a s e d . . . \ n \ n " ) ; f o r ( i = 2 8 6 8 ; i < 4 0 9 6 ; i - i - = 8 2 ) { p r i n t f ( " I t e r a t i o n # i s : % d ; " , k ) ; s e t a n a ( 2 , i ) ; * ( S R V + k ) = ( 4 . 9 9 6 * ( d o u b l e ) i / 4 0 9 5 . 0 ) - 2 . 4 8 5 ; p r i n t f ( " S R i s s e t t o : % . 3 f V ; " , * ( S R V + k ) ) ; m o m e n t = c l o c k ( ) ; d o d e l a y = c l o c k ( ) ; w h i l e ( ( f l o a t ) d e l a y / C L O C K S _ P E R _ S E C < ( f l o a t ) m o m e n t / C L O C K S _ P E R _ S E C + 0 . 7 ) ; i b t r g ( d m m ) ; i b r s p ( d m m , £ s p r ) ; d o { } w h i l e ( s p r £ 6 4 = 0 ) ; i b r d ( d m m , r e a d i n g , 2 0 L ) ; i f ( i b s t a £ E R R ) r e p o r t _ e r r o r ( d m m , " C o u l d n o t r e a d d a t a f r o m m u l t i m e t e r " ) ; r e a d i n g [ i b c n t ] = ' \ 0 ' ; f o r ( m = 0 ; m < 8 ; m + + ) c o n v [ m ] = r e a d i n g [ m ] ; c o n v [ m + 1 ] * ' \ 0 ' ; f o r ( m = 0 ; m < 2 ; m + + ) p w [ m ] = r e a d i n g [ 9 + m ] ; p w [ m ] = ' \ 0 ' ; * ( t M R + k ) - 1 0 0 0 0 0 0 . 0 * a t o f ( c o n v ) * p o w ( 1 0 . 0 , a t o f ( p w ) ) ; p r i n t f ( " M u l t i m e t e r r e a d s : % . 3 f u A \ r " , * ( t M R + k ) ) ; k + + ; N — k ; } Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 157 p r i n t f ( " \ n \ n N o t e s : " ) ; g e t s ( n o t e s ) ; / * T h e d a t a a r e s a v e d i n a u s e r - d e f i n e d f i l e l o c a t e d i n t h e . / c a l i b f o l d e r */ d o ( p r i n t f ( " \ n \ n E n t e r d a t a f i l e n a m e h e r e : " ) ; s c a n f ( " % s " , n a m e ) ; p a t h [ 0 ] = ' . ' ; p a t h [ l ] = ' / ' ; p a t h [ 2 ] = ' c ' ; p a t h [ 3 ] = ' a ' ; p a t h [ 4 ] = ' l ' ; p a t h [ 5 ] = ' i ' ; p a t h [ 6 ] = ' b ' ; p a t h [ 7 ] = ' / ' ; p a t h [ 8 ] = ' \ 0 ' ; s t r e a t ( p a t h , n a m e ) ; t e s t = f o p e n ( p a t h , " r " ) ; i f ( t e s t ! = 0 ) { p r i n t f ( " \ n \ n F i l e \ " % s \ ” a l r e a d y e x i s t s . O v e r w r i t e ? ( y / n ) " , n a m e ) ; s c a n f ( " % s " , c o n d ) ; i f ( c o n d I 0 ] = = , y ' ) b r e a k ; } e l s e b r e a k ; ) w h i l e d ) ; d a t a = f o p e n ( p a t h , " w " ) ; f p r i n t f ( d a t a , " % s \ n " , n o t e s ) ; f p r i n t f ( d a t a , " S R V o l t a g e ( V ) , A n o d e C u r r e n t ( u A ) \ n " ) ; f o r ( k = 0 ; k < N ; k + + ) f p r i n t f ( d a t a , " % . 3 f , % . 3 f \ n " , * ( S R V + k ) , * ( M M R + k ) ) ; f c l o s e ( d a t a ) ; p r i n t f ( " \ n \ n \ t \ t \ t % s h a s b e e n c r e a t e d \ n " , n a m e ) ; i b o n l ( d m m , 0 ) ; g e t c h ( ) ; f o r ( k = 0 ; k < N ; k + + ) i f ( * ( S R V + k ) < m i n ) m i n = * ( S R V + k ) ; f o r ( k = 0 ; k < N ; k + + ) i f ( * ( S R V + k ) > m a x ) m a x = * ( S R V + k ) ; f o r ( k = 0 ; k < N ; k + + ) i f ( * ( t M R + k ) > p e e k ) p e e k = * ( M M R + k ) ; / * T h e 3 2 0 x 2 0 0 c o l o r g r a p h i c s m o d e i s s e t * / i n . h . a l = 4 ; i n . h . a h = 0 ; ( v o i d ) i n t 8 6 ( 0 x 1 0 , £ i n , £ o u t ) ; / * T h e c o l o r p a l e t t e i s s e t * / i n . h . b l - 1 7 ; i n . h . a h * l l ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 158 ( v o i d ) i n t 8 6 ( 0 x 1 0 , S i n , S o u t ) ; / * T h e d a t a i a p l o t t e d * / f o r ( k = 0 ; k < N ; k + + ) ( x = 1 0 . 