UBC Theses and Dissertations

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UBC Theses and Dissertations

The structures of clean rhodium surfaces studied by low-energy electron diffraction Watson, Philip Richard 1978

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THE STBUCTUBES OF CLEAN EHODIUJ3 SURFACES ST DDI ED BY LOW-ENEBGY ELECTRON DIFFBACTION  by P H I L I P BICHABD WATSON E.A.  ( N a t . Sex. ) Hons, O x f o r d U n i v e r s i t y ,  1974  A THESIS SUBMITTED IN PARTIAL F U L F I L L H E N T OF THE BEQUIBEHENTS FOB THE DEGBEE OF DOCTOB OF PHILOSOPHY  in THE fACUITY OF GRADUATE STUDIES ( Department o f Chemistry  He a c c e p t  this  )  t h e s i s as cocformiag  to the required  standard  THE UNIVEBSITY OF B B I T I S H COLUMBIA October, @  Philip  fiichard  1978 W a t s o n , 1978  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y s h a l l I  in p a r t i a l  fulfilment of  the requ i rements f o r  the U n i v e r s i t y of Br i t i s h - C o l u m b i a ,  make i t  freely available  f u r t h e r agree t h a t p e r m i s s i o n  for  I agree  r e f e r e n c e and  f o r e x t e n s i v e copying o f  this  that  study. thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s of  this  representatives. thesis  It  is understood that copying or p u b l i c a t i o n  f o r f i n a n c i a l gain s h a l l  written permission.  Department of  CHEMISTRY  The U n i v e r s i t y o f B r i t i s h  2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date  Nov. H ,  1978  Columbia  not be allowed without my  ABSTRACT  This t h e s i s describes the of  the  {111),  (100)  electron diffraction method on  of  and  {110)  film  were  of  the  structures  s u r f a c e s o f r h o d i u m by  (LEED).  S t a i r e t a l «as  photographic  determination  In  this  work  the  low-energy photographic  r e f i n e d so t h a t LEED p a t t e r n s analysed  by  a  stored  computer-controlled  V i d i c o a T-V-  c a m e r a s y s t e m t o g i v e i n t e n s i t y v. e n e r g y , o r  curves  the  for  various  diffracted  beams.  t e s t e d f o r a C u ( 1 1 1 ) s u r f a c e ; I (E) c u r v e s say  was  determined i n t h i s  new  experimental  analyses  intensities  multiple-scattering  were with  performed  those  p r o g r a m s o f Van  the  p r o g r a m s were r u n n i n g  s u r f a c e s of both rhodium potential  from  a  constructed  and  with  a  with  long.  an  the  C h e c k s were to  ensure  F o r c a l c u l a t i o n s on ion-core  band s t r u c t u r e c a l c u l a t i o n - was  by s u p e r p o s i n g  comparing  calculations  correctly.  copper,  by  calculated  Hove and  made a g a i n s t some p r e v i o u s l y p u b l i s h e d that  previously  collector.,  Structural  one  This approach  were c o m p a r e d w i t h i n t e n s i t i e s m e a s u r e d  F a r a d a y cup  1(E),  scattering  compared  t h e c h a r g e d e n s i t i e s of  a  with cubo-  o c t a h e d r a l c l u s t e r o f m e t a l atoms. The  degree of agreement between e x p e r i m e n t a l  diffracted index  i n t e n s i t i e s was  determined with a  p r o p o s e d r e c e n t l y by Z a a a z z i and  o f Z-anazzi made  beam  of  and the  J o n a was  extended t o  uncertainties  and c a l c u l a t e d  i n the  Jona.  enable  reliability-  Here, the a n a l y s i s assessments  to  be  s t r u c t u r a l p a r a m e t e r s which  g i v e t h e b e s t c o r r e s p o n d e n c e between e x p e r i m e n t a l  and c a l c u l a t e d  iii  1(E)  curves.  The  effects  i n t e n s i t i e s , and of changes the  independent  All  three  rhodium  room t e m p e r a t u r e and  measurements  i n some  topmost  interlayer  bulk  value.  The  relative  spacing  structural  detail.  s u r f a c e s sere above,  of the derived  each  f o u n d t o be surface  unreconstructed being  t e r m i n a t i o n o f the b u l k c r y s t a l l i n e s t a c k i n g seguence. the  of  i n the n o n - s t r u c t u r a l parameters f o r  c a l c u l a t i o n s upon t h e r e l i a b i l i t y  r e s u l t s were a l s o e x a m i n e d  at  of  a  simple However,  d i d show some v a r i a t i o n f r o m t h e  (110) s u r f a c e showed a c o n t r a c t i o n o f  2.7±2.0S  t o t h e b u l k i n t e r l a y e r s e p a r a t i o n , w h i l e t h e (111) and  (100) s u r f a c e s showed respectively.  small  {-1±3%)  and  0±2.5%  contractions  i v  TABLE OF COSTENTS  Abstract  ................. .............. ..... ........ . . . . . . i i  Table o f Contents L i s t o f Figures List  ...  ..,..,.iv  ........................................vii  o f T a b l e s ............... ..^ ...................... ..xiv  Acknowledgements Chapter  ..».xv  1; I n t r o d u c t i o n ................................1  1.1 S u r f a c e T e c h n i g u e s 1.2 H i s t o r i c a l  .............................. 2  D e v e l o p m e n t O f LEED ..................5  1.3 T h e s i s O u t l i n e  ..................................8  C h a p t e r 2: L o w - e n e r g y E l e c t r o n D i f f r a c t i o n ( 1 E E . D ) And Auger E l e c t r o n S p e c t r o s c o p y (AES) ....................... 13 2.1 B a s i c  Considerations  ............................ 14  2.1(a) S e c o n d a r y E l e c t r o n D i s t r i b u t i o n ........... 14 . 2.1(b) S u r f a c e S t r u c t u r e C l a s s i f i c a t i o n s .........17 2 . 1 ( c ) The B e c i p r o c a l N e t ........................ 18 2.2 F o r m a t i o n O f The D i f f r a c t i o n P a t t e r n --.-,-..-.--20 2.3 I n t e n s i t i e s Of LEED Beams -----  -  ....-.-29  2 . 3 ( a ) K i n e m a t i c a l T h e o r y ........................30 2.3|b) C h a r a c t e r i s t i c s O f 1 ( E ) c u r v e s ..............37 2.4 A u g e r E l e c t r o n S p e c t r o s c o p y Chapter  (AES) .....................39,  3: 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 ..........-.45  3.1 P a r a m e t e r s  P o r T h e o r i e s O f LEED ................-46  3.1(a) The S c a t t e r i n g P o t e n t i a l ..................46 3.1(b) P h a s e S h i f t s .,  .............  -.51  3 . 1 ( c ) T e m p e r a t u r e C o r r e c t i o n s .....................55 3.2 G e n e r a l Schemes Of C a l c u l a t i o n 3.2(a) L a y e r  Doubling  .....-....-.-----.59  And BFS M e t h o d s ..............63  3.21b) U s e s Of Symmetry ......................  ,..-..68  3.2(c) Program F l o s Chapter  -69  4: E x p e r i m e n t a l A s p e c t s  4- 1 C r y s t a l P r e p a r a t i o n 4.2 U l t r a  -75  .............................76  H i g h Vacuum . (UHv) A p p a r a t u s ...  .......79  4.3 C r y s t a l C l e a n i n g  ................................83  4.3(a) P r o c e d u r e s  ................................83  4.3{b) M o n i t o r i n g S u r f a c e C o m p o s i t i o n  ............86  4.4 LEED I n t e n s i t y M e a s u r e m e n t s .....................89 4.4(a) P r e v i o u s Methods  91  4.4{b) V i d i c o n M e a s u r e m e n t O f - I J E ) . - c u r v e s ........93 4 . 4 ( c ) M e a s u r e m e n t s Of 1 ( E ) c u r v e s F o r Cu (111) 4.4 (d) F u t u r e D e v e l o p m e n t s Chapter  102  ----- - . . . . . . 108  5: L e e d C r y s t a l l o g r a p h y ....................... 110  5- 1 G e n e r a l C o n s i d e r a t i o n s . - , . , . . . . . . . . - . . - - - - - - - - - - 1 1 1 5-2 B e l i a b i l i t y - i n d i c e s  ...--.,,.--,........--..-.---114  5.2(a) The B e l i a b i l i t y - i n d e x Of Z a n a z z i And J o n a 5-3 S t r u c t u r a l A n a l y s i s U s i n g The Z J B e l i a b i l i t y F a c t o r : The C u ( 1 1 1 ) S u r f a c e As An E x a m p l e ........... 120 5-4 O t h e r M e t h o d s O f O b t a i n i n g S u r f a c e I n f o r m a t i o n From LEED D a t a  Structural  5.5 B i b l i o g r a p h y Of S u r f a c e S t r u c t u r e s O f Metals Chapter  6: The (111) S u r f a c e Of Rhodium  130  Clean 131 ......135  vi  6. 1 E x p e r i m e n t a l  -..-136  6.2 C a l c u l a t i o n s .................................... 142 6.3 R e s u l t s And D i s c u s s i o n .......................... 144 6.3 (a) N o r m a l . I n c i d e n c e ........ ..... ............. 144 6.3(b) D i r e c t i o n Of I n c i d e n c e ©"=10°,<^=109° ....... 159 6.4 C o n c l u s i o n s  .........,.......,.-..,-...----------165  C h a p t e r 7: The B h (100) S u r f a c e . . . . . - - . . . 7.1 E x p e r i m e n t a l  168  ..,....,..,,.---.--.,.-.--,---,----.171  7.2 C a l c u l a t i o n s  178  7-3 R e s u l t s And D i s c u s s i o n 7-4 C o m p a r i s o n s l i t h  .........................-178  P r e v i o u s S t u d i e s ............... 187  C h a p t e r 8; The S h ( 1 1 0 ) S u r f a c e .............. 8.1 E x p e r i m e n t a l  .......188 .-,.-191  8*2 C a l c u l a t r o n s • .. . ,« . ,, , «. —.—•. ,, — — • — — — — , — , — ... ..«..., 196 :  8.3 R e s u l t s And D i s c u s s i o n .......................... 197 8.4 C o m p a r i s o n s l i t h H €.£ €17 Appendices:  *  o * • • <» * « • • * *  P r e v i o u s Work m -m m  • ** • * • * • • * * » ••• •  ..202 203  ....,....----.---..--,.-,.--,..-------,-,.,-211  vii  L I S T OF FIGURES  o  2. 1  2.2  S c h e m a t i c d i a g r a m o f t h e mean f r e e p a t h L ( A ) o f e l e c t r o n s i n m e t a l l i c s o l i d s as a f u n c t i o n of t h e i r energy ( e V ) .  15  S c h e m a t i c e n e r g y d i s t r i b u t i o n N{E) o f backscattered slew e l e c t r o n s as a f u n c t i o n of t h e i r e n e r g y f o r a p r i m a r y beam e n e r g y E . ........  15  0  2.3  Examples o f the 5 d i p e r i o d i c n e t s as r e p r e s e n t e d by m o d e l s o f s u r f a c e s o f f a c e - c e n t r e d c u b i c (FCC) , and b o d y - c e n t r e d c u b i c (ECC) m e t a l s ; s i d e s a , , { s h o r t a x i s ) and a , i n t e r n a l a n g l e o C a = a , o(= 90 0, . „ sguare a) FCC (100) , BCC (100) ; primitive rectangular a + a (<= 9QO, e . g . b) FCC (110) , BCC (211) ; a, t a. , d = 9 0 ° , e . g . centred rectangular c) FCC (311) , BCC (110) ; a = a , o< = 6 0 ° , e . g . d) h e x a g o n a l FCC{111) ; a , d 4 9 0°, e . g . obligue e) FCC (321) ; z  (  z  (  e  i  g  #  z  (  z  2  2-4 2.5  A n g l e c o n v e n t i o n s f o r i n c i d e n c e o f an e l e c t r o n beam on a s u r f a c e .................................  19  A t w o - d i m e n s i o n a l r e a l n e t , d e s c r i b e d by s, , s , ( d a r k c i r c l e s ) and i t s a s s o c i a t e d r e c i p r o c a l n e t s* s * (open c i r c l e s ) . ............................  21  U n i t meshs o f t h e c o r r e s p o n d i n g r e a l a n d r e c i p r o c a l t w o - d i m e n s i o n a l n e t s a s i n 2.3.  ........  22  (a) P h o t o g r a p h o f t h e LEED p a t t e r n from a Cu(111). s u r f a c e a t {a) n o r m a l i n c i d e n c e a n d 90eV beam e n e r g y , (b) ©- = 12°, <f> =6° a n d 44eV beam e n e r g y , {c) and |d) l a b e l l i n g o f t h e d i f f r a c t i o n s p o t s . .......  24  The d i r e c t i o n o f a d i f f r a c t e d beam i s d e t e r m i n e d b y t h e a l l o w e d v a l u e s o f k and E. .................  26  (a) S c h e m a t i c d i f f r a c t i o n p a t t e r n f r o m one d o m a i n o f Au(100) - (5x1) r e c o n s t r u c t e d s u r f a c e (b) M o d e l s t r u c t u r e of c o i n c i d e n t a l hexagonal gold l a y e r s u p e r i m p o s e d on t h e u n d e r l y i n g (100) s u b s t r a t e (c) { a f t e r P a l m b e r g and R h o d i n [ 3 3 ] } .  29  z  r  2.6 2.7  2.8 2-9  2-10  19  1 ( E ) c u r v e s f o r t h e s p e c u l a r beam f r o m N i ( 1 0 0 ) and Cu{100) ,.©-=.3°. The b a r s d e n o t e k i n e m a t i c a l B r a g g c o n d i t i o n s ( a f t e r A n d e r s o n a n d Kasemo J. 34}) - ......  31  viii  2.11  2.12  Intensity of of energy i n (b) t h e p u r e S o m o r j a i and  a d i f f r a c t e d LEED beam a s a f u n c t i o n (a) t h e p u r e t w o - d i m e n s i o n a l l i m i t three-dimensional l i m i t , (after F a r r e l l f. 7 J ) . ........................  36  Schematic r e p r e s e n t a t i o n o f t h e L ^ V V auger t r a n s i t i o n : (a) i o n i s a t i o n o f a c o r e l e v e l , (fc) f i l l i n g o f t h e c o r e h o l e , <c) e m i s s i o n o f t h e Auger e l e c t r o n . ...................................  40  2.13  Auger s p e c t r u m o f a h e a v i l y c o n t a m i n a t e d Rh{110) surface. Ep=1.5KeV, I p ~ 1 0 m i c r o a m p s . .............  43  3.1  M u f f i n - t i n p o t e n t i a l |a) i n c r o s s - s e c t i o n a s c o n t o u r s , (b) a l o n g XX*. Vo i s t h e c o n s t a n t intersphere potential.  48  I l l u s t r a t i o n o f t h e r e l a t i o n s h i p between e n e r g i e s m e a s u r e d w i t h r e s p e c t t o t h e vacuum l e v e l a n d those measured w i t h r e s p e c t t o t h e l o w e s t l e v e l o f t h e c o n d u c t i o n band. ..............................  48  3.3  The c u b o - o c t a h e d r a l M , c l u s t e r u s e d t o model t h e c r y s t a l p o t e n t i a l o f FCC c r y s t a l s . ................  52  3.4  An i o n - c o r e immersed i n a p l a n e wave i n d u c i n g s c a t t e r e d s p h e r i c a l waves whose i n t e n s i t i e s a r e f u n c t i o n s o f k, 8 and r . A f t e r P e n d r y £.1.2.J. -----  54  E n e r g y d e p e n d e n c e o f c o p p e r p h a s e s h i f t s (1=0-7) f o r t h e p o t e n t i a l s : (a) V^ .^ and <(b) ........ 3 > V® C .  56  E n e r g y d e p e n d e n c e o f r h o d i u m phase s h i f t s (1=0-7) f o r t h e p o t e n t i a l s : (a) V and fb) 7 ^ . .......  57  S c h e m a t i c r e p r e s e n t a t i o n o f a s e t o f p l a n e wave i n c i d e n t from t h e l e f t m u l t i p l y s c a t t e r e d by a plane of i o n cores.  61  B u i l d i n g up s u b p l a n e s by t h e l a y e r d o u b l i n g p r o c e s s . I n d i v i d u a l s u b p l a n e s a r e marked A a n d B; t h e r e s u l t a n t c o m p o s i t e i s marked C. A f t e r Tong l 1 5 j - . .........................................  64  Diagramatic r e p r e s e n t a t i o n of the renormalized f o r w a r d s c a t t e r i n g (BPS) p r o c e s s . Inward a m p l i t u d e s A^(cj) p r o p a g a t e f r o m vacuum t h r o u g h t h e 1 s t l a y e r t o t h e N t h l a y e r where t h e y a r e t u r n e d around. The e l e c t r o n s a r e t h e n p r o p a g a t e d t o t h e 1 s t l a y e r w i t h o u t w a r d a m p l i t u d e s B^ (3) . ..........  66  A f l o w - c h a r t showing t h e p r i n c i p a l s t e p s i n a 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 , u s i n g t h e BFS o r l a y e r d o u b l i n g methods. ...........................  70  3.2  3  5  3-5  c  a  c  3.6  B  d  b  R M 3  3.7  3.8  3.9  3.10  ix  3.11  Comparison o f e x p e r i m e n t a l 1(E) at normal i n c i d e n c e w i t h curves OU3 o£l p o t e n t i a l s f o r V t h r e e d i f f e r e n t v a l u e s o f &d%.  c u r v e s f o r Cu (111) calculated f o r t i e = -9.5eV and ....................  73  L a s e r a l i g n m e n t method t o c h e c k t h e c o i n c i d e n c e o f t h e o p t i c a l f a c e and d e s i r e d c r y s t a l p l a n e . .......  78  v  a  n  d  v  o r  4-1 4.2  D i a g r a m m a t i c r e p r e s e n t a t i o n o f t h e pumping s y s t e m : I P = I o n pump; TSP = t i t a n i u m s u b l i m a t i o n pump; SP - s o r p t i o n pump.  ..................................  4.3  S c h e m a t i c o f t h e V a r i a n FC12 UHV chamber-  4-4  S i m p l i f i e d d i a g r a m o f an o f f - a x i s e l e c t r o n gun w i t h d e f l e c t i o n e l e c t r o d e and d r i f t t u b e ......... T h r e e methods o f h e a t i n g a c r y s t a l s a m p l e : (a) d i r e c t r e s i s t i v e h e a t i n g , (b) u s i n g a V a r i a n c o n d u c t i v e h e a t e r , (c) by e l e c t r o n bombardment. H a t c h e d l i n e s r e p r e s e n t s t a i n l e s s s t e e l and s t i p p l e ceramic i n s u l a t o r s Other materials g e n e r a l l y E h , P t , w" o r f a . , ........................  4.5  4.6  .........  78 81 81  85  S c h e m a t i c d i a g r a m o f LEED o p t i c s u s e d a s a r e t a r d i n g f i e l d a n a l y s e r f o r Auger e l e c t r o n s p e c t r o s c o p y : MCA = m u l t i c h a n n e l a n a l y s e r ........  87  Schematic diagram o f t h e e l e c t r o n o p t i c s used f o r LEED e x p e r i m e n t s . .................................  90  4.8  T y p i c a l v a r i a t i o n o f e l e c t r o n gun beam c u r r e n t I p a g a i n s t beam v o l t a g e Vp i n t h e LEED mode. .........  90  4.9  S c h e m a t i c d i a g r a m o f t h e a p p a r a t u s used t o a n a l y s e t h e p h o t o g r a p h i c n e g a t i v e s o f LEED p a t t e r n s . ......  S5  D i g i t i s e r o u t p u t measured f o r d i f f e r e n t r e g i o n s o f a Kodak No. 2 s t e p d e n s i t y wedge and p l o t t e d against the corresponding calibrated o p t i c a l densities. ....-... ................................  97  D i g i t i s e r o u t p u t measured f o r d i f f e r e n t r e g i o n s o f a p h o t o g r a p h i c n e g a t i v e o f t h e s t e p d e n s i t y wedge i n F i g u r e 4. 10, p l o t t e d a g a i n s t t h e o r i g i n a l c a l i b r a t e d o p t i c a l d e n s i t y o f t h e wedge. The a r r o w s n o t e t h e p o i n t s on t h e p l o t w h i c h c o r r e s p o n d t o t h e minimum b a c k g r o u n d a n d t h e maximum d e n s i t y o b s e r v e d on p h o t o g r a p h s o f t h e LEED p a t t e r n s f r o m Cu ( 1 1 1 ) . .......................  98  Flow c h a r t o f t h e c o m p u t e r program which c o n t r o l s the scanning o f t h e photographs..................  100  4-7  4.10  4-11  4.12 4.13  IJE) curves  f o r t h e (11) and (01) beams f r o m  X  Cu{111) a t n o r m a l i n c i d e n c e . 4.14  4.15  5.1  ......................  103  I|E) c u r v e s o f s y m m e t r i c a l l y e q u i v a l e n t beams f o r n o r m a l i n c i d e n c e on C u ( 1 1 1 ) . The i n s e t i n d i c a t e s t h e beam n o t a t i o n and a s p e c i f i c a t i o n o f t h e azimuthal angle the asterisk i l l u s t r a t e s the p o s i t i o n o f t h e e l e c t r o n gun f o r t h e n o n - n o r m a l incidence case. ...................................  10 5  1 ( E ) c u r v e s f o r t h e s p e c u l a r beam f o r C u ( 1 1 1 ) : (a) fr=12° , £ = 186°; (b) ©- = 12°, </>=70. i h e f i r s t two s e r e m e a s u r e d b y t h e method d e s c r i b e d i n t h i s p a p e r , a n d (c) r e p r e s e n t s m e a s u r e m e n t s made b y W o o d r u f f and M c D o n n e l l £ 1 9 ] w i t h a F a r a d a y c u p c o l l e c t or. ........................................  106  C o m p a r i s o n o f some e x p e r i m e n t a l 1 ( E ) c u r v e s f o r C u ( 1 1 1 ) w i t h c a l c u l a t i o n s f o r t h e p o t e n t i a l s V<?£ and V ,3 a t 6= 12°, ^ = 6 ° ; V = - 9 . 5 e V and Ad%=+5, 0 and - 5 % .  121  P l o t o f r ~ a g a i n s t Ad?i> f o r v a r i o u s v a l u e s o f V r f o r Cu{111) w i t h t h e V ( 3 p o t e n t i a l . E r r o r bars a r e s t a n d a r d e r r o r s i n t h e w e i g h t e d mean. .........  124  P l o t s f o r C u ( 1 1 1 ) o f • ( r K f o r 9 i n d i v i d u a l beams v e r s u s Ad$ f o r t h e V \? p o t e n t i a l w i t h V =9-5eV. The d a s h e d l i n e shows t h e d e p e n d e n c e o f t h e e n e r g y w e i g h t e d mean r" v e r s u s A d % . ...........  126  C o n t o u r p l o t s f o r Cu (111) o f " r V f o r t h e p o t e n t i a l s (a)  128  a  5.2  or  r  0  Cm>  5.3  r  CUk  or  r  5.4  o r  6.1  6.2  6.3  r  v e r s u s A cL% and a n d (b) V * . ..... c  A u g e r s p e c t r a o f Rh (111) s u r f a c e s w i t h a 1.5keV, 10 m i c r o a m p beam: (a) a s mounted, c o n s i d e r a b l e S(152eV) a n d C ( 2 8 2 e V ) contamination; (b) a f t e r a r g o n - i o n bombardment, r e d u c e d S, i n c r e a s e d C; (c) a f t e r a n n e a l i n g , r e d u c e d C, i n c r e a s e d S; id) c l e a n e d s u r f a c e . ..............................  137  P h o t o g r a p h s o f t h e (1x1). 1EED p a t t e r n f r o m t h e c l e a n Rh (111) s u r f a c e a t <a) n o r m a l i n c i d e n c e ( 1 5 8 e V ) , (b) S- = 1Q0, <f> = 1090 (122eV) i n t b e a n g l e c o n v e n t i o n o f Jona £128J. The l a b e l l i n g scheme i s shown i n (c) a n d (d) . .............................  141  P o s s i b l e r e c o n s t r u c t i o n s o f t h e (111) s u r f a c e t h a t p r e s e r v e t h e (1x1) s y m m e t r y o f t h e LEED p a t t e r n : (a) n o n - r e c o n s t r u c t e d , CEACBA. ,.C FCC s t a c k i n g ; (.fa) r e c o n s t r u c t e d , CBACBA...A s t a c k i n g ; (c) r e c o n s t r u c t e d , CBACfiA... B, HCP s t a c k i n g . The 4 t h l a y e r C i s i n d i c a t e d by s m a l l d a s h e d  xi  6.4  6.5  6.6  b a r r e d c i r c l e s , t h e 3 r d l a y e r B by l a r g e b l a n k c i r c l e s , t h e 2nd A by medium d o t t e d c i r c l e s , a n d t h e 1 s t l a y e r i s i n d i c a t e d by s m a l l b a r r e d circles. ..........................................  143  A c o m p a r i s o n f o r t h e <1G) and <01) beams o f 1 ( E ) c u r v e s measured a t n o r m a l i n c i d e n c e f o r fih(111) with those c a l c u l a t e d with the p o t e n t i a l V ^ j ^ f o r t h e n o r m a l FCC s t a c k i n g s e g u e n c e and f o r t h e HCP s t a c k i n g seguence over t h e t o p three s u r f a c e layers. ...........................................  145  A c o m p a r i s o n o f e x p e r i m e n t a l I (E) c u r v e s f o r t h e (10) a n d (01) beams a t n o r m a l i n c i d e n c e f o r Bh(111) w i t h i n t e n s i t y c u r v e s c a l c u l a t e d f o r t h e potentials and f o r three different v a l u e s o f A d % a s s u m i n g t h e n o r m a l FCC r e g i s t r y f o r the s u r f a c e arrangement.  147  C o n t o u r p l o t s f o r Bh {111) a t n o r m a l i n c i d e n c e o f r versus V a n d A d i f o r t h e p o t e n t i a l s (a) v££* and |b) - V ^ j s t a r t i n g f r o m 54 e V . ................  148  Plots beams (V = lines  152  r  6.7  o r  f o r Bh(111) o f ( r ) a t normal incidence -18eV) a n d (b). V ^ q show t h e d e p e n d e n c e r  o r  6.8  ^ f o r f i v e independent v e r s u s A d % f o r (a) (V =-10eV). The d a s h e d c f r versus ^d%. ....... o r  r  C o n t o u r p l o t o f r~ v e r s u s V and AdSS f o r Bh<111) a t n o r m a l i n c i d e n c e , u s i n g t h e d a t a o f F i g - , 6.6 o n l y f r o m 66eV f o r t h e p o t e n t i a l s (a) •v^j[' a n d (b) r  o r  1  ¥ 3 W  6-S  6.10  .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  J  154  Contour p l o t o f ~ r v e r s u s V and A d S f o r t h e p o t e n t i a l v^f and t h e m o d e l o f t h e Bh{111) s u r f a c e i n w h i c h t h e t o p t h r e e l a y e r s h a v e t h e HCP s t a c k i n g seguence. ................................  158  A c o m p a r i s o n o f e x p e r i m e n t a l I (E) c u r v e s f o r t h e C11) a n d (10) beams a t 10**, <f> = 109° f o r Rh{111) with i n t e n s i t y p r o f i l e s c a l c u l a t e d f o r the potentials and V ^ 3 f o r three different v a l u e s o f &&% a s s u m i n g t h e n o r m a l FCC r e g i s t r y f o r the s u r f a c e . ......................................  160  C o n t o u r p l o t o f F v e r s u s V r and A d S f o r Bh(111) a tft-=10«,<^> = 109O f o r t h e p o t e n t i a l s |a) v " ^ and (b) V . ........................................  161  r  o r  4  (  €.11  r  0  g M J  7. 1  S c h e m a t i c d i a g r a m o f t h e Bh(100) s u r f a c e (a) and t h e c o r r e s p o n d i n g LEED p a t t e r n (b) i n t h e n o t a t i o n of J o n a £128J. The u n i t mesh i s marked i n ( a ) . The c o m p l e t e c i r c l e s a r e f o r a t o m s i n t h e s e c o n d l a y e r , and t h e d a s h e d c i r c l e s c o r r e s p o n d t o a topmost l a y e r w i t h t h e r e g i s t r y b e l o n g i n g t o t h e  xii  7.2  7.3  7.4  b u l k i . e . atoms i n t h e t o p l a y e r a r e a b o v e t h e 4f o l d s i t e s s u c h a s A. O t h e r r e g i s t r i e s c o n s i d e r e d a r e where atoms a r e o v e r t h e 2 - f o l d s i t e ( l i k e B ) , o r d i r e c t l y o v e r atoms i n t h e l a y e r b e l o w ( a s f o r C). .... ..  170  Auger s p e c t r a o f Bh(100) s u r f a c e s f o r a 1.5KeV, 10 microamp beam: a) s u r f a c e a f t e r p r o l o n g e d h e a t i n g a t 1300K showing s u b s t a n t i a l S i and C i m p u r i t i e s b) a f t e r argon ion-bombardment, showing reduced S i and i n c r e a s e d c a r b o n c) c l e a n s u r f a c e s p e c t r u m a f t e r h e a t i n g a t 1000K i n vacuo.  172  Two-domain (3X1) LEED p a t t e r n f r o m t h e Bh(1Q0) s u r f a c e a t 100eV, t h o u g h t t o b e due t o t h e presence of s i l i c o n . ..............................  174  LEED p a t t e r n s f r o m t h e c l e a n Eh (100) s u r f a c e f o r <a) n o r m a l i n c i d e n c e ( 1 5 0 e V ) , (to) f o r 6-=9O <j> =20» (94eV) a n d t h e beam l a b e l l i n g scheme (c) a n d (d) . 0  175 7.5  7.6  7.7  I (E) c u r v e s f o r two s e t s o f beams t h a t s h o u l d be e g u i v a l e n t a t n o r m a l i n c i d e n c e on t h e Bh(1Q0) s u r f a c e ; t h e f o u r t h member o f e a c h s e t i s o b s c u r e d by t h e s a m p l e m a n i p u l a t o r . ........................  177  C o m p a r i s o n o f e x p e r i m e n t a l I (E) c u r v e s f o r t h e (11) and (20) beams a t n o r m a l i n c i d e n c e on Bh(100) with c a l c u l a t i o n s , f o r the V^kil p o t e n t i a l , f o r t h e t o p m o s t r e g i s t r i e s d e f i n e d by A,B a n d C i n E i g . 7. 1. T h e t o p m o s t i n t e r l a y e r s p a c i n g s a r e 1.90, 2.33 a n d 2.69A f o r t h e 4 - f o l d , 2 - f o l d and 1f o l d s i t e s r e s p e c t i v e l y . ..........................  179  C o m p a r i s o n o f some e x p e r i m e n t a l 1 ( E ) c u r v e s f o r Sh(100) w i t h c a l c u l a t i o n s f o r t h e and potentials. V = - 1 2 e V a n d Ad%=-5,0 and+5% f o r (a) n o r m a l i n c i d e n c e a n d (b) a t t>-=90, <j>=20 °. ......... or  7.8  8. 1 8.2  180  Contour p l o t s f o r Bh(100) of r r v e r s u s V r and A d ^ f o r {a) t h e Vgfcu and ib) t h e V p o t e n t i a l . E r r o r b a r s a r e t h e s t a n d a r d e r r o r s £j a n d £v d e f i n e d i n C h a p t e r 5. .............................  184  D i a g r a m o f a) a (110) s u r f a c e and b) t h e a s s o c i a t e d LEED p a t t e r n . ..........................  190  0  A u g e r s p e c t r a o f t h e Bh(110) s u r f a c e a t a p r i m a r y beam v o l t a g e o f 1.5KeV a n d 10 m i c r c a m p c u r r e n t : a) a f t e r i n i t i a l heat treatments showing S ( 1 5 2 e V ) , P |120eV) a n d C (272eV) c o n t a m i n a t i o n on t h e s u r f a c e  xi i i  b) c) 8.3  8-4  8.5  a f t e r a r g o n ion-bombardment; but C i n c r e a s e d clean surface spectrum.  P and S removed 192  LEED p a t t e r n f r o m t h e c l e a n E h (110) s u r f a c e a t (a) n o r m a l i n c i d e n c e (88eV) and (b) ©- = 10°, <b = 135° (90eV). The beam l a b e l l i n g scheme i s shown i n ( c ) and (d) . ..................................  194  E x p e r i m e n t a l I ( E ) c u r v e s f o r t h e Hh{110) s u r f a c e a t n o r m a l i n c i d e n c e f o r t h e 4 - f o l d e q u i v a l e n t {11} and {21J beam s e t s . The 4 t h member o f e a c h s e t i s o b s c u r e d by the sample m a n i p u l a t o r ...............  195  C o m p a r i s o n s o f two e x p e r i m e n t a l 1 ( E ) c u r v e s f o r t h e 8h(110) s u r f a c e w i t h c a l c u l a t i o n s , u s i n g t h e £M3 p o t e n t i a l f o r f o u r v a l u e s o f &d?L The v a l u e o f t h e i n d i v i d u a l beam r e l i a b i l i t y - i n d e x ( r ^ ) ^ i s given i n brackets f o r each c a l c u l a t e d curve. ......  198  ?  8.6  A c o n t o u r p l o t f o r .ah (110) o f r> v e r s u s V and b&% f o r d a t a a t n o r m a l i n c i d e n c e and a c a l c u l a t i o n f o r the V ^ p o t e n t i a l . ............................ . 200 o r  O K l  xiv  L I S T OF TABLES  1.1  3.1  C o m p a r i s o n o f some o f t h e most i m p o r t a n t s u r f a c e technigues. More d e t a i l s c a n be f o u n d i n r e f e r e n c e £22 J...................................  3  Data used f o r c o n s t r u c t i o n of s u p e r p o s i t i o n p o t e n t i a l s f o r M,^ clusters. The c r y s t a l c u b e s i d e a a n d m u f f i n - t i n r a d i u s r „ a r e f r o m £62,6,3 J and t h e values from [ 58,59j. ...................  52  D  3.2  T  R e d u c t i o n , due t o symmetry,, i n t h e number o f beams needed a t n o r m a l i n c i d e n c e f o r t h e t h r e e s i m p l e f a c e s o f r h o d i u m . The maximum g v e c t o r c o r r e s p o n d s t o t h e beam s e t w i t h t h e l a r g e s t (hk) v a l u e s n e e d e d t o c o v e r t h e e n e r g y r a n g e 4Q-250ev.  4.1  Sources o f rhodium c r y s t a l s  5. 1  C o r r e s p o n d e n c e between s i n g l e beam ( f i r s t and f o r a s t r u c t u r a l model and t h i r d r o w ) . A f t e r  5.2  v i s u a l match a n d ^ r r ^ f o r a s e c o n d r o w ) , and b e t w e e n R and i t s r e l i a b i l i t y (second Z a a a z z i a n d J o n a £23J. .....  69 77  118  Summary o f s t r u c t u r a l d e t e r m i n a t i o n o f t h e Cu(111) surface.  123  6.1  O b s e r v e d and c a l c u l a t e d A u g e r t r a n s i t i o n s f o r rhodium. ..........................................  139  6.2  C o n d i t i o n s o f b e s t agreement between e x p e r i m e n t and multiple-scattering calculations f o r three s e t s o f i n t e n s i t i e s measured a t n o r m a l i n c i d e n c e onSh(111). .  157  C o n d i t i o n s o f b e s t agreement between e x p e r i m e n t and multiple-scattering c a l c u l a t i o n s f o r three s e t s o f i n t e n s i t i e s m e a s u r e d a t &-=1[0°, <f> =109° on Bh(111) . ..... ..  164  Summary o f s t r u c t u r a l Rh(100) s u r f a c e .  183  6-3  7.1 8.1  d e t e r m i n a t i o n s of t h e  C o n d i t i o n s o f b e s t agreement between e x p e r i m e n t and 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 m e a s u r e d f o r two a n g l e s o f i n c i d e n c e on 8 k < 1 1 0 ) . ...............  201  ACKNOWLEDGEMENTS  When I r e v i e w guickly the  t h e work t h a t went i n t o t h i s t h e s i s i t  becomes a p p a r e n t  many p e o p l e  i t s eventual First  who c o n t r i b u t e d , i n l a r g e m e a s u r e o r s m a l l , t o  completion.  o f a l l I must t h a n k my c o - s u p e r v i s o r s P r o f e s s o r s  Keith Mitchell throughout  t h a t I owe a l a r g e number o f d e b t s t o  and Dave F r o s t f o r t h e i r  t h e course  of t h i s  from o t h e r  my s i n c e r e g r a t i t u d e t o t h o s e  institutions  m a t e r i a l s and computer programs. of  who g e n e r o u s l y  a t Berkeley)  Corporation)  loaned  P r o f e s s o r F. J o n a  and D r . C.W.  crystal  samples.  (Stonybrook)  supplied  Dr. D. P. W o o d r u f f  W a r w i c k , U . K . ) , P r o f e s s o r G. A. S o m o r j a i  California  and s u p p o r t  work.  X would a l s o l i k e t o e x p r e s s individuals  guidance  (University  (University of  Tucker  (General  Electric  Dr. ,E. Z a n a z z i and  p r o v i d e d a copy o f t h e i r  r e l i a b i l i t y - i n d e x p r o g r a m w h i l e D r . M. A. Van H o v e { U n i v e r s i t y o f California  at Berkeley)  Wisconsin)  kindly  and Dr. S. Y- Tong  (University of  donated a s e t of m u l t i p l e - s c a t t e r i n g  Dr. M i c h e l Van Hove was a c o n s t a n t s o u r c e  o f a d v i c e and  e n c o u r a g e m e n t on t h e u s e a n d m o d i f i c a t i o n o f t h e s e A t UBC D r . L o u i s Noodleman a s s i s t e d  programs.  programs.  i n the construction of  s u p e r p o s i t i o n p o t e n t i a l s a n d D r . A. A k h t a r o f t h e M e t a l l u r g y D e p a r t m e n t o f f e r e d a d v i c e on c r y s t a l c u t t i n g a n d p o l i s h i n g . experiments skill and  would h a v e been i m p o s s i b l e t o p e r f o r m  and w i l l i n g c o - o p e r a t i o n o f t h e s t a f f  mechanical  workshops o f t h e Chemistry  The  without the  of the e l e c t r i c a l  Department under t h e  xvi  a b l e s u p e r v i s i o n o f Joe tock  p a r t i n the c o n s t r u c t i o n  particularly the  S a l l o s and  Don  I t h a n k my  Cedric  Dr.  the M e c h a n i c a l  E s p e c i a l m e n t i o n must be  d u r a t i o n o f t h i s work,, and  my  and  present,  company and  made o f my  good  w i t h o u t whose c h e e r f u l  "rt<£..  the  preparation  the  Moore  and  cofriend  of t h i s t h e s i s .  the  expertise, would  experience-  F i n a l l y , I wish t o thank S h e i l a L i d w i l l f o r her in  in  close c o l l a b o r a t o r throughout  much l e s s e n j o y a b l e  of  McCafferty,  i n mini-computer programming, t h i s p r o j e c t  have been a p r o t r a c t e d  Shim  Borksbop-  S u n a n t h a Hengrasmee, Tom  was  Joe  Henderson, C h a r l i e  f o r t h e i r enjoyable  F r a n k S h e p h e r d , who  particularly  equipment,  f e l l o w w o r k e r s , b o t h p a s t and  Hick S t r e a t e r  operation.  Bill  Neale of  S u r f a c e Chemistry Group Dr.  r e p a i r of  Many p e r s o n s  C a t t , B r i a n G r e e n e , M i k e H a t t o n and  E l e c t r o n i c s w o r k s h o p and  E m i l M a t t e r and  and  Brin Powell-  assistance  1  CHAPTER 1  INTRODUCTION  2  1,1  Surface  Techniques  Many a s p e c t s o c c u r upon t h e of  many  of present  surfaces  fields  of  technology  of s o l i d s .  depend  The  research,  in  on  processes  ultimate  understanding  particular  heterogeneous  catalysis,  w o u l d seem t o r e g u i r e d e t a i l e d k n o w l e d g e  processes  at  the  atomic l e v e l .  One  rather than the d e f e c t s and practical  c o m p l e x and  situations.  The  s t u d i e s i s thus to provide geometrical  and  There  energetic  are  scientist  to  electronic  many  technigues  accurate  technigues  detected  of  or  the  for  composition, These  various  p r o b e , d e t e c t an  radiation In  the  Table  and  have  1-1  is  I t can  be  r e a d i l y be  surface egually  spawned  a  derived  information  and  that  in  performed i n s i t u  changing the experimental  a  r e s u l t s from  r e s u l t e d i n the e v o l u t i o n of the strategy"  from  seen t h a t each  d e s c r i p t i o n would i n v o l v e c o r r e l a t i n g the  without  and  and  complete  T h i s has  surface  methods, t h e i r acronyms, probe  yields different  t y p e s of e x p e r i m e n t a r e  in  a  i n general  "multi-technigue  of  presented  technigue  called  typical  geometry  i n f o r m a t i o n t h a t can  e a c h method a b o u t t h e s u r f a c e .  s e v e r a l methods.  structural  d e s c r i p t i o n s of s u r f a c e s  surfaces.  most i m p o r t a n t  p a r t i c l e s and  metal)  of such f u n d a m e n t a l  available  the  a r r a y o f acronyms. the  study  terms.  l a r g e v a r i e t y of p a r t i c l e s  summary o f  with  »hich a r e  goal  e m p l o y many t y p e s o f s u r f a c e  bewildering  surface  a catalytic  surfaces  composition primary  investigate structure  (of e.g.  ill-defined  uncertain chemical  of  approach has been t o  well-defined single c r y s t a l surfaces  that  so-  which s e v e r a l d i f f e r e n t on  conditions-  the  same  sample  3  Probe particle  Detected particle  Information  Low e n e r g y e l e c t r o n LEED diffraction  e l e c t r o n s primary 10-300eV e l e c t r o n s  surface  Auger e l e c t r o n spectroscopy  AES  e l e c t r o n s secondary 1-10KeV electrons  elemental composition  U.V. p h o t o e m i s s i o n spectroscopy  UPS  photons 10-40eV  electrons  valence le vels  Angle-resolved OPS  ABUPS p h o t o n s io-40eV  electrons  surface structures?  structure  energy  X - r a y p h o t o e m i s s i o n XPS spectroscopy  photons 0. 5-2KeV  electrons  core l e v e l s e l e me a t a 1 com.p -  Ion-scattering spectroscopy  ions 0.5-2KeV  primary ions  e l e m e n t a l comp. surface structures?  ioas 1-2Me¥  primary ions  e l e m e n t a l comp. surface structures?  SIMS  ions 1^30KeV  sputtered ions  elemental composition  FIM  field 10* V/cm  imaging gas i o n s  defects, surface mobility  Ion  ISS  channeling  Secondary-ion spectrometry  mass  Field-ion microscopy  T a b l e 1.1 . C o m p a r i s o n o f some .. o f t h e most i m p o r t a n t s u r f a c e techniques. More d e t a i l s c a n be f o u n d i n r e f e r e n c e j. 2 2 } .  The most b a s i c i n f o r m a t i o n t h a t we c a n w i s h  t o know a b o u t a  surface i s (i)  what  i s  the  identity  of  the  a t o m s m a k i n g up t h e  surface? (ii) That  where a r e t h e s e atoms s i t u a t e d ?  i s , we  geometrical i n Table  wish  to  know  the  elemental  s t r u c t u r e of the s u r f a c e .  