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LEED crystallographic studies of sulfur chemisorbed on the (111) surfaces of nickel and rhodium Wu, Yuk Kuen 1989

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LEED CRYSTALLOGRAPHIC STUDIES OF SULFUR CHEMISORBED ON THE (111) SURFACES OF NICKEL AND RHODIUM by YUKKUEN WU B. Sc., The Chinese University of Hong Kong, 1984 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMISTRY We accept this as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January 1989 ©YukKuenWu, 1989 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 The University of British Columbia Vancouver, Canada Date \ \ \ DE-6 (2/88) ii ABSTRACT The work in this thesis includes investigations of adsorbate-induced metal relaxations with low-energy electron diffraction (LEED) for the surface structures designated Ni(lll)-(2x2)-S and Rh(lll)-(V3xV3)30'-S; a set of LEED intensity-versus-energy (1(E)) curves have also been measured for normal incidence on the Ni(l 1 l)-(2x2)-0 surface. In the investigations of adsorbate-induced metal relaxations, 1(E) curves measured for a set of diffracted beams were compared with the corresponding curves calculated by multiple scattering methods for various structural models. The objective is to find the structure that gives the best correspondence between experiment and calculation. Levels of correspondence between experimental and calculated 1(E) curves were assessed with the reliability indices proposed by Zanazzi-Jona and Pendry as well as with visual comparison. In the LEED intensity analysis for the Ni(l 1 l)-(2x2)-S surface structure, the S-Ni interlayer spacing (doi), the lateral displacement (A) of the first nickel layer and vertical relaxations of the first two Ni-Ni interlayer spacings (di2, d23) were investigated. The best geometrical parameters were determined to be doi=1.50 A, A=+0.02 A (1.4% expansion), di2=2.09 A (2.8% expansion) and d23=2.08 A (2.3% expansion) with the S atoms adsorbed on the "expected" 3f sites of the Ni(lll) surface. The present study leads to a nearest-neighbour S-Ni bond distance of 2.10 A, which is a little shorter than those obtained by low energy ion scattering (2.16 A) and the surface extended X-ray adsorption fine structure technique (2.20 A) but agrees rather well with the value 2.12 A predicted by a bond length-bond order analysis. In the investigation of adsorbate-induced metal relaxations for the Rh(lll)-(V3xV3)30°-S surface, theoretical 1(E) curves were calculated for a range of models involving either unreconstructed or reconstructed rhodium structure at the surface. These calculations were done over appropriate ranges of the S-Rh interlayer spacing (doi), the iii lateral displacement (A) for the first Rh layer, and the first Rh-Rh interlayer spacing (di2). The best level of correspondence between calculation and experiment appears for the 3F1 model with doi=1.57 A, A=M).025 A (1.6 % contraction) and di2=2.18 A (0.5 % contraction). In this model the nearest-neighbor S-Rh bond distance is found to be 2.19 A. iv TABLE OF CONTENTS Abstract ii Table of Contents iv List of Tables vi List of Figures vii Acknowledgments xi Chapter 1 Introduction 1 1.1 Introduction 2 1.2 Low-Energy Electron Diffraction 4 1.2.1 Scattering of low-energy electrons with a solid 4 1.2.2 LEED Crystallography 7 1.2.3 Notation of LEED patterns 13 1.3 Auger Electron Spectroscopy (AES) 17 1.4 Aims of thesis 20 Chapter 2 LEED Intensity Calculation 23 2.1 Introduction 24 2.2 Muffin-tm-approxirration 25 2.3 Phase shift 28 2.4 The Layer Diffraction Matrix 30 2.5 Layer Stacking 33 2.6 Evaluation of Calculated LEED Intensity 36 Chapter 3 Experimental 38 3.1 The UHV Chamber 39 3.2 Sample Preparation and Cleaning 42 V 3.3 Auger Electron Spectroscopy 44 3.4 LEED Apparatus 46 3.4.1 Electron Gun and LEED Optics 46 3.4.2 LEED Intensity Measurement 46 Chapter 4 Investigation of the Chemisorption Structures of Sulfur on the (111) Surfaces of Nickel and Rhodium 51 Part I LEED Structure Analysis of the Ni(l 1 l)-(2x2)-S Surface: A Case of Adsorbate-induced Metal Relaxations 52 4.1.1 Introduction 52 4.1.2 Experimental 53 4.1.3 LEED Intensity Calculations 55 4.1.4 Discussion 66 Part JJ LEED Structure Analysis of the Rh(l 1 l)-(V3xV3)30°-S Structure: A New LEED Analysis 72 4.2.1 Introduction 72 4.2.2 Experimental Data Base 72 4.2.3 LEED Intensity Calculations 75 4.2.4 Results and Discussion 83 References 96 Appendix Al vi LIST OF TABLES Table 1.1 Some surface techniques and their characteristic. 3 Table 4.1.1 Energy range of experimental 1(E) curves for Ni(l 1 l)-(2x2)-S. 57 Table 4.1.2 LEED reliability index studies for adsorptions in 3f and 3h sites of the Ni(l 1 l)-(2x2)-S structure. 60 Table 4.1.3 Structural refinement for Ni(l 1 l)-(2x2)-S. 65 Table 4.2.1 Energy range of experimental 1(E) curves for Rh(l 1 l)-(V3xV3)30'-S. 76 Table 4.2.2 Models and ranges of geometrical parameters considered for the Rh(lll)-(V3xV3)30'-S structure. 82 vii L I S T O F F I G U R E S Figure 1.1 Schematic energy distribution N(E) of backscattered electrons as a function of their energy for a primary electron beam of energy Ep. 5 Figure 1.2 Typical dependence of mean free path (L) of electrons in a metallic solid as a function of electron energy. 8 Figure 1.3 The five types of (aperiodic surface meshes (a) in real space; (b) in reciprocal space. 9 Figure 1.4 Schematic diagram of the LEED geometry. The primary electron beam has energy E and its direction is defined by the angles 6 and 0. Two diffracted beams are shown and the 1(E) curve for one of them is indicated. 11 Figure 1.5 Schematic diagram illustrating how the conservation conditions determine the direction of a diffracted beam. The (0 0) beam corresponds to the specular reflection. 14 Figure 1.6 Some common translational symmetrical unit meshes for adsorption of species X on (111) surfaces of fee metals M using Wood's notation and the matrix notation. 16 Figure 1.7 Schematic diagram of an Auger process to produce a K L 2 L 3 Auger electron. 18 Figure 1.8 Auger spectra from a Be sample, (a) Energy distribution, (b) First derivative dN(E)/dE. 19 Figure 2.1 Variation of potential for the muffin model: (a) contour plot through an atomic layer, and (b) variation through a single row of ion cores along the x-axis. 26 viii Figure 2.2 Graphitic-type sulfur overlayer for Ni(lll)-(2x2)-S; there are two sulfuratoms (full circles) per unit mesh, one on a 3f site the other on a 3h site. 32 Figure 2.3 Diagram of the renormalized forward scattering method, (a) Each triplet of arrows represents the complete set of plane waves that travel from layer to layer. Ni, N 2 and N3 denote the deepest layer reached in the 1st, 2nd and 3rd order scatterings respectively, (b) and (c) Illustration of the vectors which store of the inward-traveling wave (a*) and outward-traveling waves ). 34 Figure 3.1 Schematic diagram of the FC12 UHV chamber and some of its important assessories. 40 Figure 3.2 Diagrammatic representation of the pumping system. 41 Figure 3.3 (a) Schematic diagram of laser alignment of optical and crystallo-graphic planes of a single crystal, (b) A blow-up to show the relationship between the optical and crystallographic planes. Alignment is acceptable when 6<l/2' (taken from Ref. [H86]). 43 Figure 3.4 Schematic diagram for measuring Auger electron spectra with a cylindrical mirror analyzer and glancing incidence electron gun. 45 Figure 3.5 Schematic diagram of the electron optics for the LEED display system (taken from Ref [W87]). 47 Figure 3.6 Schematic diagram for the TV analyzer system. 48 Figure 3.7 (a)-(e) are five measured symmetrical equivalent 1(E) curves of (1/2 1/2) beam for the Ni(l 1 l)-(2x2)-S surface at normal incidence. They are averaged (f) and finally smoothed (g). 50 Figure 4.1.1 Schematic indications of LEED patterns from surfaces designated: (a) Ni(l 1 l)-(lxl); (b) Ni(l 1 l)-(2x2)-S. 54 IX Figure 4.1.2 Auger spectrum from a Ni(l 1 l)-(2x2)-S surface. 56 Figure 4.1.3 Schematic LEED pattern from Ni(l 1 l)-(2x2)-S surface with beam indices. 58 Figure 4.1.4 Comparison of experimental 1(E) curves for (1/2 1/2), (1 1/2) and (0 3/2) diffracted beams from Ni(l 1 l)-(2x2)-S with those calculated for sulfur adsorbed at (a) the 3f and (b) the 3h sites over a range of interlayer spacings between sulfur and first Ni layer. 62 Figure 4.1.5 Notation used for Ni(l 1 l)-(2x2)-S surface structure. The model is viewed from above in (a) and from the side in (b) along the cross section marked by the line in (a). S atoms are represented by dark circles and Ni atoms by the larger circles. The circles which are open, dashed and shaded are for Ni atoms designated as of type A, B, and C respectivly. Lateral displacements for atoms in the first Ni layer are fixed by the parameter A whose magnitude corresponds to the displacement from the regular bulk positions and whose sense is positive when the displacements are in the direction of the arrows shown. 64 Figure 4.1.6 Reliability index for each iteration. 67 Figure 4.1.7 Comparison of experimental 1(E) curves from Ni(l 1 l)-(2x2)-S with those calculated for the 3f models: (a) doi=1.50 A, A=+0.00 A, di2=2.03 A and d23=2.03 A. (b) doi=1.50 A, A=+0.03 A, di2=2.09 A and d23=2.08 A. 68 Figure 4.2.1 Comparison of experimental 1(E) curves from Rh(l 1 l)-(V3xV3)30"-S with those calculated for the models where sulfur atoms adsorb at the 3f sites and the interlayer spacing between S and first Rh layers (doi) are either at (a) 1.45 A and (b) 1.55 A (taken from Ref. [Wth87]). 73 Figure 4.2.2 Beam notations for a LEED pattern from the Rh( 11 l)-(V3xV3)30°-S surface. 77 Figure 4.2.3 Notation used for the Rh(l 1 l)-(V3xV3)30"-S surface structure. The model is viewed from above in (a) and from the side in (b) along the cross section marked by the line in (a). S atoms are represented by dark circles and Rh atoms by the larger circles. The circles which are open, dashed and shaded are for Rh atoms designated as of type A, B, and C respectively. Lateral displacements for atoms in the first Rh layer are fixed by the parameter A whose magnitude corresponds to the displacement from the regular bulk positions and whose sense is positive when the displacements are in the direction of the arrows shown. © and x corresponding to lateral displacements into and out-of the plane of the figure. 79 Figure 4.2.4 Comparison of experimental 1(E) curves from Rh(l 1 l)-(V3xV3)30°-S with those calculated for the 3F1 (i.e. (C)ABC.) models: (a) dni=1.57 A, A= 0.00 A and di2=2.19 A. (b) doi=1.57 A, A=-0.025 A and di2=2.18 A. (c) doi=1.57 A, A= 0.00 A and di 2=2.17 A. 84 Figure 4.2.5 Comparison of experimental 1(E) curves from Rh( 11 l)-(V3xV3)30°-S with those calculated for the 3RF1 (i.e. (QBABC.) model, over a range of lateral displacement (A), where dni and di2 are fixed at 1.55 A and 2.1921 A respectively. 88 Figure 4.2.6 Comparison of experimental 1(E) curves from Rh(l 1 l)-(V3xV3)30'-S with those calculated for the two-domain 3RF2 (i.e. (C)BABC... + (C")BABC.) model, over a range of lateral displacement (A), where dni and di2 are fixed at 1.55 A and 2.1921 A respectively. 