0 + 3 0 0 . 0 * ( * ( S R V + k ) - m i n ) / ( m a x - m i n ) ; y = 1 9 9 . 0 * ( * ( * M R + k ) / ( p e e k + 5 0 . 0 ) ) ; p l o t ( ( i n t ) x , 1 9 9 — ( i n t ) y , 1 ) ; ) g e t c h ( ) ; > / * T h i s f u n c t i o n r e p o r t s o n e r r o r s w h i l e m a n i p u l a t i n g t h e D t * f v i a 6 P I B i n t e r f a c e . * / v o i d r e p o r t _ e r r o r ( i n t f d , c h a r * e r r m s g ) ( f p r i n t f ( s t d e r r , " \ n \ n E r r o r % d : % s \ n " , i b e r r , e r r m s g ) ; i f ( f d ! * - 1 ) { p r i n t f ( " C l e a n u p : t a k i n g b o a r d o f f - l i n e \ n " ) ; i b o n l ( f d , 0 ) ; } e x i t ( l ) ; > ■ i e ' k ' k ' k ' k + e ' k ' k ' k ' k ' k V X d O O Q * * * * * * * * * * * * # i n c l u d e < s t d i o . h > # i n c l u d e < s t r i n g . h > # i n c l u d e < d o s . h > v o i d c l e a r ( ) ; v o i d r _ v i d e o ( f l o a t * D C , f l o a t * D I S T ) { i n t k , N ; u n i o n R E G S i n , o u t ; c h a r n a m e [ 2 0 ] , o v e r [ 1 0 0 ] , p a t h [ 3 0 ] , t m p [ 2 ] ; f l o a t x , y , m i n , m a x ; F I L E * d a t a ; c l e a r ( ) ; d o { f o r ( k * 0 ; k < 5 1 0 ; k + + ) * ( D C + k ) = 0 . 0 ; f o r ( k = 0 ; k < 5 1 0 ; k + + ) * ( D I S T + k ) = 0 . 0 ; k = N = 0 ; x = y * q n i n = m a x = 0 . 0 ; d o { p r i n t f ( " \ n \ n E n t e r t h e f i l e n a m e t o p l o t : " ) ; s c a n f ( " % s " , n a m e ) ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 159 / * T h e p r o g r a m l o o k s f o r a u s e r - d e f i n e d f i l e l o c a t e d i n t h e . / r e s o l f o l d e r */ p a t h [ 0 ] » ' . ' ; p a t h t l ] * ' / ' ; p a t h [ 2 ] = ' r ' ; p a t h [ 3 ] = ' e ' ; p a t h [ 4 ] = ' s ' ; p a t h [ 5 ] = ' o ' ; p a t h [ 6 ] = ' l ' ; p a t h [ 7 ] = ' / ' ; p a t h [ 8 ] = ' \ 0 ' ; s t r e a t ( p a t h , n a m e ) ; d a t a = f o p e n ( p a t h , " r " ) ; i f ( d a t a ! = 0 ) b r e a k ; e l s e p r i n t f ( " \ n \ n F i l e ( % s ) d o e s n o t e x i s t . P r e s s a n y k e y t o c o n t i n u e . . . " , n a m e ) ; g e t c h ( ) ; c l e a r ( ) ; } w h i l e ( 1 ) ; /* T h e c u r s o r i s m o v e d d o w n b y t w o l i n e s t o s k i p t h e c o l u m n n a m e s a n d n o t e s */ f g e t s ( o v e r , 1 0 0 , d a t a ) ; f g e t s ( o v e r , 1 0 0 , d a t a ) ; / * T h e d a t a a r e r e a d i n t o t h e c o r r e s p o n d i n g a r r a y s / d o { f s c a n f ( d a t a , " % f " , ( D C + k ) ) ; f s c a n f ( d a t a , " , % f \ n " , ( D I S T + k ) ) ; i f ( + ( D C + k ) = * 0 . 