1.1 t h e most  common  and  composition  Of t h e t e c h n i q u e s  convenient  method  and listed  used  to  answer The  the  f i r s t • q u e s t i o n i s auger e l e c t r o n  reasons f o r t h i s are i t s experimental  simplicity  e.g.  i o n channeling, which r e g u i r e s a p a r t i c l e  the  ease  surface-sensitive to  the  electrons  Ch-  accelerator  Auger e l e c t r o n s p e c t r o s c o p y than  compared  a  X-ray  shallower  routine  penetration  the  depth  "multi-technigue  tool  i s also  and  more  photoelectron spectroscopy  w i t h t h e X - r a y s o f XPS.  is easily fitted into become  compared t o  o f i n t e r p r e t a t i o n c o m p a r e d t o e . g . s e c o n d a r y i o n mass  spectrometry (SIHS).  owing  spectroscopy(AES).  of  the  Auger  exciting  spectroscopy  strategy"  f o r surface composition  (XPS)  and  has  a n a l y s i s (see  2) . T h e r e i s only, one t e c h n i q u e  that has r e a l l y  proven  itself  to answer t h e second q u e s t i o n c o n v i n c i n g l y — l o w - e n e r g y e l e c t r o n d i f f r a c t i o n (LEED). its  ultraviolet still  i n the f i r s t  provided  as  very  high  strength, i n the angle-resolved  and i o n c h a n n e l i n g  s t a g e s o f development and, w h i l e  f o r the determination yet  of  The r e l a t i v e l y new methods o f  p h o t o e l e c t r o n spectroscopy(AfiOPS)  great p o t e n t i a l have  requirements  f i e l d s and a sample, o f h i g h c o h e s i v e  form of a needle.  not  i o n microscopy(FIM) i s r e s t r i c t e d i n  u s e f u l n e s s by t h e e x p e r i m e n t a l  electric  are  Field  showing  of surface structures,  do  t h e b a s e o f s u c c e s s f u l r e s u l t s t h a t LEED h a s  during the l a s t  decade.  5  ,1. 2  H i s t o r i c a l D e v e l o p m e n t Of The  origins  developments  of  of  LIED  atomic  t h e s i s , de B r o g l i e £ 1 ] m a t t t e r , where a f l u x correlated  with  IMP  are  closely  theory  and  a wavelength  S h o r t l y b e f o r e the  X=  angular  nickel  experimental artefacts  an  accident.  I n 1925  results.  was  oxidised.  In  but  was,  caused  which then  gave  distribution  of  interpretation "crystal  the rise  de  be e x p e c t e d  Broglie's  eV to  thesis,  backscattered anisotropics  these  were  from  in  the  interpreted  however, a c h i e v e d as t h e  n i c k e l s a m p l e t h a t was  time , to  time  and to  the  as  to  hot  annealed  order ;to  nickel  the in  obtain  sample  initial  hydrogen;  maxima  was  to  i n v e s t i g a t i o n s showed t h a t t h i s was  based  conditions, this  in  on  particles, a wave  glass  severely  the  grains angular  S h i l e the a  the  procedure  of l a r g e r s i n g l e c r y s t a l  pronounced  results  transparency"  result  such h e a t i n g c y c l e the  restore  growth  in  b a c k s c a t t e r e d slow e l e c t r o n s .  of these  mass m i s  D a v i s s o n and Germer b e g a n a s e r i e s o f  c r y s t a l was h e a t e d f o r some t i m e apparently  of  D u r i n g one  damaged order  of  £3],  at h i g h temperatures from  apparatus  In h i s  nature  v and  and m i g h t  showed  e x p e r i m e n t s on a p o l y c r y s t a l l i n e  reproducible  ll  electrons  £2J  The e s s e n t i a l i n s i g h t of  wave  the  structures.  targets  distributions  with  Hence a beam o f 150  h/mv-  publication  concerning  polycrystalline  the  of p a r t i c l e s w i t h v e l o c i t y  from p e r i o d i c c r y s t a l  experiments  up  guantum m e c h a n i c s -  p o s t u l a t e d i n 1924  e l e c t r o n s have a wavelength of about diffract  bound  first  directional  more  interference  detailed effect  6  and  i n 1927 D a v i s s o n  diffraction  maxima on t h e b a s i s o f de B r o g l i e * s  This historic which,  a n d Germer [ 4 J r e p o r t e d a n a n a l y s i s o f t h e  after  eguation.  e x p e r i m e n t was p e r f o r m e d i n g l a s s  initial  evacuation  t o a b o u t 1 0 * T o r r , was s e a l e d -  off  a n d f u r t h e r pumped b e l o w t h e d e t e c t i o n l i m i t f o r  of  about  10  getter metal. high  time  by a c h a r c o a l s o r p t i o n pump a n d e v a p o r a t e d  {UHV), u s u a l l y d e f i n e d a s < 1 0  contamination  that  Even i n t h i s e a r l y work t h e i m p o r t a n c e o f  vacuum  Torr,-to  - 9  ultraminimise  o f t h e s a m p l e s u r f a c e was r e c o g n i s e d .  However, developed  Torr  _ 8  apparatus  the  use  a t t h a t time.  of  LEED  to  study  surfaces  Due t o t h e d i f f i c u l t y  was  not  o f p r o d u c i n g fl'HV  c o n d i t i o n s and t h e l a c k o f a s u r f a c e a n a l y s i s t e c h n i g u e ,  results  could often r e f l e c t  surface  layer.  The  electrons eV)  penetration  transmission  easily  with  other  by low e n e r g y  between 0 and  on e v e n t h e t h i n n e s t small  fraction  greater  penetrating  of the  power,  and  the  b r o u g h t a b o u t i n t h e e f f e c t i v e s c a t t e r i n g power  tractable,  a l l ensured t h a t a t t h i s stage  diffraction  was t h e more i n t e r e s t i n g  theory  more  high energy e l e c t r o n  field.  I n t e r e s t i n LEED r e v i v e d i n t h e e a r l y i m p r o v e d by a d v a n c e s i n e x p e r i m e n t a l  1960's. design,  the composition  of s u r f a c e s  and  C o m m e r c i a l vacuum s y s t e m s t h a t  annealing.  films  r a i s i n g problems of s e n s i t i v i t y .  of a t o m s a t h i g h i n c i d e n t e n e r g i e s , w h i c h made t h e  was  500  g e n e r a t e d and c o n t r o l l e d h i g h e n e r g y e l e c t r o n  their  simplifications  or  sample  energies  whereas i n r e f l e c t i o n o n l y a  more  beams,  the  experiments  i n c i d e n t beam i s b a c k s c a t t e r e d , The  of  {usually defined as having  made  difficult  small  t h e c o n d i t i o n o f an o x i d e  Sensitivity and c o n t r o l o f  was made p o s s i b l e by i o n - b o m b a r d m e n t could  routinely  7  attain  UHV  became  a v a i l a b l e t o reduce background  p o i n t where d e p o s i t i o n rather  than  of a l a y e r of f o r e i g n  minutes.  In the l a t e  atoms  electron  ,spectroscopy  took  hours  1960*s t h e t e c h n i q u e s became  a v a i l a b l e t o d e t e c t Auger e l e c t r o n s e m i t t e d from Auger  gases to the  {see  surfaces,  C h a p t e r 2)  and  provided  a  convenient monitor of s u r f a c e c o m p o s i t i o n . T h e o r e t i c a l e x p l a n a t i o n s of t h e d i f f r a c t i o n advanced i n the l a t e used  i n X-ray  1960*s.  diffraction  phenomena  also  A p p l i c a t i o n o f t h e Bragg t r e a t m e n t  showed t h a t a c o m p l e t e d e s c r i p t i o n o f  t h e d i r e c t i o n s o f t h e d i f f r a c t i o n maxima was p o s s i b l e b u t n o t o f the i n t e n s i t i e s .  The  d i r e c t i o n s c o u l d be o b s e r v e d d i r e c t l y i n a  t y p i c a l LEED d i s p l a y - t y p e a p p a r a t u s and shape  of  the  s u r f a c e , t o be however  determination  an  intensities  could  The  analysis  as  in  not  be  the  of  intensities  diffraction.  simply  the  had  of  That  described  diffraction  basis  by  these  the  been  The  development  of  practical  multiple-scattering  d i d n o t come t o p a s s u n t i l t h e e a r l y  of  of l a r g e d i g i t a l computers  interactions  discussed  where  the  understood; provide  Born  realised  involved.  1970*s,  mainly  in  Ch., 3.  diffraction the  accurate  The  Many d i f f e r e n t methods f o r  t h e o r y has advanced  process  difficulty intensities  is  lies  due  t o compute the l a r g e  t h e c a l c u l a t i o n o f LEED i n t e n s i t i e s have been p r o p o s e d and be  the  a f t e r t h e p u b l i c a t i o n o f t h e r e s u l t s o f D a v i s s c n and  to the n e c e s s i t y numbers  of  X-ray  approximation adopted f o r X-ray  programs  and  determined.  maxima,  Germer.  size  i n d i r e c t i o n s p a r a l l e l t o the  reguired  soon  the  surface unit c e l l ,  diffraction  very  allowed  essentially  i n finding  without  t o the stage completely  methods t h a t  massive  will  will  computational  8  e f f o r t f o r systems of chemical Many decade.  hundreds Most  o f p a p e r s have a p p e a r e d o n LEED i n t h e  confine  diffraction  patterns,  intensities  been  calculations. has  been  interest-  themselves in  to  descriptions  comparatively  measured  and  few  compared  £1.13-  nickel  the  cases  have  with  diffraction  from  some  s u r f a c e s ; a p a r t i c u l a r l y good e x a m p l e b e i n g t h e l o w of  of  accurate  V e r y good a g r e e m e n t b e t w e e n e x p e r i m e n t and  achieved - f o r  s e v e r a l cases  last  theory  clean  metal  index  faces  unknown s t r u c t u r e s , p r o d u c e d  by s i m p l e g a s e o u s a d s o r p t i o n o n t o m e t a l l i c s u b s t r a t e s , h a v e been determined papers  by  and  intensity reviews  Thesis  are  listed  and £ 11-15j ( m a i n l y  experimental)  1.3  analyses.  A as  selection  of  r e f e r e n c e s £6-10  important J  (mainly  theoretical)-  Outline  This t h e s i s d e s c r i b e s a d e t a i l e d study of the s t r u c t u r e s o f the clean This  (111)  , {100)  and  catalytically  contrast to received  most  of  the  {111)  other  face-centred platinum  cubic group  s c a n t a t t e n t i o n by s u r f a c e s c i e n t i s t s s u r f a c e s of t h i s metal  e a r l y g u a l i t a t i v e work by T u c k e r £ 16- 17J,  a surface composition to  s u r f a c e s of rhodium using  important  s o r t on s i n g l e c r y s t a l from  {110)  doubt,  and  £18,131],  represents  the  monitor  and  (110)  first  surfaces  detailed  s u r f a c e s u s i n g modern methods.  metal, metals,  are who  rare;  the  any  apart  d i d n o t have are  s t u d i e s on t h e Bh{100) £133 J ,  in has  S t u d i e s of  and h e n c e whose r e s u l t s  recent chemisorption  LEED.  present  open and work  i n v e s t i g a t i o n of c l e a n rhodium  9  As s u r f a c e s c i e n c e experimental built, well  i s a new f i e l d i n t h i s  institution  e g u i p m e n t had t o be c o m m i s s i o n e d , o r i n some c a s e s  a n d c o m p u t e r p r o g r a m s h a d t o be a d a p t e d f o r u s e as s e v e r a l s m a l l e r d a t a  written. detail  the  handling  and m a n i p u l a t i o n  The CuJ111) s u r f a c e , w h i c h h a s been  studied  here  as  programs in  some  p r e v i o u s l y j. 19-20 J,, was u s e d a s a t e s t c a s e f o r b o t h t h e  experimental  techniques  calculations.  Only  and  to  check  the  correctness  when i t was c e r t a i n t h a t  of  t h e data o f other  workers f o rt h i s s u r f a c e could  be r e p r o d u c e d were s t u d i e s on t h e  rhodium s u r f a c e s  Examples  copper  work  commenced.  are  often  used  in  from  the  this  preliminary  t e x t i n an i l l u s t r a t o r y  manner. Chapter 2 i s devoted t o a b r i e f u n d e r l i e LEED. simple and  Surface  explanation  of b a s i c i d e a s  that  s t r u c t u r e s , t h e r e c i p r o c a l l a t t i c e and a  of the formation  i t s i n t e n s i t y are discussed  Auger  review  of the d i f f r a c t i o n  i n o u t l i n e . , The  pattern  production  e l e c t r o n s and t h e u s e o f a u g e r e l e c t r o n s p e c t r o s c o p y  of as a  s u r f a c e a n a l y s i s t o o l i s a l s o summarised. Chapter 3 calculations  outlines that,  when  surface structure. more  available  guoted  with  texts.  and  Bather,  i n  theoretical  compared  The n e c e s s a r y  little  complexities;  the  with  basis  to  programs a r e r a p i d l y  explain  such c a s e s t h e reader  a t t e n t i o n i s focussed  s t r u c t u r a l parameters that enter i n t o  the  experiment, y i e l d the  commonplace a n d h e n c e s t a n d a r d attempt  of  the  becoming  r e s u l t s are computational  i s r e f e r r e d t o standard  on t h e s t r u c t u r a l a n d n o n the  calculations,  their  m e a n i n g and i m p o r t a n c e , and t h e o v e r a l l c o n s t r u c t i o n and f l o w o f the  programs.  I n p a r t i c u l a r , ; the. i o n - c o r e s c a t t e r i n g p o t e n t i a l  10  that  leads  to  electrons  backscattering  must  be  by  the  incident  correctly . specified  theoretical intensities. were  of  to  obtain  I n t h i s work two t y p e s  used, b a n d - s t r u c t u r e  low-energy  of  reliable potentials  p o t e n t i a l s and p o t e n t i a l s c o n s t r u c t e d  t h e method o f l i n e a r s u p e r p o s i t i o n o f c h a r g e d e n s i t i e s f o r  a  c l u s t e r o f metal atoms. In  Chapter  apparatus of  a  sample,  i n n o v a t i v e new employing  a  over  be  found  as  judged  i n some d e t a i l .  by  AES,  collector, The  VidiconT-?.  which  contaminated.  time  methods  to  record  t h a t c a n be a n a l y s e d base  which  camera  in  terms  surface  of  relates  speed  experimental  could  at leisure to  o r use o f a  become data  yield to  and  hours of data  m i n u t e s and p r o v i d e s a h a r d - c o p y  unambiguously  system  advantages  of  necessitated  V i d i c o n method r e d u c e s  times  data  few  the  An  intensities,  of spot-photometry  particularly  former  T h i s new  a  described.  method o f S t a i r e t a l £ 6 8 J , i s  c o l l e c t i o n t o produce even a s m a l l b a s e during  are  production  T h i s method h a s s i g n i f i c a n t  the c o n v e n t i o n a l t e c h n i g u e s  convenience.  of the experimental  method o f m e a s u r i n g t h e e x p e r i m e n t a l  on t h e p h o t o g r a p h i c  Earaday^-cup  details  The vacuum s y s t e m a n d t h e  computer-controlled  based  covered  can  and p r o c e d u r e s .  clean  £213,  4  a  data,  seriously collection  photographic very  t h e same  large  original  surface. Chapter  5  describes  crystallography, including structure found  determinations.  progress  to  of  possible  in  LEED  surface  a b i b l i o g r a p h y o f metal; c l e a n s u r f a c e The  preferred surface structure i s  by comparing c a l c u l a t e d r e f l e c t e d  variety  date  intensities  for. a  s t r u c t u r a l models w i t h e x p e r i m e n t a l  wide data.  11  T r a d i t i o n a l l y , comparisons of experimental have  been  carried  out  visually  matching of major f e a t u r e s . crystallography accuracy  and  been, that  recently £23J  essential  has  that  of  of  the  model  a  surface  of  the  to  developed  during  thus  problem,  method  been  compare a l l t h e  data  with  with  some  the a p p l i c a t i o n of  various 8-  additions  and  of t h i s index  £h (111)  the  to  , (100)<  a c t u a l determination of the surface s t r u c t u r e s of  low-index  f a c e s of rhodium i s p r e s e n t e d  F i n e d e t a i l s o f the c l e a n i n g p r o c e d u r e s ,  and  discussed.  The  reliability-index  structure  which  method  are  uncertainties  in  calculational)  artefacts  Duplicate  of  sets  the  can  closely  results and  data  fortuitous  collected  at  i n c i d e n c e , compared t o t e s t the c o n s i s t e n c y of All  three surfaces r e t a i n  the  structure  simple t r u n c a t i o n of the bulk c r y s t a l .  from  by  to  the  assess  experimental  (or  circumstances.  o f t h e e x p e r i m e n t a l d a t a and sets,  vary  performed  examined from  6-8.  pre-treatment,  data from d i f f e r e n t experiments  assess the r e l i a b i l i t y independent  derivations  these  i n Chapters  s a m p l e t o s a m p l e d e p e n d i n g u p o n t h e i r o r i g i n s and  from  the  surfaces. The  are  LEED  This r e l i a b i l i t y - i n d e x , or  the d e t e r m i n a t i o n of the s t r u c t u r e s  three  in  over t h i s  objective  experimental  f a c t o r , method i s d e s c r i b e d t o g e t h e r refinements  numerical  structures  numerically  predictions.  data  e s t a b l i s h i n g l i m i t s on  detailed,  attempts  features  theoretical^  O10)  very crude  Despite a long-standing concern  very  proposed  by  Hence a r e c u r r i n g p r o b l e m  reliability  determined. only  has  or  and. t h e o r e t i c a l  are used the  results  various angles the  to  of  method.  expected  for  a  H h i l e t h i s i s normal f o r  12  the  {111)  close-packed {110)  some  s u r f a c e s of face-centred  (100)  and  faces  structural  reconstructions  conplex  as yet  e.g.  and  this condition.  known  £24J,  Rigorous examination  at  tendency.  A l l t h r e e s u r f a c e s were f o u n d  layer  temperature  and  (100)  The  above to  interlayer  t h r e e rhodium s u r f a c e s used i n t h e This the  these  thesis  the  new,  for  this  surface  form  understand  precise  t h i s work p r o v i d e s foundation  for  p r o p e r t i e s and  new  complete study,  at  the  for  Examples  developing  and  theoretical  while  in  themselves  are a l s o p r e l i m i n a r y to  p r o p e r t i e s and  heterogeneous  J u s t a s we c a n n o t  hope  i n f o r m a t i o n and rhodium,  ultimately i t s catalytic  will  to  cannot l o c a t e i f  d e s c r i p t i o n of the c l e a n s u r f a c e .  of  part  with  a t o m i c l e v e l i f we  studies  the  purposes.  cannot understand chemisorption  the l a t t e r  later  concerned  results,  o f r h o d i u m £26J.  catalysis  a  was  of the a d s o r p t i o n  a d s o r b e d a t o m s , so we have  i t  little  that a large  laboratory, experimental  a reasonably  understanding  data  the t e x t f o r i l l u s t r a t o r y  Moreover, these  catalytic activity  not  the  such  distance.  i s p r e l i m i n a r y i n the sense  work t h a t went i n t o  technigues. they  no  i s c o l l e c t e d i n the appendices.  main b o d y o f  (110)  and  have  of  observed i n  revealed  F i n a l l y , a comprehensive s e t of experimental  of  faces  at a d i s t a n c e from the second l a y e r c l o s e t o , or a  contracted from, the bulk  are  surface  of a g e n e r a l l y  o f t h e Rh (100)  surfaces  metals,  perform  i r i d i u m . £26J are n o r m a l l y  and  room  to  orre-arrangements  unknown n a t u r e  £25J  platinum  are  cubic  lay  we  do  I hope a  solid  i t s chemisorption  activity.  13  CHAPTER 2  LOW-ENERGY ELECTRON DIFFRACTION(LEED) AND A UGER ELECTION SPECTROSCOPY (AES)  14  _2. 1  Basic  2.1{a)  Consideratioss  secondary e l e c t r o n  distribution  Electrons with energies ideally  suited  to  b e t w e e n a b o u t 10 a n d  investigate  the  topmost  1000  eV  are  l a y e r s of s o l i d s  because t h e p r o b a b i l i t i e s f o r i n e l a s t i c s c a t t e r i n g a r e h i g h . parameter  freguently  f r e e path  l e n g t h , L.  electron  before  expressed  by  used i n t h i s c o n t e x t  i s t h e e l e c t r o n mean  T h i s i s t h e mean d i s t a n c e t r a v e l l e d  i t i s scattered  A  inelastic ally  and  by  an  can  be  I IE) = I (E) e x p I - l / L CE) j D  where t h e i n c i d e n t i n t e n s i t y I <E)  I {E)  f o r energy E i s attenuated t o  0  on p a s s a g e t h r o u g h d i s t a n c e 1. The c h a r a c t e r i s t i c  dependence  of  e l e c t r o n e n e r g y i s shown i n F i g . , 2.1. difficult  to  obtain  exact  this  property  Although  quantitative  i t i s  data,  f e a t u r e s o f t h i s d i a g r a m h a v e been w e l l e s t a b l i s h e d an 40  t h e mean f r e e p a t h and  100  eV.  ahile  the  curve  general  A  minimum between  s t e e p l y a t low path  o n l y a few a t o m i c l a y e r s -  t h e LEED e x p e r i m e n t a beam o f e l e c t r o n s w i t h a d e f i n i t e e n e r g y i m p i n g e s on  electrons Fig-  the  t h e i n c r e a s e i n t h e mean f r e e  i s s l o w a n d a t 1000 eV i s s t i l l  primary  increases  the  somewhat  o f o n l y a few A o c c u r s a t e n e r g i e s  energies, a t higher energies  In  on  that  crystal  surface  and  those  elastically  backscattered  are collected.  2.2 shows a s c h e m a t i c e n e r g y  distribution,  N(E), of the  back-scattered  are  the  electrons  as  a  function  of  energy.  This  I  0  10  r —  100  1  1000  1  1  10,000 00,000  Electron energy (eV)  l i s u j e 2*1 S c h e m a t i c diagram c f t h e Bean free e l e c t r o n s i t m e t a l l i c s o l i d s as a f u n c t i o n o f t h e i r  path L(A) o f energy O V ) .  Ha"!* 2 x 2 S c h e s a t i c e n e r g y d i s t r i b u t i o n M(£) o f backscattered elcv e l e c t r o n s a s a f u n c t i o n o f t h e i r e n e r q y f c r a p r i m a r y bean energy .  16  " s e c o n d a r y e l e c t r o n d i s t r i b u t i o n " c a n be d i v i d e d i n t o ; t h r e e  main  regions: i ) t h e l a r g e peak a t electrons"  created  low  as  a  between  incident  solid.  I n each c o l l i s i o n  of  energies result  electrons  and  ii)  the  background mainly  in  process a r e l a t i v e l y s n a i l  the  amount  that c o n t r i b u t e to  the  energies;  of Auger e l e c t r o n s  energy l o s s e s t o core  features  due  (see S e c t i o n  2.4)  e l e c t r o n s , s i n g l e and  collective  e l e c t r o n e x c i t a t i o n s J[28J;  a small fraction  ( t y p i c a l l y a few %)  actually  0  interaction  with  also contains  the  insufficient  resolution  crystal  This  scattered"  typical  lattice.  of t h e order LEED  to observe such l o s s e s or gains  f a r a s LEED i s c o n c e r n e d , t h e w h o l e i s o f t e n l o o s e l y termed  peak".  phonon s c a t t e r i n g , t h a t i s an  vibrating  of  back-scattered  "guasi-elastically  i n t e r a c t i o n s produce energy changes energy  is  t o form t h e " e l a s t i c  e l e c t r o n s t h a t have undergone  In  bound  upon w h i c h a r e s u p e r i m p o s e d s m a l l  e l a s t i c a l l y a t energy E  The  collisions  medium e n e r g y r a n g e i s c h a r a c t e r i s e d b y a smooth  t o the emission  valence  peak  "secondary  energy i s t r a n s f e r r e d so t h a t a s i n g l e primary e l e c t r o n  l a r g e b r o a d peak a t low  iii)  of i n e l a s t i c  electrons  can c r e a t e a cascade of secondaries  and  contains  the " e l a s t i c  of  These 10  meV.  instruments  is  and h e n c e ,  as  o f t h e h i g h - e n e r g y peak peak".  t h e LEED e x p e r i m e n t t h e e l a s t i c a l l y s c a t t e r e d  electrons  17  are f i l t e r e d and, in  out of the general  usually, later  distribution  d i s p l a y e d on a f l u o r e s c e n t s c r e e n -  sections  scattered  secondary e l e c t r o n  of  this  electrons  chapter  behave  how  He s h a l l s e e  these  spatially  elastically  and  their  energy  dependence-,  2. 1 (b)  surface structure  The  classifications  r e g i o n of an o r d e r e d  dimensional  symmetry p a r a l l e l  normal t o i t diperiodic  As with  surface  stuctures  surface i s given simply parallel Surfaces crystal  may  are  structures  can  vectors s  and s  form  a  be t  usually  named  classified into certain the  symmetry  of  the i n a  of the bulk etc-  Their  d e s c r i b e d i n t e r m s o f a u n i t mesh w i t h u n i t  lying  i n the surface plane.  h«,k«  f  the  a f t e r the planes  a r e p a r a l l e l e . g . ( 1 0 0 ) , J110)  h's + k » s ^  Bravais  by  perfect  by t h a t o f t h e p e r f e c t b u l k c r y s t a l  net.  In  terms " l a t t i c e " and " c e l l " replaced  be  two-  periodicity  structures,  substances  w h i c h a r e c o n n e c t e d by t r a n s l a t i o n  T =  crystal  has  t o t h e s u r f a c e under c o n s i d e r a t i o n .  t o which they  (  LEED  t o t h e s u r f a c e b u t no  triperiodic  l a t t i c e t y p e s ; f o r many p u r e  plane  s u r f a c e probed by  terms  A l l the  points  vectors  = integers  (2.1)  two-dimensional c r y s t a l l o g r a p h y the  of  triperiodic  crystallography  " n e t " and "mesh" r e s p e c t i v e l y -  Bravais l a t t i c e s of triperiodic  are  The 14  c r y s t a l l o g r a p h y a r e reduced t o 5  nets f o r d i p e r i o d i c surface structures.  These  five  types  of  18  net,  as r e p r e s e n t e d  cubic  (FCC)  Fig.  and  m o d e l s c f some s u r f a c e s o f  body-centred cubic  {BCC}  metals,  face-centered are  shown  be  Tables  of  various conventions  f o u n d i n an  a r t i c l e by  i n surface crystallography  Hood .£29. J and  f o r X—ray C r y s t a l l o g r a p h y  suffices  £ 30J.  i n the I n t e r n a t i o n a l  For  cur  purposes  An  atom i n one  by  a v e c t o r c;  interlayer  l a y e r i s r e l a t e d t o an each  layer  d i s t a n c e d.  The  e l e c t r o n s r e l a t i v e t o the and  0  ;  the  is  between the beam, and  separated  surface i s described  by  two  the a z i m u t h a l a n g l e ,  plane c o n t a i n i n g the  next  by  an  F i g . 2.4  surface  normal  c l e a r s up any  angles, the  inward-  i s the and  &•  angle  incident  ambiguities.  the r e c i p r o c a l net  Another those  as  p o l a r a n g l e tV i s between t h e beam and  the x - a x i s .  surface.  i d e n t i c a l atom i n t h e  regarded  be  o r i e n t a t i o n o f t h e i n c i d e n t beam o f  p o i n t i n g s u r f a c e n o r m a l and  2.1(c)  i t  t o o b s e r v e t h a t i n t h e b u l k , c r y s t a l s t r u c t u r e s can  b u i l t up f r o m i d e n t i c a l l a y e r s o f atoms p a r a l l e l t o t h e  The  in  2.3. Details  can  by  type  o f B r a v a i s n e t can  shown i n F i g . 2.3 reciprocal  v e c t o r s s-  and  net  ; these  are  corresponding  be c o n s t r u c t e d called to  a  f o r each  "reciprocal r e a l .: n e t  g. = h s f + k s *  nets".  defined  s ^ i s (2.2)  of  by  (a)  (b)  (c)  ^  o  o  IlS3I§ 2 3 I x a m p l e s c f t h e 5 d i p e r i o d i c n e t s a s r e p r e s e n t e d bv a o d e l s o f s u r f a c e s o f f a c e - c e n t r e d c u b i c (FCC) and tcdy-centred cubic (ECC) m e t a l s ; sides ( s h o r t a x i s ) and a ^ , i n t e r n a l an olec<: <a j s q u a r e a,« a 2 ' * = 90°, e . q . FCC<100) BCC ( 1 0 0 ) ; (t) p r i m i t i v e r e c t a c q u l a r a «* a * = 90°, e.q. PCC(110) BCC (2 1 1 ) ; (c) centred rectanqular a * a , * = 90°, e . q , FCC (211) BCC (110) ; (d) bexaqcnal a * a ,o<= 600, e . q . I C C ( 1 1 1 ) (e) oblique a a , 900, e.q. fCC(321) X  l #  x  x  z  direction of incident beam  f i f l S I S 2j.H A D g l e c o n v e n t i o n s cn a s u r f a c e  f o r i n c i d e n c e o f an  electron  beaic  20  w i t h • s- = 2 IT ( s ^ x z ) / (s  .s ^ x z )  (  |2-3) and  s ^ = 2 TT ( s  x z J/js^.sy x z )  (  where z i s a u n i t v e c t o r p e r p e n d i c u l a r t o s- a n d s ^ , a s shown i n fig-  2-5-  The r e c i p r o c a l n e t s c o r r e s p o n d i n g  to  the  real  nets  shown i n F i g - 2-4 a r e g i v e n i n F i g . 2-6At t h i s stage construction has  but  the r e c i p r o c a l net  appears  Formation  is,  incident of course,  carefully  abstract  experiments.  Of The D i f f r a c t i o n P a t t e r n -  we s h a l l c o n s i d e r beam  an  we s h a l l s e e i n t h e f o l l o w i n g s e c t i o n t h a t i t  a v e r y d i r e c t i n t e r p r e t a t i o n i n LEED  2.2  as  a  mono-energetic,  on a p e r f e c t l y a  prepared  collimated  clean well-ordered  theoretical  abstraction  as  electron  surface. even  the  This most  s u r f a c e h a s a d e g r e e o f r o u g h n e s s t h a t c a n be  s e e n on e l e c t r o n m i c r o g r a p h s .  However, b e c a u s e o f l i m i t s on t h e  c o l l i m a t i o n a c h i e v a b l e i n low energy e l e c t r o n guns, the i n c i d e n t beam  i s coherent  only  over r e s t r i c t e d areas  {of t h e o r d e r o f  o  1 0 0 A ) , and t h e r e f o r e LEED i s s e n s i t i v e 2  ever d i s t a n c e s o f t h i s Cu(11l) our  magnitude.  to  atomic  order  only  A t y p i c a l LEED p a t t e r n f r o m a  s u r f a c e i s shown i n F i g . , 2.7 £a). , interest • w i l l  centre  on  the  elastically  scattered  e l e c t r o n s t h a t p r o d u c e most o f t h e s t r u c t u r e i n t h e  diffraction  pattern.  Schrbdinger  Their  behaviour  e g a a t i o n o f the form  can  ( i n atomic  be  d e s c r i b e d by a  units)  o  l A s ^ f e 2x5 A (dark~circles) ciicles).  two-diaensional real net, described and i t s a s s o c i a t e d r e c i p r o c a l n e t £*,  by s, , s , s* (oper t  l i f l u r e 2±§. O n i t a e s h s o f t h e c o r r e s p o n d i n g r e a l and t w o - d i m e n s i o n a l n e t s a s i n F i g u r e 2.3.  reciprocal  23  - V 2 V ^(r) 2  Far  • V(r)^Cr)  = E^{r>  (2.4)  from t h e c r y s t a l t h e e f f e c t o f t h e c r y s t a l p o t e n t i a l , V ( r ) ,  c a n be n e g l e c t e d a n d t h e e f f e c t o f t h e i n t e r a c t i o n w i l l b e shown by t h e c h a n g e i n t h e w a v e - v e c t o r o f t h e p l a n e ^ w a v e  = exp ( i k . r )  before  elastic  scattering  i n the surface  diffracted and  (2.5)  and a f t e r d i f f r a c t i o n .  For atoms  eigenstates  electrons  by  region,  the diperiodic  arrangement o f  t h e wave-vectors  k*  a r e d e t e r m i n e d by c o n s e r v a t i o n  of the of energy  momentum p a r a l l e l t o t h e s u r f a c e f 1 2 J  E(k«)  before  (unprimed)  = E(k)  and a f t e r  (primed) d i f f r a c t i o n  = JS|,  with the r e c i p r o c a l  net  {2.6)  +  <3<hk)  (2.7)  vector gjhk) discussed  i n Section  2. 1 (c) a s qjhk) = h s * + k s * Physically of  t h e exact  series  of  then,  thed i f f r a c t e d aavefield  scattering  discrete  (2.8)  beams  mechanisms each  with  has,  involved, a  independent  t h e form of a  different  parallel  24  2*1 (a) P h o t o g r a p h o f t h e LEED p a t t e r n f r c i a C u ( 1 1 1 ) s u r f a c e a t (a) n o r a a l i n c i d e n c e and 90 eV beam e n e r g y (b) 0 = 12°, ^=6° a t UHeV bea» e n e r g y , (c) and (d) l a b e l l i n g c f the diffzacticc spcts.  component  of  momentum  translational  ( k | + a.) ;  this  (  i s  determined  symmetry o f t h e r e g i o n t r a v e l l e d  by t h e  by t h e  scattered  electrons. The the  directions  the d i f f r a c t e d  This  i sillustrated  E and k |, t h e d i f f r a c t i o n (  For c e r t a i n  values  evanescent, solid.  or  i n F i q . 2.8.  pattern  surface  screen  waves,  the  which  a beam w i t h  parallel  at  being  labelling  used  to  label  scheme a p p r o p r i a t e  F i g . 2-7 {a) i s shown a s F i g . Thus interacted called easily  the  {00)  beam  specularly  recognised  as l o n g a s t h e  i s  t h e beams  The s p o t  to  indices  diffracted  the  Cu(111)  produced  made  without  reflected  beams. LEED  increased,  move  increases, the angle of  the  {2.7-  The beam pattern  of  up o f e l e c t r o n s w h i c h have momentum beam.  transfer  in  and i s  T h i s s p e c u l a r beam i s  as i t s d i r e c t i o n remains constant  electrons  of  2.7(b).  field-free  d i r e c t i o n o f t h e i n c i d e n t beam d o e s n o t c h a n g e . energy  spherical  (2.9)  o r beam, t h e  the  is  with the surface  the  a  i t s focus  of £{hk).  to  component o f momentum  r e f e r r e d t o a s t h e (hk) s p o t  2.9)  jg(hk).  e s c a p e from t h e on  3 (hk) = h s ^ + k s  is  by  by  values  and c o r r e s p o n d s  cannot  crystal  a p p e a r as s p o t s , o n e f o r e a c h v a l u e  hence  For qiven  the diffracted electrons with  and  i s determined  o f jg{hk), Jc«^ i s i m a g i n a r y  Ey c o l l e c t i n g  fluorescent  by  beams a r e d e t e r m i n e d by  w a v e - v e c t o r o f t h e d i f f r a c t e d e l e c t r o n s , k»,  k , q and E. of  of  as E changes  space  and  the  As t h e i n c i d e n t  p e r p e n d i c u l a r c o m p o n e n t of momentum  diffraction  decreases  and  the  beams  2t  f i g u r e 2^8 the allowed  The d i r e c t i o n of a d i f f r a c t e d v a l u e s o f k' and F.  crowd i n t o w a r d s t h e s p e c u l a r The screet  diffraction  pattern  net  of  displayed  the surface  *esh c f t h a t n e t a r e e a s i l y •esh  cf the r e a l  (2.3)  :  s = (  a  on t h e u s u a l direct  picture  and hence t h e s i d e s  determined, s*  net i s then obtained  and  fluorescent  =•  s*.  S|  X  Z  the  The  unit  by i n v e r s i o n o f e q u a t i o n s  2TT( s * x f ) / ( § * . s * x 2 )  2TT|  cf  cf the unit  (2.10) §  oy  beam.  c f a LEED a p p a r a t u s p r o v i d e s  reciprocal  team i s d e t e r n i ^ e d  )/( £ * . S * 1  2 )  27  Although designations  equation  of diffracted  or c o n t a i n a d s o r b e d diffracted  (2-9)  beams  gives  the  most  beams, f o r s u r f a c e s  molecules i ti s often a r e indexed  with  that  substrate  vectors  of  respect  the substrate  i s theinitially  (b  (  that  the  to the reciprocal j,  and b ) , z  known s t r u c t u r e . p  reconstruct  convenient  to  lattice  fundamental  This  since  the  relation i s  p 12.  II  (2. 11) P Zl  or The obtained with  matrix  P  (2. 12)  = Pb  for a  particular  structure  d i r e c t l y b y c o m p a r i n g t h e LEED p a t t e r n o f  that calculated  equation  s  P 21.  (2.12)  f o r thesubstrate.  Matrix  those  t h e most g e n e r a l the more  surface  manipulation of  12.13)  w h i c h d e f i n e s t h e r e l a t i o n o f t h e mesh with  the  yields  s = P-*b  surface  c a n o f t e n be  of t h e s u b s t r a t e .  way o f e x p r e s s i n q  vectors  of  The m a t r i x  this relation  a n g l e b e t w e e n s- a n d s ^ i s e q u a l  the P  -1  actual  provides  [32 1, b u t  when  t o t h a t b e t w e e n b^ a n d b  c o m p a c t d e s i q n a t i c n i s o f t e n u s e d 129J.  i  a  Then t h e r e l a t i o n  b e t w e e n s a n d b c a n be s p e c i f i e d by  (2. 14)  28  in  terms of the l e n g t h s  rotation  (^)  b e t w e e n s and t ( e m i t t e d  This notation the  simplest  termination surface in  e.g.  case,  the  of the bulk  are  best i l l u s t r a t e d  surface  structure  structure along  a  £29], i n d i c a t i n g  identical  Eh (100} - {1 x1> .  especially  (adsorbates)  to  In  those  more  will  differ  so  f o r the  on  cverlayer stuctures  and t h e a n g l e  of  i n qeneral  In  by t h e  plane.  The  r e f e r r e d t o a s (1x1) the  surface  the underlying cases  deposition  will  given  given  from t h o s e o f b u l k  substrate  by e x a m p l e s . is  that  general  the  of  when & = 0) .  u n i t mesh i n s u c h c a s e s i s b r i e f l y  periodicities is  i s probably  t h e Wood c o n v e n t i o n  vectors  o f t h e u n i t mesh s i d e s  net  substrate  the  surface  substrates.  of  This  foreign  material.  (Such  atoms adsorbed  have a p e r i o d i c i t y d i f f e r e n t  from t h a t o f t h e s u b s t r a t e ) . A n o t h e r c a s e more r e l e v a n t reconstructions  of  the  m a t e r i a l s such as o c c u r £ 14J.  The  (100)  diffraction pattern designated (5x1)  face  thesis  regions  of  semi-conductors  of  gold  £33 1  and  and  the clean  metals  f o r example  yields a  i n f i g - 2.9(a).  This i s  i s associated  to that of the bulk substrate-  hexagonal arrangement o f s u r f a c e  gold  with  a  A model  atoms on t h e  (100) s u b s t r a t e h a s been p r o p o s e d t o a c c o u n t f o r t h i s  observed  in  this  patterns, as i n F i q . 2.9(a), correspond  chemically  many  p a t t e r n £ 3 3 ] a s shown i n F i g . 2.9(b) and ( c ) . pattern  concerns  for  a s a (5x1) L I E D p a t t e r n  an  underlying  surface  this  shown s c h e m a t i c a l l y  u n i t mesh r e l a t i v e  assuming  to  to  the existence  case  is  a  The  actual  superposition  r e l a t e d by a 90° o f two e q u i v a l e n t  of  rotation.  LEED two These  o r i e n t a t i o n s , or  d o m a i n s , r e l a t e d b y a 90° r o t a t i o n o f t h e s u r f a c e  layer  on  the  29  a)  b)  c)  liSUIi a) S c h e m a t i c d i f f r a c t i o n p a t t e r n f r o m one d c n a i n o f Au ( 1 C 0 ) - ( 5 X 1 ) reconstructed surface; b) H o d e l s t r u c t u r e of c o i n c i d e n t a l h e x a g o n a l g e l d l a y e r s u p e r i m p o s e d cn t h e u n d e r l y i n g (10C) s u b s t r a t e , c ) , ( a f t e r P a l i b e r g and B h c d i n F33 1 ) . underlying  substrate  i n t e n s i t i e s Of LEEE Beams The yield  the s i z e  further mesh. LEED  p o s i t i o n s of the d i f f r a c t i o n and symmetry o f t h e  information  cn  spots i n the H I D  surface  unit  mesh  but  no  the l o c a t i o n s o f the a t c i s i n the u n i t  This information i s contained  i n the i n t e n s i t i e s  cf  the  ueais I n t e n s i t i e s a r e a o s t u s u a l l y measured a t c o n s t a n t  and  pattern  azimuthal  a n g l e , ^b, see F i g . 2.4, a s a f u n c t i o n o f e n e r g y .  Flcts of intensity profiles",  are  polar,  aqainst  the  enezqy,  usual  form  1(E) curves of data  d i a g r a m s " , I fc^) f o r c o n s t  ^- and  curves",  I  E,  <f? and  "intensity  presentation  "rotation  f o r constant  or  I,  remain  and as  althouqh "rocxinq neqlected  30  alternatives. specular 8 =  30  F i q . 2.10  shows  beams d i f f r a c t e d  [34]  typical  .  s t r u c t u r e e x h i b i t i n g a number  maxima and m i n i m a a s t h e e n e r g y i s v a r i e d .  Section 2.1(a), electron scattering.  We  reflectivities  understand  such  I(E) curves.  success t o i n t e r p r e t X-ray  by  This  diffraction  h a s been used  to with  However,  e l e c t r o n s c a t t e r i n g c r o s s - s e c t i o n s a r e much l a r q e r ,  much more t h a n a r o u g h g u i d e f o r LEED  kinematical  considered  elastic  (or einqle-  intensities.  