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LEED crystallographic studies for chemisorption on rhodium and zirconium surfaces Wong, Philip C. L. 1987

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LEED CRYSTALLOGRAPHIC STUDIES FOR CHEMISORPTION ON RHODIUM AND ZIRCONIUM SURFACES by PHILIP C.L. WONG B.S. Soochow U n i v e r s i t y , 1975 M.A. U n i v e r s i t y of Texas at A r l i n g t o n , 1982 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of Chemistry) We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1987 © P h i l i p C.L. Wong, 1987 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 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6G/81) I i Abstract The work in this thesis includes crystallographic investigations with low-energy electron dif fract ion (LEED) for the surface structures designated R h ( l l l ) - ( / 3 x / 3 ) 3 0 ° - S , Rh(ll l)-(2x2)-0, Zr(0001)-(lxl)-0 and Zr(0001)-(lxl)-N. In each case intensity-versus-energy (1(E)) curves for a set of diffracted beams were measured with a video LEED analyzer, and then compared with the results of multiple scattering calculations made for various structural models. Levels of correspondence between experimental and calculated 1(E) curves were assessed with the r e l i a b i l i t y index proposed by Pendry, and surface geometries were determined by the condi-tions for the best correspondence. The LEED intensity analyses for both the R h ( 1 1 1 ) - ( / 3 x r / 3 ) 3 0 ° - S and Rh(lll)-(2x2)-0 surface structures indicate that S and 0 atoms adsorb respectively 1.53A and 1.23A above the "expected" hollow sites of three-fold coordination. These values correspond to nearest-neighbor Rh-S and Rh-0 bond distances equal to 2.18 and 1.98A respectively. For the Zr(0001)-(lxl)-0 and Zr(0001)-(lxl)-N surface structures studied, the multiple-scattering analyses suggest that the f i r s t involves 0 atoms occupying octahedral holes between successive bulk Zr layers, and that the substrate Zr layers undergo a fee type reconstruction. By contrast the N atoms in Zr(0001)-(lxl)-N appear to just occupy octahedral holes between the f i r s t and second layers of hep zirconium, exactly as reported by Shih et a l . for the analogous structure formed on titanium. The LEED-determined i i i Zr-0 and Zr-N bond distances are 2.30 and 2.27A respectively, in very close agreement with the values determined by X-ray crystallography for bulk ZrO (2.31A) and bulk ZrN (2.29A). A preliminary study of oxygen chemisorption on the Zr(0001) surface has been made in the low-exposure regime with Auger electron spectroscopy (AES) and with measurements of the width of a half-order LEED beam. Some observations and conclusions are: (i) the diffusion of 0 atoms to the bulk effectively starts at around 236°C; ( i i ) oxygen adsorbs in a disordered state at room temperature but orders sufficiently to show a (2x2)-type LEED pattern on heating to 220°C; ( i i i ) with increasing 0 exposure, 1/4, 1/2 and 3/4 of the available sites can be systematically f i l l e d , prior to the establishment of an ordered ( lxl) -0 surface; (iv) the process in ( i i i ) can be reversed by starting with the ( lxl)-O surface and heating above 236°C. LEED and AES have also been used to compare the adsorption and coadsorption of 0 2 and H2S on the Zr(0001) surface for exposures in the one to five Langmuir regime. The new observations made are: ( i ) sulfur forms a stable (3x3) surface structure after heating to 600°C; ( i i ) the Zr(0001) surface with high 0 coverage can s t i l l adsorb H 2 S, whereas the Zr(0001) surface with high S coverage does not adsorb oxygen in detectable amounts; ( i i i ) for surfaces with adsorbed H 2S the 150 eV to 92 eV Auger peak ratio suddenly increases on heating to 530°C. Observation ( i i i ) has been tentatively interpreted in terms of hydrogen desorption. F ina l ly , a set of 1(E) curves were measured for normal incidence on the Zr(0001)-(3x3)-S surface. i v Table of Contents Page Abst r a c t i i Table of Contents i v L i s t of Tables i x L i s t of Figures x Acknowledgements x v i i i Chapter 1: I n t r o d u c t i o n 1 1.1 I n t r o d u c t i o n 2 1.2 C l a s s i f i c a t i o n of Surface St r u c t u r e 5 1.3 R e c i p r o c a l Net 6 1.4 Low Energy E l e c t r o n D i f f r a c t i o n (LEED) . . . . 9 1.4.1 E l e c t r o n S c a t t e r i n g i n S o l i d s 9 1.4.2 Conditions f o r E l a s t i c LEED 10 1.4.3 Two-dimensional LEED A n a l y s i s 15 1.4.4 LEED C r y s t a l l o g r a p h y 19 1.4.5 Instrumental Response, Domains and Disorder 23 1.5 Auger E l e c t r o n Spectroscopy (AES) 27 1.6 Aim of Thesis 30 V Page Chapter 2: Calculation of LEED Intensities 33 2.1 Introduction 34 2.2 Geometrical and Non-geometrical Parameters • • 35 2.3 The Muffin-tin Approximation 38 2.4 Ion Core Scattering 42 2.5 Intralayer Scattering . 45 2.6 Interlayer Scattering 50 2.6.1 Layer Doubling Method 51 2.6.2 Renormalized Forward Scattering Method . 54 2.7 Application of Symmetry in the "Combined Space" Method 58 2.8 Evaluation of Results 59 Chapter 3: Experimental Methods 62 3.1 UHV Chamber and Apparatus 63 3.2 Sample Preparation 67 3.3 Cleaning In UHV Chamber 69 3.4 Apparatus for Auger Electron Spectroscopy . . . 71 3.5 Apparatus for LEED 73 3.5.1 LEED Optics and Electron Gun 73 3.5.2 Measurement of LEED Intensities . . . . 76 3.5.3 Measurement of Spot Profi le 82 v i Page Chapter 4: LEED Analysis for the Rh(lll)-(/Tx/3)30°-S Surface Structure 84 4.1 Introduction 85 4.2 Experimental 86 4.3 Calculations and Results 93 4.4 Discussion 98 Chapter 5: LEED Investigation of the Rh(lll)-(2x2)-0 Surface Structure 105 5.1 Introduction 106 5.2 Experimental 107 5.3 Calculations 108 5.4 Results 110 5.5 Discussion 114 Chapter 6: Adsorption of Oxygen on the (0001) Surface of Zirconium 122 6.1 Introduction 123 6.2 Experimental 126 6.2.1 Sample Preparation and Cleaning . . . . 126 6.2.2 LEED Pattern for Oxygen Adsorption on Zr(0001) 128 v i i Page 6.2.3 AES and LEED Spot Profile Measurements for Zr(0001)-(2x2)-0 129 6.2.4 Measurements of 1(E) Curves from the Lowest-coverage Zr(0001)-(lxl)-0 Surface Structure 135 6.3 Multiple Scattering Calculations for Zr(0001)-(lxl)-0 137 6.4 LEED Crystallographic Results for the I n i t i a l Zr(0001)-(lxl)-0 Structure 139 6.5 Discussion 147 Chapter 7: A LEED Crystallographic Investigation of a Surface Structure Designated Zr(0001)-(1x1)-N 151 7.1 Introduction 152 7.2 Experimental 152 7.3 Calculations 156 7.4 Results 161 7.5 Discussion 161 v i i i Page Chapter 8: Comparison of Oxygen and Sulfur Adsorption on the (0001) Surface of Zirconium 174 8.1 Introduction 175 8.2 Experimental 175 8.3 Results 176 8.3.1 Oxygen Adsorption 177 8.3.2 Hydrogen Sulfide Adsorption 177 8.3.3 Oxygen and Hydrogen Sulfide Coadsorption 180 8.3.3.1 02 on Zr(0001)-(3x3)-S with Rs > 3.1 180 8.3.3.2 02 on Zr(0001)-(3x3)-S with Rs < 3.1 180 8.3.3.3 H2S on Zr(0001)-(2x2)-0 . . . . 184 8.3.3.4 H2S on Zr(0001)-(lxl)-0 . . . . 185 8.3.3.5 Coadsorption without Annealing 185 8.4 Discussion 185 8.5 Further work 188 Concluding remarks 189 References 191 ix L i s t of Tables Page Table 1.1 Some surface techniques and their characterist ics . . 4 Table 4.1 Comparison of measured and predicted S-Rh bond lengths for S atoms adsorbed on the (111), (100), (110) surfaces of rhodium 104 Table 6.1 Five representative studies of the oxidation of zirconium using different surface techniques and surface treatments 124 Table 6.2 Values of Zr-0 interlayer spacings and V Q r corresponding to minima in contour plots of R for structural models of Zr(0001)-(lxl)-0 . . . . . . . 141 Table 6.3 Values of Zr-0 interlayer spacings and V o r corresponding to minima in contour plots of Rp for two structural models of Zr(0001)-(lxl)-0 using phase shift for negatively charged 0 148 Table 7.1 Values of Zr-N interlayer spacings corresponding to minima in contour plots of R for structural models of Zr(0001)-(lxl)-N . . . 162 X Lis t of Figures Page Figure 1.1 The five types of two-dimensional surface meshes (a) in real space (b) in reciprocal space 7 Figure 1.2 A two-dimensional net in real space ( f i l l e d c irc les) described by unit translation vectors ^ , ^ 2 a n c * t n e associated net in reciprocal space (open^circ1.es) described by unit translation vectors &i , a,2 . . . 8 Figure 1.3 Schematic energy distribution N(E) of back-scattered electrons for a primary beam of energy Ep 11 Figure 1.4 Schematic diagram of the mean free path for electrons in a metallic sol id as a function of energy 11 Figure 1.5 Conventions to describe the incidence direction for an electron beam interacting with a surface; 9 is the polar angle relative to the surface normal and <t> is an azimuthal angle relative to a major crystal lo-graphic axis in the surface plane 13 Figure 1.6 Schematic diagram i l lus trat ing how the conservation conditions determine direction of a diffracted beam. The (00) beam corresponds to the specular reflection 16 Figure 1.7 Some common translational symmetries (unit meshes) for adsorption on f c c ( l l l ) or hcp(OOOl) surfaces using both Wood's notation and the matrix notation. . 18 Figure 1.8 (a) Unit mesh of the (/3x/5)30° overlayer structure and four possible adsorption sites for sulfur adsorbed on R h ( l l l ) . The 3h and 3f sites are three-fold sites which are distinguished respectively by whether there is a substrate atom or not located direct ly below the second layer, (b) Schematic LEED pattern corresponding to the overlayer structure of (a) 20 Figure 1.9 Comparison of an 1(E) curve measured for the (1/3 1/3) diffracted beam from R h ( l l l ) - ( / 3 x / 3 ) 3 0 ° - S at normal Incidence with those calculated for the 3f and 3h adsorption sites over a range of the topmost S-Rh interlayer spacings 21 xi Page Figure 1.10 A (2x2) structure on a f c c ( l l l ) or hcp(OOOl) surface is shown bottom le f t , while the corresponding LEED pattern is drawn schematically at bottom right (the half-order beams are identified by crosses). The top shows three domains of a (1x2) type structure which are related by 120° rotations. The total LEED pattern from a surface with equal populations of these domain types w i l l be a superposition of the three individual patterns. This superposition gives spots in identical positions to the (2x2) pattern. 25 Figure 1.11 (a) Side view and (b) top view of the two types of domains resulting from the truncation of the hep bulk structure paral le l to the (0001) plane. The two domains are related to each other by a 180° rotation. (c) Superposition of the two 3-fold symmetrical LEED patterns (expected for normal incidence) to form a LEED pattern with 6-fold symmetry 26 Figure 1.12 Schematic representation of an Auger process in terms of atomic and valence band energy levels. This example is specif ical ly for the production of a K L 2 L 3 Auger electron 28 Figure 2.1 Example of relaxation at a f c c ( l l l ) surface. The three-dimensional propagation vectors A&B and ASA apply to the relaxed region and bulk region respectively. The corresponding interlayer spacings D' and D are shown to the left 36 Figure 2.2 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 39 Figure 2.3 Scattering of a set of plane waves by a layer of ion cores with diffraction matrix M 46 Figure 2.4 Graphitic-type oxygen overlayer for Rh(ll l)-(2x2)-0; there are two oxygen atoms (shaded c irc les) per unit mesh, one on a 3f site the other on 3h site (as In Figure 1.8(a)) 48 Figure 2.5 Schematic diagram of transmission and reflection matrices at the nth layer. The dashed lines are midway between consecutive layers 48 x i i Page Figure 2.6 Schematic i n d i c a t i o n of the l a y e r doubling method as ap p l i e d to s t a c k i n g four i n d i v i d u a l l a y e r s (with A.B.A.B... r e g i s t r i e s ) i n t o an slab ( a f t e r Tong [62]) 52 Figure 2.7 Schematic i n d i c a t i o n of the renormalized forward s c a t t e r i n g method, (a) Each t r i p l e t of arrows represents the complete set of plane waves that t r a v e l from l a y e r to l a y e r . (b) I l l u s t r a t i o n of the vectors which store the amplitudes of the inward- and o u t w a r d - t r a v e l l i n g waves ( a f t e r Van Hove and Tong [44]) 55 Figure 2.8 LEED p a t t e r n at normal incidence from R h ( l l l ) - ( 2 x 2 ) - 0 (a) Symmetry-related beams are i n d i c a t e d by the same symbols. (b) Beams belonging to the same beam set are i n d i c a t e d by the same number (independent of angle of incidence) . 60 Figure 3.1 Schematic diagram of the FC12 UHV chamber with some important f a c i l i t i e s used f o r the experiments made i n t h i s work (CMA = c y l i n d r i c a l m i r r o r analyzer) . . . . 64 Figure 3.2 Representation of the pumping system and gas handling l i n e ( I . P . = ion pump; S.P. = s o r p t i o n pump; T.S.P. = t i t a n i u m sublimation pump; D.P. = d i f f u s i o n pump; T.C. = thermocouple) 66 Figure 3.3 Laser method to check the angular misalignment (9) between the o p t i c a l face and desired c r y s t a l plane. . 68 Figure 3.4 Schematic diagram to i l l u s t r a t e the measurement of Auger e l e c t r o n spectra using a c y l i n d r i c a l mirror analyzer i n combination with a glancing angle e l e c t r o n gun 72 Figure 3.5 Schematic diagram of the e l e c t r o n o p t i c s f o r the LEED d i s p l a y system 74 Figure 3.6 Schematic diagram f o r the TV analy z i n g system which detects and measures d i f f r a c t e d beam i n t e n s i t i e s from the LEED screen 77 Figure 3.7 A frame on the monitor screen to i l l u s t r a t e : (a) the 256x256 p i x e l s s t r u c t u r e , (b) the scanning course. . 79 x i i i Page Figure 3.8 1(E) curves measured f o r s i x e s s e n t i a l l y e q uivalent beams f o r normal incidence on the Z r ( 0 0 0 1 ) - ( l x l ) - 0 surface. The clos e correspondence confirms the incidence d i r e c t i o n . The averaged and subsequently smoothed 1(E) curves are dis p l a y e d i n the bottom two curves 81 Figure 3.9 Measurement of spot p r o f i l e s : (a) the LEED spot to be measured i s covered w i t h a us e r - s e l e c t e d window (10x10 p i x e l s ) , (b) the spot i n t e n s i t y p r o f i l e along X w i n 8 3 Figure 4.1 Auger spectra from R h ( l l l ) s u r f ace: (a) as mounted, w i t h considerable S (151 eV) and C (272 eV) contamination; (b) a f t e r A r + bombardment, to show reduced S, but increased C; (c) a f t e r annealing, to show reduced C, but increased S; (d) a f t e r a f u l l c l e a n i n g r o u t i n e 87 Figure 4.2 Auger peak height r a t i o S (151 eV)/Rh (304 eV) p l o t t e d as a f u n c t i o n of H 2S exposure to a R h ( l l l ) surface 89 Figure 4.3 Schematic i n d i c a t i o n s of LEED patterns from surfaces designated: (a) R h ( l l l ) - ( l x l ) ; (b) Rh(lll)-(r/3x/3)30°-S; (c) R h ( l l l ) - c ( 2 x 4 ) - S 91 Figure 4.4 Beam notations f o r a LEED patter n from the R h ( l l l ) -(/3x/3)30°-S s t r u c t u r e 92 Figure 4.5 1(E) curves f o r the (2/3 2/3) and (1/3 1/3) beams measured at normal incidence f o r two independent experiments on the R h ( l l l )-(/3"x/3)30°-S s t r u c t u r e . . 94 Figure 4.6 Comparison of nine 1(E) curves measured f o r normal incidence on Rh(lll)-(/3xr/3)30°-S w i t h those c a l c u l a t e d f o r the 3f, 3h, 2f and I f adsor p t i o n models w i t h Rh-S i n t e r l a y e r spacings which give the best o v e r a l l match between experiment and c a l c u l a t i o n f o r each model 96 Figure 4.7 Contour p l o t s f o r Rh(lll)-(/3x/3)30°-S of R versus V and the Rh-S i n t e r l a y e r spacing f o r four d i f f e r e n t s t r u c t u r a l models 99 x i v Page Figure 4.8 Comparison of experimental 1(E) curves for some integral-order and fra c t i o n a l - o r d e r beams from Rh(lll)-(/3x/3)30°-S with those calculated for the 3f model with s u l f u r either 1.45 or 1.55A above the topmost rhodium layer 100 Figure 5.1 (a) Unit mesh of the (2x2) overlayer structure f o r oxygen adsorbed on R h ( l l l ) . (b) Schematic LEED pattern and beam notations corresponding to the overlayer structure of (a) 109 Figure 5.2 Comparison of experimental 1(E) curves for (1/2 1), (1/2 1/2) and (0 3/2) d i f f r a c t e d beams from R h ( l l l ) - ( 2 x 2 ) - 0 at normal incidence with those calculated for the 3f, 3h and 3f+3h models over a range of the topmost 0-Rh i n t e r l a y e r spacings . . . . I l l Figure 5.3 Contour plots for R h ( l l l ) - ( 2 x 2 ) - 0 of R versus V and the Rh-0 i n t e r l a y e r spacing for (a; 3f, (b) 3h and (c) 3f+3h s t r u c t u r a l models 115 • » • * Figure 5.4 Comparison of experimental 1(E) curves for some integral-order and fra c t i o n a l - o r d e r beams from R h ( l l l ) - ( 2 x 2 ) - 0 at normal incidence with those calculated for the 3f model with oxygen ei t h e r 1.164 or 1.264A above the topmost rhodium layer 118 Figure 6.1 Auger spectra of two Zr(0001) surfaces: (a) as mounted (b) cleaned 127 Figure 6.2 Normalized Auger peak height r a t i o R^/R^ as a function of heating temperature for oxygen on Zr(0001); the i n i t i a l coverage corresponds to R Q = 0.16 130 Figure 6.3 Measured va r i a t i o n s for the (1, 1/2) beam at 66 eV with oxygen coverage on Zr(0001): (a) normalized 1/FWHM, (b) normalized integrated i n t e n s i t y 132 Figure 6.4 Measured v a r i a t i o n with heating temperature of normalized 1/FWHM for the (1, 1/2) beam at 66eV f o r i n i t i a l oxygen coverages on Zr(0001) with R Q equal to: (a) 0.12, (b) 0.16 and (c) 0.20 . 134 XV Page Figure 6.5 Reciprocal net and beam notation for the Zr(0001)-(lxl)-0 structure 136 Figure 6.6 P a r t i a l view of the Zr(0001)-(lxl)-0 structure corresponding to the model designated (B)A(C)BAB... . Atoms i n the topmost Zr layer are i n A-type positions (open s o l i d c i r c l e s ) , while the second Zr layer has atoms i n B-type p o s i t i o n s . The oxygen overlayer (smaller shaded c i r c l e s ) has atoms i n B-type posit i o n s , while the underlayer 0 atoms (darker c i r c l e s ) occupy the octahedral holes i n C type positions 138 Figure 6.7 Contour plot for Zr(0001)-(lxl)-0 of R p versus V Q r and the Zr-0 i n t e r l a y e r spacing for the model A(C)B(A)C(B)A 142 Figure 6.8 Comparison of experimental 1(E) curves (dashed) from Zr(0001)-(lxl)-0 with those calculated for the single-underlayer model A(C)BAB... with dzT-Q equal to 1.33A (upper continuous l i n e designated a) and 1.37A (lower continuous l i n e designated b) 143 Figure 6.9 Comparison of experimental 1(E) curves (dashed) from Zr(0001)-(lxl)-0 with those calculated for the multi-underlayer model A(C)B(A)C(B)... with d Z r _ Q equal to 1.33A (upper continuous l i n e designated a) and 1.37A (lower continuous l i n e designated b) . . . 145 Figure 7.1 Auger peak height r a t i o N(383eV)/Zr(92eV) plotted as a function of nitrogen exposure 154 Figure 7.2 Normalized nitrogen Auger peak height r a t i o as a function of heating temperature for nitrogen on Zr(0001); the i n i t i a l coverage corresponds to Rjj = 0.25 155 Figure 7.3 Variations of the Zr Auger peak around 147 eV with nitrogen exposure on Zr(0001) 157 x v i Page Figure 7.4 Comparisons f o r (11) and (10) beams at normal in c i d e n c e of experimental 1(E) curves (dashed) from Z r ( 0 0 0 1 ) - ( l x l ) - N w i t h those measured f o r cle a n Zr(0001) and c a l c u l a t e d f o r two models of Z r ( 0 0 0 1 ) - ( l x l ) - N , namely f o r the model A(C)BAB... w i t h d Z r _ f l equal to 1.287A (curves designated A) and f o r the model A(C)B(C)AB... w i t h d Z r _ N equal to 1.330A (curves designated B) 158 Figure 7.5 Contour p l o t f o r Zr(0001)-(1x1)-N of R p versus V Q r and the Zr-N i n t e r l a y e r spacing f o r the model A(C)BAB 164 Figure 7.6 Comparison of experimental 1(E) curves (dashed) from Z r ( 0 0 0 1 ) - ( l x l ) - N w i t h those c a l c u l a t e d f o r the model A(C)BAB... with d Z r _ N equal to 1.287A (upper continuous l i n e designated a) and 1.330A (lower continuous l i n e designated b) 165 Figure 7.7 Comparison of experimental 1(E) curves (dashed) from Z r ( 0 0 0 1 ) - ( l x l ) - N w i t h those c a l c u l a t e d f o r the model A(B)CAB... w i t h d Z r _ N equal to 1.287A (upper continuous l i n e designated a) and 1.330A (lower continuous l i n e designated b) 168 Figure 7.8 Comparison of experimental 1(E) curve f o r the (10) beam from Z r ( 0 0 0 1 - ( l x l ) - N f o r normal incidence w i t h that c a l c u l a t e d f o r the model A(C)BAB... w i t h the Zr-N i n t e r l a y e r spacing equal to 1.287 A, as w e l l as that c a l c u l a t e d f o r the s i m i l a r model which j u s t d i f f e r s from the f i r s t by neglect of N. The i n t e r l a y e r spacing between f i r s t two Zr l a y e r s i n both models i s i d e n t i c a l 173 Figure 8.1 Experimental 1(E) curves f o r the (11) beam from (a) cl e a n Zr(OOOl), (b) Zr(0001-(2x2)-0 w i t h R = 0.16, (c) Z r ( 0 0 0 1 ) - ( l x l ) - 0 w i t h R Q = 0.23 178 Figure 8.2 Experimental 1(E) curves f o r the (11) beam from (a) clea n Zr(0001), (b) Zr(0001)-(3x3)-S w i t h R = 1.9, (c) Zr(0001)-(3x3)-S w i t h R = 2.4, (d) Zr(0001)-(3x3)-S w i t h R - 3.1 179 x v i i Page Figure 8.3 Schematic diagram for LEED pattern and beam notation f o r the Zr(0001)-(3x3)-S structure 181 Figure 8.4 1(E) curves measured for normal incidence from the Zr(0001)-(3x3)-S surface with R g = 3.1 for the d i f f r a c t e d beams: (1/3 1), (2/3 2/3), (10), (2/3 1/3), (1/3 1), (2/3 1), (4/3 1/3), (4/3 0) and (0 5/3) 182 Figure 8.5 Some possible S overlayer structures (shaded c i r c l e s ) f o r the Zr(0001)-(3x3)-S surface. The s u l f u r coverages with respect to Zr (open c i r c l e s ) are: (A) 1/9 ML, (B) 2/9 ML, (C) 1/3 ML, (D) 4/9 ML. La t e r a l s h i f t s of the S overlayers are possible 187 x v i i i Acknowledgements I t has been a rewarding experience to work under my s u p e r v i s o r , P r o f e s s o r K.A.R. M i t c h e l l , during the course of t h i s work. I have appreciated h i s guidance and encouragement of my research, as w e l l as h i s advice and comments on t h i s t h e s i s . I am a l s o g r a t e f u l to P r o f e s s o r D.C. Frost f o r j o i n t l y sponsoring the e a r l y part of t h i s study. My s i n c e r e thanks are owed to Dr. M.A. Van Hove ( U n i v e r s i t y of C a l i f o r n i a , Berkeley) and Dr. S.Y. Tong ( U n i v e r s i t y of Wisconsin, Milwaukee) f o r p r o v i d i n g us w i t h copies of t h e i r computer programs f o r LEED c a l c u l a t i o n s . I am a l s o g r a t e f u l to my Guidance Committee f o r meeting w i t h me during the course of my graduate work, and e s p e c i a l l y to Professor J . T r o t t e r f o r h i s reading, at short n o t i c e , of the f i n a l v e r s i o n of t h i s t h e s i s . I would l i k e to acknowledge the c o n t r i b u t i o n s of other members of our surface science group. I owe a s p e c i a l g r a t i t u d e to P r o f e s s o r M.Y. Zhou (Xiamen U n i v e r s i t y , China) and Dr. K.C. Hui, f o r t h e i r patience i n guiding me as a new graduate student, and l a t e r to Dr. R.A. McFarlane, f o r reading the f i r s t d r a f t of t h i s t h e s i s . I a l s o appreciate my i n t e r -a c t i o n s w i t h Dr. M.A. Karelowski, Mr. H.C. Zeng and Dr. R.N.S. Sodhi. I am indebted to many members of the e l e c t r i c a l and mechanical workshops who have c o n t r i b u t e d so much i n maintaining our equipment i n working order. i xix Finally, but foremost, a deep sense of gratitude and love is directed towards my parents and my wife, Ling Wong, who have spiritually supported me throughout the course of my study. To them, I dedicate this thesis. 