0 ) b r e a k ; k + + ; N = k ; } w h i l e ( 1 ) ; f c l o s e ( d a t a ) ; p r i n t f ( " \ n \ n \ t \ t \ t \ t % s h a s b e e n r e a d \ n " , p a t h ) ; g e t c h ( ) ; f o r ( k = 0 ; k < N ; k + + ) i f ( * ( D C + k ) < m i n ) m i n = + ( D C + k ) ; f o r ( k * 0 ; k < N ; k + + ) i f ( * ( D C + k ) > m a x ) m a x = * ( D C + k ) ; / * T h e d a t a a r e p l o t t e d a s i n t h e r e s o l . c p r o g r a m */ i n . h . a l = 4 ; i n . h . a h s 0 ; ( v o i d ) i n t 8 6 ( 0 x 1 0 , S i n , S o u t ) ; i n . h . b l * 1 6 ; i n . h . a h * l l ; ( v o i d ) i n t 8 6 ( 0 x 1 0 , S i n , S o u t ) ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. f o r ( k = 0 ; k < N ; k + + ) { x = 1 0 . 0 + 3 0 0 . 0 * ( * ( D C + k ) - m i n ) / ( m a x - m i n ) ; y = 1 9 9 . 0 * ( * ( D Z S T + k ) / 1 0 . 0 ) ; p l o t ( ( i n t ) x , 1 9 9 - ( i n t ) y , l ) ; ) g e t c h ( ) ; c l e a r ( ) ; p r i n t f ( " \ n \ n \ n M o r e p i c t u r e s ? ( y / n ) : " ) ; s c a n f ( " % s " , t m p ) ; i f ( t m p [ 0 ] = , n ' ) b r e a k ; c l e a r ( ) ; } w h i l e d ) ; ★ ★ ★ ★ ★ ★ ★ ★ ★ 'k ie ie + i c_yideo.c ♦ i n c l u d e < s t d i o . h > ♦ i n c l u d e < s t r i n g . h > ♦ i n c l u d e < d o s . h > v o i d c l e a r ( ) ; v o id c_video(double* SRV, double* M M R ) { i n t k , N ; u n i o n R E G S i n , o u t ; c h a r n a m e [ 2 0 ] , o v e r [ 1 0 0 ] , p a t h [ 3 0 ] , t m p [ 2 ] ; d o u b l e x , y , m i n , m a x , p e e k ; F I L E * d a t a ; c le a r () ; do ( f o r ( k = 0 ; k < 1 5 0 ; k + + ) * ( S R V + k ) = 0 . 0 ; f o r ( k = 0 ; k < 1 5 0 ; k + + ) * ( b W R + k ) = 0 . 0 ; k = N = 0 ; x = y = m i n = m a x = p e e k = 0 . 0 ; / * T h e c o m m e n t s a r e s i m i l a r t o t h o s e i n t h e r _ v i d e o . < do { p r i n t f ( " \ n \ n E n t e r t h e f i l e n a m e t o p l o t : " s c a n f ( " % s " , n a m e ) ; p a t h [ 0 ] * ' . ' ; p a t h [ 1 ] = ' / ' ; p a t h [ 2 ] * ' c ' p a t h [ 3 ] = ’ a ' ; p a t h [ 4 ] = ' l ' ; p a t h t 5 ] = ' i ' p a t h [ 6 ] * ' b ' ; p a t h [ 7 ] * ' / ' ; p a t h [ 8 ] = ' \ C s t r e a t ( p a t h , n a m e ) ; d a t a = f o p e n ( p a t h , " r " ) ; z p r o g r a m ); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 161 i f ( d a t a ! = 0 ) b r e a k ; e l s e p r i n t f ( " \ n \ n F i l e ( % s ) d o e s n o t e x i s t . P r e s s a n y k e y t o c o n t i n u e . . . " , n a m e ) ; g e t c h ( ) ; c l e a r ( ) ; } w h i l e ( 1 ) ; f g e t s ( o v e r , 1 0 0 , d a t a ) ; f g e t s ( o v e r , 1 0 0 , d a t a ) ; d o ( f s c a n f ( d a t a , " % l f " , ( S R V + k ) ) ; f s c a n f ( d a t a , " , % l f \ n " , ( M 4 R + k ) ) ; i f ( * ( S R V + k ) = 0 . 