6  In  for  cross-sections,  model  a s much a s 1 0 , and s o we c a n n o t e x p e c t  2.3(a)  low  c a n a t t e m p t t o use t h e k i n e m a t i c a l  model, v a l i d f o r l o w s c a t t e r i n g  energy  A l s o , as noted i n  are  scattering)  low  f o r the  f r o m C u ( 1 0 0 ) and N i ( 1 0 0 ) s u r f a c e s f o r  Such c u r v e s show c o n s i d e r a b l e of  1(E) c u r v e s  the  theory  to  be  wave  is  intensities.  theory  kinematical  to  this  produce  theory scattered  m u l t i p l e - s c a t t e r i n g are ignored.  only  the  waves  incident  whilst  double  and  F o r an i n c i d e n t p l a n e wave  ( 2 . 15)  the  kinematical  expression  wave-vector k ) s c a t t e r e d f  by  vector  f o r the t o t a l  t o the point of  wave  (corresponding  observation  r ) b y an a s s e m b l y o f s c a t t e r e r s i s  exp[ i k i r - r - 1 ]/i£-r- | e x p (i£.r: ) ( 2 . 16)  to  (denoted  31  I l S s I s JLtlfi c u r v e s f o r t h e s p e c u l a r beaa f r o r Mi(10C) and Cu(100), ©=3°. The tars denote k i n e a a t i c a l Braqq c o n d i t i o n s ( a f t e r A n d e r s o n and K a s e a o T3U1).  32  where  t h e s u m m a t i o n i s o y e r t h e s e t o f s p h e r i c a l waves  at the s c a t t e r i n g c e n t r e s  r-.  The  factor  f'  r  scattering  factor  for  the  atom  through  k_=>k^) .  term  incident  final  j  If  atomic  the  denotes  f o r e l a s t i c s c a t t e r i n g of angle  ©  the  waves a t t h e s c a t t e r i n g atoms.  value i s f i x e d  the  °  e l e c t r o n s of energy E The  is  produced  (as  r  phase A  0  defined  shifts  by  f o r the  i s a constant  whose  by t h e d e n s i t y o f atoms i n t h e i n c i d e n t beam.  the s c a t t e r e d e l e c t r o n s are detected  at a long  distance  f r o m t h e s c a t t e r i n g r e g i o n and i f t h i s r e q i o n i s s m a l l , so ir-r•| effect can  that  c a n be a p p r o x i m a t e d by r f o r t h e p u r p o s e o f a s s e s s i n g o f d i s t a n c e on s c a t t e r e d a m p l i t u d e ,  be r e - e x p r e s s e d  In general represented  by  wave-function  probability 4*  that  an  of s o l i d  angle  electron  i s t o be f o u n d i n a volume  e l e m e n t dT; t h e r e f o r e t h e nunsber o f e l e c t r o n s r e c e i v e d t i n e by a d e t e c t o r  ( 2 . 16)  as  dT g i v e s t h e a  then eguation  the  in  unit  djv. i s  dn = u A* JB* J a j l  (2.18)  where u i s t h e v e l o c i t y o f t h e e l e c t r o n s and B i s t h e s c a t t e r i n g amplitude  B = X ^ ' s f  E  e  }  exp(is.rj)  (2.19)  33  for the c o l l e c t i o n  o f a t o m i c s c a t t e r e r s and  S = k -k  i s the s c a t t e r i n g vector. area perpendicular  The number o f e l e c t r o n s  on i n t r o d u c i n g  c  = u A, 2  (2.21)  = I  0  ier  (2.22)  t h a t d<r- i s t h e v a l u e o f dn when I  differential scattering  = fB |  where I ( S )  corresponds to the f l u x ,  scattered  per  The  unit  solid  One scattering  a n g l e f r o m an i n c i d e n t  vector  S,  beam o f u n i t  s c a t t e r i n g of  a  plane  wave  basic  ty  o f s c a t t e r e r s whose d i m e n s i o n s a r e s m a l l c o m p a r e d  distance  scattering  for scattering  (2.23) and (2.19) r e p r e s e n t t h e g e n e r a l  equations f o r kinematical  the  (2.23)  2  area.  equations  assembly  i s u n i t y , we o b t a i n t h e  D  cross-section  d<r/djv = i ( j )  f l u x per unit  unit  the r e l a t i o n  dn  such  crossing  t o the d i r e c t i o n of k per u n i t time i s  I  and,  {2.20)  of observation  of the s c a t t e r e d e l e c t r o n  frcm  any with the  region. of  the  interesting  being confined  conseguences  by s t r o n g  inelastic  of  the  elastic  s c a t t e r i n g to  the  34  vicinity  of  the  surface  i s  p e r i o d i c i t y of the c r y s t a l electron. the  of  dinensional  limit  scattering,  and  inelastic  i s not  We c a n p r o c e e d  strength  the  that  v i a two l i m i t i n g  to  net defined  the  very  The  are s i t u a t e d  stronq to  two-  inelastic very  weak  s  (  and  a  two-  such that net  at p o i n t s r  |  + n s ^  (2.24)  c a s e t h e a t o m i c s c a t t e r i n g f a c t o r s f ^ c a n be r e p l a c e d  s c a t t e r i n g f a c t o r o f t h e u n i t mesh,  F  (structure  w h i c h d e p e n d s on t h e f ^ and t h e a t o m i c p o s i t i o n s mesh.  pure  t o f o l l o w ; we c o n s i d e r  by mesh v e c t o r s  r: = ms  this  scattered  scattering.  dimensional  in  a  c a s e s , d e p e n d i n q upon  three-dimensional  The f o r m e r i s r a t h e r e a s i e r  points  by  scattering.  corresponds pure  three-dimensional  experienced  inelastic  the  the f u l l  The s c a t t e r e d  by  factor) ,  within the unit  a m p l i t u d e becomes  B = F(k^k ) 2 5  e x  P  (i-S-tf)  (2.25)  i and  the d i f f e r e n t i a l cross-section i s  dff?d/i-=  IF(k-^k  ) J2 5 " e x p {iS(£.-r ) 1 ;  = ifa-^JJ )l 5  The scattering  interference vector  2  G(S)  function  (2.26) G (J3)  S s a t i f i e s t h e Laue  has  maxima  conditions  when  the  35  S. s  (  for  = 2irh  i n t e g r a l h and k-  and  S.s  = 2 IT k  z  (2-27)  These c o n d i t i o n s c a n be r e w r i t t e n as  S = <i(hk)  where  the  cj{hk)  conditions equation  are  defined  (2-28)  by  equation  (2.8);  t i e Laue"  are equivalent to the c o n d i t i o n expressed  earlier in  (2.7) a s  JS], " JS„ = S i n * )  That i s , d i f f r a c t e d determined  by  waves  equation  (2.29)  occur (2.29)  only to  in  certain  produce  the  directions LEED p a t t e r n  d e s c r i b e d i n S e c t i o n 2.2. The i n t e r f e r e n c e f u n c t i o n does n o t t e l l u s  anythinq  the energy dependence of the i n t e n s i t y o f a s p o t . factor  i s however e n e r g y - d e p e n d e n t t h r o u g h  of the a t o m i c and  hence  energy,  the  an  approximation In  scattering factors f••  1(E)  curve,  the e n e r g y dependence  The f o r m o f t h i s  v a r i a t i o n of a d i f f r a c t i o n in  the  two-dimensional  the pure t h r e e - d i m e n s i o n a l k i n e m a t i c l i m i t  predominantly  The s t r u c t u r e  variation spot  with  kinematical  i s shown i n F i g . 2 . 1 1 ( a ) t o be m o n o t o n i c .  the s u r f a c e can  crystal.  intensity  about  be the  ignored full  and  the  electron  three-dimensional  Shereas i n the two-dimensional  the e f f e c t of will  move  in  p o t e n t i a l of the bulk  limit  the perpendicular  component o f t h e w a v e - v e c t o r k , was f r e e t o assume  a  continuum  36  1(E)  1(E)  E(eV)  E(eV)  a)  b)  l i s u r e 2^.11 I n t e n s i t y o f a d i f f r a c t e d LEED t e a s a s a f u n c t i o n o f energy i n a) the pure t w c - d i n e n s i o n a l l i m i t ar.d t) t h e pure t h r e e - d i m e n s i o n a l l i m i t ( a f t e r S c E c r j a i a r d F a r r e l l [7"]). cf  values  (that  is  only k  three-din>ensiona 1 l i s i i t  i s a qcod  i t i s ccnstraired  quantum n u a f c e r ) , i t , t h e to otly certain  due t o t h e p e r i o d i c i t y i n t h e p e r p e n d i c u l a r  values  direction  (2.30)  where a, i s a r e c i p r o c a l surface. diffracted equations  Hence  in  intensity (2.29)  cf and  ^reducing a v a r i a t i o n twc e q u a t i o n s  lattice  vector  perpendicular  the  pure  three-diiensional  a  beam  will  (2.30)  are  be  zero  lisit  except  sinultanecusly  irto  k» = k •fl( h k l )  (2.31)  the the where  satisfied,  o f t h e f o r * shown i n F i q . 2.11(b) .  c a n be c o i t i n e d  tc  These  37  where j ( h k l ) i s a r e c i p r o c a l l a t t i c e dimensional  2.3(h)  vector of the  c h a r a c t e r i s t i c s o f 1(E) F i g . 2.10  curves  we  find  t h a t r e a l 1(E)  c h a r a c t e r i s t i c s i n t e r m e d i a t e between t h e  two  c u r v e s show  extremes  t w o - d i m e n s i o n a l and t h e p u r e t h r e e - d i o e n s i o n a l  linits.  The c u r v e s a r e n o t m o n o t o n i c  Eiinima;  however,  equation  (2-31), at  F i g . 2.10  mark  there  are  least  the  more  at  positions  equation  (2.31) i s  general,  maxima f a l l c l o s e  can  seen.  be  three-  lattice.  Re-examining  pure  hulk  satisfied  kinematical  do e x h i b i t  lower  energies.  of  " p r i m a r y Bragg  for  the  maxima  and  peaks than a r e p r e d i c t e d  various  The  values  bars  peaks" of  by on  where  1.  t o t h e s e v a l u e s but s u b s i d i a r y  Such e x t r a s t r u c t u r e  nultiple-scatterinq  and  of  In  naxiaia  must be a s s o c i a t e d w i t h t h e  events neglected i n the  simple  kinematical  treatment. Three  energy  according to structure fig.  the  and  regions  are often i d e n t i f i e d  magnitude  peak  widths  of  beam  i n 1(E)  intensities,  [35,12],  curves  degree  of  These a r e , r e f e r r i n g  to  2. 10: (i)  the low-enerqy peaks  are  r e g i o n , t y p i c a l l y below  numerous and  and h i g h d i f f r a c t e d t h e i n c i d e n t beam (ii)  the  intensities  with widths of (sometimes  range  (20-150eV) h a s  peaks of lower i n t e n s i t y .  s i m p l e r though  >10%  where 1-2eV of  intensity);  intermediate-energy  (up t o 10eV)  narrow  20eV,  there  are  still  more  wider  Structure i s maxima  than  predicted (iii)  the  by e q u a t i o n  hiqh-energy  wider  (2.31);  reqion,  usually  (20-30eV) p e a k s o f s t i l l  positions  that  are  broadly  a b o v e 150eV,  lower  has  intensity  consistent  with  in  equation  (2.31) . The not  kinematical  provide  information  peak w i d t h s , must the  introduced  hiqh  inelastic  In  increasinq  presented e a r l i e r ,  peak w i d t h s .  i n t o the  model  scatterinq  diffracted  temperature f 36],  Consequently,  order  form  In  order  by  to account  inelastic  (see Ch.  3) .  for  scatterinq  I t i s precisely  cross-sections  for  low-enerqy  attempts  team  intensities  often  have  in  an  decrease  exponential  been made, w i t h i n t h e  to  extract  atoms i.7]. variation  (e. q. ±20X)  d i r e c t i o n of  the  include  inelastic  double  diffraction  Debye  temperatures  f r o m beam t o beam and  I (S)  kinematical  theory,  s c a t t e r i n q and  with  in  surface  show  some  the enerqy  and  events curves  surface  £37],  (111)  essentially  k i n e m a t i c a l o v e r most o f  The  more  successful  i n Chapter  3.  is  successfully. of  even  modified  to  when  t e m p e r a t u r e e f f e c t s , and  r u l e i s the  much  factors  t h e i n c i d e n t beam.  Generally,  experimental  manner.  mean-square v i b r a t i o n a l a m p l i t u d e s o f  However, the d e r i v e d  with  kinematical  to r e l a t e such dependencies to Debye-Waller  discussed  does  t h a t make them s u r f a c e s e n s i t i v e . general,  theory,  on  i n the  removal of e l e c t r o n f l u x  be  electrons  theory,  xenon, f o r  not  able An  which  to  reproduce  exception 1(E)  even  tc  this  curves  are  t h e LEED e n e r q y r a n q e ) 3 8 ] .  multiple-scatterinq  theories  are  39  2. .4  Auqjer E l e c t r o n S p e c t r o s c o p y Seme o f t h e e l e c t r o n s  slowly  varying  observed  background  in  secondary e l e c t r o n  distribution  electrons,  Pierre  after  H i l s o n c l o u d chamber origin  £39].  in  These  (AES) as  the  snail  features  medium-energy r a n q e o f  ( S e c t i o n 2. 1) a r e  Auqer who 1925  and  first  saw  called  their  correctly  be  monitored  experiments  under  are  the  carried  sane  out.  conditions Several  a p p l i c a t i o n s h a v e been p u b l i s h e d e.g. The  Auger  2.12  solid. the  u s e f u l i n LEED  Initially,  an  electon  beam,  e l e c t r o n from  either  level  of  more  atoms o r  F i g . 2.12(b).  distinguished  such  If  probable  from  electron  the  level The  is  electron.  ionised For  by  elements  Li+  ion  i s able to  in drop  surplus energy  elected  the o r i g i n a l  than X-ray  is  in the  peaks  as  an  ionisation 2keV  Auger  i s from  a  then  Auger  production [45].  Auger  medium-energy  distribution  energy-loss  of  (X-ray f l u o r e s c e n c e ) , or i s  that  e l e c t r o n s a p p e a r a s s m a l l peaks secondary  core  1-10keV.  a h i g h e r energy  electron  F i g . 2.12(c).  is  of  of t h e p r o c e s s f o r a  with a b i n d i n g energy of l e s s than about  emission  the  usually  a s an X - r a y p h o t o n  available to a third electron,  LEED  £40-44,10].  i o n i s a t i o n of a  helium, lithium  down t o t h e i n n e r v a c a n c y , released  surface  which  F i g . 2.12(a), a core e l e c t r o n i s  ether than hydrogen, solids,  as  reviews  shows a s c h e m a t i c r e p r e s e n t a t i o n  primary  their  e f f e c t i s a two-stage r a d i a t i o n l e s s t r a n s f e r  e n e r g y t o an e l e c t r o n f o l l o w i n g Fig.  the  Auger  explained  e l e c t r o n s are p a r t i c u l a r l y  a  tracks i n a  experiments a s they a l l o w the atomic c o m p o s i t i o n of the to  on  as  and their  are  range  of  readily  energies  are  lA-SUIf 2x12 Schematic representation cf the transition: (a) i o n i s a t i o n of a c o r e l e v e l , <b) c o r e h o l e , (c) e m i s s i o n o f t h e l u q e r e l e c t r o n .  VV fillinq  Auqer c f the  41  independent t o e.q.  o f t h e p r i m a r y team e n e r q y , w h e r e a s l o s s p e a k s ,  plasmon  excitation, shift  w i t h chanqes  in  the  due  incident  ream e n e r q y . Auqer  electrons  these symbols i n d i c a t e h o l e , and solids,  the  valence  labelled  band  X-ray  quantum numoers 1 a n d  i s d e n o t e d by t h e l e t t e r  notation  Subscripts are  would  ESCA  [47]  l e v e l s can energy  level  of i o n i s a t i o n  the  and  (  but t h i s  electron.  2  -  3  2  )  j. 46.]  or  simple fornula i s  to take i n t o account  the  t h e e x t r a e n e r q y needed  been m o d i f i e d by J e n k i n s and Chung  Auqer  i s approximately  s e c o n d e l e c t r o n f r o m an a l r e a d y i o n i s e d a t o m ,  E  the  (1=0,1=1/2), 2 o r 3  3  energies,  usinq  denote  he d e s i g n a t e d a s a n E ^ V V  E  the  the  be r e a d i l y e v a l u a t e d u s i n g X - r a y  inadequate i n that i t f a i l s degrees  to  For  to  With t h i s n o t a t i o n  k i n e t i c e n e r g y of t h a t e l e c t r o n  energy  assiqned  used  -j; thus 1 f o r s s t a t e s  * ^ V V The  final  V, b u t  K,L,H... a c c o r d i n q  (1=1,1=1/2,3/2) e t c -  e l e c t r o n o f F i q . 2.12 The  h o l e , the  where  which the e m i t t e d e l e c t r o n l e a v e s -  p r i n c i p a l quantum number-  p states  the i n i t i a l  beinq quasi-atomic i n nature, are  conventional  for  by t h e n o t a t i o n ABC,  respectively  the l e v e l from  inner levels, the  are  The  different  t o remove t h e formula  has  [48]  (Z) = E ( Z ) - 1 / 2 [ E ( Z ) + E ^(Z + 1) ] - 1 / 2 [ E ( Z ) •E (Z+1) ] (  i  3  ;?  (2.33)  where  Z  i s t h e a t o m i c number c f t h e c h e m i c a l s p e c i e s  F o r atoms t h i s f o r m u l a h a s a t y p i c a l a c c u r a c y o f a b o u t  involved. 5eV.  42  The in  d i s c r e t e l e v e l s i n atcms are r e p l a c e d  solids.  The  quasi-atomic  inner  levels  s h i f t e d r e l a t i v e t o t h e f r e e atoms and the  valence  band  by  the  energy  i n s o l i d s nay  use  ability  of  i s s e n s i t i v e to chemical  for  environment.  atcms can and  aade.  be r e a d i l y f o u n d u s i n q  the  quantitative  now  on  c r o s s - s e c t i o n s but the  surface  therefore reguires  and  uniform  retarding  field  i n p u r i t i e s t o be d e t e c t e d  of  of  surface energies  n o t so  i s governed not  easily  only  the d i s t r i b u t i o n  independent c a l i b r a t i o n  analyser  type  Auqer  i n t o the c r y s t a l .  d i s t r i b u t i o n J. 51-52 J-  the  available.  a l s o by  e m p l o y i n g known g u a n t i t i e s o f d e p o s i t e d of  This  assessments are  i n t e n s i t y o f Auger e m i s s i o n  the elemental  difficult,  the i d e n t i t y  tabulated  representative spectra [50]  The  element  element.  i s g e n e r a l l y u n a m b i g u o u s and  Unfortunately,  be  in  While  q u a l i t a t i v e a n a l y s i s d e p e n d s o n l y on  t o a s s i q n peaks to a p a r t i c u l a r  assiqnment  1.4SJ  AES  be  d e n s i t y of s t a t e s  t h e c o m p l e t e a s s i q n m e n t of A u q e r t r a n s i t i o n s c a n the  oands  of  by the  Quantification  experiments,  m a t e r i a l and  usually  assumptions  Auger s p e c t r a c o l l e c t e d w i t h  b a s e d on LEED o p t i c s to approximately  (see Ch.  4)  a  allow  1% o f a m o n o l a y e r f o r  most e l e m e n t s . A typical  e x a m p l e o f an A u q e r  work i s shown i n F i g . 2. 13. 8h (110) to  surface  that  otherwise beam  T h i s shows an  from  and  the  present  Auger spectrum  i s h e a v i l y contaminated  a l e s s e r extent, carbon  presented  spectrum  phosphorus.  of  with sulphur, The  spectrum  a and is  i n t h e s e c o n d d e r i v a t i v e f o r m d N ( E ) / d E t o e n h a n c e tfce weak Auger f e a t u r e s and  current  of  about  10  was  microamps  taken at  with 1.5keV.  an  incident The  Auger  43  Rh(110)  1  100  1  1  200  1  1—  300  Energy (eV)  ZiSSLs. 2i.li Auger spectrum surface. Ep=1.5KeV, Ip=10  of a heavily fficrcamps.  contaminated  FM11  44  t r a n s i t i o n energy i s t r a d i t i o n a l l y e x c u r s i o n of the d e r i v a t i v e  peak  taken  150]-  as t h e maximum  neqative  CHAPTER 3  MULTIPLE-SCATTERING CALCULATIONS  lib  J.J  Parameters For  T h e o r i e s Of  In t h e l a s t c h a p t e r we  saw  LEED that i n t e n s i t i e s of  depend upon c h a r a c t e r i s t i c s o f t h e and  direction,  dynamics of the sinple  and  a l s o on  surface  kinematical  atoms.  theory  determine surface  slow  must  included  d e t a i l s are given  3. 1 fa)  geometry, s c a t t e r i n q power,  the  p r e d i c t 1(E)  t h a t any  theory  Such  include  are  called  important  electrons  from  solid,  such or  the  with  Fiq.  3. 1 t h e s o l i d  by  of  "dynamical"  features  that-  briefly;  full  of  involve  the of the  The  high the  the  incident remainder  various  inelastic  the  valence  potential tightly  113  excitation  backscattering  electrons  arises close  bound  1.  from to  the  core-state  "muffin-tin" approximation i s a  solid  that  accommodates  s c a t t e r i n g process.  i s modelled  of  the  plasmon  scattering involves  "ion-cores".  features  whereas  flux  particularly  regions  of  elastic  elastic  regions  c o n v e n i e n t model important  backscattered,  the  inelastic  interactions nucleus;  of  by P e n d r y A.12J.  processes,  such  the  used  primary object  i n such t h e o r i e s are c o n s i d e r e d  are e l a s t i c a l l y  scattering  of  be  any  scattering potential  removed  While  the  curves with  I n a t y p i c a l LEED e x p e r i m e n t , o n l y a b o u t 1% electrons  that  that i s to  are  more  and  multiple-scatterinq  theories  In t h i s s e c t i o n , the  be  enerqy  q e o m e t r i e s , which i s the  electrons.  theories.  i n c i d e n t beam, s u c h a s  M o r e o v e r , we a l s o saw  t h e e x p e r i m e n t s , must t h e r e f o r e the  beams  d i d not  r e a l m e a s u r e o f s u c c e s s and to  the  LEED  as  As  non-overlappinq  these  two  indicated in reqions  of  47  spherically solid  symmetric  with a constant The  potential potential  intersphere reqion  electrons  of  the  solid  inelastic scattering. treated an  in  and  on  occupied  t h e r e f o r e i s the  Inelastic  inelastic  in  by  region.  the  valence for  s c a t t e r i n q of a l l k i n d s c a n  be  the  scattering.  as  the  crystal  average  before  i t  w i t h e n e r g y E,  h/2ir=1).  In the r e g i o n  e x p [ - i (E—V ) t j .  I f we  e  the  intensity  exp (+2V jt) , as V ^ o  of c o n s t a n t  = Kc-  of  the  Hence a t t e n u a t i o n  the 1(E)  the  time-energy curves.  The  an  loses  imaginary  for  (for atomic this  Q  can  becomes  ccmponent  i V  <3.1)  wavefunction  decays with  t a k e n t o be  time  negative,  - V 2 T  be  simulated  peak w i d t h  as  and  * - > 3  by  adding  p o t e n t i a l , i v ^ , w h i c h can  uncertainty  an  units  2  o f t h e e l a s t i c a l l y s c a t t e r e d teams due  i n e l a s t i c s c a t t e r i n q can to  Q  i n vacuo  p o t e n t i a l V,  i s conventionally  6  V =  ccapcnent  V  o  v  then  as e x p ( - i E t )  allow  time  F o l l o w i n g P e n d r y [ 1 2 ] , we  d e f i n e t h e t e m p o r a l v a r i a t i o n of w a v e f u n c t i o n a m p l i t u d e electron  the  principal site  t e r m s of a l i f e t i m e , T , d e f i n e d  by  e a c h atom c f  i n the i n t e r s p h e r e  i s mainly  i n c i d e n t e l e c t r o n spends  energy  centred  principle,  from  be  an  imaginary  estimated,  peak  to  widths  satisfies  (3.3)  via in  Position  tb) Ii3U£§ 3.^.1 Muffin-tin potential ccrtcurs, (b) a l o n q XX'. Vc is p o t e n t ia1.  Energy ^  (a) the  in crcss-secticn as constant inteisphere  Energy Vacuum level  ^  E +4> c  E Fermi energy p  o Lowest level of conduction band l i f l u i g 3±2 Illustration of t h e r e l a t i o n s h i p between e n e r q i e s • e a s u r e d w i t h r e s p e c t t c t h e vacuum level and those measured w i t h r e s p e c t t o t h e l o w e s t l e v e l c f t h e c o n d u c t i o n band.  49  V ^  is  In  this  in  an  typically work, V ^  was  Q  1{E)  a b o u t -5eV  and  estimated  weakly  from  a primary  curve according to equation  energy-dependence o f the  (3.3)  Braqq and  fill.  type  was  peak  allowed  an  form  -if<E>  V = where  energy-dependent  (3.4)  JJ(E)=©cE*'3  (3.5)  a c c o r d i n g t o t h e e m p i r i c a l r e l a t i o n s h i p e s t a b l i s h e d by Demuth e t al i11J. The  For copper  <?C  was  s e t t o 0.89  f o r the i n c r e a s e i n  electron entering the c r y s t a l . potential.  Typical  are,  in  dependence  In  appears,  energy  practice,  V  energy  ¥  o r  is  least,  for  was  experienced  to  i s approximated  by  estimated  visual  e x p e r i m e n t a l 1(E)  or curves  set i n i t i a l l y  be  by  as t h e  t o -20  eV  This and  the  a s shown i n F i g -  3.2.  a  sum  is  of  priori  and  then  comparison  ; changing  in  an  the i n n e r  slight,  numerical  to a r i g i d s h i f t  T h i s t o p i c i s e x p l o r e d i n more d e t a i l o r  i n equation  o r  energy-dependent.  experience,  usually  good a p p r o x i m a t i o n ,  work V  V  f o r rhodium.  This i s usually c a l l e d  t h e work f u n c t i o n ^ ,  refined  c a l c u l a t e d and a  Often  tfr  at  from  E^- and  empirically  to  1.12  v a l u e s f o r t h i s q u a n t i t y a r e -10  principle  usually ignored. Fermi  to  r e a l p a r t of the i n t e r s p h e r e p o t e n t i a l ,  (3.1), accounts  and  and  V  of>  amounts,  i n the energy Chapter  a t -9.5eV f o r c o p p e r  5.  [ 65 ] and  of  scale.  In  this  -12. OeV  r h o d i u m £68,69j. The  p a r t of t h e p o t e n t i a l t h a t g i v e s the b a c k s c a t t e r i n g i n  LEED i s t h e s p h e r i c a l l y - s y m m e t r i c p o t e n t i a l w i t h i n tins;  the i o n - c o r e p o t e n t i a l .  the  Euffin-  V a r i o u s methods a r e a v a i l a b l e  to  50  construct used  such p o t e n t i a l s .  either  full  In general,  atomic  charge  Hattbeis [53].  distributions,  for for  linear  structure in  the  superposition  originally  £54] h a s s u g g e s t e d t h a t  superposition,  with  the  s u g g e s t e d by  calculations,  simple  muffin-  the R a p p r o x i m a t i o n of Slater  t h e exchange p o t e n t i a l £55], p r o v i d e s a LEED  potentials or,  by a l i n e a r  as  have  Recently, a study of d i f f e r e n t p r e s c r i p t i o n s f o r  ion-core potentials tin  calculations  s e l f - c o n s i s t e n t band s t r u c t u r e  more s i m p l y , t h e p o t e n t i a l g e n e r a t e d of  LEED  and t h a t  c a l c u l a t i o n s do n o t l e a d  suitable  the f u l l to  potential  self-consistent  significant  degree o f agreement o f c a l c u l a t i o n s  with  band  improvements  experiment ( i n  that instance) . In the  initial  stages  of  this  work  p o t e n t i a l f o r r h o d i u m was n o t a v a i l a n l e . on  generating ion-core potentials  densities  method.  In  method was u s e d t h a t the  a  band  structure  Hence i n t e r e s t  by t h e s u p e r p o s i t i o n  co-operation  with  e m p l o y e d some o f t h e  centred  of charge  D r . L. Noodleraan, a initial  routines  of  sea t t e r e d - wave X^k p r o g r a m s d e v e l o p e d by J o h n s o n £56.]. The (i)  method i s a s using  follows:  the  charge  tables  distribution  o f Herman and S k i l l m a n f o r an  isolated  £57], the atom  was  calculated; (ii)  using  the  MOLPOT  scattered-wave densities  of  Xet a  and  ENERGY  programs,  the  3.3.  The c h a r g e d i s t r i b u t i o n  of  the  atomic  charge  M^  cluster  cubo-octahedral  ( c o r r e s p o n d i n g t o an FCC c r y s t a l ) Fig.  routines  were s u p e r i m p o s e d . of  the  central  atom was used t o g e n e r a t e an e l e c t r o s t a t i c p o t e n t i a l  51  including  an  approximation  exchanqe  €y  tabulations fhe  of  of  3.2,  this  produced V-  , with  by  in  s u r f a c e £65 ].  q i v e n i n T a b l e 3.1. available  3. 1 (fc)  At  a  phase  a  Cu  two  electron  and  structure  LEED  a later  for  the  potential  analysis  cf  the ,  potentials  Atomic  is  potential  phase  atoms were a l s o  Marcus et  had  potential,  staqe a band s t r u c t u r e  13 s i l v e r  curves,  potential  two  £64 ].  the  superposition  This  successful  t h o s e u s e d by  the  the  ( i i ) the  multiply  express  I (E)  cluster  |3  rhodium  (i)  The  be  shifts  shown  to  a l £ 104].  conveniently  determination  solution  scattered  ion-core potentials. to  the  shifts  parts  potential,  and  .  d a t a used  f o r a c l u s t e r of to  3.1 ( b ) ,  L I E D i n t e n s i t y c a l c u l a t i o n s can into  frcm  c h e c k e d by c o m p a r i n q  A rhodium s u p e r p o s i t i o n  for  correspond c l o s e l y  method was  J.60,61],  been used  calculated  (3.6)  << v a l u e s t a k e n  t h o s e f r o m t h e band (?c  also qenerated; the  became  with  Section  Burdick-Chodorow  Cu(1G0) was  of  factors.  previously  I <3p (r)/3ir]»/3  charge density,  validity  potential,  Slater's  S c h w a r z £58,59].  scattering Section  usinq  [55].  V { r ) = -6«£  H e r e p (r) i s t h e  term  by first  of  the  of  b r o k e n down  a single  ion-core  b e h a v i o u r of an  incident  a l a t t i c e made up  of  these  step i n performing part  e l a s t i c s c a t t e r i n g o f an  incident  single  (ii)  electron  by  is a  Jil The c u b o - c c t a b e d r a l «, i o n - c o r e p o t e n t i a l f o r PCC c r y s t a l s .  3  used t c m c d i l th<  Cu  Eh  d  3.615C  3.8C31  A  r ,  1.2780  1.3449  1  0.70697  0.7C214  e  Jabis 3 ^ potentials •uffin-tin [ 5 8 , 5 9 ].  cluster  Data used for cccstructicn cf superposition f o r B, clusters. The c r y s t a l cube s i d e a, and r a d i u s r a r e f r c a r 6 2 , 6 3 ] and t h e values froir 3  m  53  single ion-core  potential.  Assuming t h a t the c o r e - e l e c t r o n s are not p o l a r i s e d incident inside  electron, a  the wavefunction  muffin-tin  Schrodinger  sphere  obtained  ]4>=  incident electron by  solving  E4/  i s the ion-core p o t e n t i a l . .  scattered  waves c o r r e s p o n d  of  F o r an i n c i d e n t p l a n e  t o s o l u t i o n s of eguation  as  point  of  observation  from  only  the  d e p i c t e d s c h e m a t i c a l l y i n F i g . 3.4.  s o l u t i o n s to eguation  (3-7)  have the  x  u  where t h e f i r s t observation wave.  The  term i s  and  the  the  The  on  the  Q , and f  the  scattering  At l a r g e r  the  f o r m .£12,66,67 J ;  + (r ,9 ) oCexp ( i k r c o s B * ) + f ( e ) e x p ( i k r / r ) C  wave,  (3.7).  t h e wave v e c t o r , k, t h e s c a t t e r i n g a n g l e  distance r of the region,  the  <3.7)  i n t e n s i t y s c a t t e r e d t o a p a r t i c u l a r p o i n t depends modulus  the  equation  £ -1/292 +  where .?  is  o f an  by  incident  wave  s e c o n d i s an o u t g o i n g  atomic s c a t t e r i n g f a c t o r f ^ i s  at  (3.8)  the  point  of  scattered spherical  usually  expanded  as  £12,66,67J; <*>  f <9 ) = r  t  iVn  (-2l*1)exp(iS j.sin^JP.^Ccose')  (3.9)  JUo in  terms  shifts  of  the Legendre polynomials  Pj^fcosG^) , and  Sj^ w h i c h c h a r a c t e r i s e t h e i o n - c o r e  value of the angular  scattering  momentum guantum number  1-  the  phase  for  each  5U  y  (  p V VJ 1L9U££ 3^4 An ion-cere imirersed in a place wave i n d u c i n q s c a t t e r e d s p h e r i c a l waves whose i n t e n s i t i e s are f u n c t i o n s c f k, 6* and i . A f t e r P e n d r y [12").  The in  scattering  the  properties  energy-dependent  described i n Section by  the  solutions  equation of  sphere  smoothly  (3.9)  quite  rapidly  shifts  (1=0-7) a r e  the  and  o u t s i d e the  equation  phase  3.1(a) t h e  numerical i n t e g r a t i o n  muffin-tin  of  of  the  sphere.  the  contained potentials  phase s h i f t s were f o u n d  large  cf  the  1,  i t  s u f f i c i e n t M5T  and  expansion  does  t o 250eV o r  of  Schicdinger  B h i l s t i n p r i n c i p l e tbe of  the  r a s y m p t o t i c forms  solution  f o r c a l c u l a t i o n s up usually  For  thus  Schrodinqer eguation i n s i d e  i s over a l l values  and  the  relevant  the  to  i o n - c o r e are  shifts.  -joininq the  c a l c u l a t i o n s presented Plots  o f ar  so,  cccverqe e phase  were used i n  all  here.  energy-dependence cf the  phase s h i f t s f o r  the  55  two c o p p e r and two r h o d i u m p o t e n t i a l s a r e shown i n F i g . . 3 . 5  and  (?<•  Fig.  3.6.  F o r c o p p e r , t h e band s t r u c t u r e  V,  potentials  produce  w e l l with those given somewhat and  1=1  greater  superposition  s i m i l a r phase s h i f t s which  p r e v i o u s l y £35J.  differences.  with  v  ^  ) 3  J  agree  The r h o d i u m s h i f t s  show  F o r e x a m p l e , t h e c u r v e s f o r 1=0  show c o r r e s p o n d i n g f e a t u r e s a t l o w e r e n e r g i e s  compared the  very  and  for  7^  also there are s i g n i f i c a n t differences i n  s l o p e s o f t h e two s e t s o f p h a s e s h i f t s e . g . f o r 1=2  at  5By  (!By=13.6eV) . 3. 1 {c) In  temperature Section  corrections  2.3{b)  i t was n o t e d t h a t LEED beam  intensities  h a v e a s u b s t a n t i a l t e m p e r a t u r e d e p e n d e n c e and t h a t s u c h suggest that l a t t i c e to  motion should  c a l c u l a t e I(E) curves.  o c c u r as t h e scattering beams  temperature and  compared  scattering  therefore with  i n t h e model  used  The l a r g e r a t o m i c d i s p l a c e m e n t s  that  is  raised  increase  In  from many  an  Detailed  instances,  stationary motion i s  on  displacements-  although  the t i m e - s c a l e  that  is  experimental  described  within the m u l t i p l e - s c a t t e r i n g  £70,71]-  sufficiently  intensities  the  stationary  guite  model [ 7 2 ] .  treatments  have been produced  incoherent  idealised  t e m p e r a t u r e - d e p e n d e n c e o f beam i n t e n s i t i e s w e l l by a k i n e m a t i c a l  the  decrease the i n t e n s i t i e s of s c a t t e r e d  those  lattice.  be i n c l u d e d  effects  have  atoms  are  effectively  of the d i f f r a c t i o n process,  r a p i d a f o r : the been  detector  averaged  The LEED measurement  over  theory  to the  their  register atomic  a v e r a g e s ; o v e r many a t o m s a t •  ZiSHIZ 3 5 I n e r q y d e p e n d e n c e c f c o p p e r phase s h i f t s t h e p o t e n t i a l s : (a) V and (b) V? . X  c  (1=0-7) f o r  57  l i S H L S Ji§ E n e r q y d e p e n d e n c e o f r h o d i u m phase s h i f t s t h e p o t e n t i a l s : (a) V ana ( t ) 1^"-  (1=0-7) f o r  58  any  one  moment.  Thus the s c a t t e r i n g o f each a t o m i c p o t e n t i a l i s  averaged over the atomic motions.  I f ae assume t h a t t h e  are uncorrelated [ 1 2 j then  we  atomic: s c a t t e r i n g  that i s related  lattice  factor  ,obtain  a  temperature-dependent t o t h a t of t h e  but w i t h m o d i f i c a t i o n s i n t h e phase s h i f t s , temperature-dependent  motions  w h i c h become  complex.  These  interfere  i n t h e c o r r e c t f a s h i o n t o p r o d u c e s t r o n g f o r w a r d , and  weak b a c k - s c a t t e r i n g . strong cancellation shifts.  The  shifts  between c o n t r i b u t i o n s from  different  truncation  of  the  series  of  (3. 9) . 13.10)  k  I n t h e c a s e of i s o t r o p i c exp (-H^)  cf  phase  h i g h e r t h e t e m p e r a t u r e , t h e more t h i s i s s o , h e n c e  f <e*,T) = e x p ( r - i g ) f ^ f e V  and  must  I n t h e b a c k - s c a t t e r i n g c a s e t h e r e must be  more s h i f t s a r e needed t o a v o i d eguation  phase  rigid  vibrations, = ex p (-M  k-jc * J )  (3  2  .11)  oC c a n be a p p r o x i m a t e d , f o r l a r g e T, a s a D e b y e - B a i l e r t y p e factor cL =  31i2I/2mk e2 ( j  '  (3.12)  where k g i s B o l t z m a n n ' s c o n s t a n t , m t h e a t o m i c mass o f c o r e and 9 In  p  ion-  t h e Debye t e m p e r a t u r e .  t h i s work, s u r f a c e a t o m i c v i b r a t i o n s were assumed t o be  i s o t r o p i c and l a y e r - i n d e p e n d e n t . surface  an  Debye  and, f o l l o w i n g  t e m p e r a t u r e was  An e x p e r i m e n t a l v a l u e  used f o r c o p p e r  van Hove and Tong £74J, a v a l u e  t h e b u l k v a l u e o f 480K £75J was  of  the  { v i z - 275K [ 7 3 ] ) of  used f o r rhodium.  J0.7^  times  59  3.2  G e n e r a l Schemes Of Having  Calculation  computed  temperature-dependent  a  suitable  ion-core  phase s h i f t s to  from  v i b r a t i n g atoms, t h e o t h e r , and  solve  f o r an i n c i d e n t  electron  l a t t i c e of s c a t t e r i n g  potential,  describe  the  scattered  by t h e c r y s t a l  for  performing  s c a t t e r i n g , or dynamical, c a l c u l a t i o n s ; t h e y d i f f e r their  range  requirements.  of  111  a p p l i c a b i l i t y , speed  the u s e f u l  surface, 3  scattered,  that  by one  f r o m an i n c o m i n g  to  a scattered  infinite this  an  c r y s t a l , can  are  electron  from  available;  wave l a b e l l e d by a,"  assemblage  of  be f o u n d . they  any  pair  the  calculation flux  on t h e  particular  (or 1»).  once t h i s  amplitude  of  beams  n l a y e r s , approximating  A number o f  take  multiple-scattering  Between  c o m p u t e r memory  wave l a b e l l e d by t h e r e c i p r o c a l v e c t o r  into  f l u x by i n e l a s t i c s c a t t e r i n g  interplanar  considerably  plane of the c r y s t a l p a r a l l e l t o the  i n t r a l a y e r s c a t t e r i n g m a t r i x i s known, t h e diffracted  multiple-  describe the electron  ( o r a n g u l a r momentum component 1, d e p e n d i n g  method)  of  and  methods s t a r t w i t h  of t h e s c a t t e r i n g m a t r i c e s multiply  tasJc i s t o  potentials.  Many m e t h o d s h a v e b e e n d e v e l o p e d  in  scattering  most d i f f i c u l t ,  multiply  with  methods  account  processes  of  doing  the removal and  allow  an  of for  events.  of l a y e r s i n the c r y s t a l i s present a s e t  p l a n e wa ves [ 1 2 J  2.  or beams, t h a t  expjajk+aj.rj  h a v e b e e n f o r m e d by d i f f r a c t i o n o f  (3.13)  the  incident  60  beam.  Each  momentum l k  of  d  these and  0  has  a  d i f f e r e n t p a r a l l e l component  t r a v e l s e i t h e r forwards or backwards  of  (±).  F o r w a r d t r a v e l l i n g beams  Z 3 —  where K* are  = £<k  incident  beams  is  0ii  u!" e x p ( K ^ -JE)  + j a ) ^ ±(2E-2v^ ^ J %  upon  the  by  the  w i t h £ 12J V/'  =  l8nZi/Ak  <£  &  o p-L  M  by  plane (the  «5  0  t  of  This set  of  ion-cores  ± signs  as  referring  to  give e x  P < ^ r -£>  (3»  i  >X \  K  the  ||  to  (3.15)  i n F i g . 3-7-  m a t r i x M ~~,  f o r w a r d o r back s c a t t e r i n g ) Z  +aJ2)A/2 j  •+ +  layer  ?  ( i  n e x t l a y e r as  multiply-scattered  described  (3-14)  <L  I  ) 11-X  16)  Y , (/(g.)) e ^ ' s i n £j/  3j»  1  L  (3. 16a) In  the  sum  over  spherical  angular  harmonics  Y  momentum and  L  m a t r i x term  are  included  temperature-dependent  s h i f t s , Sjj, «hile m u l t i p l e - s c a t t e r i n g inverse  components  is  accounted  for  phase by  the  £12]. + i  The us  of  M " / i s c o m p l i c a t e d and  h e r e ; however, i t i s worth  composed of  evaluation  the  of  a stucture  i o n - c o r e s i n the  describes  the  phase s h i f t s .  