1 C H A P T E R 1 Introduction 2 1.1 Introduction During the past two decades studies of s o l i d surfaces, to give information on chemical, e l e c t r o n i c and v i b r a t i o n a l properties, have had great impact i n materials science (e.g. i n semiconductor a n a l y s i s , hetero-geneous c a t a l y s i s , polymer coatings, corrosion phenomena). Indeed for a l l reactions between s o l i d - s o l i d , s o l i d - l i q u i d and solid-gas phase combina-tions, the boundary region (the int e r f a c e or surface region) always plays an important r o l e , p a r t i c u l a r l y i n the i n i t i a l process. T r a d i t i o n a l surface chemical studies have usually focused on macroscopic properties of " r e a l " or " d i r t y " surfaces of p o l y c r y s t a l l i n e material, but modern surface science emphasizes the use of "clean and well-defined" surfaces, e s p e c i a l -l y of single c r y s t a l s . The l a t t e r i s leading to new and fundamental insights into the physics and chemistry of condensed matter, p a r t i c u l a r l y when the surface structure i s taken into account. Attempts to understand surface properties, without having adequate knowledge of structure at the atomic l e v e l , have i n the main been unsuccessful. I d e a l l y the "clean surface approach" uses a single c r y s t a l surface which i s well characterized with regard to chemical composition and defect structure; to con t r o l composition i t must be held i n an u l t r a high vacuum (UHV) environment (pressure < I O - 9 T o r r ) . Low pressure i s also e s s e n t i a l f o r the operation of some surface a n a l y t i c a l techniques such as low energy electron d i f f r a c t i o n (LEED) and Auger electron spectroscopy (AES) which are involved i n th i s work. 3 The arrangement of atoms and the d i s t r i b u t i o n of electrons near the surface of a c r y s t a l can be d i f f e r e n t from those i n the bulk of the c r y s t a l . Insofar as one can imagine a c r y s t a l as an array of b a l l s connected by springs, then, as the springs are cut to form a surface, surface atoms would be expected to move away from the bulk p o s i t i o n s . In turn other properties can be a f f e c t e d , including chemical r e a c t i v i t y . The s t r u c t u r a l changes that occur i n the surface region may involve one or more atomic layers. The s t r u c t u r a l changes that occur on formation of a s i n g l e -c r y s t a l surface are conventionally c l a s s i f i e d i n r e l a t i o n to the structure of the corresponding plane i n the bulk. If the d i p e r i o d i c i t y does not change, the surface i s said to have relaxed, whereas i f the d i p e r i o d i c i t y changes, the surface i s said to have reconstructed. LEED distinguishes these p o s s i b i l i t i e s . For example, the (111) surface of rhodium and the (0001) surface of zirconium, involved i n t h i s work, are s l i g h t l y relaxed [1,2], while the (111) surface of s i l i c o n , annealed a f t e r cleaning by ion bombardment, undergoes a surface reconstruction and shows a (7x7) LEED pattern [3]. Recently there has been a rapid growth i n a v a i l a b l e techniques f o r characterizing surfaces. The probe sources Include electrons, photons, atoms and ions, and Table 1.1 summarizes some important surface a n a l y t i c a l techniques for assessing composition as well as geometrical, e l e c t r o n i c and v i b r a t i o n a l structure. More d e t a i l s can be found i n the references quoted under the f i r s t column i n Table 1.1. In general, each technique may have p a r t i c u l a r advantages, but a "multi-technique strategy" can provide the most detailed o v e r a l l view of a surface. In general, at least two Table t . l : Some surface techniques and their characterist ics . Technique Acronym Probe part ic le Measured part ic le Information Auger electron spectroscopy C4,5 3 AES Electron Electron Composition Secondary-ion mass spectroscopyC6 3 SIMS Ion Ion • Composition X-ray photoelectron spectroscopyC5 3 XPS Photon Electron Composition, valence states Low-energy electron d i f fract ion C.7,8 3 LEED Electron Electron Geometrical structure Reflection high-energy electron d i f f rac t ionC9 3 RHEED Electron Electron Geometrical structure X-ray d i f f rac t ion ClO XD Photon Photon Geometrical structure Photoelectron d i f fract ion C H . 12 3 PD Photon Electron Geometrical structure Near-edge X-ray absorption fine structure C13 3 NEXAFS Photon Photon, electron Intramolecular bonding Surface Extended X-ray absorption fine structure C 13,14 3 SEXAFS Photon Photon, electron Geometrical structure Rutherford back scattering C153 RBS Ion Ion Composition, geometrical structure High-resolution electron energy loss spectroscopy £163 HREELS Electron Electron Vibrat ional structure U l t ra -v io l e t photoelectron spectroscopy Cl? 3 UPS Photon Electron Valence state 5 complementary techniques are needed to answer the most fundamental questions of a surface region: ( i ) What atoms are present? ( i i ) How are these atoms arranged? Of the techniques l i s t e d i n Table 1.1 the most commonly and conveniently used methods to answer these questions are the combination of LEED and AES, although X-ray photoelectron spectroscopy i s p a r t i c u l a r l y valuable for assessing the state of atoms at a surface. LEED remains the most developed method for providing s t r u c t u r a l information, although other important techniques include photoelectron d i f f r a c t i o n , SEXAFS, and ion s c a t t e r i n g . 1.2 C l a s s i f i c a t i o n of Surface Structure A surface of a single c r y s t a l i s conveniently c l a s s i f i e d with reference to the p a r a l l e l plane within the bulk c r y s t a l . In addition, for a surface region, a l l equivalent points i n a plane p a r a l l e l to the surface are related by two-dimensional ( d i p e r i o d i c ) t r a n s l a t i o n a l vectors jt = ma i + na^2' (m,n = integers) (1«1) The unit vectors ^ and define a unit mesh i n analogy with the unit c e l l of t r i p e r i o d i c crystallography, while the complete set of values of m and n generate a net i n analogy with the use of the term l a t t i c e i n t r i p e r i o d i c crystallography. Five types of unit mesh are possible. They are shown i n 6 Figure 1.1(a) and they are analogous to the 14 Bravais u n i t c e l l s of t r i p e r i o d i c c r y s t a l l o g r a p h y . A surface studied i n LEED i s three-dimensional, but only d i p e r i o d i c s i n c e , f o r the top few l a y e r s , no p e r i o d i c i t y can be r i g o r o u s l y e s t a b l i s h e d i n the d i r e c t i o n normal to the su r f a c e . D e t a i l s of various conventions In surface c r y s t a l l o g r a p h y can be found i n an a r t i c l e by Wood [18] and i n the I n t e r n a t i o n a l Tables f o r X-ray c r y s t a l l o g r a p h y [19]. 1.3 R e c i p r o c a l Net As i n the bulk, i t Is very convenient to u t i l i z e a r e c i p r o c a l space c o n s t r u c t i o n f o r rep r e s e n t i n g d i p e r i o d i c d i f f r a c t i o n . Given u n i t vectors * * a^ and a 2 i n r e a l space, the corresponding u n i t vectors a j and a,2 i n r e c i p r o c a l space are generated from a^-a* = 2ic6 ± J, ( i , j = 1,2) (1.2) where 6^ = 0 i f i * j and 6^ = 1 i f i = j ( i . e . a j 1 a,2, and -1- a,i as i s shown i n Figure 1.2). These u n i t vectors define a r e c i p r o c a l net from * * g » h a x + ka, 2 • (h,k » i n t e g e r s ) (1*3) The f i v e p o s s i b l e types of r e c i p r o c a l net are shown i n Figure 1.1(b). Real Reciprocal °2 s qua re 92 Si SI rectangular t 92 O fO a, ° centered % rectangular g 2 sr hexagonal ob l ique (b) Figure 1.1: The five types of two-dimensional surface meshes (a) in real space (b) in reciprocal space. 8 o Figure 1.2: A two-dimensional net i n r e a l space ( f i l l e d c i r c l e s ) described by u n i t t r a n s l a t i o n vectors ai> A2 a n <* t n e a s s o c i a t e d net i n r e c i p r o c a l ^ s p a c g (open c i r c l e s ) described by u n i t t r a n s l a t i o n vectors , % 2 ' 9 1.4 Low Energy E l e c t r o n D i f f r a c t i o n (LEED) 1.4.1 E l e c t r o n S c a t t e r i n g i n S o l i d s A beam of e l e c t r o n s w i t h a d e f i n i t e energy, E^, impinging on a surf a c e , w i l l give backscattered and secondary emitted e l e c t r o n s whose energy d i s t r i b u t i o n i s shown s c h e m a t i c a l l y i n Figure 1.3. For the purpose of LEED, t h i s d i s t r i b u t i o n may be d i v i d e d i n t o three regions. Region I contains e l a s t i c a l l y s c a t t e r e d e l e c t r o n s as w e l l as the " q u a s i - e l a s t i c " e l e c t r o n s which have s u f f e r e d small energy losses (< 0.1 eV) due to i n t e r -a c t i o n s w i t h surface phonons. The l a t t e r are not detected w i t h conven-t i o n a l LEED o p t i c s , but w i t h an analyzer of high r e s o l u t i o n the surface v i b r a t i o n modes can be studied (as i n HREELS). T y p i c a l l y i n LEED only a few percent of the i n c i d e n t e l e c t r o n s are e l a s t i c a l l y backscattered. In region I I , small peaks observed on the s l o w l y - v a r y i n g background correspond to i n e l a s t i c a l l y s c a t t e r e d e l e c t r o n s a s s o c i a t e d w i t h interband and plasmon e x c i t a t i o n s [20]; i n a d d i t i o n peaks r e s u l t i n g from the emission of Auger e l e c t r o n s are present. The Auger peak energies are independent of E^, and therefore they can be d i s t i n g u i s h e d from the l o s s peaks by varying E^. The s o - c a l l e d "true secondary e l e c t r o n s " located i n region I I I at low energies are associated w i t h a s e r i e s of i n e l a s t i c s c a t t e r i n g s o c c u r r i n g i n a cascade-type process [ 5 ] . A p p l i c a t i o n s of LEED to surface c r y s t a l l o g r a p h y depend on two f a c t o r s : (1) the wave nature of e l e c t r o n s ensures that the energy (E i n eV) i s r e l a t e d to wavelength (X i n A) according to de B r o g l i e ' s r e l a t i o n 10 \ = / 150.4/E . (1.4) This immediately implies that electrons whose energies are around 100 eV have wavelengths of the order of atomic spacings. Such electron waves scattered from a periodic crystal surface can then be expected to interfere, and to give probability distributions which, as for X-ray di f fract ion, contain geometrical information. (2) The observation of elastic scattering by low-energy electrons (typical energy range from 20 eV to 500 eV) implies a process of high surface sens i t iv i ty . This is inevitable because electrons of energy to 1 keV have a high probability to be scattered ine las t ica l ly . A useful parameter for discussing inelastic scattering is L, defined as the mean distance travelled by an electron before i t is scattered ine las t i ca l ly . This satisf ies where the incident intensity, I q , at a particular energy is attenuated to I on passage through a distance x. The characteristic dependence of L on the electron energy for metals is shown in Figure 1.4; typical ly in the low-energy range L then corresponds to just a few A. That emphasizes that these electrons are ideally suited for surface studies. More details on electron mean free paths can be found in ref. 21. I = I o e x p ( - V L ) , (1-5) 1.4.2 Conditions for Elas t ic LEED In LEED, an incident electron beam with known energy (E) and 11 (lll).true ENERGY E p Figure 1.3: Schematic energy distribution N(E) of back-scattered electrons for a primary beam of energy Ep. 0 10 100 1000 10,000 100,000 ELECTRON ENERGY (eV) Figure 1.4: Schematic diagram of the mean free path for electrons in a metallic sol id as a function of energy. 12 direction (9,<t>) impinges on a face of a s ingle-crystal , as is shown in Figure 1.5, and a small portion of the incident electron flux is e la s t i ca l -ly back-scattered in discrete directions. The incident and diffracted beams are conveniently represented by plane waves <|>k(£) = expdfc.rj , (1.6) where k is a wave vector which specifies the beam direction. The magnitude of k ( i . e . 2rt/\) relates to energy by E ='n 2 |k | 2 /2m, (1.7) where m is the electron's mass and'n is Planck's constant divided by 2 IT. For incident and diffracted beams of wave vectors k^ and k' respectively, the di f ferent ia l scattering cross-section can be expressed quite generally as 1£= (m/2itn2)2|<\,|TKk > | 2 , (1.8) dQ ~ "-D where T is the appropriate transition operator [22,23,24]. For a symmetry operation S, the matrix elements in equation (1.8) satisfy < \ . | T | \ > = <cPk,|S ^ S l ^ > = <Sc|;k,|T|Sclk > (1.9) 13 diffracted beams ,1 incident beam k(E,0,0) Figure 1.5: Conventions to describe the Incidence direction for an electron beam interacting with a surface; 9 is the polar angle relative to the surface normal and <t> is an azimuthal angle relative to a major crystallographic axis in the surface plane. 14 When S represents translation by a net vector t,, then S \ ( r ) = \(r+t) = exp(ik.(r+t)), ( 1 . 1 0 ) and equation ( 1 . 9 ) requires <\,|T|4^ > - e x p [ i ( l ^ - V ) « £ ] < ^ , | T | ^ >. ( 1 . 1 1 ) This can hold only i f either <4^iIT|4^ > = 0 or exp[i(k - k ' ) « t ] = 1 . The f i r s t corresponds to zero scattered intensity, but the second necessarily holds when ( k o _ k ' ) * t / = 2nit for n integral . This is in turn automatic i f the paral le l components of the wave vectors satisfy k ' ( ) = k £ | ( + g(h,k), (h,k = integers) ( 1 . 1 2 ) where the superscripts +/- specify the wavevector directions into/out of the crysta l . The g(h,k) are vectors of the reciprocal net as in equation (1.3). The equation (1.12) is a statement of momentum conservation paral le l to the surface. That equation along with the conservation of energy for e last ic scattering, namely I^I2HCI2' ( 1 . 1 3 ) 15 forms the diffract ion conditions for LEED- The indices (h,k) conveniently label the diffracted beams (e.g. the (00), (10), (11) beams). In a conven-tional LEED experiment, the diffracted electrons are collected on a hemispherical fluorescent screen, the crystal being positioned at the center of curvature of the grid and screen system. The intersections of the diffracted beams with the screen give a distribution of spots ( i . e . the LEED pattern), which are direct ly determined by the reciprocal net associated with the particular crystal surface. An example is detailed in Figure 1.6. From equation (1.12), the (00) (or specular) beam is formed by electrons which have interacted with the surface without transfer of momentum paral le l to the surface, and therefore the position of i ts spot on the screen remains invariant as the incident energy is changed (provided that the electrons are moving in a f ield-free space and the direction of incidence is fixed). As E is increased, the perpendicular component of each diffracted beam ( i . e . k p is necessarily increased, and this results therefore in the non-specular beams moving toward the (00) beam. For off-normal incidence, the position of the (00) spot on the screen enables the angles of incidence to be fixed [7]. 1.4.3 Two-dimensional LEED Analysis The geometry of a two-dimensional LEED pattern ( i . e . the reciprocal net) gives information on the size and shape of the unit mesh for the real surface, and those for adsorption systems are generally compared with the corresponding clean surface. Two helpful nomenclatures are available for the two-dimensional LEED analyses, namely Wood's notation [18] and matrix 16 H O ) 9(-20J JX SURFACE NORMAL Figure 1.6: Schematic diagram i l lus tra t ing how the conservation conditions determine direction of a diffracted beam. The (00) beam corresponds to the specular ref lect ion. 17 notation [25,26], and they both relate the unit vectors b^ and b 2^ for the adsorption structure to those of the substrate, a^ and a£• If there is a common rotation angle, 9, between them, then Wood's notation specifies the adsorption structure as (mxn)-9, where I b J / l a J = m, Ib^l/ la^l = n. Reference to the angle is conventionally dropped i f i t is zero. The most general relation of b^ and b 2 to a^ and a 2 is — a l l a 1 2 > 2 . a 2 1 a 2 2 or jj, = A g,, the matrix A provides a general designation of a surface with respect to the substrate. Figure 1.7 shows some examples of these notations for adsorption on f c c ( l l l ) or hcp(OOOl) surfaces. The variation of LEED patterns with various parameters (e.g. coverage of adsorbed species, temperature) is often assessed to describe some surface features (e.g. reconstruction, reaction, segregation) in a qualitative sense; indeed a two-dimensional LEED analysis may be u t i l i zed to construct surface phase diagrams [27]. In addition, the sharpness of LEED spots is associated with surface order. When changes occur that result in broader and weaker diffract ion spots, and with increased diffuse scattering between them, i t can be concluded that the surface is becoming less ordered. 18 HCP(0001) FCC (111) Wood notation (1X1) (2X2) (/3"X/T)-30° (2X1) Matr i x notat ion i o o i 2 o o 2 1 i -I 2 2 0 0 I Figure 1.7: Some common translational symmetries (unit meshes) for adsorption on f c c ( l l l ) or hcp(OOOl) surfaces using both Wood's notation and the matrix notation. 19 1.4.4 LEED Crystallography The determination of the relative positions of surface atoms ( i . e . structural information) can not be made by a two-dimensional LEED analysis. For example, Figure 1.8(a) i l lustrates four possible adsites on the (111) surface of rhodium which are available for the adsorption of sulfur atoms; these can a l l exhibit a ( / 3 x / 3 ) 3 0 ° LEED pattern as is shown in Figure 1.8(b). In LEED crystallography, the two-dimensional LEED analysis is supplemented by analyzing the intensities of the diffraction spots, and this is most readily done by measuring the variation of spot intensities as a function of electron energy [8]. The production of intensity-versus-energy curves, namely 1(E) curves, or just occasionally 1(9) or I(<)>) curves (for variation of the polar or azimuthal Incident angles, respectively), serve as the basis for the experimental contribution to LEED crysta l lo -graphy. The theoretical 1(E) curves for a particular surface structure are then calculated by multiple-scattering methods (Chapter 2). By comparing the experimental 1(E) curves with the calculated 1(E) curves for various t r i a l structures, i t is possible to extract the correct structural arrange-ment. Consequently, the detailed surface structural information such as the determination of adsite for adsorbates, the distances between atoms within each unit mesh and the distances between surface layers are also obtained. Figure 1.9 shows the comparisons of one experimental 1(E) curve with calculated 1(E) curves for various topmost interlayer spacings corresponding to two given different adsites. 20 3h site 3f s i te • top s i te bridge s i t e a - • — + (01) (0 0) (1/3 1/3) l io) b Figure 1.8: (a) Unit mesh of the (/3x/3)30° over l a y e r s t r u c t u r e and four p o s s i b l e adsorption s i t e s f o r s u l f u r adsorbed on R h ( l l l ) . The 3h and 3f s i t e s are t h r e e f o l d s i t e s which are d i s t i n g u i s h e d r e s p e c t i v e l y by whether there i s a substrate atom or not located d i r e c t l y below the second l a y e r . (b) Schematic LEED pa t t e r n corresponding to the ov e r l a y e r s t r u c t u r e of ( a ) . 21 ELECTRON ENERGY (eV) Figure 1.9: Comparison of an 1(E) curve measured for the (1/3 1/3) diffracted beam from R h ( l l l ) - ( / 3 x » / 3 ) 3 0 o - S at normal incidence with those calculated for the 3f and 3h adsorption sites over a range of the topmost S-Rh interlayer spacings. 22 Figure 1.9: (continued) 23 1.4.5 Instrumental Response, Domains and Disorder In the discussion of electron diffract ion so far two Implicit assumptions have been made. The f i r s t is that a crystal surface studied by LEED can be perfectly ordered over an inf ini te extent. Secondly, i t has been assumed that the incident beam and diffracted beams are simple plane waves whose properties are uniform across the wavefronts. In fact, these two assumptions can never be satisfied exactly. In a LEED experiment the electron gun usually produces a beam about 1 mm In diameter, which is made up of electrons with angular and energy deviations associated with the f inite size and high temperature of the source; there is also a f in i te size for the detector. These experimental flaws l imit the information that can be obtained from a dif fract ion measurement. In this context, Park et  a l . [28] defined an instrumental response function which yields a charac-ter i s t i c dimension, the transfer width L , over which the instrument is sensitive as a probe of the surface periodicity [29]. In conventional LEED a typical transfer width is approximately 102A, and this dimension sets a l imit on the spatial information obtainable by the dif fract ion experiment (although s t r i c t l y the experimental precision also affects the distance over which order can be detected [142]. In our work, the Incident beam Inevitably has a cross section whose dimension is large compared with L; as a result the LEED patterns are actually made up of a sum of contributing patterns from restricted areas (of the order of L 2 ) . In any event, a real surface which is formed by cutting Inevitably has an appreciable defect 24 concentration resulting especially from the presence of steps. At the microscopic level , then, such a surface Is inevitably heterogeneous, being composed of many separate islands or domains. Aspects of disorder may affect LEED patterns in several different ways. Indeed i f a surface is well ordered within domains of dimension at least L , "good" LEED patterns can be observed even i f there are substantial imperfections between the ordered regions [29]. Secondly, beam spl i t t ing and broadening can occur with antiphase scattering [26] from areas whose dimension is small compared with L . Also domains may lead to some ambiguity in interpretation of a LEED pattern, for example one exhibiting a complete set of half-order diffracted beams from the (111) face of a fee crystal (and equally from a (0001) face of a hep crystal ) . Such a pattern can be attributed either to a simple (2x2) surface structure or to three rotationally-related domains of the types shown in Figure 1.10. The positions of spots in the LEED patterns would be identical in either case. Another interesting contrast of a similar type is shown by considering the LEED patterns resulting from the clean Rh( l l l ) and Zr(0001) surfaces. Both these surfaces have one 3-fold rotational symmetry axis and appropriate mirror symmetries perpendicular to the surface. Nevertheless at normal incidence the latter exhibits a LEED pattern with 6-fold symmetry whereas the former exhibits a 3-fold pattern. This anomalous situation for Zr(0001) is a result of the coexistence of two types of domain which are related by a 2-fold rotation as is shown in Figure 1.11. These domains correspond to the two possible terminations ( i . e . A . B . A . B . . . and B . A . B . A . . . ) when the zirconium crystal is truncated paral le l to the (0001) 25 Figure 1.10: A (2x2) structure on a f c c ( l l l ) or hcp(OOOl) surface is shown bottom lef t , while the corresponding LEED pattern is drawn schematically at bottom right (the half-order beams are identified by crosses). The top shows three domains of a (1x2) type structure which are related by 120° rotations. The total LEED pattern from a surface with equal populations of these domain types w i l l be a superposition of the three individual patterns. This superposition gives spots in identical positions to the (2x2) pattern. 26 (a) (b) (C) O Topmost-layer atoms Second-layer atoms P: monoatomic Termination A S*. e^ Termination B O • I o # O • O'O • o o • spa m o • | • o I or% o • d o • o o o 51 • o <*r# o • O i O • o • o > o • o • ' • o • o i — I * + Figure 1.11: (a) Side view and (b) top view of the two types of domains r e s u l t i n g from the t r u n c a t i o n of the hep bulk s t r u c t u r e p a r a l l e l to the (0001) plane. The two domains are r e l a t e d to each other by a 180° r o t a t i o n . (c) S u p e r p o s i t i o n of the two 3 - f o l d symmetrical LEED patterns (expected f o r normal incidence) to form a LEED p a t t e r n w i t h 6 - f o l d symmetry. 27 plane. When the p r o b a b i l i t i e s of the two domains appearing on the surface region probed by the primary electron beam are approximately equal, a 'domain averaged' LEED pattern having 6-fold symmetry appears for normal incidence. A discussion of domain averaging i n a more-complicated context has been given by Wang et_ a l . [30]. 1.5 Auger El e c t r o n Spectroscopy (AES) The phenomenon now covered by the term Auger electron spectroscopy was f i r s t observed and interpreted by Pierre Auger i n 1925 [31]. Auger electrons are ejected from a target atom by a mechanism l i k e that i l l u s t r a t e d i n Figure 1.12. The f i r s t step involves i o n i z a t i o n from an inner s h e l l ( i . e . the K-shell for the example shown), and the vacancy l e f t can then be f i l l e d with an electron from a higher s h e l l ( i . e . L 2)» The excess energy ( i . e . E K~E^ ) i s simultaneously transferred to eject another electron ( i . e . an Auger electron from L3) with a k i n e t i c energy which approximately equals E„-E T -E T . Hence Auger electrons have energies IN. 2 3' c h a r a c t e r i s t i c of the atoms from which they emerge, and this allows for t h e i r use i n i d e n t i f y i n g a l l atoms of the periodic table except for hydrogen and helium. For surface chemical analysis, the main i n t e r e s t i s i n Auger electrons with energies i n the approximate range 50-900 eV which are characterized by short mean free path lengths i n s o l i d s . Although the Auger t r a n s i t i o n process can also be i n i t i a t e d by X-radiation and ion bombardment, electron bombardment only i s used i n t h i s work. In practice the Auger electrons that are c o l l e c t e d from surface atoms are i n e v i t a b l y accompanied by large numbers of secondary electrons. Auger spectra are 28 KULo Auger E l e c t r o n Figure 1.12: Schematic r e p r e s e n t a t i o n of an Auger process i n terms of atomic and valence band energy l e v e l s . This example i s s p e c i f i c a l l y f o r the production of a K L 2 L 3 Auger e l e c t r o n . 