0 ) b r e a k ; k + + ; N = k ; } w h i l e ( 1 ) ; f c l o s e ( d a t a ) ; p r i n t f ( " \ n \ n \ t \ t \ t \ t % s h a s b e e n r e a d \ n " , p a t h ) ; g e t c h ( ) ; f o r ( k = 0 ; k < N ; k + + ) i f ( * ( S R V + k ) < m i n ) m i n = * ( S R V + k ) ; f o r ( k = 0 ; k < N ; k + + ) i f ( * ( S R V + k ) > m a x ) m a x = * ( S R V + k ) ; f o r ( k - 0 ; k < M ; k + + ) i f ( * ( » M R + k ) > p e e k ) p e e k = * ( M M R + k ) i n . h . a l = 4 ; i n . h . a h = 0 ; ( v o i d ) i n t 8 6 ( 0 x 1 0 , f i i n , f i o u t ) ; i n . h . b l = 1 7 ; i n . h . a h = l l ; ( v o i d ) i n t 8 6 ( 0 x 1 0 , £ i n , f i o u t ) ; f o r ( k = 0 ; k < N ; k + + ) { x = 1 0 . 0 + 3 0 0 . 0 * ( * ( S R V + k ) - m i n ) / ( m a x - m i n ) ; y * 1 9 9 . 0 * ( * ( I M R + k ) / ( p e e k + 5 0 . 0 ) ) ; p l o t ( ( i n t ) x , 1 9 9 - ( i n t ) y , l ) ; ) g e t c h ( ) ; c l e a r ( ) ; p r i n t f ( " \ n \ n \ n M o r e p i c t u r e s ? ( y / n ) : " ) ; s c a n f ( " % s " , t m p ) ; i f ( t m p [ 0 ] = ' n ' ) b r e a k ; c l e a r ( ) ; ) w h i l e d ) ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ** + ****•** + + ★ setana.c******** /***♦* * coded by V.K., 9-30-88. * N A M E : s e t a n a * S Y N O P S I S : * s e t a n a ( c h n l , v a l u e ) * i n t c h n l D A C c h a n n e l ( 0 - 4 ) * i n t v a l u e o u t p u t v a l u e * D E S C R I P T I O N : * A D A C o u t p u t i s s e t t o a c h o s e n v a l u e * * * * * / • i n c l u d e < d o s . h > # d e f i n e K E I T H L E Y _ S E G O x c f f O t y p e d e f u n s i g n e d c h a r b y t e ; u n i o n O N I O N { b y t e b [ 2 ] ; i n t j ; Jr- v o i d s e t a n a ( c h n l , v a l u e ) i n t c h n l , v a l u e ; { u n i o n O N I O N x , c o n t r o l ; i f ( ( c h n l < 0 ) | | ( c h n l > 4 ) ) r e t u r n ; x . j = v a l u e ; c o n t r o l . j = ( i n t ) ( 2 * c h n l ) ; p o k e b ( K E I T H L E Y _ S E G , 0 x 8 4 , * ( c o n t r o l . b ) ) ; p o k e b ( K E I T H L E Y _ S E 6 , 0 x 8 5 , * ( x . b ) ) ; c o n t r o l . j + = 1 ; p o k e b ( K E I T H L E Y _ S E G , 0 x 8 4 , * ( c o n t r o l . b ) ) ; p o k e b ( K E I T H L E Y _ S E G , 0 x 8 5 , x . b [ l ] ) ; p o k e b ( K E I T H L E Y _ S E G , 0 x 9 d , 0 x 0 1 ) ; ) ' k ' k ' k i e ' k - k ' k ' k ' t e - k -k ***** * coded by Jun M S a s u i , 7 -15-88 (fixed by V.K. 10-5-88) * N A M E : r e a d a n a * S Y N O P S I S : * x * r e a d a n a ( c h n l ) ; * i n t x ; r e t u r n e d v a l u e * i n t c h n l ; a n a l o g i n p u t c h a n n e l , 0 - 1 5 * D E S C R I P T I O N : * T h e s e l e c t e d a n a l o g i n p u t s i g n a l i s r o u t e d t o a n A D C . * f u n c t i o n r e t u r n s t h e r e s u l t o f t h e A - t o - D c o n v e r s i o n . **«**/ • i n c l u d e < d o s . h > • d e f i n e K E I T H L E Y S E G O x c f f O Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 163 t y p e d e f u n s i g n e d c h a r b y t a ; u n i o n O N I O N { b y t a b [ 2 ] ; i n t j ; } ; i n t r a a d a n a ( c h n l ) i n t c h n l ; { u n i o n O N I O N v o l t ; c h a r x ; x = c h n l ; p o k e b ( K E I T H L E Y S E G , 0 x 8 1 , l ) ; p o k e b ( k e i t h l e y " J S E G , 0 x 9 a , 0 ) ; p o k e b ( k e i t h l e y ” ~ S