TWO DIMENSIONAL PHASE EQUILIBRIA AT SURFACES

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TWO DIMENSIONAL PHASE EQUILIBRIA AT SURFACES

J. Blakely

To cite this version:

J. Blakely. TWO DIMENSIONAL PHASE EQUILIBRIA AT SURFACES. Journal de Physique Col-

loques, 1988, 49 (C5), pp.C5-351-C5-366. �10.1051/jphyscol:1988541�. �jpa-00228038�

JOURNAL DE PHYSIQUE

Colloque C5, supplbment au n010, Tome 4 9 , o c t o b r e 1988

TWO DIMENSIONAL PHASE EQUILIBRIA AT SURFACES

J.M. BLAKELY

M a t e r i a l s Science and Engineering, Cornell U n i v e r s i t y , I t h a c a , NY 14853-1501, U.S.A.

A b s t r a c t

This paper provides a b r i e f d i s c u s s i o n o f some c u r r e n t experimental work on phase t r a n s i t i o n s a t f r e e surfaces. Examples a r e used t o i l l u s t r a t e work i n t h e areas o f surface r e c o n s t r u c t i o n , roughening, atomic step coalescence, and t r a n s f o r m a t i o n s o f adsorbed and segregated l a y e r s . A l l o f these surface phenomena a r e l i k e l y t o have counterparts a t i n t e r n a l boundaries.

I. I n t r o d u c t i o n :

The i n t e r f a c e s discussed i n t h i s paper are those between a c r y s t a l and vacuum o r a l o w pressure vapor. These ' e x t e r n a l ' surfaces have been s t u d i e d much more e x t e n s i v e l y than those between condensed phases. From the e x p e r i m e n t a l i s t ' s viewpoint they a r e more accessible and t h e wealth o f data now a v a i l a b l e has encouraged t h e o r i s t s t o make major e f f o r t s i n computation ( 1 y 2 ) o f surface p r o p e r t i e s . A wide v a r i e t y o f s u r f a c e phase t r a n s i t i o n s have been documented and some r a t h e r s o p h i s t i c a t e d models o f these phenomena e x i s t i n the l i t e r a t u r e . I n many respects t h e modelling o f surface phase t r a n s i t i o n s i s more advanced than t h a t f o r 3-dimensional systems mainly due t o t h e mathematical

s i m p l i f i c a t i o n s introduced by the reduced dimensionality.

I n t h i s paper a few examples o f surface phase t r a n s i t i o n s are described.

I n most cases i t i s easy t o imagine s i m i l a r o r r e l a t e d phenomena o c c u r r i n g a t i n t e r n a l boundaries. The phase t r a n s i t i o n s discussed i n v o l v e ( i ) surface r e c o n s t r u c t i o n s , ( i i ) atomic roughening, ( i i i ) atomic step c l u s t e r i n g and f a c e t t i n g , ( i v ) adsorbed o v e r l a y e r s u p e r l a t t i c e s , ( v ) segregated l a y e r s on a1 l o y c r y s t a l s and ( v i ) 2-dintensional adsorbed a1 loys.

11. S t a b i l i t y and Coexistence o f Surface Phases

The s t a b l e s t r u c t u r e s t h a t e x i s t a t a surface a r e those which are i n e q u i l i b r i u m w i t h t h e b u l k and vapor phases as w e l l as w i t h each other. I t i s indeed r a r e t h a t t h i s s t a t e o f thermodynamic e q u i l i b r i u m i s achieved so t h a t t h e m a j o r i t y o f surface phases observed a r e i n some respect metastable. This i s o f course a l s o t r u e o f b u l k phases. T r a n s i t i o n s among surface phases may be l i m i t e d

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988541

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by n u c l e a t i o n o r atom t r a n s p o r t processes w h i l e volume d i f f u s i o n , a d s o r p t i o n and d e s o r p t i o n r a t e s may l i m i t communication between t h e s u r f a c e and t h e n e i g h b o r i n g b u l k phases. The s u r f a c e r e g i o n may t h e r e f o r e behave i n extreme cases e i t h e r as an open o r a c l o s e d system i n t h e thermodynamic sense. I n t h e f i r s t case chemical p o t e n t i a l s can be c o n t r o l l e d t h r o u g h vapor p r e s s u r e s o r a l l o y c o m p o s i t i o n w h i l e i n t h e second case t h e s u r f a c e chemical p o t e n t i a l s w i l l g e n e r a l l y d i f f e r f r o m t h o s e i n t h e b u l k phases and w i l l be determined by t h e ( f i x e d ) average d e n s i t y and c o m p o s i t i o n o f t h e s u r f a c e r e g i o n . Examples o f b o t h extreme s i t u a t i o n s w i l l be mentioned l a t e r i n t h e paper. W h i l e b o t h open and c l o s e d s u r f a c e systems may be d e s c r i b e d thermodynamically, i n t e r m e d i a t e c o n d i t i o n s a r e n o t so r e a d i l y analysed.

F o r s u r f a c e (and i n t e r f a c i a l ) phases, p r e s s u r e and volume a r e n o t u s e f u l v a r i a b l e s . D i f f e r e n t c o n v e n t i o n s f o r d e f i n i n g s u r f a c e thermodynamic

i n v o l v e somewhat a r b i t r a r y assignments t o t h e s u r f a c e volume, a problem t h a t c l e a r l y a r i s e s f r o m t h e f a c t t h a t t h e p h y s i c a l e x t e n t o f t h e s u r f a c e phase may be comparable t o t h a t o f t h e t r a n s i t i o n r e g i o n t h a t s e p a r a t e s i t f r o m t h e b u l k . The s u r f a c e t e n s i o n , y, and area, A, a r e , however, w e l l d e f i n e d q u a n t i t i e s and e s s e n t i a l l y r e p l a c e p r e s s u r e and volume f o r s u r f a c e phases. The c o n d i t i o n s f o r e q u i l i b r i u m c o e x i s t e n c e o f s u r f a c e and b u l k phases i n v o l v e u n i f o r m i t y of temperature, chemical p o t e n t i a l s , p r e s s u r e f o r b u l k phases and surface t e n s i o n f o r s u r f a c e phases, i . e . f o r a s e t o f s u r f a c e phases I, 11, 111,

...

we must have ( 4 s ) I II 111 = Y =

....

The ranges o f s t a b i l i t y f o r s u r f a c e phases m i g h t t h e n be r e p r e s e n t e d on y T - c o m p o s i t i o n phase diagrams w i t h a phase r u l e s i m i l a r t o t h a t f o r b u l k phases, i.e.,

where W i s t h e number o f parameters t h a t can be v a r i e d i n d e p e n d e n t l y ( i . e . , t h e v a r i a n c e ) and s t i l l m a i n t a i n

x

phases i n an n component system. Phase diagrams o f t h i s t y p e have i n d e e d been o b t a i n e d f o r L a n g m u i r - B l o d g e t t monolayer f i l m s on l i q u i d s b u t f o r s o l i d systems, s u r f a c e t e n s i o n i s g e n e r a l l y a q u a n t i t y t h a t i s b o t h d i f f i c u l t t o c o n t r o l and t o measure. The s t a b i l i t y o f s u r f a c e phases may be r e p r e s e n t e d on a v a r i e t y o f a l t e r n a t i v e diagrams. F o r example, f o r t h e phases of a one-component l a y e r adsorbed on an ' i n e r t ' s u b s t r a t e and i n e q u i l i b r i u m w i t h a vapor, vapor p r e s s u r e P and T would be c o n v e n i e n t v a r i a b l e s ; f i g u r e ( 1 1 )

('I

shows an example o f such a diagram. The s u r f a c e phases o f an a l l o y c r y s t a l i n which s u r f a c e t o b u l k e q u i l i b r i u m i s a c h i e v e d t h r o u g h d i f f u s i o n c o u l d s i m i l a r l y be r e p r e s e n t e d on a diagram o f b u l k c o m p o s i t i o n v e r s u s T;

f i g u r e (10) ( 8 ) shows such an example. The 2-phase c o e x i s t e n c e c u r v e s f o r these open system phase diagrams can i n f a c t b e d e s c r i b e d i n a f o r m a l way b y Clapeyron t y p e e q u a t i o n s ( 4 3 9 ) ; f o r example f o r a one component l a y e r i n e q u i l i b r i u m w i t h a

vapor, the equation

describes t h e coexistence o f two surface phases I and I 1 as a f u n c t i o n o f gas pressure and temperature.

eI

and eII a r e t h e f r a c t i o n a l occupancies ( o r

coverages) o f p o s s i b l e a d s o r p t i o n s i t e s i n the two phases, q I ads i s t h e i s o s t e r i c heat o f a d s o r p t i o n f o r phase I and qtr t h e heat o f t r a n s f o r m a t i o n from I t o 11;

b o t h o f these heats w i l l be coverage dependent. (For t h e a l l o y segregation case P would be replaced by atomic f r a c t i o n

x).

For closed adsorbed l a y e r s , t h e chemical p o t e n t i a l s are n o t f i x e d by some b u l k r e s e r v o i r b u t the average coverages can be a d j u s t e d experimentally; i t i s then more convenient t o represent t h e ranges o f s t a b i l i t y o f d i f f e r e n t phases on temperature-composition-coverage diagrams ( l o ) , ( F i g u r e (1)). F i g u r e (12) i s an example o f a T-8 diagram f o r a one component adsorbed l a y e r i.e. f i x e d

composition w h i l e f i g u r e (13) ( I 2 ) g i v e s a T-composition diagram f o r a b i n a r y adsorbed l a y e r a t f i x e d coverage. F u r t h e r comments on these diagrams w i l l be made l a t e r .

F i g u r e 1. Axes f o r phase diagram d e s c r i b i n g a b i n a r y 2-dimensional adsorbed l a y e r . The conventional diagram f o r a s i n g l e component l a y e r

corresponds t o t h e plane x=O o r 1. The dashed plane corresponds t o a s e c t i o n a t constant t o t a l coverage; t h i s s e c t i o n should have f e a t u r e s s i m i l a r t o those o f

conventional diagrams o f 3-dimensional b i n a r y a l l o y s .

111. S t r u c t u r a l T r a n s i t i o n s o f Clean Surfaces

The atomic s t r u c t u r e o f crystal-vacuum i n t e r f a c e s has been s t u d i e d by a f a i r l y impressive a r r a y o f experimental methods i n c l u d i n g s c a t t e r i n g o f e l e c t r o n s (13), x-rays ( I 4 ) , atoms o r molecules ( I 5 ) and ions (I6) as w e l l as h i g h r e s o l u t i o n techniques o f f i e l d i o n ( I 7 ) and scanning t u n n e l i n g microscopies.

A t c l e a n surfaces the atomic s t r u c t u r e o f t e n d i f f e r s from t h a t expected f o r an i d e a l l y terminated c r y s t a l . Examples o f these d e v i a t i o n s are b r i e f l y discussed.

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( i ) Surface Reconstruction

Several types of atomic rearrangements i n t h e topmost l a y e r ( s ) o f a c r y s t a l from those i n corresponding b u l k planes have been i d e n t i f i e d . I n many cases t h e r e i s an o v e r a l l expansion o r c o n t r a c t i o n o f t h e i n t e r p l a n a r spacings i n t h e surface 'layers normal t o t h e surface; t h e measurements o f such c o n t r a c t i o n s r e q u i r e s very c a r e f u l s c a t t e r i n g measurements and analyses ( I 3 ) . . The f o r m a t i o n o f s u r f a c e s u p e r l a t t i c e s i s g e n e r a l l y e a s i e r t o e s t a b l i s h through t h e appearance o f e x t r a r e f l e c t i o n s i n surface d i f f r a c t i o n p a t t e r n s ( I 9 ) and i t i s these surfaces w i t h longer p e r i o d s t r u c t u r e s which a r e r e f e r r e d t o as reconstructed.

Among t h e most s t u d i e d surfaces showing r e c o n s t r u c t i o n a r e t h e (100) and (111) surfaces of S i (20'21). Models o f t h e i d e a l and (2x1) reconstructed (100) surface of S i a r e d e p i c t e d i n F i g u r e ( 2 ) ( 2 2 y 2 3 ) . The formation o f t h e (2x1) i s

,FJ---,

(2 x 1)

w ^'[ _,;

² x 1 Surface ^R,; 2 x 1 Surface (Top view) (Side view) F i g u r e 2b. Asymmetric ( o r i o n i c ) dimer geometry. Side view i s schematic and i s n o t drawn t o scale.

[From Chadi : J. Vac. Sci

.

^Technol

. ,

16, 1291 ( 1 9 7 9 ) l -

1.1

Figure 2a. Several models f o r 2x1 reconstructed Si(100) surface. Surface atoms are shown as open c i r c l e s and second l a y e r atoms as dark c i r c l e s . The models shown are: ( a ) i d e a l , unrelaxed surface; (b) symmetric ( o r c o v a l e n t ) dimer;

( c ) and ( d ) vacancy models; ( e ) conjugated-chain model; ( f ) "double"

conjugated-chain model i n which every atom i s f o u r f o l d coordinated. [ A f t e r Chadi, J. Vac. Sci. Technol.

16,

1291 (1979)l

a t t r i b u t e d t o t h e formation o f s u r f a c e dimers w i t h an accompanying decrease i n s u r f a c e dangling bond d e n s i t y from 2 t o 1 p e r surface atom. The lowest energy c o n f i g u r a t i o n o f t h e dimers i s assymetrical (24) ( F i g u r e ( 3 ) ) and h i g h e r o r d e r r e c o n s t r u c t i o n s observed i n LEED have been a t t r i b u t e d t o t h e sense of t h i s a s ~ ~ m e t r ~ ( ~ ~ ) . Very c l e a r evidence e x i s t s i n scanning t u n n e l i n g microscope images(23) f o r t h e occurrence o f dimers on t h i s (100) surface. I n a d d i t i o n t o these and o t h e r experimental observations very extensive t i g h t b i n d i n g

c a l c u l a t i o n s have been made on the energies associated w i t h these s t r u c t u r e s . Some o f these r e s u l t s a r e summarized i n F i g u r e ( 3 ) ( 2 5 y 2 6 ) . The energy o f t h e (2x1) phase i s reduced r e l a t i v e t o t h e unreconstructed (1x1) by Q.85 eV p e r s u r f a c e atom w h i l e t h e h i g h e r order (4x2) phase i n v o l v e s a f u r t h e r r e d u c t i o n o f

A z-**V IERL (JOO) F i g u r e 3.

Calculated (25,261

o.ssev energies f o r the

r e c o n s t r u c t i o n s o f

Or0

1.7" ~ C ~ ~ ~ DI-R S C R L S i (100).

H a

v

"lilsV R s s ~ m 1 . 1 0 m c n ~ 3tr1SR

o n l y 20.03 e ~ ( ~ ~ ) . These energies a r e q u a l i t a t i v e l y c o n s i s t e n t w i t h the experimental observations t h a t t h e (2x1) r e c o n s t r u c t i o n p e r s i s t s t o h i g h temperatures w h i l e the (4x2) phase d i s o r d e r s t o (2x1) near room temperature.

The S i ( l l 1 ) surface a l s o e x h i b i t s r e c o n s t r u c t e d phases. The (2x1) observed on cleaved surfaces i s metastable and transforms t o t h e s l i g h t l y lower energy

(7x7) surface on annealing; t h e t r a n s i t i o n between (7x7) and (1x1) i s i n t h e r e g i o n o f 850°C. The s t r u c t u r e s o f these phases have been t h e s u b j e c t o f a very l a r g e experimental (") and t h e o r e t i c a l e f f o r t and w e l l supported models o f t h e reconstructed phases now e x i s t .

( i i ) The Roughening T r a n s i t i o n

On an i d e a l ( o r r e c o n s t r u c t e d ) s u r f a c e a t low temperatures t h e coordinates o f a l l surface atoms can be p r e d i c t e d from those o f one u n i t c e l l . However, as temperature i s increased and p o i n t and o t h e r d e f e c t s a r e spontaneously c r e a t e d due t o the accompanying increase i n entropy t h e s u r f a c e may become d i f f u s e o r rough so t h a t c o r r e l a t i o n i n t h e normal coordinates o f p a i r s o f outermost atoms diminishes. For a surface o f i n f i n i t e l a t e r a l e x t e n t t h e w i d t h o f the c r y s t a l vacuum i n t e r f a c e would d i v e r g e as t h e c r i t i c a l roughening temperature i s

approached. Burton, Cabrera, and ~ r a n k ( ~ O ) developed a theory f o r t h i s roughenin, t r a n s i t i o n based on an a d a p t a t i o n o f t h e I s i n g model and more r e c e n t a n a l y t i c a l d e s c r i p t i o n s (31y32) are extensions o f t h i s work. F i g u r e ( 4 ) (31) i s a view o f t h e e q u i l i b r i u m s t r u c t u r e o f a (100) s u r f a c e obtained u s i n g Monte Carlo methods, based on a nearest neighbour bonding model, a t v a r i o u s reduced temperatures. So

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F i g u r e 4. Monte Carlo

s i m u l a t i o n s ( 3 2 ) o f t h e surface o f a cubic s o l i d a t various reduced temperatures, kT/ E,

where E i s the nearest neighbor bond energy.

f a r t h e r e have been few d i r e c t measurements o f spontaneous surface roughening.

I t i s g e n e r a l l y agreed t h a t t h e c l o s e packed surfaces o f most ' s i m p l e ' c r y s t a l s do n o t show appreciable roughening below t h e m e l t i n g p o i n t . However t h e theory (31) s t r o n g l y suggests t h a t v i c i n a l and h i g h index planes w i t h lower average surface c o o r d i n a t i o n may e x h i b i t s i g n i f i c a n t roughening. Recent measurements o f t h e i n t e n s i t y p r o f i l e s o f He d i f f r a c t i o n beams (33'34) over a range o f temperatures have been used t o e x t r a c t parameters c h a r a c t e r i z i n g surface roughness. I f t h e f u n c t i o n expressing t h e c o r r e l a t i o n i n h e i g h t between any two p o i n t s on t h e surface i s expressed as a power law i n t h e i n v e r s e o f t h e d i s t a n c e between t h e two p o i n t s t h e exponent i s found ( 3 4 ) t o vary w i t h temperature f o r

F i g u r e 5. Roughness

parameter,

%,

as a f u n c t i o n o f temperature. Roughening i s taken t o correspond t o $=0.5.

the Ni(115) surface as i n d i c a t e d i n F i g u r e (5); t h e abrupt increase i n t h e roughness exponent,

x,,

a t s 4 5 0 K i s i n t e r p r e t e d as i n d i c a t i n g t h e onset o f roughness. I t i s n o t ' e n t i r e l y c l e a r , however, t h a t t h e observed s c a t t e r i n g e f f e c t s a r e i n f a c t due t o spontaneous k i n k formation. An experiment combining the d i f f r a c t i o n method w i t h STM observations o f t h e c o n f i g u r a t i o n o f s t e p edges would be extremely i n t e r e s t i n g .

( i i i ) Atomic Step C l u s t e r i n g and F a c e t t i n g

Surfaces v i c i n a l t o l o w i n d e x p l a n e s o f close-packed c r y s t a l s a r e made up o f a r r a y s o f a t o m i c s t e p s and t e r r a c e s . Such s u r f a c e s g i v e r i s e t o

c h a r a c t e r i s t i c s p l i t t i n g o f LEED beams (35336y37), (as i l l u s t r a t e d i n f i g u r e ( 6 ) ( 3 8 ) ) , w i t h t h e magnitude o f t h e d i f f e r e n c e i n s c a t t e r i n g v e c t o r between t h e

F i g u r e 6. LEED p a t t e r n s f r o m a v i c i n a l s u r f a c e o f N i . The beam s p l i t t i n g

corresponds t o t h e average t e r r a c e dimension.

( a ) corresponds t o room temperature, ( b ) t o 500°C. The s u r f a c e i s

~i ( l l l ) l O O [ l ~ O ] .

beams r e f l e c t i n g t h e peak i n t h e d i s t r i b u t i o n o f t e r r a c e dimensions. I n d i v i d u a l s t e p s on such a s u r f a c e w i l l meander i n two dimensions so t h a t n e i g h b o r i n g s t e p s w i l l have p o i n t s o f c l o s e approach. I f t h e mean i n t e r a c t i o n between s t e p s i s a t t r a c t i v e t h e r e w i l l be a tendency t o w a r d low t e m p e r a t u r e c l u s t e r i n g whereas a t s u f f i c i e n t l y h i g h t e m p e r a t u r e a s i n g l e s t e p a r r a y ( o f h i g h e r c o n f i g u r a t i o n a l e n t r o p y ) w i l l be favored. F i g u r e ( 7 ) ( 3 9 ) shows t h e average t e r r a c e w i d t h as a f u n c t i o n o f t e m p e r a t u r e deduced f r o m d i f f r a c t i o n p a t t e r n s o f t h e t y p e shown i n ( 6 a ) and (6b). The observed h y s t e r e s i s a s s o c i a t e d w i t h t e m p e r a t u r e c y c l i n g c o u l d

Temperature ( K )

6o ^{4 8 0 5 0 0 5 2 0 5 4 0 5 6 0 5 6 0} 600 6 2 0 5 0

F i g u r e 7. Average s t e p dimensions o f a c l e a n and s u l phur-covered N i ( 1 1 1 ) 5 ° [ 1 i 0 ] s u r f a c e ( h e a t i n g and c o o l i n g r a t e s a r e 20°C/h).

1 0 -

0

be i n d i c a t i v e o f a f i r s t o r d e r t r a n s i t i o n i n v o l v i n g 2-phase c o e x i s t e n c e o r may r e f l e c t k i n e t i c l i m i t a t i o n s . C a r e f u l measurements o f t h e p r o f i l e s o f t h e s c a t t e r e d beams a r e c u r r e n t l y b e i f i g made t o d e c i d e between t h e s e two p o s s i b i l i t i e s .

2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 3 4 0 0 0 Temperature ('C)

A clean NI (cool~nql 4 clean NI lhaotbnql 8 0 12 monolayers 01 S lcml8nql O 0 12 monoloyers of S (twot~ngl

- 1 0

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F a c e t t i n g may be viewed as an extreme case o f s t e p rearrangement i n which an i n i t i a l l y f l a t s u r f a c e undergoes a m o r p h o l o g i c a l t r a n s i t i o n t o one composed o f e x t e n s i v e r e g i o n s o f two o r more s u r f a c e o r i e n t a t i o n s . Most t r a n s i t i o n s o f t h i s t y p e f o r metal surfaces,seem t o be a s s o c i a t e d w i t h t h e presence o f an adsorbed l a y e r b u t t h e s u r f a c e t e n s i o n o f some i o n i c and c o v a l e n t c r y s t a l s i s s u f f i c i e n t l y a n i s o t r o p i c t h a t f a c e t t i n g occurs on c l e a n s u r f a c e s o f these m a t e r i a l s . An i n t e r e s t i n g example i s t h e f a c e t t i n g o f S i s u r f a c e s n e a r (210) t o {2111 s u r f a c e s i n o t h e r zones ( 4 1

I V . Phase T r a n s i t i o n s i n v o l v i n g Adsorbed Layers

( i ) Open Adsorbed Systems

Adsorbed l a y e r s i n e q u i l i b r i u m w i t h a vapor phase, where coverage i s determined by temperature and gas pressure, have been s t u d i e d most e x t e n s i v e l y f o r gas molecules which bond weakly t h r o u g h van d e r Waals p o t e n t i a l s t o t h e s u b s t r a t e . Rare gases on t h e g r a p h i t e b a s a l p l a n e have been w i d e l y s t u d i e d b y s t r u c t u r a l and thermal techniques. F o r t h e s e systems t h e h e a t o f a d s o r p t i o n i s s u f f i c i e n t l y s m a l l t h a t low coverages can be o b t a i n e d i n t h e e a s i l y a c c e s s i b l e gas p r e s s u r e range; w i t h s t r o n g l y chemisorbed molecules ( h e a t s o f a d s o r p t i o n

;

2eV) e x t r e m e l y small e f f e c t i v e gas pressures a r e r e q u i r e d f o r e q u i l i b r i u m coverages s i g n i f i c a n t l y below a monolayer.

F i g u r e ( 8 ) ( 4 3 ) shows a s e t o f a d s o r p t i o n isotherms f o r Xe on g r a p h i t e ; t h e a b r u p t i n c r e a s e i n coverage f r o m a low v a l u e t o t h a t o f a dense o r d e r e d o v e r l a y e r

, A - M - b 0 0 6 Q - O O - Q F i g u r e 8. A d s o r p t i o n

isotherms f o r Xe on G r a p h i t e (0001). Note t h e a b r u p t coverage i n c r e a s e s

8 2 " ~ 86'K corresponding t o f o r m a t i o n o f

an o r d e r e d dense s u r f a c e phase.

0

, ^-0-od9

lo-= I O - ~

Xe Pressure (Torr)

i s c h a r a c t e r i s t i c o f t h e f o r m a t i o n o f a dense phase o f a t t r a c t i n g molecules t h r o u g h a f i r s t o r d e r t r a n s i t i o n . Measurements on t h e s e g r e g a t i o n o f carbon t o N i ( l l 1 ) s u r f a c e s f r o m a d i l u t e s o l i d s o l u t i o n show qua1 i t a t i v e l y s i m i l a r

b e h a v i o r ( 4 8 y 8 ) ( F i g u r e ( 9 ) ) . The a b r u p t i n c r e a s e s i n carbon coverage t o f o r m a

F i g u r e 9. V a r i a t i o n i n s u r f a c e C c o n c e n t r a t i o n w i t h temperature f o r Ni (111) c r y s t a l s doped w i t h C t o v a r i o u s l e v e l s . The abrupt increases i n C c o n c e n t r a t i o n w i t h decreasing temperature correspond t o t h e formation of a g r a p h i t i c monolayer. The curves have been s h i f t e d v e r t i c a l l y f o r c l a r i t y .

Temperature (Kl

monolayer g r a p h i t e phase can be measured as a f u n c t i o n o f b u l k carbon c o n c e n t r a t i o n and used t o e s t a b l i s h t h e diagram o f f i g u r e (10) (8)

.

Figure (11) shows a pressure vs. 1/T phase diagram f o r CO adsorbed on

~ d ( 1 0 0 ) ( ' ) . For t h i s system t h e heat o f a d s o r p t i o n i s s u f f i c i e n t l y low ( h . 5 e ~ )

F i g u r e 11. Phase diagram f o r

co

on P ~ ( ~ o o ) ( ~ ) . F i g u r e 10. Phase diagram f o r C on Ni (111). The r e r t i c a l a x i s i s t h e b u l k C

concentration.

I

C

g

Z

.e

U

-

4

lo-'

0.6 0.7 0.8 0.9 ^1.0 1.1 1.2 1.3

IO'/T (KI

-

- -

I \ ' ^{\ s}

C5-360 JOURNAL DE PHYSIQUE

t h a t e q u i l i b r i u m coverages w e l l below one monolayer can be achieved. The slope o f t h e 2-phase coexistence l i n e s should be described by equation ( 2 ) .

( i i ) Closed One-component Adsorbed Systems

The vast m a j o r i t y o f t h e work on surface phases on c r y s t a l surfaces has i n v o l v e d adsorbed l a y e r s which a r e n o t i n e q u i l i b r i u m e i t h e r w i t h t h e vapor o r s o l i d s o l u t i o n . The average coverage remains f i x e d as temperature i s v a r i e d up t o some value where d i f f u s i o n o r d e s o r p t i o n r a t e s become appreciable.

S i g n i f i c a n t p o r t i o n s o f e vs T phase diagrams have been mapped o u t f o r several chemisorption systems. The case o f 0 on N i ( l l 1 ) i s among t h e most s t u d i e d and b e s t understood systems a t present. The phase diagram 111,45) o f t h i s system i s shown i n F i g u r e (12). One o f t h e most i n t e r e s t i n g f e a t u r e s o f t h e diagram i s t h e

400

-

-

Ga

Y 300-

w

,

/ / / I /

1 0 0 - /' / I /

/ 1 1 1

O60 I

01 0 2 0.3 04

Coverope. 8

F i g u r e 12. Phase diagram f o r 0 on ~ i ( 1 1 1 ) ' ~ ~ ) .

----

= first-order transitions;

- -

continuous order.

disorder transition.

existence o f a w e l l ordered ~ ( 2 x 2 ) phase which disorders, a t constant 8 ( d . 2 5 ) t o a (1x1) phase a t a temperature o f 450°C. This phase and i t s d i s o r d e r i n g were i n f a c t noted by Davisson and Germer ( 4 6 ) i n t h e i r h i s t o r i c study o f e l e c t r o n d i f f r a c t i o n from a (111) Ni surface. A s i m i l a r t r a n s i t i o n seems t o occur

(47

f o r S on N i ( l l . 1 ) . Park and coworkers ( 4 5 ) have made a c a r e f u l study o f t h e p r o f i l e s o f i n d i v i d u a l s u p e r l a t t i c e d i f f r a c t i o n beams from 0 on N i ( l l 1 ) as a f u n c t i o n o f temperature i n o r d e r t o e x t r a c t c r i t i c a l exponents f o r t h i s continuous o r d e r - d i s o r d e r t r a n s i t i o n .

( i i i ) Closed Two-Component Adsorbed Systems

The study o f b i n a r y adsorbed l a y e r s i s s t i l l a t an e a r l y stage and o n l y a very few r e s u l t s have been reported. Such quasi 2-dimensional a l l o y systems are l i k e l y t o prove extremely i n t e r e s t i n g and would be expected t o e x h i b i t a l l o f the f e a t u r e s ( - m i s c i b i l i t y gaps, e u t e c t i c s , e u t e c t o i d s , compound formation, etc.) found f o r 3-dimensional a l l o y s . I t i s a l s o l i k e l y t h a t t h e phase diagrams f o r b i n a r y adsorbed l a y e r s w i l l be o f g r e a t value i n understanding surface

r e a c t i o n s . F i g u r e (13) ( I 2 ) i s a phase diagram f o r t h e CO-Ar model system

F i g u r e 13. Phase diagram (12

r neutron d ~ f f r a c t ~ o n measurements f o r t h e b i n a r y adsorbed l a y e r ,

L E E D CO + Ar, on g r a p h i t e . CD i s a

commensurate d i s o r d e r e d ph.ase, C O - A r mlxtures I C an incommensurate phase,

HB

an o r i e n t a t i o n a l o r d e r e d phase and PW a c o m p o s i t i o n a l l y o r d e r e d phase.

-

_Y

\

\

\

I I I I

0 J v

I

L

co ^{0 5} Ar

p h y s i s o r b e d on g r a p h i t e . The phase b o u n d a r i e s were e s t a b l i s h e d f r o m measurements o f t h e t e m p e r a t u r e v a r i a t i o n o f t h e i n t e n s i t i e s o f e l e c t r o n and n e u t r o n

d i f f r a c t i o n beams. The v a r i o u s phases i n v o l v e o r i e n t a t i o n a l o r d e r i n g o f t h e CO m o l e c u l a r a x i s as w e l l as i t s l o c a t i o n r e l a t i v e t o t h e u n d e r l y i n g s u b s t r a t e atoms. As can be seen t h e r e a r e i n d i c a t i o n s o f s e v e r a l c r i t i c a l p o i n t s a t which 3 phases c o e x i s t i n e q u i l i b r i u m .

F i g u r e (14) (48a49) shows some p r e l i m i n a r y o b s e r v a t i o n s on t h e s t r o n g l y

F i g u r e 14. Schematic phase diagram(49) f o r 0 and S adsorbed on a Ni-Fe(100) s u r f a c e .

Temperature T (OC)

h I

I

I I

lattice ,7$ 1

I ^gas

I ,

,

,

c(2xZ)O

C5-362 JOURNAL DE PHYSIQUE

chemisorbed S+O o v e r l a y e r on an a l l o y s u b s t r a t e . The LEE0 s t u d i e s i n t h i s case i n d i c a t e a m i s c i b i l i t y gap i n which a S r i c h C(2x2) phase c o e x i s t s w i t h an 0 r i c h C(2x2). Whether t h e gap t e r m i n a t e s w i t h a c r i t i c a l p o i n t o r a e u t e c t o i d i s n o t w e l l e s t a b l i s h e d a t t h i s time. T h i s i s a p a r t i c u l a r l y i n t e r e s t i n g t y p e o f diagram i n c o n n e c t i o n w i t h t h e e f f e c t o f S on t h e r e a c t i o n o f t r a n s i t i o n m e t a l s w i t h oxygen.

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C. Briimt: What are the sizes of the oxygen C(2x2) and sulfur C(2x2) region; in the two phase regions?

J.M. ELLakely: We have no direct evidence yet on this question.

H m e v e r they seem to be a t least ccanparable t o the coherence of the LEED beam,i.e. 150g.

J. Naravan: Could you ccamnent on relative abundance of simple and double steps on Si(100) surfaces. Is there any work on

dependem? -ally, it would seem double steps should be favoml aver single steps.

J.M. Ellakely: The occurrence of single or double steps seems to depend on the axis about w h i c h the Surface is tilted. !There is aridem= t h a t &aces l i f t e d taward (111) have biatomic steps.

V. mritikis: The results obtained by helium beam diffraction on Cu(115) (Lapujoulade e t dl) have shown that interaction energies, Wu, between steps are quite s m a l l : W, z120K. Dislocations i n grain bmdaries interact usually elastically and the interaction energies per a t m can be much higher than those between steps. Haw is it possib:Le to expect a rcqhening of grain boundaries by analogy with what h ; ~ p p m t o free surfaces?