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by Copyright Leah Caitlin Shackman 2004 The Dissertation Committee for Leah Caitlin Shackman certi es that this is the approved version of the following dissertation: Isotope E ects in Gas-Surface Interactions: Quantum-State Resolved Studies of D2 Scattering from Cu(100) and Pd(111) Committee: Greg O. Sitz, Supervisor Michael Downer Manfred Fink Charles Mullins Philip Varghese Isotope E ects in Gas-Surface Interactions: Quantum-State Resolved Studies of D2 Scattering from Cu(100) and Pd(111) by Leah Caitlin Shackman, B.S. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Ful llment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN May 2004 Dedicated to my husband Chris. Acknowledgments I would rst like to thank Dr. Greg Sitz for teaching me about surface science and about being an experimental physicist. I will always appreciate his patience and support during my time in this lab. I wish to thank Dr. Elizabeth Watts for taking the time to teach me about this experiment and Dr. Marcia Isakson for helping run this experiment. I enjoyed working with both Dr. Watts and Dr. Isakson, they made learning about this experiment and starting my research very fun and interesting. I would like to thank Jonghyuk Jerry Kim, David Schlichte, Peter Bach, Arban Uka, Shengyuan Zhang, and Robynne Hooper for making this lab a great environment in which to work. I would especially like to thank Jerry Kim for taking on a lot of extra responsibility, along with providing emotional support, when I was injured and could not be in the lab. The entire physics department has been very helpful over my time as a student at UT. Particulary I d like to thank Norma Kotz for all of her support. The physics department machine shop built, and helped with the design of, a large portion of the apparatus used in this work. I d like to thank Allan Schroeder and the rest of the machine shop for their patience and amazing work. I would like to thank Jack Cli ord for help with machining and general moral support. I also would like to thank everyone who worked with me at Health South for getting me back on my feet and back into the lab. Finally I would like to thank my family for all of their love and support. v Isotope E ects in Gas-Surface Interactions: Quantum-State Resolved Studies of D2 Scattering from Cu(100) and Pd(111) Publication No. Leah Caitlin Shackman, Ph.D. The University of Texas at Austin, 2004 Supervisor: Greg O. Sitz State resolved experiments are presented for the interaction of D2 and HD with Cu(100) and Pd(111). For this work, D2 (v=1, J=2) molecules were scattered o of single crystal surfaces at near normal incidence. The re ected molecules were probed using quantum state speci c spectroscopy. For D2 scattered from Cu(100) the survival probability and some transition probabilities were measured over a range of incident energies. The survival probability was found to be larger then that found previously for H2 (v=1) scattered from the same surface. For H2 some of the incident ux was unaccounted for and could possibly have been lost by dissociative adsorption. In contrast, D2 molecules which do not re ect elastically from the surface are accounted for in other transition channels for most energies. The di erences found for D2 compared vi to previous work with H2 are discussed in terms of the lower zero point energy and smaller vibrational energy spacings of D2 . D2 translational energy exchange was studied for several di erent scattering channels and interpreted using simple classical calculations. These calculations agreed well with both the elastic scattering channel as well as the rotational relaxation channel. For rotational excitation some energy was gained by the molecule from the surface. The survival probability was also measured for D2 (v=1) scattered from Pd(111) at one incident energy. Pd is very reactive for D2 dissociation and this survival probability was measured to be much smaller than that for H2 (v=1) under similar conditions. Vibrational relaxation channels were studied for D2 scattering from both Cu(100) and Pd(111). The vibrational relaxation was also found to be smaller than that measured for comparable channels for H2 . The smaller survival probability and vibrational relaxation probability for D2 on Pd(111) cannot be easily accounted for by the di erence in zero point energy and vibrational energy spacings. Measurements were also done to study the rotational excitation of HD molecules scattered from one reactive surface, Pd(111), and two inert surfaces, Cu(100) and Pd(111):H(D). These measurements showed similar amounts of rotational excitation for HD molecules after scattering from these di erent surfaces. vii Table of Contents Acknowledgments Abstract List of Tables List of Figures Chapter 1. Introduction 1.1 Surface Science . . . . . . 1.2 Dissociative Adsorption . . 1.3 State-to-State Transitions . 1.4 Energy Transfer . . . . . . 1.5 Previous Work . . . . . . . 1.6 Isotope E ects . . . . . . . 1.7 Organization . . . . . . . . Chapter 2. Experimental 2.1 Overview . . . . . . . 2.2 Molecular Beam . . . 2.3 Single crystal surfaces 2.4 Probing Molecules . . 2.5 Phase Matching . . . 2.6 State preparation . . 2.7 Measurements . . . . v vi x xi 1 1 2 4 8 9 13 16 18 18 20 22 22 24 26 30 36 36 38 40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Set-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 3. Elastic Scattering of D2 from Cu(100) 3.1 Absolute Survival Probability . . . . . . . . . . . . . . . . . . 3.2 Survival Probability with Incident Energy . . . . . . . . . . . . 3.3 Translational Energy Loss . . . . . . . . . . . . . . . . . . . . viii Chapter 4. Inelastic Channels on Cu(100) 4.1 Rotational Excitation and Relaxation Versus Incident Energy 4.2 Change in Translational Energy . . . . . . . . . . . . . . . . 4.3 Preliminary Results with Cooled Raman Cell . . . . . . . . . 4.4 Vibrational Relaxation Channel . . . . . . . . . . . . . . . . . . . . 43 43 50 54 56 60 61 63 68 69 69 72 78 78 81 84 Chapter 5. Scattering of D2 from Pd(111) 5.1 Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Vibrational Relaxation . . . . . . . . . . . . . . . . . . . . . . 5.3 Transition Probabilities . . . . . . . . . . . . . . . . . . . . . . Chapter 6. HD Scattering Experiments 6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Rotational State Distribution . . . . . . . . . . . . . . . . . . . Chapter 7. Conclusion 7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix Appendix 1. Bibliography Vita Ion Gun for Surface Sputtering 85 89 97 ix List of Tables 3.1 3.2 4.1 5.1 Translational Energy Loss for v=1 J=2 D2 and v=1 J=1 H2 after scattering from Cu(100) surface. . . . . . . . . . . . . . . Energy loss to the Cu surface by one D2 or one H2 molecule calculated using the Baule equation. . . . . . . . . . . . . . . . Change in Energy After Scattering from Surface . . . . . . . . Transition probabilities for D2 v=1 J=2 scattered from Pd(111) at 500K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 42 52 68 x List of Figures 1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 2.6 Schematic of 1D Potential Energy . . . . . . . . . . . . . . Degrees of freedom for a molecule approaching a surface. . Contour plot of 2D PES . . . . . . . . . . . . . . . . . . . Processes of a diatomic molecule interacting with a surface. Letter of peaceful intent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 7 10 14 19 20 24 25 27 29 31 32 34 35 38 39 40 44 46 47 Schematic of experimental set-up, top view. . . . . . . . . . . Interaction region . . . . . . . . . . . . . . . . . . . . . . . . . Electronic Potential of D2 with (2+1) REMPI transitions . . . Examples of Ion Signals from CEMA plate . . . . . . . . . . . Schematic of Inrad Autotracker II, top view . . . . . . . . . . Schematic of Raman Scattering to Produce Light for Stimulated Raman Pumping. . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Typical TOF measurement of D2 molecules. . . . . . . . . . . 2.8 Typical TOF of v=1 J=2 D2 . . . . . . . . . . . . . . . . . . . 2.9 TOF velocity measurement of D2 scattered from Cu(100). . . 2.10 Peak times as a function of probe laser position. . . . . . . . . 3.1 Schematic of the spatial distribution of incident and scattered molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spatial Pro le Measurement of D2 Scattered from Cu(100) at 500 K at an incident energy of 79 meV. . . . . . . . . . . . . Survival Probability versus Energy for D2 (v=1,J=2) scattered from Cu(100) at 500 K . . . . . . . . . . . . . . . . . . . . . . Schematic of D2 energy levels. . . . . . . . . . . . . . . . . . . TOF measurements of elastic and inelastic scattering of D2 at 199 meV from Cu(100) at 500 K. . . . . . . . . . . . . . . . . Transition from v=1 J=2 to v=1 J=4 and J=0 versus incident energy. The dashed lines are drawn to guide the eye. . . . . . xi 3.2 3.3 4.1 4.2 4.3 4.4 4.5 4.6 4.7 5.1 5.2 5.3 6.1 6.2 6.3 1.1 Contour plot of 2D PES . . . . . . . . . . . . . . . . . . . . . Arrhenius Plot of v=1 J=2 to v=1 J=4 transition . . . . . . . TOF measurements of D2 v=1 J=0 scattered from Cu(100) . . Electronic potential energy wells for H2 and D2 showing rotational and vibrational energy spacings. . . . . . . . . . . . . . Spatial Pro le measurement of elastic scattering of v=1 J=2 D2 on Pd(111)at TS = 500K. . . . . . . . . . . . . . . . . . . . . TOF Measurement of D2 in v=1 J=2 and v=0 J=6 state scattered from Pd(111). . . . . . . . . . . . . . . . . . . . . . . . . Finding the location of the surface using the peak times of the v=1 J=2 signal. . . . . . . . . . . . . . . . . . . . . . . . . . . Rotational state distribution of HD in the beam and scattered from clean Cu(100) at 500K. . . . . . . . . . . . . . . . . . . Rotational state distribution of HD scattered from clean Pd(111) at 500K and H(D) covered Pd(111) at 95K . . . . . . . . . . . Boltzmann Plot of HD scattered from clean Cu(100) at 500K, clean Pd(111) at 500 K, and H(D) covered Pd(111) at 95 K. . Schematic of ion gun. . . . . . . . . . . . . . . . . . . . . . . . 51 53 55 59 62 64 67 74 75 76 88 xii Chapter 1 Introduction 1.1 Surface Science Physical and chemical processes at surfaces are important in many aspects of life. Surface science is an interesting eld because both the surface itself and the material which is interacting with the surface can be complicated systems. Engineers need to know that when blood interacts with the surface of a replacement heart valve a reaction will not occur that causes the blood to clot. We need to know the rate at which minerals in our water react with the surface of the pipes in our plumbing and cause them to corrode. The area of surface science which will be discussed in this thesis is the interaction of gases with metal surfaces. These reactions can cause problems as is seen, for example, when metal parts react with oxygen causing them to rust. We can also use these interactions to help, as in the catalytic converter which cleans up automobile emissions. While in some cases gas-surface interactions are understood well enough for industrial use the details of these interactions are still not understood. A complete picture of what happens as a gas molecule approaches, interacts with, and then leaves a metal surface is still needed. With this increased knowledge of gas-surface interactions the speci c industrial uses of chemical reactions at surfaces might be greatly improved. The tools devel1 oped to understand these reactions can also be used in a broader sense to help with work done on other types of reactions at surfaces. We chose to study hydrogen in this work because hydrogen is the simplest molecule. Since calculations can be done on interactions of hydrogen molecules with single crystal surfaces these experiments can be directly compared to theory. Also, hydrogen is important on its own as it is has possible uses in alternate fuel technology. 1.2 Dissociative Adsorption Dissociative adsorption is the rst step in reactions of molecules at surfaces. A gas phase H2 molecule has a bond strength of 4.52 eV [35]. This is roughly 200 times kB T at room temperature. This bond therefore will not break, at temperatures near room temperature, unless it is in the presence of a catalyst. Once the molecular bond is broken, and the H atoms are individually bonded to the catalyst surface, the H atoms can react with other chemicals to form another molecule. It is this processes that is of interest for industrial uses of surface science. There is also basic scienti c interest in how such a strong bond breaks when it interacts with some metal surfaces. The Lennard-Jones model of the potential energy of a molecule as it approaches a surface allows us to visualize an energy barrier to dissocation in one dimension [34]. As is seen in Figure 1.1, as the hydrogen molecule moves closer to the Cu surface the potential energy rises steeply in the hydrogen remains in molecular form. However, there is a potential well for the H atoms bound to the Cu surface. If the molecule can overcome the barrier (where the atomic potential well and 2 the molecular potential energy cross) it can break its molecular bond and bind to the surface as atoms, ending up in a lower energy state. For the Pd surface, in this one dimensional case, the molecule feels no barrier to dissociation as it moves closer to the surface. It will therefore fall readily into the lower energy well and become atoms bound to the surface. Figure 1.1: Schematic of 1D potential energy of an H2 molecule as a function of distance from a Cu and Pd surface. Dissociative adsorption is studied indirectly in this work by measuring 3 the molecules that re ect from the surface. If half of the molecules which are incident on a surface dissociatively adsorb the other half will be re ected and measured. The survival probability is a measure of the fraction of molecules that re ect from the surface. By changing the energy of the incident beam we can study the barrier to dissociative adsorption for di erent surfaces. For metal-gas systems for which there is a high barrier to dissociation the survival probability will be close to one until the incident energy is greater than the barrier to dissociation. 1.3 State-to-State Transitions The 1D PES does not come close to completely describing the interac- tion of a molecule with a surface. For a diatomic molecule, near the surface there are six molecular degrees of freedom which together determine the nature of the interaction. These degrees of freedom, shown in gure 1.2, are the position of the molecule over the surface (x,y), the distance between the surface and the center of mass of the molecule (z), the internuclear distance (r), the angle between the internuclear axis and the x-axis of the surface ( ), and the angle between the internuclear axis and the z-axis ( ). Recent quantum calculations include all of these degrees of freedom when studying gas surface interactions [31]. We cannot visualize the potential energy as a function of all six degrees of freedom. The potential energy is therefore plotted as a function of a subset of these variables with the rest held constant. The potential energy is often viewed in a contour plot as a 4 Figure 1.2: Degrees of freedom for a molecule approaching a surface. function of two degrees of freedom, called a potential energy surface (PES). An example of this, a contour plot of the potential energy as a function of distance from the surface, z, and internuclear distance, r, is shown in gure 1.3. The dotted lines are lines of constant potential energy. For this PES an H2 (or D2 ) molecule is dissociating from a bridge to a hollow site on a Cu(100) surface with the internuclear axis parallel to the surface. This is just one of many possibilities allowed in the calculations. As the molecule approaches the surface it may follow a minimum energy path, shown by the 5 solid line in Figure 1.3a. In order to remain on the minimum energy path the internuclear bond of the molecule lengthens. For this position and orientation over the surface there is a barrier to dissociation. If the molecule has enough energy it will overcome this barrier and dissociate into two atoms bound to the surface. However if the molecule does not dissociate it is still a ected by the interaction with the surface. In the case of gure 1.3b the molecule experiences vibrational relaxation. As the molecule approaches the surface it samples a range of r values. Since the lines of constant potential energy are curved the molecule may need to shift energy between degrees of freedom to follow the lowest energy path. In gure 1.3b the molecule shifts energy in the r coordinate, vibrational energy, to the z coordinate, translational energy. Similarly there may also be a change in the rate of the rotational motion of the molecule for it to remain in the lowest energy state as it approaches the surface. Close to the surface the potential energy can be a strong function of . As the molecule approaches the surface it experiences a di erence in potential energy for di erent values of . This torque may allow the molecule to transfer some energy to the rotational degree of freedom from another degree of freedom. The PES of a system can be probed by studying the state to state transitions which occur after scattering from a surface. The state to state transitions studied in this work are rotational excitation, rotational deexcitation, and vibrational relaxation. There are two 6 Figure 1.3: Contour plot of 2D PES for H2 on Cu(100) surface calculated using equations in [32]. The contour lines are equally spaced at 0.25 eV from the center to 3.0 eV. After 3.0 eV the contour lines are equally spaced at 1.0 eV. main processes involved in rotational excitation and deexcitation. Along with the dependence of potential energy on close to the surface there is also the lengthening of the internuclear, as seen in gure 1.3a. This has the e ect of decreasing the spacing between rotational energy states. Rotational energy states are given by 2 ER = 2I J(J + 1) in the rigid rotor approximation [7], where J is the rotational state of the molecule and I is the moment of inertia. As the internuclear bond lengthens the moment of inertia will become larger, making the rotational 7 energy spacings smaller. With a smaller energy spacings it will be easier for the molecule to transition between rotational states. The extending of the internuclear bond can also lead to vibrational state changes. For vibrational relaxation the extending of the internuclear bond, as it attempts to overcome the barrier to dissociation, couples the vibrational degree of freedom to other degrees of freedom used to overcome this barrier. This coupling allows the the molecule to transfer some of the vibrational energy into other degrees of freedom of the molecule. 1.4 Energy Transfer In the experiments discussed in this thesis the amount of energy in each degree of freedom of the molecule can be measured before and after interacting with the surface. The energy exchange is expected to be mainly between degrees of freedom of the molecule. For example, energy from the translational degree of freedom may be transferred to the rotational degree of freedom for rotational excitation. In this case the molecule will leave the surface with less kinetic energy but rotating faster. However, in some cases the total energy in all degrees of freedom is not the same before and after scattering from the surface. In these cases some energy must be transferred to or from the surface. Energy can be transferred to the nuclear motion of the surface, through excitation of phonons, or by exciting electronic states at the surface. Neither of these processes thought to be very probable for hydrogen [15]. Phonon 8 excitation is not expected due to the large mass mismatch between a H2 or D2 molecule and a surface atom. To transfer energy to the electronic states of the surface an electronic state must become excited as the molecule interacts with the surface and remain in an excited state after the molecule re ects from the surface. It is generally assumed that the electronic con guration of the molecule-surface system remains in its ground state during their interaction. This is because the nuclei of the molecule and the surface are much heavier than the electrons. Since the nuclei and electrons are subject to the same forces the electrons will move much faster than the nuclei. As the nuclei move, when the molecule approaches the surface, the electrons are always able to rearrange themselves into the ground state on a time scale much faster than the molecule-surface interaction. This is known as the Born-Oppenheimer approximation or the adiabatic approximation. In this work the energy in all degrees of freedom of the molecule is measured. By comparing the total energy of the molecule before and after interacting with the surface transfer of energy between the surface and the molecule is measured. 1.5 Previous Work There has been a vast amount of research done on H2 interacting with metal surfaces. So only a few experiments will be mentioned in this thesis. There are several methods for measuring the interaction of H2 with metal surfaces. The di erent ways in which a molecule may interact with a surface is shown schematically in Figure 1.4. 9 Figure 1.4: Processes of a diatomic molecule interacting with a surface. In this work the molecules which re ect, shown in Figure 1.4a, from the surface are measured spectroscopically. Rettner et al. performed a molecular beam experiment similar to the one discussed in this thesis [39]. In their experiment D2 molecules were scattered from a Cu(111) surface with a range of incident energies. The beam source was heated up to 2000 K and operated in an e usive mode. This resulted in a wide range of translational energy, with signi cant ux at energies up to 400 meV. At the highest energy evidence for vibrational excitation was found. This work suggests that vibrational state transitions in D2 occur at high beam energies and that the reaction path for vibrational excitation is similar to the reaction path for dissociation. For some experiments atoms are adsorbed on the surface and then the surface 10 is heated so that these atoms associatively desorb, as is illustrated in Figure 1.4b. The molecules can than be detected using a laser or mass spectrometer. Since the molecules experience the same PES regardless of the direction of the reaction path these experiments give complementary information to the measurements described here. A review of several experiments of this type, along with dissociative adsorption experiments, was compiled by Michelsen and Auerbach [37]. Associative desorption and dissociative adsorption from Cu(100), Cu(110), and Cu(111) is discussed. The purpose of this work was to study the importance of vibrational energy of the molecule in the dissociative adsorption process relative to the translational energy of the molecule. This was done by tting the work of several groups to a vibrational state speci c model and comparing those ts to a model which does not account for any vibrational states. This work showed that the vibrational degree of freedom must be considered in H2 /Cu interactions and that more experiments needed to be done to understand this process quantitatively. A related class of experiments study the rotational excitation of a molecule after scattering from a surface. One method for measuring this is to scatter molecules from a surface at a xed incident angle and measure the scattered intensity as a function of nal angle. Molecules which scatter elastically will re ect from the surface at the specular angle. However, molecules which make state transitions will experience a change in momentum which will cause them to scattered at a di erent angle. Conservation of energy and parallel momentum can than be used to connect the scattered angle with a 11 rotational state transition. Bertino et al. have performed such experiments with D2 scattered from Cu(001) [5]. In this work they were able to measure several peaks due to rotationally inelastic scattering. The intensity of this signal could then be measured as a function of incident energy. This work shows that these rotationally inelastic transitions can be used to understand the H2 /Cu PES. The initial direction of the experiments presented here was based on previous studies performed with the same experimental apparatus. Measurements done by Elizabeth Watts studied many aspects of H2 (v=1, J=1) interacting with Cu(100) [49]. She measured the survival probability of H2 as a function of energy and the transition probabilities as a function of incident energy and surface temperature. Energy transfer measurements were also performed for both rotationally inelastic and vibrationally inelastic scattering events. The work shown in this thesis was directly compared to the studies done by Watts in order to look for isotope e ects in the H2 /Cu(100) interactions. Michael Gostein performed experiments with H2 in the vibrational ground state and the rst excited vibrational state interacting with Pd(111) [22]. In the vibrational ground state experiments a rotational state resolved sticking probability was measured. The sticking probability was seen to rst decrease with increasing rotational energy and then increase. It is possible that this trend is due to steering of the H2 molecules as they approach the surface. The steering process and these supporting results illustrate the way in which H2 or D2 molecules interacting with a surface can give detailed information 12 about the PES. 1.6 Isotope E ects An isotope of an element has the same electronic structure but the mass has been changed by the addition or removal of at least one neutron to the nucleus of the atom. A di erence in only the mass opens up many possibilities for experiments. Since the electronic aspects of the system which is studied remains the same, parts of the interaction which are dependent on mass are isolated. Isotopes can also be used to make one part of the system di erent from the rest in a limited way. Deuterium is an isotope of hydrogen with one extra neutron. It was discovered in 1931 by H. Urey [46]. For hydrogen this one extra neutron approximately doubles its mass. Since the D2 nuclei have greater masses then H2 nuclei, the vibrational zero point energy is lower in the electronic potential well. Also, the vibrational and rotational energy spacings are smaller for deuterium than for hydrogen. For many purposes substituting a H atom with a D atom in a substance will change some its properties. A famous example is heavy water, D2 O, which is used in nuclear reactors. The extra neutron in heavy water makes it a good moderator for ssion chain reactions. In a ssion reaction an atomic nucleus is split into smaller pieces after absorbing a neutron. In the ssion reaction for nuclear reactors 235 U splits into two radioactive nuclei and free neutrons, which then cause more ssion events. The moderator is needed to slow down these neutrons so that they can be absorbed by another uranium nucleus [25]. D2 O 13 works much better than H2 O in this case because it is less likely to capture a neutron, so that they will be available for ssion reactions. Since this reaction is the heart of nuclear reactors and nuclear weapons, D2 O was a very valuable item just after the time of the discovery of D, just before World War II [13]. This element is still kept under close watch, exempli ed by our need to write a letter of peaceful intent in order to purchase D2 for these experiments, shown in gure 1.5. Figure 1.5: Letter of peaceful intent. When there were large enough samples of D2 O available biological stud- 14 ies using heavy water were possible. In one study rats were given D2 O instead of H2 O [45]. Various aspects of the rat s health was studied but the main result (especially for the subjects!) was that these rats died. The author states that The cause of death of deuterated rats is not entirely clear. The animals su er from anemia, renal damage, malnutrition, central nervous system damage, possibly adrenal insu ciency, and very likely many other disturbances. [45]. This is most likely due to another aspect of isotope substitution, it will change the rate of chemical reactions. In the case of the unfortunate rats the rates of many chemical reaction that take place in their bodies changed enough to cause serious illnesses. This in itself can be a way to nd out which processes are important in chemical reactions. For example the lower zero point energy of deuterium means that it takes more energy to break a deuterium bond than a hydrogen bond. So, if the breaking of a hydrogen bond is the rate limiting step in a chemical reaction, then replacing that hydrogen atom with a deuterium atom should slow the rate of the reaction. At any temperature a deuterium atom also moves slowly due to its larger mass. This may also slow reaction processes. For example if the reaction depends on some di usion process substituting D for H atoms will slow the rate of reaction. For the experiments discussed here both the di erence in energy levels within the electronic potential and the di erence in speed at the same energies are relevant. The di erence in energy levels allows us to explore a di erent region of the same PES for the H2 /Cu(100) and H2 /Pd(111) systems. There has been a lot of work done on developing a theoretical understanding of how H2 15 interacts with metal surfaces [6, 15, 31]. In some calculations all six molecular degrees of freedom are included. At the present time the extent to which the degrees of freedom of the surface can be included is limited. At this point comparison between experiment and theory becomes crucial in identifying which degrees of freedom have to be included in an accurate model. On many points the theory agrees well with experiment. For example there is good agreement for the reaction probability of v=0 and v=1 H2 , along with the survival probability of v=1 J=1 H2 , scattered from Cu(100) [33]. There are, however, some interesting di erences between theory and experiment. Six-dimensional calculations for H2 scattering from Cu(100) nd much higher values for the v=1 J=1 to v=1 J=3 transition than is measured [33]. Large di erences like this show the need for further investigation of gas-surface interactions. The data shown in this work will allow for more comparisons with calculations. The slower moving D2 molecule allows us to study the importance of the length of the interaction time in these reactions. Since D2 moves slower than H2 at the same translational energies it is more likely that the surface electronic structure will remain in its ground state during the interaction. This would lead to a di erence in the amount of energy transfer to the surface, especially during vibrational relaxation transitions. 1.7 Organization In this work the survival and transition probabilities were measured for D2 (v=1, J=2) scattered from both Cu(100) and Pd(111). In chapters 3 and 16 4 the studies of D2 scattered from Cu(100) are shown. This work is compared to the results of H2 /Cu(100) studies. Di erences in these results are discussed in terms of the PES for H2 /Cu(100). The experiments of D2 scattered from Pd(111) are shown in chapter 5. This work is compared to the H2 /Pd(111) results and the possibility of non-adiabatic coupling in this system is discussed. Finally some experiments studying the rotationally inelastic scattering of HD, in the ground vibrational state, from Cu(100), Pd(111), and H(D):Pd(111) are shown and discussed in chapter 6. 17 Chapter 2 Experimental Set-Up 2.1 Overview This apparatus has been built up over the past decade and is described in previous theses from the Sitz group [24, 50]. A pulsed supersonic beam of D2 is created in a separately pumped source chamber. The beam then goes through the skimmer into a separately pumped bu er chamber. Next the molecular beam is sent through chopper to create a well de ned pulse. The scattering takes place in a main chamber which is kept between 2X10 10 Torr and 2X10 9 Torr. The single crystal sample is held on a manipulator which is attached to the lid of the main chamber. The lid of the main chamber is placed on two di erentially pumped seals and a bearing. In this way the lid can be rotated to any position while maintaining ultra high vacuum. The sample can than be rotated into position for ion sputtering, low energy electron di raction (LEED) measurements, Auger spectroscopy, or scattering experiments. An overview of the experimental set-up is show in gure 2.1 The D2 molecules are probed with a tunable ultraviolet laser beam before or after interacting with the surface. The molecules in each pulse can be pumped into the v=1 J=2 quantum state using stimulated Raman scattering. 18 Figure 2.1: Schematic of experimental set-up, top view. The molecular beam strikes the surface at near normal incidence. Both the probe and pump laser beams are perpendicular to the molecular beam as well as the surface normal. Figure 2.2 shows the area of the experiment where the molecular beam interacts with the lasers and the single crystal sample. The ions are then collected and measured using a multichannel detector. 19 Figure 2.2: Close up view of the region where the molecular beam interacts with the surface. 2.2 Molecular Beam The molecules are delivered by a supersonic nozzle pulsed at a fre- quency of 10 Hz. The pressure behind the nozzle is typically kept at 20 psig. Since a range of incident energies is needed for these experiments the nozzle can be heated or cooled to adjust the beam energy. The nozzle is heated using a piece of tantalum wire. The wire is held around the sample in a boron nitride insulator and is heated resistively. The nozzle is typically cooled with water but can be cooled with liquid nitrogen. Since commercial nozzles use a te on tip they could not be used for these experiments since it would not be possible to heat the nozzle without damaging the tip. In order to heat the nozzle to the temperatures needed for this experiment a nozzle was designed in the lab 20 by Jennifer Siders. The nozzle design is described in reference [43]. In order to heat the nozzle a stainless steel nozzle tip is used. The disadvantage of a stainless steel tip is that it is very di cult to keep the nozzle from leaking. A te on tip will mold itself into the shape of the nozzle opening as it runs, whereas a stainless steel tip is not as malleable. Siders determined that a hemispherical nozzle tip gives the best sealing properties when the nozzle is closed. The tip and nozzle opening must be the same shape, on a fairly microscopic scale, before use in the experiment. The physics department machine shop fabricates the nozzle tip and matching ange precisely, however to prevent leaking the steel tip still has to be lapped with the nozzle opening. The nozzle can be used if it leaks slightly, since the source chamber is di erentially pumped. We use the nozzle when it leaks less than 1 psi in 15 minutes. Pure D2 was used for most of the experiments. To achieve higher incident energies the D2 was sometimes mixed with H2 . To keep the pressure in the main chamber low when the nozzle is on a skimmer is placed directly after the nozzle and only transmits molecules travelling perpendicular to the sample. The skimmer also reduces the cross section of the beam so that the molecules only strike a small area of the surface. After the skimmer, the pulse of molecules goes though a chopper, rotating at 300 Hz, to ensure a well de ned incident pulse of molecules and also to limit the amount of gas sent into the main scattering chamber. 21 2.3 Single crystal surfaces The surfaces used are single crystal Cu(100) and Pd(111) prepared commercially by the Surface Preparation Laboratory. The surface is heated by electron bombardment from a lament located behind the sample. The feed-back circuit used to control the sample temperature was designed and built in the lab by Michael Gostein. The sample temperature is measured with a thermocouple located in a hole in the side of the sample. The hole for the thermocouple is fabricated by the manufacturer using electron discharge milling (EDM). The measured temperature is compared to a setpoint temperature and the emission current from the lament behind the sample is adjusted by the feed-back circuit so that the sample temperature remains at the set temperature. The sample is cooled by conductance through a cryostat using either liquid nitrogen or water. The surfaces are cleaned using Argon ion sputtering at 300 followed by annealing at 557 for Cu or 600 for Pd. C C C The ion gun used for sputtering is discussed in detail in the appendix. The cleanliness and orientation of the crystal are checked using Auger spectroscopy and LEED. 2.4 Probing Molecules A frequency tripled dye laser is used for probing the molecules. The dye laser is pumped by a frequency doubled Nd:YAG laser. The dye laser light is then frequency doubled, using a potassium dihydrogen phosphate (KDP) crystal, and the fundamental and doubled light are mixed, using a beta-barium 22 borate (BBO) crystal, to produce the third harmonic of the dye laser light. The ultra-violet light is then focused into the molecular beam. Using this tunable ultraviolet light we can state-selectively ionize the D2 molecules using 2+1 resonance-enhanced multiphoton ionization (REMPI). The molecules are resonantly excited from the ground electronic state to the E,F excited electronic state by two ultra-violet photons. The laser can therefore be tuned to excite only one vibrational and rotational state. A third photon then ionizes the molecules which are in this excited electronic state [36], as shown in gure 2.3. The ions are collected onto a channel electron multiplier array (CEMA) plate, using steering voltages. In gure 2.4 three separate ion time-of- ight signals are shown on the same plot. In this gure the rst dip is the signal created by the laser as it passes through the chamber. The scattered laser light creates a very large signal. So, the CEMA bias voltage must be kept low enough to prevent the scattered laser light signal from masking the ion signal. The CEMA bias voltage is stepped up after the laser has passed through the chamber to amplify the ion signal. The CEMA voltage is pulsed from between 1200 and 1300 V to between 1600 and 1900 V at 10 Hz. This high voltage switching is achieved using a high voltage gating circuit designed and built in the lab by Michael Gostein [21]. The wide dip which appears after the laser signal is the response of the detector when the CEMA voltage is increased. The next three dips are the ion signals. These measurements were made of a mixture of H2 and D2 so there is a signal for H2 , D2 , and HD. The ion signal 23 Figure 2.3: Electronic Potential of D2 with (2+1) REMPI transitions appears at the time it took for the molecule to travel from the laser focus to the ion detector. Since the collection voltages used are the same for each molecule, and H2 is the lightest molecule, the ion signal for H2 is the earliest signal. 2.5 Phase Matching In order for the dye laser light to be doubled by the KDP crystal, and then the fundamental and doubled light to be mixed by the BBO cystal, the 24 Figure 2.4: Examples of Ion Signals from CEMA plate. There are three traces superimposed, each at a di erent wavelength. crystals must be kept at the maximum phase matching angle with respect to the direction of laser propagation. The phase matching angle is wavelength dependent, so as the dye laser is tuned the crystals must rotate. This is done using an Inrad Autotracker II. A schematic of the autotracker is shown in gure 2.5. The laser light rst passes through a compensating crystal and then through the BBO or KDP crystal. The compensating crystal has approximately the same index of refraction as the KDP or BBO crystal and therefore bends the laser light by the same amount. This ensures that the direction 25 of the output light remains constant as the crystal is turned to maintain the phase matching. The autotracker unit comes with a controller which automatically rotates the crystal so that they remain at the phase matching angle. To do this a fraction of the output light is split o and sent to a sensor. The sensor consists of two photodiodes placed next to each other. As the laser wavelength is tuned the doubled or mixed light signal will decrease. Since the decrease in doubled or mixed light will be greater on one side of the crystal the autotracker can determine which direction to rotate the crystal by comparing the signal from the two photodiodes. I found that over time the beam splitter became degraded by the ultra violet light. This led to dispersion of the output light which reduced the amount of light which made it to the experiment. I was able to increase the ion signal by a factor of 10 by moving the autotrackers close to the input ports of the main chamber so that the light only travels a few feet before it is focused into the beam. 2.6 State preparation The molecules in each pulse are essentially all in the vibrational ground state. Thermally populating the v=1 vibrational state, for use in this experiment, requires heating the D2 source to temperatures in excess of 700 K. In order to study molecules in the excited vibrational state the molecules were pumped into the v=1 state using stimulated Raman scattering [16, 19]. Frequency doubled Nd:YAG laser light is focused into a cell pressurized with about 50 psi of D2 . The 532 nm light scatters o of the D2 molecules to produce 26 Figure 2.5: Schematic of Inrad Autotracker II, top view Raman shifted light collinear with the Nd:YAG light. With a high intensity of laser light stimulated Raman scattering occurs. The transition associated with the most populated rotational state of the D2 molecules is ampli ed. For D2 at room temperature this is the v=0 J=2 to v=1 J=2 transition. As can be see in gure 2.6 many wavelengths of pump light are produced, spaced at the energy of one vibrational quanta of 370.8 meV. The light produced by the Raman cell is focused into the molecular beam in front of the surface before 27 the probe laser, as is shown in gure 2.2. The molecules which interact with two frequencies of laser light which have an energy di erence of one vibrational spacing are pumped from the v=0 J=2 state to the v=1 J=2 state. In this process molecules can also be pumped from the v=1 J=2 state to the v=0 J=2 state. As the pulse of molecules interacts with the pump laser it reaches a steady-state of vibrational state population. Therefore we expect to pump about half of the molecules which interact with the laser into the v=1 J=2 state. We use a pump laser power which is large enough to obtain saturation. For deuterium the pump Nd:YAG laser is set to a ash lamp voltage of 1.50 kV. Saturation is determined by noting the laser power at which the ion signal of pumped molecules stops getting larger. By cooling the Raman cell with liquid nitrogen the population in the D2 molecules shifts from v=0 J=2 to v=0 J=0. Raman scattering of the cooled molecules then produces the wavelengths of light to pump the v=1 J=0 state. I was able to pump this state by cooling the Raman cell, however the signal was smaller than the v=1 J=2 signal because the quality of the beam exiting the cooled Raman cell is very poor. The direction of the exiting beam changes as the cell is cooled and the beam diverges. So, only a fraction of the pump laser light could be accurately focused into the molecular beam. Other groups that have cryogenically cooled a Raman cell, with the same design as the one used here, have found this same beam instability [40, 44]. These groups found that the beam instability was due to a large temperature gradient across the Raman cell causing convection of the gas in the cell. This temperature 28 Figure 2.6: Schematic of Raman Scattering to Produce Light for Stimulated Raman Pumping. gradient e ect was not studied in detail, instead these groups redesigned the cell to achieve good beam quality while cooling the gas in the Raman cell. In order to successfully cool the deuterium in the Raman cell it should be redesigned. Further study of this e ect would also be very interesting. Due to the poor laser beam quality only preliminary studies could be done on D2 pumped into the v=1 J=0 state. These results will be discussed in following sections. 29 2.7 Measurements There are two types of measurements made in this experiment: a time of ight (TOF) measurement and a wavelength scan. The main one used in this report is a TOF measurement. In this case the ring time of the probe laser is scanned relative to the time the chopper sends though a pulse of molecules. The dye laser wavelength is held at the peak of the transition being studied. An ion signal is measured for each delay time. The maximum signal occurs when the center of the pulse of molecules has arrived at the probe laser position. A typical TOF measurement is shown in gure 2.7. The area under this gaussian is used as a measure of the relative number of molecules present in the quantum state which the probe laser is tuned to detect. Each pulse of molecules is about 10 microseconds wide. Given this width the molecules scattered from the beginning of the pulse will be at the probe laser position at the same time as the incident molecules at the end of the pulse. This means that the molecules which are incident on the surface cannot be distinguished from the scattered molecules. To di erentiate the incident and scattered molecules a wire is placed across an aperture after the skimmer. As the molecules enter the scattering chamber a section of the beam, 0.38 mm high, is blocked. When the laser is placed in this shadow area only scattered molecules are detected. The incident molecules are measured with the scattering chamber lid rotated so that the sample is not in the beam path and the probe laser is not in the shadow region. The width of the pumped pulse of molecules is not larger than 150 ns, 30 Figure 2.7: Typical TOF measurement of D2 molecules. since only the molecules which interact with the pump laser beam are excited. With such a short time scale the incident and scattered molecules can be measured in the same TOF scan. A TOF scan of molecules pumped into the v=1 J=2 state is shown in gure 2.8. The reader should note that the time scale in gure 2.8, of the pumped molecules, is 40 times smaller than the TOF of the unpumped molecules shown in gure 2.7. The rst peak in gure 2.8 corresponds to the incident v=1 J=2 D2 molecules. The second, smaller, peak corresponds to the elastically scattered molecules from the Cu(100) surface. 31 Figure 2.8: TOF of v=1 J=2 D2 molecules incident on and scattered from Cu(100) at 500 K. In a wavelength scan the laser ring time is kept constant, at the peak time, and the dye laser wavelength is scanned. This yields a measurement of ion signal with respect to wavelength. For this work the wavelength scan was used mainly to nd the peak wavelength to use for a TOF scan. The velocity of the beam can be found by taking TOF scans at di erent probe laser positions. The change in peak times of the TOF scans as a function of the change in the probe laser position is used to calculate the velocity of 32 the molecules. When the molecules are pumped into the v=1 J=2 state the velocity of the incident and scattered molecules can be measured at the same time. As is shown in gure 2.9, as the probe laser is moved away from the surface the TOF peak of the incident molecules appears at earlier times and the TOF peak of the scattered molecules appears at later times. Figure 2.10 shows a plot of the peak times for incident and scattered signals. The velocity is found from the slope of a linear t. From the velocity measurement the energy is easily obtained. 33 Figure 2.9: TOF velocity measurement of D2 scattered from Cu(100). 34 Figure 2.10: Peak times as a function of probe laser position. 35 Chapter 3 Elastic Scattering of D2 from Cu(100) Using spatially resolved TOF data such as that shown in gure 2.8, we can determine two quantitative results about the scattering of D2 (v=1, J=2) from Cu(100): the absolute survival probability and the net energy transfer to the surface. There is a barrier to dissociation for all orientations of the molecule and positions over the Cu(100) surface, so the survival probability is expected to be large. The energy transfer to the surface, however, should be small since the mass of the D2 molecule is much smaller than the mass of a Cu atom. 3.1 Absolute Survival Probability To measure the relative survival probability of D2 v=1 J=2 scattered from Cu(100) the ratio of the areas under the incident and scattered TOF signals, shown in gure 2.8, is found. The vibrationally excited molecules approach the surface as a band of molecules with the vertical extent of the pump laser. However, they scatter from the surface with some distribution of angles, as can be seen in gure 3.1. Since the scattered molecules leave the surface with a broader spatial pro le than the incident molecules a further 36 measurement is needed to nd the absolute survival probability. To do this TOF scans are taken with the probe laser at di erent vertical positions, also shown in gure 3.1 (with the probe laser moving in or out of the page). The area under the incident and scattered signals are found for each height. In these experiments the detection is sensitive to the density of molecules which interact with the laser pulse, not the ux of molecules crossing the path of the laser pulse. This means that molecules which are slower moving are more likely to be detected than fast moving molecules because they remain in the interaction area longer. Also, molecules which cross the laser path at an angle are more likely to be detected than molecules moving perpendicular to the laser beam direction. Both of these factors allow for a greater detection of the scattered molecules than the incident molecules. To take this into account a density to ux weighted correction was applied to the TOF measurements for the survival probability of D2 v=1 J=2 scattered from Cu(100). This correction was done using a program written by Michael Gostein and is described in detail in his dissertation [24]. The areas under the TOF curves are then plotted as a function of probe laser position. This spatial pro le measurement is t to a gaussian (for convenience) for each set of areas, incident and scattered, as is shown in gure 3.2. These measurements were taken with an incident energy of 79.0 0.6 meV and at a surface temperature of 500 K. The ratio of the area under each of these curves gives the absolute survival probability of D2 v=1 J=2 scattered from Cu(100) of 0.81 0.12. This is larger than the absolute survival probability of H2 on Cu(100) which was found to be 0.61 at an incident 37 energy of 78 2 meV [50]. Figure 3.1: Schematic of the spatial distribution of incident and scattered molecules. 3.2 Survival Probability with Incident Energy The absolute survival probability as a function of incident energy is shown in gure 3.3. The angular distribution was assumed to be the same for each energy. This means that the ratio of the relative survival probability to the absolute survival probability was found at position 0 mm in gure 3.2. Then, instead of taking the spatial distribution measurement at each energy, the relative survival probability was found, at position 0 mm, and scaled by the ratio found for an incident energy of 79 meV. The survival probability was found to be constant, at approximately 0.80, up to about 110 meV, at 38 Figure 3.2: Spatial Pro le Measurement of D2 Scattered from Cu(100) at 500 K at an incident energy of 79 meV. which point it decreased slightly to approximately 0.50. For H2 on Cu(100) the survival probability drops from 0.81 to 0.30 between 31 meV and 180 meV [49]. The decrease in survival probability with incident energy is much more pronounced with H2 than with D2 . The higher survival probability of D2 , for a wide range of energies, may be due to lower zero-point energy, and smaller vibrational energy spacing, in the D2 molecule. This will be discussed in the next chapter. 39 Figure 3.3: Survival Probability versus incident energy for D2 (v=1,J=2) scattered from Cu(100) at 500 K. The dashed line is drawn to guide the eye. 3.3 Translational Energy Loss For scattering of D2 or H2 from Cu(100) there is a large re ected signal. This makes it possible to measure both the incident and scattered translational energies accurately. These measurements were done at several surface temperatures for D2 scattered from Cu(100). For comparison the translational energy of H2 before and after scattering from Cu(100) was measured at two surface temperatures. The results of these measurements are show in table 3.1. The 40 weak surface temperature dependence is expected since the incident energy is large with respect to the surface temperature (kTS =43 meV at 500 K). Surface Incident Scattered Energy Temperature (K) Energy (meV) Energy (meV) Loss (meV) 400 81 1.4 70 2.1 11 3.5 500 80 1.8 71 2.7 9 4.5 600 81 2.2 70 2.0 11 4.2 800 81 3.5 73 2.9 8 6.4 400 72 1.1 68 0.7 4 1.8 800 71 2.3 69 3.0 2 5.3 D2 H2 Table 3.1: Translational Energy Loss for v=1 J=2 D2 and v=1 J=1 H2 after scattering from Cu(100) surface. Considering this system as a collision of a molecule with a Cu atom the energy loss can be calculated using the Baule equation [54] (which uses conservation of energy and momentum). (TS ) = 4 1 [Ei kTS ] 2 (1 + ) 2 (3.1) is the change in energy, is the mass ratio MD2 /MCu =0.063 or MH2 /MCu =0.032, TS is the surface temperature, Ei is the kinetic energy of the incident molecule, and k is the Boltzmann constant. The Baule equation gives the values for the energy loss to the surface shown in table 3.2. The loss of energy calculated using the Baule equation agrees well with the measured values for an e ective mass between 1 and 2 copper atoms, which is physically reasonable. The temperature dependence cannot be resolved 41 TS (K) D2 400 600 800 400 800 H2 (meV) (meV) (meV) (meV) (meV) Experiment 1 Cu atom 2 Cu atoms 3 Cu atoms 5 Cu atoms 11 3.5 14.3 7.6 5.2 3.6 11 4.2 12.4 6.6 4.5 2.7 8 6.4 10.4 5.5 3.8 2.3 4 1.8 6.6 3.4 2.3 1.2 2 5.3 4.4 2.3 1.5 0.9 Table 3.2: Energy loss to the Cu surface by one D2 or one H2 molecule calculated using the Baule equation. within the precision of this measurement. For elastic scattering the energy transfer to the surface is small, as is expected with the large mass di erence between the molecule and a copper atom. 42 Chapter 4 Inelastic Channels on Cu(100) Using state selective spectroscopic techniques the probability of transitions from the v=1 J=2 state to other vibrational and rotational states can be measured. Energy exchange with the surface can also be studied quantitatively. These measurements can tell us about the force acting on a molecule as it interacts with the surface. When interacting with the surface there is the restriction on the rotational state transitions of J=2. This comes about because the symmetry of the overall molecular wavefunction must be the same before and after interacting with the surface. In these interactions only the rotational state changes; the molecule remains in the same electronic state and the nuclear spin state of the molecule remains the same. The symmetry of the wavefunction goes as (-1)J , which remains the same only if J=2. Some of the transitions which can be studied are shown in gure 4.1. 4.1 Rotational Excitation and Relaxation Versus Incident Energy Along with elastic scattering from Cu(100), excitation to the v=1 J=4 state and relaxation to the v=1 J=0 state were measured for a range of incident energies. To measure rotationally inelastic scattering the laser is tuned to the 43 Figure 4.1: Schematic of vibrational pumping of D2 from v=0 J=2 to v=1 J=2. Also shown are some possible transitions made when scattering from a surface. resonant wavelength of the rotational state to be studied and a TOF scan is taken with the same laser positions and collection voltages as the elastic channel measurements. A sample TOF scan of the elastic channel as well as signals from rotationally inelastic transitions is shown in gure 4.2. Note the scale factors for the inelastic peaks: the rotationally inelastic signals are actually much smaller than the elastic signal. The molecule gains translational energy when it transfers from the v=1 44 J=2 to v=1 J=0 state, causing the molecules to move faster than the elastically scattered molecules, so the TOF signal appears slightly earlier than the elastic peak. Similarly when the molecule makes a transition from v=1 J=2 to v=1 J=4 the signal shows up later because the molecules have lost translational energy. In these TOF scans the rotationally inelastic peaks are near in time to the peak of the elastically scattered molecules. The shift in peak position is small because at the energies used in this experiment the change in energy with rotationally inelastic scattering does not change the speed of the molecule very much compared to the scale of the experiment. For example a D2 molecule which leaves the surface with 80 meV of translational energy is travelling at 1964 m/s. The molecules are probed about 0.4 mm away from the surface, as can be seen in gure 2.9. A D2 molecule with 80 meV of translational energy will travel from the surface to the probe laser position in 0.204 s. A D2 molecule with 60 meV, 20 meV less, translational energy is moving with a velocity of 1700 m/s. This molecule will travel to the probe laser position from the surface in 0.235 s. In gure 4.2 the di erence in arrival time for these two D2 molecules of 0.031 s is not even as large as a small division on the time axis, making the shift in peak times di cult to see. The relaxation and excitation probabilities as a function of incident energy are shown in gure 4.3. The probability of the relaxation to the v=1 J=0 state was the largest at all incident energies. The relaxation probability is constant over incident energies studied. The transition to v=1 J=4 grows slightly as incident energy increases from about 80 meV to about 100 meV, 45 then remains constant. Figure 4.2: TOF measurements of elastic and inelastic scattering of D2 at 199 meV from Cu(100) at 500 K. The sum of the transition probabilities to v=1 J=0 and v=1 J=4 accounts for the missing fraction of molecules in the survival probability measurement for most of the incident energies measured. At the highest translational energies the survival probability drops but no increase is seen in the transition probabilities at these energies. At the lower energies we expect that the transitions to other rotational states will account for the molecules missing in v=1 J=2 since dissociation is not very likely for D2 on Cu(100) 46 Figure 4.3: Transition from v=1 J=2 to v=1 J=4 and J=0 versus incident energy. The dashed lines are drawn to guide the eye. these at energies. The initial sticking coe cient of H2 , in the vibrational ground state, on Cu(100) at the beam energies used for these experiments is approximately 10 5 [2]. Vibrational energy will increase the probability of dissociation. Michelsen and Auerbach analyzed data from several experiments of H2 on Cu(100) and found in the barrier to dissociation is 0.259 eV in the rst vibrational level [37]. They developed a model functional form for the sticking probability as a function of translational energy and vibrational state. Using their ndings the sticking probability of an H2 molecule, in the rst 47 excited vibrational state, on Cu(100) at 79 meV is 0.005. Considering that with a lower zero point energy and smaller vibrational state spacing the D2 molecules approach the surface with 210 meV less vibrational energy than the H2 molecules, the sticking probability of D2 on Cu(100) should be smaller than 0.005. It was shown in chapter 3 that the survival probability is greater for vibrationally excited D2 than vibrationally excited H2 on Cu(100) at the same incident energies [49]. The loss of molecules in the initial vibrational and rotational state can be due to either transitions to other vibrational and rotational states or to dissociation on the surface. For D2 , at most incident energies studied, the loss of molecules in the v=1 J=2 state is accounted for in rotational state transitions. For H2 not all of the loss of the initial state population, v=1 J=1, is found in rotational and vibrational state transitions. Some of the loss of incident v=1 J=1 molecules must be from dissociation or scattering into states that could not be measured in the experiment [50]. The lower survival probability and the possibility of dissociation at the Cu surface shows that H2 is more active than D2 at the Cu(100) surface. This can be accounted for by the di erence in vibrational energy of the two molecules. In order to dissociate on the Cu(100) surface the molecule must have enough energy to overcome a barrier to dissociation. The barrier for dissociation varies with di erent molecular orientations and positions over the surface. In a theoretical calculation Kroes et al. give a minimum barrier height as 0.48 eV and a barrier height as large as 1.37 eV [31]. The D2 molecules approach the surface 48 with only 5 to 10 meV more translational energy than the H2 molecules for a room temperature nozzle. However the pumped H2 molecules approach the surface with 210 meV more vibrational energy. This is illustrated in gure 4.7. It has been shown both experimentally [37] and through calculations [26] that vibrational energy increases the probability of dissociation in this system. With the added vibrational energy an H2 molecule approaches closer to the dissociation barrier than a D2 molecule with the same kinetic energy. There is evidence that inelastic scattering is also more likely to occur when the energy of the molecule is close to the barrier height for dissociation [38, 39]. The larger amount of vibrational energy can therefore account for H2 being more active at the Cu(100) surface than D2 . In order to visualize how vibrational energy aids in dissociation and state-to-state transitions it helps to look at a calculation of the potential energy of the molecule as it approaches the surface. This is called a potential energy surface (PES). The force the molecule experiences as it approaches the surface will depend on the orientation of the molecule and its location over the surface. In calculations of molecular dynamics at surfaces the energy of the moleculesurface system is found for each molecular orientation and location over the surface. In order to look at these potentials we plot them as a PES in only two dimensions. The most useful for understanding the role of vibrational energy is a PES contour plot with the internuclear distance and the center of mass distance from the surface as variables. In gure 4.4 a PES of H2 (or D2 ), with the internuclear axis parallel to the surface, dissociating from a bridge 49 to a hollow site on a Cu(100) surface is shown. This PES was calculated using equations in [52]. The curved line through the center of the PES is the minimum energy path of the molecule. The molecule will try to follow the lowest energy path as it approaches the surface. For this system the barrier to dissociation occurs when the molecule is close to the surface but still needs to extend its bond to dissociate, as can be seen in 4.4. This is known as a late barrier to dissociation since the molecule needs energy to break the molecular bond, rather than to approach the surface. If a molecule is in an excited vibrational state it will have more energy which is being used to lengthen the internuclear axis then in the ground vibrational state. It is this lengthening of the internuclear distance which increases the probability of the molecule making a transition into another vibrational state. In the region of the PES near the barrier the vibrational and translational degree of freedom become coupled as they are both being used to cross the barrier to dissociation. Once the molecule passes over the barrier to dissociation the internuclear bond will continue to lengthen as the two atoms become bound to the surface. Similar pictures can be developed for the rotational degree of freedom when the PES is plotted versus polar angle. 4.2 Change in Translational Energy As with the elastic scattering channel the change in translational energy was measured for the v=1 J=2 to v=1 J=0 ( ER = -21.4 meV) and v=1 J=4 ( ER = 49.6 meV) channels. The translational energy gain or loss measured 50 Figure 4.4: Contour plot of 2D PES for H2 on Cu(100) surface calculated using equations in [32]. The contour lines are equally spaced at 0.25 eV from the center to 3.0 eV. After 3.0 eV the contour line are equally spaced at 1.0 eV. is shown in table 4.1. For the v=1 J=2 to v=1 J=0 channel the amount of energy lost to the surface is similar to the elastic scattering measurement, shown in table 3.1, and consistent with the Baule equation calculations, shown in table 3.2. However, for the v=1 J=2 to v=1 J=4 transition 18.6 1.0 meV of energy is gained by the molecule after scattering from the surface. When the initial translational energy of the molecule is increased by about 20 meV the molecule no longer gains any translational energy for this channel. 51 Transition ER (meV) v=1 J=2 v=1 J=4 49.6 v=1 J=2 v=1 J=0 -21.4 Ei (meV) ES (meV) ET (meV) 79 0.6 48.0 0.8 18.6 1.0 110.0 3.1 59 5.4 1.4 6.2 81.0 1.5 92.0 3.4 -10.4 5.2 Table 4.1: Change in Energy After Scattering from Surface A slight increase was seen in the probability of transition from v=1 J=2 to v=1 J=4 when the initial translation energy is increased from 80 meV to 100 meV. Over this incident energy range the energy gain by the molecule from the surface during this transition decreases. To study this further, the inelastic scattering probability was measured as a function of surface temperature, at an incident energy of 80 meV. The log of the transition probabilities was plotted against the inverse of surface temperature, called an Arrhenius plot. This can be seen in gure 4.5. From the slope an activation energy of 18 meV was found, the same as the amount of energy gained by the molecule after the v=1 J=2 to v=1 J=4 transition. These results show that the molecule uses energy from the surface to make this transition at an incident energy of 80 meV. These measurements are in qualitative agreement with calculations done by Darling, Wang, and Holloway [14]. They found that for rotational excitation of D2 scattered from Cu(100) at 600 K, in the vibrational ground state, around 20 meV of translational energy was gained by the molecule at incident energies greater than the energy needed for the state transition. They also found that the amount of energy gained was insensitive to the transition made by the molecule. 52 Figure 4.5: Arrhenius Plot of v=1 J=2 to v=1 J=4 transition It is interesting to compare this with data for H2 scattered from Cu(100) taken by Watts [49]. For H2 , the v=1 J=1 to v=1 J=3 transition was studied at a range of incident energies. The energy di erence between these rotational states is 74 meV. Watts found that energy was gained by the H2 molecule when the incident translational energy was the same as, or below, the energy needed for the rotational state transition. For an incident energy of 74 7 meV the H2 molecule gains 38 7 meV. When the incident energy is raised to 145 15 meV the molecule gains only 3 15 meV. A surface temperature dependence study 53 was also done for this transition. For an incident energy of 79 meV an activation energy of 23 meV was measured. These results are similar to the results for D2 in that at lower energies there is energy gained by the molecule when a rotational state transition is made. Also, an activation energy is found which is similar to the amount of energy gained by the molecule. These measurements show a di erence in the scattering dynamics for D2 and H2 . At an incident translational energy of 80 meV the D2 molecules have more energy than the rotational energy gap, but still use energy from the surface to make the transition. In contrast, H2 molecules only use surface energy to make the J=1 to J=3 rotational state transition when the translational energy of the H2 molecule is less than or equal to the rotational energy gap. This di erence may be a result of the di erence in total vibrational energy for H2 (v=1) and D2 (v=1) when compared to the position of the barrier to dissociation (as discussed in section 4.1) 4.3 Preliminary Results with Cooled Raman Cell As was discussed in chapter 2, the Raman cell can be cooled with liquid nitrogen to shift the peak of the rotational state population of the gas to the v=0 J=0 state. In this way the laser frequencies which are produced will pump the v=1 J=0 state. Since the quality of the pump laser beam became poor when the Raman cell was cooled, only some preliminary data were taken. The data for v=1 J=0 scattered from Cu(100) are shown in gure 4.6. A noteworthy aspect of this data is that the peak for elastic scattering and 54 rotationally inelastic scattering are nearly the same size. Fitting these peaks to a gaussian, and assuming the same angular distribution as the v=1 J=2 scattering experiments, a survival probability of 0.46 0.05 and a transition probability of 0.38 0.05 were found. No transition from v=1 J=0 to v=1 J=4 or v=0 J=6 could be measured. Figure 4.6: TOF measurements of D2 v=1 J=0 scattered from Cu(100). The data for the v=1 J=2 state are o set for clarity. 55 4.4 Vibrational Relaxation Channel For the measurement of H2 scattered from Cu(100) the energy loss measurements accompanying the vibrational relaxation channel were very interesting. A large amount of energy was found to be lost to the surface during these interactions. For the v=1 J=1 to v=0 J=5 transition 98 36 meV was lost to the surface and 39 24 meV was lost to the surface for the v=1 J=1 to v=0 J=7 transition[49]. The energy loss could be directed into phonon or electronic excitation in the surface. The Debye temperature of Cu is 315 K giving an average phonon energy of 27 meV [3]. For the v=1 J=1 to v=0 J=7 transition the phonon energy is comparable to the energy lost to the surface. However, for the v=1 J=1 to v=0 J=5 transition the energy lost to the surface is 3-5 times the phonon energy. This means that multiple phonons would have to be excited during this interaction. The muliphonon excitation process takes much longer than the interaction time of the molecule with the surface[55]. This loss channel may, therefore, be related to excitation of the electronic states at the Cu(100) surface. Calculations of H2 reacting with Cu(100) assume that the system remains in the ground electronic state during the interaction. This is known as the Born-Oppenheimer approximation. This approximation is also called the adiabatic approximation because it depends on the nuclei moving so much more slowly than the electrons that the electrons can always adjust, adiabically, to remain in the ground state. At the same nozzle temperatures and pressures the D2 molecules move slower than the H2 molecules. If this approximation is being violated when H2 scatters 56 from Cu(100), the violation should be reduced for D2 . If less energy is lost to the surface during vibrational relaxation of D2 scattered from Cu(100) it would give additional support to the hypothesis that the Born-Oppenheimer approximation is violated in the H2 /Cu(100) interaction. However, the vibrational relaxation channel of D2 scattered from Cu(100) could not be found. Figure 4.2 shows an attempt to nd a vibrational relaxation signal into v=0 J=6 along with the signal from rotationally inelastic channels. For this measurement the beam was seeded with H2 and heated to obtain a translational energy of 199 meV. Even at this beam energy, where the rotationally inelastic transitions are readily seen, no signal for the vibrational relaxation channel was found. From this measurement the upper bound on the probability of transition from v=1 J=2 to v=0 J=6 is 0.003. For a room temperature nozzle, giving an incident energy of 78 meV, a limit for the probability of transition from v=1 J=2 to v=0 J=6 was found to be 0.002. For H2 scattered from Cu(100) the probability for relaxation from v=1 J=1 to v=0 J=5 and v=1 J=1 to v=0 J=7 at 74 meV could be measured. These probabilities were found to be 0.009 and 0.0005 respectively [49]. An interesting value to look at when comparing these probabilities is the di erence in energy between the initial and nal states. In the vibrational relaxation transitions studied the molecule both loses vibrational energy and gains rotational energy. Taking both of these into account the energy di erence between the v=1 J=2 state and the v=0 J=6 state in D2 is 240 meV. For H2 the energy di erence between the v=1 J=1 state and the v=0 J=5 state is 57 309 meV and the energy di erence between the v=1 J=1 state and the v=0 J=7 state is 116 meV. These transitions are shown schematically in gure 4.1 and quantitatively in gure 4.7. For these vibrational relaxation transitions the probability of transition to v=0 J=3 in H2 is expected to be the largest, decreasing with increasing rotational state[51]. The highest probability transitions are the ones in which the energy is distributed more or less equally between the available degrees of freedom. The transition from v=1 J=1 to v=0 J=1 is less likely than the transition to v=0 J=3 because most of the vibrational energy is transferred to translational energy. Similarly the transition to v=0 J=7 would involve most of the vibrational energy being distributed to rotational energy. The probability for transition from v=1 J=1 to v=0 J=5 in H2 was in fact measured to be larger then the probability for transition to v=0 J=7. The lowest rotational states were not measured because the thermal background in these states would mask the vibrational relaxation signal. The energy di erence for the v=1 J=2 to v=0 J=6 transition in D2 is similar to the energy di erence for the v=1 J=1 to v=0 J=5 transition in H2 . However, the limit for the transition in D2 is still about three times smaller than the measured H2 transition. 58 Figure 4.7: Electronic potential energy wells for H2 and D2 showing rotational and vibrational energy spacings. 59 Chapter 5 Scattering of D2 from Pd(111) Many of the results from the scattering experiments with copper were understood by considering the di erence in zero point energy, and vibrational energy spacing, between H2 and D2 . More vibrational energy allows the H2 molecule to get closer to the barrier for dissociation than the D2 molecule. This allows more inelastic scattering to occur for H2 . It is possible that the lack of vibrational relaxation measured for scattering of D2 from Cu(100) is due to this vibrational energy di erence not allowing the D2 molecule to get close enough to the barrier for dissociation. We next chose to perform scattering experiments from a surface for which there is no barrier to dissociation for some orientations of the molecule and positions of the molecule over the surface. So, for some fraction of the incident molecules, the translational and vibrational energy of the molecule should not a ect the probability for vibrational relaxation. However, there is also a much lower survival probability for scattering from Pd(111) then for Cu(100). So the scattered signal is much smaller making it di cult to measure inelastic channels. We felt that even with the smaller signal we could measure the vibrational relaxation channel and nd out how much energy is lost to the surface during this process. 60 5.1 Elastic Scattering A spatial pro le measurement of D2 (v=1 J=2) on Pd(111) is shown in gure 5.1 and a representative TOF measurement if shown in gure 5.2. The technique for this measurement was discussed in chapter 3. As can be seen in gure 5.1 very little D2 is re ected from Pd(111). The survival probability is measured to be 0.006 0.004 with a beam energy of 81 2 meV and a surface temperature of 500 K. This is nearly 10 times smaller than the survival probability of H2 on Pd(111) which was found to be 0.05 0.01[23]. The lower survival probability suggests a di erence in the physics of between D2 and H2 interacting with Pd(111). Work done by Diekhoner et al. suggests that nonadiabatic coupling in surface reactions may reduce the sticking probability and in uence vibrational state e ects [17]. In this case, according to their argument, stronger nonadiabatic coupling for H2 than for D2 would show up as a larger amount of H2 re ected from the surface. For D2 the interaction time is long enough for the gas-surface interaction to remain adiabatic, and nonadiabatic coupling is not expected. The larger survival probability for H2 could show that as the H2 molecule interacts with the Pd(111) surface there is nonadiabatic coupling. The change in translational energy of the molecule was measured for rotationally and vibrationally elastic scattering. The molecule lost 30 5.4 meV of translational energy after scattering from the clean surface. When the surface was cooled and saturated with D2 (and the survival probability is nearly unity) an energy loss of 15 4.8 meV was measured. It is surprising that more 61 Figure 5.1: Spatial Pro le measurement of elastic scattering of v=1 J=2 D2 on Pd(111)at TS = 500K. energy is lost to the surface when D2 scatters from clean Pd(111) than from Cu(100). Less energy loss to Pd(111) is expected due to the larger mass of a Pd atom. In table 3.2 it is shown that as the surface atom mass increases the energy loss to the surface should decrease, according to the Baule equation. One possible explanation for the large energy loss to the surface for D2 rotational and vibrational elastic scattering from Pd(111) is dynamic trapping at the surface. This process has been proposed as an explanation for decreasing sticking probability with increasing translational energy of H2 on Pd(111) 62 [11]. With dynamical trapping the D2 molecule is transiently trapped in the z coordinate at the Pd(111) surface but is free in the x, y, , and r degrees of freedom. In this process the molecules may have lost energy to the surface in a trapped state but had enough energy left to escape back into the vacuum. In calculations of H2 on Pd(111) this re ection process was found to contribute about 10 percent to the total re ection but was most important in the translational energy range used in this experiment [1]. 5.2 Vibrational Relaxation As was discussed in chapter 4 no vibrational relaxation channel was found for D2 scattered from Cu(100). We suggested that the D2 molecule did not have enough translational and vibrational energy to make it far enough up the dissociation barrier to enable vibrational relaxation. For D2 on Pd(111) there is no barrier to dissociation for some molecular orientations and positions over the surface. However, the probability for vibrational relaxation was still found to be much lower for D2 than for H2 . A sample TOF of the incident and scattered v=1 J=2 molecules, along with the v=0 J=6 scattered molecules, is shown in gure 5.2. The probability of transition from v=1 J=2 to v=0 J=6 was found to be 0.0014 0.0009 for D2 , at an incident energy of 83 3 meV, at TS =500 K. The transition probabilities for vibrational relaxation of H2 scattered from Pd(111) are more than 10 times larger: 0.04 0.01 for v=1 J=1 to v=0 J=5, and 0.03 0.01 for v=1 J=1 to v=0 J=7 [23]. 63 Figure 5.2: TOF Measurement of D2 in v=1 J=2 and v=0 J=6 state scattered from Pd(111). The work done by Diekhoner et al. showed that nonadiabatic coupling is an important part of the vibrational relaxation process [17]. In their work for N2 from Ru(0001) much less vibrational excitation was seen than was expected which could only be reproduced with calculations which contained strong nonadiabatic coupling. If the nonadiabatic coupling is necessary for vibrational relaxation in the hydrogen-metal systems, then this process would be less likely for D2 then for H2 interacting with Pd(111). This idea is consistent with the lack of vibrational relaxation measured for the D2 /Cu(100) 64 system as well. A large amount of energy was found to be lost to the surface for vibrational relaxation of H2 scattered from Pd(111), as was seen for vibrational relaxation of H2 scattered from Cu(100). For the v=1 J=1 to v=0 J=5 transition 120 34 meV was lost to the Pd(111) surface and for v=1 J=1 to v=0 J=7 transition 54 15 meV was lost to the surface[23]. The energy loss to the Pd(111) surface is large compared to the Debye temperature for Pd of 275 K (corresponding to a phonon energy of 24 meV). As was discussed in chapter 4, dissipation of this energy into atomic motion of the surface would require multiphonon excitation. This is unlikely on the time scale of the molecule-surface interaction. Nonadiabatic coupling to electronic states of the surface could account for this large energy loss, as was also discussed in chapter 4. For comparison to the H2 vibrational relaxation measurement the translational energy of the D2 molecules which had undergone vibrational relaxation was measured. The signal for the transition from v=1 J=2 to v=0 J=6 of D2 scattered from Pd(111) was too small to measure the translational energy using the method discussed in chapter 2. This method for measuring translational energy requires making TOF measurements for di erent probe laser positions along the surface normal. The density of scattered molecules decreases further from the surface, as illustrated in gure 3.1. Therefore, as the probe laser is moved away from the surface the scattered signal becomes rapidly smaller. For the v=0 J=6 signal gathered close to the surface typically 300-500 laser shots, at a frequency of 10 Hz, were averaged for each point in order to get a usable signal. 65 Even longer measurements would be needed for v=0 J=6 signals further from the surface. This means that the time it would take to get useful signals at several probe laser positions would be longer than the time over which we could be certain the Pd(111) sample remained clean. The velocity of the molecules had to be calculated using the peak time of the signal at one laser position. To do this the incident and scattered v=1 J=2 TOF measurements, done just before the v=0 J=6 measurement was made, were used. The previously measured energy of the incident and scattered v=1 J=2 molecules, along with the peak times of the TOF measurements and probe laser positions, could be used to calibrate the surface position. As can be seen in part a) of gure 5.3, the peak times of the TOF measurements is rst plotted against the probe laser position for the v=1 J=2 incident and scattered signals. The slopes of these lines are used to nd the velocity of the incident and scattered molecules. In part b) the position and peak times of the incident and scattered v=1 J=2 TOF measurements are plotted. The intersection of a line drawn through these points, with a slope of the velocity of the molecules, is the location of the surface. The surface position and the time it took the v=0 J=6 molecules to move from the surface to the probe laser position is then used to nd the velocity of the v=0 J=6 molecules. From the velocity the translational energy of the molecules is calculated. For D2 vibrational relaxation a translational energy of 218 70 meV was measured. This gives only a limit of 22 70 meV lost to the surface during this transition. The error in this measurement is found from the standard deviation of several measurements. 66 Figure 5.3: Finding the location of the surface using the peak times of the v=1 J=2 signal. 67 5.3 Transition Probabilities Along with the results above the probability for transition from the v=1 J=2 state to the v=1 J=0 state was studied. No scattered signal was seen for this state, so only a limit was put on the transition probability. Since this was the largest transition probability measured in the Cu(100) scattering experiment no other rotationally inelastic states were studied. Also, we were interested in the vibrational relaxation probability as a function of energy. For this reason the vibrational relaxation transition was studied at 112 meV incident energy. No signal was found for this transition at this energy. Again only a limit was put on the probability of this transition. The results of the measured transition probabilities are shown in table 5.1. Transition Incident Energy (meV) Transition Probability v=1 J=2 v=1 J=0 82.0 0.7 < 0.0005 v=1 J=2 v=0 J=6 83 3 0.0014 0.0009 v=1 J=2 v=0 J=6 112.0 1.0 < 0.0005 Table 5.1: Transition probabilities for D2 v=1 J=2 scattered from Pd(111) at 500K 68 Chapter 6 HD Scattered from Cu(100), Pd(111), and Pd(111):H(D) 6.1 Motivation The work discussed up to this point has been on the scattering of vibrationally excited D2 . In order to increase the translational energy of the D2 molecules mixtures of D2 with H2 were made. Since some D2 and H2 will dissociate at the walls of the gas cylinder HD gas is formed when the H and D atoms recombine and desorb. This was discovered somewhat serendipitously when we were scanning the probe laser wavelength between D2 states. A signal appeared that was not at the proper time, with respect to the probe laser, and not at a resonant wavelength for D2 or H2 . After some consideration we realized that we were detecting HD gas in the molecular beam. A quick calculation of the relative travel time of D2 and the mystery signal from the laser focus to the ion detector con rmed that we were ionizing HD gas. With this gas source available we decided to try some experiments on interactions of HD from Cu(100) and Pd(111). The motivations for the course of these experiments are discussed below. Many studies of gas-surface interactions focus on rotational excitation 69 of diatomic molecules as they interact with a metal surface [42]. The probability of rotational excitation, and energy transfer within the molecule as well as between the molecule and the surface during this process, can tell us about the forces acting on the molecule as it interacts with the surface. There are several experiments which measure the probability of rotational excitation of H2 at metal surfaces with di erent incident energies and surface temperatures [22, 48, 51]. A strong surface temperature dependence has shown the need to include surface excitations in molecular dynamic calculations[47]. Also, a large discrepancy between measured and theoretical values of rotational excitation probabilities has shown the need for improvement in both calculations and experiment [51]. Rotational state changing collisions for H2 and D2 tend to have small probabilities as a result of the nearly spherical shape of the molecular charge distribution. In contrast HD is an ideal molecule for experiments on rotational excitation. The center of mass of the molecule is displaced from the electronic center. This leads to a high probability of angular momentum transfer during collisions giving rise to a large probability for rotational excitation and relaxation. In a supersonic nozzle this means that the HD molecules will be cooled to have most or all of its population in the v=0 J=0 state even at room temperature. When the HD molecules interact with the surface there is a high probability of rotational excitation. Since HD is heteronuclear, J=1 transitions are allowed, giving more rotational state transitions to study even at low incident energies. 70 There have been several di raction experiments scattering HD from reactive metals such as Pt(111) [8 10] and Ni(001) [4] as well as inert metals such as Cu(111), Au(111) [27] and Cu(001) [20]. In these measurements the molecular beam is incident to the surface at an angle and a quadupole mass spectrometer is used to detect scattered molecules. Either the incident angle of the molecules or the position of the mass spectrometer is varied to measure the angle at which the HD molecules scatter o of the surface. These experiments can also yield the translational energy of the scattered molecules by time of ight measurements. Conservation of momentum and energy are used to identify the nal state. When an HD molecule makes a rotational state transition the change in energy and momentum causes it to scatter from the surface at a speci c angle. A rotational state transition which is measured this way is a coherent, elastic, transition. Molecules which excite or annihilate a phonon when making a rotational state transition will not contribute to the di raction peaks in this measurement. These di raction measurements can determine the relative amount of rotational excitation from J=0 to higher rotational states by comparing the area under each di raction peak. Goncharova et al. noted a large di erence in the amount of rotational excitation from Cu(001) and Ni(001) and suggested the reactive channels for HD on Ni(001) as a reason for this di erence [20]. Our experimental set up allows us to perform state speci c spectroscopy on HD molecules at normal incidence. As such this work is the rst laser spectroscopy study of HD molecules scattering from a surface. We can measure 71 the relative population of rotational states of the HD molecules after they scatter from the surface. In this experiment all of the molecules exiting in a speci c rotational state are measured, regardless of the nature (coherent or incoherent) of the surface interaction. We have studied HD interacting with both reactive, Pd(111), and inert, Cu(100) and H(D) covered Pd(111), surfaces. There have also been calculations performed on HD interacting with metal surfaces. Cruz and Jackson calculated probabilities of excitation for HD scattered from Cu(100) as a function of surface temperature [12]. They present calculations of these interactions at nite temperature which have not yet been compared with experiment. Kingma et al. have calculated rotational excitation probabilities of HD scattered from Pt(111) and compared this work to Cowen s experimental work [29]. The rotational excitation probabilities were very di erent for theory and experiment. Kingma et al. suggest that this di erence is due to a large amount of out-of-plane di raction, which the experiment is not sensitive to. This shows that further study is need to understand the experimental data as well as how to model this system. 6.2 Rotational State Distribution The measurements discussed here are of vibrational ground state molecules. Since no optical pumping is done the TOF curves are much wider in time than the previous results, as was discussed in chapter 2. For these experiments the scattered TOF curves were taken with the laser in the shadow position, see 72 section 2.7 for details. The area under the TOF curves was found for each rotational state. The spatial distribution of the incident and scattered molecules is di erent. Since the re ectivity of Cu(100) is unity for HD, both sets of data are normalized so that the total area under the TOF curves is one. The incident energy of the HD molecules was 74 3.1 meV. The incident rotational state population and rotational state population after scattering from clean Cu(100) are shown in Figure 6.1. The energy of the scattered HD molecules in the v=0 J=2 state was also measured. These molecules left the surface with 38 6.6 meV less energy, which is comparable to the energy di erence between the v=0 J=0 state and the v=0 J=2 state of 33 meV. For the Pd(111) surface the percentage of molecules in each rotational state was found for scattering from both a clean Pd(111) surface and a H(D) covered Pd(111) surface. The spatial distribution of the HD molecules scattered from the clean and H(D) covered surface is assumed to be the same. The probe laser is positioned 1 to 2 mm from the surface, therefore this experiment is relatively insensitive to di erences in scattering angle. The data taken from the cleaned surface has been normalized to the data taken from the H(D) covered surface. The incident rotational state population and the rotational state population after scattering from clean and H(D) covered Pd(111) is shown in Figure 6.2. About 20% of the incident HD scatters from the clean Pd(111) surface, as most of the HD molecules dissociatively adsorb, but the percentage in each rotational state is remarkably similar. 73 Figure 6.1: Rotational state distribution of HD in the beam and scattered from clean Cu(100) at 500K. The similarities in the rotational distributions after scattering from the clean Cu(100) and Pd(111) surface as well as the covered Pd(111) surfaces is striking. To further illustrate this the data are shown in a Boltzmann plot in Figure 6.3. The Boltzmann plot was used to nd a rotational temperature for each measurement. The rotational temperature was close to 200 K for each measurement with only about a 10 % error. This is very di erent from previous results, as noted by Goncharova et al., where there was much more rotational 74 Figure 6.2: Rotational state distribution of HD scattered from clean Pd(111) at 500K and H(D) covered Pd(111) at 95K . excitation from activated systems, such as Pt(111)[8 10] and Ni(001)[4], than from non-activated systems, such as Cu(001)[20], Cu(111), and Au(111)[27]. It has been shown that the amount of rotational excitation re ects the potential energy surface (PES) the molecule feels as it approaches the surface[15]. An inert surface will have a very di erent PES than a surface for which HD has a large dissociation probability. The similarities in the rotational distributions from Cu(100), Pd(111), and Pd(111):H(D) in this experiment may show that 75 the di erences between these surfaces in the PES is seen mostly the dissociation probability. The molecules which re ect have sampled an inert area of each surface for which the potential energy may look very similar. Figure 6.3: Boltzmann Plot of HD scattered from clean Cu(100) at 500K, clean Pd(111) at 500 K, and H(D) covered Pd(111) at 95 K. Another notable result from this experiment is that there is no measurable rotational excitation into v=0 J=4 when HD is scattered from H(D) covered Pd(111) while there is for HD scattered from clean Cu(100) and Pd(111). It is expected that there would not be transitions from v=0 J=0,1,2 to v=0 76 J=4 since the incident HD molecules do not have enough kinetic energy to make this transition. The energy di erence between J=0 and J=4 is 109 meV. There is, however, excitation into v=0 J=4 when HD is scattered from clean Pd(111) and Cu(100). Since there is not enough translational energy to make the transition from J=0 to J=4 or J=1 to J=4, and just barely enough to make the transition from J=2 to J=4, in order to make this transition the HD molecules must get some energy from the surface. This has been seen previously with H2 scattered from Pd(111). Watts and Sitz measured several rotational state transitions for which the translational energy is less than the rotational energy gap[48]. It is interesting to note that no rotational excitation was seen for transitions that require more energy than the incident translational energy for HD scattered from Cu(001)[20] or for HD scattered from Ni(001)[4] in the di raction experiments. Since these transitions would require an inelastic scattering process they would not be measured in a di raction peak. This di erence in rotational excitation probabilities may be due to the large di erence in incident angle in our experiments and the di raction experiments. Cowin et al. found a strong angle dependence on rotational excitation with changing incident angle for HD scattered from Pt(111)[9]. The di erent rotational state distributions may also by due to the di erent way in which our measurement is made. In the measurement shown here all rotational state excitation mechanisms are measured, not only coherent, inelastic, interactions. 77 Chapter 7 Conclusion 7.1 Summary In this work state speci c spectroscopy was used to study the interactions of D2 molecules with Cu(100) and Pd(111) surfaces. The D2 molecules were pumped into the v=1 J=2 quantum state before interacting with the surface. The survival probability and probability of rotational state transitions of the D2 molecules was measured over a range of energies for scattering from Cu(100). The survival probability and vibrational relaxation probability were measured for D2 scattered from Pd(111) at one energy. The transfer of energy between degrees of freedom of the molecule was studied as well as transfer of energy to and from the surface. This increases the amount of experimental data for these systems which can be used to understand surface chemical reactions. The interaction between these surfaces and D2 molecules was compared to previous work done with H2 molecules in order to look at isotope e ects. Studies of HD molecules in the ground vibrational state were also performed. These studies compared the amount of rotational excitation of the HD molecule after scattering from Cu(100), Pd(111), and Pd(111):H(D). Rotationally and vibrationally elastic scattering of v=1 J=2 D2 molecules 78 from Cu(100) was studied. These measurements allowed us to nd the survival probability of D2 molecules in the v=1 J=2 state for a range of incident translational energies. When compared to the survival probability of H2 the values for D2 are larger. This was attributed to the di erence in vibrational zero point energy and vibrational energy spacing relative to the barrier for dissociative adsorption. Also, transfer of energy to the surface was studied for both D2 v=1 J=2 and H2 v=1 J=1. The results of this measurement agree well with the classical Baule equation. Transitions of the v=1 J=2 D2 molecules into the v=1 J=0,4 states after scattering from Cu(100) were also measured. The transition probability from v=1 J=2 to v=1 J=0 was found to be essentially independent of the incident energy of the molecule. However, the probability of transition from v=1 J=2 to v=1 J=4 increased from about 80 to 100 meV. To further study this the probability of transition into v=1 J=4 was measured as a function of surface temperature. It was found that the surface supplied some energy for this transition with an activation energy of 18 meV. This is consistent with the range of energy over which there is an increase in the transition probability. It has been shown that energy from the surface can be supplied for transitions to higher rotational states. It is interesting to compare D2 and H2 for this process because H2 only uses energy from the surface when the translational energy of the molecule is equal to or smaller than the spacing between the rotational states. However, D2 uses energy from the surface for the v=1 J=2 to v=1 J=4 transition even when the translational energy of the molecule is 79 greater than the rotational energy spacing. For these experiments only the v=1 J=2 state of D2 was pumped. This is due to the fact that the v=0 J=2 state of D2 is the most populated state in the Raman cell, which is used to create the frequencies for optical pumping. If the Raman cell is cooled the most populated state becomes v=0 J=0. So, by cooling the Raman cell the frequencies needed for pumping the v=1 J=0 state of D2 are created. Only preliminary studies of this pumped state could be made since the laser beam quality is greatly a ected by the cooled cell. These preliminary studies show almost equal amounts of scattered v=1 J=0 and v=1 J=2 present after scattering v=1 J=0 D2 from Cu(100). Experiments were done to look for vibrational relaxation of D2 after interacting with both Cu(100) and Pd(111) since the measurements of H2 from these surfaces showed a large amount of energy (compared to the Debye temperature of the metal) lost to the surface during vibrational relaxation. No current theory can explain this loss and we felt it would be interesting to look for isotope e ects in this process. However, no vibrational relaxation was found for D2 scattered from Cu(100). Only a limit could be put on the probability for this transition. This upper limit is about 3 times smaller than the probability for a similar transition in H2 . The smaller vibrational relaxation probabilities could be due to the D2 molecules having less vibrational energy than H2 molecules. This energy di erence is on the order of the barrier to dissociation for this system. Experiments were then also done with v=1 J=2 D2 scattered from Pd(111). For this surface the barrier to dissociation 80 is small compared to the energy of the D2 molecule. For some orientations of the molecule and positions over the surface there is no barrier at all. The probability for vibrational relaxation, for v=1 J=2 to v=0 J=6 of D2 , could be measured for Pd(111). However, the measured probability was over 10 times smaller than the values for similar transitions in H2 scattered o of Pd(111). Along with this smaller vibrational relaxation probability a smaller survival probability was also measured. While around 5 percent of the vibrationally excited H2 molecules survive the interaction with Pd(111) only around 1 percent of the vibrationally excited D2 molecules survive. Both the lower transition probability and the lower survival probability are surprising results. Studies of HD scattered from Cu(100), Pd(111), and Pd(111):H(D) were done to look at the amount of rotational excitation after scattering. It was expected that the HD molecules would show a larger amount of rotational excitation from the reactive Pd(111) surface than for the inert Cu(100) and Pd(111):H(D) surface. In fact a very similar amount of rotational excitation was found for HD scattered from all three of these surfaces. This result suggests that the scattered HD molecules sampled a very similar portion of the PES of these di erent surfaces. 7.2 Future Work More studies of D2 scattered from Pd(111) could nd the probabilities of other transitions as well as energy transfer to and from the surface. Before these studies are done some careful work will need to be done to reduce noise 81 in the experiment so that smaller signals can be detected. Experiments could be done to study the possibility of dynamical trapping of H2 or D2 on Pd(111) predicted by Crespos et al. [11]. Detailed measurements of energy loss to the surface for both H2 and D2 could be compared to theory. Since the time scale of dynamical trapping is short, on the order of 10-100 of femtoseconds, it is not possible to distinguish trapped molecules from directly scattered molecules in our experiment. This may make the measurement of the velocity of scattered molecules more di cult since there will be a group of molecules with a wide range of velocities close to the surface. Perhaps the width of the TOF signal for the scattered molecules from the clean and D covered Pd(111) could be studied to look at this e ect. The work with the cooled Raman cell would be interesting to continue. The problem of the beam quality becoming much worse as the cell is cooled is the rst problem to tackle. This e ect is probably due to convection in the gas. The convection is caused by temperature gradient between the windows of the cell and the cooled center of the cell. The windows must stay warm for the cell to remain sealed, so there is necessarily a temperature gradient. One way to work around this problem is to cool only a small part of the center of the cell. Since the Raman shifting occurs mainly at the laser focus, only the gas which the laser focuses into needs to be cooled. A cold nger which reaches into the cell with a hole in it for the laser light could be used. In this way the molecules at the laser focus will have the most population in the v=0 J=0 state. 82 For H2 molecules the v=0 J=1 state is the most populated quantum state in the room temperature Raman cell, so it produces the frequencies needed to pump the v=1 J=1 state of H2 . The H2 population will not shift from v=0 J=1 to v=0 J=0 when the cell is cooled, because there is a selection rule of J=2. The H2 molecule must break apart and reform in another rotational state for J=1 transitions to occur. With the cooled Raman cell working it could be expanded to include a catalyst to allow the H2 molecular population to shift into the v=0 J=0 state as well by breaking apart on the catalyst and reforming. This could open up a new series of measurement for H2 on Pd and Cu. Also, HD could be put in the Raman cell to see which frequencies are produced by stimulated Raman scattering. Since HD has the same electronic structure as H2 and D2 isotope e ects could be further studied. Also, with the possibility of J=1 transitions there are several di erent processes which could be studied for this molecule. Direct comparison between molecules incident on the surface in the v=0 and the pumped v=1 state could be studied. This direct comparison is possible because in the molecular beam almost all of the v=0 state is in one rotational state and only one rotational state is pumped into the v=1 state. 83 Appendix 84 Appendix 1 Ion Gun for Surface Sputtering A common technique in surface science is the use of Ar+ , or other rare gas, sputtering to remove contaminants, such as Carbon and Sulfur, from the surface that is being studied [30, 53]. Sputtering of this kind requires only about 300 V ions in a fairly wide beam. As such, commercial ion guns, which produce very high resolution and high energy ion beams, tend to be overkill. This has lead to several designs for homemade ion guns, mainly based on the ionization pressure gauge [18, 28, 30, 53]. In initial designs of these pressure gauge ion guns the chamber with the sample was back lled with Ar. However, sputtering with low background pressure is preferable as it leads to less contaminants and less outgassing from the chamber walls. To reduce the background pressure more recent designs call for Ar to be introduced directly into a di erentially pumped ionization area [53]. Building an ion gun with a separately pumped ionization region can be somewhat di cult and costly, especially if the ion gun is being added to an existing vacuum chamber. For this reason we modi ed the ion gun in the main scattering chamber in order to lower the background pressure in the chamber while sputtering, without using di erential pumping. This is done by using a 85 conductance limited technique. The entire ion gun is surrounded by a metal tube with a small aperture at the end. The gas is fed directly into the ionization region. The ions are then focused so that they exit though the aperture and strike the target sample. In this way the pressure in the ionization region can be two orders of magnitude higher than the pressure in the main chamber. The ion gun itself, shown in gure 1.1, is entirely custom fabricated. The ions are created in a cage region, which is bombarded by electrons from a lament. Since the ions are generated inside the metal cage, the voltage applied to the cage determines the ion kinetic energy at the (grounded) target. The lament geometry is such that the lament surrounds the cage. An extractor element sits directly in front of the cage. The ions are then focused with an Einzel lens arrangement of focusing elements. These focusing elements are spaced on a 0-80 threaded rod using Al2 O3 spacers. Argon is introduced to the ionization region using a leak valve. For a simple geometry such as our ion gun, the pressure in the ion gun can be calculated using the formula for the throughput of gas between two vessels of with di ering pressure v Q = A(P1 P2 ) 4 [41]. Here Q is the throughput, v is the velocity of the Ar, P1 is the pressure in the ion gun, and P2 is the pressure in the main chamber. In steady state the throughput from the ion gun to the main chamber must be the same as the throughput from the main chamber to the pump. Therefore Q is calculated 86 from the main chamber pressure and pumping speed. Using a value of 600 L/s for the pumping speed (Varian di usion pump with water ba e and LN2 trap), 379 m/s for v, and 0.000314 m2 for A we found that at a chamber pressure of 2 x 10 7 Torr the pressure in the ion gun is 1.5 x 10 5 Torr. The emission current from the lament is controlled by a home built power supply. A feedback circuit regulates the lament temperature so that the emission current is kept at a constant value set by the user. We choose 10 mA for our ion gun. This ion gun reliably produces 1 microamp of ion current, measured at the sample, with a chamber pressure of 1 to 2 X 10 7 Torr. This amount of ion current, with 300 V ions, adequately cleans our Cu(100) sample. A routine of 30 min sputtering at 500 C and 30 min annealing at 600 C yields a surface, which is clean as seen by Auger spectroscopy and LEED pattern. 87 Figure 1.1: Schematic of ion gun. 88 Bibliography [1] M. A. Di Cesare andH. F. Busnengo, W. Dong, and A. Salin. Role of dynamic trapping in H2 dissociation and re ection on Pd surfaces. J. Chem. Phys., 118:11226 11234, 2003. [2] G. Anger, A. Winkler, and K. D. Rendulic. Adsorption and desorption kinetics in the systems H2 /Cu(111),H2 /Cu(110)and H2 /Cu(100). Surf. Sci., 220:1 17, 1989. [3] N. W. Ashcroft and N. D. Mermin. Solid State Physics. Holt, Rinehart and Winston, New York, 1976. [4] R. Berndt, J.P. Toennies, and Ch. Woll. Evidence for coupled rotational and phonon quantum excitation in the scattering of a nearly monoenergetic HD beam from the Ni(001) surface. J. Chem. Phys., 92:1468 1477, 1990. [5] Massimo F. Bertino, Andrew P Graham, Lev Y. Rusin, and J. Peter Toennies. Di raction and rotational transitions in the scattering of D2 from Cu(001) at energies up to 250 mev. J. Chem. Phys., 109:8036 8044, 1998. [6] M. Bonn, A.W. Kleyn, and G.J. Kroes. Real time chemical dynamics at surfaces. Surf. Sci., 500:475 499, 2002. 89 [7] B. H. Bransden and C. J. Joachain. Physics of Atoms and Molecules. Longman Scienti c and Technical, 1991. [8] James P. Cowin, Chien-Fan YU, Steven J. Sibener, and Jerry E. Hurst. Bound level resonances in rotationally inelastic HD/Pt(111) surface scattering. J. Chem. Phys., 75:1033 1034, 1981. [9] James P. Cowin, Chien-Fan YU, Steven J. Sibener, and Lennard Wharton. HD scattering from Pt(111): rotational excitation probabilities. J. Chem. Phys., 79:3537 3549, 1983. [10] James P. Cowin, Chien-Fan YU, and Lennard Wharton. HD scattering from Pt(111): rotationally mediated selective adsorption. 161:221 233, 1985. [11] C. Crespos, H. F. Busnengo, W. Dong, and A. Salin. Analysis of H2 dissociation dynamics on the Pd(111) surface. J. Chem. Phys., 114:10954 10962, 2001. [12] Astrid J. Cruz and Bret Jackson. A nite temperature theory of rotationally inelastic di raction:H2 , HD and D2 on Cu(110). J. Chem. Phys., 91:4985 4993, 1989. [13] Per F Dahl. Heavy Water and the Wartime Race for Nuclear Energy. Institute of Physics Publishing, 1999. Surf. Sci., 90 [14] G. R. Darling, Z. S. Wang, and S. Holloway. Energy exchange in reactive scattering of hydrogen molecules from a Cu surface. Chem. Phys. Lett., 365:157 163, 2002. [15] George R. Darling and Stephen Holloway. The dissociation of diatomic molecules at surfaces. Report Prog. Phys., 58:1595 1672, 1995. [16] F. DeMartini and J. Ducuing. Stimulated raman scattering in hydrogen: A measurement of the vibrational lifetime. Phys. Rev. Lett., 17:117 119, 1966. [17] L. Diekhner, L. Hornekaer, H. Mortensen, E. Jensen, A. Baurichter, V. V. Petrunin, and A. C. Luntz. Indirect evidence for strong nonadiabatic coupling in N2 associative desorption from and dissociative adsorption on Ru(0001). J. Chem. Phys., 117:5018 5030, 2002. [18] B.D. Dove, W. Molzen, and G. Johnson. Modi cation to enhance the beam current of a simple ion gun. 47:299 300, 1976. [19] R. Frey, J. Lukasik, and J. Ducuing. Tunable raman excitation and Review of Scienti c Instruments, vibrational relaxation in diatomic molecules. Chem. Phys. Lett., 14:514 517, 1972. [20] L. V. Goncharova, J. Braun adn A. V. Ermakov, G. G. Bishop, D.-M. Smilgies, and B. J. Hinch. Cu(001) to hd energy transfer and transla- 91 tional to rotational energy conversion on surface scattering. J. Chem. Phys., 115:7713 7724, 2001. [21] M. Gostein and G. O. Sitz. Improved gating of microchannel plates for multiphoton ionization experiments. 66:3389 3390, 1995. [22] M. Gostein and G. O. Sitz. Rotational state-resolved sticking coe cients for H2 on Pd(111): Testing dynamical steering in dissociative adsorption. J. Chem. Phys., 106:7378 7390, 1997. [23] M. Gostein, E. Watts, and G. O. Sitz. Vibrational relaxation of H2 on Pd(111). Phys. Rev. Lett., 79:2891 2894, 1997. [24] Michael Gostein. Dynamical E ects in Dissociative Adsorption: Quantum State-Resolved Studies of H2 Scattering from Pd and Cu. PhD thesis, The University of Texas at Austin, 1997. [25] David Halliday, Robert Resnick, and Kenneth S. Krane. Physics, volume 2. John Wiley and Sons, Inc., 2002. [26] M. R. Hand and S. Holloway. A theoretical study of the dissociation of H2 /Cu. J. Chem. Phys., 91:7209 7219, 1989. [27] U. Harten, J.P. Toennies, and Ch. Woll. Molecular beam translational spectroscopy of physisorption bound states of molecules on metal surfaces. I. HD on Cu(111) and Au(111)single crystal surfaces. J. Chem. Phys., 85:2249 2258, 1986. 92 Review of Scienti c Instruments, [28] Mahboob Kahn and Juergen M. Schroeer. A simple ion gun. Review of Scienti c Instruments, 42:1348 1350, 1971. [29] Sikke M. Kingma, Mark F. Somers, Ernst Pijper, Geert-Jan Kroes, Roar A. Olsen, and Evert-Jan Baerends. Di ractive and reactive scattering of (v=0, J=0) HD from Pt(111): Six-dimensional quantum dynamics compared with experiment. J. Chem. Phys., 118:4190 4197, 2003. [30] J. Kirschner. Simple low-energy sputter ion gun based on a bayard-alpert pressure gauge. Review of Scienti c Instruments, 57:2640 2642, 1986. [31] G. J. Kroes. Six-dimensional quantum dynamics of dissociative chemisorption of H2 on metal surfaces. Progess in Surface Science, 60:1 85, 1999. [32] Geert-Jan Kroes and David C. Clary. Sticking of HCl and ClOH to ice: a computational study. J. Phys. Chem., 96:7079 88, 1992. [33] Geert-Jan Kroes, Axel Gross, Evert-Jan Bearends, Matthias Sche er, and Drew a. McCormack. Quantum theory of dissociative chemisorption on metal surfaces. Accounts of Chemical Research, 35:193 200, 2002. [34] J. E. Lennard-Jones. Processes of adsorbtion and di usion on solid surfaces. Transactions of the Faraday Society, 28:333 359, 1932. [35] David R. Lide, editor. CRC Handbook of Chemistry and Physics. CRC Press, 1994. 93 [36] E. E. Marinero, C. T. Rettner, and R. N. Zare. Quantum-state-speci c detection of molecular hydrogen by three-photon ionization. Phys. Rev. Lett., 48:1323 1326, 1982. [37] H. A. Michelsen and D. J. Auerbach. A critical examination of data on the dissociative adsorption and associative desorption of hydrogen at copper surfaces. J. Chem. Phys., 94:7502 7520, 1991. [38] H. A. Michelsen, C. T. Rettner, and D. J. Auerbach. State-speci c dynamics of D2 desorption from Cu(111): the role of molecular rotational motion in activated adsorption-desorption dynamics. Phys. Rev. Lett., 69:2678 81, 1992. [39] H. A. Michelsen, C. T. Rettner, D. J. Auerbach, and R. N. Zare. E ect of rotation on the translational and vibrational energy dependence of the dissociative adsorption of D2 on Cu(111). J. Chem. Phys., 98:8294 8307, 1993. [40] H. Moriwaki, A. Nakamura, S. Wada, and H. Tashiro. E cient vacuumultraviolet generation by anti-stokes raman scattering using a cryogenic raman cell. Applied Physics B, 61:319 323, 1995. [41] John F. O Hanlon. A User s Guide to Vacuum Technology. Wiley, New York, 1989. [42] Giacinto Scoles, editor. Atomic and Molecular Beam Methods, volume 2, chapter 12. Oxford University Press, New York Oxford, 1992. 94 [43] Jennifer L. W. Siders and Greg O. Sitz. Observation and characterization of direct inelastic and trapping desorption channels in the scattering of N2 from Cu(110). J. Chem. Phys., 101:6264 6270, 1994. [44] M. Spaan, A. Goehlich, V. Schulz von der Gathen, and H. F. Dobele. Experimental tests of a novel raman cell for vacuum ultraviolet generation to below Lyman- . Applied Optics, 33:3865 3870, 1994. [45] John F. Thomson. Physiological e ects of D2 O in mammals. Annals of the New York Academy of Sciences, 84:736 744, 1960. [46] Harold C. Urey, F. G. Brickwedde, and G. M. Murphy. A hydrogen isotope of mass 2 and its concentration. The Physical Review, 40:1 17, 1932. [47] Z. S. Wang, G. R. Darling, and S. Holloway. Surface temperature dependence of the inelastic scattering of hydrogen molecules from metal surfaces. Phys. Rev. Lett., 87:1 4, 2001. [48] E. Watts and G. O. Sitz. Surface temperature dependence of rotational excitation of H2 scattered from Pd(111). J. Chem. Phys., 111:9791 9796, 1999. [49] E. Watts and G. O. Sitz. State-to-state scattering in a reactive system: H2 (v=1,J=1) from Cu(100). J. Chem. Phys., 114:4171 4179, 2001. 95 [50] Elizabeth Watts. Quantum State-Resolved Studies of Elastic and Inelastic Scattering of H2 from Cu and Pd. Texas at Austin, 1999. [51] Elizabeth Watts, G.O. Sitz, D. A. McCormack, G. J. Kroes, R. A. Olsen, J. A. Groeneveld, J. N. P. Van Stralen, E. J. Baerends, and R. C. Mowrey. Rovibrationally inelastic scattering of H2 (v=1, J=1) from Cu(100): Experiment and theory. J. Chem. Phys., 114:495 503, 2001. [52] G. Wiesenekker, G. J. Kroes, and E. J. Baerends. An analytical sixPhD thesis, The University of dimensional potential energy surface for dissociation of molecular hydrogen on Cu(100). J. Chem. Phys., 104:7344 58, 1996. [53] John T. Yates. Experimental Innovations in Surface Science. Springer, New York, 1998. [54] Andrew Zangwill. New York, 1988. [55] V. P. Zhdanov and K. I. Zamaraev. Vibrational relaxation of adsorbed molecules. mechanisms adn manifestations in chemical reaction at solid surfaces. Catal. Rev. Sci. Eng., 24:373 413, 1982. Physics at Surfaces. Cambridge University Press, 96 Vita Leah Caitlin Shackman was born in Ann Arbor, MI on October 11, 1975, the daughter of Grace Miriam Shackman and Stanley Jay Shackman. After graduating from Pioneer High School in Ann Arbor, MI she attended the University of Michigan in Ann Arbor. The summer after her sophomore year in college she was in the research experience for undergraduate program at the University of California at Irvine. She graduated from the University of Michigan with an honors Bachelor of Science in physics in May 1997. In the fall of 1997 she entered graduate school in physics at the University of Texas at Austin. She married Chris Jackson in Ann Arbor, MI in October 2000. Permanent address: 515 Soule Blvd. Ann Arbor, MI 48103 A This dissertation was typeset with L TEX by the author. A LT EX is a document preparation system developed by Leslie Lamport as a special version of Donald Knuth s TEX Program. 97

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