E G , 0 x 8 0 , x ) ; p o k e b ( k e i t h l e y " S E G , 0 x 9 8 , 0 ) ; d o x = p e e k b ( K E I T H L E Y j S E G , 0 x 9 8 ) ; w h i l e ( x > = 1 2 7 ) ; v o l t . b [ 0 ] = p e e k b ( K E I T H L E Y _ S E G , 0 x 8 2 ) ; v o l t . b [ 1 ] = p e e k b ( K E I T H L E Y _ S E G , 0 x 8 3 ) ; v o l t . b [ l ] - = 2 4 0 ; r e t u r n ( v o l t . j ) ; ) *•* + * ★ * * + *•*•* + plQt>Q * * * * + + * * + + * + + / * * * * * c o d e d by Jun M a s u i , 7 -15-88. * N A M E : p l o t * S Y N O P S I S : * p l o t ( x , y , c o l o r ) ; * i n t x ; x - c o o r d i n a t a , 0 - 6 3 9 * i n t y ; y - c o o r d i n a t e , 0 - 1 9 9 * i n t c o l o r ; 0 f o r b l a c k , 1 f o r w h i t e * D E S C R I P T I O N : * W h e n i n t h e g r a p h i c s m o d e , a d o t i s p l o t t e d a t ( x , y ) i n t h e * s p e c i f i e d c o l o r . U n i o n R E G S i s d e f i n e d a s s t a t i c i n t h i s * f u n c t i o n . T h i s m a k e s p l o t g o 5 % f a s t e r a t t h e e x p e n s e o f l e s s * s t a c k s p a c e . *****/ # i n c l u d e < d o s . h > v o i d p l o t ( x , y , c o l o r ) i n t x , y , c o l o r ; ( u n i o n R E G S i n , o u t ; i n . x . d x = y ; i n . x . c x = x ; i n . h . a l = c o l o r ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 164 i n . h . a h = 1 2 ; ( v o i d ) i n t 8 6 ( 0 x 1 0 , t i n , t o u t ) ; > ★★★★★★★★★★★ cXttA? q * * * * * * * * * * * * * # i n c l u d e < d o s . h > v o i d c l e a r ( ) { u n i o n R E G S i n , o u t ; / * S e t s t h e 8 0 x 2 5 B W t e x t m o d e , w h i c h r e m o v e s a l l t h e i n f o r m a t i o n f r o m t h e s c r e e n . * / i n . h . a l = 2 ; i n . h . a h = 0 ; ( v o i d ) i n t 8 6 ( 0 x 1 0 , S i n , t o u t ) ; ) H.2 Cluster Escape Probability Calculation The cluster escape probability was calculated using the following program.5 0 •k 'k i e' i r- k' ir - ic 'i c 'i c -k -k XOR Qp p • k ' k ' k ' f c ' k ' i r - k ' i e - i r - k ' k ' i c ' k # i n c l u d e < s t d i o . h > i i n c l u d e < m a t h . h > t i n c l u d e < s t r i n g . h > v o i d m a i n ( ) ( d o u b l e 1 1 , 1 2 , 1 3 , h i , h 2 , h 3 ; d o u b l e E 2 , E 3 , B l , B 2 , B 3 , F I , F 2 , F 3 , V I , V 2 , V 3 ; d o u b l e T l , T 2 , T 3 , V X 0 ; d o u b l e m a x Y l , m a x Y 2 , m a x Y 3 ; d o u b l e p i , e , a m u ; i n t i , j , k , T C F , N , S i z e , D E T [ 1 0 0 ] [ 1 0 ] , P R B , t m p ; d o u b l e X 0 [ 1 0 0 ] , Y 0 [ 1 0 ] ; d o u b l e t l , t 2 , t 3 , C l , C 2 , C 3 , C 4 ; d o u b l e X I , X 2 , X 3 , Y l , Y 2 , Y 3 ; d o u b l e V X 1 , V X 2 , V X 3 , V Y 1 , V Y 2 , V Y 3 , M ; 5 0 The ion.exe file for the Windows as platform was generated by the Visual C++ 5.0 compiler. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. c h a r s t a t u s [ 2 0 ] ; F I L E * d a t a , ‘ m a t r i x ; / * D e f i n i t i o n s * / p i - 3 . 1 4 1 5 9 2 6 5 4 ; a = l . 6 0 2 1 8 e - 1 9 ; a m u — 1 . 