and  that  i t  is  f a c t o r , d e p e n d e n t o n l y on layer,  and  multiple-scattering  a  scattering  w i t h i n the  F u l l d e t a i l s h a v e been g i v e n by  I t i s i n the crystal  noting  need not  manner o f  computing the  assembling a stack reflectivity  v a r i o u s c a l c u l a t i o n a l schemes d i f f e r -  of  concern  essentially the  positions  factor  l a y e r i n terms  of  F e n d r y £ 12 ]. of l a y e r s i n t o  the c r y s t a l t h a t  They c a n  that  be  divided  a the  into  3 7 Schematic representation o f a s e t o f p l a n e wave i n c i d e n t f r c n i t h e l e f t m u l t i p l y s c a t t e r e d by a p l a n e c f ioz. cores. A  a) " e x a c t "  aethods (i)  (ii)  Bloch  e x a c t T - o a t r i x aethod f 7 6 ]  b) p e r t u r b a t i v e (i) (ii) (iii)  In this discussed  wave n e t h c d s  approximations  T-aatrix  layer doublinq renoraalised  work t h e l a s t  in  a  expansions r77 ]  little  r12,78]  forward s c a t t e r i n q  two a e t h o d s were detail.  The  used  ether  (RFS) [ 1 2 , 7 9 ]  and  scheies  will  b  will b  62  d i s c u s s e d i n o n l y t h e b r i e f e s t o u t l i n e and the i n t e r e s t e d is  referred  reader  t o i n d i v i d u a l r e f e r e n c e s a n d t o t h e r e v i e w o f Tong  [15].. The " e x a c t " methods a r e e x a c t i n  that  multiple-scattering  is treated exactly  b o t h w i t h i n and b e t w e e n l a y e r s .  wave  s c a t t e r i n g m a t r i c e s f o r a l a y e r a r e found  method  the  I n the B l o c h  t h e wave a m p l i t u d e s b e t w e e n two l a y e r s c a l c u l a t e d interplanar  multiple-scattering.  The  allowing  scattered  the c r y s t a l .  At the s u r f a c e the scattered  matched t o t h o s e o f t h e , i n c i d e n t amplitudes. layer  KKR  I n t h e most d e v e l o p e d  eigenvalue  problem,  Consequently,  by  one  has  where  n  to  is  solve  the  the  group  at  scattering fficffientum, matrix  T-matrix  matrices  i s  then  computed,  wavefield  scattered  from  f r o m : one  been  waves used  expresses  T  layer  matrices A  used.  to  any  the in  layer angular  layer-dependent  due  to  waves  I n o r d e r t o do t h i s ,  a s an N l a y e r s l a b  total reflectivity  of  matrix  which i n c l u d e s c o n t r i b u t i o n s  other layers.  must be a p p r o x i m a t e d  (2nX2n)  involved.  [ 76 J  so-called  a  T h i s method  [ 6 5 ] because of t h e v a s t  r a t h e r than r e c i p r o c a l , space.  scattered  The  as  method  reflected  i s t r e a t e d by t h e  number  IBM  c o m p u t e r t i m e and s t o r a g e r e q u i r e m e n t s exact  the  v e r s i o n o f t h e s e methods, t h e  t h e l a y e r KKR method h a s o n l y  extent  The  give  (KKR) method o f b a n d t h e o r y .  a c c u r a t e but slow as  great  to  modes  wavefunctions are  method [,65], i n t r a l a y e r s c a t t e r i n g  Korringa-Kohn-Bostoker is  wave  for  wavefield i s  t h e n e x p r e s s e d as a c o m b i n a t i o n of B l o c h waves, o r normal of  and  (N t y p i c a l l y  to the already  the c r y s t a l about  of t h e N l a y e r s l a b i s then found.  i n v o l v e s s o l v i n g N e q u a t i o n s each h a v i n g m a t r i c e s o f  T-  5). This  dimensions  63  ^m*>  + 1  ) * ^*mx * ) x  1  inelastic but  i s  T h i s method i s a c c u r a t e  2  s c a t t e r i n g i f enough phase s h i f t s rather  slow  and i s d i f f i c u l t  i n the presence  of  and l a y e r s a r e u s e d ,  t o extend  to complicated  surfaces, The T - m a t r i x last  method  in  expansion  method £ 77 j i s a n e x t e n s i o n  which  limit  multiple-scattering little-used  a  (inter-  i s  and  placed  the  upon t h e o r d e r o f  intraplanar)  method i s cumbersome a b o v e t h i r d  of  allowed.  This  o r d e r and c a n  fail  w i t h s t r o n g s c a t t e r e r s o r weak a b s o r p t i o n .  3.2(a)  layer doubling  and SFS methods  T h e s e two c o n v e r g e n t  perturbative  methods,  pioneered  P e n d r y , Van Hove a n d Tong £ 12,78,79 "J, a r e among t h e most in  use  today.  relatively  Their  easy  to  iterative  use  c o n s e r v a t i v e i n core space The  layer  scattering marked  as  layers  A  doubling  in  form  a  routine  and  B.  them  manner,  popular  flexible, fast  and  requirements. method  starts  matrix f o r a single layer; B {reflection)  makes  and T  with  in  the  F i g . 3.8  multiplethese  The i n t e r p l a n a r m u l t i p l e - s c a t t e r i n g i s t h e n  matrices R  and l  l a y e r s , thus doubling process until  of  c  are  then  used  to  solve  intensities  converge,  typically  The  for  t h e number o f l a y e r s i n t h e c r y s t a l .  d o u b l i n g the t h i c k n e s s of the s l a b i s then  the r e f l e c t e d  are  ( t r a n s m i s s i o n ) m a t r i c e s f o r two  s o l v e d e x a c t l y f o r t h e p a i r t o p r o d u c e a c o m p o s i t e l a y e r C. resulting  by  4  This  repeated  in 8  or  16  layers.  T h i s method i n v o l v e s m a t r i x i n v e r s i o n s and p r o d u c t s o f .  dimension  n, t h e number o f beams u s e d , t h a t  converge  even  for  :  J i f l a S f i x S E u i l d i n g up s u f c p l a n e s by t h e l a y e r d o u b l i n g p r o c e s s I n d i v i d u a l s u b p l a n e s a r e B a r k e d A and B; t h e r e s u l t a n t c o m p o s i t e i s marked C. A f t e r Tonq M 5 1.  65  small interplanar The  spacings.  renormalised  forward  s c a t t e r i n g , o r RFS,  method o n c e  more s t a r t s f r o m t h e s i n g l e l a y e r  multiple-scattering  of  are  eguation  crystal  (3.16).  with  forward  backscattering F i g . 3.9 A^(fl)  is  scattering treatedly  length  each of the  n  a t t h e oL  we  (labelled  layer.  order.  by  through  evaluated  can d e f i n e  The, i n d e x  tiffes e l e c t r o n s are propagating iteration  being  n , whose e l e m e n t s  beams  propagated  p e r t u r b a t i v e l y.  , f o l l o w i n g Tong £ 1 5 ] ,  of  crystal,  Electrons  a  the  exactly;  Referring column  to  vector  represent the amplitudes i n j)  propagating  i denotes  the  i n t o t h e c r y s t a l and  Outside the c r y s t a l  matrices  we  into  the  number  of  i s a l s o the  have  1 \ 0 A  o  MS)  (3.17)  0 0  and  The  coefficients  can  be  identical,  found  thus  by  A^Ca)  a r e e v a l u a t e d midway b e t w e e n  iteration,  assuming  a l l layers  planes are  66  I i S " I s 1..9 Diagramatic representation of the rencraalized forward scattering (BFS) process. Inward amplitudes A'^(g) p r o p a g a t e from vacuum t h r o u g h t h e 1 s t l a y e r t c the Nth layer where t h e y a r e t u r n e d a r o u n d . The e l e c t r o n s a r e t h e n p r o p a g a t e d t o t h e 1 s t l a y e r w i t h o u t w a r d a m p l i t u d e s E' (gj .  67  2  A*-(g)- =  and  ^' o  M  a  (  3  >  lJ.(g)-.= . . J 8 * * / l f *  cL-i  ft  (3  (g) -  -  T 8 )  (3- 19)  ;  u  This  is  carried  at the  N  damped s u c h t h a t a n e g l i g i b l y  small  elastic  (N + 1 ) ^  layers.  layer,  The E^tS)  on  until  t y p i c a l l y 7-14  electrons  are then turned  the e l e c t r o n s flux  a r o u n d and  through:  the  F i g - ,3-9  we  crystal  B* (a) t h e r e  t  (a) = ^  plane,  = Z  1 set  The  the  in  set B  and  1  of ia)  outwards  referring  again  H*~  A * (a)  to  {3.20)  are c o n t r i b u t i o n s from b a c k s c a t t e r i n g  («(#• 1) ^  B* <a)  Each  Therefore,  reaches  have  B  from the  once.  passing  are  we f o r m a s e t  f a r a m p l i t u d e s o f e l e c t r o n s g o i n g back o u t .  a r e a m p l i t u d e s f o r e a c h j-beam a f t e r  For  layer  ®W  and  transmission  A* m  * y  —  of c o e f f i c i e n t s  o f B*  M 7,7 B* ( a )  A , (a) 1  thus  {3.21)  (  /  {a)  of  -  i s thus obtained  from s e t s  previously  evalua ted. The back  e l e c t r o n s are e v e n t u a l l y  into  the c r y s t a l ; i=2.  after reaching B  5 iS)'  a r e  a deepest l a y e r  evaluated.  scattered  by  the  first  Again the  coefficients A  N^SH,  reflection  coefficients  reflected  amplitudes  Eventually  the the  2  (a)  layer and,  68  c o n v e r g e and a r e summed t o y i e l d t h e r e f l e c t e d The to  RFS  converge,  is  method i s v e r y f a s t , but can f a i l  intensities.  usually requiring  t o converge i f the  3-5  inelastic  t o o weak o r t h e i n t e r l a y e r s p a c i n g t o o s m a l l .  passes damping  I n such  cases  t h e l a y e r d o u b l i n g method, t h o u g h s l o w e r , i s t o b e p r e f e r r e d . In in  t h e c a l c u l a t i o n s r e p o r t e d h e r e t h e BPS method  the  layer  main.  Occasionally,  doubling  overlapped,  method  was  i t was f o u n d  3.2(b)  used;  where  the  two  similar.  exploiting  or  theory  a  plane  allows  combinations Hove £81 j .  input  to  to  consider  symmetry-related Therefore,  the  only  the  plane  i n the l i s t  together  with  a  of  instructs  the  wavefunctions and  to assign  matrices  JJ  vectors  that informs  vectors.  programs ( r a t h e r than only  one  to  use  f o r each symmetrical  and  one  This  appropriate  the simple plane row  when  along  linear  wavefunction  that  in  by is  3.2(c),  vectors  i s  the programs code  number  symmetrical  waves l a b e l l e d  column  an  Group  symmetrical  symmetry-related  code-number  be  waves, a s d e t a i l e d  about t h e omitted symmetry-related the  surface  program, as e x p l a i n e d s h o r t l y i n S e c t i o n  o n l y one v e c t o r £ f o r e a c h s e t o f read,  can  o f symmetry o f t h e s u r f a c e s t r u c t u r e -  us of  time  t h e s y m m e t r y among p l a n e waves p r e s e n t  t h e e l e c t r o n beam i s i n c i d e n t cn t h e c r y s t a l  van  both  u s e s o f symmetry  by  axis  methods  p r o d u c e d by  C o n s i d e r a b l e s a v i n g s i n c o m p u t e r s t o r a g e and made  used  at s m a l l i n t e r l a y e r spacings the  that the i n t e n s i t i e s  methods were n u m e r i c a l l y , v e r y  was  by CJ)  diffraction  ^ r a t h e r t h a n one f o r  69 Surface  Max. <j vector  Symm. axis  Rh (100) Bh (111) Rh (110)  {62} {4 3} {42}  4 3 2  Number o f beams ncsymm. w i t h symm.69 55 55  13 13 18  T a b l e 3L2 R e d u c t i o n , due t o s y m m e t r y , i n t h e number o f beams needed a t normal i n c i d e n c e f o r the three simple faces of r h o d i u m . The maximum a v e c t o r c o r r e s p o n d s t o t h e beam s e t w i t h the largest (hk) v a l u e s n e e d e d t o c o v e r t h e e n e r g y r a n g e 40250eV. each o f t h e v a r i o u s symmetry-related plane of  core  storage  and  time  can  be  waves).  considerable.  i l l u s t r a t e d i n T a b l e 3.2 where t h e r e d u c t i o n , due in  the  savings This  to  number o f beams, needed a t n o r m a l i n c i d e n c e  e n e r g y r a n g e up t o a b o u t 250eV i s shown f o r t h e and  The  i s  symmetry,  to cover the  Rh ( 1 0 0 ) ,  (111)  (110) s u r f a c e s .  3.2(c)  program  The  flow  flow-chart  events that occur programs  start  of  in by  a  F i g . 3.10  reading  code-numbers.  described vectors  by g_,  eguation that  i n a l l  k*^ t o  ( 3 . 16)  i s , over  remain r e a l ,  because  of  beams  with  their  The m u l t i p l e - s c a t t e r i n g w i t h i n a l a y e r , involves the  the  sums  over  diffracted beams  potential  reciprocal  beams.  with  Section2.2,  I n a d d i t i o n t h e r e a r e e v a n e s c e n t waves emerging  The  t h e r e l e v a n t - p h y s i c a l and  of d i f f r a c t e d  p a r t i c u l a r e n e r g y E, o n l y c e r t a i n permit  t h e sequence of  multiple-scattering calculation.  p o t e n t i a l d a t a , and a l s o a l i s t symmetry  summarises  jg  At  vectors  any that  can leave the c r y s t a l .  that  propagate  without  step at the surface.  program a u t o m a t i c a l l y i n c l u d e s i n t h e s u b s - , o v e r  The  the reciprocal  70  Bead i n (i) geometry (iv)  (ii)  v  ftr  , v  b e a n s and  e L  temperature data  Choose i n i t i a l  (v) phase  shifts  energy  F i n d teams needed  at I  Compute t e m p e r a t u r e - d e p e n d e n t phase Calculate layer diffraction  Jind  diffracted  amplitudes  beam  from s u r f a c e  substrate  C a l c u l a t e team  by  Find plus  for  FFS  shifts  m a t r i c e s tr~,  diffraction  matrices  n substrate layers  by l a y e r d o u b l i n g  intensities  Add  s u r f a c e l a y e r and  diffracted  beam  C a l c u l a t e team Vary s u r f a c e  symmetry  find  amplitudes  intensities  geometry  Vary s u r f a c e  V  qecmetry  Increment E  fisyif ixlO Flowchart showing principal s c a t t e r i n g LEED c a l c u l a t i o n , u s i n g t h e RFS programs.  steps i n a multipleor layer doubling  71  vectors  only  those  waves t h a t , f r o m one l a y e r t o t h e n e x t , do  n o t d e c a y t o l e s s t h a n 0.00 2 o f t h e i r Having i n c o r p o r a t e d shifts,  the  layer  found  by  the  the f a c i l i t y  temperature  diffraction  reflected amplitudes,  and  subseguently  layer doubling  the surface  in  slightly and  the  c r RFS r o u t i n e s . that  a  or  by  then  different metal  lateral  a  simple  The t w o methods  differ  i n t h a t t h e l a y e r d o u b l i n g , method c a l c u l a t e s r e f l e c t i o n  t r a n s m i s s i o n m a t r i c e s f o r t h e s u b s t r a t e once only  these  are  I n the case of c l e a n  layer spacing.  The  E a c h method h a s has  t o t h e bulk s t r u c t u r e  topmost  phase  are calculated.  l a y e r c o u l d be d i s t i n g u i s h e d by a  relative  the  into  intensities,  to include a surface layer  reconstruction change  effects  matrices  geometry from t h a t o f t h e s u b s t r a t e . surfaces,  amplitude.  are  used  repeatedly  and  then  f o r a s many s u r f a c e g e o m e t r i e s a s  d e s i r e d by a d d i n g t h e s u r f a c e l a y e r a s t h e  final  BFS,  l a y e r s y s t e m must be  the  whole  substrate  plus  surface  r e b u i l t f o r each geometry as the s u r f a c e the  initial  step  of  the  layer  calculation  step..  Using  i s involved  of  the  in  interlayer  scattering. The  intensities  incrementing  the  1^(E) energy  of and  each  beam  repeating  are the  stored whole  before process.  G e n e r a l l y , t h e c a l c u l a t i o n s were p e r f o r m e d o v e r an e n e r g y of  approximately  40 t o 250eV.  end  by t h e l a c k o f e x p e r i m e n t a l  These l i m i t s a r e s e t a t t h e low d a t a , and a t t h e h i g h e n d by t h e  e x p e n s e o f t h e c a l c u l a t i o n s and by d o u b t s a s t o w h e t h e r 8 shifts  are  sufficient  scattering factors.  to  range  ensure  convergence  of  phase  the atomic  &n e n e r g y i n c r e m e n t o f 2eV was used f o r t h e  r a n g e 40 t o 100eV, a n d t h e i n c r e m e n t was d o u b l e d f o r : t h e  range  72  above  100eV.  interpolated  For the l a t t e r back  interpolation  onto  method  to  2eV  £80].  s t o r e d on m a g n e t i c t a p e transferred  a  range, i n t e n s i t y values using  a  cubic  spline  A l l calculated, intensities  and  paper  grid  were; t h e n  subseguently  tape  the  f o r plotting  data by  sere  could  the  be  Nova  2  minicomputer i n the l a b o r a t o r y . In order I|E)  curves  been  t o c h e c k t h a t t h e p r o g r a m s were r u n n i n g  were c a l c u l a t e d f o r s u r f a c e s  studied  theoretically;  discrepancies before  any  calculations  •unknown r h o d i u m s u r f a c e s . (i)  careful  that checks  were  of  had  previously  were  made f o r  performed  T h e s e t e s t s were made  the c a l c u l a t i o n s  correctly,  on  the  against  L a r a m o r e £ 2 0 ] f o r Cu (111) a n d  Cu (100) ; (ii)  t h e c a l c u l a t i o n s o f Demuth e t and  Ni(110),  a l £11]  f o r N i (1Q0)  u s i n g n i c k e l p h a s e s h i f t s s u p p l i e d by  M.A. Van Hove  In a l l cases comparison with the that  previous  calculations  showed  t h e p r o g r a m s used h e r e p r o d u c e d e s s e n t i a l l y i d e n t i c a l 1 ( E )  curves.  This  determining These  gave u s c o n f i d e n c e  type  of  structures,  changes  can  occur  the  and  superposition,  V  surfaces.  i t i s gratifying  i n calculated  assumed  incidence,  programs f o r  c a l c u l a t i o n s were d e v e l o p e d t o i n v e s t i g a t e  surface  F i g . 3.11 we s e e 1 ( E ) c u r v e s normal  these  t h e unknown s t r u c t u r e s o f r h o d i o m  surface  changes i n  f o r using  using ,  that  1(E) c u r v e s geometry-  f o r only  the  potentials  minor  F o r example,  c a l c u l a t e d f o r a Cu (111)  both  significant  in  surface at  B u r d i c k - C h o d o r o w , V > , and C  discussed  earlier.  The  73  IiSl?If 3j.Il Comparison o f e x p e r i m e n t a l 1(E) c u r v e s f o r Cu(111) at normal i n c i d e n c e w i t h c u r v e s c a l c u l a t e d f o r the V and v£ p o t e n t i a l s f o r V. = -9.5eV and t h r e e d i f f e r e n t v a l u e s of A&%. t a l 3  r  c a l c u l a t i o n s a r e f o r t h e (10) a n d (11) values  of  the  topmost  interlayer  p e r c e n t a g e change from t h e b u l k  AdX  spacing  significantly,  New  grows a t a b o u t  200eV  intensities become  for a d  = £ d - d / d ] X 10035 o  relative structure f o r the  range  of  expressed as a  v a l u e d ^ , i n s t e p s o f 5%,  0-22)  0  b u t a s s u m i n g no o t h e r g e o m e t r y c h a n g e s . surface i s contracted,  beams  I n t h i s example, as the  intensities  of  peaks  change  i s i n t r o d u c e d , e . g . a new (10) ; beam,  and  the  peak  relative  o f t h e p e a k s a t a b o u t 230 and ,260eV i n t h e (11) beam  reversed.  CHAPTER H  EXPERIMENTAL ASPECTS  76  In  order  t o d e d u c e s u r f a c e s t r u c t u r e s v i a a LEED a n a l y s i s  several experimental  p r e r e q u i s i t e s must be f u l f i l l e d -  problem i s t o prepare the s u r f a c e o f i n t e r e s t i n fashion  as p o s s i b l e .  crystal  to  polishing  expose the  Having obtained and  maintain  fractions  This the  face  desired  obtained  precise  crystallographic  to  plane  Finally,  a h i g h degree of p e r f e c t i o n .  the  a monolayer of c o n t a m i n a t i o n .  level  of  small  Diffraction  of low  from well-ordered  surfaces  so  surface  before  we a r e f a c e d  the  LEED  experiment  can  with t h e problem of performing  the  of data c o l l e c t i o n  begin.  the a c t u a l  LEED e x p e r i m e n t w h i c h , a s we s h a l l s e e , c e n t r e s a r o u n d  problems  and a n a l y s i s .  C r y s t a l Preparation The s a m p l e s u s e d i n t h i s work /were t y p i c a l l y  1mm  and  must b e t r e a t e d i n s u c h a way a s t o p o s s e s s a c l e a n and  well-ordered  4, ,1  a  a w e l l - o r i e n t e d s u r f a c e we must be a b l e t o c l e a n  energy e l e c t r o n s o n l y occurs crystal  as  first  involves accurately cutting a single  i t s s t a t e of c l e a n l i n e s s , a t  of  The  t h i c k n e s s and 6mm  loan  from  other  diameter.  laboratories  e x p e r i m e n t s were r e p e a t e d lists  the sources  on new  of the c r y s t a l s  I n some c a s e s , were  used  discs  back-reflection  technique  £ 82]  was  V e r t i c a l cuts p a r a l l e l  to the plane  ("Agietron",  AGIE,  s l i c e s on but  the  here.  Table  4. 1  oriented  using  the  cut  used.  c r y s t a l l o g r a p h i c plane  cutter  precut  initially  The s i n g l e c r y s t a l r o d s were c a r e f u l l y Laue  d i s c s o f about  such  perpendicular  that  to  the  the X-ray  were made on a s p a r k  Switzerland),  desired beam. erosion  The c r y s t a l r o d was  77 Source  Treatment  ROC-SIC  Cut  Berkeley  and; p o l i s h e d a t UBC  (111) , (100) , (110)  As r e c e i v e d  GE  Table  Faces used  (111)  C u t and p o l i s h e d a t UBC  4.1  Sources  of rhodium  (100)  crystals  1. BOC-BIC = R e s e a r c h O r g a n i c / I n o r g a n i c C h e m i c a l s C o r p . 2. B e r k e l e y = C o u r t e s y o f P r o f . ,G. A. Somor j a i , L a w r e n c e B e r k e l e y L a b o r a t o r y , U. o f C a l i f o r n i a , B e r k e l e y , C a . 3. GE = C o u r t e s y o f Dr. C . . H - T u c k e r , G e n e r a l E l e c t r i c R e s e a r c h and L e v e l o p m e n t C e n t r e , S c h e n e c t a d y , N.Y. l e f t i n p l a c e on t h e g o n i o m e t e r d u r i n g t h i s o p e r a t i o n that The  t h e c r y s t a l l o g r a p h i c o r i e n t a t i o n would n o t be resulting  disc  i*'Cuickmount",  was  Fulton  carefully  mounted  Metallurgical  p o l i s h e d by hand t o a m i r r o r - f i n i s h Whilst great care ensure  was  i s important A simple  compromised.  was  (0.05 m i c r o n  to  polishing process  involved  re-orienting  d i f f r a c t o m e t e r such perpendicular  to  that the  c r y s t a l e n s e m b l e was orientation  of  c o u l d be c h e c k e d ,  the  the  c h e c k .. t h a t  the  X-ray  crystal  desired beam.  slice  plane The  occurred.  the . o p t i c a l  on  was  plane.  the  X-ray  once  again  whole goniometer  t h e n r e m o v e d t o an o p t i c a l b e n c h where o p t i c a l face r e l a t i v e to the c r y s t a l  a s shown i n F i g . 4. 1, by  a n g l e o f r e f l e c t i o n o f t h e beam from T h i s method c a n e a s i l y  detect  to  not l o s t , i t  p o l i s h e d f a c e was i n f a c t p a r a l l e l t o t h e d e s i r e d c r y s t a l This  and  alumina).  o f t h e d e s i r e d f a c e was  devised  resin  C o r p . , USA)  t o c h e c k a f t e r w a r d s t h a t an e r r o r h a s n o t  technigue  order  acrylic  Products  taken d u r i n g the  that the o r i e n t a t i o n  in  in  measurement  and the  plane  of  the  a s m a l l He-Ne l a s e r . misorientations  of  ±1/2°,  78  He-Ne Laser  l i s u r e j ^ J L a s e r a l i g n m e n t method t o c h e c k the t h e o p t i c a l f a c e and d e s i r e d c r y s t a l p l a n e .  coincidence  of  GAS LINE  9 o  BOI/sI.PJ  9  S.P.  9 o  S.R  *  A  * EXPTAL. CHAMBER  n.s.R  240 l/s XP.  l i S P I S i L i i D i a g r a m m a t i c r e p r e s e n t a t i o n o f t h e pumping s y s t e m : I P « I o n pump; I S P = t i t a n i u m s u f c l i m a t i o n pump; S P = s o r p t i o n pump  79  although In  t h e y c a n r a n g e up t o ±2°, e v e n w i t h c a r e f u l  polishing.  t h e e v e n t o f s u c h a ^ D i s o r i e n t a t i o n t h e c r y s t a l was  repolished  u n t i l i t was w i t h i n  1.2  1/2° o f t h e d e s i r e d c r y s t a l p l a n e .  U l t r a H i g h Vacuum  (t)HV) A p p a r a t u s  Once h a v i n g p r e p a r e d a w e l l - d e f i n e d c r y s t a l s u r f a c e i t must he  kept  in  contaminated completed. shows  an  environment  to  any  which  extent  i t will  that  a  contaminant  Therefore,  t h e o r y of  1 second a t  n e c e s s a r y t o work i n t h e OHV  sufficient  time  gases  to  perform  an  1-0-  will Torr.  6  pressure region  i n t h e 1Q-io T o r r p r e s s u r e range, o r b e t t e r ,  have  become  with unit sticking probability  on t h e s u r f a c e i n a b o u t  i t i s  not  before the experiments are  Simple c o n s i d e r a t i o n of the k i n e t i c  form a monolayer  i.e.  great  in  in  experiment  order  to  without the  c r y s t a l s u r f a c e becoming s e r i o u s l y . c o n t a m i n a t e d .  The  slice  In t h i s  work  V a r i a n 240 and a V a r i a n  FC12  two  i s , t h e r e f o r e , mounted i n s i d e a UHV such  chamber.  systems  Fig.  used,  a  The f o r m e r was o n l y u s e d f o r a s h o r t ; t i m e i n t h e e a r l y  stages so further system.  were  chamber.  crystal  A  discussion  schematic  will  centre  diagram : o f  this  around  the  latter  a p p a r a t u s i s shown i n  4. 2. The s t a i n l e s s  pressure  of  steel  chamber  approximately  1  can  micron  containing molecular sieve c h i l l e d  be by  roughed two  and  will  to  a  s o r p t i o n • pumps  by l i g u i d n i t r o g e n .  24 0 1/s i o n pump c a n t h e n be s t a r t e d  out  attain  The m a i n a  base-  p r e s s u r e o f <10-*° T o r r f o l l o w i n g a n o v e r n i g h t b a k e - o u t a t 200°C to  remove a d s o r b e d  g a s e s f r o m t h e chamber  walls.  80  During gases i n t o  crystal  cleaning  i t i s o f t e n necessary t o admit  t i e chamber e.g. a r g o n f o r i o n - b o m b a r d m e n t o r  for chemical  cleaning-  These gases a r e stored  oxygen  i n g l a s s b u l b s on  a g a s l i n e c o n n e c t e d t o t h e main chamber t h r o u g h a v a r i a b l e l e a k valve. and  The  gas  line  i s pumped b y i t s  amount  of  admitted  c a n be b a k e d s e p a r a t e l y f r o m  own  small  t h e chamber  ion-rpump (20 1 / s ) .  Thus,  e x t r a background i m p u r i t i e s from t h e gas l i n e  the  i n the  g a s e s c a n be k e p t t o a few p a r t s p e r m i l l i o n - , When t h e  chamber i s f l o o d e d  w i t h a r g o n f o r ion-bombardment, t h e main i o n -  pump c a n be t h r o t t l e d sublimation  o f f by  pump used  a  gate  valve  and  the  to f u r t h e r lower the p a r t i a l  titanium  pressures of  a c t i v e gases i n t h e chamber. Figchamber.  i)  4-3 shows  a  schematic  On t h e v a r i o u s  ports  a manipulator external  representation  of  the  together  sample.  manipulator  s a m p l e t o be t r a n s l a t e d i n a l l directions,  t h e FC12  are.fitted:  on w h i c h i s mounted t h e  controls  of  with  allow  Electrical  plane,  as  variation  indicated  feedthroughs t o  of the polar  permit  in  iii)  heating  a "nude" i o n gauge t o m o n i t o r t h e s y s t e m a  hypodermic  gas  doser,  i n the  F i g . 4.3. of the  s a m p l e and a t h e r m o c o u p l e m o n i t o r a r e a l s o ii)  the  t h r e e .. p e r p e n d i c u l a r  angle o f i n c i d e n c e , & , and t h e " f l i p a n g l e " vertical  The  after  provided; pressure;  Joyner  and  S o m o r j a i £83J, c o n n e c t e d t o t h e v a r i a b l e l e a k  valve.  This permits  e.g. a  chemical  relatively  cleaning  high  agent,  pressures  of  at ;the c r y s t a l  surface  81  I o n gauge  Gas doser  fiS"I§ Hi.3. S c h e m a t i c  IiS"I§ deflection  of the V a r i a n  FC12 UHV  chamber.  S i m p l i f i e d d i a g r a m o f an o f f - a x i s e l e c t r o n e l e c t r o d e and d r i f t t u b e .  que  with  82  while keeping the  t o t a l system  pressure  relatively  low; iv)  an  v)  i o n - b o m b a r d m e n t gun  the  LJSED/Auger  The  electron ; optics  p r i n c i p l e of the  shown  in  emits  electrons  The that  lens  cleaning; and  construction  F i g . 4.4.  collimating  for crystal  electron  of  the  evaporation  leave the same  drift  are  into  deflected  s y s t e m ; and  drift  tube, which . i s as  f r e e s p a c e as l o n g  tube.  The  beam  diameter  typically  an  energy  spread  Secondary  and  system  of  electrons vi)  a  The square the with  grids,  on  chamber i s  the  motion  Helmhoitz  of  off-  surface  The  electrons at  traverse  field-  fields and  of  0.75eV.  about filtered  elastically  by  the  scattered  diffraction  fluorescent  by  sample  and  screen.  three  orthogonal  sets  to reduce the r e s i d u a l magnetic f i e l d  condition  has  the  the  electrons  Although t h i s  are  screen;  observe  slow  the  on a f l u o r e s c e n t  ion-pumps, e t c . to a l e v e l  e l e c t r o n s [84J)> optimum  the  to  surrounded  Helmhoitz c o i l s  earth,  and  a  i s a b o u t 1mm  electrons are  are d i s p l a y e d  window  pattern  Auger  the  s t r a y magnetic  present.  The  maintained  t h e s a m p l e , and a s no  is  filament  of cathode m a t e r i a l .  potential  gun  o f f - a x i s itungsten  a x i s geometry p r e v e n t s c o n t a m i n a t i o n of by  gun.  which w i l l {about 20  geometry does  not  of of  interfere  m G a u s s ' f o r 50eV  not  satisfy  the  the c u b i c arrangement i s adequate  83  and  experimentally  was a c h i e v e d  more c o n v e n i e n t -  Satisfactory neutralisation  u s i n g t h e c r i t e r i o n t h a t t h e s p e c u l a r team  in  the  LEED p a t t e r n s h o u l d  remain s t a t i o n a r y f o r a l l :incident energies.  The  of  effectiveness  e x a m i n i n g 1(E) c u r v e s example,  the  this  cancellation  f o r symmetrically  {00)  beam  at  was  a l s o checked  eguivalent  equivalent angles  ,fk3  of  the  incidence.  Procedures  When  the  sample  is  first  mounted i n t h e UHV  s u r f a c e , i n w h i c h we a r e i n t e r e s t e d , w i l l by  adsorption  i m p u r i t i e s present  of  surface  atmospheric  must  be  chamber i t s  contaminated  gases  i n the o r i g i n a l single  impurities introduced The  beams  on  C r y s t a l Cleaninq  4. 3 (a)  only  for  of incidence  e i t h e r s i d e of the s u r f a c e normal or non-specular same o r d e r a t n o r m a l  beams;  by  but  also  crystal  by  rod  not bulk  and  by  o n t o t h e s u r f a c e by t h e p o l i s h i n g p r o c e s s .  also  i r r e g u l a r i t i e s remaining  be  annealed  in  i n t h e s u r f a c e and  order  t o smooth t h e  thereby  produce  a  w e l l - o r d e r e d s u r f a c e t h a t e x h i b i t s a s h a r p LEED p a t t e r n In  this  work  clean the c r y s t a l  a combination  o f two t r e a t m e n t s  was u s e d t o  surfaces;  (a)  c y c l e s o f a r g o n i o n - b o m b a r d m e n t a n d vacuum  (b)  heat  treatments  in  oxidising  or  anneals; reducing  84  atmospheres. >  Io-n-fcomhard.men.t-10-  s  gun,  and a  10~  6  was  a c h i e v e d by f l o o d i n g t h e chamber t o between  T o r r o f a r g o n and  device  operating  the  ion-bombardment  i n which a heated f i l a m e n t generates argon  w h i c h a r e a c c e l e r a t e d on t o t h e s u r f a c e o f i n t e r e s t . of  these  removing  ions  sputters  impurities.  and t h e s u r f a c e may  material  from  Fig-  4.5  (a)  surface  become t o o r o u g h  to  methods  of  heating  produce  a  impact thereby  However, t h e h o s t a t o m s a r e a l s o  p a t t e r n ; i t must t h e n be a n n e a l e d by Several  the  The  ions  removed  good  LEED  heating. the  sample  were  employed.  d i s p l a y s t h e s e methods::  the  crystal  was  spot-welded  t o Bh o r P t f o i l  resistively  heated.  produce  s u r f a c e t e m p e r a t u r e of a b o u t  main  a  disadvantage  supporting f o i l  ;  T y p i c a l l y a 50A  of  and  this  current  method  and  would  1200 K.  The  that  the  is  m a n i p u l a t o r l e g s h e a t up and  can  cause severe o u t g a s s i n g problems; (b)  the  crystal  was  p h y s i c a l l y clamped  Varian conductive heater. the  the (c)  the  This heater i s limited i n  t e m p e r a t u r e i t can produce  difficulty  to a commercial  mainly  due  to  of a c h i e v i n g good t h e r m a l c o n t a c t between  c r y s t a l and t h e main h e a t e r b l o c k ; crystal  was s p o t - w e l d e d t o t h i n Kh o r P t  a t t a c h e d t o a s u p p o r t r i n g and  heated  by  floated  to typically  +1-5kV.  strips  electron  bombardment f r o m a f i l a m e n t b e h i n d t h e c r y s t a l is  the  which  T h i s method l e a d s  85  Hi-  US [  -V  u  < >  c/)  o  •kit  < (/) > CL o C\J  *f\\\  1  \ \  _Q  Mh  03  l i S S I i i U 5 T h r e e a e t h c d s o f h e a t i n q a c r y s t a l s a m p l e : (a) d i r e c t resistive h e a t i n g , (fc) n s i n q a V a r i a n c o n d u c t i v e h e a t e r , <c) by e l e c t r o n bombardment. Batcfced l i n e s r e p r e s e n t stairless steel arc sticple ceramic insulators. Other > a t e r i a l s q e c e r a l l y Eh, F t , U o r Ta.  86  to  very r a p i d heating of just  temperatures.  the  sample  However, a c o r o l l a r y  conduction  that  high  of t h i s i s t h a t  t h e c r y s t a l c o o l s down v e r y s l o w l y due thermal  to  allows  to  the  the  poor  selective  heating.  T e m p e r a t u r e s were measured by a l u m e l - c h r o m e l thermocouples attached ijHartmann  and  in  o r by an  Pt/13XBh-Pt  optical  about  10  - 5  most  often  Torr  of  procedure f o r removing s u r f a c e ions.  heating  oxygen^ a p a r t i c u l a r l y  carbon,  The  of  which  is  useful poorly  on t h e  surface  could  u s u a l l y be removed by i o n bombardment a n d / o r  heating  hydrogen. Details  individual chapters  4,3|b)  of  the  crystal  actual  of  assumed t h a t we  i s , in fact,  Fortunately,  i n the form  given  in  the  h a v e some method  c l e a n and  when  such a s u r f a c e composition  Auger  electron  e l e m e n t s o f w h i c h were p r e s e n t e d  AES  are  used f o r t h e  composition  d i s c u s s i o n so f a r has  contaminated.  The  procedures  d e a l i n g w i t h each s u r f a c e .  o f k n o w i n g when t h e s u r f a c e  exists  heating  f a c e s of rhodium s t u d i e d  Monitoring surface  The  for  oxygen r e m a i n i n g  the  only  by  in  argon  consisted  sputtered then  pyrometer  Braun, Frankf urt) -  Chemical c l e a n i n g sample  to the c r y s t a l  or  i n Chapter  as  shown  in  F i g . 4.6.  The  is  monitor  spectroscopy(ABS),  the  2.  e l e c t r o n o p t i c s were used as a r e t a r d i n g - f i e l d ,  i t  analyser  Varian electron  gun  87  -'Electron "1 qun  Gun P  control  3CX)v  Lock - in  Neutraliser  Amp.  nrrmr s i n 2o>t  s i n cot  Freq. x/ 1  X-Y Rotter  J*JL6 S c h e m a t i c d i a g r a m o f field analyser for Auqer multichannel analyser.  ll9UI§  2  Scope  o p t i c s used as a retardinq electron spectroscopy: KCA =  LIED  88  o p e r a t i n g i n t h e A u g e r mode t y p i c a l l y 15 m i c r o a m p s first  for  a  1-5-2.5  kV  beam  of  10-  beam v o l t a g e (V^,).  The  here  simply  the  from  retard voltage V  about  30  multichannel power s u p p l y The reference  and  to  3rd g r i d s are  by  is  typically  controlled  linked  to a  sin2wt  was  sinwt  by  a  programmable  (Kepco QPS2Q00)..  frequency for  circuit  doubled  a PAR  HR-8  b a s e d on  to  neutralise  and  the c o l l e c t o r .  modulation  used  as  l o c k - i n a m p l i f i e r tuned t o detect collected  t h a t o f N a t h a n and  by  the  screen.  H o p k i n s £85]  was  a the A  used  the c a p a c i t i v e c o u p l i n g b e t w e e n t h e r e t a r d g r i d s The  output  s t o r e d i n the m u l t i c h a n n e l signal-to-noise  c o u l d be  ramp  ( F a b r i t e k 1062)  second d e r i v a t i v e of the s i g n a l simple  modulated  r  The  behind  t o e x t r a c t the  ( V < V p ) , w h i c h i s ramped  r  4Q0eV.  analyser  In o r d e r  to  field  biased f l u o r e s c e n t screen  used a s a c o l l e c t o r -  Auger e l e c t r o n s , t h e 2nd about  electrons  s p a c e , as i s the f o u r t h g r i d t o p r e v e n t  p e n e t r a t i o n from t h e p o s i t i v e l y  the  primary  a  g r i d of t h e o p t i c s i s grounded t o a l l o w the  move i n f i e l d - f r e e  it,  produces  p l o t t e d on an  of  the  a n a l y s e r and  ratio  was  1-1  plotter  lock-in  amplifier  the spectrum swept  acceptable,  was until  a t which p o i n t i t  (Hewlett-Packard  7004B).  89  4-4  LEED I n t e n s i t y M e a s u r e m e n t s The  arrangement o f t h e e l e c t r o n o p t i c s f o r o p e r a t i o n  LEED mode i s s k e t c h e d to  be  at  offset  primary  voltage  allows be  the  the  i n F i g , 4.7-  The i n n e r g r i d s a r e n o * s e t  beam v o l t a g e Vp minus  {typically  about  the  the  drift  w h o l e o f t h e " p s e u d o - e l a s t i c " peak  run  now  arrangement  { S e c t i o n 2.1) t o  biased  measurement  of  Auger  prevent  respectively.  5  s p e c t r a , t o provide  field  In this  penetration  of  microamps.  until  a  steady  r i s e from very  important  to  within  f o r the  intensities  energies  the  screen  current  a t a b o u t 1 GOe? where t h e beam 0.01 microamps-  measurement , o f  will  The  low c u r r e n t a t l o w beam  measured i n t e n s i t i e s a r e n o r m a l i s e d beam  field-free  of  U n f o r t u n a t e l y t h e beam c u r r e n t o u t p u t i s a  a plateau i s reached  stays constant  before  mode t h e e l e c t r o n g u n i s u s u a l l y  f u n c t i o n o f t h e beam e n e r g y a s d e p i c t e d i n F i g . 4-8. shows  +5keV,  beams and t h e  i n t h e r a n g e 20 t o 300eV a n d s u p p l i e s a maximum  about  at  The f i r s t a n d f o u r t h g r i d s a r e g r o u n d e d , a s  s p a c e and t o  voltage  This  optimum c o n t r a s t b e t w e e n t h e d i f f r a c t e d  background. for  (usually) a small  5eV) .  d i s p l a y e d on the f l u o r e s c e n t s c r e e n ,  with  i n the  appear  This  1(E) curves  to unit  beam  artificially  b e c a u s e o f t h e l o w beam c u r r e n t s -  curve  energies current  variation since  unless  current,  reduced  i s  at  the low  9C  Gun  Electron  control  LEED  ,  control  l i S ^ I S J4 7 S c h e m a t i c L1ID e x p e r i m e n t s . A  diagram  of  t h e e l e c t r o n o p t i c s used f o r  i ( A) D  H  1.0H  0.5H  0.04 0  50  100  150 V (eV) p  l i S - S I f i L i ? T y p i c a l v a r i a t i o n c f e l e c t r o n gun a g a i n s t beam v o l t a g e Vp i n t h e 1EED node.  bean  current  Ip  91  4.4(a)  p r e v i o u s methods  LEED i n t e n s i t y made  by  measurements i n t h e p a s t have  measuring  u s u a l l y , been .  t h e d i f f r a c t e d beam c u r r e n t e i t h e r  w i t h a F a r a d a y cup c o l l e c t o r i n s i d e t h e c h a m b e r , by  external  the  b r i g h t n e s s o f t h e s p o t s on t h e number  or  directly  indirectly  measurement, w i t h a c a l i b r a t e d s p o t - p h o t o m e t e r , o f  of  comparisons  fluorescent-display  screen.  have i n d i c a t e d t h a t b o t h m e t h o d s c a n  p r o v i d e r e l i a b l e i n t e n s i t y d a t a £86,19 3.  However, b o t h  methods  p o s s e s s some d i s t i n c t d i s a d v a n t a g e s , :  (i)  in  either  method i t i s d i f f i c u l t t o e n s u r e ; t h a t t h e  d e t e c t o r i s m e a s u r i n g t h e whole o f spot  ( i n the  angular  sense)  a p e r t u r e s i z e of t h e d e t e c t o r .  the  due  diffraction  to  the f i n i t e  This i s especially  a  p r o b l e m when beams a p p e a r t o s h r i n k a n d grow a s t h e y .*  t"  vary i n i n t e n s i t y ; (ii)  allied  t o ( i ) i s t h e problem o f p e r f o r m i n g  background  subtraction;  usually  adequate  particular  are  t a k e n w h i c h may, o r may n o t ,  be  of  the t r u e average background around a  values  representative diffraction  spot; (iii)  b o t h methods a r e t i m e - c o n s u m i n g to  use  for  complex  LEED  collecting  must  be  become  patterns.  beams move w i t h i n c i d e n t e n e r g y detector  and  and  moved t o t r a c k  awkward  Non-specular therefore  t h e beams.  the Hence  a l a r g e amount o f d a t a f o r a l o t o f beams  becomes a v e r y c l u m s y  process,  reguiring  freguent  92  re-calibration  and  re-cleaning  of  the s u r f a c e to  overcome problems from c o n t a m i n a t i o n o r beam-surface i n t e r a c t i o n s I 87 ].  R e c e n t l y S t a i r e t a l £88] photographing  t h e d i f f r a c t i o n s p o t s and  i n t e n s i t i e s by  data c o l l e c t i o n , The  This  method  l a r g e amount o f e x p e r i m e n t a l d a t a subseguently  of t h i s  approach  t h e f i l m , d e f i n e d by  recorded then  examined  by  a  associated  large  the i n t e n s i t y  The  integrated  with l o s i n g  analysis  of  intensities.  as  from e a c h f r a m e h a s  to  The point  thereby  error,  and  is  of  Possible false  diffraction t o be  checked  i s thus r a t h e r slow  procedure  analysis,  down on s o u r c e s o f  reguirements  main  each  and i t  and.time.  next stage of development i s t o combine t h e  method  the  o u t p u t of each frame i s  particles  procedure  f e a t u r e s of the photographic  cutting  The  s p o t s i n the background,  makes l a r g e demands on c o m p u t e r s t o r a g e  flexible  p r e s e n t on  of  of the  computer t o deduce t h e l o c a t i o n  f e a t u r e s means t h a t t h e o u t p u t The  of  h o w e v e r , i s i n the a n a l y s i s .  i d e n t i f i c a t i o n o f , f o r example, dust  The  relative  the a p e r t u r e o f the m i c r o d e n s i t o m e t e r  d i f f r a c t i o n s p o t s and t h e i r  visually.  the  analysed at l e i s u r e .  on c o m p u t e r m a g n e t i c t a p e .  problems  determining  of  has t h e a d v a n t a g e o f s p e e d  w h o l e o f e a c h f r a m e i s s c a n n e d and on  procedure  thus h e l p i n g t o preserve the i n t e g r i t y  p h o t o g r a p h s c a n be disadvantage  the  scanning the negatives with a m e c h a n i c a l l y - d r i v e n  microdensitometer.  surface.  investigated  attractive  w i t h a more e f f i c i e n t speeding reducing  and  up t h e  process,  the  computer  t h e p o i n t w h e r e t h e a n a l y s i s c o u l d be done  on-  93  l i n e on a m i n i - c o m p u t e r i n t h e l a b o r a t o r y . computer-controllable photographs  of  V i d i c o n T.V.  LEED p a t t e r n s  With t h e advent  of  cameras, such an a n a l y s i s o f  became f e a s i b l e  a n d was d e v e l o p e d  i n t h i s l a b o r a t o r y i n c o l l a b o r a t i o n with Dr.F.R-Shepherd.,  4.4(b)  V i d i c o n measurement o f 1 ( E )  The  curves  LEED p a t t e r n s d i s p l a y e d on t h e f l u o r e s c e n t s c r e e n  photographed  through  t h e window o f t h e , v a c u u m chamber u s i n g a  N i k o n F2 35mm c a m e r a w i t h a n 85mm f 1 . 8 ring. at  P h o t o g r a p h s were t a k e n  2eV  intervals  l e n s and a  i n the incident  0.75  microamp)  Using  a motor d r i v e u n i t and a  within checked  and  energy being  f o r t h i s type five with  The  extension  beam e n e r g y u s i n g a f i x e d beam  recorded  250  current  (typically  f o r each  photograph.  exposure  film  of energy range c o u l d  minutes.  K2  g e n e r a l l y i n t h e 20 t o 250eV r a n g e  exposure of 1 sec a t f 4 , t h e i n c i d e n t  patterns  were  surface  e n s u r e t h a t no d e t e c t a b l e c o n t a m i n a t i o n  LEED  be r e c o r d e d  condition  Auger e l e c t r o n s p e c t r o s c o p y  back,  was  after  easily  routinely  measurements t o  had o c c u r r e d  during  data  was  also  collection. A Kodak photographed  No. 2 on  calibrated  Acufine  developer  The  photographic  detailed versus  wedge  film  processed  i n a continuous  length  a t 73°F f o r 7 m i n u t e s .  response curve l o g exposure)  optical density  density  t h e same l e n g t h o f f i l m . ' S t a n d a r d K o d a k T r i - X  e m u l s i o n was u s e d a n d t h e in  step  method  depends  of theemulsion so  that  on  knowledge o f t h e  (optical  measurement  (D) o f a d i f f r a c t i o n  a  film  density  of t h e i n t e g r a t e d  spot on t h e f i l m  provides a  94  d i r e c t measure o f t h e amount o f l i g h t  which caused the  of t h e f i l m i n t h a t r e g i o n o f t h e n e g a t i v e assumed,  as  in  l u m i n a n c e £89] impinging  the  of  corresponding  spot-photometric  the  electron  £89].  screen  flux  diffracted  so  that  D  beam c u r r e n t  is  related  c  where t h e d i s t i n c t i o n beam I  f  e  intensity  l-  I Lj-  D i v i d i n g eguation  The l a t t e r Fig.  analyse  = k l ^ = I  i s made b e t w e e n a n c  A  * *  guantity  f l e  to  the  f  ^  (4.2)  absolute  relative diffracted  diffracted  beam  i s measured i n t h e p r e s e n t  intensity work.  4.9 shows a s c h e m a t i c d i a g r a m o f t h e a p p a r a t u s u s e d t o the  Computer  photographic  Eye  California)  System  which  Nova  continuously  negatives  2).  was  {Spatial  of  Data  interfaced  The f i l m  LEED  patterns.  Systems  to  a  The  of  the  I n c . , Galeta,  mini-computer  (Data  h e l d on t h e l i g h t t a b l e i s s c a n n e d  by t h e c a m e r a , a n d t h e i m a g e d i s p l a y e d on t h e T-V.  monitor i n a 512x480 (xy) a r r a y .  The i n t e n s i t y  (z-value)  e l e m e n t o f t h e image may be s a m p l e d by t r i g g e r i n g t h e with  (4.1)  ) gives  V i d i c o n c a m e r a and a s s o c i a t e d e l e c t r o n i c s c o m p r i s e p a r t  General  the  (4.1)  t h r o u g h o u t by t h e i n c i d e n t e l e c t r o n beam c u r r e n t • f i  0  the  ( i ) by  K i s a p r o p o r t i o n a l i t y constant.  |D/i ) = K ( i / i )  that  p r o p o r t i o n a l to the  D = Ki  where  In turn, i t i s  method,  i sdirectly  darkening  appropriate  shows d i r e c t l y  instructions  from  the computer.  on t h e m o n i t o r t h e v a r i a t i o n o f  o f any  digitiser A  profiler  intensity  along  9b  scanner  vidicon camera film transport light table  TV monitor  digitiser y  interface  joystick  nova 2 computer  scope  cassette drive  xy plotter  profiler  teletype  f i S H i e 4j_9 S c h e n a t i c diagram of the apparatus t h e p h o t o g r a p h i c n e g a t i v e s c f L I EE p a t t e r n s .  used  to analyse  96  any  selected  vertical  f o r example, to a l i n e The  profiler  also  by t h e  values  a  of the  i m a g e ; t h i s may  in  setting  d i g i t i s e r ; the  maximum  span  300).  Another  "joystick". the the  T.V.  useful  T h i s c o n t r o l s the m o n i t o r , and  may  image whose c o o r d i n a t e s  to the  of  about  order  to check the  number o f t e s t s were made. on  digitiser density  density  the  light  wedge,  and  zunits  t o any  is  the  spot  on  element  array are then  of  of  available  performance of The  table  Kodak and  After a preliminary  step  the  m o n i t o r when v e r y  Under n o r m a l o p e r a t i n g  was  shows t h e  values  with  at  least  warm-up, a number o f  ci  readings  1.6  the  be  density  scans  from the  of s e v e r a l hours.  intense l i g h t  observed  of  digitiser  The  presence  visually  l e v e l s were f o c u s s e d  the aperture  of  the  the  on  lens f u l l y  on the  open).  c o n d i t i o n s a s e r i e s of d i r e c t comparisons  f r o m t h e V i d i c o n c a m e r a and  a conventional  were made f r o m s c a n s o f t h e  some t y p i c a l LEED p a t t e r n s ; linear  wedge  F i g . 4.J0  calibrated  i n t h e camera o p t i c s c o u l d  microdensitometer  V i d i c o n camera, a  density  scanned.  wedge d e m o n s t r a t e d t h a t t h e  readings  the  i t seems t h a t t h e c a m e r a r e s p o n s e i s l i n e a r  V i d i c o n d e t e c t o r {e.g.  the  system  flashing  used t o " p o i n t "  output p l o t t e d against  o f f l a r e £89]  of  256  density  this  p o s i t i o n of a  show good s t a b i l i t y o v e r p e r i o d s  the  optical  resolve  2.5  of  t o a good a p p r o x i m a t i o n o v e r a r a n g e o f units.  range of  film.  i n t e n s i t y by a f a c t o r  feature  within the  the  computer.  In  placed  be  the  l a t t e r can  {corresponding t o a change i n a b s o l u t e about  correspond,  t h r o u g h a d i f f r a c t i o n s p o t on  assists  density covered over  line  density  e x c e l l e n t a g r e e m e n t was  fine-spot wedge  found  p o r t i o n of Eig.4.10, i n d i c a t i n g t h a t f l a r e i s  and  within not  a  97  250  0  0.4  0.8  1.2  .1.6  2.0  2A  2B  Calibrated optical density  lifluie C a q i t i s e r output leasured f o r d i f f e r e n t reqicns cf a KcdaJc l i e . 2 s t e p density wedqe and plotted aqainst the corresponding calibrated o p t i c a l densities.  98  250  04  0.8  1.2  1.6  2.0  24  2.8  Original optical density  l i f l u i f i b . l l D i g i t i s e r o u t p u t measured f o r d i f f e r e n t r e g i c r s o f a photographic n e g a t i v e c f t o e s t e p d e n s i t y wedge i n f i g u r e 4.10, p l o t t e d a g a i n s t t h e o r i q i n a l c a l i b r a t e d o p t i c a l d e n s i t y c f the wedge. The a r r o w s n o t e t h e p o i n t s o n t h e p l o t w h i c h c o r r e s p o n d t o t h e m i n i m a b a c k g r o u n d and t h e maximum d e n s i t y o b s e r v e d on r h c t c q r a p h s o f t h e 1EED p a t t e r n s f r o m C u ( 1 1 1 ) .  99  significant Fig.  problem  4.11  shows t h e r e s u l t s o f s c a n n i n g t h e n e g a t i v e image  of t h e d e n s i t y diffraction  i n t h e s e measurements.  wedge  which  patterns;  was  this  photographed  along  with  i n d i c a t e s t h e r e s p o n s e o f t h e 35mm  f i l m emulsion t o a s e r i e s of stepped exposures c o n t r o l l e d density  wedge.  response  of  In the the  intermediate  film  i s  a  linear  relation  i slost  region  linear  o p t i c a l d e n s i t y , b u t i n the extremes the  owing  of  function  diffraction  within  the  simplifying  spots  linear the  observed  part  of  conversion  of  plot  low  the  range o f  photographs  response  output  £89J.  density  lies  curve,  digitiser  the  densities  to reciprocity failure  on  the  the  by t h e  of t h e o r i g i n a l  o f h i g h and  I t i s a l s o n o t e d on F i g - 4.11 t h a t t h e maximum of  the  well  thereby  to  optical  density. A s i m p l i f i e d f l o w c h a r t o f t h e computer program, Dr. F. a. S h e p h e r d, c o n t r o l l i n g F i g . 4-12.  the scanning process  U n d e r 'program i n t e r r u p t * , c o n t r o l  i s given  as  particular current  reguired.  diffracted  F o r a g i v e n frame,  the  various  the analysis of a  beam p r o c e e d s by e n t e r i n g t h e  energy  and  o f t h e i n c i d e n t e l e c t r o n beam t h r o u g h t h e t e l e t y p e , a n d  the j o y s t i c k monitor.  A  i s used t o p o i n t t o t h e s p o t viewed s i g n a l from  coordinates  and  i s somewhat  larger  than  r e p e a t e d and t h e a r r a y o f averaged z - v a l u e s memory;  after  on  the  the teletype i n i t i a t e s a routine  s c a n s and d i g i t i s e s an a r e a w h i c h i s c e n t r e d  computer  i n  characters issued  from t h e t e l e t y p e c a n d i r e c t t h e program t o perform operations  w r i t t e n by  on  T.V. which  the  joystick  the spot-  This i s  i s stored  i n the  a two-dimensional smoothing  t h e c o o r d i n a t e s o f t h e maximum a r e d e t e r m i n e d and  a  ope r a t i o n , new  array  1C 0  E°3 display spot profile on CRO plot spot profile on XY plotter Store current I (E) value  input beam energy and beam current  disploy 1(E) curve on CRO plot l ( E ) curve on X Y plotter Store L ( E ) curve on cassette  scon and digitise square orroy centered on joystick coords. signal average 4 scons smooth data and find coords of spot maximum scan new orroy around spot moximum signol average 4 scons calculate average background volue integrote z volues obove background level  normalise to unitbeam current  Ham* Jlj.12 F l o w c h a r t o f t h e c o m p u t e r the scanning o f the photographs.  type integrated spot intensity on teletype  proqraa  which  controls  101  c e n t r e d on t h e s e c o o r d i n a t e s i s s c a n n e d and d i g i t i s e d . . to  In-order  measure t h e b a c k g r o u n d l e v e l , t h i s d i s t r i b u t i o n i s d i s p l a y e d  on t h e T.V. the  monitor  diffraction  u s i n g t h e p r o f i l e r , and t h e e x t r e m i t i e s  spot  are  fixed  joystick.  Assuming a G a u s s i a n  is  by  found  half i t s  determining  maximum  extremities.  JT  can  be  v i s u a l l y a n d marked u s i n g t h e  profile,  the f u l l above  the  standard  the  line  joining  inserted  the  marked  of, a l l e l e m e n t s  o f mean r a d i u s 2©- i s t a k e n a s  Experience  deviation  width of the d i s t r i b u t i o n a t  The a v e r a g e o f t h e z - v a l u e s  on a t h i n a n n u l u s l e v e l z ^ ^.  value  of  the  lying  background  h a s shown t h a t a p r e p r o g r a m m e d v a l u e o f  i n t o t h e program i n o r d e r t o a u t o m a t e t h e  background d e t e r m i n a t i o n without  degrading  the  guality  of  the  analysis. The of  integration  procedure  i n v o l v e s summing a l l t h e v a l u e s  { z - Z j ^ k ) w i t h i n t h e c i r c l e o f r a d i u s 26", a n d d i v i d i n g b y t h e  i n c i d e n t beam c u r r e n t t o g i v e a measure o f t h e intensity  (I^)*-.  distortion  of  variation  of  This  intensity incident  diffracted  normalisation- i s important values beam  at  low  current  energies  with  beam  beam  to avoid  where  the  energy  i s  s u b s t a n t i a l , a s was s e e n i n F i g . 4.8. The  a n a l y s i s o f one s p o t t a k e s  studying 1(E) be  successive  curve  only . a  few  seconds.  By  f r a m e s f o r o n e d i f f r a c t e d beam, a c o m p l e t e  i s generated  and s t o r e d on d i g i t a l c a s s e t t e  and  may  d i s p l a y e d o n * t h e o s c i l l o s c o p e a n d p l o t t e d o n t h e XY r e c o r d e r .  After  the  initial  frame,  the  coordinates of;the  diffracfion  s p o t s a r e s t o r e d i n t h e c o m p u t e r s o t h a t when t h e n e x t f r a m e positioned  in  approximately  using a marker, the  analysis  the of  same this  i s  p l a c e under t h e camera next  frame  can  start  102  without  respecifying  the  positions  of  the  spots  v i a the  j o y s t i c k . , The movement o f t h e beams f o r a 2eV e n e r g y is  sufficiently  small  that  the  d i f f r a c t i o n spot using  the  previous  always  frame  i s  initial  coordinates  1(E)  curves  4.4(c)  search  of  the  successful.  s u b s t a n t i a l s a v i n g s i n a n a l y s i s time  increment f o r t h e new  spot  This  on  the  results  so t h a t a c o m p l e t e  in  s e t of  f o r p e r h a p s 10 beams c a n be p r o d u c e d i n a f e w h o u r s .  M e a s u r e m e n t s o f I { E ) c u r v e s f o r Cu (111)  The  Cu(111)  s u r f a c e was u s e d a s a t e s t o f t h e r e l i a b i l i t y  of t h e V i d i c o n v e r s i o n of t h e p h o t o g r a p h i c experimental  I{E)  curves.  p r e v i o u s e x p e r i m e n t a l £19 3  method f o r  measuring  T h i s s u r f a c e was c o n v e n i e n t and  theoretical  a s some  s t u d i e s f 20 J  were  available. F i g u r e 4. 13 shows 1(E) c u r v e s beams  at  normal  incidence  reproducible  reanalysing  a  uncertainties  from  A l l the features  strip  measuring  of  film  optical  figure  l e s s than  that  {and  hence  5%.  This  v a r i a t i o n must be a s c r i b e d t o a d e g r e e o f u n c e r t a i n t y i n  a p p l y i n g t h e background c o r r e c t i o n . e r r o r s are probably some i n e v i t a b l e At  the  suggests  densities  d i f f r a c t e d beam i n t e n s i t i e s ) a r e t y p i c a l l y slight  in  one s e t o f m e a s u r e m e n t s t o t h e n e x t and  particular in  non-specular  where t h e beam e n e r g y i s e x p r e s s e d  r e l a t i v e t o t h e vacuum l e v e l . are  measured f o r t w o  normal  three-fold  Nevertheless t h e associated  l e s s than those i n v o l v e d , f o r example,  with  v a r i a b i l i t y i n surface conditions. incidence  the  LEED p a t t e r n f r o m C u ( 1 1 1 ) shows  s y m m e t r y , s e e F i g . 2.7, a n d  so  the  same  intensity  1C3  USSli at  renal  1 ( E ) c u r v e s f o r t h e (11) ana (01) tea»s f r c a incidence.  Cu(111)  10 4  variation beams,  i s expected  such  illustrated (11)  and  as  w i t h i n each  t h e . {10,01 ,-T"l) a n d (11,10,01) g r o u p s .  but  (01)  beams  are closely Such  eguivalent,  reguirement  beams  O f f normal  non-specular  the  this  i s consistent  represents  photographic  the  with  the  different,  an  and  incidence, the three-feld  beams  cf  t o t h e (10) and (10)  i n a u n i f o r m way t o t h e s e  and  f o r both  similar  behaviour  phosphor responding  methods.  This i s  i n F i g . 4.14 where t h e m e a s u r e d i n t e n s i t i e s  beams r e s p e c t i v e l y . screen  group o f s y m m e t r i c a l l y - r e l a t e d  essential  spot phoicffietric symmetry  i n the  i s l o s t and beam i n t e n s i t i e s d e p e n d cn b o t h  t h e p o l a r and a z i m u t h a l a n g l e s o f i n c i d e n c e . In  F i g - 4.15  photographs  with  are  a a  a  intensity  data  [ 19j- w i t h a F a r a d a y  although  the  1(E)  1(E) c u r v e s  |b) fe>= 12<>, 0 =  McDonnell  comparison  two  from  6°; (c) r e p r o d u c e s  reported  cup c o l l e c t o r  by  the  woodruff  and  f o r &- = 12°,</> = 7 ° .  a z i m u t h a l a n g l e d o e s d i f f e r by one d e g r e e i n t h i s  t h e data r e p o r t e d i n r e f e r e n c e  curves  measured  t h e V i d i c o n camera f o r t h e s p e c u l a r beam w i t h  (a) "©•= 12°, 4>= 186° experimental  shown  f o r the  specular  19  showed  that  beam v a r y s l o w l y w i t h  the  <f> a r o u n d  these values. Some d i f f e r e n c e s i n peak s h a p e s b e t w e e n t h e t w o (a)  and  {b) a r e a p p a r e n t  very w e l l . exactly  The  slight differences  attributed  eguivalent  to  a  (a) a n d (b) i n F i g . 4.15  because o f time in  degree  shape  increments  of  should  r e v e r s a l symmetry £90 1.  observed  must  therefore  be  o f e x p e r i m e n t a l u n c e r t a i n t y . , To some  e x t e n t t h i s c o u l d b e due t o t h e beam e n e r g y fixed  in  a l t h o u g h peak e n e r g i e s a r e r e p r o d u c e d  However, t h e c u r v e s  be  angles  being  increased  2eV, e v e n where t h e i n t e n s i t y  i n  i s changing  105  Cu(111)  normal incidence •T1 in •+->  01  E  1T  10  a •+->  !q -t-» c  (01)  (10)  100  (10)  200  100  200  Beam Energy (eV)  liflHIS iklif curves o f s y m m e t r i c a l l y e q u i v a l e n t beans f o r t o n a l i n c i d e n c e on C u ( 1 1 1 ) . The i n s e t i n d i c a t e s t h e beam notation and a s p e c i f i c a t i o n o f t h e a z i a u t h a l a n q l e if\ t h e a s t e r i s k i l l u s t r a t e s t h e p o s i t i c r o f t h e e l e c t r o n gun f c r t h e r c r - n c r a a l i n c i d e n c e case.  106  Cu (111) specular beam  I  0  1  -  i  1  -  i  100 200 Beam Energy (eV)  1  1  300  fiS5I§ ^U15 1 ( E ) c u r v e s f o r t h e s p e c u l a r t e a i f o r Co ( 1 1 1 ) : (a) *-=12° , ^ = 1860; (b) ©-=12<> «*=7°. The f i r s t t w c were • e a s u r e d by the »ethod described i n this p a p e r , and (c) represents •easureients Bade by W o o d r u f f and M c D o n n e l l ( 1 9 1 «itb a F a r a d a v cup c o l l e c t o r . #  107  relatively rapidly  with  energy,  but  other  possible  factors  i n c l u d e u n c e r t a i n t i e s i n the a n g l e s o f i n c i d e n c e ( t o the o r d e r of one  degree  in  each  set  of  measurements)  and  in  surface  conditions. The exhibit o u r 2eV  p o i n t of s p e c i a l s i g n i f i c a n c e i s t h a t a l l three  curves  the  within  same  f e a t u r e s a t t h e same beam e n e r g i e s t o  uncertainty.  T h i s encourages  method d e s c r i b e d h e r e Faraday  Stair  photographic  et  and  to  i s a b l e to approach  cup method f o r m e a s u r i n g  contrast.  us  al  believe  that  the r e l i a b i l i t y  of the  r e l a t i v e beam i n t e n s i t i e s .  compared  intensity  data  from  s p o t p h o t o m e t r i c methods on t h e same s u r f a c e , in  the  extent,  perhaps  be s e e n  In to  made h e r e , a l t h o u g h i t . i s o f l i m i t e d  common, may  as b e i n g t h e more s t r i n g e n t . ...  t h i s method o f measurement t h e r e i s no  physical  define the angular s i z e of a spot; the s i z e  is fixed  background  In the  b u t - s i n c e t h e s e methods h a v e a number o f a s s u m p t i o n s comparison  the  the  flexible  t h a t t h e e f f e c t i v e a p e r t u r e c a n be made l a r g e enough t o  include  whole  and,  i f  of t h e s p o t above background  neccessary,  can  Background s u b t r a c t i o n averaged spot.  which  by  is sufficiently  the  s u b t r a c t i o n procedure  aperture  value  of  be  redefined  i s handled  background  of  many e l e m e n t s  averaging  values.  only  The  short  a  during  the  i n an annulus  convenience  subseguently  of  reanalysed  a  to  the  more  r e s t r i c t e d number of data  collection  "hard-copy" at  analysis.  surrounding  c o m p l i c a t i o n s due t o c o n t a m i n a t i o n o r b e a m - s u r f a c e The  approximation  i n an a c c u r a t e manner u s i n g  T h i s seems a p r e f e r a b l e ; p r o c e d u r e  practice  t o a good  leisure,  record,  an the  common  arbitrary  times  limits  interactions. which  represents  may  be  another  108  a t t r a c t i v e f e a t u r e of the  4. 4 (d)  Future  Further  be  not  i n . the c o l l e c t i o n of i n t e n s i t y  As J o n a £ 138J o n l y be  has  f a s t , but  emphasised,  the  ideal  be o n - l i n e i . e . i n t e n s i t y  a v a i l a b l e w h i l e the experiment i s i n progress.  Vidicon  system  i n use  h e r e has  s e n s i t i v e enough to r e c o r d fluorescent generation  screen. of such  £91]  beam  cameras  reported  intensities  will  the f i r s t  the  to  is  direct  certain  have  data  will  present  from  the  the  next  that  increased  sensitivity.  s e t of measurements, Heilmann e t  successful  use  of  a different  about 5 minutes t o c o l l e c t i n t e n s i t y  these  data  make o f authors  f o r 10 beams  200eV. Many p r e s e n t  measurements the camera achieved or  solution  The  V i d i c o n camera t o make s u c h d i r e c t m e a s u r e m e n t s ; required  data  shown u n d e r t e s t t h a t i t i s n o t  However, . i t  Indeed, s h o r t l y a f t e r al  method.  developments improvements  are needed. will  photographic  i f the could  be  with  method h a s  distributions patterns with  very  is  interactions.  a  channel  and weak  to for  adequate  of t h e d i f f r a c t i o n  increased.  been used  £92],  a t t r a c t i v e aspect currents  brightness  e i t h e r externally with  internally  latter  V i d i c o n c a m e r a s w o u l d be  In  t h e use  principle  for  direct  s p o t s seen  by  this  be  can  o f an i m a g e - i n t e n s i f i e r ,  plate electron multiplier. measure the  (nanoamp)  photoemission  production beam  angular  of v i s i b l e  currents  The  £137].  LEED An  o f p o s s i b l e f u t u r e r e d u c t i o n s i n i n c i d e n t beam  the a s s o c i a t e d p o s s i b i l i t y  of r e d u c e d  beam-surface  10 9  One amount of the  o f t h e p r o b l e m s o f any of  screen  the  the  provision  of  by  the  total.  We  diffracted have  interest a  fast  in  a  can  events,  avoided  differentiate is still  the  this  a major task.,  only s i g n i f i c a n t  diffraction  spots  by  analysing The  reasonable  features, from  of  a small  manner.  on-line^ r e c o r d i n g system, at a  true  area  problem  then only  the  portions  beams i s o n l y  semi-interactive  c o s t , that automatically records yet  unwanted b a c k g r o u n d  d a t a i n a h a r d - c o p y f o r m and  features of  deviceis  At normal ; i n c i d e n t e n e r g i e s  occupied  of  recording the  time spent i n d i g i t i s i n g  t h e LEED p a t t e r n .  fraction  image a n a l y s i n g  and  spurious  110  CHAPTER  5  LEED CEYSTALLOGBAPHY  1.11  5.1  General  Considerations  We have s e e n t h a t beams  contain  the  i n f o r m a t i o n ; on  b o t h t h e p a r a l l e l and 1(E)  curves  of  experimental  LEED  the structure of the surface i n  perpendicular  directions..  Fortunately,  calculated f o r t r i a l structures are guite sensitive  t o changes i n t h e s u r f a c e Changes  intensities  in  g e o m e t r y a s we saw i n  non-structural  damping, v i b r a t i o n a l  parameters  properties  such  etc.  Section  as  3.2(c).  the i n e l a s t i c  produce  uniform  small  c r p o s i t i o n f o r a l l t h e peaks i n an 1 ( E )  c h a n g e s .in... i n t e n s i t y curve 1 1 2 J . The  usual  information  procedure  with  LEED  c o n s i s t i n g of three  (i)  followed  has  been  a  steps:  experimental  to  obtain  trial  and  structural error  process  i  data  Is  collected  for a  number  of  d i f f r a c t e d beams a t s e v e r a l a n g l e s o f i n c i d e n c e ; (ii)  a  theoretical  s e t of data  i s p r o d u c e d f o r t h e same  beams b y p o s t u l a t i n g a s t r u c t u r a l m o d e l a n d a number o f n o n - s t r u c t u r a l (iii)  structural  parameters)  calculations until experimental  agreement calculations  between for a  a c c e p t e d as t h e proof  parameters;  (and p r e f e r a b l y , b u t by no  non-structural  choosing  are  means varied  often, i n the  an a g r e e m e n t i s f o u n d b e t w e e n t h e  and t h e o r e t i c a l d a t a .  the  particular f o r the  experimental structural correctness  data model of  the  and i s  the  usually  postulated  112  model,  Underlying, t h i s i s the assumption t h a t such  especially  i f  accidental.  i t involves  Small  a ,large  discrepancies  data  base,  between  preparation of  errors i n  setting  the  t o such  incidence  the c a l c u l a t i o n s , such Therefore calculations evaluation  a s t h e s u r f a c e Debye  determining and  has  the  experiment  guality  i s  crucial.  Ihile  us  suppose  we  have  general,  and  relative  to the bulk.  contractions  parameter  such  the t o t a l  the  misfits  further increased i f ,  curves  improves  are  difficulties  i s  an  surface  layer  i n v o l v e 70  final  result.  as t h e i n n e r p o t e n t i a l i s  a  as i s often the  visual The  case,  t h e correspondence  unknown  7  for a typical  would then  discounted.  but worsens those o f o t h e r s .  for  number o f c o m p a r i s o n s t o be  made, r a p i d l y becomes u n m a n a g e a b l e i n obvious  i t is  I(E) curves  of  V i s u a l examination  then a l s o a l l o w e d t o v a r y ,  parameter  data,  f o r 10 d i f f r a c t e d  d i f f e r e n t c o m p a r i s o n s t o be s y n t h e s i s e d i n t o one non-structural  this  t h e eye i s a b l e  s t r u c t u r a l m o d e l s , a s w o u l d be t h e c a s e expansions  the  F o r example, l e t  e x p e r i m e n t a l data  beams a n d have c a l c u l a t e d t h e c o r r e s p o n d i n g  range o f  into  e v a l u a t e t h e l a r g e d a t a base needed i f  i s t o have c o n f i d e n c e i n t h e f i n a l r e s u l t . that  enter  f i t between In  one  when  poor  temperature. of  been p e r f o r m e d v i s u a l l y .  impossible t o objectively  a  factors  angle,  that  t o make f i n e d i s t i n c t i o n s b e t w e e n c l o s e l y s i m i l a r  If  be  of the c r y s t a l surface o r s l i g h t l y i n c o r r e c t . v a l u e s  t h e p o o r l y known n o n - s t r u c t u r a l p a r a m e t e r s  different  cannot  t h e t h e o r e t i c a l and  experimental s e t s o f data are u s u a l l y a t t r i b u t e d as e x p e r i m e n t a l  agreement,  The  analysis,  d i f f i c u l t i e s are a  change  with experiment conseguence  uncertainty  even  in  one  f o r some of  these  i n the values of the  113  "correct"  parameters.  Therefore, a  t h e r e i s a r e a l n e e d i n LEED c r y s t a l l o g r a p h y f o r  numerical f a c t o r  structure can  from  which  ideally  can  both  t h e e x p e r i m e n t a l and c a l c u l a t e d  g i v e some measure o f t h e r e l i a b i l i t y  reliability-factor whole  set  of  or index  features  be ween c a l c u l a t i o n s and  (i)  is  has  necessarily t o be =  the  best  intensities  complex  evaluated  observations.  the  of t h a t r e s u l t .  and  Such a  because  a  i n the comparison  These f e a t u r e s i n c l u d e :  t h e g e n e r a l s h a p e o f t h e I|E) the absolute  <ii)  select  curves  ,regardless  of  intensities;  number and e n e r g i e s o f maxima,minima,  shoulders  etc. ; (iii)  the presence  of  portions  p e c u l i a r i t i e s e.g.  of  curves  n a r r o w p e a k s , deep  with  marked  troughs.  i Several  attempts  have b e e n made t o c o n s t r u c t  reliability-  i n d i c e s t h a t t a k e r e g a r d o f seme o r a l l o f the a b o v e p o i n t s they is  are outlined  i n the next s e c t i o n .  t h a t o f Z a n a z z i and J o n a | 2 3 J  The  most c o m p l e t e  and index  which i s d i s c u s s e d i n d e t a i l -  114  5- 2  ReliaMlity-iadices Several  authors  reliability-indices  have to  attempted  complement  to  construct  visual evaluations.  t h e most s t r a i g h t f o r w a r d i n v o l v e s c a l c u l a t i n g the d i f f e r e n c e i n corresponding and  experimental  simple One  t h e mean v a l u e  peak p o s f i o o s i n t h e  of of  theoretical  curves  «S. 1 )  where  the  E ^  the c a l c u l a t e d the &E  are the e n e r g i e s at which the i and  observed  c u r v e s and  beam u n d e r s t u d y £93,94]. criterion  intensities  is and  disadvantages be matched and resolved  be  and  completely  exclusively  defect of  disregards their  in  the  the peak  positions.  Other  in  positioning  poorly-  d e c i d i n g w h e t h e r a m i n o r peak s h o u l d ,  or  considered. Hove e t a l £9.5], c o m b i n i n g  reliability-indices,  have  proposed  the  use  each o f which tend t o  I (E) c u r v e s .  The  first  employed i n s t r u c t u r e d e t e r m i n a t i o n s £96,97 J  most i m p o r t a n t  degrees of s u b j e c t i v i t y  attempts,  of  N t h e number o f p e a k s  a r e p o s s i b l e a m b i g u i t i e s i n t h e c h o i c e o f peaks to  R e c e n t l y Van  features  i t  weighs  features  should not  earlier  that  The  peak o c c u r s i n  by  the cf pick  experience five out  separate different  two a r e s i m i l a r t o X-ray  of  those  crystallography  115  R1 .=  Z. §c,I-  | - I- i J/ 2  £tL and  H2 =  where  c •i s a  calculated to  ^  E^.  I- l  ft^ l  1  ^ * ! ' . ob* ' ^ X  scaling  ^ l , * ^  2  factor  that  *5-3)  2  places  the observed  ((  The f a c t o r s fi1 and R2 t e n d t o e m p h a s i s e heights  ignoring shoulders evaluates  and and  the f r a c t i o n  of 1(E) c u r v e s  widths bumps  of  peaks  within  a  R4 =  the  valleys  peak.  This  , - 1»- [•  a  in  whilst  third,  R3,  can  measure,  better  The f a c t o r s  1  (5.4)  tiC  Eli  2  R5 =  match  of the energy range f o r which t h e s l o p e s  have d i f f e r e n t s i g n .  2.  the  and  than-Rl o r 82, d i f f e r e n c e s i n minor s t r u c t u r e .  and  and  i n t e n s i t i e s on t h e same s c a l e f o r a n e n e r g y r a n g e E .  positions,  where  (5.2)  r  1  ^.i'*  V  ^  1 Z  'l . l r *  primes i n d i c a t e d e r i v a t i v e s ,  * *  3  5  5 >  match i n g r e a t e r  detail  t h e s l o p e s o f t h e t h e o r e t i c a l :and e x p e r i m e n t a l 1 ( E ) c u r v e s .  In  principle,  R-  factors  when e x p e r i m e n t  should  a n d t h e o r y match c l o s e l y , a l l f i v e  simultaneously  attain  their  minimum  However, i f t h e p r o p o s e d s u r f a c e s t r u c t u r e i s w r o n g , v a r i o u s f a c t o r s c o u l d be e x p e c t e d  values. then  the  t o show a s c a t t e r i n g o f minima  at v a r i o u s spacings. The  most  complete  reliability-index  proposed so f a r t h a t  attempts  t o i n c l u d e a l l t h e f e a t u r e s mentioned above i s t h a t  Zanazzi  and  Jona  (ZJ) £23],  of  T h i s i n d e x has been used i n t h i s  116  work t o d e t e r m i n e t h e s t r u c t u r e s o f r h o d i u m  5.2 (a)  the r e l i a b i l i t y - i n d e x  The  surfaces.  o f Z a n a z z i and Jona (ZJ)  Z J i n d e x c o m p a r e s d i r e c t l y t h e s h a p e s o f t h e two c u r v e s  u n d e r s c r u t i n y by c o m p a r i n g t h e i r d e r i v a t i v e s , a n d a t time  takes  i n t o account the features described  the  same  i n Section  5.1.  Thus t h e r e l i a b i l i t y - i n d e x f o r a s i n g l e beam {..23J i s r w(E)|cI».  r • =  The  , - I ! . |dE /  I I- i dE  (5.6)  n o t a t i o n f o l l o w s t h a t above; t h e s c a l i n g c o n s t a n t  allows  f o r an  arbitrary  intensity  scale i n the  c^  again  experimental  curves: r  c; = c  The  | I  c  ^dE  /  I.  c J  dE  (5.7)  w e i g h t f u n c t i o n w(E)  w(E)=  -|c-I«  ,- I " , I / JI«- | I + €  (5.8)  emphasises the extrema.of the observed curve through t h e i n v e r s e d e p e n d e n c e on i - j # < }  high  curvature  derivatives. w{E)  from  have an  s  sell  as those  prominent  features  with  i n both s e t s of curves through t h e use o f second  The d i f f e r e n c e f u n c t i o n i n t h e n u m e r a t o r vanishing  inflection  disadvantage  a  ) /  at point  of equation  inflection at  the  points, unless same  energy.  (5.8) i s t h a t w{E) v a n i s h e s  prevents  both A  curves  possible i f t h e two  117  curves of  h a v e s t r a i g h t p o r t i o n s i n t h e same e n e r g y r a n g e ,  opposite  slope.  The  integral f o rsmall H»  f a c t o r £, p r e v e n t s  even i f  divergence  of the  . J a n d i s c h o s e n £ 2 3 ] t o he  L obJ y  £- = H I  This choice ensures  eguation  upper l i m i t . value; two  and t h e o r e t i c a l  (5.6)  of  the  of  scale  of  intensities.  s t a n d s , t h e i n d e x r ^ h a s no  For a given p a i r  curves  i t has  theoretical a  specific  t h e s m a l l e r t h i s v a l u e , t h e b e t t e r t h e match b e t w e e n t h e  curves.  factor  (5.9)  t h a t w (E) i s i n d e p e n d e n t  both t h e experimental As  , \  Thus i t i s c o n v e n i e n t  t o introduce the  reduced  r-  £23]  (r.)  = r- /0.027  (5. 10)  where  0.027 i s an a v e r a g e v a l u e o f r ^ f o r random p a i r s o f c u r v e s  £23].  Eandom p a i r s o f c u r v e s t h u s g i v e v a l u e s  of ( r )•  of  the  order of u n i t y . ZJ  applied  this  reliability-index  single  beams a n d made a d i r e c t  £r )  and  r  t  degrees  individuals. between  This  of  association  f i t assessed  enabled  to  ZJ  to  many  between  visually produce  examples of  a  values  of  by a number o f correspondence  v i s u a l e v a l u a t i o n s and ( r ^ . ) ^ v a l u e s w h i c h i s r e p r o d u c e d  i n T a b l e 5.1. The  d e t e r m i n a t i o n o f a s u r f a c e s t r u c t u r e i n v o l v e s more; t h a n  one  beam,  The  concept  either  a t t h e same o r d i f f e r e n t a n g l e s o f i n c i d e n c e .  