ORDERING AND DISORDERING PHENOMENA AT/NEAR THE SURFACE OF D1a TYPE ORDERING ALLOYS

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ORDERING AND DISORDERING PHENOMENA AT/NEAR THE SURFACE OF D1a TYPE

ORDERING ALLOYS

T. Kingetsu, M. Yamamoto, S. Nenno

To cite this version:

T. Kingetsu, M. Yamamoto, S. Nenno. ORDERING AND DISORDERING PHENOMENA AT/NEAR THE SURFACE OF D1a TYPE ORDERING ALLOYS. Journal de Physique Colloques, 1987, 48 (C6), pp.C6-373-C6-378. �10.1051/jphyscol:1987661�. �jpa-00226869�

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ORDERING AND DISORDERING PHENOMENA ATINEAR THE SURFACE OF Dla TYPE ORDERING ALLOYS

T. ~ i n ~ e t s u * , M. Yamamoto and S. Nenno

Department of Materials Science and Engineering, Osaka University, Suita, Osaka 565, Japan

Abstract - Ordering and d i s o r d e r i n g phenomena a t / n e a r t h e s u r f a c e of Dla type o r d e r i n g a l l o y s (Ni4Mo and Ni4W) were s t u d i e d by f i e l d - i o n m i c r o s c o p y experimentally and by t h e o r e t i c a l c a l c u l a t i o n based on a broken bondmodeland Bragg-Williams approximation. The main experimental r e s u l t s a r e a s follows:

( i ) a n o r d e r e d p h a s e n u c l e a t e s p r e f e r e n t i a l l y a t s u r f a c e s w i t h c e r t a i n l o w index o r i e n t a t i o n based on t h e f c c m a t r i x (immediately below T,), ( i i ) s u r f a c e l a y e r s of specimens become disordered (around 0.9Tc) and ( i i i ) f a c e t i n g based on t h e o r d e r e d s t r u c t u r e o c c u r s ( a r o u n d 0.8Tc). I n t h e t h e o r e t i c a l c a l c u l a t i o n s , ( i ) s u r f a c e energy, ( i i ) s u r f a c e f r e e energy, ( i i i ) e q u i l i b r i u m d e g r e e o f o r d e r and ( i v ) s u r f a c e n u c l e a t i o n r a t e were o b t a i n e d . The c a l c u l a t e d r e s u l t s e x p l a i n p e c u l i a r phenomena i n t h e above e x p e r i m e n t a l r e s u l t s .

I - INTRODUCTION

I n r e c e n t y e a r s , o r d e r - d i s o r d e r t r a n s f o r m a t i o n s n e a r a l l o y s u r f a c e 11-31, a s w e l l a s s u r f a c e s e g r e g a t i o n /,!,.I h a v e been a t t r a c t i n g a t t e n t i o n , s i n c e t h e o r d e r - d i s o r d e r t r a n s f o r m a i t o n s can be s t r o n g l y a f f e c t e d by t h e s u r f a c e and t h e r e can occur a new i n t e r e s t i n g phenomenon which i s d i f f e r e n t from t h a t i n t h e bulk. We have been i n v e s t i g a t i n g p h a s e t r a n s f o r m a t i o n s a t / n e a r t h e s u r f a c e o f o r d e r i n g a l l o y s , e s p e c i a l l y Dla t y p e o r d e r i n g a l l o y s 15-15/. These s t u d i e s i n c l u d e experimental works /5-9/ and t h e o r e t i c a l c a l c u l a t i o n s /lo-15/. I n t h i s paper, we summarize a s e r i e s of t h e above works.

I n t h e e x p e r i m e n t a l s t u d i e s f i e l d - i o n microscopy was employed, u t i l i z i n g t h e f o l l o w i n g a d v a n t a g e : (i) v a r i o u s c r y s t a l p l a n e s o f a f i e l d i o n m i c r o s c o p y (FIM) s p e c i m e n t i p c a n be o b s e r v e d s i m u l t a n e o u s l y u n d e r t h e e x a c t l y same e x p e r i m e n t a l c o n d i t i o n and ( i i ) t h r e e dimensional observation i.e., t h e observation i n t h e depth d i r e c t i o n can be performed u s i n g t h e f i e l d - e v a p o r a t i o n technique. I n t h e t h e o r e t i c a l c a l c u l a t i o n s , a broken bond model based on Bragg-Williams approximation was used.

The Dl t y p e o r d e r i n g a l l o y s such a s a Ni4Mo a l l o y have an ordered body-centered t e t r a g o n a l ?bet) s t r u c t u r e (6 phase) below a c r i t i c a l temperature Tc (8650C f o r N i Mo and 970°C f o r Ni4W), and a face-centered cubic (fcc) s t r u c t u r e (a phase) above Tc 416 -181. Upon q u e n c h i n g f r o m t h e a r e g i o n , t h e a l l o y s a r e b r o u g h t t o a

*NOW a t New M a t e r i a l s Research L a b o r a t o r i e s , Nisshin S t e e l Co., Ichikawa, Chiba 272, Japan

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987661

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short-range ordered s t a t e ( s r o ) /19-22/. On annealing t h e as-quenched a l l o y s below Tc, t h e B phase n u c l e a t e s and grows i n t h e s r o matrix /23-29/. Ordered domains of t h e f3 p h a s e w h i c h f o r m w i t h i n t h e m a t r i x c a n t a k e s i x k i n d s of d i f f e r e n t o r i e n t a t i o n (domains I-VI). The t i m e - t e m p e r a t u r e - t r a n s f o r m a t i o n (TTT) c u r v e f o r t h e d i s o r d e r - o r d e r t r a n s f o r m a t i o n i n t h e Ni4Mo a l l o y i s C-shaped and t h e n o s e o f t h e c u r v e i s around 71 0-755OC /24/.

I1 - EXPERIMENTAL

Lengths of w i r e s of a Mo-79.9 a t % N i a l l o y and a Ni-16.6 a t % W a l l o y were vacuum a n n e a l e d i n t h e a p h a s e r e g i o n and quenched i n t o i c e w a t e r . Each s p e c i m e n t i p prepared from t h e w i r e s was field-evaporated i n a n FIM, and then annealed i n - s i t u f o r a few o r s e v e r a l minutes a t various temperatures.

A. Ni-Q&

1. A t high temperatures near Tc (880-835°s 1.01-0.97Ta

A t a t e m p e r a t u r e i n t h i s r a n g e , s u r f a c e o r d e r i n g o c c u r r e d p r e f e r e n t i a l l y a t ( 1 11) cc and/or I2001 f a c e t s . A schematic r e p r e s e n t a t i o n of a c r o s s - s e c t i o n of a n FIM t i p which was annealed f o r 30s a t 865OC and f o r 290s a t 835OC i s shown i n Fig.1.

I t was f o u n d t h a t t h e o r d e r e d d o m a i n s , b e i n g d i s c - l i k e i n s h a p e , w e r e somewhat s m a l l e r i n d i a a e t e r t h a n t h e f a c e t s , .and had a f e w o r s e v e r a l - a t o m l a y e r s i n thickness. The degree of o r d e r i n t h e ordered region a t t h e f a c e t was lower t h a n t h o s e a t t h e {200}fcc f a c e t s . When t h e annealing temperature was e q u a l t o o r s l i g h t l y above Tc, t h e ordered domains were found o n l y a t t h e { 2 0 0 ) ~ ~ ~ f a c e t s . 2. & i n t e r m e d i a t e temperatures (825-72O0% 0.96-0.87Td

2.1. A t t e m ~ e r a t u r e s j u s t above t h e nose of t h e TTT curve (825-810°C. 0.96-0.95Tn) Upon i h - s i t u annkaling, l a r g e ordered domains (-500 A diameter'each) w h i c h k e r e mutually i n c o n t a c t were produced i n a t i p of t h i s alloy. The degree of o r d e r i n t h e i n t e r i o r of t h e s e o r d e r e d d o m a i n s was s o h i g h t h a t s t e p - r i n g s c o r r e s p o n d i n g t o s u p e r l a t t i c e p l a n e s were c l e a r l y o b s e r v e d . However, t h e d e g r e e o f o r d e r d e c r e a s e d w i t h d e c r e a s i n g d e p t h f r o m t h e s u r f a c e , w h i c h was a b l e t o be judged f r o m t h e observation of p e r t u r b a t i o n i n t h e arrangement of b r i g h t s p o t s corresponding t o Mo atoms. The perturbed s u r f a c e l a y e r was found t o be 15-20 A thick.

2.2. A t temperatures n e a r t h e nose of t h e TTT curve (760-720°C, 0.90-0.87Tc)

On a n n e a l i n g a t t h i s t e n p e r a t u r e range, a s u r f a c e l a y e r w i t h low degree of o r d e r was found ( s u r f a c e d i s o r d e r i n g ) , showing random d i s t r i b u t i o n of b r i g h t s p o t c l u s t e r s i n a n FIM image r e l a t i v e l y s i m i l a r t o t h o s e of t h e sro-Ni4Mo a l l o y a s shown i n Fig.2.

Within t h e s u r f a c e l a y e r , however, s m a l l h i g h l y ordered domains were detected, being d i s t r i b u t e d sparsely. An average s i z e of ordered domains increased w i t h i n c r e a s i n g d e p t h f r o m t h e s u r f a c e , u n t i l t h e d e p t h r e a c h e d a c e r t a i n v a l u e (% 1 0 0 A). I n t h e i n t e r i o r o f t h e t i p i n t h e r a n g e o f d e p t h 100-300 A, o r d e r i n g b e h a v i o r a t t h i s t e m p e r a t u r e r a n g e was e s s e n t i a l l y t h e same a s t h o s e i n a b u l k s p e c i m e n /26,27/

(homogeneous n u c l e a t i o n and growth).

The t i p i n which h i g h l y o r d e r e d d o m a i n s w e r e exposed t o t h e s u r f a c e by f i e l d - evaporation was i n - s i t u annealed again. Upon t h i s annealing, s u r f a c e l a y e r s with low degree of o r d e r were formed again. This means t h a t t h e lowered degree of o r d e r n e a r t h e s u r f a c e i s s t a b l e . The t h i c k n e s s (average value f o r v a r i o u s l y o r i e n t e d s u r f a c e s ) of t h e s u r f a c e l a y e r s of low degree of o r d e r decreased w i t h i n c r e a s i n g repeat-times of i n - s i t u a n n e a l i n g . A 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 c r o s s - s e c t i o n o f a n FIM t i p annealed a t a temperature i n t h i s range i s shown i n Fig.2.

3. & r e l a t i v e l y low temperatures (670-60O05 0.83-0.77Ta

On a n n e a l i n g f o r about t e n t o twenty minutes a t 6700C, f a c e t i n g o r i g i n a t i n g from t h e ordered s t r u c t u r e occurred a t {751}fcc r e g i o n s on t h e s u r f a c e (& f a c e t i n g ) . I t was f o u n d t h a t t h e f a c e t s a r e s u p e r l a t t i c e { 2 1 1 I b c t f a c e t s i n c e r t a i n o r d e r e d domains. The o r d e r e d domains a p p e a r e d t o h a v e a l o w e r d e g r e e o f o r d e r t h a n t h o s e produced by i n - s i t u a n n e a l i n g a t 810-825°C. S i m i l a r s u r f a c e o r d e r i n g was observed i n a n FIM image of a t i p annealed a t 6000C.

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&

A t t h i s t e m p e r a t u r e , s u r f a c e o r d e r i n g ( p r e f e r e n t i a l growth of f3 phase (Ni4W)) o c c u r r e d p r e f e r e n t i a l l y a t some o f t h e { 4 2 0 } f c c s u r f a c e s o f a t i p o f Ni-16.6 a t % W a l l o y . I t was f o u n d t h a t t h e o r d e r e d domains were d i s c - l i k e i n shape and t h a t t h e d i s c - p l a n e s w e r e p a r a l l e l t o { l l ~ } ~ , ~ t y p e s u p e r l a t t i c e p l a n e s of a p p r o p r i a t e o r i e n t a t i o n v a r i a n t s of t h e ordered phase. The t o p one o r two planes of t h e { l l O } b c t s u r f a c e were considered t o be N i planes, s i n c e t h e s e planes were q u i t e dimly imaged i n t h e FIM images.

2. & i n t e r m e d i a t e temperatures (%8600C, 0.91Tr)

On a n n e a l i n g a Ni-16.6 a t % W a l l o y t i p a t t h i s temperature a s u r f a c e l a y e r w i t h low d e g r e e o f o r d e r was f o r m e d ( s u r f a c e d i s o r d e r i n g ) . The s i t u a t i o n was a l m o s t s i m i l a r t o NihMo f o r 760-7200C i n - s i t u annealing.

I11 - THEORETICAL CALCULATION 1. Surface energy

When a b u l k c r y s t a l i s d i v i d e d by a p l a n e t o p r o d u c e t h e s u r f a c e , a l l a t o m i c bonds i n t e r s e c t e d b y t h e plane a r e broken. I n t h e c a s e of a Ni-Mo a l l o y , t h e s p e c i f i c

s u r f a c e energy i s given by t h e f o l l o w i n g equation:

where vIJ(R) i s t h e number of broken bonds between I and J atoms (I,J= N i , ~ o ) i n t h e R-th n e a r neighbor p e r u n i t a r e a of t h e s u r f a c e and U ~ J ( ~ ) i s t h e i n t e r a c t i o n e n e r between t h e 9,-th n e a r neighbor I-J atoms. I n t h e Bragg-Williams approximation VIJ

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i s given by

VIJ(R) = c p i I pjJ vij(R), i , j

where V i (i,j=a,@) i s t h e number of R-th n e a r neighbor broken bonds o r i g i n a t i n g a t i-subjlattice p o i n t and t e r m i n a t i n g a t a j - s u b l a t t i c e p o i n t p e r u n i t a r e a of t h e s u r f a c e , and pi1 t h e p r o b a b i l i t y t h a t a n I atom i s found on an i - s u b l a t t i c e point. E~

i s f i n a l l y expressed a s a f u n c t i o n of t h e Bragg-Williams l o n g range o r d e r parameter (degree of o r d e r ) 0.

The s u r f a c e e n e r g y o f t h e Ni4Mo a l l o y f o r t h e s u r f a c e s p a r a l l e l t o t h e fundamental plane was found t o i n c r e a s e w i t h i n c r e a s i n g degree of o r d e r a s shown i n Fig.3. The i n c r e m e n t o f t h e s u r f a c e e n e r g y c a u s e d by t h e i n c r e a s e of t h e d e g r e e o f o r d e r i s s m a l l e r i n t h e (002)bct(=(002)f ,,) and (1 21 )bet ( = ( I 1 1 )f cc) s u r f a c e s t h a n i n any s u r f a c e w i t h o t h e r o r i e n t a t i o n . This q u a l i t a t i v e l y e x p l a i n s p r e f e r e n t i a l s u r f a c e o r d e r i n g a t t h e ( 0 0 2 ) f c c and f a c e t s i n o u r FIM e x p e r i m e n t s . A s f o r t h e s u p e r l a t t i c e p l a n e , t h e s u r f a c e e n e r g y c a n i n c r e a s e o r d e c r e a s e d e p e n d i n g on t h e s u r f a c e o r i e n t a t i o n and Mo l a y e r p o s i t i o n from t h e t o p s u r f a c e layer.

Using Wulff's theorem, t h e e q u i l i b r i u m shape o f t h e NiqMo can be predicted. The p r e d i c t e d shape by t h i s method was c h a r a c t e r i z e d by t h e f a c e t s developed, f o r example Fig.4. The o r i e n t a t i o n of t h e f a c e t s i n t h e d i s o r d e r e d s t a t e a g r e e d w i t h t h o s e obtained by FIM experiments a t a low temperature, where ordering does n o t p r a c t i c a l - l y occur owing t o t h e s l u g g i s h n e s s of ordering.

2. Equilibrium degree of o r d e r

The f r e e e n e r g y F o f t h e c r y s t a l h a v i n g a (HKL)bct s u r f a c e c a n be e x p r e s s e d a s f u n c t i o n s o f { ~ ) ( n ) } and { x ( n ) } :

Here, ~ ( n ) and x ( n ) a r e d e g r e e of o r d e r and c o n c e n t r a t i o n of N i a t o m s i n t h e n - t h a t o m i c l a y e r f r o m t h e t o p s u r f a c e , r e s p e c t i v e l y . U and S a r e i n t e r n a l e n e r g y and c o n f i g u r a t i o n a l entropy of t h e system. The e q u i l i b r i u m degree of o r d e r i s obtained from t h e f o l l o w i n g equilibrium conditions:

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where xb i s t h e c o n c e n t r a t i o n of N i atoms, i n t h e bulk.

I n t h e c a l c u l a t i o n s , t h e e q u i l i b r i u m degree of o r d e r a t t h e s u r f a c e of t h e Ni4Mo a l l o y was found t o be lower t h a n t h a t i n t h e b u l k a s shown i n Fig.5. The d e v i a t i o n of t h e degree of o r d e r a t t h e s u r f a c e from t h a t i n t h e b u l k i n c r e a s e s a s t h e t e m p e r a t u r e a p p r o a c h e s Tc f r o m below. A t t h e (002)bc: s u r f a c e , t h e r e e x i s t s a hump n e a r t h e s u r f a c e i n a p l o t of t h e degree of o r d e r a s a f u n c t i o n of depth, and t h e hump becomes more d i s t i n c t a s t h e t e m p e r a t u r e approaches Tc a s shown i n Fig.6. The f i n i t e degree of o r d e r n e a r t h e ( 0 0 2 ) b c t s u r f a c e e x i s t s e v e n a t t e m p e r a t u r e s h i g h e r t h a n Tc, a n d t h e t h i c k n e s s of t h i s r e g i o n d e c r e a s e s w i t h i n c r e a s i n g t e m p e r a t u r e . The s u r f a c e d i s o r d e r i n g a n d t h e p r e f e r e n t i a l s u r f a c e o r d e r i n g a t t h e { 2 0 0 ) f c c s u r f a c e a t o r s l i g h t l y a b o v e Tc f o u n d i n o u r e x p e r i m e n t s c a n be e x p l a i n e d s u c c e s s f u l l y by t h e p r e s e n t c a l c u l a t i o n s .

3. S u r f a c e f r e e energy

S p e c i f i c s u r f a c e f r e e energy f s of t h e a l l o y i s given by

where f r i s t h e r e l a x a t i o n f r e e energy of t h e system and given by

H e r e , ?le(n) and r\b a r e t h e e q u i l i b r i u m d e g r e e o f o r d e r i n t h e n - t h l a y e r a n d i n t h e b u l k , r e s p e c t i v e l y . r\,(n) i s g i v e n by eq.(L), and a s i s t h e a r e a of t h e s u r f a c e . I t was found t h a t t h e s u r f a c e f r e e energy f s d e c r e a s e s w i t h d e c r e a s i n g temperature. The r e l a x a t i o n f r e e e n e r g y f r f o r t h e (002)bct and (671)bct d e c r e a s e s and t h e n i n c r e a s e s w i t h i n c r e a s i n g t e m p e r a t u r e , w h i l e f r f o r t h e (121)bct d e c r e a s e s monotonically.

4. S u r f a c e n u c l e a t i o n

It, i s assumed t h a t a d i s c - s h a p e d n u c l e u s of t h e o r d e r e d p h a s e w i t h a r a d i u s R a n d t h i c k n e s s aR ( a i s a n o n - d i m e n s i o n a l p a r a m e t e r ) i s formed a t t h e s u r f a c e . When t h e n u c l e u s h a v i n g d e g r e e of o r d e r q i s f o r m e d i n t h e d i s o r d e r e d m a t r i x , t h e f r e e energy change AFs of t h e system i s given a s a f u n c t i o n of q , R, a and T by

w h e r e Af(q,T) i s t h e change o f t h e volume f r e e e n e r g y d e n s i t y , and &(n,R,a) i s t h e i n c r e m e n t of s u r f a c e and i n t e r f a c e e n e r g i e s due t o t h e e x i s t e n c e of t h e nucleus. I f t h e f i r s t a n d t h e s e c o n d t e r m s o f t h e r i g h t hand s i d e of eq.(7) a r e n e g a t i v e and p o s i t i v e , r e s p e c t i v e l y , i t c a n be shown t h a t AFs(q,R,a,T) h a s a s a d d l e p o i n t w i t h r e s p e c t t o R and a f o r g i v e n v a l u e s of a n d T. I n t h i s c a s e , s u r f a c e n u c l e a t i o n c a n occur. To c a l c u l a t e t h e s t e a d y s t a t e n u c l e a t i o n r a t e Is of t h e disc-shaped n u c l e u s i n t h e (HKL)bct o r i e n t e d s u r f a c e , t h e f o l l o w i n g e q u a t i o n d e r i v e d by T u r n b u l l 1301 can be employed:

Here, ns* i s t h e number of atoms a t t h e i n t e r f a c e between t h e nucleus and t h e matrix, ns i s t h e number o f a t o m s p e r u n i t a r e a a t t h e f r e e s u r f a c e of t h e n u c l e u s , A F ~ * i s t h e a c t i v a t i o n f r e e e n e r g y o f n u c l e a t i o n , a n d Q i s t h e a c t i v a t i o n e n e r g y o f a t o m i c i n t e r c h a n g e . R* a n d a* a r e c r i t i c a l v a l u e s of R and a , r e s p e c t i v e l y . I n t h e c a l c u l a t i o n s it was found t h a t a t t e m p e r a t u r e s near Tc t h e n u c l e a t i o n r a t e i n Ni4Mo i s h i g h e r a t t h e s u r f a c e s t h a n i n t h e b u l k a n d t h a t t h e { 2001 c c s u r f a c e s a r e t h e h i g h e s t i n n u c l e a t i o n r a t e , a s shown i n Fig.7. However, a t t e m p e r a t u r e s n e a r t h e i n s t a b i l i t y t e m p e r a t u r e TO, t h e n u c l e a t i o n r a t e i s lower a t t h e s u r f a c e than i n t h e t h e bulk. The p r e s e n t c a l c u l a t e d r e s u l t s g i v e r e a s o n a b l e e x p l a n a t i o n s o f t h e e x p e r i m e n t a l r e s u l t s i n Ni4Mo t h a t p r e f e r e n t i a l s u r f a c e o r d e r i n g o c c u r s a t h i g h t e m p e r a t u r e s n e a r Tc and t h a t s u r f a c e d i s o r d e r i n g occurs a t i n t e r m e d i a t e temperatures n e a r t h e nose of t h e TTT curve.

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/I/ Sundram,V.S., Alben,R.S. and Robertson,W.D., Surface Sci. & (1974) 653.

/2/ Morbn-L6pez,J.L. and Falicov,L.M., Phys. Rev. (1978) 2542.

/3/ Buck,T.M., Wheatly,G.H. and Marchut,L., Phys. Rev. Letters 1 (1983) 43.

/4/ Johnson,W.G. and Blakely, J.M., Eds. Interfacial Segregation ( ~ m . Soc. for Metals, Metals Park, OH, 1979).

/5/ Kingetsu,T., Yamamoto,M. and Nenno,S., Surface Sci. 103 (1981) 13.

/6/ Kingetsu,T., Yamamoto,W., Nenno,S. and Fukura,H., Japan. J. Appl. Phys.

(1981) 1407.

/7/ Kingetsu,T., Yamamoto,M. and Nenno,S., Japan. J. Appl. Phys. 20 (1981) 2037.

/8/ Kingetsu,T., Yamamoto ,M. and Nenno ,S., Sci. Rept

.

Res. Inst. Tohoku Univ.

A29 Suppl. 1 (1981) 31.

/9/ Kingetsu,T., Yamamoto,M. and Nenno,S, Japan. J. Appl. Phys. 21 (1 982) 1421.

/I 0/ Kingetsu,T., Yamamoto ,M. and Nenno,S., Surface Sci. &I (1 984) 402.

/I I/ Kingetsu,T., Yamamoto,M. and Nenno,S., Surface Sci. (1984) 101.

/12/ Kingetsu,T., Yamamoto,M. and Nenno,S., Surface Sci. (1984) L547.

/13/ Kingetsu,T., Yamamoto,M. and Nenno,S., Surface Sci. 151 (1985) L161.

/I&/ Kingetsu,T., Yamamoto,M. and Nenno,S., Surface Sci. (1985) 189.

/I 5/ Kingetsu,T., Yamamoto,M. and Nenno,S., Surface Sci.

a

(1985) 21 2.

/I 6/ Elliott ,R.P., Constitution of Binary Alloys, I st Suppl. (~c~raw- ill, New York, 1965), p.622.

/17/ Harker,D., J. Chem. Phys. 2 (1944) 315.

/18/ Hansen,M. and Anderko,K., Constitution of Binary Alloys, 2nd ed. (~c~raw- ill, New York, 1958), p.1057.

/l9/ Spruiel1,J.E. and Stansbury,E.E., J. Phys. Ghem. Solids & (1965) 81 1.

/20/ Ruedl,E., Delavignette,P. and Amelinckx,S., Phys. Status Solidi 28 (1968) 305.

/21/ Baer.H.G. Z. Metallkd. 6 (1965) 79.

/22/ Baer,H.G. Z. Metallkd. 22 (1966) 318.

/23/ Saburi,T., Komatsu,K. and Nenno,S., Phil. Mag. 20 (1969) 1091.

/24/ Chakravarti,B., Starke Jr. ,E.A. and LeFevre ,B.G., J Materials Sci. 2 ⁽¹970) 394.

/25/ LeFevre,B.G., Surface Sci. 2 (1970) 144.

/26/ Yamamoto ,M. , ^Nenno,S., Futamoto ,M. and Nakamura, S., Japan. J. Apple Phys.

1 1 (1972) 437.

/27/ Zmamoto,~. , Futamoto,M., Nenno,S. and Nakamura,S., 20th Intern. Field Emission Symposium (Penn. State Univ., 19731, p.44.

/28/ Epremian,E. and Harker,D., Trans. Metall. Soc. AIME 185 (1949) 267.

/29/ Tong,H.C. and Washburn,J., Cryst. Lattice Defects 2 (1971) 221.

/30/ Turnbull,D., J. Chem. Phys. 3 (1952) 411.

1 1 1

311

Fig.1 Schematic representation of a (O1l)fcc cross-section of an FIM tip annealed for 3 0 s at 865OC and for 290 s at 835OC (A) an ordered domain nucleated at the (200)fcc facet. (B) an ordered domain nucleated at the ( 1 1 1 ) ~ ~ ~ facet. (c) an ordered domain nucleated in the interior (Oil CROSS-SECTION of the tip.

AT 8 6 5 - 8 3 5 2

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JOURNAL DE PHYSIQUE

HPHLY ORDERED SURFACE LAYER

DOMAINS / WITH LOW DEGREE OF ORDER

HOMOGENEOUSLY NUCLEATED ' ORDERED DOMAINS

1 I

TRANSITION REGION 50-100 A

Fig.2 Schematic r e p r e s e n t a t i o n of a c r o s s - s e c t i o n of a n FIM t i p annealed a t 760-7200C.

Fig.4 Calculated y-plot ( r a d i a l l i n e s ) and e q u i l i b r i u m shapes (white l i n e s ) of t h e disordered NiqMo alloy. V2/V1 =O.4. (1 1 0lf cc cross-section.

DEPTH ( A 1

"-

1 2 3 4 5 6 7 8

DEPTH ( NUMBER OF ATOMlC LAYERS)

Fig.6 R e l a t i o n s between depth from t h e ( 0 0 2 ) ~ ~ ~ s u r f a c e and degree of o r d e r of Ni4Mo a t temperatures h i g h e r t h a n Tc.

F i g 3 R e l a t i o n s between s u r f a c e energy change A E ~ ( = E , ( ~ ) ) - E , ( ~ ) ) a n d d e g r e e o f o r d e r r) of Ni4Mo f o r t h e s u r f a c e p a r a l - l e l t o fundamental planes. V2/VI=0.4.

DEPTH ( A )

0 2 6 8 10 12 14 16 18 20 22 I - - - - - - - . - . - - -- . - . . . - -

; I 6 ^s ⁹ ^; ⁰ ^; ^l ¹

DEPTH ( NUMBER OF ATOMIC LAVERS )

Fig.5 R e l a t i o n s b e t w e e n d e p t h f r o m t h e (121)bct s u r f a c e and d e g r e e o f o r d e r o f Ni4Mo a t v a r i o u s temperatures.

0.84 0.86 0.88 0.90 0.92 0.96 0.96 TEMPERATURE ( T I Tc )

Fig.7 R e l a t i o n s b e t w e e n a n o r m a l i z e d t e m p e r a t u r e (T/T,) a n d t h e r a t i o I ~ / I B O Is i s t h e t o t a l n u c l e a t i o n r a t e over a l l t h e ordered phases of t h e s i x v a r i a n t s a t each of t h e s u r f a c e s p a r a l l e l t o fundamental planes, and IB i s t h a t i n t h e bulk.