6 6 0 5 4 e - 2 7 ; / * L e n g t h s a n d h e i g h t s o f t h e c o r r e s p o n d i n g R e g i o n s * / 1 1 * 0 . 0 4 1 ; h l = 0 . 0 0 1 5 ; 1 2 = 0 . 0 0 5 ; h 2 * 0 . 0 0 7 ; 1 3 = 0 . 0 0 4 ; h 3 = 0 . 0 1 1 ; / * P o t e n t i a l s * / V 1 = 0 . 5 ; V 2 = 4 . 5 ; V 3 = 1 0 0 ; / * C o r r e s p o n d i n g e l e c t r i c f i e l d s * / E 2 = ( V 2 - V 1 ) / 1 2 ; E 3 = ( V 3 - V 2 ) / 1 3 ; / * M a g n e t i c f i e l d s * / B 1 = B 2 = 0 . 1 5 ; B 3 = 0 . 1 ; / * T h e p r o g r a m c l e a r s e x i s t i n g " p r o b . t x t " a n d " m a t r i x . t x t " f i l e s . d a t a = f o p e n ( " p r o b . t x t " , " w " ) ; f p r i n t f ( d a t a , " " ) ; f c l o s e ( d a t a ) ; m a t r i x = f o p e n ( " m a t r i x . t x t " , " w " ) ; f p r i n t f ( m a t r i x , " " ) ; f c l o s e ( m a t r i x ) ; /* T h e m a s s r a n g e o f i n t e r e s t i s l o o p e d . * / f o r ( N = l ; N < 1 1 1 ; N + + ) { /* S o d i u m a t o m i c m a s s a n d t h e c l u s t e r b e a m v e l o c i t y * / V X 0 = 1 0 0 0 . 0 ; M = 2 3 . 0 ; m a x Y l = h l / 2 . 0 ; m a x Y 2 = h 2 / 2 . 0 ; m a x Y 3 = h 3 / 2 . 0 ; / * T h e r e l e v a n t c y c l o t r o n f r e q u e n c i e s * / F 1 = F 2 = ( e * B l ) / ( a m u * ( d o u b l e ) M * M ) ; F 3 = ( e * B 3 ) / ( a m u * ( d o u b l e ) N * M ) ; T l = ( 2 . 0 * p i ) / F l ; T 2 = ( 2 . 0 * p i ) / F 2 ; T 3 = ( 2 . 0 * p i ) / F 3 ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 166 / * T h e n e g a t i v e i o n b i r t h p l a c e d e f i n i t i o n - b o u n d a r y c o n d i t i o n f o r R e g i o n I * / f o r ( i “ 0 ; i < 1 0 0 ; i + + ) X O [ i ] = * 1 1 * ( d o u b l e ) i / 1 0 0 . 0 ; f o r ( j = 0 ; j < 1 0 ; j + + ) Y O [ j ] = ( ( h i * ( d o u b l e ) ( j + 1 ) / I I . 0 ) - m a x Y l ) ; f o r ( i = 0 ; i < 1 0 0 ; i + + ) f o r ( j = 0 ; j < 1 0 ; j + + ) D E T [ i ] [ j ] = 0 ; t m p = 0 ; f o r ( k = 0 ; k < 1 9 ; k + + ) s t a t u s [ k ] = 0 ; / * M a i n P a r t * / / * T h e t i m e s t e p i n a s e l e c t e d R e g i o n i s d e f i n e d b y d i v i d i n g t h e c o r r e s p o n d i n g c y c l o t r o n f r e q u e n c y b y T C F f a c t o r . T h e v a l u e o f t h e l a t t e r i s d o u b l e d u n t i l t h e c o n v e r g e n c e o f t h e p r o b a b i l i t y i s a c h i e v e d . * / f o r ( T C F = 1 0 0 ; T C F C 1 0 0 0 0 0 ; T C F = T C F * 2 ) { P R B = 0 ; p r i n t f ( " C a l c u l a t i n g N a % d : " , N ) ; f o r ( i = 0 ; i < 1 0 0 ; i + + ) { f o r ( j = 0 ; j < 1 0 ; j + + ) { X 1 = X 2 = X 3 = 0 . 0 ; / * R e g i o n 1 */ /* C o n s t a n t s f o r R e g i o n I d e f i n e d f r o m t h e b o u n d a r y c o n d i t i o n s */ C 1 = 0 . 0 ; C 2 = V X 0 / F 1 ; C 3 = X 0 [ i ] ; C 4 = Y 0 [ j ] + ( V X 0 / F 1 ) ; t l = t 2 = t 3 = 0 . 