of a s i n g l e  beam  reduced  r - f a c t or  was  therefore  i  11.8 V i s u a l match f o r a s i n g l e beam  Good  Mediocre  S i n g l e beam i n d e x (r,),; or many-beam i n d e x fi  0.20  0.3 5  0.50  Probable  Doubtful  R e l i a b i l i t y of structure  Very p r o b a b l e  Bad  T a b l e 5.1 C o r r e s p o n d e n c e b e t w e e n v i s u a l , m a t c h and (t,)^ f o r a single beam (first and s e c o n d r o w ) , and between B f o ra s t r u c t u r a l model a n d i t s r e l i a b i l i t y (second and t h i r d r o w ) . A f t e r Z a n a z z i and J o n a £ 2 3 J . e x t e n d e d b y 2J t o a s e t o f beams  where  The  A E•  quantity  reliability-index  = E . -E 21 It  r in  satisfies  r  LEED  many o f t h e r e q u i r e m e n t s f o r a  crystallography.  However,  LEED  s t r u c t u r a l a n a l y s e s h a v e been p e r f o r m e d on d a t a b a s e s o f v a r y i n g degrees of completeness. the  basis  of  preferably  only  S t r u c t u r a l m o d e l s c o u l d be p r o p o s e d on  a f e w beams a t one a n g l e o f i n c i d e n c e , o r ,  f r o m a much l a r g e r r a n g e o f  accommodate  these  considerations,  experimental  ZJ  proposed  data.  To  an o v e r a l l  8-  factor  8 = C (P/n) +g] r "  where p and g a r e c o n s t a n t s , tested.  This  form  and  r  n-•. i s t h e  (5. 12)  number  of  beams  was u s e d s o t h a t t h e b r a c k e t e d t e r m s h o u l d  d e c r e a s e w i t h i n c r e a s i n g n b u t should.; n e v e r become s m a l l e r  than  119  some  asymptotic  v a l u e q.  "wrong" m o d e l f o r w h i c h could  T h i s a v o i d s the s i t u a t i o n i n which  a very  l a r g e number of beams were t e s t e d  produce a s m a l l value of The  numerical  values  a  B.  of  p  and  q  are  determined  by  e s t a b l i s h i n g a r e l a t i o n s h i p b e t w e e n t h e n u m e r i c a l v a l u e o f fi and the  reliability  of  s i m p l i c i t y ZJ found that  was  etc.  a  for  assigments  maintain  using the denominations  given  structure,  shown i n t h e s e c o n d  suggests  possible  asymptotic  the  they  and  the  t h i r d rows.  at  corresponding  This  value  The  of  increase judged  the  rapidly  f o r n<3,  assignment  from  (5.12).  ( r ) j values r  comparing  random  used  t h e r e f o r e s e t t o 2/3.  function  in  eguation  so t h a t s t r u c t u r a l  worse  in  the  A l s o , the  (5.12)  models w i l l  should not  a s v e r y p r o b a b l e on t h e b a s i s of l e s s t h a n 3 beams.  o v e r a l l R - f a c t o r proposed  B  The  probable"  s t r u c t u r e B - f a c t o r must r e m a i n  v a l u e o f g was bracketed  rows o f  g i n eguation  t h a n " d o u b t f u l " r e g a r d l e s s o f t h e number o f beams analysis.  two  the B v a l u e  v a l u e g must be s u c h t h a t , where t h e obtained  For  assignment  of "very  arrived  v a l u e s f o r p and  a r e o f t h e same o r d e r a s t h o s e curves,  to  s t r u c t u r a l model.  e s t a b l i s h e d f o r s i n g l e beams i n t h e f i r s t T h u s , by  The  corresponding  i t convenient  T a b l e 5-1-,  then  the  choice  of fi d o e s constant  for  change  = I (3/2n) •  much  structures  The  by Z J i s  (2/3) J \ r ^  (5-13)  o f p=3/2 h a s t h e a d v a n t a g e t h a t t h e n u m e r i c a l not  be  beyond  that  n=10.  B  are determined  remains w i t h 10,15  value almost or  20  120  teams.  ,  The are  d e t a i l s o f the numerical e v a l u a t i o n o f  given  in  instability  original  problems  experimental  and  common ^ l i n e a r experimental the  the  with  data  must  The  with only  output  reguirements.  5.3  Structural Cu (111)  use  of  Hoise  and  beams  corresponding using  to  minor  eliminate  range  Using  a finely-spaced  i n  t o accommodate  be u s e d  the  the  input-  Fae%or:  at  two  to  T he  illustrate  r e l i a b i l i t y - i n d e x and t h e r e f i n e m e n t s and  angles  of  curves calculated and  V,  together  »ith t h e  unreconstructed  potentials.  surface  The c a l c u l a t i o n s  inner potential of  top layer spacings  Referring  curves f o r a t o t a l of  incidence,  f o r an  work.  -9.5eV  and  were  for a  f r o m Ad%= -10S t o +-1055 o f t h e b u l k The: c u r v e s  shown  figures  a r e o n l y f o r t h r e e v a l u e s o f &&% t o a v o i d  The  c u r v e s c a l c u l a t e d f o r C u {111)  are almost  in  changes  The Z J fie1ia h i l i t y  s p a c i n g i n s t e p s o f 2.51 (Q.Q52A).  1(E)  the  was used a s s u p p l i e d by t h e  a Cu{111) s u r f a c e w i l l  f o r an i n i t i a l  of  a l l  scatter  abrupt  modifications  Analysis  the ZJ  t h e V,  performed  avoid  be removed p r i o r t o t h e c a l c u l a t i o n o f  F i g . 3.11 a n d F i g - 5 . 1 , we c a n s e e 1 { E )  four  To  involved,  a d d i t i o n s made t o i t d u r i n g t h e c o u r s e o f t h i s to  .  <5.6J  S u r f a c e A s An E x a m p l e  R e s u l t s from the  Z J .£23  integrals  programmed i n d e x  authors  of  data a r e put onto  grid.  reliability-index  derivatives.  the  theoretical  energy  paper  equation  from  the  i n the  overcrowding.  two  potentials  i d e n t i c a l , c o n s i s t e n t w i t h t h e s i m i l a r i t i e s noted f o r  121  Energy <eV)  IiSi>I£ 5 . 1 C o m p a r i s o n o f some e x p e r i m e n t a l 1 ( E ) c u r v e s f o r Cu(111) m i t h c a l c u l a t i o r s f o r t h e p o t e n t i a l s 1*and V,., a t «=12°, ^ = 6 0 ; ?  =-9.5eV  and A d * = * 5 ,  0 and 5 X .  *  122  t h e p h a s e s h i f t s i n S e c t i o n 3.1(b) In  a  surface  structure  calculated  and e x p e r i m e n t a l  variation  of A d %  This l a t t e r is  1(E) curves  parameter i s f i x e d  guantity  necessary Ad$.  involves  since,  results i n a translation  therefore  in  a  structural  of  involves  value was  of  attempted  potential.  calculated  simultaneous inner  associated  with  curve  potential along  of &&%  determination  of the  This  delicate  beams measured f r o m t h e  Cu(111). s u r f a c e and t h e s e r e s u l t s a r e s h o w n , f o r e a c h as t h e l o w e r This  rows o f T a b l e  type  of  some  beams  comparison  e.g. t h e  g u i t e poor f o r o t h e r s , /\,&%=+5%. B a l a n c i n g of  experimental  i s  very d i f f i c u l t  t o make a s a  uncertainty i n V  o p  e.g.. t h e  (10)  beam  a g a i n s t bad f i t s  calculated  and b&%  curves  i s  overall  visual  of  estimate  suggests  good t  to  Eig.,3.11  at  f o r s o many p a i r s difficult  are inevitably appreciable.  t h i s a n a l y s i s shows t h e two p o t e n t i a l s t o be The  very  (00) beam o f f i g . 5.2 a t &&%--5%  good f i t s  and  potential,  5.2.  v i s u a l e s t i m a t i o n o f t h e d e g r e e o f f i t may v a r y f r o m for  the  value  potential-  f o r a l l 16  an  i t i s  a change i n t h e i n n e r  the  a  the  a  analysis,  A v i s u a l estimation of the " b e s t - f i t "  also  "best-fit"  not- only  The i n n e r p o t e n t i a l i s c l e a r l y  a good a p p r o x i m a t i o n ,  energy a x i s .  Batching of  a p r i o r i f o r the c a l c u l a t i o n s but  t o d i s t i n g u i s h i t s e f f e c t s from those  To  procedure  the f i n a l  but a l s o a v a r i a t i o n of t h e i n n e r  a p o o r l y known g u a n t i t y .  important  analysis,  and t h e Moreover  indistinguishable.  best-fit  values of V  of  =-  9±2eV a n d &d$=-2.5±2. 5%. The as  eguivalent operation using the ZJ r e l i a b i l i t y - i n d e x  follows:  (i)  an  1(E) c u r v e  i s c a l c u l a t e d with a  i s  reasonable  123 E x t e n t of Comparison  C o n d i t i o n s of bestagreement  Pot.  n  EfeV)  Analysis  AdJ  V,  16  2382  R-factor visual  - 4 . 1±0. 6 -2. 5±2-5  -9-8±0.6 ,8± -9 ±2  0.132  Cc V,  16 16  2342 2342  R-f a c t o r visual  -4.2±0.6 -2-5±2.5  -9.0 + 0.6 -9 ±2  0. 136  CU.  T a b l e 5.2 surface.  Summary o f s t r u c t u r a l d e t e r m i n a t i o n s  v a l u e of V ;  ( i i ) the v a l u e s of  ar  cf  -  p a i r s f o r m e d by  the  curve  other.  minimum v a l u e o f  The  the c o r r e s p o n d i n g  translated  "best *  curve  on  various  one  the  c a n t h e n be  d a t a and  repeated  and  the  on  the  ( r ) j i n d i c a t e s t h e b e s t match,  and  or  r  potential  for  the  calculated  i s calculated  or  single-beam  hand  amounts A V  c u r v e i s V . * & V . , F o r a number o f beams, 6(  Cu(111)  r  by  inner  1  the  ( r ) j a r e c o m p u t e d f o r a number  observed  calculated  of  t h e . minimum i n ~iT f o u n d -  The  r  f o r o t h e r m o d e l s e.g-  from  process  a c h a n g e i n Ad35.  In t h e i r o r i g i n a l a n a l y s i s ZJ p l o t t e d t h e r e s u l t s of such procedure  as ~E~  r  (the energy- weighted  r-f a c t o r s ( ^ ) ) # as i n eguation L  the  best  combination  of  mean o f t h e i n d i v i d u a l beam  (5. 1 1 ) , a g a i n s t V  ftr  o r &d%  in  F i g . 5.2.  This  t o t a l o f 16 beams and energy  r a n g e o f 2342eV.  a n a l y s i s uses t h e V  e x p e r i m e n t a l . 1(E) The  can  note  two  curves  points  e s t i m a t e s of t h e p o s i t i o n of F  r  from  of  An  Cuj1.11)  potential, over  a  a  total  minimum v a l u e o f "ry- i s e s t i m a t e d  t h i s method t o be f o r AdI=-4±2& and V We  and  minima »as c h o s e n by i n s p e c t i o n .  e x a m p l e o f t h i s method o f p r e s e n t a t i o n i s shown f o r t h e data  a  by  =-9±2eV. such  a l o n g t h e &&%  plots. and V  or  First,  the  axes  are  s u b j e c t t o e r r o r owing t o the l a r g e s p a c i n g between p o i n t s a l o n g  12a  '  -10  — i  -5.  r  0  1  +5  r~  +10  f i a u i f 5^2 P l o t o f r a q a i n s t Ad% f o r v a r i o u s v a l u e s c f Vor for Co (111) with the ¥^3 potential. E r r o r fcars a r e s t a n d a r d e r r o r s i n the weighted l e a n . r  125  the  &d%  axis  (2.5%). > and  p a r t i c u l a r l y o f Q&% terms of computer Second, weighted  the  where  mean o v e r  n  point the  before. Fig. why  Ji^rk  is  on  one  16 beams  the  aud  e r r o r s c a n be A Fig-  5-3  2  i n  so  where are  have  a  Fig.  5.3  1  values plotted  0.173 in  are  r  indicated  at  this  bars  on  that  anomaly i s suggested  of  individual  tr^)^,  for  as a f u n c t i o n o f AdX  for V  weighting  of  corresponds the  less  to  ± £  r  the  r  {for  68%  the  The  The  from Of  others  A l s o shown i n whose  v a r i e s from  by  ainimum  degree  of  (t )^  =0.057 t o  mean  {dashed)  r  probability)  indicates  w i t h t h e topmost i n t e r l a y e r s p a c i n g c o r r e s p o n d i n g  curves  suggests  of  =-9.5eV.  of  t h a n 20%.  Ad$=-4-15L  i n d i v i d u a l curves  {r )  beams  o n l y 9 a r e shown f o r c l a r i t y ,  However, i t i s apparent  individual  as  the g u e s t i o n  so s m o o t h , g i v e n  r  contraction -4±3%.  by  of t h i s apparent  c  curve  The  (5. 13)  1 / z  T h i s o p e n s up are  is a  the other symbols are  ( r ) -=0-240 w i t h a s t a n d a r d e r r o r £ =0.047. f  in  for : analysis-  3  E  o f beams and E  i n F i g . 5-2  , as t h e d a s h e d c u r v e , i s a p l o t o f  agreement  costly  large.  combined  of  grid,  £98]  " > ^ * C  shown i n F i g . 5.2  16 beams a v a i l a b l e  value  mean i s  substantial.  rationalisation  Cu ( 1 1 1 ) , the  r >  _ Y  number  c a n be  the curves  rather  of the curves available  Some t y p i c a l v a l u e s o f  5-2  A finer  time-  each  = £  v  a x i s j2eV).  or  v a l u e s , w o u l d h o w e v e r be  s t a n d a r d e r r o r on t h e w e i g h t e d  C  V  i n F i g . 5.3  that  the  that  the  minima  of  l i e w e l l w i t h i n these  error  in  the  value  a to  a l l  the  limits,  and  o f J^d%  that  Cu(lll) VCu13  0.40 H  0.30H  (r ), r  0.20H  0.10-  Ad% f i g u r e 5^3 P l o t s f o r C u ( 1 1 1 ) o f ( r ) . for 9 individual beaas versus Ad* f o r t h e V i j p o t e n t i a l w i t h ? «-9.5eV. The d a s h e d l i n e shows t h e dependence o f t h e e n e r q y w e i q h t e d aean T, versus Ad?. r  C k  t  #r  r  127  corresponds r .  to  a best  from  corresponding  curves-  Accordingly Ai^A  £± = C ^ A E - C A d ^  where t h e A d V. fitted  of V  to  the  set  of  interlayer  separations  t o t h e minimum i n e a c h o f t h e i n d i v i d u a l we c a n d e f i n e  Z  =  -Ad~  /2>E  AB-Ad^-  c  (5.14)  L  L  )2 /  rt  (ii-1)XAEc]'/2  are determined, a f t e r  the  should  or  rr  p e r h a p s be e v a l u a t e d (6dJ^ )  f i t f o r a particular value  curves  by  extra  (5.15)  points  interpolation; A d ^  have  ±2 £J  been  ( f o r 95$  p r o b a b i l i t y ) c o r r e s p o n d s t o -4.1±1.2S. , T h i s r a n g e i s i n d i c a t e d i n F i g . . 5 . 3 a n d i t p o i n t s t o a much s m a l l e r , a n d a p p a r e n t l y  more  r e p r e s e n t a t i v e , e r r o r i n t h e geometry t h a n t h a t s u g g e s t e d  above.  It  the i n d i v i d u a l  curves  t h a t t h e mean  curve  for T  r  i s  a l s o c l e a r f r o m F i g . 5.3, p r o v i d e d  lTf)i  show s i m i l a r  will  be  a  variations with ^df,  smooth  function  of odS  even though the (r )  i n d i v i d u a l l y e x h i b i t varying degrees o f f i t . Since  theT^  are  variables,  namely  presenting  the data  functions  &&%  and  i s  in  diagram; t h i s i s depicted These  plots  of  V r, ft/  the  at  the  constant error  interpolation present  in  two  important  a more i n f o r m a t i v e method o f form  of  a  i n E i g . ,5.4 f o r b o t h  contour the  plot  involved is the  small data.  in  not  using  compared  with  a  o f ry,  l i n e s of constant  &&% t o o b t a i n an e x p a n d e d g r i d  or  potentials.  were c o n s t r u c t e d fcy t a k i n g t h e o r i g i n a l g r i d  v a l u e s and i n t e r p o l a t i n g s e p a r a t e l y a l o n g and  least  V  or  of a b o u t 900 p o i n t s ; true  other  two-dimensional errors  already  The p o s i t i o n o f t h e minimum i n r  that  f i S S I S S±!L C o n t o u r p l o t s f o r Cu (111) f o r t h e p o t e n t i a l s (a) and (b)  of r v£ . c  f  versus Ad*  acd  129  determines  t h e best, f i t v a l u e s  inspection.  Also  corresponding for  r  in  ? .  and A d S  F i g . 5.4  are  i s  the  found  error  t o ± £ j a n d ± £\j ( t h e s t a n d a r d e r r o r i n t h e  confidence  limits  these are evaluated  on  the  location  of  at t h e nearest grid  the  point  by bars  minimum  t h e i n n e r p o t e n t i a l , d e f i n e d a n a l o g o u s l y t o Q ) which  68% x;  shown  of  places  minimum and  of  provide  e s t i m a t e s o f t h e e r r o r s i n t h e l o c a t i o n o f t h e a c t u a l minimum. The  plots  of  F i g . 5.4  illustrate  r e l i a b i l i t y - i n d e x approach i n a n a l y s i n g displays  the  values  experiment  c a n be s e l e c t e d i m m e d i a t e l y .  t h e . value  LEED  o f y; p a r a m e t e r s  data;  giving Each of  of  the  with  such  best^fit  with  these  contour  p l o t s p r o v i d e s an i m m e d i a t e a s s e s s m e n t o f 784 c u r v e s o f t h e t y p e shown  in  different  F i g . 5.1  {that  i s  for  16  beams a t 7  v a l u e s o f A d $ and 7 d i f f e r e n t v a l u e s o f ? * ) 0 /  The v a l u e s o f o d S a n d V  or  identical  to  T a b l e 5.2..  values  corresponding  w i t h i n one s t a n d a r d  Both  potentials  topmost i n t e r l a y e r low  1(E) curves  e r r o r f o r t h e two  indicate  a  s p a c i n g o f -4.1±0.6% and  a n a  " <^ v  are  f  potentials.  contraction  of the o v e r a l l ZJ r e l i a b i l i t y  0.136 f o r V^i2  t o minimum : ~x  in  the  =-9.4±0.6eV.  The  f a c t o r , R,  (0.132 a n d  r e s p e c t i v e l y ) and t h e s m a l l e r r o r i n t h e  b e s t - f i t v a l u e s o f A d % and V  o r  suggest  that  this  represents  a  rather well-defined structure. Previous  studies  o f t h e (111) s u r f a c e s o f FCC m e t a l s  LEED h a v e i n d i c a t e d no l a r g e e x p a n s i o n s surface has  layer,  suggested  indicate  s e e S e c t i o n 5.5.  an expansion  the  For both n i c k e l  topmost  [ 11,120]  F o r aluminium,  o f 5% w h i l e  spacing and  or contractions  other  of  one s t u d y  studies  with the £11]  £11,120]  i s e g u a l t o t h e b u l k w i t h i n 5%. platinum  £122],  LEED  analyses  130  indicate  this  on P t { 1 1 1 )  spacing  i s w i t h i n 2.5% o f t h e b u l k  w i t h i o n - c h a n n e l i n g , £ 123 ] now s u g g e s t  value; studies an e x p a n s i o n  of  of  by  a b o u t 2%. The  one p r e v i o u s s t r u c t u r a l  JLaramore |_ 20 J c o n c l u d e d a  small  consistent  with  close-packed  between  0  and  5%  here f o r Cu{111),  this  and  i s  surface, although  the  i s  5.4  :  possible.  namely  largest  The  -4.1±0.6^,  i s  yet reported f o r a  l a r g e r c o n t r a c t i o n s a r e known f o r  more l o o s e l y p a c k e d s u r f a c e s , e.g. 10 2 f o r A l {110) and  Cu(111)  that the surface i s not d i l a t e d but that  contraction  c o n t r a c t i o n determined  determination  [101,110,111 1  £ 101, 106, 107 J .  7% f o r Ag (110)  O t h e r B e t h o d s Qf 0 b t a i n i n g S u r f a c e  Structural  Information  From LEED Data while  most  s u r f a c e s t r u c t u r a l d e t e r m i n a t i o n s by LEED h a v e  been performed by c o m p a r i s o n s 1(E)  curves  attempts  f o r various  of  experimental  s t r u c t u r a l ; models,  t o f i n d data i n v e r s i o n procedures  there  have been  that w i l l  procedure  would a v o i d t h e i n e v i t a b l y l e n g t h y and e x p e n s i v e  scattering  process  associated  experimental  produce  structure  error  from  calculated  surface  and  directly  and  with  data-  conventional  This trial  multiple-  calculations.  Two a p p r o a c h e s h a v e been p r o p o s e d s o f a r ; b o t h , a r e the  a  kinematical  b a s e d on  t h e o r y , a l t h o u g h n e i t h e r c a n y e t be c o n s i d e r e d  t o be w e l l - e s t a b l i s h e d -  One method a t t e m p t s  experimental  data  as  s t r u c t u r e and  concomitantly  so  to  enhance  diminish  to  the the  manipulate  the  single-scattering multiple-scattering  .131  features. ,  If  comparatively of  successful,  simple  this  w o u l d a l l o w a n a l y s i s with, t h e  kinematical theory;  the data-averaging  (DA) a p p r o a c h £1,02,103],  approach uses the F o u r i e r transform analogy  with  generating  the  approach  a Paterson  part  of  LIED  scattering origin,  in  (FT)  X-ray  philosophy  The a l t e r n a t i v e  method  £ 99,100 ] ,  in  analysis  of  structure  map o f t h e s c a t t e r i n g c e n t r e s .  d i f f i c u l t i e s associated the  t h i s i s the  w i t h e a c h m e t h o d , and  practitioners  a  reluctance  t o d i s c a r d data  t h e s e methods have s u f f e r e d  Because of on  of m u l t i p l e -  some  criticism.  However, t h e r e  i s a c o n t i n u i n g hope t h a t t h e y c a n become u s e f u l ,  at  the sense o f r e s t r i c t i n g  least  in  space" that  must  be  searched  in  t h e volume o f " p a r a m e t e r  a  typical  full  multiple-  scattering analysis-  5.5  B i b l i o g r a p h y Of S u r f a c e In  this  section  is  structure determinations intended clean data  compiled  list  such  the  more r e c e n t  early being  a limited  sork/of  scattering  b i b l i o g r a p h y of LEED.  surface is  s c o p e a s t o be o f l i t t l e  use.  high g u a l i t y i s given.  experimental  I n such although  or  cases some  A f e w s t r u c t u r e s a r e now  s u c h a s medium-energy  ion-channeling  not  about  t o be o f d u b i o u s g u a l i t y  and c o m p l e t e s t u d i e s a r e q u o t e d ,  (HEED) ,  It  Many e a r l y p a p e r s c o n t a i n e d  i n v e s t i g a t e d by t e c h n i g u e s  diffraction  fletals  o f every paper p u b l i s h e d  o r c a l c u l a t i o n s now r e c o g n i s e d  of  a  o f c l e a n m e t a l s by  t o be an e x h a u s t i v e  metal s u r f a c e s .  S t r u c t u r e s Qf- C l e a n  electron  (IC) and medium-energy i o n  ( I S ) and h a v e b e e n i n c l u d e d f o r c o m p l e t e n e s s .  The m e t a l s a r e l i s t e d  alphabetically  and  by  face.  The  132  crystal are  h a b i t i s a l s o l i s t e d as, l n v e s t . i g a t i . p i i s o f  now  being  surface  carried  stucture  (HI) , F o u r i e r  limited The  is  The  listed  transform  surface spacing estimated  oat.  methods u s e d as  (FT)  visual  or  data  i s c h a r a c t e r i s e d by A d %  errors.  {V),  and  sense  but  faces  of  FCC  d i f f e r e n c e s of t h e possibly  situation metals  metals  In  r a i s e d by  while  a  (100)  s l i g h t : preference  unremarkable.  of 5  s t u d i e d but The  the  not  data-  seen  t c show v e r y  from t h a t o f for  the  bulk,  contractions.  (100)  surfaces  The  of  FCC  metals appear i n g e n e r a l to  10%.  The  i n e i t h e r phase.  the b a s a l planes  only higher  small  to  interesting  t o FCC The  HCP  of T i and  index f a c e s t u d i e d so  at  about metals  Zn  are  f a r , that the  FCC  faces. Several  they  severely  close-packed  o f Cu{311) shows a c o n t r a c t i o n o f s i m i l a r m a g n i t u d e t o  e. g.  the  not r e c o n s t r u c t i n  a phase c h a n g e f r o m HCP  unexceptionally  h a v e been l i t t l e  the  s u r f a c e s o f BCC  which has  behaves  be  surface layer spacing  seems t o be s i m i l a r f o r  e x a m p l e o f Co,  (110)  The  or, experimental  general,  can  show c o n t r a c t i o n s o f t h e o r d e r  600°C  (DA).  do show v a r y i n g d e g r e e s of c o n t r a c t i o n o r  expansion of the s u r f a c e l a y e r .  with  reliability-index  i s c u r r e n t as o f Aug..,.1978..,  lateral  (111)  the  i s supplied with  I n a l l t h e s e c a s e s t h e m e t a l s u r f a c e s do a  determine  averaging  I n some c a s e s d o u b t s a r e  ranges of e i t h e r the c a l c u l a t e d  list  to  phase c h a n g e s  of  the  notable  omissions  P t ( 1 0 0 ) , Au{100) show by t h e i r c o m p l e x LEED are  laterally  y e t been s o l v e d  from  this  list  patterns  that  r e c o n s t r u c t e d ; t h e i r s u r f a c e s t r u c t u r e s have by LEED i n t e n s i t y a n a l y s e s  scattering calculations.  using  multiple-  Metal  Al  Face  Crystal habit  Method  {100) 1111) (110)  FCC FCC FCC  (100)  FCC  (111);  • FCC •  (110)  FCC  Co  (0001) (111)  HCP FCC  Cu  (100)  FCC  (111)  FCC  (311)  FCC  Fe  (100)  BCC  Ir  (111)  Ho  Adj.  Ref.  V V FT . Rl MEED  0±? 0±? -7±5 -10±1 . -5±5  104 105 101 106 107  7 y V V V V FT FT . V V V v  0±1 ? Q+? 0±5 0±5 + 5±5 0±5 -3±5 -4±5 -10±5 -10±5 -10±1 -12*3  108 109 110 110 111 112 99 101 . 110 111 108 112  1  V V  0±5 0±5  113 113  0±1 0±1.. 0±5 -2.5±2-5 -4- 1±0.6 -5.0±1.5  99 114 20 20 this 115  V  - 1 . 5±2.5  116  FCC  V  -2.5+5  117  (100)  BCC  V .. .  -11 ±5  118  Na  (110)  BCC  V  Bi  (100)  FCC  (111)  FCC  FT = V V DA . V  (110)  FCC  . FT :. DA V V RI HI  v FT IS  0±5 0±1 +5±5 0±5 0±4 -1±1 0±5 -5±1 -5±5 -4±?  119, 99 11 120 121 11 120 11 101 . 135  aork  Metal  Face  Crystal habit  .Method  AH  Ref.  Rh  (100) (111) (110)  FCC FCC FCC  BI 81 BI  0±2.5 -1+3 -2.7±2.0  Pt  (111)  FCC  V IC IS  •2.5±2.5 + 2±1 . •:i..„5±.1 :  Ii  (0001)  HCP  V  -2±1  124  w  (100) (110)  BCC BCC  V V  -11±5 Q±5  125 126  Zn  (0001)  HCP  -2±2  127  .  v  t h i s work t h i s work t h i s work 122 123 136  135  CH&PTER 6  THE  (111) SURFACE OF SBODI0&  136  Previous  LEED  studies  limited  to t h a t of Grant  mainly  cn  on  and  this  Haas  single  £130],  c r y s t a l face are  which  concentrated  A u g e r s p e c t r o s c o p y , and a r e c e n t c h e m i s o r p t i o n  by C a s t n e r e t a l £ 1 8 ] .  Both t h e s e a u t h o r s  reported a  pattern f o r the c l e a n s u r f a c e but d i d not perform measurements-  study  (1X1) LEED  any  intensity  An a s y e t u n p u b l i s h e d LEED s t u d y o f t h i s  surface  w h i c h c e n t r e s e s p e c i a l l y on t h e v i b r a t i o n a l ; p r o p e r t i e s  of the  surface  atoms,  but  which  been r e c e n t l y undertaken  6, 1  d o e s r e p o r t some i n t e n s i t y d a t a , h a s  £131].  Experimental Experimental data  two  crystals  here.  ( B e r k e l e y ) , and  Despite  the  Auger e l e c t r o n s p e c t r o s c o p y i n  t h e second  different  c r y s t a l s , they behaved i d e n t i c a l l y  mounted  taken  ( s e e T a b l e 4 . 1 ) 2 one was a p r e - c u t s l i c e  P r o f - G. A. S o m o r j a i polished  f o r t h efin(111.) s u r f a c e s e r e  loaned by  was  c u t and  p r e h i s t o r i e s of these  within experimental  of both  from  error.  t h e (111) s u r f a c e s  as  t h e vacuum chamber r e v e a l e d a p p r e c i a b l e a m o u n t s o f  c a r b o n (272eV) a n d s u l p h u r ( 1 5 2 e V )  contaminants  Auger  A r g o n i o n bombardment removed S  spectrum  of F i g - 6.1(a).  from t h e s u r f a c e b u t increase. caused  by  Sputtering  F i g - 6.1 ( b ) -  carbon  This  Auger  sputtering  tends  leave  to  Annealing  contamination  the bulk c r y s t a l , b u t w i l l  signal  shown  showed  a  i n the  relative  a p p e a r s t o be a common s i t u a t i o n  the low  e n r i c h e d i n carbonof  the G  as  cross-section  islands a t about  of  C  of  carbon.  or a surface layer  13QQK r e d u c e s  the  level  on t h e s u r f a c e by b a c k - d i f f u s i o n i n t o induce the re-appearance  of  sulphur  137  Rhdn)  i  100  1  1  200  1  1  300  eV  l i ^ u i S 6^1 Auger spectra o f Eh (111) s u r f a c e s w i t b a 1.5keV, 10 n i c r o a m p b e a n : (a) as aounted, considerable S(152eV) and C |282eV) ccrtaaination; (b) a f t e r a r g o n - i o n b c a t a r d a e n t , r e d u c e d S, i n c r e a s e d C; (c) a f t e r a n n e a l i n g , r e d u c e d C, i n c r e a s e d S; <d) c l e a n e d s u r f a c e .  138  as  i s shown i n F i g - 6 . 1 ( c ) ., The  subseguent  to  temperature  bombardment  control-  (about  can  be  produced  1  such  by  microamp  c r y s t a l a t 1000K) f o l l o w e d  by  a t 2kV 10  of t h e c r y s t a l becomes d e p l e t e d ,  carbon.  The  only  spectrum  Fig.  6.1(d).  are  listed  The  in is  difficulties to  contact  position  the  of the  surface is  made  and  relative  part  surface  in  intensities  r e s u l t s of  this  attributed  to  i n e s t a b l i s h i n g a s t r i c t l y l i n e a r energy s c a l e  and  differences.  must  are  the  peak  in  this  The  shown  c o l u m n s 2 t o 4, /Some v a r i a t i o n i n r e p o r t e d  g o o d , w h i c h may guoted e n e r g i e s  Also  be  estimation  the and  weak  free are  experimental  data.  atoms in  spectrum  features  below  two  with  reasonably  columns. an  These  ionisation good  s i g n i f i c a n t amount o f b o r o n  is  220e7.  (Auger peak a t  not in The  U i l s o n £49j calculations  correction  agreement  the  error,  l a r g e spread  a s s i g n m e n t s o f P a c k e r and  i n the f i n a l  of  s u b j e c t t o s e v e r a l eV  account f o r the r e l a t i v e l y  of  energies  nevertheless  No  1300K-  is  i f t h e s i g n a l t o n o i s e r a t i o of the  for  the  for  obvious;  are a l s o l i s t e d are  ion-  listed  potential  calculated  S  at  cleaning  5 o f T a b l e 6.1. of  hot  anneal,  and  C and  minutes with  surface  r h o d i u m peak e n e r g i e s  studies  low  i s t h e n r e g u i r e d t o remove  cleaned  o f weak p e a k s i s p r o b a b l y  especially very  the  f o r TO  careful  of  the sulphur content  short anneal  i n c o l u m n s 1 and  comparison energies  a  of  other experimental;  by  cycles  minute  region  surface  cycles  a  many  several  often  contamination  regulated  After  easier;  C  A clean s u r f a c e showing very  Auger s i g n a l s c o u l d be bombardment  l e v e l o f S and  with  but the  180eV) c o u l d  139  OBSERVED  ASSIGNMENT  • REL.  Iila;J : a)  b)  139  c)  a>.  a)  145  e)  5  141  170  174  175  170  5  175  203  208  210  200  5  208  225  226  227  222  15  225  257  260  259  256  30  258  302  306  303  302  100  303  t h i s w o r k , b) r e f e r e n c e 1 3 0 , 1 8 , e) r e f e r e n c e 4 9  c)  T a b l e 6 , 1 - O b s e r v e d and c a l c u l a t e d  reference  131,  M  d)  a  N  reference  Auger t r a n s i t i o n s f o r rhodium.  140  be d e t e c t e d i n the  contaminated or c l e a n s u r f a c e s ,  This  c o n t r a s t t o another study I 18J i n which a b u l k boron diffused  to  the  very d i f f i c u l t reported studyto  The  was  the  One  c f the c r y s t a l s  same  crystal  to  communication). from a d i f f e r e n t  In  many c l e a n i n g  work  earlier  boron  be t h e r e s u l t o f t h e s e w o r k e r s h a v i n g r e m o v e d n e a r l y  bulk boron c o n t a m i n a t i o n through  proved  used i n t h e  as u s e d i n t h i s  d i f f e r e n c e i n behaviour i n r e l a t i o n  in  contaminant  s u r f a c e d u r i n g c l e a n i n g p r o c e d u r e s and  t o remove.  here  is  seems a l l the  cycles  (private  t h e s e c o n d c a s e , t h e c r y s t a l was  purchased  source from that of the f i r s t  crystal; i n  this  c a s e we h a v e t o c o n c l u d e t h a t n e i t h e r t h e m a n u f a c t u r i n g p r o c e s s , nor  the  polishing  method e m p l o y e d , i n t r o d u c e d a n y  amounts c f b o r o n i n t o After (1X1)  the c r y s t a l .  s e v e r a l c y c l e s o f bombardment and a n n e a l i n g , a  LEED p a t t e r n  was  s p e c i e s o t h e r t h a n rhodium.  p a t t e r n and The  of d i f f r a c t e d  i n C h a p t e r 4 up t o a b o u t 0- = 1OO,<£ =109° of  and n e g l i g i b l e  Sample p h o t o g r a p h s  t h e beam l a b e l l i n g scheme  intensities  250eV  are  shown  Auger  in  Fig-  LEED 6.2.  beams were measured a s d e s c r i b e d at  normal  m e a s u r e m e n t s was  on s e p a r a t e o c c a s i o n s t o a s s e s s t h e e f f e c t on t h e s t r u c t u r a l  work  signals  o f the  incidence  i n t h e a n g l e c o n v e n t i o n o f J o n a £ 128 J .  experimental intensity  variations  sharp  o b s e r v e d , i n agreement w i t h e a r l i e r  J. 18,130,131 J , w i t h a l o w b a c k g r o u n d for  significant  analysis.  and  for  Each s e t  repeated three  times  of s m a l l experimental  141  a)  t  b)  21  JO •01  .11  .12 #01  '10 »11  '11  (180-  ffi\.11  .12  01 yi <* ' » 0 0 *01 • 11  #02  »10 »11  '21  c)  d)  f i g u r e &j2 P h o t o g r a p h s o f t h e ( 1 i 1 ) LEED p a t t e r n f r o i t h e c l e a n Rh (111) s u r f a c e a t (a) n o r a a l incidence (158eV) , (b) 9- = 10°, y*=109° (122eV) i n the angle convention o f J o n a T128]. I h e l a b e l l i n g s c h e i e i s shove i n (c) and ( d ) .  142  6.2  Calculations The  (1x1) LEED p a t t e r n o b t a i n e d  d o e s n o t r e c o n s t r u c t i n s u c h a way symmetry  from  that  of  the  i n d i c a t e s t h a t the  as  bulk  to  change  structure.  possible f o r the surface t o reconstruct i n preserve the  the  surface  such  (1x1) p a t t e r n , t h a t i s by a l t e r i n g layer  with  respect  to  those  surface  the  surface  However a  way  i tis as  the r e g i s t r y  underneath.  I f the  reconstruct  c u b i c s t a c k i n g seguence  continued Two  the  face-centred  t o t h e s u r f a c e , a s shown  in  fa)  s u r f a c e : does  namely  or t o a CBACBA-,,B s t a c k i n g , < c ) , t h e l a t t e r s t u c t u r e  This  last  surface  plausible  and  reconstruction  was  the  f o r the seems  top  not is  CBACEA..-C.  p o s s i b l e r e c o n s t r u c t i o n s a r e t o a CBACBA.-.A s e q u e n c e ,  t h e h e x a g o n a l c l o s e packed seguence  of  Such  p o s s i b i l i t i e s a r e shown i n F i g - ., 6.3then  to  (b) ,  possessing  three  layers.  physically  t h e more  o n l y , r e c o n s t r u c t i o n , model  that  was  i n v e s t i g a t e d here with d i r e c t c a l c u l a t i o n s . Calculations  were  both the v ^  and V ^  a  55  total  of  diffraction incidence.  as d e t a i l e d i n Chapter 3 f o r  p o t e n t i a l s i n the energy range  |3  beams  matrices  performed  were  depending  30-260eV;  available  t o determine the l a y e r  upon  energy  the  and  angle  of  143  c)  ZiasiS. £x3 P o s s i b l e reconstructions o f t h e (111) s u r f a c e t h a t p r e s e r v e t h e (1x1) s y i a e t r y o f t h e LEED p a t t e r n : <a) n o n - r e c o n s t r u c t e d , CBACBA...C FCC s t a c k i c q ; <b) r e c o n s t r u c t e d , CBACEA...A s t a c k i n g ; <c) r e c o n s t r u c t e d , CBACBA...B, HCP s t a c k i n g . The 4 t h l a y e r C i s i n d i c a t e d by s a a l l d a s h e d b a r r e d c i r c l e s , t h e 3 r d l a y e r B by l a r q e b l a n k c i r c l e s , t h e 2nd A by a e d i u a dotted c i r c l e s , and t h e 1 s t l a y e r i s i n d i c a t e d by s i a l l b a r r e d c i r c l e s .  6, 3  R e s u l t s And  6.3(a)  Normal  Discussion  incidence  Three; independent normal i n c i d e n c e . general in  sets  Although  these  detail  A p p e n d i c e s A1-A3).  expected  i f the  Within  diffracted  the  bulk  any  intensities,  data  of data closely  perpendicular  to  artifacts  in  curves  the  symmetry the  three-  planes  {by  two  appropriate  f o r s e t s of  beams  operations of a three point  compares e x p e r i m e n t a l  beams a t n o r m a l i n c i d e n c e  F i g . 6.3 { a ) ,  and  in  pattern;could domains).  which  are and  smoothing  calculations. I(E) curves w i t h I {E)  for  the  {10)  curves c a l c u l a t e d  s t a c k i n g seguences; a c o n t i n u a t i o n - o f the b u l k  seguence.  shown  measured  the  (111)  in  the comparison w i t h c a l c u l a t e d  p r i o r t o comparing with the  F i g u r e 6.4  of  is  e g u i v a l e n t , on t h e a b o v e b a s i s , w e r e a v e r a g e d  d i g i t a l l y smoothed  f o r two  set  beams show  populations  measured 1(E)  theoretically  (01)  peak i n t e n s i t i e s and  ( a l t e r n a t i v e l y : t h e symmetry i n t h e LEED  be a s s o c i a t e d w i t h e g u a l  and  each  differences  a c t u a l s u r f a c e arrangement maintains  r o t a t i o n a x e s which are  minimise  measured f o r  were s m a l l  ( a l l the experimental  fold  filter)  sere  i n d e p e n d e n t s e t s showed a good  a s , f o r example, i n r e l a t i v e  i n t e n s i t i e s of the  To  intensities  agreement w i t h each o t h e r , t h e r e  s t r u c t u r e s u c h as s h o u l d e r s in  of  stacking  t h e h e x a g o n a l r e c o n s t r u c t i o n model*  F i g . 6 . 3 ( c ) , with the topmost l a y e r spacing  egual  to  the  bulk  o  value  of  between t h e  2.195A.  A  experimental  detailed and  matching  calculated  of  curves  p e a k s and could  troughs only  be  145  Rh Cm) V ^ r Ad % = 0.0  50  100  J50  200  Energy (eV)  250  50  100  150  200  250  Energy (eV)  ZiSUIS * comparison f o r t h e (10) and (01) cea»s c£ 1 ( E ) c u r v e s measured a t n o r t a l incidence f o r Rh(111) with those calculated with the potential f o r t h e n o r a a l FCC s t a c k i n g s e q u e n c e a n d f o r t h e HCF s t a c k i D q s e q u e n c e e v e r t h e t o p thrfre surface layers.  146  achieved other  f o r the normal f a c e - c e n t r e d cubic packing  diffracted  beams  aresimilarly  arrangement f o r the t o p three To  determine  f o r different  expressed  a s i n t h e Cu (111)  bulk value to  i n c o n s i s t e n t w i t h an HCP  layers.  the surface  performed  relaxation,  calculations  v a l u e s o f the. t o p i n t e r l a y e r case as percentage  i n steps  o f 2.5%  c o m p a r e s 1(E) c u r v e s f o r t h e (10) a n d calculated  f o r &d%= -5,0  potentials.  It i sdifficult  visually  which  and  describes the experimental  of  index  r  attempts  and V  o r  averaging  these contour (01),  The and  r e f e r r e d t o above, t h e e x p e r i m e n t a l p l o t s f o r normal . i n c i d e n c e - i n v o l v e s  ( 1 1 ) , (20)  V  o r  5.  With  d a t a used i n the (10)>  r  = -19. 1±0.9eV,  where  respectively)  v  minima  t h e u n c e r t a i n t i e s i n 6d% and V are the standard  means deduced f r o m t h e s p r e a d  of  the r e l i a b i l i t y  index (r^)^  i n d i v i d u a l beams a s d e t a i l e d i n C h a p t e r errors  really  lies  within  5,  errors  o r  i n the  i n v a l u e s g i v e n by f o r the  various  To t h e e x t e n t  that  do r e p r e s e n t a gauge o f t h e . u n c e r t a i n t y i n  each r e s u l t then t h e r e i s a minimum  reduced  a n d (02) beams.  energy-weighted  these  more  minimum o f r ~ i n F i g . 6-6 (a) o c c u r s f o r AdS = -3-7± 1. 1%  (± £j a n d ± £  the  best  , f r o m one o f  the s e t s o f independent data, as d e s c r i b e d i n Chapter the  core  set to  a  p l o t s o f t h e mean  as • f u n c t i o n s o f  r  ion  data  6.5  those  the surface relaxation  complete assessment by showing c o n t o u r reliability  f o r . t h e two  d a t a , b u t F i g - 6.6  the  Figure with  even w i t h t h i s l i m i t e d  value  spacing,  {dilation)  (0.0551).  (01) beams  *5%  were  changes frem  T h i s q u a n t i t y was varied--..from +10%  -108 ( c o n t r a c t i o n )  assess  sequence; t h e  68%  t h e area  probability  that  defined  the e r r o r bars i n  by  the actual  147  Rh(iii) e = o  Rh (in)G = 0°  e  (10) beam  (01) beam  Exp  WJM >-5%  Rhl3  >0%  v  Rh  '  Rh13  ,WJM  W5%  >+5%  Rh!3  100  150  200  Energy (eV)  250  50  100  150  200  250  Energy (eV)  Jifluie * c o m p a r i s o n o f e x p e r i m e n t a l 1 ( E ) c o r v e s f o r t h e (10) • r d (01) beams a t n o r m a l i n c i d e n c e f o r Bh_(111) w i t h intensity curves calculated f o r t h e p o t e n t i a l s v"ftk and V for three d i f f e r e n t v a l u e s o f A d * a s s u m i n q t h e n o r m a l FCC r e q i s t r y f c r t h e s u r f a c e arrangement.  146  fiSi?J§ 6^.6 Contour p l o t s f o r Fh (111) a t n o r a a l v e r s u s V^. and AdX f o r t h e p o t e n t i a l s <a) s t a r t i n g f r o a 54 eV.  incicence and (b)  of r F^,,  f  149  150  Fig-  6.6(a),  F i g u r e 6.6(b) shows t h e c o r r e s p o n d i n g  which compares t h e e x p e r i m e n t a l from  the  superposition  o c c u r s f o r Ad%= sets  of  with  potential  +3.5±1..2X  calculated  curves  and  V  I  of  v„„ . or  t h e p a r a m e t e r s Ad$ *• can  and  see t h a t  good  f  over  9eV  traced  The  values  f o r t h e two  energy  spheres.  shift  another  of  as  calculated large  potentials-.  the  two  analysis,  this  will  The  are  in  values  given  F i g . 6.6  p o t e n t i a l as g i v i n g We  can  from F i g . 6.6  from  differences  a p p e a r s more s e r i o u s .  a  and  edge  of  3  (see  The  V  e x h i b i t elongated  the  relative  f o r the  one  shift where  (01)  in the  beam a t  another.  The  the r e l i a b i l i t y - i n d e x i n t h e two  of two  be  Fig-3-6).  Ad&  potentials.  g i v e n by  the  minimum v a l u e s  two  o f ~r~  seem s u f f i c i e n t t o p r e c l u d e c h o o s i n g the "best  can  by  r e s u l t s i n an  F i g - 6.5  either  fit".  probe i n t o the o r i g i n s o f the V  and  r e l a t i v e t o one  deduced  potentials in  in  c u r v e s a t +5%  the  judged  differ  of t h i s d i f f e r e n c e  Chapter  result  displaced  reflect further  difference  values  of phase s h i f t s r e l a t i v e t o in  6.5)  Z a n a z z i - J c n a (ZJ)  values of V  curves a s , f o r example, i n  o f a b o u t 3eV,  may  the  i n p o t e n t i a l a t the  discussed  incidence shift  Part  sets  peaks i n the c a l c u l a t e d  normal extra  1(E)  (see F i g .  different  T h i s a m o u n t s t o a b o u t 6eV  was  Correspondingly,  within  of t h e r e f i n e d  back to the d i f f e r e n c e  muffin^tin  both  t h e o v e r a l l l e v e l o f a g r e e m e n t , as  by t h e v a l u e o f r . , i s v e r y framework.  calculated  although  curves are b a s i c a l l y s i m i l a r p l o t s are a t r a t h e r  plot  minimum o f IT now  t i i e  t h e minima i n t h e c o n t o u r  He  those  =- 9-7±1.2eV.  Qr  contour  by  noting  that  different  values  the c o n t o u r  valleys running diagonally  of  plots i n  across  the  151  diagrams; for  a s i m i l a r e f f e c t c a n fee s e e n i n  C u ( l i t ) i n the d i s c u s s i o n of Chapter  result  of these  agreement  between e x p e r i m e n t  c a n be a c h i e v e d For  v a l l e y s i n the contour  plots,  and c a l c u l a t i o n s - , (as judged  V = - 1 6 e V , Ad£=-6g t o V or  of  ZJ-  S i n c e t h e degree to  of  the  f i t worsens  rapidly  or  measured  ;  r  To s e e t h e e x t e n t o f t h i s the  for  small  corresponding  w i t h t h e o t h e r two i n d e p e n d e n t  give values  results  of  of  equal  Aa? overall  in  changes  i n  sets of  to  mean  the  two  with s m a l l u n c e r t a i n t i e s  -5.6±1.3S  and  v a l u e o f -4.7%.  plots  for  show t h e c o r r e s p o n d i n g  data  were urn  with .  -4.8±0.8$, The f u r t h e r  and plots  value  of  w h i l e t h e s e mean v a l u e s o f A d % a r e  potentials  this  o f ( r )^ r  i a (a) , a n d 7 ^ variations  f o r ; the  in  data. individual  i n - (by ; t h e d o t t e d  ( 3  of r  r e s u l t s , t h e minima o f c u r v e s  discrepancy  i s not p r i m a r i l y associated  i n the experimental  F i g u r e 6.7 shows p l o t s  would  experimental  experimental  o u t s i d e t h e 9 6 % c o n f i d e n c e l i m i t s (±2€j) ,  above  <0.25,  reliability-index calculations  the a d d i t i o n a l contour  I t seems c l e a r t h a t >  &&%  r  along the v a l l e y .  g i v e Ad%=*3. 8±1.3% a n d +3.5±1.2%, a n d mean  against  r  directions  with V ^ - j  from  kdSI.  on t h e d a s h e d  an  geometry  r  and  6 r  therefore  +3-6$.  by T )  1(E) c u r v e s  move t h e l o c a t i o n o f t h e minimum o f ~F  The  good  v a l l e y , i t seems p r o b a b l e t h a t any m i n o r  deficiencies i n the calculated  made.  As a  g i v e "good" agreement a c c o r d i n g t h e c r i t e r i o n o f  perpendicular  intensities,  V  =-6eV., Ad«= + 6% h a v e  or  therefore  plots  relatively  a l l p a i r s o f v a l u e s which f a l l  and  mainly  analogous  5 (see Fig.5-4)-,  f o r a number o f c o m b i n a t i o n s  F i g - 6.6(b),  l i n e from  the  p  .  In  accord  with  beams lines the  f o r t h e i n d i v i d u a l beams i n  F i g . 6.7(b) a r e g e n e r a l l y s h i f t e d t o more p o s i t i v e v a l u e s o f A d $  f i S " I f 4 x 2 P l o t s f o r Bh (111) o f ( r ) ; f o r f i v e i n d e p e n d e n t beams a t nc«al~incidence v e r s u s A d X f o r (a) l V , = 18eV) and (b) VjlVO ( »r **10eV) . T i e dashed l i n e s shew t h e dependence o f r versus AdX. r  r  v  =  r  153  compared w i t h t h e c o r r e s p o n d i n g for  v a l u e s i n F i g . 6.7 (a) .  t h e (10) a n d £01) beams t h e r e i s a  negative  much  steeper  rapidly  in  (Fig-  £01) this  beam  appears  region  6.7(a)).  The  to  for  origin  deteriorate  of  this  behaviour  in  fcM3  the c a l c u l a t e d I(E) curves  ^  s  *  G r  curves.  beginning index  i n  the  from a this  the  large  f o r t h e (10) beam a t a r o u n d  under  n  *  a  s  t  b  dominant  e  o f such  o u t t o be u n d e s i r a b l e . c^ can  in  both  with  the  reliability-  T h i s i s because t h e values  change  substantially  over  the  s h i f t s employed; t h i s problem a r i s e s from the areas  Q r  the  constant  feature  a strong feature right at the  o f I (E) c u r v e s b e i n g c o m p a r e d  turns  range o f V  a  The p r e s e n c e  of t h e s c a l i n g  is  for  T h i s peak i s a p p r o x i m a t e l y ; t w i c e a s l a r g e a t A d S = - 5 $ f o r a  1(E)  more  e v a l u a t i o n o f t h e I (E) . c u r v e s i n F i g . 6.5, a l t h o u g h  54eV.  at  than  obvious  d i f f e r e n c e i s a s c r i b e d here as being a s s o c i a t e d with  V  much  ( F i g - 6.7 (b))  r e l i a b i l i t y - i n d e x a n a l y s i s may n o t be i m m e d i a t e l y  peak  rise  v a l u e s o f o d l i n F i g . 6-7 ( b ) ; i n p a r t i c u l a r t h e d e g r e e  of f i t f o r the  visual  HoSever,  1(E) c u r v e s c h a n g i n g  truncated at different  a p p r e c i a b l y a s the energy range  p o i n t s w i t h i n t h i s peak when t h e v a l u e  of the i n n e r p o t e n t i a l i s v a r i e d . To  a v o i d t h i s p r o b l e m , i t was f o u n d  comparison  of  shows c o n t o u r in  the  1(E) c u r v e s  necessary  to start  at a higher energy.  Figure  6.8  p l o t s f o r t h e same s e t o f n o r m a l i n c i d e n c e d a t a a s  F i g . 6,6 when t h e c o m p a r i s o n i s s t a r t e d a t  54eV a s was done e a r l i e r .  66eV  instead  that t h e best f i t of t h e i n n e r p o t e n t i a l i s lowered  1eV  f o r t h e band s t r u c t u r e p o t e n t i a l but  little  of  By c o m p a r i n g t h e s e t w o f i g u r e s s e c a n  see  truncation,  the  effect  on  by about  by t h i s s m a l l e n e r g y  range  V , i s discernable f o r the  154  f i g u r e .ii.8 C o n t o u r p l o t o f r versus r c r j a l i n c i d e n c e , u s i n g the data c f F i g . t h e p o t e n t i a l s (a) v"^ and (b) V . r  R M i  and A d * f o r Bh(111) a t 6.6 o n l y f r c m 66eV f o r  155  156  superposition potential. Ad% a  The  however; i n the 7 ^ slightly  smaller  opposite appears to  case,  after  from  the  T a b l e 6.2.  on  results  potential V^,j . between  only  positive  values  started  from  Thus  0.01  and  54eV.  0-4$.  yet  while  curve  The  on  of  and  r e g i s t r i e s have strongly  s h i f t s t o more  the  comparison  curve  is  peak c l o s e t o 54eV i n than  for  v  ^/^  »  energy ranges i s o n l y  data the  and  for  normal  surface  localised  f o r the  much  the  p l o t o f r<- s h o w i n g t h e c o m p a r i s o n c f  top l a y e r (CBA.,B).  valley  not  occurs c l o s e to  arise  comparison.  for  f o r t h e HCP  topography  increased  problem with n o r m a l i s a t i o n could  experimental  p l o t s i n F i g u r e 6.6 contours  o f &&%  when  d$ f o r t h e two  is  r  6-9  shifted  with the steep  ~z~  the  f u r t h e r the top l a y e r r e g i s t r y , i n Figure  calculations for V ^ laterally  average  strong  of  a contour  the  value  a  to  end  the energy range of the  set  of  has  1/2%  analysis for  i s somewhat s m a l l e r  of  same  index  , where t h e  when a l a r g e p e a k i n an 1(E)  i s presented  extension  value  the  For  value  consider  this  the  0.02,  by o v e r 3%  t h e change i n the  To  results  comparison are c o l l e c t e d i n  from the r e l i a b i l i t y  t h e c a l c u l a t e d 1(E)  about  The  S t a r t i n g a t 54eV r a t h e r t h a n 66eV a d d s o n l y  t h e t o t a l e n e r g y r a n g e , and effect  range  at  t r u n c a t i o n , whereas f o r  an a p p r e c i a b l e c h a n g e o f a l m o s t 2% i s s e e n . energy  for  occurs  r  contraction  shortened  true  t h e minimum v a l u e o f t  fchl3  V  be  arrangement  the  contrast  minimum f o u n d i n e a c h o f  values  of  investigated,  t o a c o n t i n u a t i o n of  with  with  These c o n t o u r s  arrangement  higher been  incidence  bulk s t a c k i n g sequence  surface  one  (CBA-i.C);  have  a  r^.  Although  these  the  rather  results  the  flat other point  the b u l k s t a c k i n g seguence a t  the  157 u-i  o  00  CN  o  O  o  O  c 41 H  01 01  u CO  >  4J  v/1  CO  03 01 J3  u o  O  >  11  d  d  •H  o  > d  •  ao  CJ\  I  I  ao ~* i  oo d  m d  •H  >  >  O  O  01  d  4)  •••I  m  00 •  >  41  O  •H sO  d  ao  I  CO  e  o c o  94  U)  d cn  +1 -a  cn  CN  »4 •  o  CO  d  d  d o  ft  o +i  CI  d  i  I  »4  i  d +  01 30  c w -a 01 CO  >01  >01  >01  30 CN  o CM  >»  u  3 0 CO  u a. oi S c oU M  >  01  CO •CM  o  o  CM  >  01  o  to e  <0 0>  -n -a 01  0  u-i  CO Q.  • B  O z  O U  c  01  o cu  c  01 CU O  e  -H U ' 01  • a. o x z u  x  x  r  3 06 >  3 2  3 OS  cn OS  cn -C OS  »H CO >  CO >  e  C  X  06  co 01 a  en 01 3 CO 01  rn  CM  CO 01  X  T a b l e 6j_2 C o n d i t i o n s o f b e s t a q r e e m e n t between experiment and ffuItiple-scatterinq calculations f o r t h r e e s e t s of i n t e n s i t i e s m e a s u r e d a t n o r m a l i n c i d e n c e on E h ( 1 1 1 ) .  158  Rh(11i)V" e = O JM  e  CBA--B  Ad%  l l . 9 u . I f £i5 C o n t o u r p l o t of r versus V^r a n d A d S f o r t h e potential'v ^ and t h e model o f t h e R h ( 1 1 1 ) s u r f a c e i n w h i c h t h e t o p t h r e e l a y e r s have t h e HCP s t a c x i n q s e q u e n c e . r  1  159  Bh(111)  surface,  as  suggested  above  with  Figure  6.4.,  6.3(b)  D i r e c t i o n o f i n c i d e n c e O=l0 ,^>=1 QS°  reference  o  Depending  on  the  data  set  i n v o l v e d up  t o 16  individual  beams were m e a s u r e d a t t h i s a n g l e o f i n c i d e n c e f o r s t h e surface;  these  of e x p e r i m e n t a l curves Fig.  to  data are c o l l e c t e d 1(E)  calculated  6.10,  curves for  f o r the  the  two  Rh(1.11)  i n A p p e n d i c e s A4-:A6.: - A  plot  (11)-- and  with  potentials  (10) is  beams presented  in  f o r the n o r m a l b u l k s t a c k i n g s e q u e n c e .  Following  on  the  individual calculated  p r e v i o u s e x p e r i e n c e , the, c o m p a r i s o n s o f and  measured  1(E)  curves  were  closely  c h e c k e d t o a v o i d m i s l e a d i n g c o n c l u s i o n s a s s o c i a t e d w i t h -dominant peaks  in  1(E)  energy range. curved  LEED  curves  at the beginning  For d i f f r a c t i o n screen,  o r end  of t h e  s p o t s c l o s e to the  considered  edge  our measured i n t e n s i t i e s a r e  of  the  artificially  diminished because both the s o l i d angle subtended at  the  point  of  are  lower  observation  and  compared w i t h t h o s e  the  grid  and  presented for as  1(E)  curves  were  made  of with  (and d i f f e r e n t numbers o f beams) f o r t h e  measured s e t s of d a t a .  i n F i g . 6.11  To  a d d i t i o n a l f a c t o r s , comparisons  theoretical  d i f f e r e n t energy ranges independently  £129]  f o r spots near the centre of the screen.  assess the i n f l u e n c e of such experimental  transmission  and  Sample c o n t o u r  plots  the r e s u l t s from t h e c o n t o u r  these data at .off-normal :incidence are  plots  given i n Table  are of 6.3  w e l l a s s p e c i f i c a t i o n s o f t h e e x t e n t o f t h e c o m p a r i s o n s made  b e t w e e n 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 and  each  set  of  the  160  50  I00  150  200  Energy (eV)  250  ~I00  150  200  250  Energy (eV)  EiSSIf 6AJ0 * c c i p a r i s o n of experimental I ( E ) curves f c r the (IT) and (10) l e a n s a t * = 1 0 ° , + = 109° f o r Bh(111) w i t h i n t e n s i t y p r o f i l e s c a l c u l a t e d f o r t h e p o t e n t i a l s V^™ and ¥<^u f° three d i f f e r e n t v a l u e s o f AdX a s s u m i n q t h e n o r m a l F C C r e q i s t r y f o r t h e surface. r  161  163  experimental All  data.  three  independent  sets  of  data  ^ = 1 0 9 ° g i v e c o n s i s t e n t v a l u e s o f G d % and l this  direction  contraction contrast was  (about  with  noted  i n c i d e n c e , both 1%)  . , Furthermore,  gr  topmost  layer  i s also  i n Table  at  positive  the  muffin-tin; radius.  i n Table  of  (-10.6eV)  6-2 a r e more n e g a t i v e  than  V r e s p e c t i v e l y T a b l e 6.2 than  are  the  The  more  the values i n Table  off-normal  6-3 f o r V*,,, different  c o n t r a s t t h e mean more  v a l u e s i n T a b l e .6-3 f o r ,7^^  and  values  of  Ad&  (-4.3%) a n d more p o s i t i v e  6.3; i n r e l a t i o n  to  the  in  (+0-3%)  results  for  i n c i d e n c e , a t n o r m a l i n c i d e n c e t h e m i n i m a i n r" h a v e r  been d i s p l a c e d s l i g h t l y the contour  of & d % and V  or  i n opposite d i r e c t i o n s along the valleys  p l o t s o f F i g u r e 6-6-  Even t h o u g h t h e mean  f o rt h i s off-normal angle  of incidence  c l o s e l y f o r t h e two p o t e n t i a l s , t h e r e l i a b i l i t y not  the  (-18.8eV) a n d  corresponding  negative  that  from the  Ey  in  discrepancy  interesting  i s v e r y c l o s e t o t h e 6 eV e x p e c t e d  values of V  spacing,  t h e d a t a a t n o r m a l i n c i d e n c e where a I t  for  potentials indicate a small  between t h e mean v a l u e s o f V .  potentials  in  f o r the  (Table 6.2).  difference and  of  m e a s u r e d at0"?10°,  indicate  the  overall  agreement  index  values  correspond r ^  does  i s any b e t t e r than t h a t  a c h i e v e d a t normal incidence., Although that  the  t h e minimum values...of;,,!^  general  level  of  agreement  i n Table  6.3  indicate  between c a l c u l a t e d and  m e a s u r e d 1 ( E ) c u r v e s d i m i n i s h e s a s t h e c o m p a r i s o n s a r e made i n c r e a s e d energy ranges v a l u e s o f O d l , and V This  suggests  that  0f  (and f o r more b e a m s ) , t h e  over  corresponding  a r e c l o s e l y s i m i l a r f o r each s e t of data. the  neglect  of  variations  in  the g r i d  U -4  Iu  MS  o  e a 0>  o  > at  > V  01  u 60  o  CM CM  >  >  as  Ml  •  «,.  MS  O  W  « '  «  +  01  o  •I  o  o  >  o  o ©  o I  o  S3  »4 O  O  •w CM  c < o  CO  co  o *4  o CO  I  I  o  co  co •  CM  O  >  41  o  •  o  -*  I  I  *4  *4 •  MS O •H  -9  >01  >01  >01  CM  MS  >»• «»•  O I  01  MS  o  *M  o  0>  CM co  »4  MS o •I o  O  O I  >  01  •  •I  GO  >  > O  o o d  o  CM  CM  •  *4  MS I  01  c <B  ed  U  u  < o a. 01 s c 0 u  >01  >  CM lA •M  >»  01  CO MS  >  01  CM o CM  u i -M  —1  MS  > 01  «H CM  CM o CM  > 0) >»• CM o CM  01 e <8 0)  •a "o  01 o ra a •E o o z u e  o  U-l  O  e c o  c90 - H 3 O  01  a  O  au  e 0) e  i* u 01  o a e  0 iw 10  •H Ifi  e  e  CO  CM  II  z  3  >  oe  as  z 2 OS  Z >  at 0) 9  -M CO  >  3 ad >  co 0) 3  <0 >  c 3 « CM CM z *4 X l a t l e 6 j j C o n d i t i o n s o f test aqreenent between experi»erit •ultitle-Ecattering calculaticrs f o r three sets of i n t e r s i • e a s u r e d a t *-=10<>, «< = 1090 on E h ( 1 1 1 ) . •  0  aX  e  165  t r a n s m i s s i o n and t h e a n g l e  subtended a t t h e p o i n t of o b s e r v a t i o n  are  c o n c l u s i o n s about  not s t r o n g l y a f f e c t i n g  although  there  Another source angle  of  may  be  reductions  of experimental  incidence.  angles  w i t h experiment  of  achieved  i n the overall  agreement.  uncertainty  T a b l e 6.3  is  in  setting  incidence  comparing  does  The f i r s t  not  experiment  the  of  these  improve the l e v e l  w i t h © " = 1 0 0 , ^ =109°, a s m o n i t o r e d  i n d i c a t e s a much p o o r e r  the  level  of  f o r a d d i t i o n a l c a l c u l a t i o n s made w i t h  ^=109° a n d 9-= 12°, <^ = 1G9°.  £-=80,  geometry,  To a s s e s s t h i s f o r t h e d a t a o f  3, i n f o r m a t i o n i s g i v e n i n agreement  surface  agreement.  additional of a g r e e m e n t  b y ~ r , but the r  This suggests  second  that the value  10° i s c o r r e c t t o w i t h i n 1 ° , and t h i s e x p e r i m e n t a l u n c e r t a i n t y does  not  interlayer  6.4  seriously  t h e ,determination  o f t h e topmost  spacing.  Conclusions By a v e r a g i n g  for  affect  the results of the r e l i a b i l i t y - i n d e x  t h e t h r e e i n d e p e n d e n t s e t s o f measurements a t each a n g l e o f  i n c i d e n c e we f i n d { I a b l e s 6.2 a n d 6.3) t h e f o l l o w i n g the  analysis  surface  (i)  structural  from  parameter  values  and t h e i n n e r  Ad%=-4.,3±0. 751 and 7  o r  potential  =-18.8±0.5eV a t  normal i n c i d e n c e and  for  6dS=-0.8±Q.8% and V =-17.5±0.5eV a t or 4>=10o, <p =109o  166  (ii)  from  Adg= + 0.3±0-9S a n d V  normal  =- 1 0.6±0.7eV a t  of  incidence and £>d%=-0. 5±C.7% and V  0fN  =- 11.0±0.7eV a t  9-=10o, 0=109°  As a f i n a l the  s t e p , r e s u l t s from each p o t e n t i a l need a v e r a g i n g o v e r  two a n g l e s o f i n c i d e n c e .  superposition  of  T h i s c o u l d be  done  to  the  each  an e n e r g y - w e i g h t e d angle  of  mean o f  incidence.  parameter  With  the  significant figures this yields a f i n a l (i)  from V ^  The  effects minor  &&%=-2±2%  small  errors  here  and e r r o r s i n s e t t i n g results  incidence necessarily debatable. allow the  given f o r  =-11±1eV  to  encompass  the  independent  measurements  the angle of i n c i d e n c e .  from t h e V ^  structural  values  o f an e x p e r i m e n t a l n a t u r e , i n c l u d i n g  n e c e s s i t y f o r i n c l u d i n g more t h a n surface  as o b j e c t i v e l y by  appropriate rounding of  appear  d i f f e r e n c e s i n 1(E) curves from  The  be  or  of  u n c e r t a i n t i e s guoted of  would  and ? = - 1 8 ± 1 e ?  (CKI3  final  This  result;  f r o m v . . , , o.d%= 0±2$ a n d V  (ii)  direct  a p p r o a c h o f Z J . However, a t t h i s s t a g e t h e  o v e r a l l r e s u l t s f o r Rh (111) c a n be g a u g e d j u s t taking  a  the i n d i v i d u a l contour p l o t s , a f t e r w e i g h t i n g  them a c c o r d i n g t o t h e a p p r o p r i a t e e n e r g y r a n g e . eguivalent  by  potential clearly indicate the one  determinations;  angle whether  of  incidence  two  angles  provides s u f f i c i e n t data i s s t i l l  in of  perhaps  The r e l i a b i l i t y - i n d e x a p p r o a c h i n t h i s c a s e d o e s n o t  a statement t o the e f f e c t  o t h e r i s wrong.  Bithin  the  t h a t one p o t e n t i a l i s r i g h t and present  calculational  scheme  167  both  potentials  although  describe  some c l a r i f i c a t i o n  apparent  i f further  in  the  of t h e i r  o r  i s needed  1(E)  at  the  data  relative are  equally  merits  may  when  This  there  beginning  are  (or  well, become  made e . g . i n c l u d i n g t h e  and b e t t e r d e s c r i p t i o n s of  calculations.  s p e c i a l care curves  experimental  refinements  energy dependence o f V vibrations  the  end)  work  does  dominant of  the  atomic  show t h a t  features  the  energy  in  range  considered. The surface  zero  i s t y p i c a l of the v a l u e s  face-centred (111)  o r s m a l l c o n t r a c t i o n found here  cubic metals.  surfaces  of  contractions while Section As  t h e work  found f o r other  A s was  Ag,Al>Co,Ir  f o r : the  listed and  presented  in  Eh(111)  (111}. f a c e s o f  Section  5.5  N i a l l show s m a l l earlier  on  the  to zero  Cu (111)  in  5. 3 i n d i c a t e s a somewhat l a r g e r c o n t r a c t i o n o f a b o u t 5%.  y e t P t r e m a i n s t h e o n l y FCC m e t a l t h o u g h t t o show a  o f i t s (111) proportions.  surface,  though, the  modification  dilation  i s of  small  168  CHAPTEB 7  THE BHfTOO) SO BE ACE  169  The  (1.00.)  surfaces  of  intensely studied f o r their for Au  the are  discussed are  fact  chemisorption  S e c t i o n 2.2,  s u p e r i m p o s e d on t h e b u l k  those  (1x1)  stable reconstructed  Eh (100)  t h e symmetry o f t h e s u r f a c e . this criterion  the  surface  As  hexagonal  surface  layer  e t a l J. 18 J ,  p r o p e r t i e s , and n e i t h e r  Tucker*s r e s u l t s s u f f e r e d monitor,  but  both  sets  of  f o r the clean surface.  s u r f a c e t h e r e f o r e appears occur,  from  A  unlikely;  i t would have t o p r e s e r v e  Two p o s s i b l e r e c o n s t r u c t i o n s  that  by s i m p l e , r e g i s t r y s h i f t s o f t h e s u r f a c e  l a y e r a r e shown i n F i g . 7^.1. reguires  a  pattern  such a r e c o n s t r u c t i o n s h o u l d  fulfill  temperature.  w o r k , t h e o n l y o t h e r LEED s t u d i e s o f  composition  a  if  o f F t , I r and  r e c o n s t r u c t i o n s of FCC m e t a l s  with chemisorption  lack of a surface reported  room  and  (100) s u b s t r a t e .  of which r e p o r t e d any 1(E) d a t a .  authors  p r o p e r t i e s £ 14 j  o f T u c k e r £16,171 a n d o f C a s t n e r  both concerned mainly  the  at  involve  Aside from the present are  these  m e t a l s h a v e been  (100) s u r f a c e s  £-25,26,33 J  thought t o e s s e n t i a l l y  Eh (100)  transition  t h a t t h e most s t a b l e  reconstructed in  the  The n o r m a l b u l k s t a c k i n g  atoms  t o occupy the A s i t e s .  seguence Two  other  p o s s i b l e r e g i s t r i e s a r e w i t h t h e t o p - l a y e r atoms o n t h e o n - t o p C s i t e s o r on t h e b r i d g e  s i t e s B.  l i S P I s Jj.1 S c h e n a t i c d i a g r a n o f t h e Rh(100) s u r f a c e (a) and the corresponding LIED pattern (b) i n t h e D o t a t i o n of J o n a r 1281. The u n i t a e s h i s B a r k e d i n ( a ) . The c o m p l e t e circles are for atcas i n t h e s e c o n d l a y e r , and t h e d a s h e d c i r c l e s c o r r e s p o n d t c a topaost layer with the registry belcnging t c the bulk i.e. atcas i n the t o p l a y e r a r e above t h e 4 - f o l d s i t e s such as A. C t h e r r e g i s t r i e s c o n s i d e r e d a r e where atoms a r e e v e r t h e 2fcld site (like B ) , o r d i r e c t l y o v e r a t o n s i n t h e l a y e r below las f o r C).  171  7-iJ  Experimental The  f i r s t e x p e r i m e n t s were c a r r i e d  crystal  used b y T u c k e r £ 1 6 , 1 7 J -  as  however, t o  be  misoriented  by  Tucker In  the  reported  present  spectroscopy  sharp  work  appreciable shown  in  the  (5G0 eV,  detectable  The  Annealing  temperatures i n oxygen, limit.  p r e c i s e time and  was  Auger  found  by  to  a  several  procedures,  at  this  electron 1300K,  case,  the  caused  on t h e s u r f a c e a s  for  10  minutes. lower  t h e C Auger s i g n a l t o b e l o w However,  of  depending  annealing.  Si  the  upon t h e  was  sometimes  surface.  that  a  sharp  (1x1),LEED  pattern,  m i n i m a l c o n t a m i n a t i o n as  spectroscopy,  final  was  1600K-  1000K i n vacuum, o r s l i g h t l y  could  annealing  be heat  for  with  low  indicated  by  obtained from treatment  in  several oxygen  a f e w m i n u t e s a t 900K i n  600K i n h y d r o g e n  be u s e f u l f o r r e m o v i n g  f i n a l stages of On  in  2  F i g . 7.2(b).  vacuum., H e a t i n g a t o r b e l o w found  heating  used  c y c l e s o f a r g o n i o n bombardment and followed  Auger  microamps/cm )  reduced  i n t e n s i t y and  electron  5  temperature  slice  S i _ c o u l d be r e m o v e d by a r g o n i o n  at  f o u n d t o r e a p p e a r on t h e  background  prolonged  about  the  found,  orientation-  crystal.  heater  F i g - 7.2(a)-  7.2(b).,  It  so  a m o u n t s o f C and S i t o a c c u m u l a t e  bombardment Fig-  this  that  temperature l i m i t of  single  (100) s l i c e was  4°,  (100)  same  LEED p a t t e r n s on h e a t i n g t o  with  showed  The  some  c a r e f u l l y r e p o l i s h e d t o the c o r r e c t  o u t on t h e  (1x10  - 7  Torr)  was  any r e s i d u a l o x y g e n d u r i n g t h e  cleaning. occasions  faint  during  the  cleaning  and  ordering  f r a c t i o n a l - o r d e r d i f f r a c t i o n s p o t s were f o u n d  172  RhflOO)  a)  A  Ir I  A  rb) /V^/^VV/1If. r V  f  I 100  I  I 200  I 300  I eV  I i 5 i J I g 2*2 A u g e r spectra o f Eh (100) surfaces for a .5KeV, 10 l i c r c a m p b e a n : a) surface after prolonged heating at 1300K showing s u b s t a n t i a l S i and C i m p u r i t i e s t) after a r g c n ion-fccmbardment, showing reduced Si ana i n c r e a s e d carbon c) c l e a n s u r f a c e s p e c t r u m a f t e r h e a t i n g a t 1000K i n vacuo-  173  f o r l i m i t e d e n e r g y r a n g e s ; t h i s LEED p a t t e r n c o r r e s p o n d e d two-domain  (3x1)  surface  structure  Auger  e l e c t r o n spectroscopy  simply  due  with  92eV) w h i c h had would  be  the  to  silicide  metal of  s e g r e g a t e d t o and  involved; a coincidence rhodium  top  presence  interesting  F i g - 7-3)-  know  layer  but  S i impurity  ordered the  on  was  not  rather  was  { A u g e r peak  at  surface.  It  the  actual  surface  structure  s i t e s u p e r p o s i t i o n , perhaps i n v o l v i n g  layer,  may  seem  more  a  However,  indicated that t h i s pattern  to a reconstructed  associated  (see  to  p l a u s i b l e than a  a 1/3  m o n o l a y e r c o v e r a g e of a t o m i c S i . Later experiments using different  source,  pattern.  see  T a b l e 4.2,  hence  the  occurence  f a c t seem t o be a s s o c i a t e d surface.  When  described  clean  and  a  s u r f ace.  eV with  with  second surface  "clean"  i t was  139  compared 7.2  a  Eh (111)  and  this  earlier,  crystals, eV  failed  Auger e l e c t r o n s p e c t r o s c o p y  impurity;  pattern  s l i c e s c u t from a  of t h i s  not  was  exhibiting  was  n o t i c e a b l e t h a t t h e low  were  relatively  those  from the  intense (111)  of  cleaned a  (3x1)  any  Si by  sharp  Auger spectrum s i m i l a r F i g . 6 . 3 (d),  reveal  a  Si  ( 3 x i ) , p a t t e r n does i n  presence  crystal  from  to d u p l i c a t e t h i s  did  the  crystal  on  the  method  (1x1)  LEED  to those of  obtained-  For  f a c e s , see  the both  energy f e a t u r e s at for : the  the  (100)  170 face  F i g - 6. 1 (d)  and  (c) . A t y p i c a l LEED p a t t e r n and  depicted  in  F i g . 7.4.  incidence  and  f o r 6^=9°, ^ = 2 0 ° ,  J o n a I 1283incident  The current  1(E)  the  beam  curves in  labelling  were the  and  measured a t  angle  i n t e g r a t e d beam i n t e n s i t i e s ,  scheme  normal  convention  normalized  is  of  to u n i t  c o r r e c t e d f o r background i n t e n s i t y ,  were  174  U f l B I S 2a.3 Two-doiain (3X1) liED pattern from the Eh (100) s u r f a c e ~ a t 100eV, t h o u g h t t o be due t c t h e p r e s e n c e o f s i l i c o n  175  F i g u r e 7^4 LEEC p a t t e r n s f r o m t h e c l e a n Eh (100) s u r f a c e f c r (a) n o r m a l i n c i d e n c e (150eV) , (b) f c r © ^ 9 ° , £=20<> (94eV) and t h e team l a b e l l i n g scheme (c) and (<3) .  176  stored  on d i g i t a l c a s s e t t e p r i o r t o t r a n s f e r t o an  computer  for  the  reliability-index  experimental data a r e c o l l e c t e d Experimental eguivalent although for  by  1(E)  symmetry  at  The I (E)  t h e (11) s e t o f beams, w h i c h s h o u l d  i n c i d e n c e , a r e shown i n t h e u p p e r h a l f peak the  positions  (02)  beams h a v e a l m o s t  be  sere  averaged,  curves  measured  be e g u i v a l e n t a t n o r m a l of  and o v e r a l l i n t e n s i t y  ( 1 1 ) , (11) and (11) beams.  that.> should  incidence  t h e d i f f e r e n c e s were s m a l l .  The  k7~&9.  f o r beams  normal  370/168  calculations.  i n Appendices  curves  IBB  F i g - 7.5;  the  same  v a r i a t i o n i s observed f o r  S i m i l a r l y , the  identical profiles.  ( 2 0 ) , (02)  and  Small variations i n  t h e r e l a t i v e p e a k i n t e n s i t i e s f o r beams i n  the  always  a t normal i n c i d e n c e ,  present  i n independent experiments  w h i l s t t h e agreement between i n d i v i d u a l and  other  beam  sets  variations  have  to  (involving  such  factors  imperfections i n setting  the  be  the  angle  was  as  of  to  uneven  set  were  beams i n t h e { 2 0 } ,  general  attributed  crystal  a g r e e m e n t t o be e x p e c t e d 1(E)  in  (11}  slightly betterexperimental  response  surface,  (22}  and  of  Such errors  the screen,  uncertainties i n  i n c i d e n c e ) , •an:a-•vthey^.Ma•it^ A.tie• :le.v el ;.:Of :  between c a l c u l a t i o n and  c u r v e s f o r a l l beams were s m o o t h e d by  !  !  experiments two  operations  of a t h r e e - p o i n t s m o o t h i n g ' . f i l t e r . ..©rior- t o t h e : r e l i a b i l i t y - i n d e x :  calculations.  To a v o i d s p u r i o u s r e s u l t s i n t h e s e  b a c k g r o u n d and s c a t t e r i n t h e e x p e r i m e n t a l  calculations,  d a t a were e l i m i n a t e d .  177  fJ9y£§ 2*_5 1 ( E ) c u r v e s f o r two s e t s c f teams t h a t should be equivalent at normal incidence on t h e Bh (100) s u r f a c e ; t h e f o u r t h member o f e a c h s e t i s o t s c u r e d by t h e s a m p l e manipulator.  17.8  ls.2.  Calculations  and  The  c a l c u l a t i o n s were p e r f o r m e d as d e t a i l e d  5,  f o r t h e two  Chapters  a l t e r n a t i v e r e g i s t r i e s shown i n F i g - 7-1  w e l l as f o r a t r u n c a t e d hulk c r y s t a l ; r a n g e d f r o m a -10  in  t o +101  the  3 as  topmost l a y e r  spacings  c h a n g e from t h e b u l k v a l u e o f  1.9022A,  o  •o  i n s t e p s o f 2.5% and cf  69  o r 0.04751.  beams b e i n g a v a i l a b l e  Fig-  7-6  incidence  f o r the  model  experimental  (11) and  1(E)  registries  f o r atomic  using  t h e 7^^  radii  theoretical  f o r r e g i s t r i e s B and  concluded  of  Consideration interlayer  agreement of  other  for  a r e f i x e d by by  from  as t h o s e f o r the b u l k s t a c k i n g seguence level  an  Fig-  7.7  shows  diffracted  from  calculated  f o r an  the  packing 1(E) 8h (100)  hard-  C do n o t a g r e e as  well  (registry  &} ,  i s by no  beams  and  although  means i d e a l -  other  ;topmost  E and C; i t  i s interpreted  measured  surface,  the  F i g - 7.6  seguence f o r the top curves  these  the  the l a t t e r  diffracted  for  the b u l k s t r u c t u r e  spacings f u r t h e r preclude the r e g i s t r i e s  unreconstructed  normal  that  seems t h a t t h e s u r f a c e s t r u c t u r e o f Rh (100) by  at  potential; In  |3  determined  It is  curves  curves  (20) beams w i t h t h o s e c a l c u l a t e d  of r h o d i u m £62,63]-  the  diffraction  40-30Oey.  c a l c u l a t i o n s the t o p i n t e r l a y e r s p a c i n g s sphere  the l a y e r  total  Discussion  compares  different  to determine  range of  potential  were used w i t h a  t  R e s u l t s and  the  t h e band s t r u c t u r e  t h e s u p e r p o s i t i o n p o t e n t i a l V^ j  m a t r i c e s f o r an e n e r g y 7.3  Both  best  layer-  for  together  u n r e c o n s t r u c t e d s u r f a c e u s i n g both  six with  beams curves  potentials,  179  J i j g u r e 7^6 C o m p a r i s o n o f e x p e r i m e n t a l 1 ( E ) c u r v e s f o r t h e (11) and (20) beans a t n o r m a l i n c i d e n c e on fib (100) v i t b c a l c u l a t i o n s , fcr t h e ¥^(j p o t e n t i a l , f o r t h e t o p m o s t r e g i s t r i e s d e f i n e d by A,E a n d C i n F i g . 7 . 1 . The t o p m o s t interlayer spacinqs are 1. 9 0 , 2. 33 a n d 2.69A f o r t h e i»-fold, 2 - f o l d and 1 - f o l d s i t e s respectively. a  18C  fi5i?£§ 2 x 2 C o m p a r i s o n o f some e x p e r i m e n t a l 1(E) curves f o r Bh(100) with calculations f o r t h e vJf and M potentials V =-12eV and Ad%=-5,Q and+5* f o r (a) n o r i a l i n c i d e n c e and (b) a t £- = 9°, i =200. H  fk0  or  Energy (eV)  182  f o r A d g = - 5 I , 0 and - 5 % . of  calculated  curves  are  s h i f t t o h i g h e r energy Otherwise  F o r e a c h beam a n d s p a c i n g , t h e two s e t s c l o s e l y s i m i l a r a p a r t from a s l i g h t  for  r e l a t i v e to 7 ^  the d i f f e r e n c e s noted  .  e a r l i e r i n t h e behaviour of  t h e p h a s e s h i f t s do n o t a p p e a r t o have much v i s u a l e f f e c t on t h e c a l c u l a t e d 1(E) c u r v e s . difference  mentioned  the  real  12eV  for  1(E)  shift  in  Chapter  V  to the  6,  and  and - 18eV f o r V ^  curves  to lower  these  .  To  a  good  shift  approximation,  i n the calculated  energy.  values of V  some  beams  ( e . g . (11)  quite  poor f o r o t h e r s  flr  , t h e agreement w i t h experiment  beam  at  from  of  the  very  may  good  for  n o r m a l i n c i d e n c e , Ad$=-5%) t o  ( e . g . (11) beam a t © - = 9 0 ,  estimation  distinguish  t h e two s e t s o f  r  be e s t i m a t e d b y v i s u a l c o m p a r i s o n t o v a r y  visual  this  ( i . e ... V ) : a r e t a k e n a s -  more n e g a t i v e c a u s e s a r i g i d  o r  assuming  w o u l d show p e a k s a t t h e same e n e r g i e s i f  parts of the inner p o t e n t i a l  With  A  relates  t h e main d i f f e r e n c e i n t h e p o t e n t i a l s ,  c a l c u l a t e d 1(E) c u r v e s  making  observed  i n p o t e n t i a l at the r a d i u s of the m u f f i n - t i n spheres  of a b o u t 6eV, a s provides  The  overall  (/>=20o, o d S 5 - - 5 S ) .  degree  of  f i t cannot  between t h e two p o t e n t i a l s , b u t i t s u g g e s t s  has a v a l u e b e t w e e n 0 a n d +51-., T h i s  estimate  i s  that  &%  included  in  T a b l e 7. 1. The of  16  r e s u l t s of a r e l i a b i l i t y - i n d e x beams  analysed  tabulated i n Table for  both  at  the  two  a n a l y s i s f o r the angles  7.1 and shown a s c o n t o u r  potentials.  of best f i t "  as noted  precautions  noted  of  incidence are  plots  in  Once a g a i n we n o t i c e a p r o n o u n c e d i n Chapter  there  6  f o r the  concerning  strong  total  (111)  F i g - 7.8 "valley  face.  features  The  at the  183 Extent of Comparison Pot. 9  Conditions of b e s t agreement  n  JleVl  Analysis  Adj§  J  402 16  1548  8-factor visual  +2.5±0.9 t-2-5±2.5  -11.5±0.7 -12 ±2  0-155  WW V , 402 16  1684  E-f a c t o r visual  -1-8± 1-0 +2-5±2.5  -19-6±0-8 -17 ±2  0.167  V  1786  R-f a c t o r  *2.7±1-0  -11.0±0.9  0.188  V  p  w  ftk(3  250 16  T a b l e 7.1 surfacebeginning  Summary  of  structural  o r end o f 1(E) c u r v e s  R-  6 r  d e t e r m i n a t i o n o f t i e Rh(1Q0)  were t a k e n  into  account.  D e s p i t e t h e s i m i l a r degree o f v i s u a l agreement between experimental contour and V  V  data  plots exhibit  of  the  sphere;  The  the observed  reflecting  calculated  curves, the values of Ad%  differences  values of the surface r e l a x a t i o n  i n the  p r e d i c t e d by  confidence  limits  ( 1  t h e y a r e w i t h i n 95% c o n f i d e n c e  limits  i 2 s t a n d a r d e r r o r s ) - , . The minimum v a l u e o f R i s s l i g h t l y  lower  for V^  e r r o r ) , although  68%  edge  d i f f e r e n c e i s 8eV, t h e  further  t h e two p o t e n t i a l s a r e o u t s i d e t h e standard  of  From t h e d i s c u s s i o n a b o v e , a 6eV s h i f t i n  presumably  potentials.  sets  because of d i f f e r e n c e s i n p o t e n t i a l a t the  muffin-tin  e x t r a 2eV  both  minima a t somewhat d i f f e r e n t  ( T a b l e 7. 1 ) .  4 r  i s expected  o r  and  the  (0- 155)  K D  As  an  than  forV ^  (0. 167) -  e x p e r i m e n t a l v a l u e o f t h e s u r f a c e Debye  temperature  |°/) was n o t a v a i l a b l e f o r r h o d i u m , a f u r t h e r c a l c u l a t i o n the  potential  values  of  ( T a b l e 7,1) c9- =402K. 0  Ad%  V^rj and  although  was p e r f o r m e d w i t h ®^=2 50KV  or  R  have has  been  changed  using  The b e s t f i t  only  slightly  i n c r e a s e d t o 0-188 f r o m 0- 155 f o r  A l l values o f a guoted i n Table  7.1  are  below  0.20,  184  f i s u i e li.8 Contour plots f o r Bh(100) o f r v e r s u s V* and f o r (a) t h e V ^ j and (h) t h e potential. Error tars the standard e r r o r s ana d e f i n e d i n C h a p t e r 5. r  r  AdX are  185  186  and  axe  therefore  w i t h i n the, r a n g e f o r w h i c h Z a n a z z i  proposed a s t r u c t u r e i s "very such c o n s i d e r a t i o n s  on  a  probable".  more  The  and  Jona  a n a l y s i s here  puts  guantitative  basis.  Further  s t u d i e s with contour p l o t s f o r r e g i s t r i e s that are  i n c o r r e c t , on  the  of S a t  basis  of  visual  a n a l y s i s , give high  minima as w e l l a s l a r g e Comparison of  u n c e r t a i n t i e s a s m e a s u r e d by  the  determinations  p o t e n t i a l s , w i t h b o t h the  v i s u a l and  as  higher B  well  as t h e s l i g h t l y  make i t t e m p t i n g t o l a b e l t h e potential  and  Unfortunately  therefore  potentials.  of  the  &&%  v  from  potential  quote  V^  as  potential,  the  ft  relatively  minor with  Nevertheless  the  that  uncertainties  at  therefore  believe  g u o t e d as  0±2.5%.  feature  for in  the an  (111) I (£)  c o m p a r i s o n between experience this that  stage  of  the  value  curve  caution  LEED o f AdS  value.  the  for  full  the  produce  surface  experiment  suggests  "better" &%  possible to assess of  two  analyses,  a more d e f i n i t e  d i f f e r e n t n values  noted  the  reliability-index f o r the  local  c j and c" .  C a r e f u l e x a m i n a t i o n of the d a t a d i d not  a n o m a l i e s of the s o r t  interfered  to  of  value  '^13  a t p r e s e n t i t i s not  significance  values  where  two any a  significantly and in  theory. attaching  crystallography; f o r Eh (100)  must  we be  187  7. 4  Comparisons With P r e v i o u s The  (100)  bibliography  faces  show any  of  of Section  face-centred  5-5  reliability-index  (100)  surfaces £114]  from  although  Fourier  analyses  on  the  p r o b a b l e , we c a n with the  see  conclusions  two  or  that  of  the  till  now  far,  no  been p e r f o r m e d  for  dilation.  calculations  none  have  transform  up  Thus  £99J  and  data  d a t a f r o m C u ( 1 0 0 ) c l a i m low  margins w i t h r e s u l t s of a s u r f a c e results  shows  cubic metals studied  substantial contraction  ether  averaging  .Studies  c o n t r a c t i o n o f 0±1%.  potentials  used  here  appear  t h a t t h e r e s u l t o f &d%=0±2.5% i s reached f o r ether  FCC  (10 0)  As  error the  equally  consistent  surfaces-  CHAPTER 8  TEE RH O 10) SURFACE  189  The by  {110) s u r f a c e s o f s e v e r a l FGC  1EED;  the  m e t a l s have b e e n  b i b l i o g r a p h y o f S e c t i o n 5.5 i n d i c a t e s t h a t  surfaces often  e x h i b i t c o n t r a c t i o n s f o r the surface  to  the  10%  studied  from  bulk  a p p e a r t o be c o n f i n e d  value.  these  l a y e r of  S t u d i e s o f t h e Rh{110)  t o t h e e a r l y oxygen a d s o r p t i o n  up  surface  experiments  o f T u c k e r J 1 6 J , a s h o r t i n f r a r e d s t u d y o f CO a d s o r p t i o n o n  (110)  o r i e n t e d Rh f i l m s 1132 J a n d , most r e c e n t l y , a d e t a i l e d s t u d y CO  adsorption  on  the  single  L a m b e r t £133 3-  In this l a t t e r  clean  surface  Eh (110)  h e n c e was u n l i k e l y an  ideal  for  with  2  and  i s correspondingly seemingly  Al(110)  bulk i n t e r l a y e r A  (100) s u r f a c e s .  found  the  absolute  guestion  A l £ 1 0 1 , 108, 110- 112J  in  the  and  The  roughness  in in  two-fold  i s relatively  may  account  open  in  part  f o r t h e Aq{110)  contractions  LEED  may  be  some the  cases,  but  of  s t u d i e s o f t h e (110) surface  Ag C 101,106- 1 0 7 ]  and t h e o r e t i c a l  discrepancies  surface roughness, as evidenced patterns  with the  d i s t a n c e s l e a d t o l a r g e r percentage changes.  recurring  obtained.  of  on t h e l e s s open s u r f a c e s b u t t h e s h o r t e r  agreement between e x p e r i m e n t a l been  A diagram  The b u l k i n t e r p l a n a r  s h o r t , and t h i s  s u r f a c e s o f A l and Ag i n v o l v e s t h e r o l e For  and  large contractions reported  surfaces; thus  s i m i l a r t o those  planes  the  (1x1) LEED p a t t e r n a n d  This surface possesses only a mirror  and  that  (110) s u r f a c e i s shown i n F i g . 8.1, t o g e t h e r  axis  the  a simple  found  to be l a t e r a l l y r e c o n s t r u c t e d .  c o m p a r e d w i t h t h e (111) o r spacing  s u r f a c e by Marbrow  work t h e a u t h o r s  showed  a s s o c i a t e d LEED p a t t e r n . symmetry  crystal  of  have  by p o o r a  only  modest  I (E) c u r v e s  been  has  attributed  contrast  simple  roughness.  attempt  in  the  to  multiple-scattering calculations  to  LEED  include did  not  190  191  substantially recently  a  i m p r o v e the a g r e e m e n t w i t h e x p e r i m e n t £108 ] . UPS/XPS  study  £134}  has  the  angular  the c l e a n Ag(110}-(1x1)  surface  dependence o f p h o t o e m i s s i o n  from  is  nature  m a r k e d l y a l t e r e d by  However, gave  both  chemically  apparently  1(E)  curves  the  and  identical  were  of  shown  the  measured.  patterns;  The  authors  c l e a n i n g does i n f a c t  produce  a  incomplete  removal  of  disordered  mechanical  polishing  difficulties experimental  8.J -  the be  experienced and  in  "smoother"  t h e o r e t i c a l LEED  unfortunately  surface  material  responsible obtaining  specimens  for  a  rod purchased  chemical and  that  induced  some  by  of  the  good a g r e e m e n t b e t w e e n  data.  The  S(152eV) c a n  small  peak  element  at  is  initial  heat  treatments  about  have  P e a k s due  116eV found  an  slice  produced  is  assigned  a t . 120eV  Chemicals the  but  Sh  peaks.  no  other  detected.  again  no  trace  of  and  obtained  B s i g n a l s almost as  of  strong  the  8.2(c).  b o r o n peak a t 180eV c o u l d  T h i s i s i n marked c o n t r a s t t o t h e r e s u l t s  L a m b e r t £133 J who  this  Rhodium d o e s  n e a r t h i s e n e r g y £49]  a  A  common  peak i s n o t a p p a r e n t i n t h e c l e a n s u r f a c e s p e c t r u m , F i g . Once  Auger  t o phosphorus;  A u g e r peak i n t h i s r e g i o n .  not have a c a l c u l a t e d t r a n s i t i o n  cut  t o s m a l l a m o u n t s o f C (272eV)  be s e e n i n a d d i t i o n t o t h e m a i n  usually  contaminants  crystal  from R e s e a r c h O r g a n i c / I n o r g a n i c  spectrum of F i g - 8.2(a).  and  no  Experimental  Corporation.  and  polishing.  suggest that  E x p e r i m e n t s were p e r f o r m e d on a s i n g l e from  crystal  non-cheraically polished  LEED  may.  that  Host  be  Marbrow as  the  192  Rh(110)  ~ i  100  1  1  200  1  1  3 0 0 eV  Ii^Jl£g JL2 Auqer s p e c t r a o f t h e Bh(110) s u r f a c e a t a p r i m a r y bea« v o l t a g e o f 1.5KeV and 10 a i c r o a n p c u r r e n t : a) a f t e r i n i t i a l heat t r e a t a e n t s showing S ( 1 5 2 e V ) , P(120eV) and C{272eV) c o n t a a i n a t i o n on t h e s u r f a c e t) after argcn icn-bcabardaent; P and S r e a o v e d tut C increased c) c l e a n s u r f a c e spectrum.  193  main  Rh  peak  concluded  at  302eV upon h e a t i n g  again  that  these  t o 1300K.  contrasting  I t can  observations  o r i g i n a t e i n d i f f e r e n c e s i n manufacture or p o l i s h i n g The  S and  ty a r g o n - i o n but  P contaminants could  bombardment  again  only  at  the  concentration  of  Fig-  However,  8.2(b).  the bulk  on  and  obtained having (1x1)  C  shown this  of  in  for  increasing  the  The  and  the  surface of  s u r f a c e carbon d i f f u s e d back  into  After an  Auger  several; cycles  apparently  clean  in  appearance  of  170ev  ion-  surface  that  of  . between  Rh(111),  F i g . 6-1-  peaks remain very s i m i l a r i n a l l t h r e e c a s e s . 139  minutes)  a  was sharp  Auger spectrum of the c l e a n s u r f a c e i s  intermediate and  surface  20  t h e A u g e r s p e c t r u m o f F i g . 8.2 (c) w i t h  Eh (100) ( F i g . 7.2)  at  procedures.  spectrum  1000K.  annealing  LEED p a t t e r n .  roughly  a t 5 microamps  be  must  be removed f r o m t h e  expense  as  heating at  bombardment  (1keV  only  The  that  of  The  major  minor  peaks  appear t o i n c r e a s e i n r e l a t i v e i n t e n s i t y  as  (111)< (110) < (100) A t y p i c a l LEED p a t t e r n and F i g . 8.3  for  Rh{110).  1(E)  and curves  incidence of  the  {11}  similarity  for  data  directions  of  scheme i s shown i n  were r e c o r d e d incidence  6>= 1Q<>,<^. =1350 i n t h e a n g l e c o n v e n t i o n that should  be  eguivalent  by  were a v e r a g e d p r i o r t o s m o o t h i n g and  {21}  of  each  beam s e t s a r e member  members o f t h a t s e t i s n o t found  labelling  Intensity  r a n g e 50 t o 250eV f o r two 6>=0°,  the  the  (111)  and  of  as  depicted an  symmetry  the  defined  by  J o n a I 128]at  normal  Eguivalent  members  in  F i g - 8.4-  e q u i v a l e n t set to the  satisfactory  (100)  Of  for  surfaces-  as This  that may  a s s o c i a t e d w i t h some d e g r e e o f s u r f a c e r o u g h n e s s of  The other  typically perhaps this  be  (110)  194  c)  d)  Ii51i£f 5 x 3 LEED p a t t e r n from t h e c l e a n Bh<110) surface at tcrial incidence (88eV) and (b) P-=10«, ^ = 135° <90eV). fceai l a b e l l i n g scheme i s shewn i n (c) a n d ( d ) .  (a) The  195  RhCllO)  I  100  1  1——I  200 eV  —I 1  1 0  0  1  200 eV  1  f i g u r e 8.4 E x p e r i a e n t a l 1 ( E ) c u r v e s f o r t b e Rh(110) surface at uorial incidence f o r t h e 4 - f c l d e q u i v a l e n t |11> and 121} beam sets. The 4 t h nember o f each s e t i s o b s c u r e d by t h e s a m p l e tariculator.  196  surface.  Two  complete  sets  cf  independent experiments  were  performed f o r e a c h a n g l e o f i n c i d e n c e , and t h e i n t e n s i t y d a t a i s gathered  together  in  A p p e n d i c e s A10-A13,  where  the  good  a g r e e m e n t b e t w e e n t h e two s e t s c a n be s e e n .  8.2  Calculations Due  to  the  low  symmetry  o f t h e (110) s u r f a c e  s c a t t e r i n g c a l c u l a t i o n s a r e r e l a t i v e l y s l o w and it  is  desirable  and  (100)  (1x1)  LEED  1(E) c u r v e s  Firstly,  for  a laterally  bulk  different  data  then  i t  registry  were  Secondly, the experience  i s  potential  LEED;  degrees o f agreement o f t h e o r y  very  previously,  they  did  unlikely  differ  with to  u n t i l t h e f i t of the  and  superposition be  assessed.  (100)  judged  experiment.  however  in  surfaces  p o t e n t i a l nor the to  be  both gave e s s e n t i a l l y with  i f  b u l k l a y e r and c a l c u l a t i o n s  deferred  could  for  that  i n i t i a l l y assumed  o f t h e (111)  n e i t h e r the V ^ p  band s t r u c t u r e p o t e n t i a l suitable  hence  surface are a  s t a c k i n g c a l c u l a t i o n s w i t h e x p e r i m e n t had been  that  the  produce t h e o r e t i c a l 1(E) c u r v e s  F o r Bh( 110) t h e s u r f a c e was  alternative  reveals  by  top-layer  therefore  unreconstructed  have t h e r e g i s t r y o f t h e a p p r o p r i a t e with  the s t u d i e s of  I t seems r e a s o n a b l e  another r e g i s t r y w i l l  a better f i t .  effort  p a t t e r n , do i n f a c t g i v e c l e a r l y d i s t i n g u i s h a b l e  good match t o t h e e x p e r i m e n t a l that  Hence  t h e symmetry o f t h e s u r f a c e , and  c a l c u l a t e d 1(E) curves. the  learnt during  surfaces.  r e g i s t r i e s that preserve a  costly.  i n t h i s case to l i m i t computational  taxing note of s e v e r a l lessons (111)  multiple-  As  a  more  identical discussed  the inner p o t e n t i a l  197  n e e d e d and  i n the v a l u e of s u r f a c e c o n t r a c t i o n . s u g g e s t e d , .  T h i r d l y i t appears  that  d i r e c t i o n s of i n c i d e n c e can t h e same a n g l e s b u t Taking  and  layer  unlikely  using both  as  3  to  be  the r e n o r m a l i s e d  formalisms the  very  from  different  use helpful  beam  intensities  forward  scattering  f o r , only  of  the at  structural  p a r a m e t e r s used f o r t h e  t a k e n , and  c a l c u l a t i o n s were  made  results for  potential.  points together, diffracted  doubling  p o t e n t i a l V^,  derived  v a r y a t l e a s t a s much a s  with a d i f f e r e n t  these  were c a l c u l a t e d  results  the  second  this (111)  superposition  potential  s t a g e , , The and  (100)  assuming  s t r u c t u r e f o r w h i c h t h e s u r f a c e s p a c i n g was  a  seems  same non-  s u r f a c e s were  truncated  allowed  bulk  to vary from o  a  15% c o n t r a c t i o n t o a 5%  in 8-3  steps of  B e s u i t s And  Discussion  Sets  experimental  the  from the b u l k value  of  (00)  f o r the  beam  and  calculated  a t ©"=1QQ, 4> =135°.  reliability  i n d i c e s f o r i n d i v i d u a l beams,  evaluations,  f i t for  These  values  especially  for  o f f - n o r m a l i n c i d e n c e i s judged relatively calculated  poor 1(E)  the e x p e r i m e n t a l  the  A  better  F i g . 8.5.  (11)  seem  data.,  are  incidence  and  the  visual  beam;  (11)  by t h e  b e t w e e n 50 and  comparison  values  of  the  (r^.) , are a l s o given c  consistent  f i t , presumably  curves  I (E) c u r v e s  (11) beam a t n o r m a l  indicates a  in  (1..345.A)  2.5%,  compared i n F i g . .8.5 for  expansion  beam.  The  ( r ^ ) ^ values because  with (00) to  structure  visual team a t show in  100eV i s n o t r e p r o d u c e d  a the in  198  RhOlO)  Energy (eV)  Energy (eV)  f i g u r e 8 5 C c a r a r i s o n s o f two e x p e r i a e n t a l 1 ( f ) c u r v e s f o r t h e Eh ( 1 1 0 ) ~ s u r f a c e w i t h c a l c u l a t i o n s , u s i n g t h e V^, potential for four values of The v a l u e of the individual beam r e l i a b i l i t y - i n d e x ( r ) ^ i s g i v e n i n b r a c k e t s f c r each c a l c u l a t e d curve. A  3  r  199  F i g u r e 8.6 shows a c o n t o u r reliability-index set  of  (111)  data  p l o t of the energy-weighted  r , as a f u n c t i o n o f V f  a t normal i n c i d e n c e .  andAdS f o r a  Q r  As n o t e d  f i t " running diagonally  minimum.  The v a l u e o f r  close correspondence 1(E) c u r v e s  between  f o r this  valley  of  a c r o s s t h e p l o t and a pronounced  a t t h e minimum  r  single  previously f o r the  a n d (100) s u r f a c e s a n d f o r Cu (111) , t h e r e i s a  "good  mean  the  ( v i z . 0.10) i n d i c a t e s a  experimental  and  calculated  s e t of data a t normal i n c i d e n c e ; i n t h i s  case t h e c o n d i t i o n s f o r t h e  minimum  are  V  =-11.*2±0.6eV  and  £ d I - - 2 . 5±1-.23L . The  results  independent incidence both  sets of experimental employed  between  experiments  of the r e l i a b i l i t y - i n d e x  i s at  data  angles  least  As was  at  the  two  c o l l e c t e d i n T a b l e 8-1.  different  f a c e s o f rhodium. incidence  are  data  a n a l y s e s f o r t h e two  as found  of  incidence  appears result  and  f o r Rh (111) ,  shows a s m a l l e r c o n t r a c t i o n  the  contraction  of  faces  the  same  the  the  second  again i t  accuracy  the  mean o f t h e r e s u l t s i n T a b l e 8.1  of  a  yields  t o p m o s t i n t e r l a y e r s p a c i n g o f 2.1±2.Q%, =-10.7±1-OeV-  t h e i n n e r p o t e n t i a l compares r a t h e r  with  contraction  a n g l e t o 1 o r 2% o f t h e b u l k s p a c i n g .  c o m p a r e d w i t h t h e b u l k s p a c i n g , and V cf  off-normal  than t h e f i r s t ;  t h a t e x p e r i m e n t a l e r r o r must l i m i t  The e n e r g y - w e i g h t e d a  different  good a s t h a t f o u n d f o r t h e o t h e r  a p p e a r t o show a g r e a t e r p e r c e n t a g e  at a particular  of  The a g r e e m e n t  t h a n do t h e n o r m a l j i n c i d e n c e d a t a . , F o r b o t h a n g l e s experiment  angles  ion-core  potential  ( v i z . -11.5±0.7 a n d - 1 1 . 0.±O. 6ev) .  well  with  f o r the  This value those  ether  found rhodium  200  f i s a i i 8^6 A c o n t o u r r l c t f o r Eh (110) o f r r v e r s u s V« and f o r d a t a a t n o n a l i n c i d e n c e and a c a l c u l a t i o n for the potential.  A&%  201  uc i i - u ai  01  o f t o  •  >  u  01  60 CO 01 01 «o  o  u u o  •  +1 CM o  00 c o  •  O  T3  0) oc c CO  U T5  OJ u 00 co u o. 01 e c o til u  • o  >  0)  oo o  •  +1  •  > o  •  +1 CO  •  o iH  •4 CM  CM  CM  f t  f t  1  +1 m CN  > 01 co  1  •  +1 O  •  o r-l  m CM  o  O  •  >  >  >  o  o  •  <-l  +1  o  •  1  +1 00  •  >  »4 O • CM  •  •*  01 oo 00  01 00 CM  •  o  •H  •  f t  m CM  cu  V  i-H i-t  •  C K  ON O  01  f t  •  +1  •  CU  f t  •  +1 in  •  ON 1  o f t  i-l  O • CM +1 in • cn  i  •  CM +1 •  CM  > HI  as  oo  en 6 CO  01 £> "0 0> U - l t-i O  CO  CO  a • E o o z u  1  -  3  "  CO  zX 01 w  i-t  CO  c > CM  CO 01  e  >E  f  e  m r->  t« N  e  CO 01  e  m  P I  e o> o o  •H C  u  oi CJ " O  a £  ?  ?  V  V  O  ct>  a>  co  ce  5  lafcle J 1 Conditions o f best aqreeaent between e x p e r i a e n t lultiFle-scatterinq calculations Measured f o r two a n q l e s i n c i d e n c e on Rh ( 1 1 0 ) . A  and of  8.4  Comparisons H i t h Previous  Work  On a p e r c e n t a g e b a s i s , t h e Rh(110) s u r f a c e slightly  more c o n t r a c t e d  appears  t h a n t h e (11.1} o r (100) s u r f a c e s .  c o n t r a c t i o n o f a b o u t 3.% f o r R h ( 1 1 0 ) i s t o be c o m p a r e d contractions  of  555  for  Ag (110) £ 106,107 J a n d b e t w e e n Al£ 108, 11Q-112 "] r e p o r t e d calculations. indicated  previously  f o r t h e l a t t e r s u r f a c e s by However,  with  comparisons of experimental visually  and  error associated  and The  are  with  to  the  1015 f o r  multiple-scattering  on  con volution-:-transform  exception  of  Ag( 110)£ 1 0 6 j ,  the  latter  a l l the  other  a n d c a l c u l a t e d i n t e n s i t i e s h a v e been l i a b l e t o unknown d e g r e e s o f  w i t h s u b j e c t i v e e v a l u a t i o n of t h e d a t a .  guestion  of surface roughness r a i s e d over  Al(110)£108]  Ag (110) £ 106,134 j c a n n o t be c o n c l u s i v e l y r e f u t e d f o r Rh ( 1 1 0 ) . sharpness  of  t h e LEED  agreement o f t h e o r y the  other  patterns,  curves  the  r e l a t e d beams  generally  and  the  and e x p e r i m e n t a r g u e a g a i n s t  hand,  substantial  such a p r o b l e m .  beam s e t s and t h e  f o r t h e 6 = 10°, <f> =135° d a t a  effect  assessment  of  experimental  1 ( E ) c u r v e s r e g u i r e s d e t a i l e d and  o f a t y p e t h a t h a v e n o t y e t been  of  experimental  do show p o o r e r a g r e e m e n t  with c a l c u l a t i o n s than i s t h e case f o r n o r s a l the  similar  t h e r e a r e s i g n i f i c a n t d i f f e r e n c e s between  members o f s y m m e t r i c a l l y - r e l a t e d 1(E)  with  the  the  therefore  appearance o f s y m m e t r i c a l l y  On  5  The  10 and 1555 f o r t h e (110) s u r f a c e o f  a p p r o a c h and t h e l a t e s t work  The  N i (110) £ 1,1,1 35 J ,  be  S i m i l a r o r s l i g h t l y l o w e r c o n t r a c t i o n s h a v e been  method £ 1 0 1 j .  made  to  surface  initiated.  incidence. imperfections careful  The on  studies  203  REFERENCES -  204  1.  L. ae B r o g l i e , P h i l .  2.  C. J . D a v i s s o n and C.  3.  H. , E. F a r n s w o r t h , P h y s .  4.  C. J . Da v i s s o n and L. fl. G e r m e r , 705  5.  C. E c k e r t , P r o c . N a t . A c a d . Amer. 13  6.  G.  1.  G. A. S o m o r j a i and H. H. F a r r e l l , Adv. (1971) 215  8.  i '  9.  K-  Hag.  47  (1924)  446  B. Kunsman, S c i e n c e 52 B e v . , 25  P. Thomson, Contemp. P h y s . 9  (1925)  Rev.  (1927)  M. B. i e b b and M. G. (1973) 301  Solid  (1927)  1 Chera.  , I  Laqally,  30  460  A. R. M i t c h e l l , Contemp.. Phys- . 14 (1973) 1  522  41  Phys.  (1968)  (1921)  State  Phys-  20  251 Phys.  28  TO.  G. , E r t l and J . K u p p e r s , "Low Energy Electrons and S u r f a c e C h e m i s t r y " , Monographs i n Modern Chemistry 4, V e r l a g C h e m i e , H e i n h e i m 1974, C h . 9  11.  J. E- Demuth, P. H. B11 (1975) 1460  12.  J . B. P e n d r y , "Los Energy A c a d e m i c P r e s s , Sew Y o r k , 1974  Electron  13.  C.  27  14.  G. A- S o m o r j a i , " P r i n c i p l e s of P r e n t i c e H a l l , Engleaood C l i f f s ,  15.  S-  Y. Tong, P r o g r e s s i n S u r f a c e S c i e n c e 7 (1975) 1  16.  C.  W-  17.  C. W.  18.  D. G. C a s t n e r , B. A. S e x t o n Sci. 71 (1978) 519  19.  L. M c D o n n e l l and D. 505  20.  G.  21.  D. C. F r o s t , K- A. 8. M i t c h e l l , F. R. S h e p h e r d , and P. R. W a t s o n , J . V a c . S c i . T e c h n o l . 13 (1976) 1196  2 2-  R. L. P a r k , i n Research 3",  B. Duke, Adv.  M a r c u s and D-. W.  Chem.  Tucker J r . , J .  Phys.  Appl.  T u c k e r J r . , A c t a Met.  Diffraction",  (1974)  1  37  (1967)  and G. A.  (1966) 3 0 1 3 ,  Bev..  B9  (1974)  4147  1465 Somorjai, Surface  P. W o o d r u f f , S u r f a c e S c i . 46  E. L a r a m o r e , P h y s -  Rev.  Surface Chemistry", New J e r s e y , 1972  Phys. 15  Jepsen, Phys.  (1974)  1204  "Experimental Methods e d . R.,8. A n d e r s o n and  in Catalysis P. T. Dawson,  205  Academic  P r e s s , 1976  23.  E. Z a n a z z i a n d F. J o n a , S u r f a c e S c i .  2 4.  H. P. B o n z e l , C- 8. H e l m s a n d S. K e l e m a n , L e t t e r s 35 (1975) 1237  25.  A. I g n a t i e v , A. V. J o n e s a n d T. N. 30 (1972) 573  fihodin,  26.  F. J o n a and P. H. M a r c u s , Comment (1977) 1  S o l . State  27.  G. C. Bond, L o n d o n , 1962  28.  D.,Pines, "Elementary E x c i t a t i o n s i n S o l i d s " , New Y o r k , 1964  29.  E. A. Hood, J .  30.  N. F. M. H e n r y a n d K. L o n s d a l e , e d s . " 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 * V o l . 1 ( 1 9 5 2 ) , The Kynoch P r e s s , B i r m i n g h a m  "Catalysis  Appl.  by  Phys.  62 (1977) 6 1  Metals",  Phys.  Eev.  SurfaceS c i . Phys. 8  Academic  Press,  Benjamin,  3 5 (1964) 1306 n  31.  P. J - E s t r u p a n d E. G. McRae, S u r f a c e S c i .  32.  8. L . P a r k and H. H. Madden S u r f a c e S c i .  33.  P. . 1 . P a l m b e r g and T. N. R h o d i n , P h y s . 586  34.  S. A n d e r s s o n a n d B. Kasemo, S u r f a c e S c i . 25 (1971) 273  35-  C. H. T u c k e r a n d C. B. Duke, S u r f a c e S c i .  36.  M. B. Webb and M. G. L a g a l l y , (1973) 301  Solid  37.  E . G. McRae, J .  45 (1966)  38-  A. I g n a t i e v , J . B. P e n d r y a n d T. N- R h o d i n , L e t t e r s 26 (1971). 189  39.  P. A u g e r , J . P h y s . R a d i u m 6 (1925) 205  40.  T. W. Haas, G . J . G r a n t , A. G. J a c k s o n and M. P. H o o k e r , "A B i b l i o g r a p h y o f LEED a n d AES" i n P r o g r e s s i n S u r f a c e S c i e n c e V o l . , 1 ( 1 ) , Pergamon P r e s s , O x f o r d , 197 1  4 1.  J . C- T r a c y , i n "Electron Emission Spectroscopy", e d . W- D e k e y s e r e t a l , S e i d e l P u b l i s h i n g Co., D o r d r e c h t , 1973  42-  D- T- H a w k i n s ,  Chem.  Phys.  "AES:A B i b l i o g r a p h y ,  25 (1971) 1  11.(196.8)  Rev.  161  188 (1967)  15 (1969) 231  State  Phys.  28  Phys.  Rev.  3258  1925-1975,  IFI-  206  P l e n u m , New Y o r k , 1977 43.  T. E- G a l l o n a n d J . A- D. Matthew, (1972) 31  4 4.  C. C. Chang i n " C h a r a c t e r i z a t i o n o f S o l i d S u r f a c e s , e d . P. F J Kane, G.,B. l a r r a b e e . P l e n u m P r e s s , New Y o r k , 1974  45.  fl. E. B i s h o p a n d J . C. R i v i e r e , (1969) 1740  Bev. P h y s . T e c h n o l . 3  J.  Appl.  Phys-  46.  J . A- B e a r d e n a n d A. P. B u r r , l e v . Mod. P h y s . 125  47.  K. S i e g b a h n e t a l , " E S C A : A t o m i c , Molecular and S o l i d State Structure Studied by Means of Electron S p e c t r s c o p y " , A l m g u i s t a n d S i k s e l l s , U p p s a l a , 1967  48.  M. F. Chung a n d L. H. J e n k i n s , S u r f a c e 479  49.  M. E- P a c k e r a n d J . M. H i l s o n , "Auger I n s t i t u t e o f P h y s i c s , London,: 1973  50.  P. W. P a l m b e r g e t a l , "Handbook o f A u g e r Spectra", P h y s i c a l E l e c t r o n i c s I n d u s t r i e s I n c . , M i n n e s o t a , 1972  51.  E. E. Weber a n d A- L. J o h n s o n , (1969) 314  52.  M. P e d e r e a u , S u r f a c e  53.  L . F- M a t t h e i s , P h y s .  54.  S. Y- Tong, J . B. P e n d r y a n d L- L. K e s m o d e l , Sci. 54 (1S76) 21  55.  J . C. S l a t e r , Adv. Quantum Chem. 6 (1972) 1  56.  K. H- J o h n s o n , A d v . Quantum Chem. 7 (1S73) 143  57.  F. Herman a n d S. S k i l l m a n , "Atomic Structure Calc u l a t i o n s " , P r e n t i c e H a l l , E n g l e w o o d C l i f f s , N. J . , 1963  58.  K. S c h w a r z , P h y s .  59.  K. S c h w a r z , T h e o r e t . C h i m .  60.  G. A. B u r d i c k , P h y s .  6 1.  M. I . Chodorow, Ph.D. o f T e c h n o l o g y , 1939  62.  R. W- G- W y c k o f f , "Crystal I n t e r s c i e n c e , N. Y., 1963  J.  Sci.  39  40  22  (1967)  (1970)  Transitions",  Appl.  Phys-  40  S c i . . 24 (1971) 2 3 9 Bev.  Bev.  133 (1964) A 1399 Surface  B5 (1972) 2466  Bev.  A c t a 34 (1974) 225 129 (1963)  Thesis,  138  Massachusetts  Institute  Structures",  V o l . 1,  207  63.  J . D. H. Donnay, G. B o n n a y , E. G. C o x , 0. K e n n o r d , and M- 0. K i n g , " C r y s t a l D a t a " , Am. C r y s t a l l o g r a p b i c Assoc., 1963  64.  V. L. M o r r u z z i , J . F. J a n a k and A. R. W i l l i a m s , culated Electronic Properties of M e t a l s " , P r e s s , New Y o r k , 1978  "CalPergamon  65.  D. W. J e p s e n , P. M. (1973) 3933  Bev.  66.  L. J . S c h i f f , Y o r k , 1968  67.  1. G. N e w t o n , "Scattering P a r t i c l e s " , M c G r a w - H i l l , New  68.  D. E. G r a y , e d . "American Institute Handbook", M c G r a w - H i l l , New Y o r k , 1972  69.  K. A. B. M i t c h e l l , F. R. S h e p h e r d , P. R. W a t s o n D. ,C. F r o s t , S u r f a c e S c i . 64 (1977) 737  70.  G- E. L a r a m o r e 4783  71.  B. W.  H o l l a n d , S u r f a c e S c i . 28  72.  J . M. Rev.  M o r a b i t o , R. F- S t e i g e r and G- A179 {1969) 638  Somorjai,  Phys.  73.  D. P. W o o d r u f f and M. P. S e a h , P h y s . S t a t u s S o l i d i (1970) 4 29  (a) 1  7 4.  K. 91  A. Van  75.  K.  A. G s c h n e i d e r , S o l i d  76.  S.,Y. 3753  77.  S. Y. Tong and T. N. (1971) 711  78-  M. A. Van Hove and S. 12 (1975) 230  79-  J - B. P e n d r y , Phys-  80.  See U. B.C.  C o m p u t i n g C e n t r e M a n u a l "0-B.C.  81.  M. A. Van 1362  Hove and J . , B .  M a r c u s a n d P. J o n a ,  "Quantum  and C-  Mechanics",  Phys.  Waves of  and  Physics  Rev.  and B2  S u r f a c e S c i . 54  S t a t e P h y s . , 16  Tong and I . L. K e s m o d e l , P h y s . Phys..  Y. T o n g , J . Rev.  New  (1970)  (1971), 258  Y. T o n g ,  Rhodin,  B5  McGraw-Hill,  Theory of Y o r k , 1966  B- Duke,  Hove and S-  Phys.  Rev.  Vac.  J.  275 B8  Rev.  L e t t e r s 27  Pendry,  (1964)  (1976)  (1973)  Letters  Sci.  (1971)  26  Technol.  856 Curve".  Phys.  C8  (1975)  208  N. F- H . - H e n r y , H- L i p s o n and W. A. B o o s t e r , "The Interpretation of X-Ray Diffraction Photographs", M a c M i l l a n , L o n d o n , 1960 G. , A. S o m o r j a i , R. W. J o y n e r Soc. L o n d o n , 331 (1972) 1586  and  B. L a n g ,  Proc-  Roy.  N. J . T a y l o r , "The E f f e c t o f S t r o n g flagnetic F i e l d s on t h e O p e r a t i o n o f t h e LEED I n s t r u m e n t " , V a r i a n Vacuum D i v i s i o n , 1966 R. N a t h a n and B. J . H o p k i n s , J . J . E. Demuth a n d T. 261 H-  N.  Ehodin,  H. Madden and G. E r t l ,  Phys. Surface  Surface S c i .  P. C- S t a i r , T- J . K a m i n s k a , G. A. S o m o r j a i , P h y s . Rev. B11 A. H a r d e r , "The L o n d o n , 1971 D. P. W o o d r u f f (1970) 207  Manual  and B. W.  E6  of  (1973)  1040  S c i . 42 35  (1974)  (1973)  211  L. L. K e s m o d e l (1975) 623  and  Photography", F o c a l  Press,  H o l l a n d , Phys. L e t t e r s  P. H e i l m a n n , E. L o n g , K. H e i n z and Phys. 9 (1976) 247 S. P. Weeks and J . E. R o s e , J . (1978) 659  A31  K. l l u l l e r ,  Vac.  Sci.  Appl.  Technol.  J . E- Demuth, D. W. J e p s e n a n d P. M. M a r c u s , S o l i d Commun. 13 {1973) 1311,  15  State  P. M. M a r c u s , J . E. Demuth and D. W. J e p s e n , Sci. 53 (1975) 501  Surface  M. A- Van H o v e , S. YSci. 64 (1977) 85  Surface  l o n g a n d M. H. E l c o n i n ,  " C r i t i c a l E v a l u a t i o n o f C h e m i c a l and P h y s i c a l S t r u c t u r a l Information", Eds* P. R. L i d e J r . And H. A. P a u l , N a t i o n a l Academy o f S c i e n c e s , W a s h i n g t o n , D-C-, 1974 L. V. A z a r o f f , H c G r a w - H i l l , New  "Elements o f Y o r k , 1968  X-Ray  J . T o p p i n g , " E r r o r s o f O h s e r v a t i o n and Chapman and H a l l , L o n d o n , 1962 D. L-  Adams and 0. Landman, P h y s .  S. L. C u n n i n g h a m , C-M.  Chan and W.  Rev.  Crystallography", Their B15  Treatment", (1977)  H. S e i n h e r g ,  3775 Phys.  209  Rev-  ( i n press)  101-  C-M. C h a n , S. 1. C u n n i n g h a m , W. H- W e i n b e r g , S u r f a c e S c i -  10 2.  M. , G. L a g a l l y , I . C. Ngoc a n d fl. B- Webb, L e t t e r s 26 (1971) 1557  103-.  M. G. L a g a l l y , T. C , Ngoc a n d M. B. Webb, J Technol. 9 (1972) 645  10 4-  D. 8- J e p s e n , P. S. M a r c u s a n d F. J o n a , {1973) 5528  105.  F. F o r s t m a n , J a p . J . o f (1974) 657  106.  M- M a g l i e t t a , E. Z a n a z z i , F. J o n a , B. H. J e p s e n P. M. M a r c u s , J . P h y s . , C 1 0 (1977) 3 7 5  107.  N. i l a s u d , G. G. K i n n i b u r g h a n d J . B. P e n d r y , C10 (1977) 1  108-  Group  109.  R. H. T a i t , S. Y. Tong a n d T. N. B h o d i n , L e t t e r s 28 (1972) 553  110.  G. E. L a r a m o r e a n d C. B. Duke, P h y s . 267  111.  D. W. J e p s o n , P. M- M a r c u s a n d F. J o n a , (1972) 3684  112-  M- S. M a r t i n and G. A. S o m o r j a i , P h y s . 3607  113.  B- W- L e e , R- A l s e n z , A- I g n a t i e v P h y s . Rev. B15 (1978) 15*10  114.  G. G. K l e i m a n and J . M. B u r k s t r a n d , (1975) 493  115.  R. W. S t r e a t e r , W. T. M o o r e , P. R. W a t s o n , D- ,C- F r o s t and K- A. R. M i t c h e l l , S u r f a c e S c i . 72 (1978) 744  116.  K. 0- L e g g , F. J o n a , D. W- J e p s e n a n d P. M. M a r c u s , P h y s . C10 (1977) 937  117.  C-M. C h a n , S- L. C u n n i n g h a m , M-A. Van H o v e , H. H. W e i n b e r g and S. P. W i t h r o H , S u r f a c e (1977) 394  118-  d'Etude  M- A. Van Hove (1977)  67  Appl.  and  Phys-  Bev.  Vac.  Phys-  Sci.  Bev.  B8  P h y s - , S u p p l . 2, P a r t 2, and  J.  Phys.  d e s S u r f a c e s , S u r f a c e S c i . 62 (1977) 567 Phys.  Rev.  and  B5  Phys. Rev.  Rev. i1972) Rev.  B7  B6  (1973)  M. A- Van H o v e ,  Surface  Sci.  Sci-  A- I g n a t i e v , F. J o n a , H. ,D. S h i h , D. W. J e p s e n and P. M- M a r c u s , P h y s . R e v . B11 (1975) 4787  50  J.  66  210  P. E c h e n i g u e , J G-  Phys.  E. L a r a i o r e , P h y s .  C9 Bev.  W. N. U n e r t l and M . B .  (1976) B8  3193  (1973)  515  Webb, S u r f a c e S c i . , 59  L. 1. K e s m o d e l , P. C. S t a i r and G. Sci. 64 (1977) 342  (1976)  A. S o m o r j a i ,  373  Surface  J . A. D a v i e s , D. P. J a c k s o n and P. B. N o r t o n , P r o c . 7th Int. Vacuum C o n g r e s s and 3rd I n t . Conf. On Solid S u r f a c e s , V i e n n a , 1977, p.,2527 H. D. S h i h , F. J o n a , D. P h y s . C9 (1976) 1405  w. J e p s e n and P. M.  Harcus,  B. W. L e e , A. I g n a t i e v , S- Y. Tong and M. A. Van J. Vac. , S c i . T e c h n o l i , 14 (1977) 291 M. A. Van Hove and S. Y. l o n g . S u r f a c e S c i . 91 ». N. U n e r t l and H. V. T h a p l i y a l , Technol. 12 (1975) 263  J.  (1976)  Vac.  Sci.  K. 0. L e g g , M . , P r u t t o n and C. K i n n i b u r q h , J . (1974) 4 236 W.  Haas, S u r f a c e S c i .  J . T. Y a t e s , J r . , p r i v a t e  Hove,  54  F- J o n a , I . B . a . J . Res. , D e v e l o p . , 14 (1970)  J . T. G r a n t and T.  J.  21  444 Phys.  C7  (1970)  76  communication  R. A. H a r b r o w and R. M. L a m b e r t , S u r f a c e S c i . 67 489  (1977)  H. E c k s t r o m , , G . G. P o s s l e y and S. E. Hannum, Phys. 52 (1970) 5435  Chem.  J.  D. B r i g g s , R. A. M a r b r o a and R. M. L a m b e r t , S o l i d Commun. 26 (1978) 1 H. C. Sci.  T u r k e n b u r g , R. G. 74 (1978) 181  Smeenk  and F. ...W.  Saris,  State Surface  J . F. van d e r Ween, R. G. Smeenk and F. W- S a r i s , 7th I n t . Vacuum C o n g r e s s and 3 r d I n t . C o n f . On S u r f a c e s , V i e n n a , 1977, p i 2 5 1 5 M. D. C h i n n and S. C. F a i n , J . (1977) 314 F. J o n a , S u r f a c e S c i .  68  (1977)  Vac. 204  Sci.  Proc. Solid  Technol.  14  APPENDICES  212  The f o l l o w i n g a p p e n d i c e s from  rhodium  surfaces  c o n t a i n a l l the experimental  used  during  e x c e p t one, t h e d a t a i s as c o l l e c t e d or  manipulated  beam  current.  averaged cassette  i n a n y way The  this instance.  work.  and has n o t  In a l l cases been  for a correction to unit  exception  and s m o o t h e d ; has  save  this  (A7)  unfortunately  shows the  ANGLE  A1  (111)  ^ = 00,d>= 00  failure  of  are l i s t e d  DATA  SET  1  A2  2  A3  3  Al  6-=  100,gS= 1090  1  A5  2  A6  3 (100)  00,(0= 00  A8 ©-= 9 0 , ^ = (110)  9-=  20O  0 o ^ i = 00  A11 A12 A13  1 2  A9 A10  incident  d a t a t h a t has been  The c o n t e n t s o f t h e a p p e n d i c e s  5 PR FACE  A7  smoothed  l e d to i r r e c o v e r a b l e l o s s of t h e o r i g i n a l  UJ?JNDIX  data  1 1 2  ©- = 100,^= 1350  1 2  a  tape  data i n below.  U3  Rh(H1) 0=0 Expt.1 x4  A1  Alt  (02)  1 200  A1  1  r 300 eV  2/5"  RhdH)  9=0°  Expt.2  -•. x4  x4  (10) x4  (11) x4  x4  (01)  x4  100  200  300  eV  A2  200  300  ZI4  (02)  (20)  200  A2  300  eV  2R-  Rh(111) e=o  Expt3  x4  •• x4  (10) ~  X4  (11) x4  X4  (01)  x4  i  r  100  T — — r  200  300 eV  A3  200  i  r  300  (02)  (20)  200  A3  300 eV  211  RK111) e=ioV=io9 Expt.1 x4  (TO)  (00)  (2D  (11)  (12)  (10)  (01)  '  "  ( 2 2 )  (11)  -i  100  1  1  200  r  eV  A4  100  i  200  r  22o  Rh(111) 0=10,0=109 Expt. 2 x2  (00)  <H)  (1T)  <™  (10)  (22)  (10) ~  (01)  (12) (21>  .  T  100  1  1  -r  TTI 200 '  • ".  eV  A5  100  1  1 200  f  (02)  (23)  Rh(111) 6=10,jzM09 Expt.3  (01)  (00)  (TD  (ii)  (11)  (10)  (02)  do)  •.  (01) (12)  —i 100  1  1 200  1—  — i  eV  A6  1 100  1  i  200  r  (12)  (21)  (21) (22)  1  (23)  (13)  T  100  /  1 — H  200  r~  eV  A6  1  200  1—  eV  RhfiOO) e=o° Expt.1 x4  —i  100  1  1 200  1  r 300  A7  i  100  1  1  200  22 b  200  — I  -  300  A7  eV  200  300  Rhdoo) e--o  c  Expt.2  x4  x4 (20)  (11)  X4  i  100  200  300  A8  100  200  r-  eV  229-  (31)  (22)  200  300  eV  A8  200  300  21*  RhClOO) 0=9,0=20 (00)  (20)  •'  (1T)  (11)  —, 100  (02)  (22)  •  (11)  . (22) .  (20)  (13)  (02)  (3D  1  r  200  AQ  1 100  1  f  200 eV  Rh(HO) 0=0° Expt.1  (10)  (20)  (21)  (01)  150  (11)  ~r~ 50  150  250 eV  A10  250 e  230  Rh(110)  e=o°  Expt.2  (10)  (11)  (01)  (21) (20)  100  200  eV  A11  100  200  Z3I  Rh(110) 0-10° 0=135° Expt. 1 (00)  (11)  (02) (01)  (11)  (20)  (TT)  "lOO  '  (21)  200  A12  eV  100  200  232  Rh(1lO) e^0 ^3b° Expt.2 0  (02) (if)  100  (1T)  (11)  100  eV  200  A13  200  PUBLICATIONS "Use of a Vidicon camera for the measurement of LEED beam intensities by the photographic method," D.C. Frost, K.A.R. Mitchell, F.R. Shepherd and P.R. Watson, Journal of Vacuum Science and Technology, 13 (1976), 1196-98. "Structure determination of the (100) surface of rhodium by LEED," K.A.R. Mitchell, F.R. Shepherd, P.R. Watson and D.C. Frost, Surface Science, 64 (1977), 737-750. "Surface Structures of Rhodium Studied by LEED," D.C. Frost, K.A.R. Mitchell, F.R. Shepherd and P.R. Watson, Proceedings of the 7th International Vacuum Congress and 3rd International Conference on Solid Surfaces, Vienna, 1977, pA-2725 (Poster). "LEED intensities from Cu(311) and Ni(311)," D.C. Frost, K.A.R. Mitchell, W.T. Moore, R.W. Streater and P.R. Watson, Ibid, p2403-2406. "Applications of the r e l i a b i l i t y factor proposed for LEED by Zanazzi and Jona to structure determinations of the Rh(100) and Cu(lll) Surfaces," P.R. Watson, F.R. Shepherd, D.C. Frost and K.A.R. Mitchell, Surface Science, 72 (1978), 562-576. "The Structure of the (311) surface of copper as determined by multiple scattering calculations of LEED intensit i e s , " R.W. Streater, W.T. Moore, P.R. Watson, D.C. Frost and K.A.R. Mitchell, Surface Science, 72 (1978), 744-748. "An investigation with LEED of the structure of the (111) surface of rhodium," F.R. Shepherd, P.R. Watson, D.C. Frost and K.A.R. Mitchell, Accepted for publication by Journal of Physics. "The structure of the (110) surface of rhodium,"D.C. Frost, I S. Hengrasmee,K.A.R. Mitchell,F.R. Shepherd and P.R. Watson,Surface Science,76(1978)1585-1589.  

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