29 commonly presented in the f i r s t derivative form of the relative energy distribution in Figure 1.3; differentiation can minimize the effect of the high but slowly-varying background of scattered electrons. It is customary to catalog Auger energies by positions of the negative peaks in differen-t i a l spectra. A representative AES spectrum for a sulfur and carbon conta-minated Rh( l l l ) surface is shown in Figure 4.1(a). High Auger electron yields are advantageous for the application of AES to surface chemical analysis. A relaxation process which competes with Auger emission is X-ray fluorescence. This occurs when the excess energy associated with the electron relaxation into the i n i t i a l vacancy is released as a photon (in l ieu of being transferred to eject an Auger electron). In general, for atoms with atomic numbers below 30, the Auger transition process is more probable than that for X-ray fluorescence; for heavier atoms Auger emission s t i l l dominates provided the energy of the Auger transition is less than around 2 keV. The use of AES for qualitative surface analysis is achieved by comparing measured spectra with standard representative spectra [32] or with tabulated energies [33]. Although changes in chemical environment can result in energy shifts of the order of a few eV [34], these are too small in general to seriously affect applications to qualitative analysis. When AES is studied under low resolution, some overlapping of Auger peaks occurs not Infrequently (e.g. the S 1 5 0 and Z r 1 1 + 7 peaks in Figure 6.1(a)). The existence of several Auger energies for most elements (e.g. Auger energies at 92, 116, 124 and 174 eV for zirconium) usually eliminates any ambiguity in assignment. The technique is capable of being quantified, although this 30 i s done most o f t e n by c a l i b r a t i n g w i t h other measurements ra t h e r than using the f i r s t - p r i n c i p l e s approach [35]. To avoid instrumental a r t e f a c t s , adsorbate concentrations on a s i n g l e c r y s t a l surface are f r e q u e n t l y q u a n t i -f i e d by comparing values of a r e l a t i v e Auger peak height r a t i o of adsorbate to that of the substrate (e.g. the r a t i o A 1 5 1 / A 3 Q 1 ( used i n Chapter 4 ) . 1.6 Aim of Thesis The o b j e c t i v e s of the studies presented i n t h i s t h e s i s are to c o n t r i b u t e to the subject of LEED c r y s t a l l o g r a p h y , and to r e l a t e the new surface s t r u c t u r a l information to s t r u c t u r a l chemical p r i n c i p l e s . The p a r t i c u l a r surfaces studied were made by gas adsorption on the R h ( l l l ) and Zr(0001) s u r f a c e s , to form new s t r u c t u r e s designated Rh(111)-(/3x^3)30°-S, R h ( l l l ) - ( 2 x 2 ) - 0 , Zr(0001)-(2x2)-0, Z r ( 0 0 0 1 ) - ( l x l ) - 0 , Z r ( 0 0 0 1 ) - ( l x l ) - N and Zr(0001)-(3x3)-S. Both rhodium and zirconium have important t e c h n o l o g i c a l a p p l i c a t i o n s . For example, the i n t e r a c t i o n of oxygen with rhodium plays an important r o l e i n s e v e r a l c a t a l y t i c r e a c t i o n s i n c l u d i n g ketone re d u c t i o n [36], methanation [37], n i t r o g e n oxide r e d u c t i o n [38], and the o x i d a t i o n of hydrogen [39]. In c o n t r a s t to oxygen, s u l f u r i s a known c a t a l y t i c poison f o r rhodium. Nevertheless, the s t u d i e s of s u l f u r on the R h ( l l l ) surface i n t h i s work attempt to f u r t h e r our understanding at the atomic l e v e l f o r such features as adsorption s i t e and surface bond length. The s t u d i e s f o r s u l f u r on R h ( l l l ) should give f u r t h e r i n s i g h t i n t o the nature of the Rh-S surface chemical bond, p a r t i c u l a r l y by comparing w i t h e a r l i e r s t u d i e s f o r s u l f u r adsorption on the Rh(100) and Rh(110) surfaces [40,41]. The s u b s t a n t i a l p o t e n t i a l i n t e r e s t i n the surface chemistry of zirconium [42], as w e l l as the very l i m i t e d experimental data a v a i l a b l e so 31 far for adsorption on surfaces of hexagonal close-packed metals, provided an impetus for analyses of surface structures formed by chemisorption on the Zr(0001) surface. Such studies are not helped by the high reactivity of this metal. Other factors which have possibly retarded the studies of the surface chemistry of zirconium can be summarized as follows: (1) Single crystals of zirconium are not commercially available. (2) The bulk phase transition (hep bec) at 862°C restricts poss ib i l i t i es for surface preparation, in relation to cleaning and to annealing as required to achieve an ordered surface. (3) The common low-weight atoms have a strong tendency to diffuse into the bulk, thereby resulting in d i f f i cu l t i e s in cleaning and in defining proper exposure ranges for the formation of the intended surface structures. For zirconium this work aims to develop a rel iable method for surface cleaning and to c lar i fy some uncertainties associated with the one earl ier structural investigation for adsorption at the Zr(0001) surface, as reported by Hui ejt a l . [43] for the Zr(0001)-(2x2)-0 structure. The new work made here analyzes the lowest-coverage Zr(0001)-(lxl)-0 structure, with the view to gaining more Information about the i n i t i a l stages of the oxidation of Zr(0001). Additionally, this work aims to elucidate the structure of two previously unstudied surfaces, namely Zr(0001)-(lxl)-N and Zr(0001)-(3x3)-S. The coadsorption of oxygen and H 2S on Zr(0001) was also studied in an attempt to gain Insight into the interactions between adsorbed sulfur and oxygen at this surface. 32 The layout of this thesis is described as follows. Chapter 2 br ie f -ly discusses the 'combined space' approach in LEED multiple scattering calculations, and the important non-geometrical parameters required in the calculations. The r e l i a b i l i t y index routine used for making comparisons of experimental and calculated 1(E) curves is also described. Chapter 3 reviews the experimental aspects of these LEED/AES studies. Chapter 4 reports observations for the adsorption of H2S on R h ( l l l ) . An analysis of diffracted beam intensities is performed for the R h ( l l l ) - ( / 3 x / 3 ) 3 0 ° - S structure. Chapter 5 reports investigations of the Rh(lll)-(2x2)-0 surface structure, including LEED intensity measurements in the presence of some electron beam disordering of the adsorbed oxygen overlayers. Chapter 6 includes an examination of the oxygen coverage in surface structures which give Zr(0001)-(2x2)-0 type LEED patterns. The emphasis involves measuring a half-order diffracted beam profi le as a function of exposure and heating temperature. Chapter 7 reports LEED crystallographic and AES investigations of a surface designated Zr(0001)-(lxl)-N. F ina l ly , Chapter 8 reports observations for the Zr(001)-(3x3)-S structure, and includes comparisons between oxygen and sulfur adsorption on this surface. LEED intensity curves were measured from the Zr(0001)-(3x3)-S structure, although a multiple-scattering analysis has not yet been undertaken. 33 CHAPTER 2 C a l c u l a t i o n of LEED I n t e n s i t i e s 34 2.1 Introduction The analysis of LEED intensities requires a theory of the di f fract ion process. A simple single-scattering theory (such as is used in X-ray crystallography) is not suitable for describing the scattering of low-energy electrons from a sol id surface. This is mainly due to the fact that the low-energy electrons interact very strongly with solids (the high surface sensit ivi ty results especially from strong inelast ic scattering), but even for elast ic scattering electrons in the low-energy range have much larger scattering cross-sections than for X-ray scattering (by a factor of around 10^). Compared with X-rays a much larger fraction of electrons is backscattered; also there is a much larger probability that the back-scattered electrons w i l l scatter several times before emerging from the surface. The latter gives rise to the multiple scattering peaks which are readily observable in measured 1(E) curves, and which cannot be accounted for by single scattering theory with reasonable geometries. Inevitably, then, multiple scattering or dynamical calculations are required for LEED intensity analyses. Detailed descriptions of the theoretical methods are discussed in books by Van Hove and Tong [44] and by Pendry [45]. A l l the main computing programs used in the research of this thesis are from either Van Hove and Tong's book [44] or the magnetic tape provided by Van Hove [46]. The objectives of this chapter are to provide an overview of the physical processes involved and to outline the computer subroutines u t i l i zed in this study. 35 2.2 Geometrical and Non-geometrical Parameters A l l ordered surface regions, whether they involve adsorbed layers, or relaxed or reconstructed clean surfaces, can be envisaged as b u i l t from d i p e r i o d i c layers which are stacked p a r a l l e l to the surface plane. Usually the o v e r a l l d i p e r i o d i c i t y of the surface region can be recognized d i r e c t l y from the form of the LEED pattern; however the way the (surface) layers are related to one another can only be determined by analyzing the d i f f r a c t e d beam i n t e n s i t i e s . LEED analyses p a r t i c u l a r l y aim to determine those geo-metrical parameters which e s t a b l i s h the r e l a t i o n s h i p between a l l surface layers and the underlying substrate, whose structure i s generally known. For the underlying substrate, the r e l a t i v e atomic positions can be described by the known geometrical parameters such as two-dimensional t r a n s l a t i o n a l vectors (t,) and three-dimensional propagation vectors (ASA) for the intraplanar atoms and interplanar atoms, r e s p e c t i v e l y , as i s i l l u s t r a t e d i n Figure 2.1. The LEED cr y s t a l l o g r a p h i c studies i n t h i s thesis p a r t i c u l a r l y aim to determine adsorption s i t e s , i n t e r l a y e r spacings and layer r e g i s t r i e s which are i d e n t i f i e d from a t r i a l - a n d - e r r o r type of analysis [8]. Apart from geometrical parameters, various non-geometrical para-meters describing the strong i n t e r a c t i o n of a LEED electron with a s o l i d are also required for the computation of 1(E) curves. The p o t e n t i a l s responsible for the s c a t t e r i n g within and between these v i b r a t i n g s c a t t e r i n g centers ( i . e . the "non-local ion cores") play important roles i n a multiple scattering c a l c u l a t i o n . The p o t e n t i a l of a s o l i d i s usually approximated by the "muffin-tin" model, i n which the p o t e n t i a l i s assumed 36 • X Figure 2.1: Example of relaxation at a f c c ( l l l ) surface. The three-dimensional propagation vectors ASJJ and ASA apply to the relaxed region and bulk region r e s p e c t i v e l y . The corresponding Interlayer spacings D* and D are shown to the l e f t . 37 spherically symmetrical within each atomic region, while in the region between ion cores the potential is treated as a constant. Section 2.3 w i l l use this model for a so l id ; i t is natural to express the wave function of a LEED electron as either a spherical wave (in angular-momentum or L-space) or a plane wave (in linear-momentum or K-space). In general, plane waves can be described in terms of a series expansion of spherical waves [23], and vice versa. The spherical waves are convenient for describing scattering by the spherically symmetrical ion cores, as well as the multiple scattering between atoms in individual layers paral le l to the surface. On the other hand, the plane waves are convenient for describing the interlayer multiple scattering (the diffraction by each layer produces a discrete set of "beams", each of which can be represented by a plane wave). The usual procedures for calculating LEED intensities sp l i t the whole scattering problem into a series of simpler steps as indicated in the following sequence: (1) Compute the single atom scattering amplitude in L-space-(2) Calculate in L-space a l l scatterings among atoms within a single layer. (3) A l l individual layers are stacked and the interlayer scattering is calculated in K-space. In the f ina l step, the wavefield outside the crystal (P o u t (r) = e x p ( i k + « r ) + £ C exp(ik--r) (2.1) 38 is matched to the wavefield inside the crystal at the solid-vacuum inter-face [47]. In equation (2.1) k + and k~ depict the incident beam and diffracted beams respectively, and the C are coefficients in the expansion 8 of the total wavefield outside the crysta l . The calculated intensity of the beam g is est X g = ^gXl^ gl2' (2'2) where k*^ and k ^ represent the perpendicular components of the incident and diffracted beams, and the superscripts '+/-' denote wave propagation in the +x/-x directions (Figure 2.1). 2.3 The Muffin-tin Approximation The muffin-tin model is i l lustrated schematically in Figure 2.2. Surrounding each atom is a spherically symmetrical potential , V G , which extends to an appropriate radius; the region between the atoms has a constant potential, V q ( i . e . the muffin-tin constant). Roughly speaking, V q i s responsible for the interaction of a LEED electron with the relat ively delocalized valence electrons, whereas V relates to the J s Interaction with the ion cores. The actual potential varies smoothly through the surface from vacuum to the solid's Interior, so the scattering resulting from any discontinuity in a model potential must be ignored for Figure 2.2: 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. 40 comparing with experimental intensit ies . In LEED multiple scattering calculations, the muffin-tin constant V q is generally represented as the sum of a real component ( v o r ) a n d a n imaginary component (VQ^)' V = V + i V . (2.3) o or oi v ' The real part ^ Q X typical ly has a value between -5 and -15 eV, and i t accounts for an electron inside a crystal experiencing a lower potential than in vacuum. This effect speeds up an electron inside a so l id , so giving the electron a lower wavelength compared with the electron in vacuum. In practice appropriate values for V Q r vary with the specif ic atomic potential used In the multiple scattering calculations. Therefore this parameter is generally set empirically from the comparisons between calculated and experimental 1(E) curves. S t r i c t l y , exchange and correlation effects give V an energy dependence [48], although i t is most often treated as energy-independent for LEED crystallographic studies. In this thesis, V Q r is often referred, following a common usage, to the 'inner potential' [49-51], a term that has tradit ional ly noted the constant shift in experimental intensity-voltage curves required to align with the corresponding calculated curves [44]. The imaginary component is a negative quantity which accounts for the electron damping effect due to inelastic scattering. The l ifetime, x, defined as the average time an incident electron spends in the sol id prior to being ine last ica l ly scattered relates to according to 41 T = " h 7 2 | V o i | ( 2 . 4 ) An increase in inelastic scattering gives a decrease in lifetime which corresponds in turn to an increase in | V D ^ | ' Appropriate values of V ^ can be determined from peak widths, A E w , in experimental 1(E) curves. By using the time-energy uncertainty principle , Pendry [45] relates the peak width AE to V . according to w oi 6 AE > 2 | V , I ( 2 . 5 ) w 1 oi 1 In general, is treated as either constant or weakly energy-dependent in LEED intensities calculations. For the latter , Demuth et a l . [52] used expressions of the type 1/3 V Q i = - B E W J , (2.6) where B Is a material-dependent parameter. This equation was used in the 2/3 studies here for rhodium surfaces, where B was set equal to 0.819 (eV) However, for the studies on zirconium, V ^ was kept constant at -5 eV. This was found to eliminate some non-convergence problems which occurred at low energies when equation (2.6) was used. The ion-core potential, V , depends on the specific atom considered. For metals i t is generally derived from band-structure potentials [53], whereas for light atoms appropriate potentials have been developed from superposition models [54] designed to simulate atoms in overlayer 42 situations [55]. A variety of atomic potentials for these atoms has been supplied by Van Hove [46]. 2.4 Ion Core Scattering By solving the Schrodinger equation [-^l)V2+Vs]4> = E<1>, (2.7) where E is energy set by the vacuum level , the scattering of a plane wave with wavevector k by a spherically symmetric ion core potential, V , gives s the asymptotic form [23] V r ,V = e x P ( i k r c o s 9 s ) + T (k ,e s ) exp( ikr ) / r . (2.8) In equation (2.8) r is the distance from the atomic nucleus, 9 is the s scattering angle, and T(k,9^) is the ion core scattering amplitude which can be expanded as T(k,9 ) = 4u S (2*+l)t.(k)P 5(cos9 ), (2.9) s 1=0 where P^ is the Legendre polynomial associated with the angular momentum quantum number A, and t .(k) is the t-matrix element ( l /4ik)[exp(2i6 J l )-l] (2.10) 43 In equation (2.10), the 6^  are phase shifts which can be evaluated by solving equation (2.7) for the appropriate ion core potential and matching to solutions In vacuum at the muffin-tin radius. Although equation (2.9) suggests an inf ini te number of A values are needed, in practice the expansions converge quite rapidly; the numbers required increase with both the atom's scattering strength and the energy. Additionally, the atomic phase shifts relate to the total elastic scattering cross-section according to 6 = (4n/k 2) S (2A+l)sin 26 . (2.11) The atomic phase shifts are important Input parameters for a LEED calculation. It has been known since the earliest LEED studies by Davisson and Germer [56] that beam intensities decrease with increasing temperature; indeed a Debye-Waller analysis can be applied in close analogy with that used in X-ray crystallography. Assuming the harmonic approximation for the lat t ice vibrations [57], the effects of thermal vibrations are usually included in LEED calculations by multiplying each ion core's scattering amplitude T(k,9 g ) by an isotropic Debye-Waller factor [50] T ( k , 8 g ) T = T(k,9 s)exp(-M) (2.12) With the temperature-dependent ion core scattering amplitudes, a set of temperature-dependent phase shifts 6- can be obtained from 44 t . T (k) = (-L_)[exp (2 i6 , ) - l ] . (2.13) 4ik T The value of M in the exponential term of equation (2.12) is [44] M = I |Ak| 2 <(Ar) 2 > (2.14) 6 1 In equation (2.14) Ak is the momentum transfer resulting from the atomic 2 scattering and <(Ar) >^ , is the mean square vibration amplitude given as a function of the temperature. For the latter , Van Hove and Tong [44] propose using the low-temperature and high-temperature limits as in the average « A r ) 2 > T = / t< (Ar) 2 > T > o ] 2 +[<(Ar) 2 > T > m ] 2 (2.15) where: <( Ar) 2> T+ 0 = 9/mk B 9 D (l /4+l.642T 2 /9 2 ) , (2.16) <(A£)2V» - 9T/mkg92. (2.17) The k D and m are the Boltzmann constant and the atomic mass in atomic a units, respectively. In most LEED structural determinations the atomic vibrations are taken as isotropic In the calculations, although an anisotropic M can also be used in equation (2.12). With a vibrating latt ice more phase shifts are required for convergence than is the case for the stationary latt ice model; 45 in practice for LEED cr y s t a l l o g r a p h i c studies to about 220 eV, eight phase s h i f t s are generally s u f f i c i e n t for each atom type [44,54]. Further d e t a i l s of the implementation of these points are discussed by Van Hove and Tong [44]. 2.5 Intralayer Scattering The d i f f r a c t i o n of plane waves by an ordered atomic layer, having one atom per unit mesh ( i . e . a subplane), w i l l be outlined b r i e f l y here. An incident plane wave of unit amplitude and wavevector k , which i s scattered on either side of the subplane, w i l l give scattered plane waves of wavevector k' as shown i n Figure 2.3. The i n t r a l a y e r s c a t t e r i n g + + d i f f r a c t i o n amplitudes are p a r t i c u l a r elements M , of the sin g l e - l a y e r s § ++ d i f f r a c t i o n matrix ^ which describes the scattering of plane waves + + incident on either side of a layer p a r a l l e l to the surface. The M , are 8 8 given by Pendry [45] as + + 16n 2i + * ± - - = i Q M Z Y T (k")Y T ,(k ) T T T ,(k ) (2.18) 8 8 Ak+ , LL' L ~* ~B LL' V o' 8 i where the superscript signs '+/-' specify propagation d i r e c t i o n s of the plane waves with respect to the x axis, L and L' represent, r e s p e c t i v e l y , pairs of angular momentum quantum numbers (A,m) and (A',m'), A i s the unit 46 Incident plane waves m Eb;exp ( i s s V D s g 2 2 Figure 2.3: S c a t t e r i n g of a set of pl|ne waves by a l a y e r of i o n cores w i t h d i f f r a c t i o n matrix ^ — . 47 mesh area, and the Y (k ) are spherical harmonics for the angle between k and the surface normal; '* ' represents a complex conjugate. Also in equation (2.18), t T T , ( k ) is the LL' element of the planar scattering LiLt O matrix, j(k ) which is defined as where £ ( k Q ) is the diagonal ion core t-matrix whose non-zero elements are given by equation (2.10). The unit matrix, represents unscattered plane waves and the intraplanar scattering matrix, g , is defined as The structural factor 9»(k ) describes the intraplanar propagator in L-space. ±± The evaluation of ^ is complicated in general, although discussions are available in the l i terature [44,45,58]. Additionally, when more than one atom per unit mesh is considered, the layer should be treated as a composite layer in which the entire layer of atoms (heterogeneous or homogeneous) is sp l i t Into separate subplanes. Figure 2.4 shows a graphitic (2x2) oxygen overlayer on Rh( l l l ) where the composite layer has two oxygen atoms per unit mesh ( i . e . two oxygen subplanes). In such cases the individual planar scattering matrix is calculated for each isolated o (2.19) X = fi(k+)t(ko). (2.20) + Figure 2.4: Graphitic-type oxygen overlayer for Rh(ll l)-(2x2)-0; there are two oxygen atoms (shaded circles) per unit mesh, one on a 3f site the other on 3h site (as in Figure 1.8(a)). Figure 2.5: Schematic diagram of transmission and reflection matrices at the nth layer. The dashed lines are midway between consecutive layers. 49 subplane i , and subsequently the total scattering matrix T is obtained for that particular subplane resulting from multiple scattering with other subplanes within the composite layer. Following Beeby [59], the matrix can be calculated for a composite layer having N subplanes by solving a set of linear equations such that t ,N -1 (2.21) 2 i 1 The matrix ^ consists of N smaller matrices, called 4 which are defined as: I = J , and A - - J g 1 (2.22) where, the structural factor G"^ describes the interplanar propagator from subplane j to subplane i . The general expression for the diffract ion + + matrix element M , of a composite layer having N subplanes Is given by [44,60] 50 .+ ± 16lTi ± * + N i+ ( t -1 1 M , = _ * S Y (k )Y T,(k~,) S R 1 - ( R , ) T T\ ,, (2.23) 8 8 A k ^ L L ' L ^ L 8 l - l 8 8 «V rV g X ^ /V/v" /V i± ± where R = exp(±k ) describes the p o s i t i o n vector r. r e l a t i n g to an g g ~L ~L /v /v + + a r b i t r a r y o r i g i n of the composite layer. The expressions M , i n equations s s /v /v (2.18) and (2.23) are v a l i d only i f the o r i g i n of the coordinates within ++ a layer i s at an ion core center. The subroutine that computes M i s c a l l e d MSMF on the magnetic tape provided by Van Hove [46]. 2.6 Interlayer Scattering ++ Computations for the single layer d i f f r a c t i o n matrix M , whether for subplanes or a composite layer, can be done by exact methods which calculate a l l scatterings to i n f i n i t e order i n L-space, although the exact methods are very demanding on both computing time and storage [60]. However big s i m p l i f i c a t i o n s are possible with perturbational approaches to the problem of c a l c u l a t i n g the t o t a l d i f f r a c t i o n by a slab of such layers. The i n e l a s t i c s c attering experienced by electrons propagating among i s o l a t e d layers ensures that a f i n i t e stack of layers w i l l be s u f f i c i e n t to represent the whole surface d i f f r a c t i o n . Often the f i n a l stacking proce-dures can be done just with plane waves ( i n K-space) rather than with sphe r i c a l waves ( i n L-space), although for close i n t e r l a y e r spacings L-space c a l c u l a t i o n s are needed [44]. An e f f i c i e n t perturbational approach 51 called the combined space method [60] has been developed for LEED calculations. In the combined space method, the interlayer scattering can be treated either by the layer doubling method [45] or the renormalized forward scattering method [61]; these methods are now outlined. 2.6.1. Layer Doubling Method As indicated in Figure 2.5 a single layer is associated with a pair of layer reflection matrices (g) and a pair of layer transmission matrices ++ (.%)', they relate to the dif fract ion matrix M according to r 4 - = M 4 " ; r - 1 " = M ~ t 4 4 " = M 4 4 " + I; t " = M~~ + I. (2.24) S3 53 ' S3 S3 ' & (3 » ' 5 f S3 S3 V ' -| (-In practice, with mirror plane symmetry, these matrices satisfy £ = £ I | and t = t Further the subscripts '+/-' specify the propagation of waves into and out of the layer respectively; these subscripts are read from right to l e f t . A schematic diagram i l lus trat ing the layer doubling method is shown in Figure 2.6, where the stacking is started with a pair of layers A and B, whose reflection and transmission matrices are known. The combined slab C has new diffraction matrices given by [44]: Figure 2.6: Schematic i n d i c a t i o n of the l a y e r doubling method as a p p l i e d to s t a c k i n g four i n d i v i d u a l l a y e r s (with A.B.A.B... r e g i s t r i e s ) i n t o an s l a b ( a f t e r Tong [62]). 53 ++ ++„+ r T +-„ K,+. -1 ++ +- +- .+++ +- p- r T H- + +- - -1 — » (2.25) where g and g are diagonal matrices describing the propagations of plane waves from a reference point in layer A to a reference point in layer B and vice versa. For the stacking of four layers, the results from the left-hand sides of equation (2.25) are substituted into the right-hand sides to produce a new left-hand side; this can be further iterated for 8 ,16 , . . . layers unt i l the matrix r-*" corresponding to a f ini te thick slab has converged. For most metals three or four iterations are suff icient. In Van Hove and Tong's program the subroutine DBG is used to add an overlayer to the 'combined s lab' . Beam intensities calculated by the layer doubling method are obtained from the f ina l reflected amplitudes | r *~ | such that 54 x g = ( v koi ) | r r | 2 , (2,26) The layer doubling method requires a l l interlayer spacings to be greater than around 0.5A. The method is most convenient for bulk structures having a A . B . A . B . . . type of stacking sequence. The composite layer method has to be used when there are interlayer spacings of less than 0.5A. 2.6.2 Renormalized Forward Scattering Method In the renormalized forward scattering (RFS) method , forward scattering processes are treated exactly, while the weaker backward scatterings are treated perturbationally. This results In considerable saving of computational effort . Figure 2.7(a) i l lustrates the i terative interlayer scattering treated in the RFS method. The f irst-order calculation includes a l l scattering paths with a single beam reflect ion process; correspondingly the second and third order calculations have three and five back reflection processes respectively. The computation Is continued unt i l the sum of the amplitudes of forward scattered beams at the deepest level considered is less than some predetermined fraction of the incident beam amplitude on the f irs t layer (e.g. 0.3%). This l imits the numbers of penetrated layers and iterations that are s ignif icant . Typical ly , the RFS method uses 12-15 layers and 3-4 iterations for convergence. 55 Incident beam ' order nd 2 order rd 3 order /I [\ \]? /IV * /I\ 1 JW Jl\ N-Nl (a) N x, N 2 and N 3 denote the deepest l a y e r reached i n the 1 s t , 2 n d , 3 r d p e n e t r a t i o n , r e s p e c t i v e l y . (b) Amplitude of the i n w a r d - t r a v e l l i n g waves (aj) and o u t w a r d - t r a v e l l i n g waves (ap. Figure 2.7: Schematic i n d i c a t i o n of the renormalized forward s c a t t e r i n g method, (a) Each t r i p l e t of arrows represents the complete set of plane waves that t r a v e l from l a y e r to l a y e r , (b) I l l u s t r a t i o n of the vectors which store the amplitudes of the inward- and o u t w a r d - t r a v e l l i n g waves ( a f t e r Van Hove and Tong [44]). 56 The mathematical treatment of the RFS method i s now b r i e f l y described i n r e l a t i o n to Figure 2.7(b). For s c a t t e r i n g at the nth l a y e r , the amplitude a + ( n ) can be expressed as [44] a j ( n ) = t ^ p t n - D ^ n - l ) + r ^ P ~ ( n + l )aj[(n), (2.27) where n runs from 1 to (the deepest l a y e r included f o r the i t h i t e r a t i o n ) . The corresponding amplitude f o r beams moving i n the outward d i r e c t i o n i s given by: a^(n) = " P ~ ( n + l ) a ^ ( n + l ) + £ H " P + ( n - l ) a ^ ( n ) , (2.28) where n runs from (N^-l) to 0. The c a l c u l a t e d amplitudes a^(n) and a^(n) are conveniently stored as column vectors and, on t h i s b a s i s , a u n i t amplitude of the i n c i d e n t beam i n vacuo can be w r i t t e n as I o o (2.29) w h i l e a l l other §^(0) f o r i > 1 are n e c e s s a r i l y n u l l v e c t o r s . Somewhat s i m i l a r l y a l l a j ( n ) are n u l l v e c t o r s . The i t e r a t i o n s t a r t s w i t h the input 57 of g^CO) ( i . e . n = 1) into the right-hand side of equation (2.27) to obtain the a j t l ) , which w i l l i n turn be input to equation (2.27) for c a l c u l a t i n g g,* (2). This i s repeated through to g,i(Ni), which Is substituted into the right-hand side of equation (2.28) to obtain aJ^Nj). Equation (2.28) i s then used successively to generate a^(0), the r e f l e c t e d amplitude for the f i r s t i t e r a t i o n . Similar procedures are repeated to obtain the next orders a 2 ( 0 ) , a 3 ( 0 ) The sum of the t o t a l r e f l e c t e d amplitudes i s A~ = a^(0) + 3,2(0) + 3 ,3(0) + (2.30) snd at convergence the beam i n t e n s i t i e s are given by I = (k~ / k + ) |A~|2. (2.31) g g x oL' 1 g 1 In practice, the RFS method f a i l s to converge well when the multiple s c a t t e r i n g between any pair of successive layers i s very strong or the i n t e r l a y e r spacing i s small (< 1.0A), i n such cases either the layer doubling method or the composite layer method have to be used, even though they are slower. In Van Hove and Tong's progrsm, the subroutines RFS02 snd RFS03 are responsible r e s p e c t i v e l y for stacking the A.B.A.B... and A.B.C.A.B.C... type of d i f f r a c t i o n l a y e r s . The more-recently s v s i l a b l e subroutine RFSG has been generalized by Vsn Hove [46] to handle a v a r i e t y of stacking sequences, and It has been used extensively i n t h i s work for 58 the c a l c u l a t i o n s on zirconium. In the RFSG program, the surface i s divided into regions which are periodic and non-periodic i n the d i r e c t i o n normal to the surface. Each region may contain any stacking sequence of l a y e r s . Within these regions, the layers can be c l a s s i f i e d as corresponding to a p r i m i t i v e ( l x l ) type structure (as for the substrate) or to a s u p e r l a t t i c e structure (as for adatom layers of d i f f e r e n t t r a n s l a t i o n a l symmetry). For example, i n the (B).A.(C).B.A.B... model for the Zr(0001)-(lxl)-0 surface structure (where the l e t t e r i n parenthesis depicts an oxygen l a y e r ) , the three top layers (B).A.(C) represent a non-periodic region involving three p r i m i t i v e structures, whereas the underlying substrate layers constitute a periodic region with the B.A.B.A... stacking sequence. Det a i l s of the a p p l i c a t i o n of the subroutine RFSG are discussed i n Chapters 6 and 7. 2.7 A p p l i c a t i o n of Symmetry i n the 'Combined Space' Method The number of plane waves involved i n K-space c a l c u l a t i o n s , such as with the layer doubling or RFS methods, determines the dimension of the ++ layer s cattering d i f f r a c t i o n matrix ^ , and therefore t h i s d i r e c t l y controls the time required to calculate LEED i n t e n s i t i e s . By u t i l i z i n g symmetry elements within the surface region, i n d i v i d u a l beams can often be grouped into symmetrized wavefunctions. This procedure reduces the number of plane waves ( i . e . beams) required for the c a l c u l a t i o n . For example, i n the c a l c u l a t i o n of R h ( l l l ) - ( 2 x 2 ) - 0 , the adsorbed oxygen layer with a unit mesh area four times that of the substrate produces four times as many d i f f r a c t e d beams as the clean R h ( l l l ) surface at a given energy. This i s 59 shown in Figure 2.8(a), where the beams in the (2x2) pattern divide into the subsets labelled 1-4 in Figure 2.8(b). In the case of normal incidence ( i . e . the incident beam coincides with the 3-fold rotational axis and the (xz) mirror plane), the beam sets labelled 2-4 can be grouped as a single symmetrized set. Hence, only this set plus the remaining beam set are needed for this calculation. At off-normal incidence the situation is less favorable in general, although i f the Incident beam coincides with the mirror plane the beam sets 2 and 3 can s t i l l be grouped together. 2.8 Evaluation of Results The determination of surface structure with LEED involves a t r i a l -and-error analysis designed to find that geometrical model which gives calculated 1(E) curves which have the best correspondence with the experi-mental 1(E) curves. This comparison may be done visually by comparing the positions and shapes of peaks, troughs and other structure in the two sets of curves. However such an approach Inevitably has a subjective content; also i t quickly becomes unwieldly in practice. Therefore, considerable effort has been expended in LEED to find suitable r e l i a b i l i t y indices (or R-factors to use the terminology of X-ray crystallography). The objective here is to find mathematical measures of correspondence so that the closer the match-up between the sets of experimental and calculated 1(E) curves, the smaller is the index. Various R-factors have been constructed for LEED [63], but those introduced by Zanazzi and Jona [64] and by Pendry [65] are perhaps the most commonly used. The latter emphasizes the positions of peaks and troughs, while the former is sensitive also to peak shapes and Figure 2.8: LEED pattern at normal incidence from Rh(lll)-(2x2)-0. (a) Symmetry-related beams are indicated by the same symbols. (b) Beams belonging to the same beam set are indicated by the same number (independent of angle of incidence). 61 heights [66]. A l l the R-factor analyses in this work were done with the Pendry R-factor (Rp)» which uses only f i r s t derivatives and is cheaper than the use of the Zanazzi-Jona R-factor. Pendry's multi-beam R-factor is expressed as R = Z J (Y, . - Y, J 2 d E / Z / (Y? . + Y 2 . ) dE, (2.32) p j 1 c a l c * e x P f c i c a expt where the summation Is over the individual beams, the Y^ are defined as Y t = L _ 1 / ( L " 2 + V * ± ) , (2.33) where L = d £ n I ( E ) / d E , (2.34) and V ^ is simply the imaginary component of the constant muffin-tin potential used in the calculation. Normally in LEED crystallography, values of R-factors are plotted as functions of appropriate geometrical parameters and of V Q r in order to find conditions for the best correspondence between experiment and calculation (I.e. the smallest value of R )• The variation with V is important for v p or r refining the value used in the multiple-scattering calculations. Specific R-factor analyses for LEED crystallography are discussed in Chapters 4 and 6. Representative contour plots for R h ( l l l ) - ( / 3 x / 3 ) 3 0 ° - S of R p versus V Q r and the Rh-S interlayer spacing for four different adsorption sites are shown in Figure 4.7. 62 CHAPTER 3 Experimental Methods 63 3.1 UHV Chamber and Apparatus A l l the experiments i n this work were ca r r i e d out i n a Varian FC12 vacuum chamber, made of non-magnetic s t a i n l e s s s t e e l components joined together by flanges with copper gaskets. Figure 3.1 shows an o v e r a l l schematic diagram of t h i s p a r t i c u l a r chamber, which i s equipped with LEED optics and screen (Varian 981-0127), a single-pass c y l i n d r i c a l mirror analyzer (Varian 981-2043) coupled with a glancing incidence electron gun as well as various other f a c i l i t i e s . The instrumental d e t a i l s related to AES and LEED w i l l be discussed i n Sections 3.4 and 3.5 r e s p e c t i v e l y , but the functions of other f a c i l i t i e s inside the vacuum chamber are reviewed b r i e f l y i n the following. The manipulator (Varian 981-2530) i s equipped with a f l i p assembly (Varian 981-2532) and includes a sample heater and l i q u i d nitrogen cooling c o i l , on which the sample i s mounted with a molybdenum sample cup. The manipulator flange has a pair of l i q u i d nitrogen feed-throughs and several e l e c t r i c a l feed-throughs mounted on i t which can be used for cooling or heating the sample and measuring the temperature by means of a thermocouple welded to the sample cup. The manipulator allows the sample to be rotated i n the plane of the CMA and LEED op t i c s , as well as allowing h o r i z o n t a l and v e r t i c a l displacements. This design also provides r o t a t i o n around an axis perpendicular to the surface plane, which i s necessary for i n t e n s i t y measurements at off-normal d i r e c t i o n s of incidence. Other basic f a c i l i t i e s i n the chamber are: (1) a window to monitor the sample p o s i t i o n and d i f f r a c t i o n pattern on the fluorescent screen; 64 G l a n c i n g inc idence e l e c t r o n gun C M A ) L E E D optics and e l e c t r o n gun Sample Manipulator 3 Hypodermic Ion gun V i e w i n g gas doser w i n d o w Figure 3.1: Schematic diagram of the FC12 UHV chamber with some Important f a c i l i t i e s used for the experiments made i n th i s work (CMA = c y l i n d r i c a l mirror analyzer). 65 (2) a nude ion gauge to monitor the system pressure; (3) a hypodermic gas doser connected to a variable leak valve for dosing gas on to the sample and for introducing argon for ion sputtering; (4) an ion-bombardment gun for cleaning the sample. The chamber enclosing the above system i s connected to a series of pumps. These include a pair of sorption pumps, an o i l - d i f f u s i o n pump, a titanium sublimation pump, a main ion getter pump (200 L s and a small ion pump (20 L s ^ ) on the gas handling l i n e . A schematic i l l u s t r a t i o n of the pumping system and gas handling l i n e i s shown i n Figure 3.2. The pumping sequence from atmospheric pressure to the 10 ^ Torr range Is as follows: (1) The system i s roughed with the sorption pumps, which consist of z e o l i t e cooled by l i q u i d nitrogen. Once the pressure of the chamber -3 i s reduced to around 10 Torr, the valve between the rough l i n e and the main chamber i s closed. (2) The d i f f u s i o n pump i s used to pump the system to around 10 ^  Torr, and then i t i s i s o l a t e d from the main chamber. (3) The main ion pump i s then turned on, and the system's pressure would —8 normally reduce quickly to the ~10 Torr range. (4) The whole chamber i s baked, t y p i c a l l y at 200°C for 10 hours. The titanium sublimation pump i s turned on to pump away excess gaseous molecules (e.g. H2O) which desorb from the walls of the chamber. (5) A l l filaments (e.g. ion gauge, electron gun) are degassed while the chamber i s s t i l l hot (~80°c) to ensure that they do not produce unwanted degassing during normal operation. (6) The baking and subsequent procedures may be repeated u n t i l a pressure 66 L E A K V A L V E L E A K V A L V E O T C G A U G E Figure 3.2: Representation of the pumping system and gas handling l i n e (1.P. = ion pump; S.P. » s o r p t i o n pump; T.S.P. = t i t a n i u m s u b l i m a t i o n pump; D.P. = d i f f u s i o n pump; T.C. = thermo-couple ) . 67 of the order of 10 Torr is attained. The gas handling line is baked separately with heating tape wrapped around i t ; the pressure in the line is monitored by the gauge on the small ion pump or by the thermocouple gauge. 3.2 Sample Preparation The samples used in this work were obtained from high purity single crystal rods. In each case, the crystal was mounted on a goniometer, and oriented using the Laue back reflection method [67] to ensure that the desired crystallographic plane was perpendicular to the X-ray beam. After orientation, cuts paral le l to the desired plane are made using the spark erosion technique ( 'Agietion', Agie, Switzerland) to produce a sample disc form, which is then mounted in an acryl ic resin ('Quickmount', Fulton Metallurgical Products Corp., U.S.A.) and glued to a polishing assembly equipped with alignment micrometers. That enables checks of sample orien-tation with Laue X-ray di f fract ion, and readjustment to minimize any errors resulting from the cutting or the later polishing steps. The mechanical polishing of the sample is done with progressively finer diamond paste (from 9 to 3 micron) while the j ig is mounted on a planetary lapping system (DU 172, Canadian Thin Film L t d . ) . Subsequently, a one-micron polish is accomplished by hand using an a r t i f i c i a l deer skin (Microcloth, Buchler 40-7218). The whole j ig with crystal assembly is then fixed to an optical bench with a He/Ne laser in order to check that the optical polished face is paral le l to the desired crystallographic plane to within half a degree (this alignment test is indicated in Figure 3.3). Once the orientation is deemed satisfactory, the sample assembly is dismounted and immersed in 68 C r y s t a l p lane Opt ica l plane f o r l a rge R, — - = 0 rads 2R Figure 3 . 3 : Laser method to check the angular misalignment ( 9 ) between the optical face and desired crystal plane. 69 acetone to dissolve the resin. The sample is washed, degreased progressi-vely with acetone, methanol and d i s t i l l e d water in an ultrasonic bath, dried, and mounted in the sample cup with a resistive heater (Varian 981-2058). A 0.005" alumel-chromel thermocouple is then spot-welded to the top of the sample cup in order to be able to monitor the temperature of the sample during procedures carried out in the UHV chamber. 3.3 Cleaning in UHV Chamber After following the pumping procedures described in Section 3.1, i t i s important to sputter-etch the surface of the metal sample with a short and gentle argon ion bombardment before heating the sample for the f i r s t time. Such a treatment eliminates many impurities that may have been left over on the surface from washing and rinsing processes, and which may otherwise diffuse into the sample during the f i r s t heat treatment. The A r + bombardment is done with the main ion pump off, and high-purity argon (99.9995% Matheson) is introduced into the chamber unt i l the pressure i s approximately 10 ^ Torr. The i n i t i a l gentle A r + bombardment is done with the gun voltage set at about 600 V; the ion current on the surface should be around 3 to 4 uA. It is also advisable to operate the titanium sublima-tion pump during the A r + bombardment to pump away impurities bombarded off from the surface and maintain the purity of argon gas. After the i n i t i a l A r + bombardment, Auger electron spectroscopy is employed to monitor the behaviour of impurities on the surface, including as a function of tempera-ture. Also the sample and the sample-holder need to be outgassed at this point. The appropriate temperature depends on the characteristics of the 70 metal, but in general this outgassing should be done at a somewhat higher temperature than what w i l l be required for annealing in the later stages of surface preparation. Ultimately, the pressure in the chamber should remain in the 10 ^ Torr range while the sample is kept hot for periods of the order of one hour. After the f i r s t heating treatment, the main surface cleaning operations can start . In most cases, the cycl ic A r + bombardments followed by annealing treatments are sufficient to achieve a well-ordered and clean surface without any appreciable impurities detected by Auger electron spectroscopy. The chemical cleaning method works successfully in some cases, in which impurities (e.g. C) on a surface are reacted with an dosing gas (e.g. 0 2 ) to form a product which is easily desorbed and pumped away. However, the key to obtaining a clean and well-ordered surface is to understand the behaviors of a l l the impurities on the surface as a function of temperature. This is determined with Auger electron spectroscopy; then recipes for A r + bombardment (e.g. ion energy, bombardment time) and heating temperature and time can be derived for an efficient cleaning procedure. Vigorous A r + bombardment w i l l result in much surface damage; a careful balance is required since higher annealing temperatures may also cause problems with impurity segregation or diffusion. In addition to following chemical composition with AES, i t I B also important to regularly examine the LEED pattern (e.g. after each A r + bombardment and annealing treatment) to ensure that the whole preparation procedures are ordering, as well as cleaning, the surface. In general, the combination of a low background and sharp LEED pattern, without any additional fractional order beams, 71 Indicates that a well-ordered and clean surface has been obtained, although the presence of any impurities on the surface has to be primarily detected by AES. After a sharp (1x1) pattern of the clean surface has been obtained, then gas molecules can be adsorbed; the surface after a proper annealing procedure may then show a well-defined LEED pattern of an adsorption system. The adsorbate coverage plays an important role in a LEED analysis, although this cannot in general be determined directly from the LEED pattern. For example, an observation of a ( / 3 x / 3 ) 3 0 ° LEED pattern often indicates a surface coverage of 1/3 monolayer, although Shih et al^ [68] recognized a pattern formed by N on the Ti(0001) surface which occurs after the one monolayer coverage. It is often helpful to monitor the coverage of adsorbates on surfaces by measuring adsorption uptake curves using AES, or by monitoring the intensities and or profiles of fractional order beams [69]. In general, the more quantitative information on coverage available from the experiments, the easier i t is to eliminate unreasonable structural models prior to undertaking the analysis with the multiple scattering calculations. 3.4 Apparatus for Auger Electron Spectroscopy AES is an invaluable analytical tool , by which the elemental composition of a surface can be qualitat ively, and even seml-quantitati-vely, monitored. The experimental arrangement for obtaining Auger spectra is i l lustrated in the Figure 3.4. The glancing incidence electron gun provides a primary electron beam having an energy around 2-3 keV, a current up to 200 uA, and a cross-sectional area of about 1 mm2. Auger electrons 72 Glancing angle elect ron gun Sample}<j. X - Y P lotter Scope Figure 3.4: Schematic diagram to illustrate the measurement of Auger electron spectra using a cylindrical mirror analyzer in combination with a glancing angle electron gun. 73 emitted from the surface are detected with a single-pass c y l i n d r i c a l m i r r o r analyzer (CMA). The CMA i s a d i s p e r s i v e type analyzer which c o n s i s t s of a channel e l e c t r o n m u l t i p l i e r and two c o a x i a l c y l i n d r i c a l e l e c t r o d e s . A f i e l d w i t h c y l i n d r i c a l symmetry i s created when a negative p o t e n t i a l (U ) £1 i s a p p l i e d to the outer c y l i n d e r while the inner c y l i n d e r Is grounded. For a p a r t i c u l a r value of the outer c y l i n d e r p o t e n t i a l U , the e l e c t r o n s i n a narrow energy range E±AE can pass through two g r i d s i n the inner c y l i n d e r and be focussed e l e c t r o s t a t i c a l l y f o r d e t e c t i o n by the e l e c t r o n m u l t i p l i e r . By sweeping the r e t a r d i n g voltage on the outer c y l i n d e r and measuring the r e s u l t i n g current c o l l e c t e d , an energy d i s t r i b u t i o n curve of the e l e c t r o n s emanating from the sample surface (Figure 1.3) Is generated [4]. In order to emphasize the Auger e l e c t r o n peaks, the energy d i s t r i b u t i o n i s d i f f e r e n -t i a t e d . This i s accomplished by modulating the r e t a r d i n g voltage U with an a l t e r n a t i n g voltage, U^'sinwt, where i s approximately 3V and the frequency w i s around 5-10 KHz. The s i g n a l c o l l e c t e d by the CMA with the dN(E ) modulated frequency i s p r o p o r t i o n a l to ^ [70]. 3.5 Apparatus f o r LEED 3.5.1 LEED Optics and E l e c t r o n Gun The e l e c t r o n energy analyzer used i s i n d i c a t e d i n Figure 3.5. An i n c i d e n t beam i s produced by heating the filament i n the e l e c t r o n gun, and i t i s c o l l i m a t e d by the lens system. The e l e c t r o n beam passes through the d r i f t tube and s t r i k e s the sample surface; the d r i f t tube being held at the 74 FLUORESCENT Figure 3.5: Schematic diagram of the electron optics for the LEED display system. 75 same p o t e n t i a l as the sample. The energy of the electron beam i s fixed by the p o t e n t i a l difference (U) between the filament and the sample. Ty p i c a l energies used i n our work are between 10 and 300 eV, for which the diameter of the incident beam i s about 1 mm at the sample surface due to the f i n i t e size of the cathode. The energy spread i n the beam i s t y p i c a l l y 1 eV as a re s u l t of the thermal energy d i s t r i b u t i o n from the heated filament [4]. The beam current i s usually kept at around 1 MA for energies above 100 eV, but the current a v a i l a b l e declines almost l i n e a r l y to about 0.2 uA as the energy i s reduced below 100 eV. This v a r i a t i o n has to be recorded for normalizing the measured beam i n t e n s i t i e s , otherwise the measured i n t e n s i -t i e s would appear a r t i f i c i a l l y reduced at low energies. For displaying the LEED pattern corresponding to the energy eU, the electrons which are e l a s t i c a l l y backscattered from the sample surface are passed through a l l four hemispherical concentric grids ( i . e . Gl to G4 i n Figure 3.5), and they are accelerated on to the fluorescent screen by a p o s i t i v e p o t e n t i a l (~5 kV). For the normal mode of operation the f i r s t g r i d (Gl) i s grounded, as are the sample and d r i f t tube to ensure that the scattered electrons t r a v e l i n a f i e l d free region between sample and the f i r s t g r i d . The double retarding grids (G2 and G3) have a negative p o t e n t i a l whose magnitude i s s l i g h t l y smaller than U, so that e s s e n t i a l l y a l l of the i n e l a s t i c a l l y scattered electrons are f i l t e r e d out. The fourth g r i d (G4) i s grounded to screen the double grids from the high voltage on the c o l l e c t o r screen. Thus a series of LEED patterns corresponding to varying energies can be displayed on the screen by systematically modifying the primary beam energy and simultaneously the p o t e n t i a l applied to the retarding g r i d s . 76 3.5.2 Measurement of LEED Intensities A commercial video LEED analyzer (Data-Quire Corp., Stony Brook, N.Y.) is used in conjunction with an intensified s i l i con intensified target type of TV camera (COHU 4A10/ISIT) to measure 1(E) curves for diffract ion spots exhibited on a LEED display screen. A schematic diagram of the system for measuring the real-time LEED spot intensity using a video LEED analyzer (VLA) is shown in Figure 3.6. An ISIT camera basically contains a photocathode tube and a s i l i con target. As light from the LEED spots is focussed through the camera lens on to the photocathode tube, photoelectrons are emitted and accelerated to the s i l i con target. This results in the production of secondary electrons, and hence higher currents to improve the measurement of the LEED spots. This magnifying effect can allow a reduction in the incident beam current required for producing a measurable LEED pattern, and thereby reduce the poss ib i l i t ies for unwanted electron-beam effects during the measurements. The latter is also favored by the on-line TV camera method which can measure intensities of LEED spots much faster than the more-traditional methods of using a moveable Faraday cup collector or an external spot photometer [71,72]. A detailed review of recent approaches to quantitative measurements of LEED intensities has been given by Martin and Lagally [73]. Along with the TV camera, a central part of the system in Figure 3.6 is the 32K microprocessor (Motorola 6800), by which the video signals from the camera are digit ized using an A/D converter and the LEED gun voltage is remotely controlled via a D/A converter. When the camera is directed at a LEED pattern, the image on the monitor screen defines a frame consisting X - Y RECORDER T. V. MONITOR VIDEO A/D CONV. VIDEO ISIT INTERFACE SIGNAL T . V . CAMERA MOTOROLA 6800 D/A CONV. INTERFACE SCREEN GUN LEED CONTROL UNIT TERMINAL FLOPPY DISKS MODEM M A I N -FRAME Figure 3.6: Schematic diagram for the TV analyzing system which detects and measures diffracted beam intensities from the LEED screen. 78 of 256 x 256 picture elements (or pixels) . Such a frame corresponds to fixed parameters of the incident beam (energy, direction of incidence). The intensity of each pixel within a frame is digit ized using an intensity scale (or gain level) between 0 and 255. The scanning of such a single frame is completed in 1/60 s. Each scanning starts from the upper left corner of the frame (Figure 3.7) and i t proceeds horizontally one pixel at the time along the topmost row unt i l the 256th pixel is reached. This scanning course is repeated on the next horizontal l ine, and so on unt i l a l l 256 horizontal lines have been scanned from the left to right . In contrast to the scanning course, the d ig i t iz ing course is always perpendicular to the scanning course, and only the intensities of pixels within a single column can be simultaneously digit ized and recorded during each scanning. On the other hand, i f there are n pixels within a row paral le l to the scanning course, i t w i l l take n scans ( i . e . n/60 s) to complete the dig i t izat ion processes. Therefore the complete d ig i t izat ion of the whole frame needs 256/60 s, although that is not needed in practice for LEED, where only the diffract ion spots are dig i t ized. The VLA provides user-selected 10 x 10 pixel windows as shown in Figure 3.9(a), which define the region to be dig i t ized, and which are superimposable on particular LEED spots observed on the video screen. Just 10 scans ( i . e . 1/6 s) are needed for d ig i t i z ing an isolated window, and the intensity of each individual LEED spot is obtained by summing the intensities of a l l 100 pixels within the window. The VLA system in this laboratory provides up to 49 isolated windows for d ig i t i z ing the LEED spots simultaneously for each 7 9 column • •  pixel rOW—r| 1 2 3 4 5 • • • • • .......... y... 2 - T -r *. 7 " ' i ' ' " V ..i..'..J..'..!. 3 • 4-'- - :-! - •-• -. • • • • ~ ^ . • r • • • V t , H - r - > - | - r -« _ ' - J — . —I L J. _. _ • - -1 - • r H r -< • * , ™1 — w — i ~ ' . ' . 1 1 1 , r • n A " T f ' : " ' " i ~; T v 2 5 6 > ' . • • > • , ' 1 1 • : , i ' • . t - - j - . - r - t ; - . - , - ) * T - T 7 f r , - , - r - - r T i t _ -Jrx- rr r i T -»-'-.-J-T • 1 1 1 1 1 1 1 "1 t 1 " l 1 . 1 1 1 1 1 • 1 . 1 . , . , . - R J J . . , . . ( . . ( . . ( . . . - J - C •'- k 1 J L L I —' — 2 5 6 i *• r-! H ?.J i i i ^ "'• • * . i "l ~ i . , .-i Figure 3 . 7 : A frame on the monitor screen to ill u s t r a t e : (a) the 256x256 pixels structure, (b) the scanning course. 80 frame ( i . e . at a fixed energy). Once a frame i s d i g i t i z e d , the next frame appears when the voltage of the incident beam i s changed by an increment. Each 10 x 10 window i s then automatically matched to the new spot p o s i t i o n for the next d i g i t i z a t i o n process. This matching i s done by the computer using previously supplied information on unit mesh dimensions and d i r e c t i o n of incidence. The present software does not allow us to vary the window size during measurements, so precluding separate measurements f o r background subtraction. The e f f e c t of the background in measurements i s minimized by appropriately s e t t i n g the gain l e v e l i n the d i g i t i z a t i o n process for i n d i v i d u a l beams. In practice i t i s better to measure f r a c t i o n a l order beams separately from i n t e g r a l beams, with d i f f e r e n t gain l e v e l s e t t i n g s . There i s no serious loss i n t h i s for the purpose of LEED crystallography since the f i n a l comparisons between measurements and c a l c u l a t i o n s emphasize r e l a t i v e i n t e n s i t i e s only. Nevertheless, beam i n t e n s i t i e s measured with the VLA are normalized with respect to the incident beam according to I = i / i Q , (3.1) where i and i Q are d i f f r a c t e d and incident beam currents r e s p e c t i v e l y . In practice i n our laboratory, the incident beam for LEED Is chosen to coincide with a symmetry element of the surface structure. The d i f f r a c -t i o n pattern then exhibits symmetrically related beams, and correspondingly the fast VIA method can enable the user to check rapidly that the measured 1(E) curves do indeed show the expected symmetries. As an example, Figure 3.8 shows 1(E) curves measured for s i x beams from a Zr(0001)-(lxl)-0 surface; 81 1 0 0 U 0 1 6 0 2 2 0 E N E R G Y ( e V ) F i g u r e 3.8: 1(E) curves measured f o r s i x e s s e n t i a l l y equivalent beams f o r normal incidence on the Z r ( 0 0 0 1 ) - ( l x l ) - 0 s u r f a c e . The c l o s e correspondence confirms the incidence d i r e c t i o n . The averaged and subsequently smoothed 1(E) curves are d i s p l a y e d i n the bottom two curves. 82 that they are essentially equivalent confirms the incidence direction is very close to normal. Such sets of 1(E) curves are averaged to minimize any further small experimental uncertainties [74]. F ina l ly , our usual practice is to smooth the resulting averaged curve with two cubic spline operations to establish a f inal experimental 1(E) curve (bottom curve In Figure 3.8), which is then available for the comparison with calculated 1(E) curves. 3.5.3 Measurement of Spot Profi le The intensity of a LEED spot, corresponding to an individual frame (or energy) described in Section 3.5.2, is defined as the summation of the digit ized intensities of the 100 pixels in the window covering the spot. An additional measurement is of the intensity distribution across the spot, which is generally referred to as the spot (or beam) prof i le . Such measurements at fixed energy, especially for fractional order beams, can provide useful information about surface ordering phenomena (see Chapter 6). The LEED spot profi le measurement is outlined in Figure 3.9(a) where the user-selected window (10x10 pixels) covers completely the spot to be measured. Ten scans are needed to digit ize this whole spot, and as shown in Figure 3.9(b) the intensity profi le along the direction can be obtained by joining the maximum positions of ten prof i les . The full-width at half-maximum (FWHM) for such a profi le provides a quantitative measurement of spot sharpness; generally the larger the value of 1/FWHM the greater is the surface order, although i t must be recognized that there Is always a beam broadening effect Introduced by the instrument [29]. 83 T p r o f i l e s I 2 3 4 5 6 7 8 9 10 YN win ( a ) - 1 i d win LEED spot —I LO C ZJ i _ >-»— LO LU (b) A I ' 2 ' 3 ' 4 " 5 ' G ' 7 ' 8 ' 9 ' 10' X win Figure 3.9: Measurement of spot profiles: (a) the LEED spot to be measured is covered with a user-selected window (10x10 pixels), (b) the spot intensity profile along X w i n. 84 CHAPTER 4 LEED Analysis for the Rh(ll l)-(/3x/3)30 Surface Structure 85 4.1 Introduction So far only very l i m i t e d s t r u c t u r a l data are ava i l a b l e f o r the ordered adsorption of sul f u r atoms on close-packed (111) surfaces of face-centered cubic (fee) metals, and that provided a motivation f o r the present study [75]. At the time t h i s work was undertaken, s t r u c t u r a l information for surfaces of this type were r e s t r i c t e d to the (111) surfaces of i r i d i u m and n i c k e l . In each of these cases, low coverages of ordered S atoms apparently adsorb on the so-called "expected" 3-coordination s i t e s [76,77], and s i m i l a r observations have since been reported for S chemisorption on the P d ( l l l ) and P t ( l l l ) surfaces [78,79]. (The "unexpected" and "expected" hollow s i t e s of 3-coordination are distinguished by whether the 3-fold r o t a t i o n axis which passes through each s i t e respectively i n t e r s e c t s an atom or not i n the second metal layer; these s i t e s can be Id e n t i f i e d as 3h or 3f, a notation that recognizes the hep and fee stacking sequence for the topmost three layers as i s indicated i n Figures 1.8(a).) A simple Inter-pretative model developed on the basis of ava i l a b l e s t r u c t u r a l data from surface crystallography [80] predicts a S-Ir bond length of 2.25A for S adsorbed on I r ( l l l ) , and this compares quite c l o s e l y with the value of 2.28A reported from the LEED c r y s t a l l o g r a p h i c analysis [77]. By contrast, the predicted S-Ni distance (2.15A) for S adsorbed on N I ( l l l ) seems rather long compared with the reported measured value of 2.02A [76]. In order to have more information for assessing the adsorption bond lengths for S on f c c ( l l l ) surfaces, a LEED c r y s t a l l o g r a p h i c analysis has been made for the surface structure designated Rh(lll ) - ( / 3 x / 3 ) 3 0°-S. This system also allows further comparisons to be made with the s t r u c t u r a l data 86 already a v a i l a b l e for S adsorbed on the two other low-index surfaces of rhodium, namely the surface structures Rh(100)-(2x2)-S [40] and Rh(110)-c(2x2)-S [41]. Additional LEED cry s t a l l o g r a p h i c analyses have been reported for adsorption on R h ( l l l ) surfaces, and they span a range of s t r u c t u r a l s i t u a t i o n s . For example, for the system Rh(lll)-(/3x / T)30°-CO at a coverage of one-third monolayer (ML) [81], the CO molecules adsorb perpendicularly and on-top of Rh atoms (adsorption s i t e referred to as If to emphasize the 1-fold coordination), while for Rh(lll)-(2x2)-CO, at the coverage 0.75 ML, CO adsorbs both near If s i t e s and on the bridge s i t e s of two-fold (2f) coordination [82]. However, the ethylidyne group in R h ( l l l ) -(2x2)-C 2H3 at 0.25 ML [83] apparently adsorbs at the "unexpected" s i t e s of 3-fold coordination ( i . e . the 3h s i t e s ) . These l a t t e r examples remind of the s i g n i f i c a n c e of organo-rhodium systems in c a t a l y t i c reactions, and therefore of the p o t e n t i a l importance for developing an understanding of structure and bonding for chemisorption on rhodium. 4.2 Experimental The R h ( l l l ) surface was cut and polished as described in Section 3.2. After mounting i n the vacuum chamber, Auger electron spectroscopy revealed s u b s t a n t i a l structure at 151 and 272 eV (Figure 4.1(a)) and there-fore appreciable amounts of s u l f u r and carbon contamination. It was found that A r + bombardment (800 V, ~5 uA cm - 2) f o r one hour was the most e f f e c t i v e way to remove the s u l f u r from the surface, although the Auger peak for carbon showed a r e l a t i v e increase a f t e r the bombardment (see the Figure 4.1(b)). This l a t t e r e f f e c t appears to r e s u l t from the low 87 Rh {111) 1 0 0 ' 2 0 0 ' 3 0 0 e V Figure 4.1: Auger spectra from Rh( l l l ) surface: (a) as mounted, with considerable S (151 eV) and C (272 eV) contamination; (b) after A r + bombardment, to show reduced S, but increased C; (c) after annealing, to show reduced C, but increased S; (d) after a f u l l cleaning routine. 88 sputtering cross-section of carbon, nevertheless the carbon Auger s i g n a l could be simply removed by annealing the sample at 1000°C for 15 minutes. This annealing apparently causes the carbon to d i f f u s e into the bulk c r y s t a l , although simultaneously s u l f u r segregates to the surface region , (see Figure 4.1(c)). Cycles of A r + bombardment followed by annealing at around 1000°C were found to provide an e f f e c t i v e method for reducing the levels of S and C contamination within the surface region probed by AES. Reactive treatment with oxygen appeared i n e f f e c t i v e to remove the surface carbon from the surface. During these cleaning procedures, the LEED pattern was assessed from time to time. That for R h ( l l l ) exhibits a three-f o l d r o t a t i o n a l symmetry and appropriate symmetry planes at normal incidence. The above procedures led to the preparation of a well-ordered and clean R h ( l l l ) surface which showed a sharp ( l x l ) LEED pattern (see Figure 4.3(a)) without any C and S contamination as detected by AES (Figure 4.1(d)). High purity H 2S (Matheson) was then dosed on to the clean R h ( l l l ) surface at room temperature and a pressure of about 1 0 - 8 Torr. Figure 4.2 displays a t y p i c a l s u l f u r up-take curve as measured by R = A 1 5 l / A 3 0 4 ( i . e . the r a t i o of the Auger peak height for S at 151 eV to that of Rh at 304 eV) as a function of exposure i n Langmuirs (1 L = 10~ 6 Torr s ) . This curve, and others measured independently show d e f i n i t e breaks i n slope (close to R = 0.65 and 0.85) which are suggestive of change i n structure. LEED indicates that the f i r s t break corresponds to the formation of the 89 LU 0-2 10 20 30 AO EXPOSURE (Langmuirs) 50 Figure 4.2: Auger peak height r a t i o S (151 eV)/Rh (304 eV) p l o t t e d as a f u n c t i o n of H 2S exposure to a R h ( l l l ) s u r f a c e . 90 ( / 3 x / 3 ) 3 0 ° surface structure (see Figure 4.3(b)), whereas the second break appears to be associated with the formation of a high coverage c(4x2) structure as is shown in Figure 4.3(c). Good quality ( / 3 x / 3 ) 3 0 ° LEED patterns are observed with R around 0.75 after exposing the clean Rh( l l l ) surface at room temperature and annealing for a few minutes at 200°C. It is believed that dissociatively adsorbs on the Rh( l l l ) surface. A ( /3x /3)30° LEED pattern could also be obtained by heating the Rh( l l l ) sample under conditions where some sulfur impurity migrates to the surface from the bulk as noted in the cleaning process. Corresponding observations have been reported by others, including Hengrasmee et a l . [40] in their preparation of Rh(100)-(2x2)-S, and Castner et a l . [84]. The 1(E) curves measured from the R h ( l l l ) - ( / 3 x / 3 ) 3 0 ° - S surface obtained by the migration of the bulk sulfur impurity agreed closely with those prepared by H2S adsorption. Some evidence for H2S dissociating on a metal surface has been provided by Keleman and Fischer's study on the Ru(0001) surface with the additional techniques of ultra violet photoemission and thermal desorption spectroscopy [85]. This work indicated that dissociated upon adsorption over the entire range of coverage. In R h ( l l l ) -( / 3 x / 3 ) 3 0 ° - S , the adsorbed sulfur atoms are held strongly to the surface and could only be removed by extensive A r + bombardment. Intensity-versus-energy (1(E)) curves were measured for the R h ( l l l ) -(/3xv /3)30°-S surface structure at normal incidence for the diffracted beams designated (01), (10), (20), (11), (02), (1/3 1/3), (1/3 4/3), (2/3 2/3), -and (4/3 1/3), using the.beam notation shown in Figure 4.4 The unit mesh of the superstructure corresponding to the LEED pattern has been shown in 91 (a) ( b ) • • • . • • • (c) • I • . " Figure 4.3: Schematic indications of LEED patterns from surfaces designated: (a) R h ( l l l ) - ( l x l ) ; (b) Rh(lll)-(/3x/3)30°-S; (c) Rh(lll)-c(2x4)-S. 92 4k-4 8 3 3 27 3 3 0 2 57 33 2 2 • • I 2 45 33 33 3 3 i I 3 3 £ 4 33 11 3 3 I 2 33 3 3 54 33 84 3 3 3 3 2 I 3,3' 1 2 3 3 •_ 4 2 3 3 10 5 i 3 3 *-3 3 2 0 3 3 33 i i 3 3 T r 2 2 3 3 1 I 3 3 I 0 20 J 1 3 3 Otf 33 11 33 _• 84 3 3 2 i 3 3 _• 4 2 3 3 2 I 54 3 3 -• 3 3 I I -3 3 3 3 22 3 > ' ' -TI 01 1 i 3 3 I I 2 4 3 3 3 3 1 5_ 3 3 02 45 33 I 2 2 7 3 3 22 51 33 3 3 Figure 4.4: Beam notations for a LEED pattern from the R h ( l l l ) -(/3x/3)30°-S structure. 93 Figure 1.8(a). These measurements were made using the VIA system as described in Section 3.5.2. At the outset, 1(E) curves for sets of beams which are expected to be equivalent at normal incidence were displayed on the oscilloscope. This enabled the normal-incidence setting to be f ine-tuned on-line. With the normal-Incidence direction set, integrated beam intensities were measured as the energy was varied from 50 to 250 eV with a constant increment of 2 eV. Each spot on each frame was scanned five times, and the multiply-summed integrated intensities were normalized to the incident beam current. The symmetrically equivalent beams were averaged with equal weighings to minimize some further minor experimental uncertainties associated with any misalignment of the sample [74], and the averaged intensity curves were f inal ly smoothed with two cubic spline operations. Figure 4.5 shows two 1(E) curves collected from two indepen-dent sets of measurements. 4.3 Calculations and Results The simplest models for the ( / J x / J ) 3 0 ° structure have sulfur atoms adsorbed on the unreconstructed (111) surface of a fee metal, and they are conveniently designated according to the site of adsorption as indicated in Section 4.1 and Figure 1.8(a). 1(E) curves for the various diffracted beams were calculated using the renormalized forward scattering method for models with adsorption on the expected 3-fold (3f) s i tes , the unexpected 3-fold (3h) sites, the on-top (If) sites and the bridge (2f) s i tes . These calculations included symmetry, for example the 3-fold rotation and mirror plane symmetries were ut i l i zed for the models corresponding to the p31m 94 I— LO LU 1 expt.1 \ (1/3 1/3) b e a m e x p t . 2 \ • i i i > 40 8 0 120 160 E L E C T R O N E N E R G Y ( e V ) Figure 4.5: 1(E) curves for the (2/3 2/3) and (1/3 1/3) beams measured at normal incidence for two independent experiments on the Rh(lll)-(/3x/3)30°-S structure. 95 diperiodic space group, and a maximum of 29 inequivalent beams were used (13 integral-order and 16 fractional-order beams). For adsorption on the 2f sites only a single mirror plane reflection symmetry is present. Then, the beam intensities require the appropriate averaging to account for the expected presence of rotationally-related domains. A maximum of 64 inequi-valent beams were included to 200 eV for the 2f model. The non-structural parameters used in these calculations are as follows. The atomic potential of rhodium was characterized by phase shifts (up to A = 7) derived from a band structure calculation [53], and the real part of the constant potential (V ) between the atomic spheres (in the muffin-tin model) was set i n i t i a l l y at -10.0 eV. For the sulfur overlayer region, the superposition potential obtained by Demuth et^  al_. [86] was used. The Debye temperatures were taken equal to 480 K for rhodium and 335 K for sulfur [86], while the imaginary part (V )^ of the constant 1/3 potential between a l l spheres was equated to 0.819 E eV (where E is the electron energy in eV with respect to the vacuum level ) . The structural parameters for R h ( l l l ) - ( / 3 x / 3 ) 3 0 ° - S were simplified by fixing a l l interlayer spacings for rhodium at the bulk value (2.195A). This follows Shepherd's observations that the clean Rh( l l l ) surface is not reconstructed and has a topmost interlayer spacing which is very close to the bulk value [1]. The Rh-S interlayer spacings were varied over the ranges: 1.15 - 1.75A for the 3f and 3h models, 1.84 - 2.44A for the If model and 1.68 - 2.28A for the 2f model. Figure 4.6 shows comparisons for nine diffracted beams between the experimental and the closely optimized calculated 1(E) curves from the four to c "D >s L . o 4—* >-(10) beam 96 T 1 1 1 I I I I I I / N (1 1) beam 40 80 120 160 200 240 120 160 200 240 CO z: LU 180 220 60 100 U0 180 200 240 160 200 240 E L E C T R O N E N E R G Y ( e V ) Figure 4.6: Comparison of nine 1(E) curves measured f o r normal incidence on Rh(lll)-(/3x / 5)30°-S with those c a l c u l a t e d f o r the 3 f , 3h, 2f and I f adsorption models with Rh-S i n t e r l a y e r spacings which give the best o v e r a l l match between experiment and c a l c u l a t i o n f o r each model. 97 98 models. These comparisons at the visual level apparently suggest that the 3f site is favored over the others. This is confirmed by Figure 4.7 which shows contours plots for the r e l i a b i l i t y index as a function of over-layer spacing and V Q r for the four different adsorption sites; the lowest values of R^ are clearly for the 3f adsorption s i te . Consequently, both a visual comparison of the calculated and experimental 1(E) curves, as well as an analysis with the r e l i a b i l i t y index R^ shows that the best correspon-dence is for the 3f site with the S-Rh Interlayer spacing in the v i c in i ty of 1.45 and 1.55A. Comparisons for the various diffracted beams are shown in Figure 4.8 for these structures. The minimum value of R (0.27), which P indicates a moderate level of agreement between experiment and calculation, corresponds to a S-Rh interlayer spacing which equals to 1.53 A; for these conditions V equals -9.8 eV. or ^ 4.4 Discussion The evidence presented in the previous section suggests that the Rh(lll)-(/3x/3)30°-S structure has S atoms adsorbed on the expected (3f) sites of the Rh( l l l ) surface at about 1.53A above the topmost rhodium layer. If no surface relaxation is experienced by the metal atoms, each S atom is then bonded to three neighbouring Rh atoms at a distance of 2.18A. This value is s ignif icantly less than the average Rh-S distances in Rh 2S 3 (2.37A) [87] and R h 1 7 S 1 5 (2.33A) [88], although Rh-S distances in unhindered coordination complexes are known to range from 2.23 to 2.38A [89-91]. With a hard-sphere model for the Rh and S atoms, the bond length determined here corresponds to a S atomic radius equal to 0.83 A, which is a 99 3 f model 3h model Rh-S spacing Figure 4.7: Contour p l o t s f o r Rh(lll)-(/3x/3)30°-S of R versus V and the Rh-S i n t e r l a y e r spacing f o r four d i f f e r e n t s t r u c t u r a l models. 100 T 1 1 1 1 1 r (2/3 2/3) beam 80 120 160 200 240 E L E C T R O N E N E R G Y (eV ) Figure 4.8: Comparison of experimental 1(E) curves for some integral-order and frac t i o n a l - o r d e r beams from Rh(lll)-(/3x/3)30°-S with those calculated for the 3f model with s u l f u r e i t h e r 1.45 or 1.55A above the topmost rhodium layer. 101 E L E C T R O N E N E R G Y ( e V ) Figure 4.8: ( c o n t i n u e d ) 102 relatively low value for S (values from 0.77A to 1.04A have been reported from surface crystallography [92]). An objective of surface crystallographic research is to relate the determined structure to chemical bonding concepts. I n i t i a l studies have been made u t i l i z i n g Pauling-type expressions to predict adsorption bond distances [80,93,94], for example with r = r Q - 0.85 logs, (4.1) where r is the interatomic distance (e.g. from an adsorbed atom X to a neighboring metal atom M) for a bond valence s, and r Q is the corresponding distance for the bond of unit valence. Given r , X-M bond lengths can be calculated with equation (4.1) on the assumption that the sum of bond valencies at each X equals the atomic valence v, which in the following is taken as the normal group value (e.g. 1 for F, C l , . . . ; 2 for 0, S, . . . ) . For the case that X adsorbs on a metallic surface with n equivalent neighboring M atoms, a l l the bond valencies equal v/n. The crystallographic ana lysis for Rh( l l l ) - ( /3x A)30 ° -S completes i n i t i a l information for surface bond lengths for S adsorbed on the three low-index surfaces of rhodium, and Table 4.1 summarizes these experimental results. In a l l these examples the S atoms are believed to adsorb on the expected sites ( i . e . those sites which would be occupied i f another layer of metal were added). In addition to the S-Rh bond lengths from LEED crystallography in Table 4.1, the corresponding predicted values are given from a study by Mitchell e_t al_. [93]. Two sets of predictions are given 103 u t i l i z i n g equation (4.1); they differ by the method used to estimate TQ. In set I r is deduced from a modified algorithm of Brown and Altermatt o ° [95], whereas in Set II r is derived from the structural details of the o bulk solid R h 1 7 S 1 5 [88]. It is clear that each set of experimental data in Table 4.1 broadly follows the trend anticipated for atoms adsorbed on the expected sites for (111), (100), (110) surfaces of fee metals, for which values of n are 3, 4 and 5 respectively. For a fixed valency for the adsorbed atom, average bond orders should reduce along this series and correspondingly the bond lengths increase. Exact correspondence between the experimental and predicted values in Table 4.1 is not expected in general, and this is both because of the incomplete information currently available for surface bonding (which in turn is required as input to an empirically-based predictive model) and because of the uncertainties present in the currently-reported surface crystallographic determinations. Nevertheless, a general level of consistency is found. Some clear discrepancies in structural features between the calcula-ted and experimental 1(E) curves for R h ( l l l ) - ( / 3 x / 3 ) 3 0 ° - S are apparent in Figure 4.8, for example that in the (01) beam in the v ic in i ty of 170 eV. Their existence suggests some refinement to current analysis may be necessary. It is hoped later to undertake calculations of LEED intensities for structural models which allow both vert ical and lateral relaxations for atoms in the surface region. Such relaxations in the positions of the metal atoms have been reported by surface crystallography in one or two other contexts involving S adsorption (e.g. lateral relaxations on Fe(110) [96], vert ical relaxations on Ni(110) [97]). Table 4.1: Comparison of measured and predicted S-Rh bond lengths for S atoms adsorbed on the (111), (100), (110) surfaces of rhodium. o v S-Rh bond lengths (A) System n Predicted Set I Set II LEED crystallography R h ( l l l ) - ( / 3 x / 3 ) 3 0 ° - S 3 2.28 2.16 2.18 Rh(100)-(2 x 2)-S k 2 . 3 9 2 . 2 7 2 . 3 0 Rh(110)-c(2 x 2)-S if 2 . 5 2 ZM 1 2 . 3 1 2.11 2.12 105 CHAPTER 5 LEED Investigation of the Rh(lll)-(2x2)-0 Surface Structure 106 5.1 Introduction The chemisorption of oxygen on surfaces of the Group VIII t r a n s i t i o n metals has s t i r r e d much i n t e r e s t due to the important roles played by oxygen and oxygen-containing molecules as surface species i n heterogeneous c a t a l y s i s . In general, the interactions between oxygen and these metals can be complex, and the experimental work reported to date s t i l l leaves many questions to be answered. An understanding i s required for developing atomistic models, both for simple chemisorption and ultimately for surface r e a c t i v i t y [98]. Surface c r y s t a l l o g r a p h i c analyses have been made, with either LEED or SEXAFS, for three examples of oxygen adsorption on the (111) surfaces of face-centered cubic metals, and, at low coverage, the 0 atoms adsorb above this type of surface i n hollow s i t e s of three-fold coordina-t i o n for aluminum [99-101], i r i d i u m [102] and n i c k e l [103]. Further, the measured oxygen-to-metal interatomic bond lengths can be accounted for quite well by assuming a bond order of 2/3, which i s reasonable for divalent 0 i n t e r a c t i n g with three neighbouring metal atoms. Such analyses to date have emphasized using a Pauling-type bond length-bond order r e l a t i o n [94]. Af t e r completing the LEED c r y s t a l l o g r a p h i c analysis for the R h ( l l l ) -(/3x/3~)30°-S surface, i t seemed natural to study the low-coverage structure formed by oxygen on the R h ( l l l ) surface. In e a r l i e r work, T h i e l et a l . [104] studied t h i s chemisorption system with thermal desorption spectroscopy,, AES and LEED; these authors reported the formation of a (2x2) overlayer structure but no surface c r y s t a l l o g r a p h i c analysis was made. A major focus of th i s chapter i s provided by a LEED c r y s t a l l o g r a p h i c analysis to determine the geometric d e t a i l s for the Rh( l l l ) - ( 2 x 2 ) - 0 surface [105]. 107 5.2 Experimental A well-ordered and clean (111) surface of rhodium, showing a sharp ( l x l ) LEED pattern, was prepared by following the procedures described i n Section 4.2. When the R h ( l l l ) surface was exposed to approximately 6 L (1 L = 10~ 6 Torr s) of research grade oxygen (Matheson 99.99%) at room temperature, a sharp (2x2) LEED pattern was observed, although the super-structure spots became weaker and d i f f u s e with continued exposure to the electron beam, apparently as a r e s u l t of the adsorbed layer disordering. Nevertheless, i t was found that for an incident beam density of 0.8 uA/cm2 the f r a c t i o n a l beams remained v i s i b l e on the screen for about 2 minutes before disordering dominated. This indicated the maximum period over which i n d i v i d u a l measurements of beam i n t e n s i t y curves could be made, although a sharp (2x2) LEED pattern could be restored by either rotating the sample away from out of the incident beam pr switching off the incident beam for a few seconds. In addition, according to T h i e l e_t a l ^ [104] any thermal dissolution/desorption for chemisorbed oxygen on R h ( l l l ) takes place at around 400 K, and therefore some 100 K higher than the surface temperature used i n t h i s work ( i . e . room temperature). Thus the LEED measurements here were made for conditions that precluded the adsorbed oxygen atoms from undergoing any appreciable dissolution/desorption processes during the experiment. With the sample cooled to about 215 K, we found i t possible to measure with the VLA system, as described In Section 3.5.2, a set of normal-incidence 1(E) curves from 60 to 250 eV i n increments of 2 eV. Each i n d i v i d u a l measurement was performed by rotating the face of the sample away out of the electron beam prior to s e t t i n g the e s s e n t i a l parameters for 108 the VLA system, and then accomplishing the measurement within 2 minutes, starting as soon as the sample was relocated for the normal incidence orientation. A total of ten inequivalent 1(E) curves were measured for normal incidence on the Rh(lll)-(2x2)-0 surface; these covered five integral beams and five fractional beams, namely (10), (01), (11), (20), (02), (1/2 1/2), (1 1/2), (1/2 1), (0 3/2) and (3/2 0), using the beam notation indicated in Figure 5.1(b). The unit mesh of the superstructure corresponding to the (2x2) LEED pattern is shown in Figure 5.1(a). The detailed procedures for normalization, averaging and smoothing of 1(E) curves were done exactly as described in Section 4.2. 5.3 Calculations The most-probable models for the Rh(lll)-(2x2)-0 surface structure have 0 atoms adsorbed on sites of three-fold coordination. There are two adsorption sites of this type indicated in Figure 1.8(a), namely the 3f and 3h sites as defined in Section 4.1. For simple adsorption on these s i tes , with the (2x2) translational symmetry, a surface of Rh( l l l ) has a coverage of 0.25 monolayer (ML), and i t belongs to the p3ml diperiodic space group. In addition, we also considered a graphitic overlayer model with 0 atoms adsorbed on both 3f and 3h sites to give a total coverage of 0.5 ML (see Figure 2.4). This model was f i r s t proposed for the Pt( l l l ) - (2x2)-0 surface structure [106], although LEED crystallography indicates i t is applicable for the Ni( l l l ) - (2x2)-H surface structure [107]. 1(E) curves for the simple 3f, simple 3h and 3f + 3h graphitic models were calculated using the renormalized forward scattering method 109 F i g u r e 5.1: (a) Unit mesh of the (2x2) ove r l a y e r s t r u c t u r e f o r oxygen adsorbed on R h ( l l l ) . (b) Schematic LEED pa t t e r n and beam notations corresponding to the overlayer s t r u c t u r e of ( a ) . 110 [44,45], although the composite-layer method as described in Section 2.5 was used to calculate the 0 overlayer diffraction matrices for the 3f + 3h graphitic model. A maximum of 43 inequivalent beams were included in the calculation; the non-structural parameters being assumed to have values which correspond to those used in the previous analysis for R h ( l l l ) -( / 3 x / 3 ) 3 0 ° - S . Therefore the atomic potentials were characterized by phase shifts to A = 7; for rhodium they were derived from a band structure potential [53], while those for oxygen originated with the superposition potential obtained by Demuth et a l . [86]. The real part of the muffin-tin potential (V Q r ) was set i n i t i a l l y to 10 eV below the vacuum level , while 1/3 the imaginary part (VQ^) was equated to 0.819 E ; where E is the electron energy (in eV) Inside the crysta l . The effective Debye temperatures of rhodium and oxygen were taken respectively as 480 and 843 K [44]. The structural models were simplified by fixing a l l interlayer spacings for rhodium to the bulk value (2.195A); the 0-Rh interlayer spacings Included in the calculations range from 1.064 to 1.564A for the simple 3f and simple 3h models, but from 1.100 to 1.550A for the graphitic overlayer. 5.4 Results Figure 5.2 compares the experimental 1(E) curves of the (1/2 1/2), (1 1/2) and (0 3/2) beams with the corresponding 1(E) curves calculated for the above three models. Visual comparisons show poor correspondence for the 3h model compared with either the simple 3f model or graphitic model. However, as a result of the disordering effect of the incident beam, the I l l ' I 1 1 1 I 1 1 r-(1/2 1) beam E L E C T R O N E N E R G Y ( e V ) Figure 5.2: Comparison of experimental 1(E) curves for (1/2 1), (1/2 1/2) and (0 3/2) diffracted beams from Rh(lll)-(2x2)-0 at normal incidence with those calculated for the 3f, 3h and 3f+3h models over a range of the topmost 0-Rh interlayer spacings. m o d e l : 3 f + 3 h a: 1-100 40 80 120 1G0 200 240 80 120 160 E L E C T R O N E N E R G Y (eV ) 2 0 0 2 40 Figure 5.2: (continued) c O \E ^_ >-r— Lo z : LU (1/2 1) beam ' 113 T 1 1 I expt. 40 BO 120 160 200 240 TT 1 1 1 1 1 r m o d e l : 3 h d R h - 0 ; ( A ) a : 1 064 b : 1 164 c 1 264 d : 1 364 e : 1 464 f : 1 564 (1/2 1/2)beam expt. (0 3/2)beam BO 120 160 200 80 120 160 E L E C T R O N E N E R G Y (eV ) 200 240 Figure 5.2: (continued) 114 experimental 1(E) curves were inevitably measured with higher than usual background, and in principle this could affect assessments of the favored model from visual comparison alone. Nevertheless, a visual comparison over the complete range of data did suggest that the best correspondence between the experimental and calculated 1(E) curves is obtained either for the simple 3f model or for the 3f + 3h graphitic model, with the O-Rh inter-layer spacing in the ranges 1.164 to 1.264 A and 1.100 to 1.175 A, respecti-vely. The r e l i a b i l i t y index (Rp) proposed for LEED by Pendry was used in an attempt to make the above observations more precise. Figure 5.3 shows contour plots of R as a function of the 0-Rh interlayer spacing and V p or for each of the three models. This evidence suggests that the 3f model is favored; the minimum value of R^ (0 .394) , which indicates a moderate level of correspondence between the experimental and calculated 1(E) curves, corresponds to an 0-Rh interlayer spacing equal to 1.23A while V Q r is -12.6 eV. Figure 5.4 displays comparisons between the experimental 1(E) curves and the corresponding 1(E) curves calculated for the 3f model with the 0-Rh interlayer spacing equal to 1.164 and 1.264 A. 5.5 Discussion The evidence presented above indicates that the Rh(lll)-(2x2)-0 structure has oxygen atoms adsorbed on simple 3f sites of the Rh( l l l ) surface while held at about 1.23A above the topmost rhodium layer. This value may be reasonable since the associated value for the 0-Rh bond length is 1.98A, which agrees closely with the value of 1.99A predicted for this system with bond order equal 2/3 [ 9 4 ] . Although this correspondence is 115 3 f m o d e l 0450 1.064 1.164 1.264 1364 1.464 1.564 R h - 0 s pac i ng (A) (A) Figure 5.3: Contour p l o t s f o r R h ( l l l ) - ( 2 x 2 ) - 0 of R versus V and the Rh-0 i n t e r l a y e r spacing f o r (a) 3f, (b) 3h and (c] 3f+3h s t r u c t u r a l models. 116 3 h m o d e l 1.064 1.164 1264 1-364 1-464 1564 R h - 0 spacing(A) (B) 5.3: (continued) 117 Graph i t i c mode l 1100 1.175 1250 1325 1-400 W75 1-550 R h - 0 spac ing (A ) (C) Figure 5.3: (continued) 118 Figure 5.4: Comparison of experimental 1(E) curves f o r some i n t e g r a l - o r d e r and f r a c t i o n a l - o r d e r beams from R h ( l l l ) - ( 2 x 2 ) - 0 at normal incidence with those c a l c u l a t e d f o r the 3f model w i t h oxygen e i t h e r 1.164 or 1.264A above the topmost rhodium l a y e r . 119 (1/2 1/2) beam i 1 1 r 1.164A (1/2 1) beam T 1 1 1 r 4 0 8 0 1 2 0 1 G 0 2 0 0 2 4 0 E L E C T R O N E N E R G Y ( e V ) Figure 5.4: (continued) 120 J — — i 1 1 1 1 1 1 i i I r~ • . . — i 60 100 U 0 180 220 180 220 260 E L E C T R O N E N E R G Y ( e V ) Figure 5.4: (continued) 121 close, nevertheless contours in the v ic in i ty of equal to 0.400 are rather shallow in the diagonal direction in Figure 5.3(a). The uncertainty in the 0-Rh interlayer spacing, derived from the standard error in the R^ values associated with the individual beams [108], is ±0.09A. This r e l a t i -vely large uncertainty is perhaps not unexpected given the tendency for the 0 layer to disorder while the measurements were being made. Indeed the disordering effect of the incident beam found in this study was such that the LEED crystallographic analysis could not have been possible without a fast measurement system [73]. Moreover this study suggested that the standard procedures used in LEED crystallography [109] can s t i l l allow a plausible structural analysis even though some electron beam-induced disordering inevitably occurred while the measurements were being made. Such observations could be helpful for developing interest in using LEED to characterize surface defects [110,111] as well as geometrical structure. Overall the study here is satisfying in that the measurements made with the LEED video analyzer for a system which is unstable in the electron beam were able to lead to a structural conclusion which appears reasonable; furthermore this evidence supports the use of a Pauling-type bond-order expression for predicting bond lengths for the adsorption of 0 atoms on other surfaces of rhodium [93,94]. 122 CHAPTER 6 Adsorption of Oxygen on the (0001) Surface of Zirconium 123 6.1 Introduction Zirconium has s i g n i f i c a n t i n t e r e s t i n materials science, p a r t i c u l a r -l y i n the nuclear industry. This i s e s s e n t i a l l y due to i t s low absorption cross section for neutrons, as well as i t s high resistance to corrosive environments ins i d e nuclear reactors. The unique corrosion resistance of zirconium and i t s a l l o y s i s believed to depend on the formation of th i n protective oxide films on the surface; therefore the oxidation of zirconium has considerable technological Interest [42,112]. Many studies of the oxidation of zirconium have been reported, but most of these are concerned either with p o l y c r y s t a l l i n e zirconium or with thick films of oxide formed under high oxygen exposures at high temperatures. Five representative studies using d i f f e r e n t surface techniques and surface treatments are l i s t e d i n Table 6.1, although there are considerable v a r i a t i o n s i n the conditions of these experiments. High-temperature heating of the zirconium i s e f f e c t i v e to obtain a clean surface by d i f f u s i n g some contaminants (e.g. C, N, 0) into the zirconium bulk structure, but i t has to be noted that pure a-zirconiura (hep structure) undergoes a phase t r a n s i t i o n to the 6-zirconium form (bec structure) at 1135 K [116]. C l e a r l y the heating temperature i s l i m i t e d to below t h i s value for cleaning s i n g l e c r y s t a l surfaces. So far only a very l i m i t e d number of studies have been made for the i n i t i a l steps of the oxygen chemisorption process on well-characterized zirconium surfaces ( i . e . at 0 coverages of the order of one monolayer) [112]. In part t h i s may be at t r i b u t e d to the d i f f i c u l t i e s of obtaining clean well-characterized zirconium surfaces, the l i m i t a t i o n s being set both by the high r e a c t i v i t y of this metal and by the bulk phase change. Even Table 6.1: Five representative studies of the oxidation of zirconium using different surface techniques and surface treatments. Sample Cleaning Method Exposure of C U (L) Surface Technique Ref. Zr(OOOl) Poly. Zr, Zr(0001), ZrOo Poly. Zr Poly. Zr, ZrCU Poly. Zr Ar bomb, heat to 8 7 3 K Ar bomb. heat to 1 0 0 0 K Ar bomb, heat to ^ 1 1 0 0 K Ar bomb. heat to ^ 1 6 5 0 K Ar bomb, heat to -1800 K 0-1 0-108 0 - 5 0 0 - 1 0 -0 - 6 x l 0 3 LEED,AES XPS,AES AES,UPS LREELS ,AES SIMS L 4 3 : C11 2 • m 13: C114D C115J *: Zirconium metal undergoes hcp«—•bcc t r a n s i t i o n at 1 1 3 5 K. **: Low resolution electron energy loss spectroscopy. 125 though surface structure studies are s t i l l very l i m i t e d for zirconium, the same statement also holds for chemisorption at a l l hep metals. Currently there i s evidence that oxygen d i s s o c i a t i v e l y chemisorbs on p o l y c r y s t a l l i n e zirconium, and that with heating d i f f u s i o n into the bulk occurs rather than desorption [113, 117, 118]; consistently, a recent preliminary surface c r y s t a l l o g r a p h i c analysis with low energy electron d i f f r a c t i o n indicated that the surface structure designated Zr(0001)-(2x2)-0 involves subsurface adsorption. Nevertheless, this l a t t e r analysis remains less than complete from several points of view, including the i n a b i l i t i e s to assess: ( i ) whether the surface r e a l l y has the (2x2)-type t r a n s l a t i o n a l symmetry or whether i t a c t u a l l y involves r o t a t i o n a l l y r e l a t e d domains of the (2x1) types [119]; ( i i ) the role of disorder i n surface structure; ( i i i ) the degree of warping of Zr layers i n the presence of (2x2) oxygen layers; and ( i v ) whether 0 should be represented as a negatively charged species. For the cry s t a l l o g r a p h i c study, the designa-t i o n Zr(0001)-(2x2)-0 was used as a convenience since, from point ( i ) above, i t i s clear that u n t i l more information i s av a i l a b l e for coverage and structure, the designation "(2x2)" cannot be seen as representing more than a shorthand for a surface that gives appropriate half-order d i f f r a c t e d beams. A d d i t i o n a l characterizations are therefore needed for surfaces which show (2x2)-type LEED patterns. This leads to the f i r s t objective of t h i s chapter, namely to use the LEED spot p r o f i l e technique and AES to probe further some aspects of oxygen coverage for the i n i t i a l stages of chemisorption on the Zr(0001) surface [120]. The second objective i s to attempt to e s t a b l i s h conditions for the i n i t i a l ( i . e . lowest coverage) 126 ordered Zr(0001)-(lxl)-0 structure and then to make a LEED c r y s t a l l o g r a p h i c analysis on th i s structure [121]. 6.2 Experimental 6.2.1 Sample Preparation and Cleaning The zirconium s i n g l e - c r y s t a l sample used In t h i s work was kindly provided by P.R. Norton (AECL, Chalk River Nuclear Laboratories). The surface had been i n i t i a l l y oriented to within 2° of the (0001) plane, but on receipt we reoriented i t to within 0.5° of this plane and cut i t to a suitable s i z e for the sample holder i n this laboratory. Then the sample was mechanically polished with increasingly f i n e r diamond paste (9-1 u); this was followed by a 30 s chemical etch i n acid s o l u t i o n (45% HN03, 50% H 20, 5% HF by volume) [122]. F i n a l l y the sample was degreased with trichloroethylene and i n s t a l l e d i n the UHV chamber. After pumping down, AES showed that the Zr(0001) surface region contained large quantities of carbon and oxygen; t h i s was indicated by the Auger peaks at 272 eV and 510 eV respectively, as i n the spectrum for the contaminated Zr(0001) surface shown i n Figure 6.1(a). Argon ion bombard-ment (2 kV, 3 uA) was then c a r r i e d out at room temperature u n t i l carbon was the only detectable contaminant. I t i s worthwhile to note that the oxygen contamination could only be removed from the surface i f the titanium sublimation pump was operated during the sputtering process. The r e s i d u a l carbon contamination was reduced by annealing the sample at about 700°C for 20 minutes, although heating at 600°C resulted i n the segregation of sul f u r from the bulk. Several cycles of gentle argon ion bombardment (800 V, Figure 6.1: Auger spectra of two Zr(0001) s u r f a c e s : (a) as mounted (b) cleaned. 128 3 uA), followed by annealing at 600°C for 20 minutes, were found e f f e c t i v e to minimize the S and C contaminations. The s u l f u r coverage was d i f f i c u l t to quantify by AES as a r e s u l t of the overlap of the S (150 eV) and Zr (147 eV) Auger peaks. To monitor the presence of s u l f u r i t was necessary to measure the r e l a t i v e Auger peak heights at 92 eV and 147 eV. The LEED pattern also served as a s u l f u r detector; even low coverages produced an increased background and a f a i n t (3x3) pattern. However a f t e r a t o t a l of about 60 hours of gentle argon ion bombardment, covering 15 bombardment-annealing cycles, the Auger peak r a t i o A l i t 7 / A g 2 reached a l i m i t i n g value of approximately 1.40, as i s shown i n Figure 6.1(b). This spectrum compared well with published data for a clean zirconium surface [123]; i n addition a sharp ( l x l ) LEED pattern with 6-fold symmetry at normal incidence indicated that the Zr(0001) surface was well-ordered. 6.2.2 LEED Pattern for Oxygen Adsorption on Zr(OOOl) Exposure of a clean and ordered Zr(0001) surface at room temperature to about 1.2 Langmuir (1 L = 1 0 - 6 Torr s) of oxygen resulted i n the obser-vation of a d i f f u s e ( l x l ) LEED pattern, although a sharp and apparently stable (2x2)-type pattern could be established by heating b r i e f l y to 220°C It i s noted that a l l heat treatments referred to here involve heating the sample to the stated temperature, followed immediately by cooling back to room temperature (the heating and cooling rates both being approximately 1°C s - * ) . The (2x2)-type surface corresponds to an oxygen coverage for which the index R = A 5 1 0 / A 9 2 ( i . e . the r a t i o of the Auger peak height for 129 0 at 510 eV to that of Zr at 92 eV) equals 0.16. For Zr i t appears advantageous to use the 92 eV Auger peak which involves emission from the N s h e l l ; t h i s l i m i t s the influence of attenuation and shift/broadening e f f e c t s which have been noted i n valence s h e l l spectra [113,124]. With greater exposure to oxygen the half-order beams weaken, and sharp higher-coverage (1x1) patterns can be established. For example that with R q equal to 0.23 i s obtained a f t e r a 3.6 L exposure and heating to 220°C. LEED also shows that this ordered (1x1)-0 structure r e a d i l y reconverts to give (2x2)-type patterns on heating at temperatures which are s u f f i c i e n t l y high to cause a loss of surface oxygen as a r e s u l t of bulk d i f f u s i o n . After each adsorption experiment, the sample was cleaned by A r + bombardment and reordered by heating to 600°C. 6.2.3. AES and LEED Spot P r o f i l e Measurements for Zr(0001)-(2x2)-0 An assessment of the conditions under which oxygen at a Zr(0001) surface d i f f u s e s into the bulk i s needed in order to define appropriate surface preparation procedures. The data i n Figure 6.2 apply to an oxygen-treated surf ace for which R i s i n i t i a l l y 0.16 (referred to as R )• This o J o sample was heated to a temperature T and cooled back to room temperature T for measuring the new Auger peak height r a t i o ( R Q ) ' Figure 6.2 shows a plot of the normalized oxygen peak height r a t i o (R Q/R o ) obtained for. successively increasing T. This curve provides evidence that 0 d i f f u s i o n into zirconium e f f e c t i v e l y s t a r t s at around 236°C, and i t gives part of the 130 I I I I I 1_ 0 80 160 240 320 400 TEMPERATURE (°C) Figure 6.2: Normalized Auger peak height r a t i o K^/Rznz as a f u n c t i o n of heating temperature f o r oxygen on Zr(0001); the i n i t i a l coverage corresponds to R Q = 0.16. 131 basis for the choice used above of heating to 220°C to encourage surface ordering. Figure 6.3 reports measurements made with the video LEED analyzer (VLA), described in Section 3.5.3, for the development of the (2x2)-type diffract ion pattern with increasing exposure to oxygen; speci f ical ly information is given for the (1, 1/2) beam at 66 eV as a function of RQ (the beam notation in this Chapter is the same as that used in Figure 5.1). After each exposure to oxygen, the sample was heated to 220°C and cooled to room temperature before making the measurements. Figures 6.3(a) and (b) plot, respectively, the reciprocal of beam width (FWHM, i . e . f u l l width at half maximum) and the integrated beam intensity (I); In each case values are plotted as a fraction of the maximum value. Variations in beam width reflect variations in size of the ordered regions which contribute to the LEED pattern; specif ical ly larger values of 1/FWHM correspond to larger ordered regions [110]. The information in Figure 6.3 suggests the existence of at least two separate "ordered" regions over the exposure range, an observation that is broadly similar to conclusions reached by Madey e_t a l . [125] in studies of oxygen adsorption on the Ru(0001) surface, although Yates et a l . [126] observed only a very small low-coverage peak for oxygen on R h ( l l l ) . Nevertheless in neither of these latter cases does an ordered (1x1) adsorption structure exist, and so the detailed observations for 0 on Zr(0001) are inevitably different from the other cases. Another approach to the type of information in Figure 6.3 is made by measuring 1/FWHM for the (1, 1/2) beam at 66 eV and room temperature after heating to different higher temperatures. Three i n i t i a l surfaces were used with oxygen coverages corresponding to R = 0.12, 0.16 and 0.20; they a l l 132 Figure 6.3: Measured vari a t i o n s for the (1, 1/2) beam at 66 eV with oxygen coverage on Zr(0001): (a) normalized 1/FWHM, (b) normalized integrated i n t e n s i t y . 133 gave (2x2)-type LEED patterns and the three parts of Figure 6.3 show the i n d i v i d u a l plots obtained for 1/FWHM versus temperature. Two e f f e c t s appear to be associated with the heating: one i s the increase i n surface ordering as larger surface domains are formed, and the other (for tempera-tures greater than 236°C) relates to the onset of bulk d i f f u s i o n which decreases the R q value. With the l a t t e r , c o n t r o l l e d increases i n tempera-ture can give systematic v a r i a t i o n s i n the amount of surface oxygen. Starting with the lowest i n i t i a l coverage ( i . e . R q = 0.12) only one ordered region occurs as the surface oxygen successively orders and depletes (Figure 6.4(a)); indeed this curve for increasing temperature i s c l o s e l y related to that i n Figure 6.3(a) as R q decreases from 0.12. By contrast, when the i n i t i a l surface corresponds to R q = 0.20, three ordered regions are indicated by Figure 6.4(c), although the f i r s t one i s apparently i d e n t i f i e d by just the high-coverage shoulder (which i s s i m i l a r l y recognized in Figure 6.3(a)). The existence of the high-temperature (low-coverage) peak i n Figure 6.4(c) shows that surface ordering can occur simultaneously with the surface depletion process which i s i n i t i a t e d at 236°C For the i n i t i a l intermediate coverage (R q = 0.16) considered i n 6.4(b), two ordered regions are indicated as R q decreases from 0.16, and this i s broadly consistent with the peaks at R Q equal to 0.15 and 0.11 as shown i n Figure 6.3(a). TEMPERATURE ft) Figure 6.4: Measured v a r i a t i o n w i t h heating temperature of normalized 1/FWHM f o r the (1, 1/2) beam at 66eV f o r i n i t i a l oxygen coverages on Zr(0001) with R Q equal to: (a) 0.12, (b) 0.16 and ( C) 0.20. 135 6.2.4 Measurements of 1(E) Curves from the Lowest-Coverage Zr(OOOl)- ( l x l ) - O Surface S t r u c t u r e In Figure 6.3, i t was shown that the exposure of a (0001) surface of zirconium to around 3.6 L of 0 2 r e s u l t s i n an i n i t i a l ( i . e . lowest coverage) Z r ( 0 0 0 1 ) - ( l x l ) - 0 s t r u c t u r e w i t h R =0.23. LEED i n t e n s i t y -o versus-energy (1(E)) curves f o r d i f f r a c t e d beams from t h i s surface were measured w i t h the video LEED analyzer system over the approximate range 50-230 eV. These measurements were made with a constant increment of 2 eV, and a n o r m a l i z a t i o n was made to the i n c i d e n t beam cu r r e n t . The incidence s e t t i n g s were fine-tuned o n - l i n e to check f o r the appropriate symmetrical equivalences. In the f i n a l p r ocessing, 1(E) curves measured f o r symmetri-c a l l y r e l a t e d beams were averaged and smoothed as described In the previous study f o r Rh(lll)-(/Jx/3)30°-S. A t o t a l of seven Independent 1(E) curves was so measured from the Z r ( 0 0 0 1 ) - ( l x l ) - 0 surface. These were f o r the beams (10), (11), (20) at normal incidence; (00), (10), (2-1), (20) at a polar angle of 16° w i t h the azimuthal d i r e c t i o n p a r a l l e l to a m i r r o r plane i n the s u r f a c e , using the beam n o t a t i o n shown i n Figure 6.5. The p o l a r angle 9 f o r which the measurements were made was determined from the p o s i t i o n of the specular beam i n the screen w i t h respect to the normal d i r e c t i o n . A previous c a l i b r a t i o n was made to r e l a t e measurements of the specular beam p o s i t i o n on the screen to angular r o t a t i o n s of the manipu-l a t o r from the normal p o s i t i o n . For the azimuthal angle <t>, the sample was o r i e n t e d so that the incidence d i r e c t i o n c o i n c i d e s w i t h a (xz) r e f l e c t i o n symmetry plane as i s shown i n Figure 6.5. Hence appropriate p a i r s of 136 23 2 2 I 3 I I 00 I I I 2 0 I I 0 2 I 0 2 I I 20 0 3 I 2 2 I 3 0 2 2 3 I 2 2 3 I 32 Figure 6.5: Reciprocal net and beam notation for the Zr(0001)-(lxl)-0 structure. 137 d i f f r a c t e d beams were av a i l a b l e to ensure the presence of the r e f l e c t i o n symmetry plane at the p a r t i c u l a r polar angle used ( i . e . 9 = 16°). 6.3 Multiple Scattering Calculations f o r Zr(0001)-(lxl)-0 In t h i s work 1(E) curves were calculated for various types of models appropriate to the Zr(0001)-(lxl)-0 surface, and some of these models are indicated i n Table 6.2. The symbols A, B, C i d e n t i f y close-packed zirconium layers which are l a t e r a l l y displaced so that the hep and fee structures follow re s p e c t i v e l y the f a m i l i a r stacking sequences ABAB... and ABCABC...; the symbols i n parentheses have the analogous meaning for oxygen. For example, the model type (B)A(C)BAB..., as i s shown i n Figure 6.6, indicates zirconium with the unreconstructed stacking sequence while the adsorbed 0 atoms occupy both overlayer and underlayer s i t e s (these are respectively the "expected" 3-coordinate s i t e s and octahedral hole s i t e s between the f i r s t and second metal l a y e r s ) . For each model type, the calc u l a t i o n s treated the neighbouring Zr-0 i n t e r l a y e r spacing (d Z r_Q) as a v a r i a b l e . For the multiple scattering c a l c u l a t i o n s , the overlayer spacings were varied over the range 0.60 to 1.20A, while the underlayer spacings were varied between 1.20A and 1.46A with the 0 atoms midway between the adjacent Zr layers. However for models with both overlayer and underlayer, the underlayer Zr-0 spacing was fixed at 1.35A; also a l l d i r e c t l y neighbouring Zr-Zr i n t e r l a y e r spacings were held at the value for zirconium metal (2.57A) [127]. The m u l t i p l e - s c a t t e r i n g c a l c u l a t i o n s used procedures discussed i n Chapter 2. The scattering by the zirconium structure, including incorpo-138 Figure 6.6: P a r t i a l view of the Z r ( 0 0 0 1 ) - ( l x l ) - 0 s t r u c t u r e corresponding to the model designated (B)A(C)BAB... . Atoms i n the topmost Zr l a y e r are i n A-type p o s i t i o n s (open s o l i d c i r c l e s ) , w h i l e the second Zr l a y e r has atoms i n B-type p o s i t i o n s . The oxygen ove r l a y e r ( s m a l l e r shaded c i r c l e s ) has atoms i n B-type p o s i t i o n s , w h i le the underlayer 0 atoms (darker c i r c l e s ) occupy the octahedral holes i n C type p o s i t i o n s . 139 rated 0 layers, was determined with the renormalized forward s c a t t e r i n g method, while 0 overlayers were added with the layer doubling method. For the c a l c u l a t i o n s at normal incidence the 3-fold r o t a t i o n and mirror r e f l e c -t i o n symmetries were u t i l i z e d , while at off-normal incidence only the single mirror r e f l e c t i o n plane was present; the maximum number of inequiva-lent beams ava i l a b l e for the c a l c u l a t i o n s at normal and off-normal incidence was 28 and 56 r e s p e c t i v e l y . The c a l c u l a t i o n s treated the s o l i d ' s p o t e n t i a l i n the muffin-tin form, and the atomic potentials were characterized by phase s h i f t s up to A = 7; for zirconium they were derived from a band structure p o t e n t i a l [53], while those for neutral oxygen have the same values as those used in the previous analysis for R h ( l l l ) - ( 2 x 2 ) - 0 . In addition, a set of oxygen phase s h i f t s obtained by Zhong e_t a l . [121,128], s p e c i f i c a l l y for negatively charged 0 and the structure of bulk ZrO, was also used i n some further multiple-scattering c a l c u l a t i o n s for models of the Zr(0001)-(lxl)-0 surface. The r e a l part of the constant p o t e n t i a l (V ) between the atomic spheres was set i n i t i a l l y at -10.0 eV, and the imaginary p o t e n t i a l (V j) was fixed at -5.0 eV; the value of the former was refined during the comparison with the experimental 1(E) curves. 6.4 LEED Crystallographic Results for the I n i t i a l Zr(0001)-(lxl)-0  Structure Assessments of the q u a l i t y of correspondence between experimental and calculated curves were made both v i s u a l l y and with Pendry's r e l i a b i l i t y index (R ). For each model type contour plots of R were made as a 140 f u n c t i o n of d__ n and V ; the minimum i n R i n d i c a t e s a c o n d i t i o n f o r best ^ r - u or p correspondence between the c a l c u l a t e d and experimental 1(E) curves. The corresponding values of d, n . V and R are reported i n Table 6.2. Some Zr-0' or p v immediate conclusions from the r e s u l t s i n Table 6.2 are: ( i ) o v erlayer models are l e s s favored compared w i t h underlayer models; ( i i ) there i s no support, f o r the co n d i t i o n s of our surface p r e p a r a t i o n , f o r the proposal that 0 atoms adsorb simultaneously as an ove r l a y e r and as an underlayer between the f i r s t and second metal l a y e r [129]; ( i i i ) the most favored surface s t r u c t u r e according to R i s f o r the model P A(C)B(A)C(B)..., which corresponds to s e v e r a l l a y e r s of N a C l - l i k e bulk Z r O ( l l l ) . With regard to ( i i i ) above, Figure 6.7 shows that R i s minimized at P a value of 1.34A f o r d Z r_Q. This corresponds to a LEED-determined Zr-0 bond distance equal to 2.30A, i n very close agreement with the value (2.31A) given by X-ray d i f f r a c t i o n f o r bulk ZrO [130]. Nevertheless the l e v e l of correspondence according to R^ reached between experiment and c a l c u l a t i o n f o r the model A(C)B(A)C(B)... i s rather s i m i l a r to that f o r the s i n g l e underlayer s t r u c t u r e designated A(C)BAB... I n d i v i d u a l experimental 1(E) curves are reported i n Figures 6.8 and 6.9 f o r Z r ( 0 0 0 1 ) - ( l x l ) - 0 and they are compared w i t h those c a l c u l a t e d f o r both the s i n g l e - u n d e r l a y e r ( i . e . A(C)BAB...) and the bulk-underlayer ( i . e . A(C)B(A)C(B)...) s t r u c t u r e s ; the o v e r a l l l e v e l of correspondence between experiment and c a l c u l a t i o n i s at the moderate l e v e l i n each case. The r e l a t i v e f l a t n e s s of some experimental 1(E) curves (e.g. f o r the (10) and (20) beams at 141 Table 6.2: Values of Zr-0 interlayer spacings and V Q r corresponding to minima in contour plots of R for structural models of Zr(0001)-(lxl)-0. P Model dZr-0< A> V o r ( e V ) R P (B)ABAB...(hcp) 1.00 -10.4 0.403 (C)ABAB...(hcp) 0.94 -12.4 0.416 A(C)BAB...(hcp) 1.37 -8.1 0.366 A(B)CAB...(hcp) 1.34 -7.7 0.375 A(B)CBA...(hcp) 1.34 -7.8 0.370 (C)A(C)BA...(hcp) 0.99* -7.5 0.406 (B)A(C)BA...(hcp) 0.99* -7.2 0.429 C(B)A(C)BA...(hcp) 1.34 -7.3 0.370 A(C)B(C)A(C)...(hcp) 1.32 -6.0 0.388 A(C)B(A)C(B)...(fcc) 1.34 -6.4 0.350 * d 7 _ f o r underlayer f i x e d at 1.35A. 143 100 HO 180 220 160 200 ELECTRON ENERGY (eV) Comparison of experimental 1(E) curves (dashed) from Z r ( 0 0 0 1 ) - ( l x l ) - 0 w i t h those c a l c u l a t e d f o r the sin g l e - u n d e r l a y e r model A(C)BAB... with d Z r_Q equal to 1.33A (upper continuous l i n e designated a) and 1.3/A (lower continuous l i n e designated b ) . 144 ELECTRON ENERGY (eV) Figure 6.8: (continued) 145 ELECTRON ENERGY (eV) Figure 6.9: Comparison of experimental 1(E) curves (dashed) from Zr (0001)-(lxl ) -0 with those calculated for the multi-underlayer model A(C)B(A)C(B)... with d Z r _ Q equal to 1.33A (upper continuous l i n e designated a) and 1.37A (lower continuous l i n e designated b). 146 n — 1 — i — i — 1 — c — r - r 1 — r (00) beam 6 = 16,0=90 J3 >-60 100 HO 180 220 LO Z Ld "I 1 1 1 T T - 1 7 (10) beam 6=16,0 = 90 -I 1 1 1 1 i (20) beam 6=16,0=90 J i I I I 1 L 100 HO 180 2 20 ELECTRON ENERGY (eV) Figure 6.9: (continued) 147 normal Incidence) r e f l e c t s the fact that the i n t e n s i t i e s are low and there-fore contain s i g n i f i c a n t background contributions. In an attempt to d i s t i n g u i s h between the a p p l i c a b i l i t y of the s i n g l e - and multi-underlayer models, Table 6.3 summarizes r e s u l t s of the new comparisons with for the two model types compared i n Figures 6.8 and 6.9, i n which the ca l c u l a t i o n s were made using phase s h i f t s for negatively charged 0. The r e s u l t s i n Table 6.3, along with those obtained for other s t r u c t u r a l models, suggest that no appreciable change i n s t r u c t u r a l conclusions follow from the use of 0 phase s h i f t s appropriate to a negatively charged atom. The LEED analysis with R^ s t i l l favors the multi-underlayer model over the single-underlayer model, and o v e r a l l we believe t h i s conclusion i s also s l i g h t l y favored by the v i s u a l comparisons between the curves shown in Figure 6.8 and 6.9. Some other models, such as C(B)AB... and A(C)B(C)AB..., which were not included i n Table 6.2, have been tested i n r e l a t i o n to the 1(E) curves measured for normal incidence; those data were used to guide the s e l e c t i o n of the model types to be tested i n greater d e t a i l ( i . e . against measurements at both normal and off-normal incidence as reported i n Table 6.2). 6.5 Discussion Our current conclusion for the lowest-coverage Zr(0001)-(lxl)-0 surface structure i s that the 0 atoms occupy octahedral hole s i t e s , possibly f o r several layers below the surface, with the Zr-0 i n t e r l a y e r spacing equal to 1.35 ± 0.03A. The s t r u c t u r a l resemblance to ZrO appears strong, but i t i s also recognized that the f i n a l oxidation product for the 148 Table 6.3: Values of Zr-0 i n t e r l a y e r spacings and V o r corresponding to minima i n contour plots of R for two s t r u c t u r a l models of Zr(0001)-(lxl)-0 using phase s h i f t for negatively charged 0. M o d e l d Z r - 0 ( A > V or ( e V > *p_ A(C)BAB...(hcp) 1.37 -6.4 0.401 A(C)B(A)C(B)...(fcc) 1.37 -3.0 0.380 149 oxygen-zirconium system is Zr0 2 [112]. In addition, an earl ier analysis with X-ray photoelectron spectroscopy indicated that a significant change in oxidation behavior of Zr(0001) occurs at around 3.5 L exposure to oxygen [112]. The new information given in the LEED spot profi le analysis suggests that the situation is close to that characterized here with R Q = 0.23, at which point the lowest-coverage ( lxl)-0 LEED pattern Is f i r s t established. This indiates that the i n i t i a l ( lxl)-0 structure ( i . e . ZrO) is an intermediate in the oxidation process of Zr(0001) surfaces. The i n i t i a l formation of Zr0 2 may involve the f luorite structure with 0 occupy-ing a l l tetrahedra holes In (fee) zirconium. In this structure the 0 to Zr ratio is 2:1, although the surface geometrical structure has not yet been explored in the higher 0-coverage regime. However, even for the system studied here, some incipient occupation of tetrahedral holes could occur; that along with other surface inhomogeneities may account for some differences found between the experimental and calculated 1(E) curves. The structural information obtained for the init ial ly-formed Zr(0001)-(lxl)-0 surface, which apparently reinforces that found previously [43] for the lower-coverage structure Zr(0001)-(2x2)-0, provides a basis for interpreting measurements made here in the spot profi le analysis for the Zr(0001)-(2x2)-0 LEED patterns. The simplest models for the (2x2) structure have an ordered occupation of 1/4 of the octahedral holes, either between several Zr layers or just between the f i r s t and second Zr layers. An increasing 0 content beyond this occupation level must inevitably increase disorder, which in turn is expected to decrease the half-order beam intensity as well as increase the beam width. In principle these 150 trends could reverse In the approach to 1/2 occupation of the a v a i l a b l e octahedral holes (as required for the (2x1) l a y e r ) , and the whole cycle repeat between 1/2 and 3/4 occupation (where (2x2) ordered layers are again also p o s s i b l e ) . Beyond the 3/4 occupational l e v e l the half-order beam i n t e n s i t i e s must decrease as ( l x l ) regions become increasingly important over those of the (2x2) type. We were unable to detect half-order beams for values of R less than o about 0.09, and hence 0 repulsions apparently prevent the formation of ordered adsorption domains at very low coverage. The maxima shown i n Figure 6.3 for R q around 0.11 are reasonably assigned to a structure which approximates one of the i d e a l (2x2) forms with 1/4 octahedral s i t e occupation, and s i m i l a r l y the maxima at around R q equal to 0.15 apparently correspond to a structure with 1/2 s i t e occupation. A corresponding peak i s not resolved for 3/4 s i t e occupation, but consistently the high-coverage maxima are broad. Indeed, i n t h i s range of coverage, the 0 atoms are probably d i s t r i b u t e d s t a t i s t i c a l l y over the possible s i t e s according to the o v e r a l l coverage. Computer simulation studies on s i m i l a r systems [131] suggest there may s t i l l be s u f f i c i e n t short-range order for a (2x2)-type LEED pattern to be displayed. Cert a i n l y studies with the high-resolution spot p r o f i l e technique [132] would help to probe the surface order i n more d e t a i l , although the low-temperature shoulder i n Figure 6.3 for R q close to 0.18 p l a u s i b l y i d e n t i f i e s the 0 structure for 3/4 s i t e occupation. 151 CHAPTER 7 A LEED Crystallographic Investigation of a Surface Structure Designated Zr(0001)-(lxl)-N 152 7.1 Introduction The chemisorption of nitrogen on (0001) surfaces of hexagonal close-packed metals has not been widely studied at the quantitative leve l , although a number of qualitative observations have been reported including those on the surfaces of beryllium [133], ruthenium [134] and rhenium [135]. An exception is the LEED crystallographic analysis for the Ti(0001)-(lxl)-N surface for which Shih e t _ £ l . [68] reported that N atoms form an underlayer structure by occupying a l l octahedral holes between the top two layers of titanium. By contrast, the study in the previous chapter for the Zr(0001)-(lxl)-0 structure suggested that 0 atoms occupy octahedral holes, possibly through several layers below the surface. In this chapter we describe a LEED crystallographic study for the chemisorption of nitrogen at the Zr(0001) surface [136]; comparisons w i l l be made with the previous studies for both N adsorbed on Ti(0001) [68] and 0 adsorbed on Zr(0001) [43,121]. Another point of comparison is with some investigations by Foord et a l . [H3] for nitrogen adsorption on polycrystalline zirconium; these latter authors concluded that this room-temperature adsorption is dissocia-tive and that the f inal product is an underlayer structure. 7.2 Experimental The apparatus and i n i t i a l cleaning procedures used were as described previously in Section 6.2.1. Adsorption studies were made on a surface which showed sharp (1x1) LEED patterns, and for which no contaminants were detected with AES. Such a surface at room temperature was exposed to 153 nitrogen gas (Matheson, 99.999% pure) at around 2x10"8 Torr. Figure 7.1 reports a typical nitrogen uptake curve as measured by ^ " A 3 8 3 / A 9 2 ( i . e . the ratio of the Auger peak height for N at 383 eV to that of Zr at 92 eV). Unlike oxygen on Zr(0001), which shows an i n i t i a l (2x2) LEED pattern, no superstructure beams were observed with nitrogen adsorption. It was however necessary to order the nitrogen structure by annealing. This was done by heating the surface to 220°C followed by immediate cooling (heating and cooling rates both being around 1°C s - 1 ) . The onset of effective bulk diffusion was assessed by measuring values after cooling from progressively higher temperatures following the procedure described in 6.2.2. For a sample, with an i n i t i a l R^ j value of 0.25, the diffusion of N into the bulk becomes significant at around 438°C (Figure 7.2); this is some 200°C more than the corresponding value found earl ier for 0 diffusion. For the LEED analysis from the i n i t i a l ( lxl)-O structure on Zr(0001), the appropriate adsorption conditions could be chosen by the cr i ter ion that the intensities of the half-order spots vanish from the previous (2x2) diffract ion pattern. For N adsorption, the hope was to analyze an analogous surface structure, although i t could be recognized only on indirect evidence. Nevertheless three types of measurements show changes for exposures of around 5 to 6 L; speci f ical ly: (1) the slope of 10 20 30 EXPOSURE (Langmuirs) Figure 7.1: Auger peak height r a t i o N(383eV)/Zr(92eV) plotted as a function of nitrogen exposure. 155 io r CO LU < UJ o o cc < cc 0.8 0.6 ONSET OF DEPLETION o x ui o OA 2 UJ £ < O LJ Z Q_ 0.2 X X J 100 200 300 400 500 600 TEMPERATURE ,°C Figure 7 . 2 : Normalized nitrogen Auger peak height r a t i o Rjjj/Rjj as a function of heating temperature for nitrogen on Zr(0001); the i n i t i a l coverage corresponds to RJJ = 0 . 2 5 . 156 the lower-coverage part of the N uptake curve s t a r t s to reduce, ( i i ) the Auger peak of Zr at 147 eV suddenly s h i f t s by -1.3 eV as seen i n Figure 7.3 (although t h i s peak s h i f t remains constant f o r f u r t h e r exposures to at l e a s t 42 L ) , and ( i i i ) changes i n 1(E) curves from those of the clean surface become w e l l - e s t a b l i s h e d (Figure 7.4). An exposure of 5.5 L gave a Z r ( 0 0 0 1 ) - ( l x l ) - N s t r u c t u r e f o r which R^  = 0.22, and t h i s s t r u c t u r e was used f o r the LEED a n a l y s i s . I n c i d e n t a l l y Foord et a l . [113] a l s o reported a s i g n i f i c a n t change i n slope at around 6 L i n an uptake curve measured by the work f u n c t i o n v a r i a t i o n as ni t r o g e n i s adsorbed on p o l y c r y s t a l l i n e zirconium. 1(E) curves f o r LEED beams from the Z r ( 0 0 0 1 ) - ( l x l ) - N s t r u c t u r e w i t h = 0.22 were measured w i t h a video LEED analyzer f o r the energy range 50(2)230 eV e x a c t l y as described p r e v i o u s l y f o r the Z r ( 0 0 0 1 ) - ( l x l ) - 0 s t r u c t u r e . Nine independent 1(E) curves were measured f o r the beams (10), (11), (20) at normal incidence, (00), (10), (20), (2-1), (3-1), (3-2) at a polar angle of 18° w i t h the azimuthal d i r e c t i o n p a r a l l e l to a m i r r o r plane i n the surface. The same beam n o t a t i o n i s used as described p r e v i o u s l y f o r the Z r ( 0 0 0 1 ) - ( l x l ) - 0 s t r u c t u r e . 7.3 C a l c u l a t i o n s A l l s t r u c t u r a l models considered i n t h i s a n a l y s i s f o r the i n i t i a l Z r ( 0 0 0 1 ) - ( l x l ) - N surface s t r u c t u r e were b u i l t from the s t a c k i n g of hexa-gonal c l o s e packed l a y e r s of e i t h e r N atoms or Zr atoms. These models were r e s t r i c t e d to four c a t e g o r i e s : 157 J 1 I I - l 80 100 120 140 1G0eV KINETIC ENERGY Figure 7.3: Variations of the Zr Auger peak around 147 eV with nitrogen exposure on Zr(0001). 158 80 120 160 200 ELECTRON ENERGY(eV) Figure 7.4: Comparisons f o r (11) and (10) beams at normal incidence of experimental 1(E) curves (dashed) from Z r ( 0 0 0 1 ) - ( l x l ) - N w i t h those measured f o r clean Zr(0001) and c a l c u l a t e d f o r two models of Z r ( 0 0 0 1 ) - ( l x l ) - N , namely f o r the model A(C)BAB... w i t h d£r-N equal to 1.287A (curves designated A) and f o r the model A(C)B(C)AB... w i t h d Z r _ N equal to 1.330A (curves designated B). 159 i I i I 1 1 1 1 r BEAM (10) j l — i — i i i i i . i AO 80 120 160 200 ELECTRON ENERGY (eV) ure 7.4: (continued) 160 ( i ) Simple overlayer models where N atoms occupy 3-fold coordination sites above the unreconstructed zirconium surface ( i . e . models designated (B)ABAB... and (C)ABAB... , where the symbols in paren-theses identify lateral positions of N with respect to the hep structure of zirconium). ( i i ) Underlayer structures where N atoms occupy octahedral holes within an unreconstructed zirconium structure. These models are designated A(C)BAB.. . , A(C)B(C)ABAB..., A(C)B(C)A(C)B(C)... according to whether the N atoms occupy a l l octahedral holes respectively between the f i r s t and second metal layers, between the f i r s t three metal layers, between a l l metal layers probed by the LEED electrons. ( i i i ) Underlayer structures where N atoms occupy a l l octahedral holes between zirconium layers that have reconstructed to the local fee type packing arrangement (e.g. A(B)CABAB...). ( iv) Overlayer plus single underlayer models (e.g. (B)A(C)BABA...). For each model type, the neighboring Zr-N interlayer spacing (d„ _„) was varied, specif ical ly from 0.60 to 1.20A for overlayer N, and from 1.20 to 1.46A for underlayer N. However for the category ( iv ) , with both overlayer and underlayer, the underlayer Zr-N interlayer spacing was fixed at 1.30A (the value suggested by results below). A l l directly neighboring Zr-Zr interlayer spacings were kept at the value (2.57 A) for zirconium metal [127]. Multiple scattering calculations of 1(E) curves were made with standard procedures [44,45]. Specif ical ly the scattering by the zirconium structure, including incorporated N layers, was determined with the 161 renormalized forward scattering method, while N overlayers were added with the layer doubling method. A l l computational details followed those used in the previous analysis for Zr(0001)-(lxl)-0, except that the N potential , characterized by phase shifts to A = 7, was constructed from a super-position of free atom charge distributions for a hypothetical bcc sol id [137]. 7.4 Results Assessments of the quality of correspondence between calculated and experimental 1(E) curves for Zr(0001)-(lxl)-N were made both visually and with Pendry's r e l i a b i l i t y index (Rp)- An i n i t i a l pruning out of some less favored models was made by comparing with just the normal Incidence data, although most models were assessed for normal and off-normal incidence data combined. For those latter cases, contour plots of R were made as a P function of the Zr-N interlayer spacing and the real part of the constant muffin-tin potential ( v o r ) » values of ^ J — J J which minimize R^ are reported in Table 7.1 for various different structural models. One representative contour plot of R^ for the A(C)BAB... model type Is shown In Figure 7.5. In addition, particular comparisons of experimental and calculated 1(E) curves for the surfaces A(C)BAB... and A(B)CAB... are shown in Figures 7.6 and 7.7 respectively. 7.5 Discussion The best correspondence between experimental and calculated 1(E) curves for the Zr(0001)-(1x1)-N surface structure has been reached for 162 Table 7.1: Values of Zr-N i n t e r l a y e r spacings corresponding to minima i n contour plots of R_ for s t r u c t u r a l models of Zr(0001)-(lxl)-N. P Model dZr-N <A> R P (B)ABAB..(hcp) 0.68 0.374 (C)ABAB..(hcp) 0.99 0.360 (C)B(C)AB..(hcp) 1.08* 0.358 (A)B(C)AB..(hcp) 0.65* 0.400 A(C)BAB..(hcp) 1.30 0.268 A(C)B(C)AB..(hcp) 1.32 0.276 A(C)B(C)A(C)..(hcp) 1.30 0.303 A(B)CABAB..(hcp) 1.30 0.269 C(B)A(C)BA..(hcp) 1.25 0.333 A(C)B(A)C(B)..(fcc) 1.27 0.350 * d_ „ for underlayer fixed at 1.30 A 163 models i n which nitrogen atoms occupy a l l octahedral holes between the f i r s t and second layers of zirconium metal. However the present analysis i s unable to d i s t i n g u i s h between the surface structure designated A(C)BAB..., which has no zirconium reconstruction, and that designated A(B)CAB... with a l o c a l zirconium reconstruction. The l a t t e r i s equivalent to A(C)BAC..., and for i t s f i r s t s i x atomic layers i t d i f f e r s from the f i r s t structure only by a l a t e r a l displacement of zirconium i n the fourth metal layer. This r e l a t i v e l y small difference i n structure, for the probe depth of LEED, res u l t s i n sets of calculated 1(E) curves which are too s i m i l a r for this technique to d i s t i n g u i s h between the surface models (as seen i n Figures 7.6 and 7.7). The single underlayer model i s c l e a r l y favored compared both with overlayer models (including the combined over-layer and single underlayer model [129]) and with multiple underlayer models, although the model designated A(C)B(C)AB..., with a double under-layer of N, also gives a reasonable account of the experimental i n t e n s i -t i e s . Following the experience for oxygen on zirconium, where disorder phenomena appear prominent, the actual nitrogen on zirconium surface studied here could quite p l a u s i b l y contain s i n g l e - and double-underlayer domains, perhaps with regions of only p a r t i a l order. Such e f f e c t s could l i m i t the correspondence between experimental and calculated 1(E) curves to just the moderate l e v e l (two representative comparisons are shown i n Figure 7.4). The LEED analysis for the model of Zr(0001)-(lxl)-N designated A(C)BABA... indicates that the i n t e r l a y e r spacing d Z r _ N i s equal to 1.30A and, using the l a t e r a l Zr-Zr distance i n zirconium metal [127], this gives a Zr-N bond length equal to 2.27A, which agrees reasonably c l o s e l y with the 164 1 2 0 0 1 2 4 4 1 . 2 8 7 1 3 3 0 1 . 3 7 4 1 . 4 1 8 U Zr-N SPACING(A) Figure 7.5: Contour plot for Zr(0001)-(lxl)-N of R versus V o r and Zr-N interlayer spacing for the model A(C)BAB... . 165 KO 180 220 120 160 ELECTRON ENERGY (eV) Figure 7.6: Comparison of experimental 1(E) curves (dashed) from Zr(0001)-(lxl)-N with those calculated for the model A(C)BAB... with d z M equal to 1.287A (upper continuous l i n e designated a) and 1.330A (lower continuous l i n e designated b). 166 1 ' 1——i r (00) beam 6=18°, 0 = 90* V) c a 15 a >-h-L/5 LU model :A;C)SA3 • a dZr-N=1 287A b . c l Z r . N z 1 . 3 3 0 A 80 120 1G0 200 * • i i i \ (10) beam i (3 | J 1 -2) beam i /•» \ \ \ \ i \ \ A » / \ \. \ / i , — r 1 \ I 1 i i 80 120 160 100 HO 180 E L E C T R O N E N E R G Y (eV ) Figure 7.6: (continued) model :A(C)BAB-a:dZr-N=1-287A b:clZ r.N=1 3 3 0 A E L E C T R O N E N E R G Y ( e V ) 167 n 1 r (2-1) beam - i -j r -6=18,0 = 90* Figure 7.6: (continued) 168 Figure 7.7: Comparison of experimental 1(E) curves (dashed) from Zr(0001)-(1x1)-N w i t h those c a l c u l a t e d f o r the model A(B)CAB... w i t h d ^ - ^ equal to 1.287A (upper continuous l i n e designated a) and 1.330A (lower continuous l i n e designated b). 169 E L E C T R O N E N E R G Y ( e V ) Figure 7.7: (continued) 170 E L E C T R O N E N E R G Y (eV ) Figure 7.7: (continued) 171 value of 2.29A for bulk ZrN [138]. In this surface structure N incorpo-rates between the f i r s t and second zirconium layers to give effectively three layers of Z r N ( l l l ) , while the metal-metal interlayer spacing is changed hardly signif icantly from that in the clean metal (2.60A in l ieu of 2.57A). This model for the Zr(0001)-(lxl)-N surface repeats in basic features that reported earl ier by Shih et^  a l . for the related structure Ti(0001)-(lxl)-N [58], although these authors apparently did not investigate double and multiple underlayer models. The use of AES in this work indicates that nitrogen diffusion occurs less readily than oxygen diffusion into the zirconium metal, and similar observations were made by Foord et al_. [113]. Consistently with these observations i t seems that the LEED analysis for the Zr(0001)-(1x1)-N surface structure can rule out the multiple underlayer model, for the conditions of our surface preparation, although the corresponding statement cannot be made in the previous LEED analysis for Zr(0001)-(lxl)-0. Incidentally, the 1(E) curves calculated for multiple underlayer models of Zr(0001)-(lxl)-N have significant differences from those of the corresponding single underlayer models (which result in differences reported in Table 7.1). That indicates the N atoms can contribute s ignif icantly to the analysis, even though no new LEED beams are introduced and the Zr-Zr interlayer spacing is hardly changed from that in the clean metal. It is important that LEED can s t i l l contribute to the determination of surface structure in cases such as this where, in addition, the adsorbed species is a re lat ively weak scatterer. For example, 1(E) curves calculated from models which ignore the presence of N atoms agree 172 signif icantly less well with the experimental 1(E) curves from Zr(0001)-( lx l ) -N than do 1(E) curves calculated with the inclusion of N atoms (as seen in Figure 7.8). 173 to E O lo o >-h-LO UJ (1 0) BEAM A—(O — B A B -287A I.287A expt A-25 74 A ^ BAB 4 0 80 120 160 200 E L E C T R O N E N E R G Y (e V) Figure 7.8: Comparison of experimental 1(E) curve for the (10) beam from Zr(0001-(lxl)-N for normal incidence with that calculated for the model A(C)BAB... with the Zr-N interlayer spacing equal to 1.287A, as well as that calculated for the similar model which just differs from the f i r s t by neglect of N. The interlayer spacing between f i r s t two Zr layers In both models i s identical. 174 CHAPTER 8 Comparison of Oxygen and Sulfur Adsorption on the ( 0 0 0 1 ) Surface of Zirconium 175 8.1 Introduction In the process of cleaning the Zr(0001) surface we have observed that bulk sulfur impurity atoms segregate to the surface on heating above 600°C. This contrasts with the behaviour of the lighter atoms l ike N and 0 which preferentially diffuse into the bulk on heating at above 500 K. Since we have studied the chemisorption of oxygen and nitrogen at coverages of the order of one monolayer on the Zr(0001) surface, and provided evidence in Chapters 6 and 7 that both these molecules react with zirconium to form the incipient structures ZrO and ZrN respectively, in this chapter we attempt to use LEED and AES to compare the adsorption and coadsorption of oxygen and H2S on the Zr(0001) surface [139]. By way of comparison, we propose some possible sulfur "overlayer" models correspon-ding to an observed Zr(0001)-(3x3)-S structure. LEED 1(E) curves have been measured from this surface at normal incidence, although a complete crystallographic analysis has not yet been attempted. Furthermore, i t is also of interest to explore whether any surface reaction takes place between adsorbed oxygen and sulfur, as well as to investigate the adsorption properties of oxygen on a sulfur pretreated Zr(0001) surface and vice versa. 8.2 Experimental These experiments use high-purity oxygen and H2S gases which were directed to the cleaned and well-ordered Zr(0001) surface via a nozzle in the UHV chamber. For various exposures of the adsorbing gases, the relative amounts of adsorbed species were assessed with appropriate Auger peak height ratios , speci f ical ly for oxygen 176 R0 " A51()/ A92 ( i . e . the ratio of the Auger peak height for 0 at 510 eV to that Zr at 92 eV) and for sulfur Rs = A 1 5 o/ A92 (where A 1 5 0 is the peak height for overlapping Zr and S Auger signals at 150 eV). After each adsorption experiment, the sample surface was cleaned by argon ion bombardment and re-ordered by heating to 600°C followed by immediate cooling (the heating and cooling rate are approximately 1°C s - *) . The clean zirconium surface is characterized with R =0.0 and R = 1.40. o s 8.3. Results 8.3.1 Oxygen Adsorption For the convenience of comparison, the adsorption of 0 2 on Zr(0001) is brief ly described again here. The exposure of a clean, ordered Zr(0001) surface to oxygen at room temperature yields a ( lx l ) LEED pattern with high background, although (2x2) patterns are observed after heating below 220°C ( i . e . at less than the temperature at which diffusion into the bulk occurs); we interpret this heating as providing just an ordering effect. The sharpest (2x2) pattern was obtained for an i n i t i a l oxygen exposure (1.2 L) which gives RQ equal to 0.16; the associated surface structure appears suff ic iently stable at room temperature and 10~ 1 0 Torr for the sharp LEED pattern to be maintained for at least 3 days. With larger i n i t i a l 177 exposures to oxygen the (2x2) pattern gives way to a (1x1) pattern, which i s best established with an exposure of about 3.6 L and a surface coverage corresponding to R q = 0.23. The LEED intensity-versus-energy curves for t h i s structure have clear differences from those of the clean Zr(0001) surface; examples for (11) beams are indicated i n Figure 8.1. 8.3.2. Hydrogen Sulfide Adsorption When a cleaned and ordered Zr(0001) surface was exposed to about 4.2 L of H 2S at room temperature, s u l f u r adsorption occurred (R = 2.8), s but no extra LEED beams were detectable even a f t e r heating to 500°C However, on heating to 530°C, R G was found to increase to 3.1, an observation, which i n conjunction with a report by L i n and G i l b e r t [140], appears to be associated with hydrogen desorption. Further, with a short heating to 600°C, a very sharp (3x3) LEED pattern was observed on cooling to room temperature, for which R remained at 3.1. Higher S coverages, as s monitored by R G, can be obtained by giving larger i n i t i a l exposures to H 2S however, following annealing at 600°C, the (3x3) LEED pattern shows increasing disorder as R increases beyond 3.1. Intensity-versus-energy s (1(E)) curves for the d i f f r a c t e d beams (e.g. Figure 8.2) suggest that the moderate-coverage (3x3) structures, with R less than 3.1, correspond to s mixed regions of clean surface and of (3x3) domains. The l a t t e r regions appear to remain stable for long periods. 1(E) curves for LEED beams from the Zr(0001)-(3x3)-S structure with R = 3.1 were measured with the video LEED analyzer for the energy range 178 (11) b e a m H O 180 220 E L E C T R O N E N E R G Y (eV) Figure 8.1: Experimental 1(E) curves for the (11) beam from (a) clean Zr(0001), (b) Zr(0001-(2x2)-0 with R Q = 0.16, (c) Zr(0001)-(lxl)-0 with R Q - 0.23. 179 (11) beam \ V in "E p >-v_ O k-i _ >-»— LD Z UJ C / \ / \ .. • .-• - • -.. y i • i ! 1 i Figure 8.2: HO 1 80 220 ELECTRON ENERGY(eV) Experimental 1(E) curves for the (11) beam from (a) clean Zr(0001), (b) Zr(0001)-(3x3)-S with R - 1.9, (c) Zr(0001)-(3x3)-S with R_ - 2.4, (d) Zr(0001)-(3x3)-S with R e «= 3.1. 180 50(2)200 eV exactly as described i n Section 3.5.2. Ten independent 1(E) curves were measured for normal incidence for the beams designated (10), (11), (2/3 0), (4/3 0), (0 5/3), (2/3 1), (4/3 1/3), (1/3 1), (2/3 2/3) and (2/3 1/3) using the beam notations i n Figure 8.3. The f i n a l averaged and smoothed experimental 1(E) curves are shown i n Figure 8.4. 8.3.3. Oxygen and Hydrogen S u l f i d e Coadsorption A s e r i e s of experiments for assessing s t r u c t u r a l aspects of the coadsorption of 0 2 and H 2S on an i n i t i a l l y clean Zr(0001) surface have been made, and the r e s u l t s are summarized i n the following subsections. 8.3.3.1 0 2 on Zr(0001)-(3x3)-S with Rc>3.1 No evidence could be found from AES or LEED for oxygen chemisorption occurring on the (3x3)-S surface, with R greater than 3.1, when i t was s exposed to oxygen at room temperature. The same statement holds for these surfaces when annealed following the procedures described above for forming the Zr(0001)-(2x2)-0 and Zr(0001)-(lxl)-0 surface structures. These obser-vations suggest that the surface combination of S and 0 (with subsequent desorption of, for example, S0 2) does not occur to any s i g n i f i c a n t extent for the conditions used. 8.3.3.2 0 2 on Zr(0001)-(3x3)-S wlth-R <3.1 When a p a r t i a l l y - c o v e r e d (3x3)-S structure was exposed to oxygen, and treated according to the conditions that give the (2x2)-0 structure (as 181 t k, 0 0 * v 02 U 3 « 3 3 I 4 •-•*2 * 3 3 2*4 , 0 3 • 3 1 3 3 •••0 4 2- i | ky 3 # _ 3 3 1 1 ZZ. 1 1 3 3 • 3 3 • V 2 1 33 • 3 • 42. 3 3 • 3 3 i l • 3 3 • ±0 * • 3 3 3 • • 3 • 20 • • • • Figure 8.3: Schematic diagram f o r LEED patter n and beam n o t a t i o n f o r the Zr(0001)-(3x3)-S s t r u c t u r e . E ZD >-u_ O v_ +—> JE> i _ a >-i — Co zz. L U 182 1 1 1 (1/3 1) beam (2/3 2/3) beam A V, ,(1 0 ) beam (2/3 1/3) beam (1/3 1) beam j_ 40 80 120 1G0 ELECTRON ENERGY (eV) Figure 8.A: 1(E) curves measured for normal incidence from the Zr(0001)-(3x3)-S surface with Rg = 3.1 f o r the d i f f r a c t e d beams: (1/3 1), (2/3 2/3), (10), (2/3 1/3), (1/3 1), (2/3 1), (4/3 1/3), (4/3 0) and (0 5/3). 183 (2/3 1) beam / (A/3 1/3) beam • r . . . V wAO 80 120 160 1 ^ 1 r , (A/3 0) beam A / \ i i i y (0 5/3) beam A c o >-t — L O LU AO 80 120 160 200 ELECTRON ENERGY (eV) Figure 8.4: (continued) 184 i n Section 8.3.1), the LEED pattern shows a superposition of the i n d i v i d u a l (2x2)-0 and (3x3)-S patterns. This observation i s consistent with the existence of separate (2x2)-0 and (3x3)-S domains on the surface with l i n e a r dimensions larger than the transfer width of the instrument used (~100A) [29]. For an i n i t i a l surface, with a p a r t i a l S coverage correspon-ding to R =2.3, values of R and R were found to be 2.1 and 0.13 s s o r e s p e c t i v e l y , a f t e r preparation of the mixed surface. The decrease of R s appears to be associated with the oxygen modifying the zirconium Auger s i g n a l at 150 eV [113,124]. On further heating to 600°C, the (3x3) part of the LEED pattern remains e s s e n t i a l l y unchanged while R returns to 2.3; i n s addition the (2x2) pattern disappears and R q goes to zero as expected for oxygen d i f f u s i o n into the bulk. The following scheme summarizes the above observations: 2 2 0 ° r Zr(0001)-(3x3)-S + 0 2 > Zr(0001)-(3x3)-S + Zr(0001)-(2x2)-0 (with R = 2.3) (with R = 2.1 and R = 0.13) s v s o ' 600°C Zr(0001)-(3x3)-S + 0 U bulk (with R = 2.3, R = 0) s ' o 8.3.3.3 H 0S on Zr(0001)-(2x2)-O When an oxygen adsorbed surface which shows a (2x2) LEED pattern with R =0.16 and R = 1.3 was exposed to about 3.5 L of H^S at room o s z temperature, and annealed at 530°C, a d i f f u s e (1x1) LEED pattern with high background was observed. However, with further heating at 600°C, a 185 moderately sharp (3x3) LEED pattern was restored on cooling to room temperature (R q = 0.0, R G =2 .3) . 8.3.3.4 H2S on Zr(0001)-(lxl)-0 The observation in Section 8.3.3.3 was found to extend even to a surface with the highest oxygen coverage considered here (viz. Zr(0001)-( lx l ) -0 with R Q = 0.23). After exposure to H2S at room temperature, the LEED pattern becomes diffuse with high background ( R G = 2.3, R q = 0.26), but after annealing at 600°C and cooling to room temperature a sharp Zr(0001)-(3x3)-S pattern results with R = 2.9 and R = 0.0. s o 8.3.3.5 Coadsorption without Annealing AES shows that the basic tendencies observed in 8.3.3.1 and 8.3.3.4 extend also to a Zr(0001) surface which is treated entirely at room temperature. Specif ical ly i t was found that oxygen does not s ignif icantly adsorb on a high-S-coverage Zr(0001) surface, whereas w i l l adsorb on a high-O-coverage surface. 8.4 Discussion This work highlights the contrasting behaviors of oxygen and sulfur chemisorption on the Zr(0001) surface. Thus while the highest coverage oxygen surface is s t i l l able to adsorb H 2 S, the highest coverage sulfur surface does not adsorb oxygen in detectable amounts. These observations are consistent with oxygen forming subsurface structures (see Chapter 6), whereas sulfur atoms probably form a coincidence-site (3x3) structure in 186 which the overlayer involves e i t h e r a s u f f i c i e n t l y high density of S atoms to block 0 adsorption, or a protective combined layer of Zr and S, perhaps with a zirconium s u l f i d e structure. A detailed determination of the geometry of the Zr(0001)-(3x3)-S surface structure i s needed, but so far the analysis has been i n h i b i t e d by the large computing cost that i s expected to be involved. Nevertheless the general chemical observations reported here do appear to set some l i m i t s on possible s t r u c t u r a l arrange-ments for the S-chemisorption structure. Some models for S-overlayer structures are shown i n Figure 8.5. These cover a range of coverage from 1/9 to 4/9 monolayers. The model designated A for the lowest coverage seems u n l i k e l y , since i t may not be able to block subsequent oxygen adsorption; the structure C was previously proposed for the P t ( l l l ) -(3x3)-Cl structure [141], although no confirming evidence has yet been provided. The formation of the immiscible structures corresponding to Zr(0001)-(2x2)-O + Zr(0001)-(3x3)-S suggests that this coadsorption should be c l a s s i f i e d as a competitive coadsorption, rather than as a cooperative coadsorption which i s most favorable for surface c a t a l y s i s . Apparently within the adsorbed layers l i k e - l i k e i n t e r a c t i o n energies are favored over l i k e - u n l i k e i n t e r a c t i o n s . Overall t h i s work provides no evidence for s i g n i f i c a n t s u l f u r and oxygen combination processes, either when surfaces with coadsorbed S and 0 are heated, or when S-saturated surfaces are heated i n oxygen. 187 F i g u r e 8.5: Some p o s s i b l e S o v e r l a y e r s t r u c t u r e s (shaded c i r c l e s ) f o r the Zr(0001)-(3x3)-S s u r f a c e . The s u l f u r coverages w i t h respect to Zr (open c i r c l e s ) are: (A) 1/9 ML, (B) 2/9 ML, (C) 1/3 ML, (D) 4/9 ML. L a t e r a l s h i f t s of the S ov e r l a y e r s are p o s s i b l e . 188 8.5 Further work Two s i g n i f i c a n t temperatures have been i d e n t i f i e d for the s u l f u r on Zr(0001) system. One corresponds to the increase i n R at 530°C, while s the other relates to the formation of an ordered (3x3)-S structure on heating at around 600°C. These temperatures appear to be associated with the desorption of hydrogen, and with the S overlayer ordering process r e s p e c t i v e l y ; a l t e r n a t i v e l y they may r e l a t e to the formation of a zirconium s u l f i d e overlayer structure. More detailed investigations are required, both with the techniques used here and with XPS and thermal desorption spectroscopy (TDS). For example, TDS can be used to examine the desorption of hydrogen around 530°C, whereas XPS can assess the uptake curve of H 2S on Zr(0001) by measuring a s u l f u r peak without the overlapping peak problem which occurs i n AES. Furthermore, i t should be useful to examine the extent of surface s u l f u r a t i o n by probing s h i f t s i n zirconium 3d structure on exposing to H 2S and heating to give the (3x3)-S structure. C e r t a i n l y the undertaking of a LEED cr y s t a l l o g r a p h i c analysis for the Zr(0001)-(3x3)-S surface structure must remain a high p r i o r i t y . 189 Concluding Remarks At present LEED crystallography inevitably involves a t r ia l -and-error search for that structure in the multiple-scattering calculations which best agrees with the experimental data. Discrepancies always occur, although in some situations the agreement is better than in others. After determining a surface structure some uncertainties are necessarily left on whether other structures not considered could actually give better accounts of the experimental 1(E) curves. Obviously some systems are in tr ins i ca l ly more complicated than others, but in a l l cases the studies must be done to minimize deficiencies from both the experimental and computational sides. Also a l l conclusions should be scrutinized to see i f they seem reasonable in relation to basic structural chemical principles. Some discrepancies reported in this thesis between experimental and calculated intensities suggest refinements may be needed, perhaps on both the theoretical and experimental sides. In the analysis of the R h ( l l l ) -( /3x/~3)30°-S surface structure, the deficiency reported in the 1(E) curve calculated for the (01) beam at 170 eV could perhaps be due to neglect of metal relaxations Induced by the chemisorbed species; nevertheless from the experimental side surface disorder and defects may have influenced the measurements. That emphasizes a general need to characterize surface defects more closely than we are currently able to do. Our use of the spot profi le analysis seems helpful , although the "display-type" LEED system used in this work was not primarily designed for spot profile analysis. A 190 more h e l p f u l approach i s provided by the fine-beam system w i t h l a r g e r t r a n s f e r width (e.g. 1000A) introduced by Henzler [143] and marketed by Leybold-Heraeus. I d e a l l y Information from that approach would be comple-mented by the use of scanning tunneling microscopy, which can provide d i r e c t images of atomic defects on surfaces [144]. Our LEED c r y s t a l l o g r a p h i c study f o r the R h ( l l l ) - ( 2 x 2 ) - 0 surface s t r u c t u r e emphasized both the advantages of having a f a s t video measurement system (the data could not have been measured w i t h the e a r l i e r spot photo-meter or Faraday cup methods) as w e l l as the need to have an awareness of p o s s i b l e e l e c t r o n beam e f f e c t s . In p r i n c i p l e the beam d i s o r d e r i n g observed could be minimized by using a p o s i t i o n - s e n s i t i v e detector system as described f o r LEED by McRae et a l . [145]. Such an approach can enable the primary beam current to be reduced by three orders of magnitude compared w i t h the system used i n the present work. D e f i c i e n c i e s i n the LEED c r y s t a l l o g r a p h i c analyses of Zr(0001)-( l x l ) - 0 and Z r ( 0 0 0 1 - ( l x l ) - N p o s s i b l y a r i s e from the model c a l c u l a t i o n s not c o n s i d e r i n g that the underlayer oxygen or n i t r o g e n atoms may be d i s t r i b u t e d somewhat s t a t i s t i c a l l y over d i f f e r e n t depths and areas. Such p o s s i b i l i t i e s have not, to my knowledge, been considered yet i n LEED s t r u c t u r a l work. The subject of LEED c r y s t a l l o g r a p h y i s developing f a s t , and more e f f o r t i s c e r t a i n l y needed on both the experimental and computational s i d e s . Incomplete l e v e l s of correspondence between c a l c u l a t i o n and experiment are apparent i n some of my work, and t h i s i n d i c a t e s that f u t u r e refinements may be needed. 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