0 ; d o { / * I o n t r a j e c t o r y i n R e g i o n I * / X l = C l * c o s ( F l * t l ) + C 2 * s i n ( F l * t l ) + C 3 ; Y l = C l * s i n ( F l * t l ) - C 2 * c o s ( F l * t l ) + C 4 ; V X l = C 2 * F l * c o s ( F l * t l ) - C l * F l * s i n ( F l * t l ) ; V Y l - C 2 * F l * s i n ( F l * t l ) + C l * F l * c o s ( F l * t l ) ; i f ( ( Y l > m a x Y l ) | | ( Y l < - m a x Y l ) ) { D E T [ i ] [ j ] - 0 ; b r e a k ; ) i f ( X l > » l l ) ( Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 167 /* R a g i o n I I * / / * C o n s t a n t s f o r R e g i o n I I d e f i n e d f r o m t h e b o u n d a r y c o n d i t i o n t a k e n f o r t h e i o n e x i t i n g R e g i o n I * / C 1 = V Y 1 / F 2 - E 2 / ( B 2 * F 2 ) ; C 2 = V X 1 / F 2 ; C 3 = X 1 - V Y 1 / F 2 + E 2 / ( B 2 * F 2 ) ; C 4 = Y 1 + ( V X 1 / F 2 ) ; d o { / * I o n t r a j e c t o r y i n R e g i o n I I * / X 2 = C l * c o s ( F 2 * t 2 ) + C 2 + s i n ( F 2 * t 2 ) + C 3 ; Y 2 = C l * s i n ( F 2 * t 2 ) - C 2 * c o s ( F 2 * t 2 ) + C 4 + ( E 2 * t 2 ) / B 2 ; V X 2 = C 2 * F 2 * c o s ( F 2 * t 2 ) - C l * F 2 * s i n ( F 2 * t 2 ) ; V Y 2 = C 2 * F l * s i n ( F 2 * t 2 ) + C l * F 2 * c o s ( F 2 * t 2 ) + E 2 / B 2 ; i f ( ( X 2 > = ( 1 1 + 1 2 ) ) ( ( Y 2 » n a x Y 2 ) | | ( Y 2 < - m a x Y 2 ) ) ) { D E T [ i ] [ j ] = 0 ; b r e a k ; ) e l s e { / + R e g i o n I I I * / / * C o n s t a n t s f o r R e g i o n I I I d e f i n e d f r o m t h e b o u n d a r y c o n d i t i o n t a k e n f o r t h e i o n e x i t i n g R e g i o n I I * / C 1 = V Y 2 / F 3 - E 3 / ( B 3 * F 3 ) ; C 2 = V X 2 / F 3 ; C 3 = X 2 - V Y 2 / F 3 + E 3 / ( B 3 * F 3 ) ; C 4 = Y 2 + ( V X 2 / F 3 ) ; d o ( / * I o n t r a j e c t o r y i n R e g i o n I I I * / X 3 = C l * c o s ( F 3 * t 3 ) + C 2 * s i n ( F 3 * t 3 ) + C 3 ; Y 3 = C l * s i n ( F 3 * t 3 ) - C 2 * c o s ( F 3 * t 3 ) + C 4 + ( E 3 * t 3 ) / B 3 ; V X 3 « C 2 * F 3 * c o s ( F 3 * t 3 ) - C l * F 3 * s i n ( F 3 + t 3 ) ; V Y 3 « C 2 * F 3 * s i n ( F 3 * t 3 ) + C l * F 3 * c o s ( F 3 * t 3 ) + E 3 / B 3 ; i f ( ( X 2 > - ( 1 1 + 1 2 + 1 3 ) ) £ & ( ( Y 3 > m a x Y 2 ) | | ( Y 3 < - m a x Y 3 ) ) ) { D E T [ i ] [ j ] = 0 ; b r e a k ; ) e l s e { D E T [ i ] [ j ] = 1 ; b r e a k ; ) t 3 « t 3 + ( T 3 / ( d o u b l e ) T C F ) ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 168 } w h i l e ( 3 ) ; } i f ( X 3 ! « 0 . 0 ) b r e a k ; t 2 = t 2 + ( T 2 / ( d o u b l e ) T C F ) ; ) w h i l e ( 2 ) ; > i f ( X 2 ! = 0 . 0 ) b r e a k ; t l = t l + ( T l / ( d o u b l e ) T C F ) ; } w h i l e d ) ; ) > / * T h e n u m b e r o f e s c a p e d i o n s i s d e f i n e d . * / f o r ( i = 0 ; i < 1 0 0 ; i + + ) f o r ( j = 0 ; j < 1 0 ; j + + ) P R B = P R B + D E T [ i ] [ j ] ; /* T h e c o n v e r g e n c e s t a t u s i s c h e c k e d . T h e p r o b a b i l i t y h a s c o n v e r g e d , i f t h e t o t a l n u m b e r o f e s c a p e d p a r t i c l e s i s n o t c h a n g e d u p o n f u r t h e r d e c r e a s e o f t h e t i m e i n c r e m e n t . * / i f ( a b s ( P R B - t m p ) > 1 ) { s t a t u s [ 0 ] n ' ; s t a t u s [ l ] = ' o ' ; s t a t u s [ 3 ] = ' ' ; s t a t u s [ 4 ] = ' c ' ; s t a t u s [ 6 ] = ' n ' ; s t a t u s [ 7 ] = ' v ' ; s t a t u s [ 9 ] = ' r ' ; s t a t u s [ 1 0 ] = ' g ' ; s t a t u s [ 2 ] = ' t ' ; s t a t u s [ 5 ] = ' o ' ; s t a t u s [ 8 ] = ' e ' ; s t a t u s [ l l ] = ’ e ' s t a t u s [ 1 2 ] = ' d ' ; s t a t u s [ 1 3 ] = ' \ 0 ' p r i n t f ( " P = % . 