92 ACKNOWLEDGEMENTS xi I would like to thank sincerely Dr. K.A.R. Mitchell for his interest, encouragement and supervision throughout the course of this work. I also acknowledge many helpful discussions with the other members of his research group. Special thanks are due to Dr. P.C.L. Wong and Dr. R.N.S. Sodhi for introducing me to the instruments for LEED measurements and Mr. H.C. Zeng for introducing me to the LEED calculations. I should like to express my gratitude to the capable staff of the mechanical and electronic workshops for their assistance in the maintenance of the instrument. Financial support in the form of a University of British Columbia Graduate Fellowship is also gratefully acknowledged. Finally, I wish to thank my parents and my husband for their patience and encouragement. This thesis is dedicated to them. Chapter 1 2 1.1 Introduction In recent decades, surface science has been extensively explored in describing the structure, morphology, chemical and physical properties of crystal surfaces and interfaces of a large variety of materials of interest in solid-state physics, electronics, metallurgy, biophysics and heterogeneous catalysis [BV81]. In addition, the research has clearly shifted its interest from the macroscopic properties of "real" surfaces of polycrystalline materials to microscopic scale information about clean and well-defined surfaces, especially of single crystals [RE79]. This has allowed greatly improved understandings of atomic aspects of surface phenomena, which are greatly influenced by the structure of surface regions. In the "clean surface" approach, single crystals with well-defined crystallographic surfaces are studied under conditions in which the accumulation of contaminants is negligible for the time of the experiment [MJ82]. In practice, this requires experiments to be carried out in an ultrahigh vacuum (UHV) environment (pressure < 10~9 torr). With the commercial availability of ultrahigh vacuum systems, various experimental techniques have been developed to characterize solid surfaces through the observation of the scattering of ions, electrons, photons or atoms. The aims of a crystallographic analysis are manifold : the atomic species at or near a surface need to be identified, the positions of atoms relative to each other and the bond lengths between them have to be determined, and - as the ultimate task- the character of the bonding should be established. Table 1.1 summarizes some common surface techniques which provide information on structure, composition, bonding and vibrations at surfaces. More details for each individual technique are to be found in the references given. Among the methods listed in Table 1.1, low-energy electron diffraction (LEED) is a most common and fruitful tool for characterization of the geometrical arrangement of atoms Table 1.1 Some surface techniques and their characteristics Technique Acronym Probe particle Measured particle Information Auger-Electron Spectroscopy [EK85] AES Electron Electron Composition High-Resolution Electron Energy Loss Spectroscopy [IM82] HREELS Electron Electron Vibrational Mode Low-Energy Electron Diffraction [P74] I FED Electron Electron Geometrical Structure Reflection High-Energy Electron Diffraction [VLP&83] RHEED Electron Electron Geometrical Structure Scanning Electron Microscopy [OTY&80] SEM Electron Electron Topography Angular Resolved Photoelectron Spectroscopy [BBH&83] ARPES Photon Electron Geometrical Structure Ultra-violet Photoelectron Spectroscopy [H83] UPS Photon Electron Valence State X-ray Photoelectron Spectroscopy [C75] XPS Photon Electron Composition, Valence State Near-edge X-ray Adsorption Fine Structure [S85] NEXAFS Photon Photon, Electron Intramolecular Bonding Surface Extended X-ray Absorption Fine Structure [S85] SEXAFS Photon Photon, Electron Geometrical Structure X-ray Diffraction [NAB&81] XD Photon Photon Geometrical Structure Rutherford Backscattering [RFW&81] RBS Ion Ion Composition, Geometrical Structure Ion Scattering Spectroscopy [HT77] ISS Ion Ion Composition, Geometrical Structure Secondary Ion Mass Spectroscopy [GWH78] SIMS Ion Ion Composition Helium-atom Diffraction [CB80] HEAD Atom Atom Geometrical Structure 4 on a single-crystal surface. The combination of Auger electron spectroscopy (AES) and LEED has proved a most useful combination for characterizing surfaces. 1.2 Low-Energy Electron Diffraction LEED is the most widely used technique for surface structure determination. Its potential was discovered in the Davisson-Germer experiment of 1927 [DG27]. However, a number of theoretical and experimental difficulties delayed the immediate development of LEED as a method of structural chemistry. It was not until the 1970s that sufficient experimental and theoretical advances occurred to allow its application to the determination of the geometrical structure of surfaces. In the LEED experiment, a monoenergetic beam of electrons (typical energy 20-300 eV), with known angles of incidence, is directed onto a well-defined surface of a crystalline solid. The incident electrons are scattered by the surface atoms and only the elastically back-scattered electrons are selectively collected on a fluorescent screen to give a (iiffraction pattern. The resulting diffraction pattern consists of a number of bright and well-defined spots, the arrangement and intensities of which are determined by the surface structure of the sample. 1.2.1 Scattering of Low-Energy Electrons with a Solid Electrons of an initial energy, Ep, bombarding a solid sample, will give rise to the appearance of backscattered and secondary emitted electrons. Their energy distribution is displayed schematically in Figure 1.1 and may be divided into the following regions: (a) In the low energy range (region I), the so-called "true secondary electrons" are created as a result of inelastic collisions of primary electrons inside the solid. This in turn creates more secondaries and initiates a "cascade" process, whereby more electrons are emitted with ever decreasing average energies. 5 Figure 1.1 Schematic energy distribution N(E) of backscattered electrons as a function of their energy for the primary beam of energy Ep 6 (b) In the medium energy range (region II), there are small peaks superimposed on a relatively smooth background. They may correspond to inelastic scattering because of plasmon excitation and electronic excitation, or to Auger electron emission. (c) At the high energy limit of the distribution (region Ul), there is a sharp peak corresponding to electrons which are elastically, or quasi-elastically, scattered from the ion cores. The quasi-elastically scattered electrons correspond to small energy losses ( « 1 eV) resulting from excitation of surface vibrations. These losses cannot be resolved with conventional LEED optics, but with a high resolution spectrometer (used in HREELS) they are studied to provide information on the vibrational motion of atoms and molecules on and near the surface. Typically, only a few percent of the incident electrons are elastically back-scattered from the surface. These are the electrons studied in low-energy electron diffraction (LEED) to provide structural information of surfaces. According to the de Broglie hypothesis, if E (in eV) is the energy of the primary electron then the corresponding wavelength (in A) is given by the equation For low-energy electrons (typically < 500 eV), their wavelengths are comparable to the atomic spacings in crystals. That such electrons scattered from a single crystal can interfere constructively for particular conditions provides the structural information, somewhat analogously to the situation in X-ray diffraction. Low-energy electrons are particularly suited to investigate the surface because of the strong inelastic scattering they experience in a solid. An useful parameter, the electron mean free path L, is defined to describe the distance traveled by an electron before it loses energy according to (1.1) I = I0exp[-d/L] (1.2) 7 where the initial beam intensity Io at particular energy is attenuated to I after propagating through a distance d in the solid. The characteristic dependency of this property on the electron energy can be seen in Figure 1.2. Typically, LEED uses an electron energy range between 20 and 500 eV where L corresponds to just a few A. This ensures high surface sensitivity. Further with the appropriate electron wavelength, LEED becomes a very suitable probe of surface geometrical structure. 1.2.2 LEED Crystallography The aim of LEED crystallography is to determine the arrangement of the atoms at and near a crystalline surface, which is most simply classified by the Miller indices for reference parallel planes within the bulk crystal. For a surface, all lattice (or net) points within the diperiodic space are described by translation vectors t = maj + na2 (m, n = integers) , (1.3) where a} and a2 are the unit mesh vectors. Analogous to the 14 Bravais unit cells of triperiodicity, there are only five possible diperiodic Bravais unit meshes, which are shown in Figure 1.3a. Details of various conventions in surface crystallography can be found in an article by Wood [W64] and in the International Tables for X-ray Crystallography [HL52]. In order to represent diffraction conditions in simple mathematical form, a complementary reciprocal lattice space is constructed. The reciprocal lattice points are defined by translation vectors g = ha.j + ka2 (h, k = integers), (1.4) * * where ax and a 2 are unit reciprocal mesh vectors which relate to the unit mesh vectors in real space by the following expression: 8 I • 1 • 1 1  10 100 1000 10,000 100,000 ELECTRON ENERGY (eV) Figure 1.2 Typical dependence of mean free path (L) of electrons in a metallic solid as a function of" electron energy. 9 REAL RECIPROCAL £2 SQUARE • a RECTANGULAR CENTERED RECTANGULAR HEXAGONAL ti OBLIQUE a ~ i Figure 1.3 The five types of diperiodic surface meshes (a) in real space; (b) in reciprocal space. 10 a.-a* = 2TC6.. , (1.5) - i - j ij v ' where the Kronecker symbol has values: 8jj = 0 if i * j and Sjj = 1 if i = j (i.e. &x ± a 2 and a 2 i aj). The relationship between the reciprocal and real space vectors and their meshes are listed in Figure 1.3. The elements of a LEED experiment are illustrated in Figure 1.4. The electrons in an incident beam, with known energy (E) and direction (e, are scattered by the surface atoms. As a result, some of the incident electrons are elastically backscattered and constructively interfere along certain directions. Outside the influence of the crystal, both the incident and diffracted electrons can be represented simply by plane wave Y k ( r ) = exp(ik-r) . (1-6) In Equation 1.6, r is the position vector, k is the wave vector which specifies the electron beam direction and is related to electron energy (E) by the expression (1.7) where m is the mass of electron and "h" is Planck's constant divided by 27C. For an incident and a diffracted electron beam of wave vectors ko and k respectively, the scattering cross section resulting from the interaction with a surface can be expressed conveniently as [Mes61] 0-8) Here T is the transition operator and < *F.. ITI *F. > is the transition matrix element which 11 Figure 1.4 Schematic diagram of the LEED geometry. The primary electron beam has energy E and its direction is defined by the angles 0 and <j>. Two diffracted beams are shown and the 1(E) curve for one of them is indicated (taken from Ref. [E77]). 12 gives the scattered amplitude. When the surface structure is invariant under a symmetry operator S, the transition matrix < ^ ITI *Fk > is also invariant [Mes61,SJJ75]. This gives < ¥ . I T I ¥ . > = < » P , I S * 1 T S ! ¥ . > = < S » F . I T I S X P V > (1.9) k *o k £o k Bo' If S represents a translation operator of the surface, then s ^ ( r ) = Y k (r + t_) , (1.10) where t is a translation vector defined as in Equation 1.3. Then, Equation 1.9 becomes < ^ I T I ^ > = exp^i(k^-k')tj < ^ I T I ^ > , (1.11) and Equation 1.11 is satisfied only if either < ITIW. > = 0 or exp £i (k0 - k' )-tj = 1. The former implies zero scattered intensity, while the latter is the necessary condition for the occurrence of a diffracted beam, that is - k)-t=2nic where n is an integral value. Hence, the conditions for elastic backscattering from the crystal surface can be summarized by energy conservation 2 _ i 2 | k o + | = |k' f (1.12) and by momentum conservation parallel to the surface £// = - V I ( h ' k ) • ( L 1 3 ) In these equations, the superscripts +/- identify the wave vectors (hrecting into/out of the crystal surface, g (h,k) is a reciprocal space vector defined in Equation 1.4; the indices (h,k) conventionally label the diffracted beams (e.g. (0,0), (1,0), etc.). In most LEED systems, the diffracted beams are collected on a hemispherical fluorescent screen with the 13 sample at the centre. The arrangement of diffracted spots, the so-called LEED pattern, results from the intersection of the diffracted electron beams with the fluorescent screen, and is direcdy determined by the reciprocal net of the surface. A detailed example is shown in Figure 1.5. According to Equation 1.13, the position of the specular beam (i.e. (0,0)) is invariant with the change of incident electron energy since there is no transfer of momentum parallel to the surface. However, as E increases, the perpendicular components of all other diffracted beams (i.e. k) increase, so that all non-specular beams move toward the (0,0) beam on the screen. The diffracted intensity distribution results from the electron scattering occurring within the 3-dimensional region where the probe electrons can penetrate without experiencing energy losses. However, the pattern of the diffracted spots on the screen can only provide information on the diperiodicity of this surface region, specifically information on the size and shape of the associated unit mesh. Understanding of the precise atomic arrangement in this region can only be achieved by analyzing the intensities of the diffracted beams, especially as a function of electron energy which forms the intensity-versus-energy (1(E)) curves. The analysis of structural information from 1(E) curves is made by a "trial-and-error, approach. 1(E) curves for various surface structure models are calculated by the multiple scattering formalisms described in Chapter 2, and they are compared with experimental 1(E) curves to find the surface model which gives the best agreement with experiment. By this means, surface structural information such as adsorption sites, interlayer spacings and bond lengths can be obtained. 1.2.3 Notation of LEED patterns Ordered structures resulting from adsorption on clean surfaces usually give a larger unit mesh than that of the clean surface. This leads to "extra" spots compared with the Figure 1.5 Schematic diagram illustrating how the conservation conditions determine direction of a diffracted beam. The (0 0) beam corresponds to the specular reflection. >— 4*. 1 5 corresponding LEED pattern of the clean surface. There are two nomenclatures in common use, namely Wood's notation [W64] and matrix notation [PM68.EM71] to classify the surface structure. Both these notations relate the unit mesh vectors bj and b2 for the surface region to those of the substrate, &l and a2. In Wood's notation, the surface region probed by the LEED electrons is designated as Ibil Ibjl S ( h k l ) - ( f - x — ) a - r , X , (1.14) where S(hkl) is the particular crystallographic plane (hkl) of the substrate S, X is the adsorbate species, TJ is the number of X species in the unit mesh, and a is the angle of rotation between the two unit meshes. Conventionally, a is omitted in the notation if bj is parallel to a} and b2 is parallel to a2. In the Matrix notation, the relations of the unit mesh vectors are expressed as ^ = m 1 1a 1 +m 1 2 S 2 , (1.15) and h~2 = ^llh + m 2 2 a 2 • C1-16) or more concisely as b = Ma, where the matrix M provides a more general designation of the surface region with respect to the substrate, and the surface can be designated as S ( h k l ) - M -T iX , (1.17) where S(hkl), TJ and X are as in Wood's notation and M is the matrix defined by Equations 1.15 and 1.16. Figure 1.6 shows some examples of these notation for adsorption on (111) surfaces of fee metals. Figure 1.6 Some common translational symmetries (unit meshes) for adsorption of species X on (111) surfaces of fee metals M using both Wood's notation and the matrix notation. 17 1.3 Auger Electron Spectroscopy (AES) The production of electrons by the Auger process was first identified by Pierre Auger [A25] in 1925. The mechanism of the Auger process is simply depicted in Figure 1.7. After an atom is initially ionized in one of its inner shells, either by electron or photon impact, the excited ion rearranges itself by filling the ionized shell with an electron from a higher energy orbital. The energy released in this transition may be used to eject another electron, which becomes an Auger electron on leaving the atom The kinetic energy EKE of the Auger electron is determined by the three energy levels involved; therefore it is independent of the primary energy used to ionize the atom and it is characteristic of the parent atom. This allows Auger Electron Spectroscopy to "fingerprint" all the elements in the periodic table except hydrogen and helium. Another de-excitation process which competes with Auger electron emission is X-ray fluorescence in which the released energy is used to emit a photon. For the lighter elements with atomic number Z smaller than 30, the Auger effect is relatively efficient, but even for heavier elements, Auger emission dominates if the binding energy of the initial core level is about 2 keV or less. In surface analysis, Auger electrons with energies between about 50 and 1000 eV are of interest since their escape depths are limited to just a few interatomic layer spacings. As mentioned in Section 1.2.1, the Auger peaks are generally superimposed on a rather large background, and therefore differentiation methods are commonly used to extract the Auger information from the background. The energy distribution N(E) and the first derivative dN(E)/dE for a beryllium sample [H68] is shown in Figure 1.8 to illustrate the advantage gained by differentiation. Conventionally, the Auger energy is identified by the position of m a x i m u m negative derivative. In this work, AES is mainly used for the qualitative analysis of sample surfaces. This is efficiendy accomplished through the comparison with standard spectra [PRW&72] 1 8 KLJLJ AUGER ELECTRON HOLE Figure 1.7 Schematic diagram of an Auger process to produce a K L 7 L 3 Auger electron. 0 Figure 1.8 Auger spectra from a Be sample, (a) Energy distribution, (b) First derivative dN(E)/dE (taken from Ref. [H68]). vo 20 and tabulated energies [PW73]. For semi-quantitative analysis, the relative Auger peak height ratio provides a simple and convenient way for expressing relative concentrations of adsorbates on a surface (see Section 4.1.2), but the determination of absolute adsorbate concentrations requires a suitable calibration with an other technique [EK85] such as LEED [P71], radioactive tracer [P72], evaporated films [BP72] and ellipsometry [MV72]. 1.4 Aims of thesis The studies presented in this work represent a contribution to the application of LEED crystallography for surface structural determination. In particular, specific investigations on adsorbate-induced metal relaxations have been made when S is adsorbed on the Ni(l 11) and Rh(l 11) surfaces to form structures designated as Ni(l 1 l)-(2x2)-S and Rh(lll)-(V3xV3)30°-S. A developing topic in structural chemistry is surface structural chemistry. Studies over the last few years with a range of experimental probes, but especially LEED, are helping to establish principles for the detailed atomic arrangements in systems which involve the chemisorption of electronegative atoms or small molecules on well-characterized surfaces of transition metals [M85,MSS86]. In certain cases substantial reconstructions of the metallic structure have been indicated [E84], although even where this is not the case relaxations can still occur. Indeed, even for clean transition metal surfaces, the relaxations found at surfaces of lower symmetry provide an interesting area for the interplay of theory and experiment [JJM87]. In this situation, relaxations at close-packed surfaces are generally indicated to be of the vertical type and of small magnitude, although with chemisorption the situation could be different. For example, some 10 years ago Theodorou [T79] used a force-constant model to predict lateral displacements of magnitude 0.08 A for the (110) surface of tungsten when O is chemisorbed in a (2x1) 2 1 structure; a more recent theoretical analysis [CHN85] for O at the (111) surface of nickel indicated lateral displacements of similar magnitude for subsurface bonding although not for above-surface chemisorption. Nevertheless some experimental evidence seems compelling for metallic lateral relaxations with chemisorption, and this includes the (110) surface of iron in the presence of adsorbed S where displacements of magnitudes 0.12 A and 0.20 A have been reported [SJJ&81], and, for more open surfaces, the indications of p4g space group symmetry for the (100) surface of nickel with half-monolayer coverages of either C [OWH79] or N [DLI86]. The motivations for this work are three-fold. Firstly, the chemisorption bond lengths reported earlier in LEED studies for the (2x2) surface structure formed by S [DJM74a] chemisorbed on the Ni(lll) surface appear to disagree with predictions (by 0.10 A or more) from current bond order-bond length relations [MSS86], and that suggests the need for reanalyses. Secondly, the indications that lateral displacements in metallic surface structures may sometimes occur with chemisorption opens the need for further assessments of their occurrence; indeed close-packed surfaces are an important type insofar as they may seem least likely to undergo such relaxations. Lastly , a point of interest here is the Rh(l 1 l)-(V3xV3)30°-S surface for which.an earlier LEED from this laboratory [WZH&85] showed a less than totally convincing correspondence between experiment and calculation for the favoured surface structure. That opens the question of whether the earlier discrepancies indicate the existence of some relaxations in the metal structure which are not included previously. The layout of this thesis is described as follow. Chapter 2 briefly describes the "combined space" approach in LEED multiple scattering calculations for the diffracted beam intensities, and the important non-geometrical parameters required in the calculations. The reliability index routines used for making comparisons of experimental and calculated 1(E) curves are also described. Chapter 3 examines some general experimental aspects in 2 2 LEED/AES studies. Chapter 4 reports the LEED crystallographic studies for both NifJ 1 l)-(2x2)-S and Rh(l ll)-(V3xV3)30°-S surface structures. A set of experimental 1(E) curves has also been measured in the present work for the Ni(l 1 l)-(2x2)-0 surface, and these curves are shown in the appendix. Chapter 2 LEED Intensity Calculations 24 2.1 Introduction Structural determination by LEED is mainly achieved by comparison of experimental and calculated 1(E) curves. Hence a proper theoretical treatment of LEED intensities is an essential requirement. It is recognized that low-energy electrons interact very strongly with a solid so that the probability that an electron is scattered by an atomic centre can be many orders of magnitude larger than that encountered in X-ray scattering [VT79]. As a result, multiple scattering processes are involved, and this gives rise to the complexities of LEED. For example, many structures in 1(E) curves cannot be explained by the simple single scattering theory used in X-ray diffraction. Thus, LEED intensity analysis should be accomplished with multiple scattering calculations; the latter are often referred to as "dynamical" calculations because they consider not only the geometrical parameters but also the non-geometrical parameters which describe the strong interaction of a low-energy electron with the atomic scattering centres. The potential within and between the atomic scattering centres (vibrating ion cores) plays an important role in the "dynamical" calculations. To a good approximation, the potential of a solid can be described with the muffin-tin-model, where the potential between ion cores is assumed constant and the potential within the cores is spherically symmetric. Details of the muffin-tin model will be discussed in Section 2.2. In multiple scattering calculations, the electron wave function may be expressed in terms of spherical waves or plane waves. Some methods for calculation use only one such representation, whereas more commonly both representations are used in different parts of a calculation. The use of spherical waves defines the L-space representation. This is used to describe the scattering of low-energy electrons by the spherically symmetrical ion cores, as well as the multiple scattering between atoms within a single layer parallel to the surface. The use of plane waves defines the K-space representation, and it is conveniently used to describe the wave function between successive layers in so far as the potential can be taken 25 as constant The LEED intensity calculations made in this work were accomplished with the following steps: (a) The atomic scattering amplitude was calculated in L-space. (b) The multiple scattering between atoms within a single layer was calculated in L-space. (c) The stacking of individual layers and the interlayer multiple scatterings were perturbationally treated in K-space. The end effect is that the calculated intensity of a diffracted beam g can be obtained as k " I = — 5 k + - O J . where superscripts"+/-" denote wave vectors directing into/out of the crystal surface, and kg depict the incident and diffracted beam respectively while C is the coefficient in the expansion of the total wavefield outside the crystal, namely ¥ o u t ( r ) = exp[ik:.r] + £c g e x p [ i k - r] . (2.2) g Full detailed descriptions of the theoretical methods are available in the literature [P74,C85,HWC86], and the computer programs used in this study are mainly from Van Hove and Tong's book [VT79] and the magnetic tape provided by Dr. Van Hove of the University of California, Berkeley. The purpose of this chapter is to briefly introduce the general physical ingredients of the LEED intensity calculations used in this study. 2.2 Muffin-tin- approximation The muffin-tin-model shown in Figure 2.1 is commonly used for representing the potential of an ordered solid It considers the crystal as composed of ion cores embedded in (2.1) 26 X ION CORES Figure 2.1 Variation of potential for the muffin-tin model: (a) contour plot through an atomic layer, and (b) variation through a single row of ion cores along the X-axis. 27 a "sea" of electrons. The potential within each ion core, V s , is assumed to be spherically symmetrical, while the potential between ion cores is taken as constant V 0 , which is the so-called muffin-tin constant. Generally, the muffin-tin constant Vo is given as the sum of a real part (Vor) and an imaginary part (V0j), i.e. V 0 = V 0 r + iVoi . (2.3) The real potential V o r deterrnines the change in kinetic energy that a LEED electron undergoes on entering or leaving the solid through the surface. Owing to the exchange and correlation effects, V o r is strictly energy-dependent. However the variation is not generally great for LEED calculations, where it is usually treated as an energy-independent and adjustable parameter. Typically its value is between -5 and -15 eV [HWC86], and it can be refined during the optimal matching between the experimental and calculated 1(E) curves. The imaginary part V 0i is a negative quantity which simulates the attenuation of the electron beam due to inelastic processes. Its value can be estimated from peak widths, AEW, in the experimental 1(E) curves. From the time-energy uncertainty principle, Pendry [P74] relates AEW to V 0 i as AE W > 2lVoil . (2.4) In practice, V 0 i is treated as constant or slighdy energy-dependent, Demuth et al. [DMJ75] proposed a energy-dependent V 0 i as V o i = - B E 1 / 3 • (2.5) where B is a material-dependent parameter and E is the incident electron energy. 28 The ion core potential Vs can vary considerably from one chemical species to another, but the effect of environment is generally small since electrons are scattered primarily by the nuclear potential. For the purpose of surface structural determination by UEED, appropriate metal potentials are generally derived from band structure calculations [MJW78], while for the light atoms an appropriate potential is often derived from a superposition model [D74] designed to simulate atoms in overlayer situations [MDJ75]. 2.3 Phase shift The wave function of electron scattered by a spherically symmetrical potential,Vs, can be obtained by solving the Schr&linger equation - r 2 - ( 2 n T ) V + V s (2.6) where E is the energy set by the vacuum level. The asymptotic solution is written as [Mer61,MM65] ¥ k ( r, 0s) ~ exp [i k r cos 61. + F(k, 9() exp [—] , (2.7) where r is the distance from the atomic nucleus, 9 S is the scattering angle and F(k,8s) is the atomic scattering amplitude which is defined as F(k, 9s) = 4 Tt ] £ ( 21 + 1) L(k) P (cos 9s) 1=0 (2.8) Here PT is the Legendre polynomial associated with the angular momentum quantum number 1 and tj(k) is the t-matrix element defined as 1 tj(k) = ^ exp[i8,] sin5j (2.9) 29 The quantities 6j are phase shifts which determine the total elastic scattering cross-section according to °ei = ~7 2/ 21 + 1) sin28j . (2.10) k i=o Oj can be obtained by solving Equation 2.6 for the appropriate ion core potential Vs and matching smoothly to solutions outside the muffin-tin sphere. In Equation 2.8, it involves a sum over 1 from zero to infinity but in practice the sum can be truncated at a tractable limit which depends on both electron energy and atomic scattering strength. The effect of thermal vibrations is included by multiplying a Debye-Waller-type factor (exp(-M)) to each atomic scattering amplitude F(k,9s): F(k, 0s)T = F(k, 6s) exp(-M) , (2.11) where M = I | A k | <(Ar)2>T • (2.12) In Equation 2.12, Ak is the momentum transfer resulting from the atomic scattering and 2 <(Ar) > is the mean-square vibrational amplitude as a function of temperature T. With the high-temperature and low-temperature limits proposed by Van Hove and Tong [VT79], 2 <(Ar) > can be expressed as <(Ar)2 >T - 7 [ < ( ^ 2 > T J ^ [ < ^ ) 2 > T J 2 , < 2 ' 1 3 > where 30 9T (2.15) Here m is the atomic mass in atomic units, ks is Boltzmann's constant and GD is the Debye temperature which measures the rigidity of the lattice with respect to vibration. 2.4 The Layer Diffraction Matrix The scattering of plane waves incident on either side of a layer parallel to the surface is described by the diffraction matrix M - . For a Bravais-lattice layer with only one atom per unit mesh, the diffraction amplitude between the incident plane wave exp(i k - r) and the scattered plane wave exp(i k ,• r) is the particular matrix element M*, 1 which can be written as [P74] where the g and g' are reciprocal lattice vectors of the surface which has a unit mesh area A, the superscript sign "+/-" specify the propagator toward the bulk or toward the vacuum respectively, L and L' correspond to pairs of angular momentum quantum numbers (1, m) and (1', m') respectively, YL(kg) is a spherical harmonic, "*" represents the complex conjugate, and TLL' is the LL' element of the planar scattering matrix which is defined as ( (2.16) ~ g ± LL |(ko) = |(ko) [J-X] l - l (2.17) where X = G(k;)t(ko) (2.18) 31 In Equation 2.18, t (kQ) is a diagonal t-matrix of a single ion-core, its non-zero elements are given in Equation 2.9. In Equation 2.17, X is the intraplanar multiple scattering matrix, which is a product of a structure factor G (k*) and the t-matrix. For a layer with more than one atom per unit mesh (for example N atoms), the layer should be treated as a composite layer with N subplanes, which have identical Bravais lattices but their atoms may be of different species. A graphitic (2x2) sulfur overlayer on Ni(lll) is shown in Figure 2.2, where each unit mesh has two sulfur atoms. Then, the sulfur layer is split into two subplanes. According to Beeby [B68], the total scattering matrix T 1 for particular subplane i is obtained by solving the equation " l 1 " V " T 2 • = A"1 • *** where T 1 is the individual planar scattering matrix calculated for each isolated subplane i, and A is a matrix of N 2 smaller matrices A *J defined as A* = I, and A i j = _ T j G i j . (2.20) Here G y is the structural propagator which describes the interplanar propagator from subplane j to subplane i. The diffraction matrix elements M^.* for the entire composite layer are expressed as Figure 2.2 Graphitic-type sulfur overlayer for Ni(l 1 l)-(2x2)-S; there are two sulfur atoms (full circles) per unit mesh, one on a 3f site the other on 3h site. 33 (2.21) where Rg* = exp[ ±ik*. T{ ] . (2.22) The quantity r is a position vector which relates the reference atom in subplane i to an arbitrary reference point of the composite layer. 2.5 Layer Stacking The total diffraction by a crystal can be calculated by exact methods (i.e. to infinite order in the number of scatterings) but this is very demanding for both computer time and computer storage. Based on the assumption of strong inelastic scattering inside the crystal, the combined-space method proposed by Tong and Van Hove [TV77,VT79] can be employed to operate the LEED calculation. This method treats the layer (either a Bravais layer or a composite layer) scattering matrix M** exactly in L-space (as mentioned in Section 2.4) and then forms the diffraction matrix for a stack of such layers in K-space. In this work, the total diffraction of the crystal is mainly done by a perturbation scheme which is known as the renormalized forward scattering (RFS) method [P74], The RFS technique introduced by Pendry [P74] follows the assumption that forward scattering is much stronger than backward scattering. Hence, it is possible to treat the former exactly but the latter perturbationally. The mechanism of RFS is depicted in Figure 2.3a. The first-order calculation considers all scattering paths which involve a single reflection process; the second-order calculation contains only triple-reflection paths, and so on. This procedure is repeated for higher orders until the sum of successive order results 34 P * ( n - 1 ) P*(n) - irc»). = u / a~(n)V f " ( n ) (n) P"(n + 1) (b) (c) Figure 2.3 Diagram of the renormalized forward scattering method, (a) Each triplet of arrows represents the complete set of plane waves that travel from layer to layer. Ni, N 2 and N3 denote the deepest layer reached in the 1st, 2nd and 3rd order scatterings respectively, (b) and (c) Illustration of the vectors which store of the inward-traveling wave (a*) and outward-traveling waves (a7). 1 35 converges. The amplitude of the plane wave in the nth interlayer spacing can be expressed for inward direction (Figure 2.3b) as [VT79], a+(n) = £ + P + ( n - l ) a ^ ( n - l ) + r + - P_(n)a^(n) , (2.23) and for outward direction (Figure 2.3 c) a~(n) = f ' P l n + lJa^n+lJ + r"* P+(n)a*(n) (2.24) where i is the index of the i * order of iteration (i.e. the number of times that the electron has propagated into the crystal), t and r are layer transmission matrices and reflection matrices respectively, P are plane wave propagators between appropriate reference points in neighbouring layers. The calculated amplitude can be conveniently stored as a column vector. At n=0, the amplitude of the incident beam in vacuum is 1 0 0 while all other a*(0) (i>l) are necessarily zero vectors because there are no inward-traveling plane waves in vacuum for the higher order iterations. The iteration starts with the input of the unit vector a*(0) and the zero vectors a~(n) into Equation 2.23, as the calculation of a* (n) is run from n equal 1 to Ni-1, where Ni is the deepest layer penetrated by the electron in the first propagation into crystal. Thus, the calculated a*(n) is substituted into Equation 2.24 to obtain the a~(n). After the first iteration, the reflected wave amplitude in vacuum is stored in a~(0). A similar procedure is repeated to obtain &~( 0), a^ ( 0),... and then the total reflected amplitude A can be expressed as A = aj (0) + a2(0) + a3 (0) + (2.25) and at convergence the beam intensities are given by 36 g 2 Typically, the RFS method uses 12-15 layers and 3-4 iterations for convergence. It has proved to be an efficient technique for calculating LEED intensities for different surface structures provided the electron damping is sufficient and all interlayer spacings are greater 2.6 Evaluation of Calculated LEED Intensity Structural determinations with LEED are based on the so-called trial-and-error method. Among a variety of plausible surface models, the one that gives the best agreement with the measurement is considered to be the most likely model. Traditionally this evaluation was done by the visual comparison between the experimental and calculated 1(E) curves. However, this comparison is inevitably subjective, and it becomes less reliable when large numbers of curves must be compared. Consequendy, a quantitative and objective criterion for comparison is needed. Various reliability factors (R-factors) have been proposed for LEED [VK84], but those introduced by Zanazzi and Jona [ZJ77] and by Pendry [P80] are most commonly used. The former emphasizes the peak shapes and heights, whereas the latter emphasizes the positions of peaks and troughs. The Zanazzi and Jona index attempts to quantify all those features evaluated in a visual comparison. For a single beam, the Zanazzi-Jona R-factoris defined as than about 1.0 A. (2.26) 1 where (2.27) 37 is used to make the index dimensionless. Icaic and IeXpt are the calculated and experimental intensities respectively, and the single and double primes stand for the first and second derivatives with respect to energy E respectively; c is a scaling constant defined as I , dE expt c = • (2.28) J J When comparing many beams, the many-beam Zanazzi-Jona R-factor can be written as XATZJAE1 RZJ = - i , (2.29) i where i runs over all the individual beams and AE1 is energy range in each individual beam. The many-beam R-factor proposed by Pendry is defined as y f ( Y . - Y . )2dE *-*J 1 expt 1 cacl R = _J , (2.30) p XJ(Y i 2 .__.+Y l 2 . . . t )dE where and expt 1 cacl Y = — £ - . (2.31) L + V . 0 1 V 0i is the imaginary component of the muffin-tin constant potential used in the calculation. Chapter 3 39 3.1 The UHV Chamber The experiments in this work were carried out in a Varian FC 12 vacuum chamber which is made of demagnetized stainless steel components joined together by flanges with copper gaskets. Figure 3.1 is a schematic diagram of the UHV chamber equipped with the following facilities : an electron incidence gun (Varian 981-2125) and hemispherical 4-grid LEED optics (Varian 981-0127) for LEED study; a glass viewing port for observing diffraction pattern; a glancing incidence electron gun (Varian 981-2454) for Auger study, a single pass cylindrical mirror analyzer (Varian 981-2607) for analyzing Auger electrons; an ion bombardment gun (Varian 981-2043) for cleaning by Ar + ion bombardment; a nude ion gauge for measuring the pressure; a variable leak valve (Varian 951-5100) for letting in gases; and a molybdenum sample holder with a resistive heater (Varian 981-2058) mounted on a manipulator (Varian 981-2530). The manipulator allows three degrees of translational and two degrees of rotational freedom, and the temperature of a sample is measured by a 0.005 inch chromel-alumel thermocouple. Any stray magnetic Melds in the chamber are effectively neutralized by the use of mutually perpendicular Helmholtz coils. The pumping system for this FC 12 chamber, shown in Figure 3.2, consists of a central ion pump (200 Ls~l), an oil diffusion pump, an auxiliary titanium sublimation pump, two sorption pumps and a small ion pump (20 Ls"l) for the gas inlet line. In the start-up procedure, rough pumping from atmospheric pressure to the 10~2 torr range is achieved by the sorption pump. Further pumping to 10"? torr range is obtained by a water-cooled and liquid-nitrogen-trapped oil diffusion pump. At this stage, the central ion pump can be used to reach the 10~8 torr range. In order to achieve the ultrahigh vacuum, the chamber is baked at -200 °C for 12-15 hours with the titanium sublimation pump on. After baking, all filaments are degassed while the chamber is still hot Then, the chamber is allowed to cool to room temperature and pressure in the 10"10 or even 10"!1 torr range can be reached. 40 LEED OPTICS VIEW WINDOW Figure 3.1 Schematic diagram of the FC12 UHV chamber and some of its important assessories. 41 GAS BULBS LEAK VALVE SMALL ION PUMP DIFFUSION PUMP SORPTION PUMPS S.P. MAIN ION PUMP S.P. TITANIUM SUBLIMATION PUMP Figure 3.2 Diagrammatic representation of the pumping system. 42 3.2 Sample Preparation and Cleaning The Ni(l 11) face used in this work was prepared from a 1/4 inch diameter single-crystal rod of 99.999 % purity (grown by A. Akhtar, Department of Metallurgy, University of British Columbia). The crystal was mounted on a goniometer and oriented using the Laue back-reflection method [HLW60,KJ74]. After orientation, the sample was cut by the spark erosion technique ('Agietron', Agie, Switzerland) with the surface parallel to the crystallographic plane (111). It was then mounted in an acrylic resin CQuickmount1, Fulton MetaUurgrical Products Corp., USA), and glued to a polishing jig equipped with alignment micrometers. This allowed the orientation of the surface to be adjusted and checked during cutting and polishing until it corresponded with the (111) plane. The jig assembly was put on to a planetary lapping system (DU 172, Canadian Thin Film Ltd.) for mechanical polishing with succesively finer diamond paste from 12 to 6 micron. Then 3-\x and 1-JJ. diamond polishings were done manually on artificial deerskin (Microcloth, Buehler 40-7218). After the polishing, the jig was fixed on an optical bench, and as illustrated in Figure 3.3, a Ne/He laser was used to check that the orientation of the optical face was parallel to the desired plane to within 1/2 degree. When the satisfactory orientation was obtained, the resin was dissolved in actone. The sample was then degreased in trichloroethylene and consecutively washed in acetone, methanol and distilled water. After drying, the sample was mounted on the UHV manipulator and a set of 0.005 inch chromel-alumel thermocouple wires were spot-welded onto the top of the sample cup. The sample was then placed in the vacuum chamber. Following the pumping procedure described in Section 3.1, the base pressure of the chamber reached was about 2xl0"!0 torr. AES showed that C, O and S were the main impurities at the nickel surface. The cleaning process in the UHV chamber was initially performed by Ar+ ion bombardment (-2-3 uA/cm2, 600-1000 V) followed by annealing at -600-700 °C for 5 min. During the ion bombardment, the titanium sublimation pump was operated to pump away impurities LASER SOURCE He/Ne identical brass stands • • paper micrometers (a) mn crystal mm in i ii i III mi ii 11 mi III III i III ii 11 parallel optical benches Figure 3.3 (a) Schematic diagram of laser alignment of optical and crystallographic planes of a single crystal, (b) A blow-up to show the relationship between the optical and crystallographic planes. Alignment is acceptable when 6^1/2* (taken from Ref. [H86]). 44 sputtered from the surface. After eight cycles of Ar4" ion bombardment and annealing, all the carbon and oxygen could be removed but sulfur segregation still occurred after each heating treatment. Therefore, during ion bombardments (~2-3 hour), the sample was kept at elevated termperature (~600-700 C) to drive the sulfur to the surface. After ten cycles of high-temperature Ar+ ion sputtering, the sulfur segregation was eliminated, even for severe annealing to 800 °C for 5 minutes, no impurities could be detected by Auger analysis. The clean surface was also characterized by a (lxl) LEED pattern with sharp and intense diffraction spots. 3.3 Auger Electron Spectroscopy In this work, AES was mainly used as a qualitative technique for surface composition analysis. The general components of the Auger spectrometer are illustrated in Figure 3.4. The glancing angle electron gun provides a primary electron beam with energy around 2 keV, a current up to 200 uA and a spot area of 1 mm .^ The Auger electrons are detected by a single-pass cylindrical niirror analyzer (CMA) which basically consists of two co-axial cylindrical electrodes. The inner cylinder is earthed and a variable negative potential -U a is applied to the outer cylinder. For a particular U a , only the electrons in a restricted energy range can be deflected and re-focussed to the electron channel multiplier [EK85]. By scanning the potential -Ua applied to the outer cylinder, the signal received by the multiplier directly gives the energy distribution of electrons N(E) [EK85]. As noted in Section 1.3 (see Figure 1.8), the Auger spectrum is expressed in a differential format; this is accomplished by modulating Ua with a small sinusoidal signal, Umsin cot. In this work, Um was about 10 V and the frequency co was set at 17 kHz. The amplitude of the signal recorded by the lock-in-amplifier at frequency co gives the differential distribution dN(E)/dE [EK85]. 45 SAMPLE GLANCING INCIDENCE ELECTRON GUN P R O G R A M M A B L E POWER S U P P L Y Umsin cot E L E C T R O N M U L T I P L I E R S I G N A L G E N . L O C K - I N A M P . R A M P G E N . H.V. + ISOLATION P R E A M P . 4 SCOPE X-Y PLOTTER Figure 3.4 Schematic diagram for measuring Auger electron spectra with a cylindrical mirror analyzer and glancing incidence electron gun. 46 3.4 LEED Apparatus 3.4.1 Electron Gun and LEED Optics Figure 3.5 shows a schematic diagram of a 4-grid LEED display system used in this work. Electrons emitted from a heated filament are collimated by a lens system and leave the drift tube with an energy deteraiined by the potential difference between the filament and the earthed sample. The drift tube is also earthed so that electrons traverse a field-free space to the sample. The typical incident electron beam used fpr LEED experiments in this work had an energy range of 30-250 eV, a beam diameter of 1 mm at the sample surface and a beam current which varied linearly from ~0.1 \iA at energy 40 eV to ~1 uA for energy above 100 eV. The beam current as a function of the incident electron energy had to be recorded in order to normalize the measured LEED spot intensities. The display-type LEED system consists of a hemispherical fluorescent screen and four concentric grids labelled Gi to G4 in Figure 3.5. Since the grid Gi is grounded, the back-scattered electrons travel in a field-free space between the sample and G1 . A suitable negative potential which is slightly smaller than the incident electron energy is applied to both grids G2 and G3 to suppress the inelastic back-scattered electrons. Grid G4 is also earthed to reduce the capacitance effects between the suppressor grids and the fluorescent screen; the latter has a positive voltage (~5 keV) to accelerate the elastically scattered electrons onto the screen to render the diffracted spots visible. 3.4.2 LEED Intensity Measurement A real time LEED intensity measurement was performed in a combined system which consists of a Cohu 4410ISJT TV camera and a video LEED analyser (VLA) from Data-Quire [DQ82]. Its principal features are shown in Figure 3.6. The ISIT camera is basically equipped with a photocathode tube and a silicon target A complete LEED pattern Figure 3.5 Schematic diagram of the electron optics for the T.FRn display system (taken from Ref [W87]). T.V. MONITOR X-Y RECORDER SCOPE TERMINAL T.V. CAMERA SCREEN VIDEO A/D CONVERTOR V I D E O S I G N A L ISIT LENS MOTOROLA 6800 D/A CONVERTOR FLOPPY DISKS MODEM SAMPLE / GUN LEED CONTROL UNIT MAIN COMPUTER Figure 3.6 Schematic diagram for the TV analysing system. 49 focussed by the TV camera is continuously displayed on the monitor. The videosignal from the camera is sent simultanously to the microprocessor (Motorola 6800) via an A/D converter. The microprocessor is also used to control the LEED gun voltage via a D/A converter. The image of the LEED pattern on the monitor defines a video frame which consists of 256x256 pixels. The intensity values for each pixel vary from 0 to 255. For LEED intensity measurement, the required spot is covered by a window of 10x10 pixels on the monitor and its intensity is obtained by integration of the video signals within that window. The VLA system used in this work can simultaneously measure up to 49 isolated spots. Both selection and integration procedures are performed with the aid of the processing computer which controls the window for following the movement of the spot as the incident electron energy is changed. In practice, it is better to measure fractional and integral beams separately with different gain level settings in order to minimize background effects. The required 1(E) curves are then normalized according to the expression i = r/i0 , (3-D where I' and Io are measured diffracted and incident beam currents respectively. In this work, the 1(E) curves were recorded with the primary electron beam coincident with the 3-fold axis of the (111) face. Hence, the symmetrically equivalent beams could be measured simultaneously. Figure 3.7 shows a set of 1(E) curves for the Ni(lll)-(2x2)-S system. The curves (a) to (e) represent 5 of the 6 equivalent (1/2 1/2) beams. These equivalent curves were averaged (curve (f) in Figure 3.7) and then smoothed (curve (g) in Figure 3.7) twice using the cubic spline method [UBC84], The smoothed experimental 1(E) curve was used for comparison with the calculated 1(E) curves, and similar procedures were used for the other measured beams. 50 Figure 3.7 (a)-(e) are five measured symmetrical equivalent 1(E) curves of (1/2 1/2) beam for the Ni(l 1 l)-(2x2)-S surface at normal incidence. They are averaged (f) and finally smoothed (g). 5 1 Chapter 4 Investigation of the Chemisorption Structures of Sulfur on the (111) Surfaces of Nickel and Rhodium 52 Parti LEED Stricture Analysis of the Ni(lll)-(2x2)-S Surface: A Case of Adsorbate-induced Metal Relaxation 4.1.1 Introduction In addition to the general interest of extending fundamental knowledge on chemisorption, the adsorption of sulfur on surfaces of transition metals is also a subject of practical interest which has been under active investigation. In particular, sulfur acts as a powerful modifier of certain catalytic reaction rates. For example, sulfur effectively poisons the methanation of CO on nickel [BK80.GK81] but promotes the nickel carbonyl formation reaction [GM81]. The determination of geometrical structure of these chemisorption systems is therefore fundamental and urgently needed for better understanding of such technologically important processes as S poisoning in catalysis and sulphidisation [N80,S72]. However, most studies of chemisorption on low-index metal surfaces have assumed that the basic metallic structure is maintained, even though reconstructions are sometimes apparent from diffraction patterns in low-energy electron diffraction (LEED) [E84]. Therefore, the quantification of adsorbate-induced geometrical changes to metallic surface structure is important for developing detailed accounts of surface electronic structures and ultimately other properties. Part I of the present work reports a LEED crystallographic study which assesses the metal relaxation for the (2x2) surface structure obtained by the adsorption and presumed dissociation of H2S on the (111) surface of nickel. An investigation of the adsorbate-induced metal relaxations for the Rh(lll)-(V3xV3)30°-S surface will be featured in Part II of this chapter. A number of structural studies for the Ni(lll)-(2x2)-S surface have agreed [DJM74a,CSG&82,FDH86,OKS&86] that S chemisorbs above the threefold sites (3h or 3f)t of the unreconstructed Ni(lll) surface, that is the adsorption occurs at sites of highest coordination on the surface. However, angle-resolved Auger electron spectroscopy [AW84] and angle-resolved inverse photoemission [DDD&] suggest that only one of the two threefold sites is occupied but cannot distinguish between them, while the previous LEED studies [DJM74a], as well as that of low-energy ion scattering in the impact collision mode (ICISS) [FDH86], show that sulfur adsorbs in the threefold hollow site (3f). Moreover, an earlier LEED study which assumed no relaxation in the metal structure proposed that the topmost Ni-S interlayer spacing is 1.40 A [DJM74a]. This leads to a nearest neighbour S-Ni distance of 2.02 A which is significantly smaller than the value found when sulfur is adsorbed on other Ni surfaces (-2.18 A [DJM74a]). In addition, the ICISS study [FDH86] reported a nearest neighbour S-Ni distance of 2.16 A for the Ni(l 1 l)-(2x2)-S surface which is quite consistent with the value of 2.20 A found by the recent surface extended X-ray absorption fine structure study [OKS&86]. In view of the evidence that adsorption can cause distortion of substrate atom geometry [VTS&79,SJJ&81,ZFM88], it is worthwhile to undertake a new LEED crystallographic study to refine the previous analysis by incorporating relaxations into the first two Ni layers. 4.1.2 Experimental The apparatus and sample-cleaning procedures used in this work have been described in Chapter 3. The clean (111) surface of nickel which was characterized by a sharp (lxl) LEED pattern (Figure 4.1.1a) was exposed to high-purity H2S (Matheson Research Grade) at room temperature and at a pressure of -5x10*8 torr. A sharp (2x2) LEED pattern (Figure 4.1.1b) was obtained, as reported by others [DJM74a,CSG&82, t These two types of threefold sites arc distinguished by the respective presence (3h) or absence (3f) of a Ni atom in the second layer along the threefold axis. (a) • • • • • • • • • • • (b) Figure 4.1.1 Schematic indications of LEED patterns from surfaces designated: (a) Ni(lll)-(lxl); (b) Ni(lll)-(2x2)-S. 55 FDH86], after an exposure time of ~2 minutes. The Auger spectrum (Figure 4.1.2) taken after the formation of this pattern was used to assess the amount of adsorbed sulfur according to the measured Auger peak height ratio As=Ai52/A 6 i = 0.52 where A152 is the Auger peak height of sulfur at 152 eV while A^i is that of nickel at 61 eV. Intensity-versus-energy (1(E)) curves for diffracted beams from the Ni(lll)-(2x2)-S surface were measured with the TV camera and video LEED analyser (see Section 3.4.2) at normal incidence and at room temperature. As mentioned in Section 3.4.2, the final experimental 1(E) curves for symmetry-equivalent beams were averaged with equal weights to mirdmize any experimental uncertainties associated with small misalignments of the sample [DN82], and the averaged intensity curves were smoothed with two cubic spline operations. A total of ten symmetry-inequivalent beams were measured over the energy range 40-230 eV (see Table 4.1.1) with a constant increment of 2 eV. This set of 1(E) curves consists of three integral beams and seven fractional beams, (10), (0 1), (1 1), (1/2 0), (01/2), (1/2 1/2), (1 1/2), (1/2 1), (3/2 0), (0 3/2), are specified with the beam notation shown in Figure 4.1.3. 4.1.3 LEED Intensity Calculations Multiple-scattering calculations of 103) curves for the S/Ni(l 11) system were based on the combined-space method [VT79] using the computer programs provided by Dr. Van Hove of the University of California, Berkeley. Diffraction matrices for the relaxed Ni layer were calculated with up to four atoms per unit mesh and the layer stackings were done Table 4.1.1 Energy range of experimental 1(E) for Ni(lll)-(2x2)-S Beam Energy Range Index (eV) 10 50-228 01 50-228 11 140-228 1/2 0 48-100 01/2 48-94 1/2 1/2 44-150 1/21 90-148 1 1/2 90-198 3/2 0 120-228 0 3/2 120-228 58 1' -2 2 1 -2 3/2 -2 1 -3/2 3/2 # # I -2 1/2 -3/2 1 • • • .20 -3/21/2 .1 1 -1/23/2 02 -3/2 0 -1 1/2 • • t *<*^ • -3/2-1/2 _ -10 _ -1/2 1/2 01 1/2 3/2 1/21 • -3/2 2 • • -12 • -13/2 • -1/2 2 • -1/2 3/2 • -1/2 1 0 3/2 -1-1/2 -1/2 0 , -01 /2 -• • — — — t e : * 0 0 -1-1 -1/2-1/2 0 0 1/21/2 ^ 11 -1/2-1 _ 0-1/2 1 1/2 0 11/2 ^ -1/2-3/2 0-1 1/2-1/2 10 3/2 1/2 • • • • • 0-3/2 1/2-1 I 1-1/2 3/2 0 • • + • • 0-2 1/2-3/2 ! _ ! 3/2-1/2 2 0 • • I • • 1/2-2 1-3/2 I 3/2-1 2-1/2 1 -2 3/2-3/2 2-1 # I # 3/2-2 I 2 -3/2 2 -2 Figure 4.1.3 Schematic LEED pattern from Ni(l 11 )-<2x2)-S surface with beam indices. 59 with the renormalized forward scattering method [P74]. The calculations were performed on the Cray X-MP supercomputer at the University of Toronto in the energy range 40-230 eV in steps of 4 eV. A maximum of 32 symmetry-inequivalent beams were used in the calculations. The details of the non-structural parameters used in the calculations are as follows. Phase shifts up to 1=7 were derived from Wakoh's band structure potential for nickel [W65]; the real part of the constant potential (Vor) between the muffin-tin spheres was initially set at -11.2 eV for both the surface layer and the bulk, but the value of V o r was refined during the analysis according to the change in energy scale required to match the experimental and calculated 1(E) curves. The qualities of matching were evaluated by the LEED reliability indices RMZJ and Rp- The first is the modified form of that introduced by Zanazzi and Jona [ZJ77], which has been described in detail by Van Hove and Koestner [VK84], while the second is the reliability index introduced by Pendry [P80]. The sulfur phase shifts used in the present calculations were obtained from Van Hove-Tong's LEED package. These phase shifts were calculated by Demuth et al. [DJM74b] from a superposition potential associated with a hypothetical bcc sulfur lattice. The imaginary part (Vo0 of the potential between all atomic spheres was equated to -0.9E1/3 eV (where E is the electron energy in eV with respect to the vacuum level). The Debye temperatures were taken as 335 and 440 K for nickel and sulfur respectively [VT79]. The structures considered for the initial LEED calculations were models in which S atoms are held above the topmost Ni layer in one of the two types of threefold sites (3f or 3h), assuming no relaxation in the metal structure. For these LEED calculations, all Ni-Ni interlayer spacings were kept at the bulk value (2.033 A), while the topmost S-Ni interlayer spacings were allowed to vary from 1.30 to 1.65 A for the 3f site and from 1.10 to 1.65 A for the 3h site. Table 4.1.2 shows the results of the reliability index studies, including the optimization of appropriate geometrical parameters for the two adsorption sites (3f and 3h). 60 Table 4.1.2 LEED reliability index studies for adsorptions in 3f and 3h sites of the Ni(lll)-(2x2)-S structure Adsorption Site doi (A) 3f 1.49(1.50)t 3h 1.24(1.41) Vor (eV) rehability index -8.0(-7.6) 0.1226(0.1847) -7.2 0.2187(0.3113) t When two numbers are given as M(N), they correspond in order to numbers from the RMZJ and Rp analyses. 61 Relevant comparisons between experimental 1(E) curves for the (1/2 1/2), (1 1/2), (0 3/2) beams and the corresponding calculated 1(E) curves for models of 3f and 3h chemisorption sites are shown in Figure 4.1.4. Visual comparison shows poorer correspondence for the 3h site model than the 3f site model. This is confirmed by the reliability index analyses for which RMZJ (Rp) show respectively the minimum values 0.2187(0.3113) for the 3h site and 0.1226(0.1847) for the 3f site. Therefore, it is clear that S atoms chemisorb at 3f sites rather than 3h sites; this shows a strength of LEED: other techniques such as angle-resolved Auger electron spectroscopy [AW84] and angle-resolved inverse photoemission [DDD&] have agreed that only one of the two threefold sites is occupied, while not being able to identify which. However, even for LEED the level of agreement between experiment and calculation is still less than satisfactory, and it is clear that further structural refinement is essential. After the best adsorbate binding site was determined, a range of structures resulting from metal relaxation experienced by nickel atoms when S atoms is adsorbed at the 3f site have been studied. It is assumed that the possible relaxations are constrained by the diperiodic space group symmetry p3ml exhibited by the experimental LEED intensities, which includes both the threefold rotational symmetry and the mirror-symmetry. A sketch of the atomic arrangement in the adsorbate-induced metal relaxation model is shown schematically in Figure 4.1.5. This work therefore considers possible changes in values of the first nickel layer lateral displacement (A), the height of the sulfur atoms above the first nickel layer (dni), the spacing between first and second nickel layers (di2) and the spacing between second and third nickel layers (d23). That provides four separate structural variables and it is only feasible to optimize them over reasonable ranges of their values. Table 4.1.3 shows the structures which have been investigated in this work. In the present LEED structural refinement, surface structure determination was based on the matching of experimental and calculated 1(E) curves as indicated by the (a) 3f sites OT H-> • i-H cd H-> • i-H &H > H E-« i — i CO i i r 40 60 80 100 120 140 160 80 100 120 140 160 180 200 i 1 r 100 120 140 160 180 200 220 240 ELECTRON ENERGY (eV) Figure 4.1.4 Comparison of experimental 1(E) curves for (1/2 1/2), (1 1/2) and (0 3/2) diffracted beams from Ni(l 1 l)-(2x2)-S with those calculated for sulfur adsorbed at (a) the 3f and (b) the 3h sites over a range of interlayer spacings between sulfur and first Ni layer. (a) Top view © O / *" ** \ » t * / V _ + 0 o © ® / *" \ ' I * / v _ • o o / *" \ ' 1 * / s. ^_ ^» © ® 0 o I I * / N _ y 0 o o o o o .... o o . . . . © I I I I ' I ' I 0 o'; © o . © r © r. © ^ ^ O O -" o 0 0 0 0 © ° 0 ® 0 ? 0 ° o ° © # • I I I < I - ® -0 © (b) Side view o -I L. -I U a o T H2 <*23 bulk value o o o Figure 4.1.5 Notation used for Ni(l 1 l)-(2x2)-S surface structure. The model is viewed from above in (a) and from the side in (b) along the cross section marked by the line in (a). S atoms are represented by dark circles and Ni atoms by the larger circles. The circles which are open, dashed and shaded are for Ni atoms designated as of type A, B, and C respectively. Lateral displacements for atoms in the first Ni layer are fixed by the parameter A whose magnitude corresponds to the displacement from the regular bulk positions and whose sense is positive when the displacements are in the direction of the arrows shown. 65 Table 4.1.3 Structural refinement for Ni(l 1 l)-(2x2)-S Run dni A di2 d23 (A) (A) (A) (A) 1 1.30-1.65 0.0 2.033 2.033 2 1.50 -0.10-0.15 2.033 2.033 2 1.50 0.03 1.978-2.153 2.033 4 1.50 0.03 2.088 2.000-2.175 5 1.47-1.54 0.03 2.088 2.075 6 1.50 0.00-0.06 2.088 2.075 66 reliability index. Optimization of the four structural parameters (dfjl, A, di2, d23) was carried out iteratively over the range of values for each parameter as shown in Table 4.1.3. Six iterations were made by varying the value of one parameter at each iteration while the other parameters were fixed at values as indicated by the previous iteration. The iteration procedure was repeated until convergence of all the optimum parameters were obtained. The optimal values of the parameters were found by minimizing the basic LEED reliability index first introduced by Zanazzi-Jona [ZJ77], but in the modified form proposed by Van Hove and Koestner [VK84]. Further parallel evaluations of the experimental-calculation comparison of 1(E) curves were also made with the Pendry reliability index, Rp [P80]. Figure 4.1.6 gives the change of RMZJ corresponding to each iteration in Table 4.1.3 and Figure 4.1.7 reports the comparison of 1(E) curves for the ten experimental beams with those calculated for the models according to optimal geometrical parameter for iterations 1 and 5 in Table 4.1.3. The best geometrical parameters were determined to be dfjl = 1.50 A, A = +0.02 A (1.4 % expansion), dl2 =2.09 A (2.8 % expansion) and d23 = 2.08 A (2.3 % expansion). 4.1.4 Discussion The evidence reported above suggests that the Ni(l 1 l)-(2x2)-S structure has the S atoms adsorbed on the expected 3f sites of the Ni(l 11) surface, which is in agreement with the result reported by Demuth et al. [DJM74a], but the spacing between S and the topmost layer is 1.50 A rather than 1.40 A as reported by Demuth et al. [DJM74a]. It is clear that the value of 1.40 A is too small because it leads to a nearest neighbor S-Ni distance of 2.02 A which is significantly smaller than that found by the other surface techniques (see below), while the value of 1.50 A leads to a nearest neighbour S-Ni distance of 2.10 A which is closer to the value 2.16 A reported by Fauster et al. [FDH86] using the low-energy ion scattering technique and the value 2.20 A reported by Ohta et al.[OKS&86] 0.13 0.12 H 0.11 H 0 .10 H • 1 • 1 • 1 • 1 • 1 « r 1 2 3 4 5 6 Iteration Figure 4.1.6 Reliabilty index for each iteration w • i-H C SH CO + J • i-H I —H CO W E-(1 0) BEAM Expt . \ (a) v (b) 40 60 80 100 120 140 160 180 200 220 240 (1 1) BEAM Expt. (a) 1 i 1 1 1 r 40 60 80 100 120 140 160 180 200 220 240 1 120 140 160 180 200 220 240 E L E C T R O N E N E R G Y (eV) Figure 4.1.7 Comparison of experimental 1(E) curves from Ni(l 1 l)-(2x2)-S with those calculated for the 3f models: (a) doi=1.50 A, A= 0.00 A, di2=2.03 A and d23=2.03 A. (b) doi=1.50 A, A=+0.03 A, di2=2.09 A and d23=2.08 A. CO 69 OL 7 1 using the surface extended X-ray absorption fine structure technique (SEXAFS). Moreover, the present work agrees rather well with a bond valence-bond length analysis which predicates a S-Ni bond length of 2.12 A for sulfur on the Ni(l 11) surface [MSS86]. In this work, it is noted that relaxations really appear to be experienced by the metal atoms during the chemisorption of S (see Figure 4.1.7). It is clear that the calculated 1(E) curves corresponding to the metal relaxation model give a better match to the experimental curves compared with the curves calculated for the no relaxation model, in particular for the (0 1) and (0 3/2) beams. Owing to the limitation of computing cost, it is however only feasible to study a reasonable range of these relaxed structures and the present work should be seen as a progress report of a current LEED crystallographic investigation for the S on Ni(lll) sulfur structure. 72 Part II LEED Structure Analysis of the Rh(l 1 l)-(V3xV3)30°-S Structure: A New LEED Analysis 4.2.1 Introduction The first surface crystallographic study on the Rh(lll)-(V3xV3)30°-S structure was performed earlier in this laboratory by Wong et al. [WZH&85]. Under an assumption of no surface relaxations experienced by the underlying metal atoms, this previous LEED study concluded that the Rh(lll)-(V3xV3)30°-S structure has S atoms adsorbed on the 3f sites of the Rh(l 11) surface [WZH&85] with a S-Rh bond length (2.18 A) that agreed reasonably well with bond order-bond length predictions [MSS86]. Even so, some clear discrepancies were noticed in structural features in corresponding experimental and calculated 1(E) curves for this LEED analysis [WZH&85], as shown in Figure 4.2.1. Particular discrepancies were observed in the vicinity of 160 eV for the (1 0) beam and 170 eV for the (0 1) beam. The existence of these discrepancies suggests that further refinement is needed for the Rh(l ll)-(V3xV3)30°-S surface structure. One possibility relates to adsorbate-induced metal relaxations, as have been observed when S is adsorbed on a number of metal surfaces, for example lateral relaxations on Fe(110) [SJJ&81], vertical relaxations on Ni(110) [VTS&79] as well as lateral relaxations on Ni(lll) as reported in Part I of this chapter. Therefore, as part of this continuing project, the present study investigates the possibility of adsorbate-induced metal relaxations on the Rh(l 1 l)-(V3xV3)30°-S structure. 4.2.2 Experimental Data Base The experimental data used in the present analysis consists of the nine intensity-versus-energy (1(E)) curves measured by Wong et al. [WZH&85]. These 1(E) curves were 73 LO z: LU 5 a O T 6 0 7 0 0 (1/3 A/3) beam 80 120 160 200 240 > 1 1 " 7 • • 7 1 1 (4/3 1/3) beam / \ /A V • • . * ""I, _ ,1 1 1 1 . \ 80 120 160 200 240 ELECTRON ENERGY (eV ) Figure 4.2.1 Comparison of experimental 1(E) curves from Rh(l 1 I H V S X VS J S O ' - S with those calculated for the models where sulfur atoms adsorb at the 3f sites and the interlayer spacing between S and first Rh layer (dni) equals either (a) 1.45 A or (b) 1.55 A (taken from Ref. [W87]). 7 4 40 80 120 160 200 240 c 13 (2 0) beam j i_ 180 220 O >-to LU 40 80 120 160 200 240 160 200 240 40 160 120 160 200 240 ELECTRON ENERGY (eV) Figure 4.2.1 (continued) 75 collected at normal incidence as described in Section 3.4.2 over the energy ranges indicated in Table 4.2.1. The diffracted beams available are labeled as (1 0), (0 1), (1 1), (2 0), (0 2), (1/3 1/3), (2/3 2/3), (1/3 4/3), (4/3 1/3), using the beam notations shown in Figure 4.2.2. Specific experimental details have been described previously [W87, WZH&85]. 4.2.3 LEED Intensity Calculations The calculated intensity-energy curves for the Rh(l 1 l)-(V3xV3)30e-S surface in the present study were obtained by performing the multiple scattering calculations using the computer programs developed by Van Hove and Tong [VT79]. In these calculations, diffraction matrices for the relaxed Rh layers were calculated by the combined-space method [VT79], with up to three atoms per unit mesh, and the layer stackings were done with the renormalized forward scattering method [P74]. Calculations were done on the Cray X-MP supercomputer in the energy range 56-240 eV in steps of 4 eV. A maximum of 41 symmetry-inequivalent beams were employed in the calculations A set of eight phase shifts calculated for the muffin-tin potential for rhodium reported by Moruzzi et al. [MJW78] was used. In this work new phase shifts for sulfur were computed; they were derived from a superposition potential associated with hypothetical bcc sulfur with a lattice constant of 3.106 A. The real part of the constant potential (Vor) between the muffin-tin spheres was initially set at -10.0 eV for both the surface layer and the bulk, but its value was allowed to be refined during the analysis according to the shifting in energy scale required for optimal match to the experimental curves. The imaginary part (V0i) of the potential between all atomic spheres was assumed to be energy-dependent, according to the equation V 0 , = - 0.819E1/3 eV, where E is the electron energy in eV with respect to the vacuum level. The Debye temperatures were taken as 480 7 6 Table 4.2.1 Experimental intensity-energy curves for Rh(lll)-(V3xV3)30o-S Beam Energy Range Index (eV) 10 60-240 01 60-240 11 130-240 1/3 1/3 66-150 2/3 2/3 60-200 1/3 4/3 100-236 4/3 1/3 100-240 20 180-240 02 174-240 77 • • f • • 4/3-8/3 5/3-7/3 2-2 7/3-5/3 8/3-4/3 2/3 -7/3 1/3 -2/3 4/3 -5/4 5/3 -4/3 2/3 -1/3 7/3 -2/3 0-2 1/3-5/3 2/3 4/3 1-1 4/3-2/3 5/3-1/3 2 0 -2/3-5/3 -1/3 4/3 0-1 1/3-2/3 2/3-1/3/ 10 x^4/3 1/3 5/3 2/3 -4/3 4/3 -1 -1 -2/3 -2/3 -1/3 -1/3 0 0 V \ V 3 1/3 2/3 2/3^''' 11 4/3 4/3 • • • • -5/3-2/3 -4/3-1/3 -10 -2/3 1/3 -1/3 2/3 0 1 1/34/3 2/3 5/3 -20 -5/3 1/3 -4/32/3 -1 1 -2/34/3 -1/3 5/3 02 • • • -7/3 2/3 -2 1 -5/3 4/3 • • • -4/3 5/3 -12 -2/3 7/3 -8/3 4/3 -7/3 5/3 -22 -5/3 7/3 4/3 8/3 Figure 4.2.2 Beam notations for a LEED pattern from the Rh(l 1 1M^3XV3)30*-S structure. 78 and 335 K for rhodium and sulfur respectively [WZH&85]. The evaluation of experimental and calculated 1(E) curves were done by visual analysis and by the two LEED reliability indices, RMZJ and Rp, as described in Section 2.6. Wong et al. [WZH&85] reported that the Rh(lll)-(V3xV3)30°-S structure has 1/3 monolayer of S atoms adsorbed on the Rh(lll) surface. Based on this coverage, the possible models involving lateral and vertical relaxations of Rh atoms and/or reconstruction of Rh structure are shown in Figure 4.2.3. In this figure the lateral registries of the stacked layers are indicated with the familiar A, B, C notation such that bulk fee Rh is designated as ABCABC... and the layer of sulfur atoms is indicated in parentheses. In all the models considered the S atoms occupy the three fold coordinate sites (3f or 3h) on the Rh(lll) surface; this may be as a unreconstructed Rh structure (3F1 model-(C)ABC.) or as a reconstructed Rh structure (3RF1 model-(C)BABC...; 3RH1 model-(A)BABC...; two domain 3RF2 model-(C')BABC...+(C")BABC...)t. It is assumed for simplicity that the possible relaxations for each of these models are constrained by the diperiodic space group symmetry p31m exhibited by the experimental LEED intensity, which includes both the threefold rotational symmetry and the mirror symmetry. Three structural parameters are considered here: the first rhodium layer lateral relaxation (A), the height of the sulfur atoms above the first rhodium layer ( d o i ) , and the spacing between the first and second rhodium layers (di2). It is only feasible to do the computations over a reasonable range of values for these parameters. Table 4.2.2 summarizes the ranges of structural parameters which have been investigated for each of the models considered. t With lateral relaxations of the first Rh layer, the originally equivalent 3f sites split into three types: C, C and C", as shown in Figure 4.2.3. The C sites maintain the threefold and mirror symmetries while the C and C" sites only have the threefold symmetry. The lateral relaxations of Rh atoms around the C sites are in clockwise direction while those around the C" sites are in anticlockwise direction. 79 3F1 • i 0 .., © .., O .., 0 .. © O O ®c o ^ © !r 0 u ® 'X OCT • i 0 .., 0 X 0 : 0 : 0 O © ° 0 ; * ••• -0 • 1 ©°®° 0 ^ © ^ O ° 0 i l © O •Q-©> O 01 bulk value bulk value (a) Top view (b) Side view Figure 4.2.3 Notation used for the Rh(l 1 l)-(V3xV3)30°-S surface structure. The model is viewed from above in (a) and from the side in (b) along the cross section marked by the line in (a). S atoms are represented by dark circles and Rh atoms by the larger circles. The circles which are open, dashed and shaded are for Rh atoms designated as of type A, B, and C respectively. Lateral displacements for atoms in the first Rh layer are fixed by the parameter A whose magnitude corresponds to the displacement from the regular bulk positions and whose sense is positive when the displacements are in the direction of the arrows shown. © and * corresponding to lateral displacements into and out-of the plane of the figure. 80 .... o.... o O 'X ® o o r o o i 11 o x o x © x o x o ' > » ° o o ® o ® O T O ^ O o ^ o x o o 3RF1 o o o _/ t -* _ * bulk value bulk value 3RH1 X _ X o o o o ®.... ^ 1 ; '"' o ® ;r O '"' o o / "* "* \ \') V _ * o o ^ O "' ®^o o x: Q ® O ''X o ® o o o o o o ® o ' I 1 S «. ® o ' I 1 _ > ® o o / *" * \ o bulk value bulk value (a) Top view Figure 4.2.3 (continued) (b) Side view 81 3RF2 ( C ) B A B C . o.... o.... o.... o „ o ° o ° o -I ^ \ I I I I -'"' ® "" O ' o o : o ! r o : O %" o . o ; , o ° k o r o o * f / * / o ° o ? • ' 1 > > / » t / O " ® "' o o o T dm bulk value bulk value 3RF2 (C" ) B A B C . . . .... o.... o. I l l 1 ^ I ' ® O '' o^o^r I ^ I i i i © o ' • i i • ~v i ® "• o o :i o :i • ^ i 111 ° o ° o o , o.... o.... • I ' I I I I O '"' ® "' o o o © . o r o r I I" I I I I / > T / « / O "' ® '• o o "' © "' o o o (a) Top view Figure 4.2.3 (continued) O •Q-(b) Side view bulk value bulk value Table 4.2.2 Models and ranges of geometrical parameters considered for the Rh(l 1 l)-(V3xV3)30*-S structure. A A 3F1 3RF1 3RH1 3RF2 doi d n A A doi d n A A doi d n A A doi di2 A A 0.2 1.25-1.7 2.1921 — 1.55 2.0721-23121 1.60 2.0721-23121 0.15 — — — — — — 1.46-1.70 2.0721-23121 0.1 1.3-1.7 2.1921 1.55 2.1021-2.2821 1.60 2.1021-2.2821 — — 1.55 2.0721-23121 1.60 2.0721-Z3121 0.075 1.45-1.63 2.1921 — — — — — — 0.05 13-1.7 2.1921 1.57 2.0421-2.4421 1.55 2.0721-23121 1.60 2.0721-23121 — — — — 0.025 1.57 Z0921-23321 — — — — — — 0.0 13-1.7 2.1921 1.57 2.1021-2.2821 13-1.7 Z1921 1.3-1.75 2.1921 13-1.7 2.1921 -0.025 1.57 2.0621-23321 — — — — — — -0J 1.57 2.0921-2.2721 1.55 Z0721-2.3121 1.60 2.0721-2.3121 — — — -0.1 1.3-1.7 2.1921 1.55 Z0721-23121 1.60 2.0721-23121 — — 1.55 2.0721-23121 1.60 2.0721-23121 -0.2 — — — — — — 1.55 2.0721-23121 1.60 2.0721-2.3121 83 4.2.4 Results and Discussion 3F1 model Wong et al. [WZH&85] concluded that the Rh(l 1 l)-(V3xV3)30°-S structure has the S atoms adsorbed on the expected 3f sites of the Rh(lll) surface. The refinement of this structure was carried out as follows. With doi fixed at the best value (1.57 A) found in this work for S atoms adsorbed in the 3f sites assuming no metal relaxation, the possibility of lateral relaxation (A) was investigated by allowing Rh atoms in the first layer to be laterally relaxed by amounts ranging from +0.075 to -0.050 A. A reliability index minimum (RMZJ) was obtained for a very slight lateral contraction of 0.025 A (i.e. A=-0.025 A). With doi and A fixed at the initial optimal values (1.57 A and -0.025 A respectively), the interlayer spacing between the first and second Rh layer (di2) was changed from 2.062 to 2.332 A in steps of 0.03 A, and a minimum of the reliability index (RMZJ) w a s found for di2=2.18 A. The reliability index RMZJ (0.1367) was only 0.0011 smaller than the zero-lateral relaxation model (RMZJ = 0.1378). No distinction was discernible in a visual analysis (see Figure 4.2.4 curves (a) and (Jo)), and therefore this lowering in RMZJ might be too small to support a significant lateral relaxation in the first Rh layer due to the adsorption of sulfur for the 3F1 model. Under the assumption of no lateral relaxation (i.e.A=0), a vertical relaxation was considered between the first and second Rh layers. Keeping doi fixed at 1.57 A, the interlayer spacing di2 was varied from 2.102 to 2.282 A in steps of 0.03 A, and the minimum of the reliability index (RMZJ) was found corresponding to di2=2.17 A. This is just slightly smaller than the bulk spacing (2.1921 A). The minimum value of RMZJ equals 0.1369 which is only 0.0009 smaller than the model without vertical relaxation. Furthermore, visual inspection of the corresponding experimental and calculated 1(E) curves of the 3F1 model (see Figure 4.2.4 curve (c)) did not indicate any improvement in the agreement of the (1 0) and (0 1) beams as compared with the relaxation model for 84 • r—I SH CTJ u -4-> • l-H SH E-1 CO w E-i 1 1 1 1 i r 40 60 80 100 120 140 160 180 200 220 240 260 i 1 1 1 1 i r 40 60 80 100 120 140 160 180 200 220 240 260 ELECTRON ENERGY (eV) Figure 4.2.4 Comparison of experimental 1(E) curves from Rh(l 1 l)-(V3xV3)30°-S with those calculated for the 3F1 (i.e. (C)ABC.) models: (a) doi=1.57 A, A= 0.00 A and di2=2.19 A. (b) doi=1.57 A, A=-0.025 A and di2=2.18 A. (c) doi=1.57 A, A= 0.00 A and di2=2.17 A. 85 w H-> • i-H >-> u cd u • r H rO r H > -i—i in E-i 1 r 120 140 160 180 200 220 240 260 1 1 r 160 180 200 220 240 260 T—~1 1 T 160 180 200 220 240 260 n 1 1 r 60 80 100 120 140 160 ELECTRON ENERGY (eV) Figure 4.2.4 (continued) ELECTRON ENERGY (eV) Figure 4.2.4 (continued) 87 A=-0.025 A. In summary, both the reliability index and visual analyses suggest that the 3F1 model, either with or without relaxations of the topmost Rh layer, does not give a completely satisfactory account of this surface structure. Reconstructed models : 3RF1, 3RH1 AND 3RF2 It is of interest to note that the early LEED crystallographic study of the clean Rh(l l l ) surface by Watson et al. [W78] showed the calculated 1(E) curves for the (1 0) and (0 1) beams, from the reconstructed surface model of BABC... layer stacking, contain structural features which appear to show a better match to the Rh(lll)-(V3xV3)30°-S experimental (10) and (0 1) curves respectively. That therefore provides a new direction for refinement of the geometrical structure of the Rh(l 1 l)-(V3xV3)30°-S surface. Considering S atoms adsorbed on the reconstructed Rh(l 11) BABC... surface, the S atoms may be adsorbed on the 3f (3RF1 model) or 3h (3RH1 model) sites. Assuming no relaxations for the Rh atoms, a visual comparison of corresponding experimental and calculated 1(E) curves suggested that the 3RF1 model is preferable to the 3RH1 model. This appears consistent with the previous LEED study by Wong et al. [WZH&85] insofar as the S atoms adsorb at 3f sites, and the 3RH1 will not be considered further. Keeping the S-Rh interlayer spacing at 1.55 A and other Rh interlayer spacings at 2.1921 A (bulk value), the effects of lateral relaxations on the 3RF1 model were studied as A was changed from +0.1 to -0.2 A. The best lateral relaxation appears to be in the region of A=-0.1 A. Compared with the no relaxation unreconstructed model (i.e. 3F1 model when A=0), calculated 1(E) curves for (1 0), (0 1) and (1 1) beams show improved agreement with experiment (see Figure 4.2.5); this demonstrates the effect of reconstruction of the Rh layers on the LEED intensities. On the other hand, the 88 in -»-> • r H u cd SH H-> • r H r Q r H c^d >-E-r—I CO r ^ EH rz; i 1 1 1 1 1 1 1 1 1 r 40 60 80 100 120 140 1 60 1 80 20 0 220 240 260 1 1 1 1 1 1 1 1 1 1 r 40 60 80 100 120 140 160 180 200 220 240 260 ELECTRON ENERGY (eV) Figure 4.2.5 Comparison of experimental 1(E) curves from Rh(l 1 l)-(V3xV3)30°-S with those calculated for the 3RF1 (i.e. (C)BABC.) model, over a range of lateral displacements (A), where doi and di2 are fixed at 1.55 A and 2.1921 A respectively. 89 -t-> • r—I n i i i 1 1 1 r 120 140 160 180 200 220 240 260 ~] 1 1 r 160 180 200 220 240 260 GO W "i 1 1 r 160 1 80 200 220 240 260 -i 1 1 1 r 60 80 100 120 140 160 Figure 4.2.5 ELECTRON (continued) ENERGY (eV) 90 (2/3 2/3) BEAM . , — i 40 60 80 100 120 140 160 180 200 220 SH CTJ ELECTRON ENERGY (eV) Figure 4.2.5 (continued) 91 correspondences for the fractional beams as well as the (2 0) beam, are worse (Figure 4.2.5). Therefore, further refinement in the geometrical model is still required. It should be noted that with lateral relaxations of the first Rh layer, the originally equivalent 3f sites split into three types: C, C and C", as shown in Figure 4.2.3. Therefore the two-domain 3RF2 (C'BABC...+C"BABC...) model can be considered as another possible model for the Rh(lll)-(V3xV3)30°-S structure. Lateral relaxations in the 3RF2 model were studied as A was changed from +0.2 A to -0.2 A while keeping the S-Rh interlayer spacing at 1.55 A and other Rh interlayer spacings at 2.1921 A (bulk value). The best lateral relaxations appear to be close to A =+0.1 A (see Figure 4.2.6). It should be noted that this value of A corresponds to a contraction of the C and C" sites, which is consistent with the result in the study of the 3RF1 model that adsorption of S atoms induces contraction on the adsorption sites. In other words, both models suggest that the Rh atoms will move closer to each other to form a local RI13S type cluster. However, the agreement between the corresponding experimental and calculated 1(E) curves is still less than complete, in particular for the fractional beams. All the models considered so far are under the assumption of 1/3 monolayer coverage of S atoms on the Rh (111) surface as suggested by Wong et al. r\VZH&85]. Since the adsorbates have important contributions to the fractional beam intensities, the possibility of 2/3 monolayer coverage of S atoms has also been tested as an alternative model by relaxing the above constraint. The calculated 1(E) curves for both integral and fractional beams however showed poorer matching to the corresponding experimental data as compared with all the 1/3 coverage models (3F1, 3RF1, 3RH1, 3RF2). Therefore no further study was performed on this direction. In summary, considerations of lateral and vertical relaxations for the 3F1 model did not improve the agreement between the corresponding experimental and calculated 1(E) 92 <72 -+-> •r—I SH co SH i 1 1 1 1 1 1 1 i i r 40 60 80 100 120 140 160 180 200 220 240 260 SH CO I—i GO fr-iz; i i i i i i i 1 1 1 r 40 60 80 100 120 140 !60 180 200 220 240 260 ELECTRON ENERGY (eV) Figure 4.2.6 Comparison of experimental 1(E) curves from Rh(l 1 l)-(\3xV3)30°-S with those calculated for the two-domain 3RF2 (i.e. (C)BABC... + (C")BABC...) model, over a range of lateral displacements (A), where dni and d\2 are fixed at 1.55 A and 2.1921 A respectively. (1 1) BEAM 160 180 200 220 240 260 (2 0) BEAM Expt. 0.20 0.15 0.1D 0.00 -0.10 -0.20 I 1 1 1 1 r~ 160 180 200 220 240 260 ( 1 / 3 1/3) BEAM I 1 1 1 1 r~ 60 80 100 120 140 160 ELECTRON ENERGY (eV) Figure 4.2.6 (continued) 94 (2/3 2/3) .BEAM ELECTRON ENERGY (eV) Figure 4.2.6 (continued) 95 curves, particularly for the (1 0) and (0 1) beams. While for the reconstructed models (3RF1, 3RH1, 3RF2), the agreements for the (1 0) and (0 1) beams did improve but the matching for the fractional beams was not as good as that of the 3F1 model. Therefore for all the models considered in the present investigation of adsorbate-induced metal relaxations on the Rh(lll)-(V3xV3)30°-S structure, the agreement between the experimental and calculated intensities was still less than satisfactory. These discrepancies remaining suggest that other refinements are needed, perhaps on both the theoretical and experimental sides of the analysis. At this stage the best level of correspondence between calculation and experiment appears for the 3F1 model with doi=1.57 A, A=-0.025 A (1.6 % contraction) and di2=2.18 A (0.5 % contraction). In this model the nearest-neighbor S-Rh distance 2.19 A in close agreement with that reported by Wong et al. 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Mitchell, Surf. Sci. 163 (1985) 172. [ZFM88] H.C. Zeng, R.A. McFarlane and K.A.R. Mitchell, submitted to Phys. Rev. [ZJ77] E. Zanazzi and F. Jona, Surf. Sci. 62 (1977) 61. 101 APPENDIX The following appendix contains three independent sets of experimental 1(E) curves (a, b and c) for Ni(l 1 l)-(2x2)-0 surface measured during this work. In all cases, the 1(E) curves are smoothed arid averaged as described in Section 3.4.2. The beam notations are the same as those of Ni(l 1 l)-(2x2)-S surface. Their energy ranges are listed as below. Beam Energy Range Index (eV) 1 0 50 -248 0 1 62 -228 1 1 160-240 1/2 0 44 -158 0 1/2 44 - 94 1/2 1/2 44 -200 1 1/2 80 -198 1/2 1 86 -198 3/2 0 120-246 0 3/2 108-230 102 ELECTRON ENERGY (eV) 103 40 60 80 100 120 140 160 180 200 220 40 60 80 100 ELECTRON ENERGY (eV) IOA T | 1 1 1 1 1 1 I I I 1 1 1 1 I I I 100 120 140 160 180 200 220 240 100 120 140 160 180 200 220 240 260 ELECTRON ENERGY (eV) 

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