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Leed crystallographic studies of structures formed on the (110) and (111) surfaces of Rhodium Wong, Kin-chung 1996

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L E E D C R Y S T A L L O G R A P H I C STUDIES O F S T R U C T U R E S F O R M E D O N T H E (110) A N D (111) S U R F A C E S O F R H O D I U M by K I N - C H U N G W O N G B.Sc. (Hons.), The Chinese University of Hong Kong, 1988 M . S c , The University of British Columbia, 1991 A THESIS SUBMITTED IN P A R T I A L F U L F I L L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A February 1996 © Kin-chung Wong, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University -of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of QUhHiSTR. The University of British Columbia Vancouver, Canada D a t e 6" HAZ °lb . DE-6 (2/88) Abstract Surface crystallographic analyses have been undertaken with the tensor L E E D approach in low-energy electron diffraction (LEED) in order to contribute to the development of the principles of surface structural chemistry. For the Rh(l 10)-c(2x2)-S surface structure, each S atom chemisorbs on a center site of the Rh(l 10) surface. It bonds to the second layer Rh atom directly below, with a bond distance equal to about 2.27 A, and to four neighboring First layer Rh atoms at close to 2.47 A. A significant feature of this structure is that the second metal layer is buckled; those Rh atoms directly below the S atoms relax down by about 0.11 A compared with the other second layer Rh atoms. This buckling is apparently driven by the need to reduce the difference that would otherwise occur between these two types of S-Rh bond lengths. A component in the observed difference between the S-Rh distances appears to be dependent on the metallic coordination number for the Rh atoms. For the corresponding higher coverage Rh(l 10)-(3x2)-S surface, the result supports an arrangement of chemisorbed S atoms at 2/3 monolayer (ML) coverage on a basically unreconstructed metallic structure. Alternating [110] channels in the metal surface are occupied differently, although each has two S atoms per unit mesh. In one set, the S atoms occupy long-bridge and center sites with a constant separation along the channel of 4.03 A. In the other set of channels, all S atoms occupy equivalent positions, displaced from regular center sites by 0.39 A, to give successive S to S separations of 3.47 and 4.60 A. The long-bridge site bonding is a novel feature which is facilitated by the neighboring topmost Rh atoms relaxing laterally by about 0.27 A perpendicular to the [110] row. Bucklings of 0.20 and 0.10 A are indicated to occur in the first and the second Rh layers respectively; the latter value essentially equals that (0.11 A) in the corresponding c(2x2) surface. For S atoms at or near center sites in the (3x2) structure, the average S-Rh bond ii distances to the first and the second Rh layer atoms are 2.42 and 2.29 A respectively; the corresponding values at the long-bridge sites are 2.20 and 2.27 A. New analyses for the Rh(l 1 l)-(>^x>/3)R30o-S and Rh(l 1 l)-c(4x2)-S surface structures indicate S coverages of 1/3 and 1/2 M L respectively. For the lower-coverage form, S adsorbs on the regular three-coordinate sites which continue the fee packing sequence; the S-Rh bond lengths are indicated to equal 2.23 A, and relaxations in the metallic structure are negligible. In the c(4x2) form, the adsorption occurs equally on both types of three-coordinate site (fee and hep), although some surface Rh atoms bond to two S atoms while others bond to only one, and this sets up some interesting relaxations. Specifically, the S atoms displace laterally from the center of the threefold sites by 0.20 to 0.29 A, and the first metal layer is buckled by about 0.23 A. The first-to-second interlayer spacing in the metal expands to 2.26 A from the bulk value of 2.20 A. The average S-Rh bond length equals 2.22 A, and is not significantly changed from that in the low-coverage form. The structural evolution with increasing coverage for S chemisorbed on the (111) surface of Rh shows a close relation to the corresponding evolution on the Rh(110) surface. ln the Rh(l 1 l)-(2xl)-0 surface structure formed by chemisorption of O on the Rh(l 11) surface, O atoms chemisorb close to the regular fee sites. The structure shows significant relaxations; for example, a buckling of about 0.07 A is indicated in the first metal layer and O appears to displace laterally by about 0.05 A. The individual O-Rh bond lengths are around 2.01 and 1.92 A to top layer Rh atoms which bond to two and one O atoms respectively. Comparison is made with O-Rh bond lengths determined recently by another group for the Rh( 110)-p2mg(2x l )-0 surface structure. iii Table of Contents Abstract . . . . i i Table of Contents iv List of Tables viii List of Figures..... -• - x Acknowledgments • xvi Chapter 1: Introduction — —. . ' • 1 1.1 Surface Science 1 1.2 Low Energy Electron Diffraction (LEED) ............3 1.2.1 Introduction r 3 1.2.2 Diffraction Conditions 5 1.2.3 Notations for Surface Structures .7 1.2.4 Approach in L E E D Crystallography 9 1.3 Auger Electron Spectroscopy (AES) . —•• 10 1.4 Bond Length - Bond Order Relationship...... 12 1.5 Purpose of Studies .13 Chapter 2: Multiple Scattering Calculation for L E E D Intensities 17 2.1 Introduction 17 2.2 Muffin-Tin Approximation 19 2.3 Phase Shifts and Atomic Vibrations .19 2.4 Diffraction by a Stack of Layers : 22 2.4.1 Introduction ; 22 2.4.2 Layer Diffraction Matrices. 23 2.4.3 Renormalized Forward Scattering Method ..25 2.4.4 Combined Space Method 25 2.5 Reliability Indices (R-factors) ..27 iv 2.5.1 Formulation of R-factor 27 2.5.2 Error Estimation 29 2.6 TensorLEED ....31 2.6.1 General Principles of T L E E D 31 2.6.2 Implementation of T L E E D 33 Chapter3 : Experimental 34 3.1 Ultrahigh Vacuum (UHV) Apparatus and Instrumentation 34 3.2 Crystal Preparation 36 3.2.1 Crystal Structure of Rhodium 36 3.2.2 Crystal Cutting .36 3.4 Measurement in Auger Electron Spectroscopy 38 3.5 Measurement of LEED 1(E) Curves 41 3.5.1 Experimental Equipment 41 3.5.2 Data Collection using Video L E E D Analyzer : 44 3.5.3 Data Processing 46 Chapter 4 : Structural Analysis for the Rh(l 10)-c(2x2)-S Surface 48 4.1 Introduction , 48 4.2 Experimental. .50 4.3 Parameters used in the Calculations 52 4.4 Results of T L E E D Analysis 52 4.5 Discussion : — 62 4.6 Summary 66 Chapter5: Structural Analysis for the Rh(l 10)-(3x2)-S Surface....... ...68 5.1 Introduction 68 5.2 Experimental 68 5.3 Parameters used in the Calculations 69 5.4 ModelConsiderations 71 v 5.5 Results of T L E E D Analysis ...74 5.6 Discussion 76 5.7 Summary 85 Chapter 6 : Structural Analyses for the Rh(l 1 l)-(V3x>/3)R30o-S and Rh(l 11)-c(4x2)-S Surfaces 87. 6.1 Introduction. 87 6.2 Experimental — 87 6.3 Parameters used in the Calculations 89 6.4 Model Considerations 91 6.5 Results and Discussion 91 6.6 Summary 107 Chapter 7 : Structural Analysis for the Rh(l 1 l)-(2x l)-0 Surface 109 7.1 Introduction 109 7.2 Experimental :. „ . 1 0 9 7.3 Parameters used in the Calculations 110 7.4 Model Considerations , 110 7.5 Results and Discussion 112 7.6 Summary 123 Chapter 8 : Conclusions and Future Work 124 8.1 Comparison between the Structures at Low and Higher Coverages of S on the (111) and (110) Surfaces of Rh 124 8.1.1 Distributions of S. 124 8.1.2 Adsorption Site 128 8.1.3 Dependence of Surface Relaxations and Surface Bond Lengths on Adsorbate Coverage 128 8.2 Effect of Coordination Number on Adsorbate-Metal Bond Lengths 129 8.3 Future Work 130 vi References 131 vii List o f Tables Table 1.1 Some techniques for study of surface properties 2 Table 1.2 Comparison of chemisorbed bond lengths from L E E D experiment and from prediction with Eq (1.7) for some surfaces where all bonding metal atoms are equivalent .14 Table 1.3 Comparison of chemisorbed bond lengths from L E E D experiment and from prediction with Eq (1.7) for some surfaces where there are inequivalent bonding metal atoms .15 Table 4.1 Values of geometrical parameters (in A) for the Rh(l 10)-c(2x2)-S surface from structural refinement with T L E E D using Rp and / ? o s 55 Table 4.2 Individual r p values for twelve beams from the Rh(l 10)-c(2x2)-S surface structure for normal incidence 58 Table 4.3 Atomic coordinates (in A) for the TLEED-determined structure of the Rh( 110)-c(2x2)-S surface 60 Table 5.1 T L E E D optimized values of Rp for each of the six model types considered for the Rh(l 10)-(3x2)-S surface structure — 75 Table 5.2 Atomic coordinates (in A) for the TLEED-determined structure of the Rh(110)-(3x2)-S surface 77 Table 5.3 Individual rp values for fourteen beams from the Rh(l 10)-(3x2)-S surface structure for normal incidence 80 Table 5.4 Comparison between values of geometrical parameters (in A) for the Rh(110)-(3x2)-S and Rh( 110)-c(2x2)-S surfaces structures determined by TLEED 81 Table 6.1 T L E E D optimized values of Rp for each of the model types considered for the (V3xV3)R30o and c(4x2) structures formed by S on R h ( l l l ) 93 viii Table6.2 Individual rp values for eleven beams from the R h ( l l l ) -(V3x^)R30°-S surface structure for normal incidence 98 Table 6.3 Individual rp values for twelve beams from the Rh(lT l)-c(4x2)-S surface structure for normal incidence 99 Table 6.4 Atomic coordinates in A for the TLEED-determined structures of the Rh(l 1 l)-(V3xV3)R30<>-S and Rh(l 1 l)-c(4x2)-S surfaces 103 Table 6.5 Comparison between the values (in A) of geometrical parameters for the (V3xV3)R30°and (4x2) surfaces structures formed by S on Rh(l 11), and corresponding values for the c(4x2) structures formed by CO and NO on Ni( l 11) ...104 Table 7.1 T L E E D optimized values of Rp for each of the model types considered for the Rh(l 1 l)-(2xl)-0 surface structure... . . . . .— 114 Table 7.2 Individual rp values for fourteen beams from the Rh( 111 )-(2x 1 )-0 surface structure for normal incidence , 117 Table 7.3 Atomic coordinates (in A) for the TLEED-determined structure of the Rh( l l l ) - (2xl ) -0 surface .....119 Table 7.4 Geometrical parameters (in A) for the Rh(l l l ) - (2xl ) -0 surf ace... ... 120 Table 8.1 Comparative features observed in the S/Rh( 111) and S/Rh(110) surface structures 125 IX List of Figures Figure 1.1 Representative inelastic mean free path of electrons in a solid as a function of their kinetic energy. 4 Figure 1.2 Schematic energy distribution N(E) of backscattered electrons as a function of their exiting energy. Ep is the primary beam energy in iow-energy'range 6 Figure 1.3 Diagrams showing (a) unit mesh vectors for one of three domains of the Rh( 111 )-(2x 1 )-0 surface and the Rh( 111). substrate; and (b) the corresponding reciprocal space vectors — . — : — 8 Figure 1.4 Processes associated with the removal of atomic.core holes by: (a) X-ray emission and (b) Auger electron emission 11 Figure 2.1 Schematic diagram showing that a diffracted beam in L E E D will have single, double, triple ••• scattering contributions which in general are covered by the term'multiple scattering'.:... 18 Figure 2.2 Muffin-tin approximation: (a) potential contour plot through a single atomic row and (b) variation of potential through the row of ion cores along X X ' (V Q is the muffin-tin zero) 20 Figure 2.3 Schematic diagram showing the transmission (/) and reflection (r) matrices for scattering by a single layer of atoms.. 24 Figure 2.4 Mechanism of the renormalized forward scattering perturbation method. Horizontal lines represents layers. Each triple of arrows represents the complete set of plane waves that travels from layer to layer; at each layer the beams are either transmitted (t) or reflected (r) i 26 x Figure 2.5 Diagram showing the relation between the error width of a structural parameter (Ap) and the var Rmin on a /?-factor versusparameter plot : 30 Figure 3.1 Schematic diagram of the U H Y chamber .35 Figure 3.2 Illustration of the three low index surfaces of a rhodium crystal: (100), (110) and (IT 1). In each case, the open circles represent the first layer Rh atoms and the filled circles represent the second layer atoms 37 Figure 3.3 The laser beam reflection setup to measure the angular misalignment (a) between the crystallographic plane of interest and the optical plane 39 Figure 3.4 Schematic diagram of an cylindrical mirror analyzer with glancing incidence electron gun. 40 Figure 3.5 Auger spectrum for the clean Rh (110) surface 42 Figure 3.6 Schematic diagram of the L E E D optics 43 Figure 3.7 Schematic diagram of the video LEED analyzer system 45 Figure 3.8 Measurement of L E E D 1(E) curve for the (5/4 1/4) beam from the Rh(l 1 l)-c(4x2)-S surface for normal incidence. Three symmetrically equivalent beams were averaged and then smoothed. . . . . . 47 Figure 4.1 Views of the structure of the Rh(l 10)-c(2x2)-S surface from: (a) the top and (b) the side. The open circles represent Rh atoms and the smaller, filled circles represent S atoms 49 Figure 4.2 Auger spectrum for the Rh (110)-c(2x2)-S surface 51 Figure 4.3 One quadrant of the L E E D pattern from the Rh(l 10)-c(2x2)-S surface showing the diffracted beams included in the structural analysis 53 xi Figure 4.4 1(E) curves for twelve diffracted beams from Rh( 110)-c(2x2)-S for normal incidence: (a) experimental 1(E) curves, (b) calculated curves including buckling in the second metal layer and (c) calculated curves with the second metal layer kept flat : 56 Figure 4.5 The variation of Rp versus d22 with all other geometrical parameters fixed at the optimal values found for the Rh(l 10)-c(2x2)-S surface structure 61 Figure 4.6 Top view of the structure of the Ni( l 10)-(2xl)-O surface structure. The solid and dotted open circles respectively represent the first and the second layers Ni atoms, whereas the smaller, filled circles represent O atoms 64 Figure 5.1 One quadrant of the L E E D pattern from the Rh(l 10)-(3x2)-S surface showing the diffracted beams included in the structural analysis 70 Figure 5.2 Model types included in the T L E E D analysis for the Rh( 110)-(3x2)-S surface structure with the unit mesh outlined in each case. The first and the second layer Rh atoms are represented by the larger open circles which are based respectively on continuous and dashed lines; the smaller filled circles represents S atoms. The directions of mirror and glide line symmetries are shown respectively by the continuous and dashed lines at the edge of each model 72 Figure 5.3 1(E) curves for fourteen diffracted beams from Rh(l 10)-(3x2)-S for normal incidence. The dash-dot lines represent experimental curves and the solid lines represent curve calculated for the structure (Table 5.2) optimized by the T L E E D analysis 78 xii Figure 5.4 Views of the structure of the Rh(l 10)-(3x2)-S surface from: (a) the side and (b) the top. The open circles represent Rh atoms and the smaller, filled circles represent S atoms. 82 Figure 6.1 Schematic indication of the L E E D pattern observed from the Rh(lll)-('V^x>/3)R30o-S surface structure. The open and filled circles represent the integral and fractional beams respectively 88 Figure 6.2 Schematic indication of the L E E D pattern observed from the Rh(l 1 l)-c(4x2)-S surface structure. The open and filled circles represent the integral and fractional beams respectively 90 Figure 6.3 Model types included in the T L E E D analyses for the Rh(l 11)-(V3x>/3)R30o-S and Rh(l 1 l)-c(4x2)-S surface structures. The smaller filled circles and the larger open circles represent S and Rh atoms respectively. The model designations are specified in the text, but adsorption in the three-coordinate sites may correspond to fee or hep local packing. The calculations maintain the mirror symmetries indicated by short lines at the edges of some models 92 Figure 6.4 1(E) curves for eleven diffracted beams at normal incidence for the Rh(lll)-(>/3xV3)R30o-S surface. The dash-dot 1 ines represent experimental curves and the solid lines represent curves calculated for the structure (Table 6.4) optimized by the T L E E D analysis 94 Figure 6.5 1(E) curves for twelve diffracted beams at normal incidence for the Rh(l 1 l)-c(4x2)-S surface. The dash-dot lines represent experimental curves and the solid lines represent curves calculated for the structure (Table 6.4) optimized by the T L E E D analysis 96 Figure 6:6 Views of the Rh(l 11 )-(V3x'v'3)R30o-S surface, and some notation used for structural parameters. The smaller, filled circles represent S atoms, and the larger circles represent Rh atoms. In the top view, xiii the atoms in the first Rh layer are open, while those in the second Rh layer are shaded. 101 Figure 6.7 Views of the Rh(l 1 l)-c(4x2)-S surface, and some notation used for structural parameters. The smaller, filled circles represent S atoms, and the larger circles represent Rh atoms. In the top view, the atoms in the first Rh layer are open, while those in the second Rh layer are shaded ;. .....102 Figure 7.1 Indication of the form of the L E E D pattern observed for normal incidence from the O on Rh(l 11) surface structure. The open circles are integral beams, while the filled symbols identify the three sets of half-order beams expected from a model involving a distribution of rotationally-related (2x1) domains. The mirror symmetries identified apply closely to the measured 1(E) curves, but the fractional beam intensities correspond to a slightly unequal proportion of domain types I l l Figure 7.2 A schematic indication of model types included in the T L E E D analysis for the O on R h ( l l l ) surface structure. Rh atoms are represented by the larger circles, and the smaller circles are O atoms (dashed circles represent O atoms below the first complete close-packed Rh layer). Overlayer O atoms on three-coordinate Rh sites are identified by either f or h depending on whether the site corresponds respectively to fee or hep local packing; underlayer (u) sites have an additional o or t to distinguish absorption into octahedral or tetrahedral holes; model designations including an r correspond to reconstructed metal surfaces ; 113 Figure 7.3 1(E) curves for fourteen diffracted beams at normal incidence for the Rh(l 1 l)-(2xl )-0 surface. The dashed-dot lines represent xiv experimental curves and the solid lines represent curves calculated for the structure (Table 7.3) optimized by the T L E E D analysis.. 115 Figure 7.4 Views of the Rh( 11 l)-(2x l ) -0 surface from: (a) the top and (b) the side. The open circles represent Rh atoms while the smaller, filled circles represent O atoms. In the top view, the atoms in the first Rh layers are open, while those in the second Rh layers are shaded 118 Figure 8.1 Diagram showing the top views of (a) Rh( 111 )-(V3xV3)R30°-S and (b) Rh( 11 l)-c(4x2)-S surface structures 126 Figure 8.2 Diagram showing the top views of (a) Rh(l 10)-c(2x2)-S and (b) Rh(l 10)-(3x2)-S surface structures 127 xv Acknowledgments I would first like to thank my supervisor, Professor K . A . R . Mitchell, who introduced me to interesting research in surface science. I am grateful for his invaluable discussion and guidance throughout my Ph.D. study. I owe special gratitude to my colleague, Mr. W. Liu, for his collaboration in the L E E D experimental measurements and for sharing his valuable experiences in the various projects described here. I also acknowledge Dr. D.T. Vu for her patience in teaching me the TLEED computer programs, which were provided by Dr. M . A . Van Hove (Lawrence Berkeley Laboratory). I extend my gratitude to Dr. P.C. Wong and Dr. Y.S. L i for their collaboration and valuable help in an additional XPS project; that experience was also very enjoyable and instructive. Throughout 1 have been indebted to the staff in the Electronics and Mechanical Workshops for their assistance in developing equipment and keeping it working. Finally, and most importantly, I wish to express my deepest gratitude and love to my parents and my wife, So-han, for their continuous encouragement and support throughout these years of my study. To them, I dedicate this thesis. xvi Chapter 1 : Introduction 1.1 Surface Science Surface science aims to study and understand the chemical and physical properties of surfaces and interfaces. A surface can be seen as the transition region between a bulk material and either vacuum or a gas phase. Although the surface region, which is 7 composed of the first few atomic layers of the solid, constitutes perhaps only 1 part in 10 of the mass of a macroscopic sample, it plays an important role in determining certain chemical and physical properties. The surface region is the place where different reactant phases 'communicate'. A crystal surface can be visualized as resulting from cleavage along a crystallographic plane of the bulk, but in general the surface atoms have some unsatisfied bonding capability since neighboring atoms are missing on one side. The surface atoms show a strong tendency to lower the free energy by forming more chemical bonds or by undergoing a relaxation or reconstruction. As a result, surfaces can possess structural, chemical, electronic and vibrational properties different from those of the bulk material 11, 2 | . Knowledge on how adsorbates interact with a surface is important in understanding the chemical processes that occur on it, including those in corrosion science, heterogeneous catalysis, adhesion and friction [3, 4, 5 J . Nowadays, numerous techniques are available for providing information on surface properties, and some examples are listed in Table 1.1. Each technique has a different physical basis and provides different information about the surface. For example, SEXAFS and ARPEFS aim to give bond lengths, whereas AES and SIMS especially probe the surface composition. Among these methods, low-energy electron diffraction (LEED) is the prime technique for determining atomic positions in surface regions of single crystal samples. The method of L E E D crystallography is proving to be very powerful at providing the fundamental surface structural information needed to develop concepts of surface Table 1.1 Some techniques for study of surface properties Surface Technique Acronvm Probe with Physical Basis Information Provided Refs. Low-energy electron LEED diffraction Scanning tunneling STM microscopy High-resolution electron energy-loss spectroscopy Surface extended X-ray absorption fine structure Angle-resolved-photoemission extended-fine-structure Electrons Elastic back diffraction Electrons Electron tunneling between surface and probing tip HREELS Electrons Auger electron . AES spectroscopy Secondary ion mass SIMS spectrometry Ion scattering ISS spectroscopy Noble gas ions SEXAFS X-ravs ARPEFS X-ravs X-ray photoelectron XPS spectroscopy Surface X-ray SXRD diffraction UV photoelectron UPS spectroscopy Thermal desorption TDS spectroscopy Infrared spectroscopy IRS Measure small energy losses Electrons Electron emission from deexcitation of core holes Ions Sputtering of ions from surface Ion scattering Absorption structure related to electron interference Interference effects in photoemitted electrons X-rays Photoemission of core electrons X-rays Diffraction at glancing incidence UV light Photoemission from valence shells Heat Measure desorption and decomposition products IR light Vibrational excitation by absorption Atomic surface structure and bonding Electronic and geometrical structure; topography Vibrational excitations (1 and //) Surface composition Surface composition Atomic structure, composition Bond lengths Bond lengths Surface composition and chemical states Surface structure Valence structure Multiple bonding states, desorption energy Perpendicular modes, surface-adsorbate bonding 16] 171 18] 19] [101 UU [12] [13] [9] |14] [15] [16] [17] 2 chemical bonding, and it can be applied to a wide range of system types, including reconstructed surfaces of semiconductors, chemisorbed gas-metal interfaces and metal-metal surface alloys [18]. The existence of detailed knowledge of atomic arrangements at or near surfaces represents the starting point for developing understanding of other surface properties, and overall surface structure must be seen as being fundamental for understanding surface physics and chemistry. 1.2 Low Energy Electron Diffraction (LEED) 1.2.1 Introduction The first L E E D experiment was performed in 1927 by Davisson and Germer [ 19] on a nickel crystal cut parallel to the (111) plane. It was found that the angular variations in the reflected flux for an incident electron beam could be explained by diffraction resulting from the electrons having a wave-like nature consistent with the hypothesis of de Broglie. Much subsequent work, particularly over the last 25 years, has been done to improve the experimental technique and to establish the theory, and this has resulted in L E E D becoming a major technique for surface structure determination. Two physical factors which are particularly important for this are the limited penetration depth and the favorable wavelength. For electrons in the Tow energy' range (e.g. 20 - 500 eV), the wavelength (A) relates to the kinetic energy (£) by the equation: where h is Planck's constant and m the electron's mass. Diffraction can occur since the corresponding wavelength (3 - 0.5 A) is comparable to the lattice spacings in crystals. Electrons in this energy range have a high probability to experience inelastic scattering in a solid. Figure 1.1 shows schematically the typical form, as a function of energy, of the inelastic mean free path; this can be defined as the average distance traveled by an electron 3 Figure 1.1 Representative inelastic mean free path of electrons in a solid function of their kinetic energy. 4 in the crystal without energy loss. For the L E E D energy range, inelastic mean free paths of 5 to 15 A are typical; this corresponds to a probing depth of a few atomic layers and so makes L E E D a surface sensitive technique. -When an electron beam is directed at a solid material, most electrons lose energy through the interaction. Figure 1.2 shows the number of scattered electrons, N(E), as a function of their exiting energy for an incident energy E . The large peak at low energies is due to secondary electrons created as a result of inelastic collisions between the incident electrons and electrons bound to the solid. The elastic peak (E = E p ) , which typically constitutes 1 to 5% of the incident electrons, corresponds to the electrons studied directly in LEED. Superimposed on the slowly varying intermediate region are small peaks resulting from Auger electrons and electron loss peaks. That most of the incident electrons in LEED. lose energy is primarily the result of plasmon excitations in the solid [20]. 1.2.2 Diffraction Conditions An incident electron beam in field free space can be represented by a plane wave as: f i n(r) = e ' V ' (1.2) where kQ is the wavevector (magnitude 2;r/A) and r the position vector with respect to the reference origin. Constructive interference takes place in elastic L E E D when the following two conditions are satisfied: •l*l = l* 0 l (1.3) and = kQ + g h k (1.4) where kft and ko/j are the components parallel to the surface of the wavevectors of the diffracted and incident beams, and g h k = ^ * i + k s2 with h and k being integers. The * * reciprocal space vectors sx and s 2 are defined with respect to the unit mesh vectors S j and s, in real space as follows, 5 Energy (eV) Figure 1.2 Schematic energy distribution N(E) of backscattered electrons as a function of their exiting energy. 'E is the primary beam energy in 'low-energy' range. 6 s r s * = 2ndu (i,j= 1,2) . (1.5) * * where o-. is the Kronecker delta. Eq (1.5) ensures sl _L s2 and s 2 i S j , and the * * magnitudes of s j and s2 are inversely related to those of s j and s2 respectively. Eq (1.3) corresponds to the conservation of energy and the conservation of momentum parallel to the surface in Eq (1.4) indicates that there is a direct correspondence between individual diffracted beams and vectors in the reciprocal net of the surface. ^ 1.2.3 Notations for Surface Structures Changes in the diperiodicity of the surface result in changes in the diffraction pattern that are easily observed and often are easily interpreted. Such changes are commonly observed when gases adsorb on a well-ordered crystal surface, and frequently the new surface has unit mesh vectors («j and s2) that are simply related to those of the substrate {al and a2). That is the case for all systems studied in this thesis, for which a standard notation of type M(hkl)-(nxm)Ra°-C is used. In this notation, M i s the chemical symbol for the substrate with its surface parallel to the (hkl) crystalline plane; the (nxm) shows that the new surface structure has periodicities n times that of the substrate in the ax direction and m times that in the c 2 direction; if the new unit mesh is rotated relative to that of the substrate the angle a is added to indicate this rotational relationship; and C is the chemical symbol for the adsorbate. Finally, it is sometimes convenient to insert a 'c ' before the (nxm) term to indicate that the unit mesh being considered is centered. For the structure formed by chemisorption of O on the Rh(l 11) substrate, the unit mesh of the surface structure, as outlined in Figure 1.3(a), defines the surface vectors s, and s2 which can be described in terms of the substrate unit vectors ax and a2 as follows, Sj = 2 o, (n = 2) s2=a2 (m=l) 7 o o o o o o o o - • o o * o * p o o o (b) o Figure 1.3 Diagrams showing (a) unit mesh vectors for one of three domains of the Rh(l 1 l)-(2xl)-0 surface and the Rh(l 11) substrate; and (b) the corresponding reciprocal space vectors. 8 Therefore the notation for this surface structure is 'Rh(l 1 l)-(2xl)-0 ' . According to Eq * * (1.5), the corresponding reciprocal vectors for the surface (S j and s2 ) relate to those of the substrate (at and a2 ) as shown in Figure 1.3(b). There can be three equally probable orientations of the surface unit mesh on the substrate (Figure 1.3(a)) and they are related by 60° rotation. For the real surface, there will be ordered regions corresponding to each type of domain and, provided the dimension of the domains is greater than the instrumental transfer width, the observed L E E D pattern will correspond to a sum of the patterns from the individual domains [21]. A consequence is that the diffraction pattern is composed of three sets of diffraction spots, rotated by 60° to each other, and they correspond to the three sets of differently filled symbols in Figure 1.3(b). In fact, this diffraction pattern from the three types of (2x1) domains is identical in general appearance to that from a (2x2) translational symmetry on the fcc( 111) substrate [21 ]. Although the net vectors for an adsorption structure can frequently be related to those of the substrate, this conveys only limited information about the surface structure. It neither indicates the registry of an overlayer structure (i.e. the relationship between the overlayer and underlying atoms) nor does it provide details about the arrangement of atoms within the unit mesh. Such information (and indeed the distinction between the three-domain (2x 1) and (2x2) models noted above) can only be achieved by analyzing intensities of the diffracted beams. This is done by interpreting the measured beam intensities as a function of electron energy. 1.2.4 Approach in LEED Crystallography L E E D crystallography aims to determine the coordinates of atoms in an ordered surface region. Measured intensities of diffraction spots as a function of electron energy (1(E) curves) serve as the basic input for a surface structural analysis. The diperiodic symmetry indicated by the L E E D pattern helps to define possible model types, but the approach of L E E D crystallography is necessarily a trial-and-error one. 1(E) curves are 9 calculated using electron multiple scattering theory (Chapter 2), for various structural models, and a search through coordinate space is made to find the best correspondence between the calculated and experimental 1(E) curves. This is done with numerical reliability indices or R-factors (Section 2.5) and the geometry in the calculation which corresponds to the lowest value of R defines the 'best geometry' for the surface region. The tensor L E E D approach in effect allows the calculation and assessment steps to be done simultaneously within certain limits discussed in Section 2.6. 1.3 Auger Electron Spectroscopy (AES) In 1925, P. Auger observed, in a cloud chamber, tracks due to electrons produced in a radiationless two electron process initiated by a relaxing core hole 122]. This process is shown schematically in Figure 1.4, along with the competing process of X-ray emission. The probabilities for Auger electron and X-ray production vary with the atomic number Z and the binding energy associated with the core vacancy. But Auger production always dominates if the core binding energy is 2 keV or less [9]. Furthermore, the kinetic energy of the emitted Auger electron is then necessarily less than this value, in which case the inelastic mean free path will , according to Figure 1.1, be of the order of 10 - 30 A. Consequently, only Auger electrons emitted from atoms in the general surface region can be detected without energy loss, and this results in A E S being a surface sensitive technique. Auger electrons are classified by the three energy levels involved, and an example of a KLXL^ transition is illustrated in Figure 1.4. To a first approximation, the kinetic energy of the Auger electron (EKJ L) is given by the following equation: EKL,L^EK-EL,-Eh ( L 6 ) where EK, £ L ) and EL^ are the binding energies of K, L{ and L 3 shells respectively. 10 Excitation r (a) h v K a , (b) Figure 1.4 Processes associated with the removal of atomic core holes by: (a) X -ray emission and (b) Auger electron emission [21]. 11 Corrections are strictly needed for relaxation and correlation effects [23], but this equation is sufficient to indicate that each element has its characteristic set of Auger electron kinetic energies which are easily distinguishable from those of other elements. Bonding effects do show up in Auger electron spectra, but the effects are small compared with differences from an element to another. In this thesis, Auger electron spectra are mainly used for qualitative analysis, which effectively depends on identifying elemental 'fingerprints'. 1.4 Bond Length - Bond Order Relationship To a first approximation, when an electronegative atom X chemisorbs on the topmost layer of a metal surface, the chemisorbed bond length, measured by L E E D or by other surface structural techniques, can be predicted quite well by the Pauling-type bond length - bond order relation: r = rQ- 0.85 log s (1.7) parametrized to an appropriate solid state structure [24]. In Eq (1.7), r is the X - M chemisorbed bond length for bond order s (which for equivalent bonds can be taken as the valency of X (v) divided by the number of neighboring M atoms (n) on the surface) and rQ is the X - M single bond length. The basic bond length - bond order equation summarizes the empirical relations which have usefully correlated large amounts of measured bond length information in bulk solid structures [25, 26]. Furthermore, this type of relation can be helpful for estimating surface bond lengths [24], particularly when the metal atoms involved have constant coordination number with respect to metal-metal bonding. In applications for O on Ni surfaces, as an example, the structure of bulk NiO can be used to estimate a value for rQ equal to 1.67 A (i.e. this is the effective O-Ni single bond length). Then the chemisorption bond lengths for O on the (100) and (111) surfaces of Ni can be readily predicted by Eq (1.7) to be 1.93 A and 1.82 A respectively, given that the respective adsorption sites are 12 four and three coordinate. These values are in close agreement with the corresponding values from the latest structural determinations of 1.92 A [27, 28] and 1.83 A (29]. Some other examples of this type are shown in Table 1.2, where most of the predicted values match the experimental ones to within about 0.01 A. However the situation is less satisfactory when the adsorbate bonds to metal atoms of different metallic coordination number. Examples of this type are presented in Table 1.3, and differences between the experimental and calculated values can now be as large as 0.10 A. In these latter structures, the adsorbate bonds to metal atoms in both the first and the second layer. Since atoms in the first metal layer are necessarily more exposed than those in the second, the latter have larger metallic coordination numbers than the atoms in the first metal layer. This must result in these inequivalent metal atoms having different bonding capabilities and in turn affect the associated adsorbate-metal bond lengths. However, close attention does not appear to have been made of this point in the wider discussions of surface bond lengths. In view of this circumstance, there is a need to include consideration of the metallic coordination number in refinements to the bond length - bond order relation (Eq (1.7)) used for surface bond lengths, and that provides one objective in the present work. 1.5 Purpose of Studies The evolution of chemisorption structures with increasing coverage has been the subject of frequent discussion for many years [30, 31, 32], but a common problem has been a lack of hard information on the surface structures concerned. L E E D crystallographic studies are undertaken here to provide a stronger basis for such discussion, and in particular investigations are made for the structural details as coverage increases for S on both the (110) and (111) surfaces of Rh. The objective is to provide new knowledge and insights into adsorption sites and surface bond lengths, and the factors that influence the determined values. In turn, this can help develop the principles of surface 13 Table 1.2 Comparison of chemisorbed bond lengths from L E E D experiment and from prediction with Eq (1.7) for some surfaces where all bonding metal atoms are equivalent Structure 1EFD Eq(1.7) Ni(100)-c(2x2)-O 1.92 A (4) [27,28] 1.93 A (4) Ni(l l l )-(2x2)-0 1.83 A (3) [29] 1.82 A (3) Ni(10G)-c(2x2)-S 2.19 A (4) [33] 2.23 A (4) Cu(100)-(2x2)-S 2.24 A (4) [34] 2.25 A (4) Rh(100)-c(2x2)-S 2.30 A (4) [35] 2.30 A (4) 14 Table 1.3 Comparison of chemisorbed bond lengths from L E E D experiment and from prediction with Eq (1.7) for some surfaces where there are inequivalent bonding metal atoms I FED Eq(1.7) Ni(110)-(2xl)-O 1.78 A (2), 1.95 A (2) 136] 1.81 A (2), 2.09 A (2) Cu(110)-(2xl)-O 1.81 A (2), 1.98 A (2) [37] 1.84 A (2), 2.09 A (2) Ni(110)-c(2x2)-S 2.20 A (1), 2.32 A (4) [38] 2.19A(1) , 2.35 A (4) Cu( 100)-(2V2x V2)R45°-0 1.81 A (1), 1.84 A (2), 2.04 A (1) |39] 1.81 A (3), 1.94A (1) Cu(100)-c(2x2)-N 1.81 A (4), 2.00 A (1) [40] 1.81 A (4), 1.96 A (1) 15 structural chemistry. Improved knowledge for the comparative surface structures formed by different adsorbed species on the same metal surface is also important, and a study has accordingly been made for the structure formed by O on the Rh(l 11) surface. In summary, new research described in this thesis involves investigations with tensor L E E D for the five structures: Rh(110)-c(2x2)-S [41], Rh(l 10)-(3x2)-S [42], Rh(l 1 l)-(>/3x>/3)R30o-S [43], Rh(l 1 l)-c(4x2)-S [43] and Rh(l 1 l)-(2xl)-0 [44]. Throughout, there is an emphasis to refine the arguments given in the previous section. 16 Chapter 2 : Multiple Scattering Calculation for L E E D Intensities 2.1 Introduction Low energy electrons interact strongly with matter; their scattering cross sections are around 106 times larger than those for X-rays. Strong inelastic scattering has already been noted in Section 1.2.1, but the large probabilities for elastic scattering enable incident electrons to be backscattered by an atomic layer, and also for scattering to occur by successive layers during either inward or outward directions of propagation. This gives the 'multiple scattering' which is shown schematically in Figure 2.1. The kinematic theory, which has been proved to be very successful in treating X-ray diffraction, is insufficient to handle low-energy electron diffraction due to its multiple scattering nature. Therefore, a full dynamical theory is needed for calculating the L E E D intensities which is required in turn in order to make a LEED structural analysis. There are a number of excellent reviews on this subject (45, 46, 47], therefore only some of the important aspects of the dynamical theory are outlined briefly in this chapter. The full dynamical calculation uses approaches introduced for electron band structure calculations on solids. For L E E D from a well-ordered surface region, an incident plane wave is backscattered into a set of plane waves corresponding to the diffracted beams, where each can be classified by a reciprocal space vector as noted in Section 1.2. The scattering solid is modeled by a set of atomic layers stacked parallel to the surface. Accordingly, the electron scattering calculation starts with the scattering by a single atom. Then the scattering amplitudes of all atoms in a single layer are summed, including the effect of intralayer multiple scattering, to determine the scattering properties of the whole layer. Finally, the diffraction from all layers, including the interlayer multiple scattering, is added up to give the total diffraction amplitude from the whole surface region. 17 incident beam diffracted beam surface layers Figure 2.1 Schematic diagram showing that a diffracted beam in L E E D will have single, double, triple ••• scattering contributions which in general are covered by the term 'multiple scattering'. 18 2.2 Muffin-Tin Approximation Figure 2.2 illustrates the muffin-tin approximation commonly used in L E E D theory for representing the potential in a solid [20]. It is assumed that each atom of the surface region is represented by a spherical ion core potential, extending out to a radius that prevents overlap with neighboring muffin-tin spheres, while the potential between the spheres (called the 'muffin-tin zero' V ) is constant. V Q is given the complex form ^ o ^ o r + ^ o i (2-1) where the real component V o r gives the gain of kinetic energy experienced when an electron enters the crystal. V o r is referenced to the vacuum level and it therefore has a negative value; commonly V o r is taken to be independent of the incident electron energy in the range studied by L E E D and that is the case in this work. Variation in its value primarily shifts the energy scale of the calculated 1(E) spectra; here V o r is chosen to optimize the fit between the experimental and calculated 1(E) curves at each stage in a structural analysis [45]. The imaginary component (V o i ) , when negative, accounts for the attenuation of the electron beam intensity, caused by inelastic processes such as phonon and plasmon excitations, as the beam propagates in the crystal. Also, V ; determines the width of the interference peaks in the 1(E) spectra in the sense that the larger I V o j l , the broader the peaks. Some have 1/3 suggested a weak energy (E) dependence for this parameter (e.g. to vary as E ' [48]), but a constant value of -5 eV has been used for V o j throughout this work. 2.3 Phase Shifts and Atomic Vibrations ik • r For elastic scattering of an incident plane wave e ° by a spherical ion core potential, the scattered wave *Psc(r) has the following asymptotic form [46]: vjr)= e'k°'r+ w ) e - r <2-2) 19 (a) Potential Position Figure 2.2 Muffin-tin approximation: (a) potential contour plot through a single atomic row and (b) variation of potential through the row of ion cores along X X ' (V is the muffin-tin zero). 20 where t(0) is the atomic scattering amplitude (0 is the scattering angle) and r is the distance from the atomic nucleus. The scattering amplitude can be expressed in terms of Legendre polynomials P( by a partial wave expansion: 00 H0) = 4JC 2) (2^+1) t( P((cos 0) (2.3) ( =o where te is a /-matrix element with 2ib( _ . e'6e sin 6, >,=-mr=^K- (2'4) The 6f, in Eq (2.4) are the phase shifts (for angular momentum values £ - 0, 1, 2,—) [49] and they are characteristic of the particular atomic potential and the energy. In practice, for the L E E D energy range, Eq (2.3) converges for a restricted number of IL values. This is important since increase in ^ m a x increases the dimension of the matrices involved in the multiple scattering calculations. In effect, the use of phase shifts allows the atom to be treated as a point scatterer without the need to consider its extension in space in the full calculation. L E E D beam intensities reduce with increasing temperature, and the atomic scattering amplitudes need to be reduced by a effective Debye-Waller factor <?"'w to take account of the atomic vibrations [46], where M = ^\Ak\2<(Ar)2> (2.5) Here AA: = k - ko (the momentum transfer due to diffraction from one plane wave into another) and <(Ar) > is the mean-square amplitude of vibration. For isotropic harmonic vibrations <(Ar)~> is given by: <(Ar)2> * -Z-z (2.6) mkB€r in the high temperature limit, where T is the system temperature, © is the Debye temperature, m is the atomic mass and kB is the Boltzmann's constant. The Debye 21 temperature indicates the rigidity of a solid with respect to vibrations; the higher © the stronger the bonding in the solid [2]. Jepsen et al. [50] have shown that the effect of the vibrating spherical atoms, to account for the temperature dependence, can be included in the multiple scattering calculations by a renormalization of the atomic phase shifts. In practice for a vibrating lattice, £ m a x = 7 (i.e. eight phase shifts) is generally satisfactory for energies no higher than about 250 eV. That has been followed in the present work. The phase shifts for Rh were obtained originally from a band structure potential [51], whereas those for S and O atoms were determined by Demuth et al. [52] from atomic potentials calculated for appropriate clusters by the superposition of atomic charge density procedure [53]. The parameters required in a L E E D multiple scattering calculation divide into two groups: (i) the geometrical (or structural) parameters which depend directly on the atomic positions within the model of the surface, and (ii) the 'non-structural' parameters which include the atomic phase shifts, the Debye temperatures and muffin-tin zero parameters ( V o r and V ( ) l ) . 2.4 Diffraction by a Stack of Layers 2.4.1 Introduction In multiple scattering calculations, the total wave function outside the solid-vacuum interface can be written as: ¥'out< r) = ' ' ' k : ' r + Z S V K G ' R < 2 - 7 > where e ' k ° r and e ' k « ' r represent the incident and diffracted plane waves respectively (the superscripts '+/-' specify into-the-crystal/out-of-the-crystal directions). The coefficient c represents the scattered amplitude for the beam with wavevector k £, and its intensity is: (2.8) 22 where k~ ± and kQ± are the perpendicular components of the diffracted and incident beams measured outside the crystal [54]. Therefore the objective of the calculations is to calculate the c from which/(£) curves are readily obtained. Two different types of mathematical description have natural application to this scattering problem, and the calculational methods accordingly divide into two categories. In the angular-momentum (L-space) representation, the scattering is described in terms of spherical waves. This is a natural basis insofar as the electrons are scattered by spherically symmetric ion cores. In the linear momentum (K-space) representation, the scattering within the crystal is described by plane waves; this is natural insofar as these functions represent diffracted beams traveling in a region of constant potential. Mathematical transformations between these two representations have been discussed by Marcus [55]. 2.4.2 Layer Diffraction Matrices The diffraction matrix M " for a single layer is determined in the L-space representation using spherical waves, as has been discussed by Van Hove and Tong [46]. The element M*T specifies the amplitude of the diffracted beam kt, given an incident plane wave k^ of unit amplitude. The Mt± matrix distinguishes between reflected and transmitted plane waves, and the following notation represents the layer reflection (r) and transmission (t) matrices [46]: r +" = M + " , f+ = M'+, r + + = M + + + /, t" = M" + I. (2.9) / is the unit matrix for representing the unscattered plane wave when it is transmitted without change of direction through the layer; this notation is illustrated schematically in Figure 2.3. 23 Figure 2.3 Schematic diagram showing the transmission (t) and reflection (r) matrices for scattering by a single layer of atoms. 24 2.4.3 Renormalized Forward Scattering Method In L E E D , forward scattering is normally stronger than backward scattering, and this guided the setting up by Pendry of a perturbative approach called the renormalized forward scattering (RFS) method [45]. Figure 2.4 illustrates a number of the possible scattering paths in which beams propagate into the crystal, and undergo various numbers of scatterings in both the forward and backscattered directions according to the layer reflection (r) and transmission (/) type matrices respectively. The longer the path the greater the damping, and all possible paths that can scatter significant amplitude back into vacuum are grouped, on the basis of the number of backscattering events, into first, second, third and higher order categories. Thus all paths with a single reflection contribute to the first order events, all with three reflections contribute to the second order events, all with five reflections contribute to the third order events, and so on. Contributions from successively higher orders are added until convergence of the reflected amplitudes is obtained. Typically, the RFS scheme uses 20 layers and 5 orders of iteration for convergence, however it may fail to converge when the interlayer spacings between layers are less than about 1.0 A, or when the ion cores are very strong scatterers. For smaller spacings (e.g. 0.5 - 1.0 A), the layer doubling method [45] may be applicable; otherwise for smaller spacings (e.g. < 0.5 A) the full matrix inversion procedures [46] are needed. 2.4.4 Combined Space Method Although the scattering amplitude for a single layer is generally calculated in the L-space representation [46, 55], calculations of the multiple scattering between layers can in principle be performed in either the K- or L-space representations. Since A'-space calculation generally requires less computational times, it is favored when it converges satisfactorily. However for closely spaced atomic layers, the A^-space methods (layer doubling or RFS) become intractable because a greatly increased number of plane waves are needed. Then full matrix inversion is required within the L-space representation. The 25 3rd order 2nd order 1st order incident beam 1 ^ —t————t — t — LA Figure 2.4 Mechanism of the renormalized forward scattering perturbation method. Horizontal lines represents layers. Each triple of arrows represents the complete set of plane waves that travels from layer to layer; at each layer the beams are either transmitted (?) or reflected (r) [46]. 26 complexity of this calculation is relatively insensitive to geometrical factors and that makes it suitable for handling scattering calculations involving small interlayer spacings, or different types of atom within a single plane, even though this approach is inherently more time consuming. The 'combined space method' [56] is a scheme which combines the use of both the A'-space and L-space representations in the calculation of multiple scattering from a stack of layers. For parts of the system With close subplanes (< 1.0 A), composite layer(s) are defined, for which the scattering matrices are evaluated with an /.-space calculation. Then the scattering from the stack of layers, which is composed of composite layers and other more widely spaced layers, is calculated in A'-space, for example with RFS method. The RFS scheme, with the combined space approach, optimizes the overall computing time for complex surface structures and that defines the basic computational scheme used in this work for calculating/(£) curves. 2.5 Reliability Indices (/^-factors) 2.5.1 Formulation of /^-factor The approach of L E E D crystallography requires the comparison of experimental and calculated /(£) curves, and the geometry in the calculation which gives the best . correspondence is considered to have the highest probability of being the correct model for the surface. Initial studies on simpler systems emphasized visual comparison but, as the number of structural parameters and diffracted beams increases, this becomes less and less objective. Consequently, quantitative measures of comparison a're now generally achieved by the use of numerical reliability indices (or R-factors); A useful /^-factor should be most sensitive to structural parameters, like atomic positions, arid less sensitive to non-structural parameters sUch as Debye temperature and V' o j . However, all analyses must optimize V o r continually during the experiment-calculation comparisons because of the way it affects the peak positions in 1(E) curves. A number of different R-factors have been proposed for L E E D as reviewed by Van Hove et al. [6, 57]. The first was that defined by Zanazzi and Jona (R7J) [58] which is based on both the first and second derivatives of the 1(E) spectra; the simplest, known as RQS [6, 57], uses the fraction of the total energy range with experimental and calculated 1(E) curves having slopes of opposite sign. A l l the reliability indices are defined so that the closer the correspondence between experimental and calculated 1(E) curves, the smaller is R. The L E E D R-factor most commonly used today is that due to Pendry (Rp) [59] and it has been used throughout this work. Rp is designed to emphasize the matching of peak positions, and it is based on the function L(E) defined as: I'(E) L ( £ ) = w ( 2 " 1 0 ) It follows the idea that all peaks in 1(E) curves carry structural information caused by constructive interferences, and this /?-factor weighs all peaks (large or small) equally. In part, this is because the higher energy peaks are usually smaller than those at lower energy due to the increased thermal diffuse scattering in the former case. However, L(E) by itself is not sufficient since it would become infinite whenever 1(E) is zero. To avoid that divergence problem, a new function Y(E) is defined: Y(E) = L { E ) 2 2 (2.11) 1 + VJL2(E) This function is readily derived from an 1(E) curve, but it has a form that emphasizes features such as the position (energy) of peaks and valleys, while relatively suppressing the absolute intensities. A single-beam r,> is defined based on the Y(E) function as: f [ ( > ; , P ^ - > c a ^ - ) ) ] 2 ^ r v = K . (2.12) K2(E) + Yj(E)]dE The overall R-factor (Rp) for use in a structural analysis is then a weighted average of all the single-beam rp values (r p ) according to their energy ranges (AE') as: 28 RP = J (2.13) where the summations are over the various diffracted beams. 2.5.2 E r r o r Estimation Pendry designed his index to be approximately unity when there is no correlation between the calculated and experimental curves; other L E E D R-factors do not have clearly defined upper limits. Also Pendry attempted to estimate the reliability of a comparison between experiment and calculation by considering the probability that a minimum in /?,, is a local minimum due to the operation of random fluctuations. He defined a 'double reliability factor' (RR) as: var/? /8 IV -I RR = l^Ll2- = * (2.14) • R V AE where var R is the variance of R, V o j is the imaginary part of the muffin-tin potential V 0 and A£i s the total energy range. Then he proposed that the reliability of a minimized Rp value is: var R. = RR x R . (2.15) min min v ' which can correspond to an error width for a structural parameter on the Rp versus parameter plot, as shown in Figure 2.5. Another approach to uncertainty is provided by the method proposed by Andersen et al. [60] in which it is assumed that the R-factor near the minimum can be written as a quadratic form of the different parameters p(i), i = 1, 2, ... k as shown in Eq (2.16), where k is the total number of parameters to be determined. R = * m i n + 2 (P - PoPJ'G <P - / 'opt ) W i t h Gij = dp(i)dp(j) (2-16) Then an error matrix (£) can be defined by: 29 Pupt Paramenter(p) Figure 2.5 Diagram showing the relation between the error width of a structural parameter (zip) and the var RMIN on a /?-factor versus parameter plot. 30 e = G (2.17) and the uncertainty Ap(//results from: Ap(i) = (2.18) where F is the number of degrees of freedom resulting from the total number N of main peaks appearing in the experimental 1(E) curves (F = N - k). This method can be applied in principle to any design of/?-factor. However, there is still a lack of independent measure of errors in surface structure determinations, and also no agreement as to which approach, even using RP, is most appropriate for estimating uncertainty in a L E E D analysis. The uncertainties in geometrical parameters determined from the Pendry procedure are generally at least twice those from the scheme of Andersen et al., and they have been seen as giving upper and lower limits respectively |47,61]. 2.6 Tensor L E E D In the early development of L E E D crystallography, an analysis depended on a trial-and-error search which was controlled at each step by human intervention. This was too cumbersome to solve complex surface structures with a large number of unknown structural parameters, but a major recent advance has been the development of tensor LEED (TLEED) which can, within certain limits, provide an automatic optimization procedure [61, 62, 63, 64]. The T L E E D method combines a numerical search algorithm with an efficient scheme for calculating 1(E) curves for structures which are varied within a range of parameter space around that for a reference structure for which a full dynamical calculation has been made. 2.6.1 General Principles of T L E E D A plane wave incident on an atom can be scattered by the ion core potential into a 31 spherical wave originating at the center of an atom. The scattering /-matrix (//) of the atom is expressible in terms of phase shifts 6f as in Eq (2.4). However, if the atom is displaced, the new /-matrix of the displaced atom (/ ' J ) can be expressed as: t'J = tj + dtJ(drj) (2.19) where 6tJ is the change in the /-matrix of the j t h atom produced by displacing it through d/v. This change can be rewritten in an angular momentum basis as: * V Cm • = I <*lm A m ,<6ry > ' *, 9tt m , Cm • (2-20) ('i m I where g is a spherical wave propagator which converts a spherical wave centered on the original position of the atom r- into a set of spherical waves centered on the position of the displaced atom #•• + dr.. The change in the amplitude of a L E E D beam (6A) is related to 6t1 by: 6A = 2 < nk„f6tJ I V(kQ„) > • (2-21) J where A o and kt, are the parallel component of wavevectors of the incident and scattered waves. After substituting Eq (2.20) into (2.21), plus considerable algebraic manipulation, the final form results as follows: " M = ^ T 2 I * L . ™ W « ' < < V (2.22) j fm, f 'in' where N is the number of displaced atoms, the matrix S is a function of atomic displacements alone and the tensor J contains the information which depends only on the reference structure. A T L E E D calculation starts with the full dynamical (FD) calculation for the reference structure, and the J is stored. Distortions of the structure are described by a set of atomic displacements br- which fix S for this new trial structure. Then resumming Eq (2.22) with the original J gives the change in diffracted amplitude between the trial and reference surface structures, and that readily leads to calculated 1(E) spectra for the new trial 32 structure. This provides a very efficient method for the repeated calculation of 1(E) curves for many trial surface structures which are related to a single reference structure. This approach can dramatically reduce the time required for a structure determination, and in turn enable a detailed analysis for complex surface structures resulting from non-symmetrical relaxations and reconstructions including those that are adsorbate induced. 2.6.2 Implementation of T L E E D A l l the T L E E D analyses in this thesis were carried out using the program provided by Van Hove ['61, 62, 63]. The layer stacking in the T L E E D program was performed by the renormalized forward scattering method and the automated search was performed using the direction-set Powell algorithm option. Symmetry elements possessed by a particular type of trial model could be maintained through the search procedure. This program provided an efficient way to explore the local R-factor hypersurface in the neighborhood of a particular reference structure, although strictly the T L E E D approximation maintains its validity only over fairly restricted changes in geometry. For example, Rous [64] suggested the approximation can remain reliable over a vertical separation of lip to 0.4 A in a simple adsorption structure. However, in more complex structures with substantial vertical and lateral displacements, much care is needed in the implementation of this method. After each FD/TLEED cycle, it is vital to compare the optimized geometry with that of the reference structure and the corresponding Rp values. Our approaches were to optimize the vertical positions of the atoms before the horizontal ones and to repeat cycles of FD calculation, followed by direct search, until the TLEED-optimized structure showed clear convergence in the atomic displacements [65]. Typically, five to eight cycles of iteration were needed to reach the final best-fit structure; each optimization was considered to be complete when Rp could not be improved by more than 0.01 from the previous cycle. 33 Chapter 3 : Experimental 3.1 Ultrahigh Vacuum (UHV) Apparatus and Instrumentation Under atmospheric pressure, surfaces are never clean or free of adsorbates. They are always covered with a layer of atoms or molecules which come from the ambient atmosphere. When atoms or molecules approach a surface, they will encounter a net attractive potential. This process involves trapping of the atoms or molecules incident on the surface and is known as 'adsorption'. Based on the kinetic theory of gases, the flux (F) of incident molecules striking a surface is: F t m o l e c u l e c m V ' y ^ ^ x 10 2 2 P(Torr) (MT)V2 (3.1) where P is the pressure, M is the molecular weight of the gaseous molecules and T is the temperature. As a guide, for a gas with M = 28 g mole"1 at 1 atm (760 Torr) and 300 K , 23 2 1 23 Eq (3.1) gives F = 10 molecule cm s . Thus, at ambient conditions, 10 ~ molecules can be incident on each 1 cm of surface per second. If every molecule encountering the 1 ^ 2 surface (whose surface concentration is about 10 ~ atoms cm ) adsorbs, a 1 monolayer -8 (ML) coverage can be built up in around 10 s. Sticking coefficients are frequently less -9 than unity, but nevertheless it is clear that ultrahigh vacuum conditions, with P « 10 Torr or less, are required to maintain a surface in a controlled state while experiments are performed over a period of half an hour or more. A l l the experiments in this work used an UHV stainless steel chamber (Varian 639701), which was pumped by an ion pump (Varian Diode Vaclon®) to maintain a base pressure of around 2x10 1 0 Torr. Various instruments were mounted on the chamber through the use of Conflat® Flanges; vacuum seals between the flanges were made using copper gaskets pinched between steel knife-edges. A top view of the chamber is depicted in Figure 3.1. 34 Leak Valve Figure 3.1 Schematic diagram of the UHV chamber. 35 The crystal sample was mounted on a high precision manipulator (Varian Model 981-2527) which was capable of three degrees of translation al motion (x.yz) and two degrees of rotation (primary and tilting) for sample positioning. The primary rotation of 360° allowed positioning of the sample in front of different instruments for different measurements. Sample heating was achieved by electron bombardment and the temperature of the sample was measured with a chromel-alumel thermocouple spot welded to the sample cup. Argon and gases for chemisorption studies Were introduced into the chamber through a variable leak valve (Varian Model 953-5070) from a gas inlet manifold. The pressure and composition of the residual gas inside the chamber could be monitored respectively by an ionization gauge (Varian Model 971-5008) and a residual gas analyzer (Leybold Inficon: Quadrex 100). Helmholtz coils were added around the UHV chamber to compensate for the earth's magnetic field. Also installed in the chamber were the L E E D optics and a cylindrical mirror analyzer respectively for the display of L E E D patterns and measurement of Auger electron spectra. 3.2 Crystal Preparation 3.2.1 Crystal Structure of Rhodium Rhodium (Rh) is a metallic element in the second transition series with an atomic number of 45. Its melting and boiling points are 2482 and 3970 K respectively. This metal crystallizes in the face-centered-cubic (fee) structure with lattice constant 3.8042 A. The three low-index (100), (110) and (111) surfaces are shown in Figure 3^2. 3.2.2 Crystal Cutting The R h ( l l l ) and (110) samples used in the work described in this thesis were respectively prepared by Dr. P.C. Wong and Dr. J.R. Lou. Briefly, the crystal samples were cut from a high-purity (99.99%, LEICO Industry) single crystal rod. Laue X-ray diffraction was used to identify the orientation of each desired crystallographic plane. Then 3 6 (100) (110) (111) Figure 3.2 Illustration of the three low index surfaces of a rhodium crystal: (100), (110) and (111). In each case, the open circles represent the first layer Rh atoms and the filled circles represent the second layer atoms. 37 spark erosion was employed to cut a 1 to 2 mm thick slice off the rod with the correct plane exposed. Initial surface polishing was done with a planetary lapping system (DU 172, Canadian Thin Film Ltd.) with progressively finer diamond pastes (Micro Metallurgical Ltd.) from 9 to 3 pm. Finally, the sample was hand-polished on a deer skin cloth (Microcloth, Buchler 40-7218) mounted on an universal polisher (Micro Metallurgical Ltd.) with successively 0.3 and 0.05 pm alumina (Linde) polishing suspension. After polishing, the misalignment angle (a) between the desired crystallographic plane (oriented using Laue diffraction) and the optical face of the sample was checked with the HeNe laser set-up depicted in Figure 3.3. The angle a is given by: a(rad) = ^ ; (3.2) A l l samples used in this work had misalignment angles of less than 1°. Before entry into the U H V chamber, each sample was rinsed with trichloroethylene, acetone and then methanol to remove any grease from the surface. After putting into the chamber and pumping down to UHV conditions, the sample was cleaned by argon ion bombardment (600 eV, 1.5 uA cm" , 1 h) at room temperature and then briefly annealed at 1300 K. Cycles of bombardment and annealing were repeated until no significant impurity could be detected by AES, and the surface gave a sharp L E E D pattern. Similar procedures were necessarily applied to restore the clean sample surface following each adsorption experiment and before preparations could be made for the next experiment. 3.4 Measurement in Auger Electron Spectroscopy °i • • • • . The cylindrical mirror analyzer (CMA) used in this work (Varian Model 981-0127) is shown schematically in Figure 3.4. A potential V applied between the two coaxial cylindrical electrodes creates an electrical field with cylindrical symmetry. The outer cylinder is held at a negative potential with respect to the inner cylinder which is grounded. Electrons enter the analyzer at 42° to ensure second order focusing [9]. Only those 38 Figure 3.3 The laser beam reflection setup to measure the angular misalignment (a) between the crystallographic plane of interest and the optical plane. 39 Sweep Supply Electron Beam Sample Data Acquisition Electron multiplier Magnetic Shield Figure 3.4 Schematic diagram of a cylindrical mirror analyzer with glancin incidence electron gun. 40 electrons in a narrow energy range can pass through the exit slit to an electron multiplier collector. By ramping the potential V, electrons in a specific energy range can be detected. The primary electron beam (typical energy 2 keV and current 100 uA) was directed at a glancing angle (19°) to the sample in order to enhance the surface sensitivity. The Auger electrons (Section 1.3) ejected,from the sample generally appear as small features superimposed on the slowly varying background of secondary electron emission (Figure 1.2). Accordingly, the Auger signal is magnified by detecting in the differential mode. This is accomplished electronically by superimposing a small sinusoidal voltage (AV = k sin cot) on the outer cylinder voltage and synchronously detecting with a lock-in amplifier the component of the signal from the electron multiplier with frequency co. This directly generates the derivative curve as V is ramped provided that k is sufficiently small [9J. The modulation voltage k should be less than half the width of an Auger peak (« 10 eV) for good resolution [9]; typically k was 2 V at 16.5 kHz. The peak-to-peak distance in a differentiated Auger spectrum gives a measure of relative surface concentration provided that the Auger peaks being compared have a constant peak width. But the Auger current also depends on several other experimental parameters, such as the incidence angle, energy of the primary beam, and the modulation voltage. Therefore, surface concentrations can be compared this way only when all measurement parameters are held constant. A l l Auger spectra collected in this work were recorded with a time constant of 100 ms and a sweep time of 1.5 min for an energy range of 600 eV. An example of an Auger spectrum for a cleaned Rh(l 10) surface is shown in Figure 3.5. 3.5 Measurement of L E E D 1(E) Curves 3.5.1 Experimental Equipment Figure 3.6 schematically indicates the four-grid L E E D optics (Varian model 981-0127) used in this work. The electron beam, generated by a directly heated tungsten 41 0 100 200 300 400 500 600 Energy (eV) Figure 3.5 Auger spectrum for the clean Rh (110) surface. 42 Fluorescent Screen Crystal Sample 5 k V Beam Energy Figure 3.6 Schematic diagram of the LEED optics. 43 filament at around 2000 K, is collimated by a lens system and accelerated to the desired energy E. The final electrode in the gun and the sample are grounded so that the electrons move in a field free region. Typically the electron beam has a diameter of 1 mm at the crystal surface, an energy spread (AE) of up to 1 eV (caused mainly by the thermal energy distribution |45J) and a current of around 1 uA. The crystal specimen is positioned at the center of an arrangement of four concentric hemispherical grids (transparency for each about 80%). The first grid (nearest to the sample) is grounded, while the second and third grids are maintained at a negative potential whose magnitude is slightly below the accelerating voltage experienced by the incident beam. These grids therefore act as a high pass energy filter to prevent most inelastically scattered electrons from reaching the fluorescent screen. The fourth grid is grounded to isolate the screen potential (5 kV) which accelerates the elastically scattered electrons for visual display of a diffraction pattern, with viewing from the front glass window. 3.5.2 Data Collection using Video L E E D Analyzer A l l the experimental 1(E) curves used in this study were recorded as close to normal incidence as possible in order to get the best control on direction of incidence and to aid the calculations. Normal incidence is a symmetry direction in the surfaces studied, and 1(E) curves for diffracted beams related by symmetry elements possessed by the real surface should be identical insofar as the incidence direction is exactly at the normal. 1(E) curves were measured, over the energy range 40 to 252 eV, with a commercial video L E E D analyzer system [66] (Data-Quire Corp., Stony Brook, N.Y.) whose functions are outlined schematically in Figure 3.7. Viewing the L E E D pattern with a silicon-intensified T V camera (Cohu 4410/1SIT) allowed monitor display. The camera defined the full viewing area as a 256x256 pixel frame. The intensity of each diffracted beam was recorded by summing the digitized intensities over an adjustable window frame (normally lOx 10 pixel), which was set to completely cover the diffraction spot to be measured. The computer unit 44 LEED Unit T .V. Video A/D Camera Monitor Converter LEED Controller Modem Main Computer Figure 3.7 Schematic diagram of the video LEED analyzer system. Intel 486 D/A Converter 45 was programmed to automatically track the position of the spot on the monitor screen, as the incident electron energy was varied, during the 1(E) curve measurement. In principle, the program allowed up to 49 beams to be measured simultaneously, but typically in practice no more than six beams were measured in one pass; usually ten passes were made for each set of beams to improve the signal-to-noise ratio (S/N depends on Vno. of scans). In addition, different gain level settings were used for measuring beams pf different overall intensity. 3.5.3 Data Processing Treatments of the raw experimental 1(E) curves were needed before use in a structural analysis. The maximum incident current from the L E E D electron gun varies linearly with increasing energy to about 100 eV, at which point it becomes constant at approximately 1 pA. Because of this variation with energy, the raw intensities had first to be normalized to a constant incident beam current. Then, beams which are expected to be equivalent by symmetry are averaged together; this acts to minimize the effects of experimental error associated, for example, with some small deviation from normal incidence or a slight misalignment of the surface [67]. Finally, the averaged 1(E) curves are smoothed to reduce noise which could adversely affect the later /f-factor analysis. Corrections for background intensity were made when needed. Figure 3.8 illustrates these procedures as applied to the treatment of experimental data for the (5/4 1/4) beam from the Rh(l 1 l)-c(4x2)-S surface structure. 46 50 100 150 200 250 Energy (eV) < Figure 3.8 Measurement of LEED/(£) curve for the (5/4 1/4) beam from the Rh(l 1 l)-c(4x2)-S surface for normal incidence. Three symmetrically equivalent beams were averaged and then smoothed. 47 Chapter 4 : Structural Analysis for the Rh(110)-c(2x2)-S Surface 4.1 Introduction An early use of the bond length-bond order relationship Eq (1.7) for S-Rh chemisorption bonding, parametrized by R h , 7 S 1 5 (the rhodium sulphide of lowest oxidation state), predicted bond lengths on the (100), (110) (two) and (111) surfaces as 2.27. 2.45, 2.11 and 2.16 A respectively, in surprisingly close correspondence with the experimental values then available (namely 2.30, 2.45, 2.12 and 2.18 A) [24]. Those initial structural determinations did not include metallic relaxations resulting from the chemisorption bonding to S, although such effects have recently been studied for S chemisorbed on the Rh(lOO) surface [35]. There appears to be a need to refine the initial study for the Rh(l 10)-c(2x2)-S system in which the S atoms chemisorb on the center sites of the Rh(llO) surface [68] as shown in Figure 4.1(a). In this c(2x2) structure, each S atom is simultaneously bonded to four symmetrically equivalent first layer Rh atoms labeled as 'Rhj' in the figure. At the same time, the S atom also bonds to one second layer Rh atom (labeled as 'Rh n ') directly underneath: Obviously, these two kinds of S-Rh bonds will be different and they will be referred to as S-Rhj and S-Rh n respectively in the following discussion. Based on the simplest grounds of geometry, the S-Rh n bond length is expected to be shorter than S-Rhj. However, since the R h n atom bonds to eleven other Rh atoms, while each Rhj atom bonds to only seven other Rh atoms, R h n is expected to have a smaller potential than the Rhj atoms for bonding to a chemisorbed species. Consequently, this counteracting factor may favor some increase in the S-Rhjj bond distance compared with that for S-Rhj. The metallic structure, as a result of S chemisorption, may reasonably be expected to relax in order to reach some compromise between these opposing 48 (b) Figure 4.1 Views of the structure of the Rh(l 10)-c(2x2)-S surface from: (a) the top and (b) the side. The open circles represent Rh atoms and the smaller, filled circles represent S atoms. 49 tendencies, and such effects are investigated in the present chapter which reports a new L E E D crystallographic analysis for the Rh(l 10)-c(2x2)-S surface structure. 4.2 Experimental The Rh( 110) sample used in this study was cut from a high-purity single crystal rod to within 1° of the (110) plane. Then it was cleaned in a U H V chamber, which has a base pressure of 2x10 Torr, by cycles of argon ion bombardment (1.5 uA/cm at an ion energy of 600 eV) until no impurity could be detected by A E S using a single-pass cylindrical mirror analyzer. Each bombardment is followed by annealing to 1300 K using electron bombardment to order the surface. This cleaning procedure results in a ( l x l ) L E E D pattern which is sharp and free of diffuse background intensity. The deposition of S atoms on the Rh(110) surface was achieved by dosing the surface with high-purity H 2 S gas (Matheson) at around 2x10" Torr via a leak valve into the chamber With the sample held at room temperature, followed by an anneal at 800 K . The amount of S on the surface was monitored by the quantity (Rs) which is defined as: where A , s , and AMr are the Auger peak-to-peak heights for S at 152eV and Rh at 302 eV respectively. It. is observed that a good c(2x2) pattern is formed when Rs is around 0.45. As the amount of S on the surface increases, a (3x2) pattern forms when Rs reaches about 0.75. A typical AES spectrum for the Rh(l 10)-c(2x2)-S surface is shown in Figure 4.2. Independent study of the interaction of H 2 S with the Rh(100) surface indicates dissociative adsorption with H 2 desorption at even 300 K [69]. Therefore, under our experimental conditions, similar dissociation and desorption are expected to occur on the other low index Rh surfaces, such as (110) and (111), leaving strongly chemisorbed S on the surface. The 1(E) curves of twelve symmetrically independent diffracted beams with a cumulative energy range of around 1520 eV were measured for the Rh(l 10)-c(2x2)-S 50 Energy (eV) Figure 4.2 Auger spectrum for the Rh (110)-c(2x2)-S surface. 51 surface; symmetrically equivalent beams were measured at the same time, which allowed a check that normal incidence was closely set. Appropriate 1(E) curves were averaged and smoothed; the diffracted beams measured are (1 0), (0 1), (1 1), (2 0), (0 2), (2 1), (3 1), (1/2 1/2), (1/23/2), (3/2 1/2), (3/2 3/2) and (5/2 1/2) according to the beam notation shown in Figure 4.3. 4.3 Parameters used in the Calculations The calculations of phase shifts for Rh and S atoms have been described in Section 2.3. The temperature correction of the phase shifts was done by using the bulk Debye temperature of 480 K for Rh [70]; that for S was taken as 860 K so that all the vibrating atoms probed by L E E D have a constant root-mean-square amplitude [46]. V o r was initially set at -12.0 eV. Comparisons between experimental and calculated 1(E) curves were done with the two reliability factors /? p and RQS described in Section 2.5.1. In the optimization process, the positions of the S atoms, and of the Rh atoms in the two outermost metallic layers, were allowed to vary in three dimensions, subject to maintaining the two perpendicular mirror planes in the [001] and the [110] directions as indicated in Figure 4.1(a). The previous L E E D crystallographic analysis for the Rh(l 10)-c(2x2)-S surface structure [68] established that the S atoms adsorbed on the center sites of the Rh(l 10) surface (i.e. the sites that continue the fee metal structure), and that the distance between S and the topmost Rh layer was about 0.77 A, assuming all Rh atoms remain at the bulk positions. The structure from the earlier L E E D study was used as the initial reference structure for the present T L E E D analysis. 4.4 Results of T L E E D Analysis In the first stage, it was attempted to optimize the correspondence between the experimental and calculated 1(E) curves by varying three interlayer spacings: (i) between the S atom layer and the topmost Rh layer (dQ,), (ii) between the First and the second Rh layers 52 4 0 0 2 O o O 1/2 3/2 3/2 3/2 0 1 0 1 l o 2 1 o 3 1 1/2 1/2 3/2 1/2 5/2 1/2 o- 0 1 o O 20 o Figure 4.3 One quadrant of the L E E D pattern from the Rh(l 10)-c(2x2)-S surface showing the diffracted beams included in the structural analysis. 53 (J, 2 ) , and (iii) between the second and the third Rh layers (^23)- Designations of spacings among layers are illustrated in Figure 4.1(b), and it is noted that the ceriter-of-mass plane is used as the reference position for each layer. The initial optimization of these parameters yields calculated 1(E) curves for which the corresponding Rp is 0.3602. The geometrical parameters determined are listed in Table 4.1; briefly, dQV dX2 and d23> equal 0.84, 1.40 and 1.36 A respectively. The calculated 1(E) curves are shown in Figure 4;4(c); the agreement between the experimental and calculated spectra for all the integral beams and some of the fractional beams is good, however, the fittings for the fractional beams (3/2 1/2), (3/2 3/2) and (5/2 1/2) remain unsatisfactory. The good correspondence between the calculated and measured 1(E) curves for most of the beams suggests that the structural model considered may be basically correct; however, it appears that some small surface modifications have been overlooked in the analysis, and that such a deficiency causes some discrepancies between the experimental and calculated curves for those beams which are more sensitive to that particular modification. That leads us to investigate more surface relaxations in the c(2x2) structure. In the analysis described above, it is assumed that the second Rh layer is planar. However, the side view of the model in Figure 4.1(b) shows that the Rh atoms in the second layer are divided into two different kinds labeled as R h n and Rh,],. Each Rhjj atom has a S atom positioned above, whereas those designated R h i n do not. Since there are two different environments for the Rh atoms, it is understandable that the two subplanes respectively formed by Rh n atoms and by R h m are not necessarily coplanar. Actually, such buckling in the second metal layer has been observed in other surface structures, for example S/Ni(100) [33, 71], O/Ni(100) [28, 72] and N/Cu(100) [40]. Accordingly, further optimization of interlayer spacings (dov dl2, d23) and of the second Rh layer buckling (d22) was performed. Significant improvement in the R-factor analysis, compared with the simple non-buckled model, is obtained with Rp reduced to 0.2521, and the individual rp for the twelve beams are reported in Table 4.2. Comparisons 54 Table 4.1 Values of geometrical parameters (in A) for the Rh(l 10)-c(2x2)-S surface from structural refinement with T L E E D using Rp and RQS starting from the structure given in reference [68]. Rh(110)-c(2x2)-S without buckling with buckling * P * P ^os 4)1 0.84 0.83 0,82 d\2 1.40 1.39 1.39 d22 0.11 0.11 1.36 1.35 1.35 ^bulk 1.35 1.35 1.35 55 Figure 4.4 1(E) curves for twelve diffracted beams from Rh(l 10)-c(2x2)-S for normal incidence: (a) experimental 1(E) curves, (b) calculated curves including buckling in the second metal layer and (c) calculated curves with the second metal layer kept flat. 56 Beam (1 0) Beam (0 2) Beam (1/2 3/2) 0 50 100150200250300 Beam (0 1) 0 50 100150200250300 Beam (11) 0 50 100150200250300 Beam (2 0) 0 50 100150200250300 0 50 100150200250300 Beam (2 1) 1 1 1 ! A 1 1 . > ( « ) • •"/(b): Jjic). 0 50 100150200250300 Beam (3 1) 0 50 100150200250300 Beam (1/2 1/2) 0 50 100150200250300 Energy (eV) 0 50 100150200250300 Beam (3/2 1/2) 0 50 100150200250300 Beam (3/2 3/2) 0 50 100150200250300 Beam (5/2 1/2) 0 50 100150200250300 57 Table 4.2 Individual r p values for twelve beams from the Rh( 110)-c(2x2)-S surface structure for normal incidence Beam Label rl> (1 0) 0.1814 (0 1) 0.1961 ( U ) 0.1868 (2 0) 0.3606 (0 2) 0.1153 (2 1) 0.1480 (3 1) 0.3383 (1/2 1/2) 0.1973 (1/2 3/2) 0.3489 (3/2 1/2) 0.3296 (3/2 3/2) 0.2686 (5/2 1/2) 0.2465 58 of the experimental 1(E) curves with these two levels of optimization are shown in Figure 4.4. In general, all the beams after the second optimization show improvement in correspondence with the measured 1(E) curves; the buckling of the second Rh layer has the largest effect on the curves of the fractional beams (3/2 1/2), (3/2 3/2) and (5/2 1/2). Comparing 1(E) curves of the buckled model with those from the unbuckled model, substantial reduction is seen for the (3/2 1/2) beam in the intensity of the peaks at around 110 and 160 eV. Also for the (3/2 3/2) beam, the strongest peak switches from 160 eV for the non-buckled model to 190 eV for the buckled model, and there is significant improvement in the relative intensities of the peaks in the (5/2 1/2) beam. The atomic positions for the fully optimized model are reported in Table 4.3, and some associated geometrical parameters are included in Table 4.1. The new refinement indicates that the values of dQ,, d]2 and <i23 are 0.83, 1.39 and 1.35 respectively. Also it is found that the second metallic layer is buckled with the atoms R h n displaced by 0.11 A (d21) below the R h ] n atoms. The same structural refinement was repeated with another R-factor (Ros) and the results in Table 4.1 clearly show that the structural conclusions are insensitive to whether Rp or RQS is used. In order to determine the uncertainty in the parameter d22, the variation of Rp is plotted versus d22 as in Figure 4.5 with the other geometrical parameters fixed at their optimal values. The uncertainty in d22 is then estimated to be about ±0.04 A according to the criterion discussed by Andersen et al. (Section 2.5.2). Overall it is clear that the Rh atoms directly below the S atoms are displaced downwards compared with the other Rh atoms in the second layer. Incidentally when the analysis is widened to allow S to move off the center site, T L E E D lowers Rp to 0.2202, and S appears shifted by components of magnitude 0.15 and 0.14 A parallel respectively to the [001] and the [110] directions. However, on visual analysis, this change is not accompanied by any obviously improved feature in the calculated 1(E) curves; also the other structural parameters are essentially unchanged from 59 Table 4.3 Atomic coordinates (in A) for the TLEED-determined structure of the Rh(110)-c(2x2)-S surface Atomic label X • .V 7 S(l) 0.00 0.00 3.55 Rh(2) 1.90 -1.35 2.74 Rh(3) 1.90 1.35 2.74 Rh(4) 3.80 0.00 1.40 Rh(5) 0.00 0.00 1.29 bulkRh 1.90 1.35 0.00 Thex, y and c. directions are parallel to [001], [110] and [110] respectively. 60 0.30 0.29 - \ 0.28-^ £ 0.21-\ 0.26 H 0.25 0.24 - I 0.00 0.05 0.10 d „ (A) 0.15 0.20 Figure 4.5 The variation of Rp versus d22 with all other geometrical parameters fixed at the optimal values found for the Rh(l 10)-c(2x2)-S surface structure. 61 those given in Table 4.1. Accordingly we do not believe that this S displacement is structurally significant. 4.5 Discussion The good level of correspondence reached between the experimental and calculated 1(E) curves for the Rh(l 10)-c(2x2)-S surface (Figure 4.4) supports the conclusion that this structure involves each S atom chemisorbing on a center site of the Rh(l 10) surface with one S-Rh bond close to 2.27 A (to the second layer metal atom designated Rh^) and four S-Rh bonds equal to about 2.47 A (to the first layer metal atoms designated Rh,). The buckling of the second metal layer, which is indicated to have a magnitude in the vicinity of 0.11 A, acts to reduce the S-Rh bond length inequality that would otherwise occur. The earlier L E E D analysis for this system [68.], which did not include metallic relaxations, reported the S-Rh bond lengths to be 2.45 A to the four neighboring Rhj atoms and 2.12 A to the Rhjj atom in the second metal layer. Interestingly an earlier study with the angular resolved photoemission extended fine structure technique, for the analogous structure formed by S chemisorbed on the Ni( l 10) surface [73], pointed to a second metal layer buckling (magnitude 0.13 A), closely similar to that reported here for S on Rh(l 10). The new structural details for Rh(l 10)-c(2x2)-S give an indication of the effect of the S chemisorption on the metallic Rh-Rh bonding near to the surface. Clean Rh(110) manifests a damped oscillatory relaxation (Ac/, 2 and A t / 2 3 correspond to -6.9% and +1.9% respectively [74]), as commonly observed for the more open metallic surfaces. This gives for clean Rh(110) a net contraction of 0.13 A in the first to third interlayer spacing compared with the bulk metal structure. With chemisorbed S present, this double spacing increases by 0.05 A from the bulk value of 2.69 A. The net increase in A<i ] 3 of 0.18 A from the clean surface situation appears to indicate that the chemisorbed S acts to reduce the strength of the metallic Rh-Rh bonding in the immediate vicinity of the surface. That some rearrangement seems probable for the metallic bonding is highlighted by the very short S-62 Rhn bond length to the second layer R h n atom, which itself is already bonded to eleven other Rh atoms. More generally, when a species X chemisorbs on metal M , some balance may be expected between the more covalent X - M bonding and the more metallic M - M bonding, but each inevitably sets constraints on the other. The S on Rh(llO) system highlights two opposing effects where (i) the basic adsorption geometry (for center site) encourages S-Rh,, to be shorter than S-Rh,, but (ii) Rh,, bonds to eleven other Rh atoms while Rh, bonds only to seven other Rh atoms. The effect (ii) should act to lengthen S-Rh,, compared with S-Rh,, but constraints from Rh-Rh metal bonding apparently prevent a reordering from the effect of (i) in the absence of a reconstruction [75]. Nevertheless the effect (ii) does affect predictions of bond lengths from Eq (1.7), and some extension in the bond length - bond order type relation is accordingly required. The structural result reported for S on Rh(l 10) supports the concept that variation in the metal atom coordination number can have a significant effect on the chemisorption bond lengths, but this effect cannot be accommodated by Eq (1.7) when the parametrization is done through a bulk structure. Another relevant example is for O on Ni( 110) as shown in Figure 4.6. This situation has a missing row reconstruction with two different types of O-Ni bonds present. We will simplify the recently reported structure [36] (by ignoring the possible asymmetry in the O position) and take it that in this case O bonds on a long-bridge site to two top layer Ni atoms at 1.78 A and to two second layer Ni atoms at 1.95 A. On average O bonds to four Ni atoms at 1.87 A, which is less than the value of 1.93 A predicted by Eq (1.7) when parametrized by bulk NiO (Section 1.4). But already Kleinle et al. [36] have noted that the shorter O-Ni bond lengths may be expected because of the reduced metallic coordination number of the Ni atoms bonded to O on the (110) surface (these numbers are five and nine compared with the coordination of eight and nine on the (100) and (111) surfaces respectively). On (110) the shorter O-Ni bond lengths (1.78 A) correspond with the Ni atoms which bond only to five other Ni atoms, consistently with 63 Top view of the structure of the Ni(l 10)-(2xl)-O surface structure. The solid and dotted open circles respectively represent the first and the second layers Ni atoms, whereas the smaller, filled circles represent O atoms. 64 the effect (ii) noted above. Such effects are likely to have wider significance, although currently there appears to be a scarcity of detailed structural information for surfaces where an atom X simultaneously bonds to different M atoms with non-equivalent M - M bonding. Of course a first principles approach must be favored ultimately, but to help initiate the development of surface structural principles there are advantages (as for solid state structural chemistry) in having a framework through which trends in structural relationships can be assessed; that defines the spirit of the current discussion. To accommodate trends from the variation in metallic coordination number (as noted by effect (ii) above), it seems necessary to parametrize Eq (1.7) with a chemisorption reference structure where the metallic coordination number is more appropriately defined. Further, it is tentatively proposed that a correction term (Ar): Ar=K(NrN^) (4.2) be added to Eq (1.7) to estimate the X - M bond length to the M atom which bonds to A^. other M atoms in the metal structure. Then rQ is deduced from the experimentally determined X - M bond length in the reference surface structure, where the M bonding to X also bonds to other M atoms, and K is an empirical factor. The latter is chosen from structural data for O on Ni after parametrizing rQ to the O on Ni(100) surface in which the O-Ni bond distance is 1.92 A (requires rQ - 1.66 A), and fitting experimental bond lengths for O on Ni( l 10) starting with the average O-Ni distance equal to 1.92 A from Eq (1.7). That suggests K is approximately equal to 0.04 A, whereupon the corrected O-Ni distances are indicated as 1.85 A on Ni( l 11) (experimental value 1.83 A) and 1.80 A, 1.96 A on Ni(l 10) (experimental values 1.78 A, 1.95 A). Attention is now redirected to S on Rh(110). The same approach is then used for the S-Rh bond lengths to Rh atoms of different coordination number with the value of K = 0.04 A deduced for O on Ni . Firstly, r o i s determined to equal 2.04 A by parametrizing to the S on Rh(100) chemisorption structure (where the S-Rh bond distance is taken as 2.30 A). Then the predicted values for the S-Rhj and S-Rh n distances, based purely on the 65 geometrical factor, are indicated to be 2.47 and 2.16 A respectively. The coordination number effect is included by evaluating correction terms using Eq (4.2) as follows: Ar (S-Rhj) = 0.04 (7 - 8) = -0.04 A (4.3) Ar(S-Rh n ) = 0.04.(11 -8) = 0.12 A " (4.4) Then, the predicted bond lengths for the two types of S-Rh bonds are: r (S-Rh,) = 2.47 - 0.04 A = 2.43 A (4.5) - r (S-Rh H ) = 2.16+'0.12A = 2.28A (4!6) in close correspondence to the experimental values of 2.47 and 2.27 A respectively. 4.6 Summary Details have been established by T L E E D for the structure formed by the chemisorptipn of a 1/2 M L of S on the Rh(l 10) surface. The S atoms chemisorb on an unreconstructed metal surface, but they cause relaxations particularly with regard to a significant buckling in the second metal layer, and to a net expansion in the interlayer spacing between the first and third metal layers. In the c(2x2) surface structure, each S atom is positioned on a center site at 0.83 A above the topmost Rh layer. Compared with the regular bulk spacing (1.35 A), the c(2x2) structure has its di2 expanded by 3.4% while the d2?i spacing remains unchanged. A significant downward-buckling by 0.11 A is observed for the second layer Rh atoms, which are directly underneath adsorbed S atoms. There are two different sets of S-Rh bond lengths: one of 2.27 A to the second layer Rh atom directly below S, and four of 2.47 A to neighboring Rh atoms in the first metal layer. The difference of 0.20 A is substantial, but it appears that the relaxations present in the metal structure, as a result of the S chemisorption, have actually reduced the difference that would be present between the two types of S-Rh bonds in the absence of any modification in the metal atom positions. Evidence is presented that the observed chemisorption bond 66 lengths depend on the coordination number of the metal atom involved with regard to metal-metal bonding. An exploratory attempt has been made to quantify this effect through comparison with structural details for the chemisorption system formed by 1/2 M L of O atoms on the Ni( l 10) surface. 67 Chapter 5 : Structural Analysis for the Rh(110)-(3x2)-S Surface 5.1 Introduction On the Rh(llO) surface, S initially forms a 1/2 M L system of c(2x2) type symmetry and for which the structural details have been established in Chapter 4. The next well-ordered structure with increasing coverage is a Rh(l 10)-(3x2)-S surface; such an evolution from the c(2x2) to (3x2) structure has broad interest since it has also been observed for S chemisorbed on the Pd(l 10) [76] and Ni(l 10) [77, 78] surfaces. Indeed, (3x2) ordered adsorption patterns are fairly common for fcc(llO) surface [79, 80], although no detailed determination appears to have been made for any of these structures. As well as making a first attempt at determining a (3x2) surface structure, we will also try to relate the structural details to those identified previously for the Rh(l 10)-c(2x2)-S surface in regard to the adsorbate induced surface relaxations, the S concentration, as well as the effect of metallic coordination number on the S-Rh bond lengths. 5.2 Experimental As described in Section 4.2, S deposition on the Rh(l 10) surface was achieved by dosing high-purity H 2 S gas at a pressure of 2x10" Torr. With increase in S coverage, a c(2x2) pattern first forms and that changes to a (3x2) pattern when the Auger ratio R^, defined in Eq (4.1), reaches 0.75. However, instead of increasing the coverage of S through a number dosing/annealing cycles, it was found that the sharpest (3x2) pattern is obtained with a single-step process in which the (110) face was dosed with sufficient H 2 S to make Rs equal to about 0.75, followed by an anneal at 800 K . The L E E D 1(E) curves were measured at normal incidence and appropriate 1(E) curves were averaged and smoothed for the fourteen symmetrically independent diffracted beams designated as (1 0), (0 1), (1 1), (2 0), (0 2), (2 1), (3 1), (3/2 2/3), (3/2 1/3), (3/2 5/3), (1/2 5/3), (1 5/3), (0 68 2/3) and (3/2 0) using the beam notation shown in Figure 5.1. The total energy range used in the analysis was around 1810 eV. 5.3 Parameters used in the Calculations The non-structural parameters used in the T L E E D analysis of the Rh( 110)-(3x2)-S structure followed those outlined in Section 4.3 except that only Rp was used to assess the correspondence between the experimental and calculated 1(E) curves. The calculation includes a composite layer composed of the S layer together with the six Rh atoms in the first metal layer (six Rh atoms per (3x2) unit mesh); likewise the six Rh atoms per unit mesh in the second metal layer form another composite layer. A l l atoms included in these composite layers are allowed to displace in three dimensions during the T L E E D optimization subject to maintaining the mirror plane and/or glide line symmetry of each particular model. Results from our study of Rh(l 10)-c(2x2)-S in Chapter 4, in relation to the interlayer spacings, S position and Rh layers buckling, have been used to guide the setting-up of the initial reference structure for each of the models considered for the (3x2) structure. For trial models which involve S atoms located on center sites, the S atoms are placed 0.83 A above the first Rh layer, and each second layer Rh atom directly underneath a S atom is buckled downwards by 0.11 A. However, for the other models with S adsorbed on the long-bridge site, the S-Rh bond length is chosen to be 2.37 A based on the average S-Rh bond length in the Rh-,S3 crystal structure [81] in which the coordination number of S is four. Furthermore, the center-of-mass separations between the first and second, and between the second and third Rh layers are set to equal 1.39 and 1.35 A respectively. 69 4 0 0 2 O o O 0 1 1 0 2/3 1 • • • • 1/2 5/3 15/3 3/2 5/3 o 3/2 2/3 3/2 1/3 o 2 1 o 3 1 o 10 3/2 0 -o 2 0 Figure 5.1 One quadrant of the L E E D pattern from the Rh(l 10)-(3x2)-S surface showing the diffracted beams included in the structural analysis. 70 5.4 Model Considerations Figure 5.2 shows schematically the six model types included in this analysis of the Rh( 110)-(3x2)-S surface structure. The two factors influencing their choice are included in the following: (i) since the integral beams measured from the clean surface, the c(2x2) and the (3x2) chemisorption structures are quite similar, it is probable that the (3x2) structure, like that of c(2x2), does not involve any substantial metallic reconstruction; (ii) as noted in Section 4.2, R& is considerably larger for the (3x2) system compared with c(2x2) and therefore the S coverage for the former structure is expected to be larger than 1/2 M L . The model types included in the analysis maintained the basic Rh(l 10) metallic structure, but with the (3x2) translation symmetry determined by an alternating arrangement of chemisorbed S atoms in the [ 110] channels. These models differ by showing variations in either the local coverage or the adsorption sites. For model 1 in Figure 5.2, there are three S atoms in each unit mesh and they correspond to strips of the Rh(l 10)-c(2x2)-S structure separated by an antiphase boundary. It gives a total coverage of only 1/2 M L which may appear somewhat unlikely, but it is included for completeness in relation to possible (3x2) models which involve no metallic reconstruction. To achieve a coverage of 2/3 M L , we can modify model 1 by adding one more S to the available center site and there are two possibilities. First, the S can be added to the center site in the middle of the unit mesh outlined, and this gives model 2. In this model, alternating grooves parallel to the 1110] direction are completely filled while their neighbors have 1/3 M L coverage and this model has mirror planes along the | llOJ and [001] directions. The second possibility is that the additional S atom is put in the center site near the upper corner of the unit mesh to give model 3. In this model, each [110] groove has identical coverage of 2/3 M L and all the S atoms are equivalent. It possesses a mirror plane along the [110] direction and a glide line along [001]. The latter 71 Figure 5.2 Model types included in the T L E E D analysis for the Rh(l 10)-(3x2)-S surface structure with the unit mesh outlined in each case. The first and the second layer Rh atoms are represented by the larger open circles which are based respectively on continuous and dashed lines; the smaller filled circles represents S atoms. The directions of mirror and glide line symmetries are shown respectively by the continuous and dashed lines at the edge of each model. 72 3 6 73 symmetry element requires a systematic extinction of the (h/2 0) beams at normal incidence [82], which is not observed experimentally in our (3x2) pattern. However, we still consider this model in the calculation because there may be some possibilities of a heterogeneous surface composed partly of model 3, and partly of ordered domains from other models (e.g. model 1) which can give rise to the non-zero intensity for the (h/2 0) beam. The other three models considered involve multi-site occupancy of the S atoms. In model 4, the S atoms occupy each groove with a density of 2/3 M L , but with adsorption on center sites in one groove and bridge sites in the next. In model 5, the S atoms are also distributed in grooves at 2/3 M L coverage in an alternating basis: S atoms occupy center sites and long-bridge sites in one, and only center sites in the next. Adding one S atom in the middle of the unit mesh of model 5 creates model 6 with an overall coverage of 5/6 M L . For the last three models, there are two perpendicular mirror planes respectively along the [001J and | HO] directions. 5.5 Results of T L E E D Analysis After full optimization, final Rp values for the various models are summarized in Table 5.1; the best correspondence is for model 5 with Rp equal to 0.1986. Although models 5 and 6 may both appear to give a somewhat comparable level pf correspondence, it must also be noted that these are related structures; they differ only by model 6 having one more S atom adsorbed in a center site. This leads to differences in the calculated 1(E) curves, which are often only quite subtle; even so Rp indicates that model 5 corresponds better than model 6 for nine of the fourteen diffracted beams. Moreover some structural features in the measured 1(E) curves (e.g. around 140 eV for the (3/2 2/3) beam) are only picked up by model 5. 7 4 Table 5.1 T L E E D optimized values of Rp for each of the six model types considered for the Rh(l 10)-(3x2)-S surface structure Model 1 0.3841 2 0.3430 3 0.3514 4 0.4090 5 0.1986 6 0.2485 75 The atomic positions for the optimal model of the Rh( 110)-(3x2)-S surface structure are shown in Table 5,2. Figure 5.3 compares the experimental 1(E) curves and those calculated for this model for the fourteen diffracted beams, and their individual r p values are reported in Table 5.3. Interlayer spacings between S and the first Rh layer (dQl), between the first and the second Rh layers (dl2), and between the second and the third Rh layers (<i23) are reported in Table 5.4. Briefly, the S plane is found to be 0.69 A above the first Rh layer, and the first and the second Rh-Rh interlayer spacings (based on center-of-mass planes) are 1.46 and 1.32 A respectively. The illustrations in Figure 5.4 use the atomic labels adopted from Table 5.2. A top view of the final structure is shown in Figure 5.4(b). In the (3x2) unit mesh, one S(3) atom chemisorbs exactly on the regular center site, S(l) and S(2) are laterally displaced off the regular center sites towards each other by 0.39 A (^01), while S(4) adsorbs on a long-bridge site. Buckling is observed in both the first and the second Rh layers. For the topmost Rh layer, the atoms designated (7, 8, 9 and 10) are coplanar by symmetry, whereas those designated (5, 5', 6 and 6') are laterally displaced away from the S atom in the neighboring long-bridge site by 0.27 A ( A 0 2 ) . Accompanying this lateral displacement, these four Rh atoms also buckle up by 0.20 A (<iH) relative to the other first layer Rh atoms. For the second metal layer, the center-of-mass plane formed by the Rh( 14. 15 and 16) atoms, each of which has one S atom above, is 0.10 A (d22) below the plane formed by the Rh( 11,12 and 13) atoms which do not have S atoms directly above. 5.6 Discussion In the (3x2) structure, the first interlayer spacing (d]2) of 1.46 A corresponds to a 9% expansion compared with the bulk value (1.35 A). The same phenomenon was observed in the low coverage c(2x2) system as a consequence of the strong S-Rh bonding, which in turn reduces the ability of the first Rh layer atoms to bond to the underlying metal atoms as discussed in Section 4.5. The increase of S coverage from c(2x2) to (3x2) 76 Table 5.2 Atomic coordinates (in A) for the TLEED-determined structure of the Rh(110)-(3x2)-S surface Atomic label x y S(D 0.00 2.30 3.58 S(2) 0.00 -2.30 3.58 S(3) 3.80 0.00 3.49 S(4) 3.80 4.04 3.23 Rh(5) 1.63 4.04 2.91 Rh(6) -1.63 -4.04 2.91 Rh(7) 1.91 1.34 2.72 Rh(8) -L91 -1.34 2.72 Rh(9) -1.91 1.34 2.72 Rh(10) 1.91 -1.34 2.72 Rh( l l ) 3.80 2.70 1.39 Rh(12) -3.80 -2.70 1.39 Rh(13) 0.00 0.00 1.33 Rh(14) 0.00 2.69 1.29 Rh(15) 0.00 -2.69 1.29 Rh(16) 3.80 0.00 1.23 bulk Rh 1.90 1.35 0.00 The x, y and z directions are parallel to [001 ], [110] and 1110] respectively. 77 1(E) curves for fourteen diffracted beams from Rh(l 10)-(3x2)-S for normal incidence. The dash-dot lines represent experimental curves and the solid lines represent curve calculated for the structure (Table 5.2) optimized by the T L E E D analysis. 78 Beam (1 0) Beam (0 2) Beam (3/2 1/3) 0 50 100150200250300 Beam (0 1) 0 50 100150 200 250 300 Beam(1 1) 0 50 100150200250300 Beam (2 0) 0 50 100150200250300 -Beam (0 2/3) 0 50 100150200250300 0 50 100150200250300 Beam (2 1) 0 50 100150200250300 Beam (3 1) 0 50 100150200250300 Beam (3/2 2/3) 0 50 100150200250300 Beam (3/2 0) \ / \ ' • -L 0 50 100150200250300 Energy (eV) 0 50 100150200250300 Beam (3/2 5/3) 0 50 100150200250300 Beam (1/2 5/3) 0 50 100150200250300 Beam (1 5/3) 0 50 100150200250300 Table 5.3 Individual r p values for fourteen beams from the Rh(l 10)-(3x2)-S surface structure for normal incidence Beam label rp (1 0) 0.1074 (0 1) 0.1855 (11) 0.1841 (2 0) 0.3011 (0 2) 0.3395 (2 1) 0.2566 (3 1) 0.1609 (3/2 2/3) 0.2029 (3/2 1/3) 0.2526 (3/2 5/3) 0.1912 (1/2 5/3). 0.2711 . (15/3) 0.1334 (0 2/3) 0.2008 (3/2 0) 0.2571 80 Table 5.4 Comparison between values of geometrical parameters (in A) for the Rh(110)-(3x2)-S and Rh(l 10)-c(2x2)-S surfaces structures determined byTLEED Parameters Rh(110)-(3x2)-S Rh(110)-c(2x2)-S d o \ 0.69 0.83 d\2 . 1.46 1.39 d23 1.32 1.35 dn 0.20 -0.10 0.11 A M 0.39 -A02 0.27 -dQ j , dl 2, d2?i are center-of-mass interlayer spacings and AQl, A02 are lateral displacements defined in Figure 5.4; dX{ is the buckling in the first Rh layer, e.g. the vertical separation between Rh(5) and Rh(7); d22 is the center-of-mass vertical separation between second-layer Rh atoms directly below S atoms in center or off-center adsorption sites and second-layer Rh atoms that do not have S atoms directly above (e.g. Rh( 11) and Rh( 13)). 81 * [110] (a) Figure 5.4 Views of the structure of the Rh(l 10)-(3x2)-S surface from: (a) the side and (b) the top. The open circles represent Rh atoms and the smaller, filled circles represent S atoms. 82 results in a more pronounced effect on the interlayer spacing expansion; thus dx 2 increases by 9% in the (3x2) versus 3% in the c(2x2) structure. The second interlayer spacing (^23) of 1.32 A represents a 2% contraction which is also larger than the corresponding change in the c(2x2) system (0%). This kind of damped oscillatory relaxation is very common for systems involving electronegative atoms adsorbed on a metal surface [83], and this work gives a new view of such a trend in relation to the dependence on adsorbate coverage. In the Rh(l 10)-c(2x2)-S structure, where the S atoms adsorb on regular center sites, the chemisorption bond length to the metal atom in the second layer directly below S (i.e. the S-Rh„ bond) is considerably shorter (2.27 A), as a result of basic geometrical constraints, than those (i.e. S-Rh]) to the neighboring top layer Rh atoms (2.47 A), even though the metallic coordination number is larger for R h H (eleven) than for Rh, (seven). For the (3x2) structure, the S(3) atom is located 0.77 A above the undistorted center sites formed by Rh(7, 8, 9 and 10) giving the S(3)-Rh, bond length of 2.45 A. With the downward buckling for the Rh(16) atom, the S(3)-Rh„ bond length is determined to be 2.26 A. These two S(3)-Rh bond lengths are essentially the same as the corresponding values for the Rh(l 10)-c(2x2)-S structure (2.47 and 2.27 A respectively). It indicates that the S(3) atoms in the (3x2) structure have very similar local environment to those S atoms in the c(2x2) structure. The lateral shift of the topmost Rh atoms bonded to S in a long-bridge site, together with the S(l , 2) displacements off the regular center sites, ensures a considerable distortion in the adsorption sites for these S atoms. Compared with the corresponding bond lengths associated with S(3), the displacement of S( l , 2) off the center site by 0.39 A towards each other reduces the S(l)-Rh(7) distance to 2.30 A and, at the same time, increases the S(l)-Rh(14) distance to 2.32 A. These displacements, to a certain extent, achieve the equalization in the S-Rh bond lengths involving the Rh atoms designated (7, 9 and 14). Without the lateral displacement AQ2, the lateral shift of S(l) atom would give an unreasonably long S(l)-Rh(5) distance of 2.66 A. However, with the pairing of Rh(5, 83 5'), the S(l)-Rh(5) distance is restored to approximately the same (2.47 A ) as the S-Rh, bond length in the Rh(l 10)-c(2x2)-S structure. In summary for the (3x2) structure, the S(l)-Rh„ length is 2.32 A , and the four S(l)-Rh, bond distances (individually 2.30 A (2) and 2.47 A (2)) average to 2.38 A . The identification of the S(4) atom in a long-bridge site certainly appears as an interesting new feature which, to our knowledge, has not been observed before in other systems for chemisorbed S. Normally, the long-bridge sites of fcc(l 10) surfaces are only large enough for small adsorbate such as O in the Cu(l 10)-(2xl)-O and Ni( l 10)-(2xl)-0 [84] systems. The lateral displacement (A01), which opens up the site, appears essential to allow the effective four-coordinate bonding by S(4) to Rh atoms. In the event there were no metallic relaxations at this bonding site, an average S-Rh distance of 2.30 A (as at the Rh(100) surface [35]) could only be attained by having two bonds at 2.06 A to the first layer Rh atoms and two at 2.53 A to the second layer, which are in turn clearly too short and too long. The relaxations actually allow the formation of two S-Rh bonds to the second metal layer at 2.27 A and two to the first metal layer at 2.20 A . Their average is 0.06 A less than expectation from Rh(100), a difference that may be associated with the modified coordination arrangements now being established in the (3x2) structure. The driving force for the whole structure can be viewed as the need to accommodate 2/3 M L of S atoms on the Rh( 110) surface, and at the same time to minimize the S-S lateral repulsive interaction. Therefore in one of the [110] channels, the atoms S(l) and S(2) basically occupy the center sites, but they are displaced by 0.39 A (AQ,) to increase the S-S separation to 3.47 A , which is still less than the conventional Van der Waals distance for two S atoms (3.70 A [85]). The need to minimize repulsion between channels then encourages adsorption in the long-bridge sites for the next channel along with the regular center sites. In order to accommodate the relative large S atom on the long-bridge site, the atoms Rh(5,5') need to displace laterally to open up the site so that the atom S(4) can bond effectively to four Rh atoms. A s each Rh(5) atom shifts laterally by 0.27 A (AQ2), it also 84 "rides up" on the second layer Rh atoms; This gives rise to the upward buckling of 0.20 A (d{also found in this surface structural analysis for the Rh(5, 5') atoms. The closest S-S distance in the Rh(l 10)-(3x2)-S structure (3.47 A) is much larger than the S-S single bond length (e.g. 2.04 A in S 8 [86]), that there is unlikely to be significant direct S-S bonding interaction on the surface. 5.7 Summary The structural determination reported in this chapter gives some initial insight into the evolution of surface structure for the S on Rh(l 10) surface, although it is likely to have implications to other similar systems, for example S on (110) surfaces of Pd and Ni . One important parameter for consideration is the coverage: the radiochemical dosage method used on S/Pd(l 10) [76] and the scanning tunnel microscopy (STM) study on S/Ni(110) [78] had earlier indicated that the c(2x2) and (3x2) structures formed on both surfaces had S coverages of 1/2 and 2/3 M L respectively. That is in full consistency with the structural determinations made in this work for S on Rh(l 10). Furthermore, the S atoms in and near center sites appear consistent with the bright spots seen in the S T M images from the corresponding S/Ni system. On the Rh(l 10)-(3x2)-S surface, there is no evidence that S results in surface compound formation, as for example has been suggested on Cu(l 10) [87]. Nor indeed is there any evidence for direct S-S bonding. Another important parameter for consideration is the adsorption site, and in that context this work can provide only partial support for the concept of adsorption on high coordination sites [30, 31, 32]. The details in the Rh(l 10)-(3x2)-S surface show unique features. Indeed the existence of this structure seems associated with an interesting balance in the S bonding to the first and the second layer Rh atoms, as well as to different adsorption sites, and the consequent relaxations in the metallic structure. The evolution of structure from c(2x2) to (3x2) apparently depends on the S-S repulsive interaction keeping the adsorbed species evenly distributed within and between the [110] channels. 85 The (3x2) result shows a general consistency regarding the coordination number effect highlighted in the c(2x2) study in which the Rh atoms with S atoms on top are buckled down compared with those without. The details of the (3x2) surface, as reported here, appear to show an overall self-consistency, but the novel features of this structure, particularly in relation to the long-bridge adsorption site, should help challenge the ongoing development of principles for surface structural chemistry. 86 Chapter 6 : Structural Analyses for the Rh( l l l ) - (>/3xV3)R30°-S and Rh(lll)-c(4x2)-S Surfaces 6.1 Introduction There has been some interest in the details of c(4x2) surface structures formed on fcc(l 11) surfaces, and recent examples include studies for NO [88, 89, 90, 91, 92] or CO [93, 94] chemisorbed on the (111) surface of Ni . As part of a continuing project to investigate the structures formed by S chemisorbed on surfaces of Rh, we have undertaken a crystallographic analysis with T L E E D for the c(4x2) structure formed by S on the R h ( l l l ) surface. Moreover, since there is also an interest in developing detailed knowledge for the way these structures change with increasing coverage, we have additionally taken the opportunity to refine an earlier analysis made in this laboratory for the Rh(lll)-(V3"xV3)R30°-S surface structure [66], and to. compare details in these two structures as a result of changing the S coverage. Further comparisons are also made with the corresponding structural evolution for S on the Rh(l 10) surface described in Chapter 4 and 5, specifically from the c(2x2) surface at 1/2 M L coverage of S to the (3x2) structure with 2/3 M L coverage. 6.2 Experimental The experimental system and cleaning procedures used in this work have been described in Section 4.2. Briefly, the S adsorption was accomplished by dosing H 2 S at about 2x10" Torr via a leak valve into the chamber with the Rh( 111) sample held at room temperature. The amount of S adsorbed was monitored by the Auger ratio Rs. A dosing for 4 min gave rise to the (V3xV3)R30° L E E D pattern as shown in Figure 6.1, when Rs was about 0.39, but the quality of the pattern improved after an anneal to 800 K for 1 min. 87 o • • o • • o • • • o • • o 0 2 • o • • o • • 0 1 1/3 4/3 2/3 5/3 • • o • • o 1/3 1/3 2/3 2/3 1 1 • o • • o • • 1 0 4/3 1/3 5/3 2/3 • • o • • o 2 0 • o • • O • • o • Schematic indication of the L E E D pattern observed from the Rh(M 1)-(V3x'v'3)R30o-S surface structure. The open and filled circles represent the integral and fractional beams respectively. 88 Further dosing under the same conditions for 2 more min yielded a c(4x2) pattern (Figure 6.2), which sharpened after a brief anneal, whereupon /? s was around 0.72. 1(E) curves were measured at normal incidence and all symmetrically equivalent beams were measured at the same time to ensure that the normal incidence was properly set. For the (y/3xyj3)ft30° structure, 1(E) curves were averaged and smoothed for the eleven independent beams designated as (0 1), (1 0), (1 1), (0 2), (2 0), (1/3 1/3), (1/3 4/3), (2/3 2/3), (2/3 5/3), (4/3 1/3) and (5/3 2/3) according to the beam notation in Figure 6.1;the total energy range of the data available for the analysis was about 1500 eV. For the c(4x2) structure, 1(E) curves were similarly measured for the twelve independent beams (0 1), (1 0), (1 1), (2 0), (1/2 1/2), (1/2 -1/2), (-1/4 3/4), (3/4 -1/4), (-1/2 3/2), (3/2 -1/2), (5/4 1/4) and (1/4 5/4), as in Figure 6.2, over a total energy range of around 1620 eV. 6.3 Parameters used in the Calculations The non-structural parameters for the multiple scattering calculations and the T L E E D analyses were done as detailed previously in Section 4.3. The real part of the constant potential between muffin-tin spheres (V o r ) was initially set at -12.0 eV, but it was continuously refined during each set of T L E E D calculations (final values -11.3 and -11.4 eV for the (V3x'v'3)R30o and c(4x2) structures respectively); the imaginary part (V o i ) was fixed throughout at -5.0 eV. The general form of the integral beams from both surfaces suggested that the metallic structure was not markedly changed from that of the clean Rh(l 11) surface, and therefore each model considered for these chemisorption systems emphasized a S overlayer above the unreconstructed substrate. For all structural models, the optimization of geometrical parameters included the topmost S layer, together with all atoms in the first and second metal layers within the appropriate unit mesh. Initial reference structures had Rh atoms in bulk positions; S positions in threefold coordination sites were guided by the result of the earlier analysis for the (y/3x'\j3)R30° structure [66], and assessments for other adsorption sites were made with Eq (1.7). 89 o o o o o o o o o o -1/2*3/2 o 1/4 3/4-0 • 01 1/4 5/4, o # 1/2*1/2.3/4*1/4 1/2*1/2 o • 10 5/4 1/4 . o o ,3/2 -1/2, o 20 o o Figure 6.2 Schematic indication of the L E E D pattern observed from the Rh(l 11)-c(4x2)-S surface structure. The open and Filled circles represent the integral and fractional beams respectively. 90 6.4 Model Considerations Most model types considered for the Rh(l 1 l)-(V3xV3)R30o-S and R h ( l l l ) -c(4x2)-S surface structures have the S atoms adsorbed in sites of threefold coordination; they may be referred to as fee sites if they continue the fee packing sequence (i.e. S is directly above a third layer Rh atom), or as hep sites if there is a local hep stacking sequence (i.e. S is directly above a second layer Rh atom). Figure 6.3 illustrates the model types considered in this work. For each model, the number in the model designation indicates the number of S atoms per primitive unit mesh; the f, h or fh followed identifies respectively whether the S atoms are in fee, hep or fee and hep sites. One model (2br) considered for the c(4x2) structure has S atoms in bridge sites, and two high-coverage models (3frh and 3hrh) have added Rh atoms in the surface layer. Additional models with glide-line symmetry are possible for the c(4x2) form, but since the required systematic beam extinctions ['82] were not observed, consideration was restricted only to models directly consistent with the observed spots in the L E E D patterns. 6.5 Results and Discussion Table 6.1 summarizes results of the analyses with Rp for the model types included. These analyses are consistent with the (4\j3xyf3)R30o structure involving S chemisorbed on the regular fee sites, while in the c(4x2) structure the cherhisorption occurs on both types of three-coordinate sites; the coverages are indicated to be 1/3 and 1/2 M L respectively. These coverages are broadly consistent with their Auger ratios Rs measured during the experiment, although an exact proportional correspondence may not be expected insofar as disordered S can contribute to R& without contributing to the diffracted beams. Figures 6.4 and 6.5 compare experimental and calculated 1(E) curves for the optimized forms of the two structures, and the r p values of individual beams for both structures are shown in Tables 6.2 and 6.3. The correspondence reached can be described as good for both surfaces; the 91 (V3xV3)R30° (V3xV3)R30 c(4x2) 3f or 3h 3frh or 3hrh 2br Figure 6.3 Model types included in the T L E E D analyses for the R h ( l l l ) -(V3xV3)R30°-S and Rh(l 1 l)-c(4x2)-S surface structures. The smaller filled circles and the larger open circles represent S and Rh atoms respectively. The model designations are specified in the text, but adsorption in the three-coordinate sites may correspond to fee or hep local packing. The calculations maintain the mirror symmetries indicated by short lines at the edges of some models. 92 Table 6.1 T L E E D optimized values of /? pfor each of the model types considered for the (V3xV3)R30° and c(4x2) structures formed by S on Rh(l 11) model (V3x>/3)R30o If 0.2474 lh 0.7863 2f 0.3872 2h 0.8032 c(4x2) 2fh 0.2145 • 3f . 0.4756 3h 0.5238 3frh 0.5879 3hrh 0.6037 2br 0.3029 93 Figure 6.4 1(E) curves for eleven diffracted beams at normal incidence for the Rh(lll)-(v5x>/3)R30 o-S surface. The dash-dot lines represent experimental curves and the solid lines represent curves calculated for the structure (Table 6.4) optimized by the T L E E D analysis. 94 Beam (+0.0.+1.0) Beam (+2.0.+0.0) Beam (+1/3.+4/3) 0 50 100150200250300 Beam (+1.0.+0.0) [1 v w V " 0 50 100150200250300 Beam (+1.0.+1-0) 0 50 100150200250300 Beam (+0.0.+2.0) 0 50 100150200250300 0 50 100150200250300 Beam (+1/3.+1/3) 0 50 100150200250300 Beam (+2/3,+2/3) . A 1 1 1 1 if V v V 0 50 100150200250300 Beam (+4/3.+1/3) 0 50 100150200250300 Energy (eV) 0 50 100150200250300 Beam (+5/3,+2/3) 0 50 100150200250300 Beam (+2/3,+5/3) 0 50 100150200250300 95 1(E) curves for twelve diffracted beams at normal incidence for the Rh(l 1 l)-c(4x2)-S surface. The dash-dot lines represent experimental curves and the solid lines represent curves calculated for the structure (Table 6.4) optimized by the T L E E D analysis. 96 Beam (+0.0.+1.0) —I T— 0 50 100150200250300 Beam (+1/2.+1/2) 0 50 100150200250300 Beam (-1/2.+3/2) 0 50 100150200250300 Beam (+1.0.+0.0) Beam (+1/2,-1/2) 0 50 100150200250300 Beam (+3/2,-1/2) 0 50 100150200250300 0 50 100150200250300 Beam (+1.0.+1.0) Beam (-1/4.+3/4) 0 50 100150200250300 Beam (+5/4.+1/4) 0 50 100150200250300 0 50 100150200250300 Beam (+2.0.+0.0) Beam (+3/4,-1/4) 0 50 100150200250300 Beam (+1/4.+5/4) 0 50 100150200250300 0 50 100150200250300 Energy (eV) 97 Table 6.2 Individual r p values for eleven beams from the Rh(l 1 1)-(>/3XV3)R30°-S surface structure for normal incidence Beam label (0 1) 0.2088 (10) 0.2933 (1 1) 0.1165 (20) 0.3252 (0 2) 0.1128 (1/3 1/3) 0.1622 (2/3 2/3) 0.1716 (4/3 1/3) 0.3387 (1/34/3)' 0.1815 (5/3 2/3) 0,2528 (2/3 5/3) 0.1836 98 Table 6.3 Individual rp values for twelve beams from the Rh( 111 )-c(4x2)-S surface structure for normal incidence Beam label rP (0 1) 0.2088 (10) 0.2933 0 l) 0.1165 (2 0) 0.3252 (1/2 1/2) 0.1128 (1/2-1/2) 0.1622 (-1/43/4) 0.1716 (3/4.-1/4) 0.3387 (-1/2 3/2) 0.1815 (3/2-1/2) 0.2528 (5/4 1/4) 0.2678 (1/45/4) 0.1836 99 associated Rp values are 0.2474 and 0.2145 for the (>/3x>/3)R30o and c(4x2) surfaces respectively. The structural details are illustrated in Figures 6.6 and 6.7 respectively. Further tentative support is provided for the favored model for the c(4x2) surface insofar as from experiment the (1/4 1/4) beam is too weak to be reliably measured, particularly at lower energies. When considering only the S layer and the first Rh layer, this structure would have a glide line symmetry element (referred to by Mapledoram et al. |88] as a pseudo-glide line in a related system), which would require zero intensity for that beam. However the glide-line symmetry is not maintained after consideration of the second and deeper Rh layers, but because of the special effect of the topmost layers, low intensities are reasonably expected for the (1/4 1/4) beam with the particular structure favored. Atomic coordinates for these optimized structures are given in Table 6.4, and related descriptive parameters are compared in Table 6.5. In the (V3xV3)R30° structure, each S atom bonds equally to three Rh atoms with a S-Rh bond length of 2.23 A. This refines the value of 2.18 A given in the earlier analysis |66], which did not include the possibility of metallic relaxations, although in any event the relaxations in the metallic structure are now confirmed to be negligibly small. However, the corresponding c(4x2) structure has appreciable relaxations, and additionally the S atoms displace off the center of the three-coordinate sites by 0.2 - 0.3 A ( A 0 ] , A 0 2 ) . These features apparently arise because the Rh atoms which are bonded to S in the c(4x2) structure have different environments with different bonding capabilities. For example, for S(l) atoms on the hep sites, the Rh atoms designated Rh(6) bond tb only one S atom whereas those designated Rh(3) and Rh(4) each bond to two S atoms. The displacements given by the T L E E D analysis yield S(l)-Rh(3,4) and S(l)-Rh(6) bond lengths of 2.24 and 2.16 A respectively, for an overall average of 2.21 A. Similarly for S(2) atoms at fee sites, the chemisorption bond lengths show the same trends, those for S(2)-Rh(3,4) and S(2)-Rh(5) being 2.24 and 2.17 A respectively, and an overall average of 2.22 A. To a good approximation, for the c(4x2) structure, the average S-Rh bond distance for adsorption in the fee sites equals that 100 N H 2.690 A [111] Figure 6.6 Views of the Rh(l 1 l)-(V3x>/3)R30°-S surface, and some notation used for structural parameters. The smaller, filled circles represent S atoms, and the larger circles represent Rh atoms. In the top view, the atoms in the first Rh layer are open, while those in the second Rh layer are shaded. 101 Figure 6.7 Views of the Rh(l 1 l)-c(4x2)-S surface, and some notation used for structural parameters. The smaller, Filled circles represent S atoms, and the larger circles represent Rh atoms. In the top view, the atoms in the first Rh layer are open, while those in the second Rh layer are shaded. 102 Table 6.4 Atomic coordinates in A for the TLEED-determined structures of the Rh( 111 )-(V3xV3)R30°-S and Rh( 111 )-c(4x2)-S surfaces Surfaces Atomic label V z (V3xV3)R30° S(D 0.00 0.00 6.00 Rh(2) 0.00 - 1.56 4.41 Rh(3) 1.35 0.78 4:41 Rh(4) - 1.35 0.78 4.41 Rh(5) 0.00 1.53 2.19 Rh(6) 1.32 -0.76 2.19 Rh(7) - 1.32 - 0.76 2.19 bulk Rh 0.00 0.00 0.00 c(4x2) S(l) 0.00 1.76 6.06 S(2) 2.69 - 0.29 6.05 Rh(3) 1.34 0.73 4.57 Rh(4) - 1.34 0.73 4.57 Rh(5) 2.69 - 1.64 4.35 Rh(6) 0.00 - 1.61 4.34 Rh(7) 2.69 1.47 2.22 Rh(8) 1.39 - 0.85 2.19 Rh(9) - 1.39 - 0.85 2.19 Rh(10) 0.00 1.49 2.19 Thex, y and j directions are parallel to [110], [112] and 1111] respectively. 103 Table 6.5 Comparison between the values (in A) of geometrical parameters for the (V3xV3)R30°and (4x2) surfaces structures formed by S on Rh(l 11), and corresponding values for the c(4x2) structures formed by CO and NO on N i ( l l l ) [93,90] Rh(lll)-(V3xV3)R30 0-S Rh(lll)-c(4x2)-S Ni(lll)-c(4x2)-CO Ni(lll)-c(4x2)-NO 1.60 1.60 1.27 1.24 2.21 2.26 2.07 2.08 d2J> 2.19 2.20 1.95 2.00 d n - 0.23 0.10 0.16 dbu\k 2.20 2.20 2.03 2.03 A) i - 0.20 * 0.10 A 0 2 - 0.29 * 0.10 d0], d{2, d2?i are center-of-mass interlayer spacings, the buckling in the first Rh layer d and the lateral displacements AQ,, A02 are defined in Figure 6.7. * not investigated 104 for adsorption in hep sites; additionally both essentially equal the value (2.23 A) found for the (y/3xyf3)R30° structure, where each Rh atom involved in the chemisorption bonds to only one S atom. For Rh(l 1 l)-c(4x2)-S, the alternating Rh rows parallel to [110], namely those based on atoms designated as Rh(5,6) and Rh(3,4), have different degrees of bonding to S, and this affects the metallic relaxations as well as the S-Rh bond lengths noted above. Thus the fact that each atom in the Rh(3,4) rows bonds to two S atoms, whereas those in the Rh(5,6) rows bond to only one, gives the former a reduced capability to bond to other metal atoms. This results in a buckling for the first metal layer by 0.23 A (J,,), with the Rh(3,4) rows raised above the Rh(5,6) rows. The relaxations observed in the c(4x2) structure can therefore be summarized as: (i) each S atom displaces from the center of the adsorption site toward the Rh atom with least S bonding; (ii) the Rh rows which are bonded to more S atoms displace vertically up compared with the Rh rows bonded to a smaller number of S atoms; and (iii) the first Rh-Rh interlayer spacing (dl2) expands by about 0.06 A (3%) compared with the bulk spacing. Similar trends have been indicated for the c(4x2) structures formed by CO and NO on N i ( l l 1), and Table 6.5 details these comparisons. The higher valency for atomic S, compared with molecular CO or NO, may contribute to these relaxation effects appearing larger in the example reported here. A key feature of the c(4x2) surface structure is that the adsorption occurs at both the fee and hep type sites. Given that only the former type is occupied for the (yf3xyj3)K30° structure, the hep sites must be seen as energetically less favorable at low coverage. However, with increasing coverage beyond the 1/3 M L situation, occupation of only the low-energy fee sites appears restricted because of the close approach required by neighboring S atoms. In this case, without any displacement, the S-S separation will be 2.69 A, which seems too small in the absence of direct bonding. However, with occupation of both fee and hep sites as in the favored model, this distance can increase to 3.11 A, although that may still appear short compared with the Van der Waals distance of S 105 (3.70 A) for non-bonding interactions. The surface relaxations found in this determination for the Rh(l 1 l)-c(4x2)-S structure actually increase the S-S non-bonding "contact" distance further to 3.38 A, a value in close correspondence with the 3.47 A found for the Rh( 110)-(3x2)-S surface structure in Chaper 5. The lowest coverage ordered S structures on both the R h ( l l l ) and Rh(110) surfaces correspond to a closest S-S separation of 4.66 A, with the S atoms evenly distributed over each metallic surface. Then the adsorption occurs in the lowest energy sites (center site in the Rh(l 10)-c(2x2)-S surface at 1/2 M L coverage, and fee site in Rh(l 1 l)-(V3xV3)R30° surface at 1/3 ML) . More S can be adsorbed in each case, with an increase in the direct S to Rh chemisorption bonding, but that energy term must be balanced against the off-setting energy penalties associated with change in adsorption site, restructuring in the metallic structure and increases in the non-bonding S to S repulsive interactions. For example on Rh(110), the higher coverage S structure with (3x2) translational symmetry (2/3 M L coverage) involves three out of every four S atoms bonding to the center or distorted center sites, while every fourth S atom bonds to a long-bridge site with considerable modification tb the metallic environment. This supports the view that multiple adsorption sites become more prevalent as the S coverage increases. Additionally, the overall constancy in the average S-Rh bond length, for three-coordinate adsorption in different binding site situations, may suggest that each metallic structure is able to adapt closely to the S valency requirements, whatever the details of the local environment. This is consistent with observations that surface bond lengths between an electronegative chemisorbed atom and a metallic surface are determined primarily by the bonding capability of the adsorbed species [24]. In the c(4x2) structure, each surface Rh atom bonds to an equal number of other metal atoms, but the number of S atoms varies, and as noted above this appears to affect the individual S-Rh bond distances (although not the average bond length at each S). In other contexts, the number of metal-metal contacts may affect individual surface bond 106 lengths, as discussed previously for the Rh(l 10)-c(2x2)-S surface structure in Chapter 4. Indeed that discussion gives a basis for testing whether the average S-Rh bond length of 2.22 A, found here for S adsorbed on three-coordinate sites of the Rh(l 11) surface, is generally consistent with measurements for other S-Rh bond lengths. On the Rh(100) surface, S bonds to the fourfold site with an average S-Rh bond length equal to about 2.30 A [35]. By considering an increase in the bond order .v from 2/4 (valency of S divided by 4 neighbors) to 2/3, as is appropriate for adsorption on a three-coordinate site, Eq (1.7) alone predicts a reduction in the S-Rh length by 0.11 A (i.e. to 2.19 A). However, the metallic coordination number is eight at the reference Rh(100) surface, but nine for Rh(111). Empirically, according to the previous discussion in Section 4.5, this could be expected to increase the S-Rh distance by 0.04 A (i.e. to 2.23 A), thereby bringing it into satisfactory correspondence with the average values (both 2.22 A) reported here for the Rh(l 11)-(V3x>/3)R30°-S and Rh( 111 )-c(4x2)-S surface structures! 6.6 Summary The evolution of structure found here, as the coverage of chemisorbed S increases from 1/3 to 1/2 M L on the Rh(l 11) surface, appears to follow some similar trends to those reported in Chapter 4 and 5 on the Rh( 110) surface, as the S coverage increases from 1/2 to 2/3 M L . On both surfaces, the metallic structure is basically unreconstructed and there is no direct S-S bonding. In each case also the initially ordered overlayer corresponds to a uniform arrangement of S atoms with a constant non-bonding distance (4.66 A), and all S atoms chemisorb in a constant adsorption site (fee site on Rh(l 11) and five-coordinate center site on Rh(l 10)). A similarity in the structural evolutions can be seen by considering rows of S atoms along [112] on Rh(l 11) and along [001] on Rh(110); thus, as the overall coverage increases on both surfaces, the separation between S atoms within the individual rows remains constant, but the packing density increases in the direction perpendicular to the rows. The average first Rh to second Rh interlayer spacing (d{2) is indicated to dilate 107 from 2.21 to 2.26 A on Rh(l 11), as the S coverage increases from 1/3 to 1/2 M L , and from 1.39 to 1.46 A on Rh(llO), as the S coverage increases from 1/2 to 2/3 M L . Consistently these observations support the principle that as the first metal layer bonds to more chemisorbed atoms, there is less bonding capability to the second metal layer, with the consequence that the interlayer spacing di2 increases. Additionally, with higher coverages, the increases in non-bonding S to S repulsive interactions force changes to mixed adsorption sites, and in turn the different environments of the chemisorbed S atoms lead to significant relaxations in the metallic structures. 108 Chapter 7 : Structural Analysis for the Rh(lll)-(2xl)-0 Surface 7.1 Introduction Diffraction patterns with half-order beams have frequently been observed for O chemisorbed on the (111) surface of Rh [95, 96, 97]. A common early assumption was that this indicated a (2x2) system at 1/4 M L coverage [98, 99, 100], although the spot streaking reported by Castner and Somorjai [101 ] was strongly indicative of a three-domain (2x1) model at 1/2 M L coverage. This conclusion was supported by the energy- and angle-resolved neutral particle (EARN) technique [102], which additionally indicated that the O chemisorbed in the regular fee sites. The latter result had also been indicated by an early LEED crystallographic analysis [103] which assumed that the surface corresponded to the 1/4 M L coverage, although that surface structure showed poor stability in the electron beam. At this point the structure of an 0 / R h ( l l l ) surface, which shows half-order diffraction spots, remains poorly characterized compared, for example, with the corresponding S systems described in Chapter 6. The purpose of this chapter is to report a L E E D crystallographic determination of structural details for an 0/Rh(l 11) surface which manifests these fractional beams, and which appears more robust in the electron beam than the surface studied previously with this technique [103]. 7.2 Experimental Oxygen exposures were given to the R h ( l l l ) surface after the surface had been shown to be clean (no impurity detected in the Auger electron spectrum) and well-ordered (sharp L E E D pattern). The experimental system and cleaning procedures used in this work correspond closely to those described in Section 4.2. The sharpest and most stable half-order L E E D patterns were obtained after a three-step dosing/annealing cycle, for which the individual steps involved exposing the surface at room temperature to 0 2 gas (2x 10" Torr, 109 6 min) followed by a flash anneal to 800 K . The final pattern from this preparation is very sharp, and it deteriorates in the electron beam over a period of around four hours, so enabling reliable intensity measurements with a video L E E D analyzer system. 1(E) curves were measured for normal incidence over the 40 to 252 eV energy range. A l l available symmetrically equivalent beams were measured at the same time to ensure that normal incidence was closely set. Measured 1(E) curves were averaged and smoothed for the fourteen symmetrically independent beams designated as (0 1), (1 0), (1 1), (0 2), (2 0), (1/2-1/2), (-1/2 1/2), (1/2 1/2), (1/2 -3/2), (-3/2 1/2), (3/2 -3/2), (-3/2 3/2), (3/2 1/2) and (1/2 3/2), to give a total energy range of 2020 eV available for the structural analysis. Although individual 1(E) curves from symmetrically equivalent fractional beams matched well, according to the mirror symmetries noted in Figure 7.1, strictly these are pseudo-mirror symmetries since systematical variations were observed in the beam intensities. The trends followed expectation for an unequal distribution of three rotationally-related (2x1) domains, presumably resulting from a slightly misoriented sample; the different filled symbols in Figure 7.1 identify the three sets of fractional beams from the individual domains. 7.3 Parameters used in the Calculations The calculation of phase shifts for O has been described in Section 2.3. The temperature correction for the O phase shifts used the Debye temperature of 843 K, to ensure that all the vibrating atoms probed by L E E D have a constant root-mean-square amplitude [46]. V o r was initially set at -12.0 eV, but was continuously refined during each set of the T L E E D calculations (final value-11.9 eV). 7.4 Model Considerations Allsurface structural models considered in the analysis have the O in atomic form since 0 2 is believed to dissociate on Rh(l 11), even at temperatures as low as 100 K [104]. 110 m Indication of the form of the L E E D pattern observed for normal incidence from the O on Rh(l 11) surface structure. The open circles are integral beams, while the filled symbols identify the three sets of half-order beams expected from a model involving a distribution of rotationally-related (2x 1) domains. The mirror symmetries identified apply closely to the measured 1(E) curves, but the fractional beam intensities correspond to a slightly unequal proportion of domain types. I l l Although beam intensities in the L E E D pattern suggested that the actual structure did not have a threefold rotation symmetry, nevertheless for completeness fourteen different model types were investigated, including those with the less likely (2x2) translational symmetry according to the L E E D pattern. These models are derived from the eight illustrations shown schematically in Figure 7.2. Models If, lh , 2fh, 3f, 3h, 5f and 5h are overlayer structures in which the O atoms are assumed to chemisorb in threefold sites on the unreconstructed metal surface; the letter f or h in the labels of the models identifies whether the fee or hep sites are occupied. The models designated 4fut, 4huo, 6fuo, 8fuo and 8hut include O in underlayer positions (identified with an o or t depending on whether octahedral or tetrahedral holes are occupied respectively). Models 7fr and 7hr have metallic reconstructions consistent with the (2x 1) translational symmetry. Composite layers were included in the calculations where necessary. Initial reference structures for the T L E E D calculations were made with Rh atoms at bulk positions, while O atoms in threefold adsorption sites were positioned to give local O-Rh bond distances of 1.98 A as found in the previous L E E D crystallographic study [103]; for other adsorption sites, the initial O positions were estimated with Eq (1.7). 7.5 Results and Discussion The final Rp values after the T L E E D optimization for each model type investigated are reported in Table 7.1. The best experiment calculation correspondence (Figure 7.3) occurs for model 5f, and the r p values for individual beams are reported in Table 7.2. This model (Figure 7.4) has a simple overlayer structure with O adsorbing in the threefold fee sites in the (2x1) symmetry arrangement for 1/2 M L coverage. Optimized atomic coordinates and structural parameters are listed in Tables 7.3 and 7.4 respectively. The interlayer spacings quoted in Table 7.4 correspond to vertical spacings between center-of-mass planes; in summary, the O plane is indicated to be 1.22 A above the first Rh layer, and the first and second Rh-Rh interlayer spacings are respectively 2.23 and 2.21 112 If or lh 2fh 3f or 3h 7fror7hr 8fuoor8hut Figure 7.2 A schematic indication of model types included in the T L E E D analysis for the O on Rh(l 11) surface structure. Rh atoms are represented by the larger circles, and the smaller circles are O atoms.(dashed circles represent O atoms below the first complete close-packed Rh layer). OverlayerO atoms on three-coordinate Rh sites are identified by either f or h depending on whether the site corresponds respectively to fee or hep local packing; underlayer (u) sites have an additional o or t to distinguish absorption into octahedral or tetrahedral holes; model designations including an r correspond to reconstructed metal surfaces. 113 Table 7.1 T L E E D optimized values of Rp for each of the model types considered for the Rh(l 11 )-(2xl )-0 surface structure Model RP If 0.3589 lh 0.6690 2fh 0.4801 3f 0.3987 3h 0.7308 4fut 0.4501 4huo 0.6441 5f 0.3143 5h 0.6715 6fuo 0.5424 7fr 0.8277 7hr 0.6289 8f uo 0.4803 8hut 0.6184 114 1(E) curves for fourteen diffracted beams at normal incidence for the Rh( 111 )-(2x 1 )-0 surface. The dashed-dot lines represent experimental curves and the solid lines represent curves calculated for the structure (Table 7.3) optimized by the TLEED analysis. 115 B e a m (+0.0,+1.0) B e a m (+2.0,+0.0) B e a m (+1/2,-3/2) 0 50 100150200250300 B e a m (+1.0.+0.0) 0 50 100150200250300 B e a m (+1.0.+1.0) A / 0 50 100150200250300 B e a m (+0.0.+2.0) 0 50 100150200250300 B e a m (+3/2.+1/2) 0 50 100150200250300 0 50 100150200250300 B e a m (+1/2,-1/2) 0 50 100150200250300 B e a m (-1/2.+1/2) 0 50 100150200250300 B e a m (+1/2.+1/2) 0 50 100150200250300 B e a m (+1/2.+3/2) 0 50 100150200250300 Energy (eV) (i6 0 50 100150200250300 B e a m (-3/2.+1/2) 0 50 100150200250300 B e a m (+3/2,-3/2) 0 50 100150200250300 B e a m (-3/2,+3/2) 0 50 100150200250300 Table 7.2 Individual rp values for fourteen beams from the Rh( 11 l)-(2x 1 )-0 surface structure for normal incidence Beam Label rP (0 1) 0.1906 (1 0) 0.2581 (11) 0.1232 (0 2) 0.6373 (2 0) 0.1817 (1/2-1/2) 0.2866 (-1/2 1/2) 0.2825 (1/2 1/2) 0.2855 (1/2-3/2) 0.2942 (-3/2 1/2) 0.3487 (3/2 -3/2) 0.2633 (-3/2 3/2) 0.5148 (3/2 1/2) 0.5708 (1/2 3/2) 0.3630 117 mirror plane [110] 2.690 A [112] Views of the Rh(l 1 l)-(2xl)-0 surface from: (a) the top and (b) the side. The open circles represent Rh atoms while the smaller, filled circles represent O atoms. In the top view, the atoms in the first Rh layers are open, while those in the second Rh layers are shaded. 118 Table 7.3 Atomic coordinates (in A) for the TLEED-determined structure of the Rh( l l l ) - (2xl ) -0 surface Atomiclabel X V z 0(1) 1.35 2.27 5.65 Rh(2) 0.00 - 1.49 4.47 Rh(3) 1.35 0.82 4.40 Rh(4) 1.35 - 0.80 2.22 Rh(5) 0.00 1.53 2.19 bulk Rh 0.00 0.00 0.00 Thex, v and -. directions are parallel to [110], [112] and [111] respectively. 119 Table 7.4 Geometrical parameters (in A) for the Rh(l 1 l)-(2xl)-0 surface Parameters Rh( l l l ) - (2xl ) -0 4)1 .1.22 d l 2 2.23 d23 2.21 4, 0.07 A0l 0.05 4ml k . 2.20 120 A, only marginally expanded over the bulk spacing of 2.20 A. Such expansions are commonly observed for the adsorption of electronegative atoms on metal surfaces [83]. The first metal layer shows a buckling of 0.07 A (J,,) with the atoms designated Rh(2) displaced upwards compared with Rh(3). Additionally the O atoms appear laterally displaced off the exact center of the fee site by about 0.05 A ( A 0 1 ) . The structural details reported correspond to the 0-Rh(2) and 0-Rh(3) bond lengths of 2.01 and 1.92 A respectively. Since O is a weak scatterer, the 1(E) curves may be relatively insensitive to the O position, and therefore substantial uncertainty may be expected. The scheme proposed by Andersen et al. [60] indicates the uncertainty in these bond lengths to be around 0.08 A, which suggests in turn that the difference reported (0.09 A) is barely significant. The average O-Rh distance found here (1.98 A) is close to that in the R h 0 2 crystal (1.96 A) in which each O atom also bonds to three Rh atoms [105]: Debate continues on the appropriate procedure for estimating uncertainty in the results of L E E D crystallography; for example the procedures of Andersen et al. and of Pendry mentioned in Section 2.5.2 have been seen as giving lower and upper limits respectively (the uncertainty from the Pendry procedure are generally at least twice that from the scheme of Andersen et al.) [47, 61]. The difficulty comes from not having independent measures of the errors. In the absence of a fundamental definition, there is nevertheless another more practical approach, which involves assessing significance in structural details by testing the apparent reasonableness, or otherwise, of the overall trends. For example, the uncertainty found in this work for dx, is 0.03 A according to the criterion of Andersen et al., and it seems reasonable that the Rh(2) atoms, each of which bonds to two O atoms, should lift up compared with atoms Rh(3) which each bond to only one O atom. This depends on the concept that atoms Rh(2), by bonding to two O atoms, have less "free valency" available for bonding to second layer Rh atoms than those designated Rh(3). This same argument extends through to the O-Rh bond lengths insofar as the Rh atoms which bond to two O atoms may reasonably have longer O-Rh distances than those 121 Rh atoms that bond to only one O atom. The sense of the displacement indicated by the parameter AQl from the L E E D analysis is fully consistent with this principle, even though the uncertainty appears large (e.g. 0.10 A according to the criterion of Andersen et al.). Why a 1/2 M L adsorption structure on a fcc(l11) surface should favor the three-domain (2x1) model, as found here, over the higher symmetry (2x2) form, as represented by model 2fh, provides an interesting question. At one level this must be associated with nearest neighbor interactions being energetically favored over those for next nearest neighbors, but at another level there may be a connection with the common tendency for chain structures to show stability in surface structures. For example, in the -O-Rh- chain found here the O-Rh distance is 2.01 A and the O-Rh-0 angle 84°, while the corresponding parameters for the similar chain in bulk R h 0 2 are 1.96 A and 103° respectively [105]. For models 3h/3f with O above the symmetrical three-coordinate site to give O-Rh bond distances equal to 1.98 A, the OTRII-O angle would be 144°. The confirmation that O chemisorbs on the fee adsorption site is consistent with other similar adsorptions on f c c ( l l l ) surfaces (e.g. N i ( l l l ) [29] and P t ( l l l ) [106]), and interestingly even with O adsorption on the Rh( 110) surface. In both the p2mg(2x 1) and pg(2x2) structures for the 0/Rh(l 10) system, O adsorbs on a threefold site, formed by two first layer Rh atoms and one second layer Rh atom which corresponds to a micro-(l 11) plane [107, 108]. For the p2mg(2xl) case, the bond distance to the First layer Rh atoms (O-Rh,) is indicated to be about 0.21 A shorter than the bond distance to the second layer Rh atoms (0-Rh„). A factor in this variation in O-Rh bond length may be the metallic coordination numbers of the different Rh atoms, as discussed previously for the Rh(l 10)-c(2x2)-S surface in Chapter 4. Using the average O-Rh bond length (1.98 A) determined in this work as a reference, estimates can be made for the bond lengths in the p2mg(2xl) structure of 0/Rh( 110) [107] with the correction term Ar in Eq (4.2) as follows: r(0-Rh,)= 1.98 + 0.04(7 - 9)= 1.90 A (7.1) 122 r (O-Rh,,) = 1.98 + 0.04 (11 -9) = 2.06 A (7.2) The respective values determined by L E E D crystallography are 1.86 and 2.07 A [107]. Hence, as a minimum, the average O-Rh bond length determined in this work for 0 / R h ( l l l ) appears broadly consistent with the determinations of the individual bond lengths made previously for the p2mg(2x 1) structure formed by 0/Rh( 110). Another comparison is with the Ru(0001)-(2xl)-0 surface [109] where the L E E D -determined values for du (0.07 A) and A Q , (0.06 A) are within 0.01 A of the corresponding values found here for the Rh(l 1 l)-(2xl)-0 structure. However, there is a difference between the two surfaces insofar as Ru(0001) shows a pairing tendency between Ru atom rows, and, for a particular adsorption site, this results in all three O-Ru bond lengths having equal values. 7.6 Summary A T L E E D analysis is reported for the Rh(l 1 l)-(2xl)-0 surface structure in which the O atoms chemisorb close to the regular fee sites. The structure shows significant relaxations; for example, a buckling of about 0.07 A is indicated in the first metal layer and O appears to displace laterally by about 0.05 A. The two kinds of O-Rh bond lengths are around 2.01 and 1.92 A to top layer Rh atoms which respectively bond to two and one O atoms. Comparison is made with the earlier determination for O-Rh bond lengths in the Rh( 110)-p2mg(2x 1) surface structure. 123 Chapter 8 : Conclusions and Future Work 8.1 Comparison between the Structures at Low and Higher Coverages of S on the (111) and (110) Surfaces of Rh Table 8.1 summarizes comparative structural features in relation to the S/Rh systems studied in this work by the T L E E D analyses. The following paragraphs discuss changes identified as each low coverage system evolves to the higher one with regard to (i) S distribution on the surface, (ii) adsorption site, and (iii) dependence of surface relaxations and surface bond lengths on S coverage. 8.1.1 Distributions of S In all four systems formed by chemisorbed S on the Rh(l 10) and (111) surfaces, the S atoms adsorbed as an overlayer without causing any reconstruction to the metal, and the adsorbing atoms tend to distribute reasonably evenly on each surface. For the (V3x*\/3)R30° and c(4x2) systems on Rh(l 11), the closest S-S distances are determined to be 4.66 and 3.38 A which are very close to the corresponding values of 4.66 and 3.47 A for the c(2x2) and (3x2) structures on Rh(110). In none of these systems are there significant direct S-S bonding interactions; in each case the S-S separations are appreciably longer than the single S-S bond length of 2.04 A in S 8 [86]. However, the separations for higher coverage structures are a little less than the regular Van der Waals distance of 3.70 A [85]. Figures 8.1 and 8.2 help identify a similarity in the structural evolutions on both the (111) and (110) surfaces; this can be seen by treating these structures as involving the packing of rows of S atoms which are parallel to the [112] direction on Rh(l 11), and to the [001] direction on Rh(110). On each surface, as the overall coverage increases, the 124 Table 8.1 Comparative features observed in the S /Rh( l l l ) and S/Rh(110) surface structures S/Rh( 111) S/ Rh(110) (V3xV3)R30° c(4x2) c(2x2) (3x2) . S overlayer with no substrate reconstruction S overlayer with no substrate reconstruction S-S dist. = 4.66 A S-S dist. = 3.38 A S-S dist. = 4.66 A S-S dist. = 3.47 A no S-S bonding no S-S bonding CN(S)* = 3 CN(S)*=3- CN(S)* = 5 CN(S)*=5,4 fee site fee + hep sites center site center + distorted center + long-bridge sites S-Rh = 2.23 A S-Rh =2.22 A (ave.) S-Rh, = 2.47 A S-Rh„ = 2.27 A S-Rh, = 2.45 A S-Rh„ = 2.26A <*12 = 2.21 A J ] 2 = 2.26A J 1 2=1 .39A J, 2=1.46A S linear density constant along [ 112] packing density increases in [110] direction S linear density constant along [001 ] packing density increases in [ 110] direction coordination number of S atom 125 Figure 8.1 Diagram showing the top views of (a) Rh(l 1 l)-(y/3xy/3)R30°-S and (b) Rh(l 1 l)-c(4x2)-S surface structures. 126 Diagram showing the top views of (a) Rh(l 10)-c(2x2)-S and (b) Rh(l 10)-(3x2)-S surface structures. 127 separation between S atoms within the individual rows remains constant, but the packing density increases in the direction perpendicular to the rows. 8.1.2 Adsorption Site For the low coverage structure on Rh( 111), S occupies the three-coordinate fee site, whereas on Rh(l 10), S occupies the five-coordinate center site. In both cases, the S atoms occupy sites with the maximum coordination number in the absence of a reconstruction. These sites therefore appear as energetically favored for low coverage. However as the S concentration increases in both cases, the direct bonding energy term appears to be offset to some degree by an increase in the non-bonding S-S repulsive interaction. Changes in adsorption site are observed as the structures evolve to higher coverage in each case: on Rh(l 11), the S atoms occupy both hep and fee sites, whereas on Rh(l 10), four-coordinate long-bridge sites are occupied as well as the center sites. Clearly, on both surfaces, multiple adsorption sites become more prevalent as the S coverage increases; 8.1.3 Dependence of Surface Relaxations and Surface Bond Lengths on Adsorbate Coverage For both the S/Rh(111) and S/Rh( 110) systems, strong evidence is presented that the magnitude of the.first interlayer spacing in the metal structure increases with the S coverage. Thus on R h ( l l l ) , the parameter d}2 increases from 2.21 to 2.26 A as the S coverage increases from 1/3 to 1/2 M L ; similarly on Rh(l 10), <i1 2 increases from 1.39 to 1.46 A as the S coverage increases from 1/2 to 2/3 M L . Clearly, as more S-Rh bonds are formed in each case, the ability of the first metallic layer to bond to the underlying metal structure is reduced. By contrast, the average S-Rh bond length on each particular surface, and for constant adsorption coordination number, is essentially constant with the S coverage. For example, the average S-Rh distance remains close to 2.23 A as the S coverage increases 128 from 1/3 to 1/2 M L on the Rh(l 11) surface. Similarly, for the S atoms adsorbed on the undistorted center sites of the Rh(l 10) surface, the S-Rhj and S-Rhjj distances change only slightly from 2.47 and 2.27 A for c(2x2), to 2.45 and 2.26 A for the (3x2) structure, as the coverage increases from 1/2 to 2/3 M L . Such a constancy suggests that each metallic structure is able to adapt closely to the S valency requirements regardless of the details of the adsorbate coverage. 8.2 Effect of Coordination Number on Adsorbate-Metal Bond Lengths The results of our studies provide evidence for the coordination number effect of both adsorbate X and metal M atoms on their associated X - M bond lengths. Firstly, the X -M bond length depends on the coordination number of the X atom. For example, the average S-Rh bond length in the Rh(l 10)-c(2x2)-S structure (2.43 A) is greater than the corresponding value in the Rh(100)-c(2x2)-S [35] structure (2.30 A), and this in turn is greater than the S-Rh distance in the Rh(l 1 l)-(V^xV3)R30°-S surface (2.23 A). These trends follow the coordination numbers of S atoms on the (110), (100) and (111) surfaces as five, four and three respectively, in general terms as expected with Eq (1.7). However superimposed oh this tendency are effects of coordination number experienced by the metal atom, and two variations of this are indicated by this work. The present work clarifies that the X - M bond length also depends on the coordination number, with respect to metal-metal bonding, of the metal atoms to which the adsorbate is bonded. An exploratory attempt has been made to quantify this second effect by the use of Eq (4.2), which was parametrized through the use of O-Ni bond lengths determined by Kleinle et al. [36] for the Ni( l 10)-(2x l ) -0 structure. This approach appears to work quite well in estimating the S-Rh, and S-Rh n bond lengths for the Rh(l 10)-c(2x2)-S structure; the coordination numbers of the Rhj and R h n atoms with respect to metal-metal bonding are seven and eleven respectively. Further, it is shown in this thesis that this 129 approach can help rationalize the variation in the O-Rh bond lengths reported very recently by Batteas etal. 1107] for the Rh(l 10)-p2mg(2xl)-O surface structure. A third effect identified here concerns a dependence for the X - M bond length on the number of adsorbate atoms to which M is bonded. This is shown by the new structural results for both the Rh(l 1 l)-c(4x2)-S and Rh(l 1 l)-(2xl)-0 surfaces. In both structures, two types of first layer Rh atoms are involved in the bonding. For one type, each surface M atom bonds to two X atoms, but for the other, each surface M atom bonds to just one X atom. Consistently with the bond order argument, the former turns out to have the longer bond lengths in both the S/Rh(l 11) and 0/Rh(l 11) systems. 8.3 Future Work The work reported here has established some fundamental understanding about the chemisorption of S on low index Rh surfaces regarding the structural parameters and their coverage dependence. It should be useful to extend this work in several directions, one being to S/Rh systems of higher complexity. This should involve exposing low-index surfaces of Rh directly to S 2 molecules, for which there is evidence 1110, 111] that higher coverages may be obtainable than provided by H 2 S as used here. Also chemisorption on stepped surfaces based on terraces of (110) and (111) orientations should help to clarify how the principles discussed here in relation to bond lengths, adsorption sites and relaxation effects are modified when equally spaced atomic height steps are also present. 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