3 f S t a t u s : % s \ r " , ( d o u b l e ) P R B / 1 0 0 0 , s t a t u s ) ; ) e l s e { s t a t u s [ 0 ] = ' ' ; s t a t u s [ 3 ] = ' ' ; s t a t u s [ 6 ] = ' n 1 ; s t a t u s [ 9 ] = ' r ' ; s t a t u s [ 1 2 ] = ' d ' ; p r i n t f ( " P = % . 3 f s t a t u s ) ; b r e a k ; 1 s t a t u s [ 2 ] = ' ' ; s t a t u s [ 5 ] = ' o ' ; s t a t u s [ 8 ] = ' e ' ; s t a t u s [ 1 1 ] = ' e ' t m p = P R B ; s t a t u s [ 1 ] = ' s t a t u s [ 4 ] = ' c ' ; s t a t u s [ 7 ] = ' v ' ; s t a t u s [ 1 0 ] = ' g ' ; s t a t u s [ 1 3 ] = ' \ 0 ' ; S t a t u s : % s \ n " , ( d o u b l e ) P R B / 1 0 0 0 , ) / * " 0 / 1 " m a t r i x i s r e c o r d e d f o r e v e r y c l u s t e r m a s s ( s e e t e x t ) * / f o r ( i * 0 ; i < 1 0 0 ; i + + ) ( m a t r i x > f o p e n ( " m a t r i x . t x t " , " a " ) ; f p r i n t f ( m a t r i x , " % d , % d , % d , % d , % d , % d , % d , % d , % d , % d \ n " , D E T [ i ] [ 0 ] , D E T [ i ] [ l ] , D E T [ i ] [ 2 ] , D E T [ i ] [ 3 ] , D E T [ i ] [ 4 ] , D E T [ i ] [ 5 ] , D E T [ i ] [ 6 ] , D E T [ i ] [ 7 ] , 0 E T [ i ] [ 8 ] , D E T [ i ] [ 9 ] ) ; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 169 f c l o s e ( m a t r i x ) ; > / * P r o b a b i l i t y i s s a v e d t o g e t h e r w i t h t h e c l u s t e r s i z e a n d c o n v e r g e n c e s t a t u s . * / d a t a = f o p e n ( " p r o b . t x t " , " a " ) ; f p r i n t f ( d a t a , " % d , % . 3 f , % s \ n " , N , ( d o u b l e ) P R B / 1 0 0 0 , s t a t u s ) ; f c l o s e ( d a t a ) ; > } Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Creator Kasperovich, Vitaly Golfrid (author)

Core Title Interaction of low -energy electrons with beams of sodium clusters, nanoparticles, and fullerenes

Contributor Digitized by ProQuest (provenance)

School Graduate School

Degree Doctor of Philosophy

Degree Program physics

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

Tag OAI-PMH Harvest,physics, condensed matter,physics, molecular

Language English

Advisor Kresin, Vitaly V. (committee chair), Bergmann, Gerd (committee member), Bozler, Hans M. (committee member), Chang, Tu-Nan (committee member), Koel, Bruce (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-153478

Unique identifier UC11334955

Identifier 3054760.pdf (filename),usctheses-c16-153478 (legacy record id)

Legacy Identifier 3054760-0.pdf

Dmrecord 153478

Document Type Dissertation

Rights Kasperovich, Vitaly Golfrid

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 au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA