THE STRUCTURE OF INTERFACES

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THE STRUCTURE OF INTERFACES

R. Bonnet

To cite this version:

R. Bonnet. THE STRUCTURE OF INTERFACES. Journal de Physique Colloques, 1985, 46 (C4), pp.C4-61-C4-70. �10.1051/jphyscol:1985405�. �jpa-00224654�

JOURNAL DE PHYSIQUE

Colloque C4, suppl6ment au n04, Tome 46, a v r i l 1985 page C4-61

THE STRUCTURE OF INTERFACES

R. Bonnet

I n s t . Nat. PoZytechnique de GrenobZe, Laboratoire de [Phermodynmnique e t Physioo-Chimie ~ 6 t a Z Z u r ~ i ~ u e s + , E. N. S. E. E. G., Domaine Universitaire, B. P. 75, 38402 Saint Martin drH8res, France

A b s t r a c t

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Some o f t h e l i n e a r f e a t u r e s v i s i b l e on g r a i n and phase boundaries a r e considered i n terms o f e s t a b l i s h e d d i s l o c a t i o n theory. The natures o f i n t r i n s i c DSC phase boundary d i s l o c a t i o n s , i m p e r f e c t and DSC d i s l o c a t i o n s l y i n g on t w i n boundaries, a r e i d e n t i f i e d by t h e matching techni,que.

During t h e l a s t t e n years, g r e a t advances have been made i n our knowledge of t h e s t r u c t u r e o f i n t e r f a c e s . These are l a r g e l y due t o t h e f o l l o w i n g f a c t o r s : ( i ) obser- vations, a t t h e atomic scale, o f t h e atom arrangements a t tilt boundaries [ll. ( i i ) t h e i d e n t i f i c a t i o n o f some t y p i c a l l i n e a r i n t e r f a c i a l f e a t u r e s l i k e DSC and imperfect d i s l o c a t i o n s a t h i g h order t w i n boundaries [2]. ( i i i ) t h e computer s i m u l a t i o n o f t h e atomic s t r u c t u r e o f t h e i n t e r f a c e [ 3 t o 61. ( i v ) t h e computation o f t h e c o n t r a s t of boundary d i s l o c a t i o n s i n transmission e l e c t r o n microscopy b y t h e simultaneous two- beam method (STBM), e.g. [2,7 t o 121. Less successful have been t h e i n v e s t i g a t i o n s i n t o t h e n a t u r e o f phase boundaries where, o f course, t h e s i t u a t i o n i s f a r more complex. T h i s i s due l a r g e l y t o experimental d i f f i c u l t i e s i n producing two-phase b i - c r y s t a l s [13 t o 181 and t o t h e f a c t t h a t f r e q u e n t l y one o f t h e phases i s an i n t e r - m e t a l l i c compound o f g r e a t c r y s t a l l o g r a p h i c complexity.

4 r i s i n g o u t o f t h e advances which have been made i n our understanding o f t h e exact nature o f i n t e r f a c e s , a number o f i m p o r t a n t questions have y e t t o be s a t i s f a c t o r i l y answered. I n t h e present paper, p a r t i c u l a r emphasis w i l l be placed on t h e i n t e r p r e t a - t i o n o f T.E.F.I. images obtained using STBFI which has t h e p o t e n t i a l t o enable informa- t i o n t o be gained on any deformation c o n t r a s t o r t r a n s l a t i o n s t a t e r e l a t e d t o a given i n t e r f a c i a l f e a t u r e .

I n passing, i t i s worth n o t i n g t h a t w i t h STBM, t h e r e i s no r e s t r i c t i o n whatsoever on t h e o r i e n t a t i o n o f t h e specimen and d e f e c t f o r c l e a r i d e n t i f i c a t i o n o f s t r u c t u r a l features. On t h e o t h e r hand, w i t h h i g h r e s o l u t i o n e l e c t r o n microscopy, t h e range-: of

? o s s i b l e specimen o r i e n t a t i o n s i s s e v e r e l y r e s t r i c t e d and t h e r e a r e even p r a c t i c a l 1 im i t a t i o n s i n t h e nature o f t h e m a t e r i a l which can be examined.

With STBM, curved d i s l o c a t i o n s can be s t u d i e d provided t h a t t h e r e a r e segments of these d i s l o c a t i o n s which a r e s u f f i c i n e t l y long and s t r a i g h t f o r t h e e l a s t i c i n t e r a c - t i o n s w i t h o t h e r p a r t s o f t h e d i s l o c a t i o n t o b e ' n e g l i g i b l e . F i g . 1 i l l u s t r a t e s such a case f o r a g l i s s i l e Shockley d i s l o c a t i o n ( 1 / 6 ) [I211 i n a (111) coherent plane of a C t w i n boundary o f t h e a l l o y Cu-6 a t % S i . The ends o f these d i s l o c a t i o n s i n t e r a c t s t r o n g l y w i t h t h e f r e e surfaces o f t h e f o i l s!nce they can move i n t h e boundary a t room temperature r81 (these ends a r e p r a c t i c a l l y screw d i s l o c a t i o n s ) . A comparison o f t h e columns f i g . 1 shows t h a t f o r t h e s t r a i g h t c e n t r a l segment o f t h e d i s l o c a t i o n , t h e agreement between t h e experimental and simulated images i s most s a t i s f a c t o r y . Many o t h e r i l l u s t r a t i o n o f t h e v a l i d i t y o f STB'I have a l r e a d y been demonstrated 12, 7, 8 t o 111 and i n t h e present paper t h e technique w i l l be a p p l i e d t o p r o v i d e answers t o one o f t h e important questions r e f e r r e d t o a b o v e - s p e c i f i c a l l y : some d i f f e r e n t i n t e r f a c i a l domains o r f a c e t s on g r a i n - o r phase- boundaries c o n t a i n l i n e a r f e a t u r e s 'associ6 au CMS ( L A . 29)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985405

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C4-64 JOURNAL DE PHYSIQUE

C2,4,19,20,211 which are known t o include imperfect dislocations. How can the nature of these l i n e a r features be i d e n t i f i e d and how then do these i n t e r a c t with t h e perio- d i c network of i n t r i n s i c dislocations forming the boundary ?

I

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OBSERVATIONS AND IDENTIFICATION OF LINEAR DEFECTS CONSTITUTING BOUNDARIES BET- WEEN INTERFACIAL DOMAINS

. I t i s now established t h a t a planar twin boundary may contain d i f f e r e n t domains, each one being related t o p a r t i c u l a r r e l a t i v e positions of the unit c e l l s of both c r y s t a l s , remote from the boundary region. These positions are referred t o as "trans- l a t i o n s t a t e s " . These l a t t e r have even been observed recently f o r the common coherent plane (111) i n C3 boundaries i n Cu-6 % Si [ I l l . The l i m i t s of such domains a r e l i n e a r features which necessarily contain the so-called "imperfect dislocations" o r "partial grain boundary dislocations (GBD)" t o accomodate the d i f f e r e n t t r a n s l a t i o n s t a t e s of two adjacent domains. So-called "dihedral" dislocationsthat occur a t intersecting twin boundary f a c e t s often include such imperfect dislocations [221. These dislocations have been shown t o occur as components of t h e i n t r i n s i c GBD network i n a near C9 boundary by Forwood and Clarebrough [21, f o r a Cu-6 a t % Si alloy. These authors con- cl uded t h a t there are two d i s t i n c t trans1 ation s t a t e s f o r t h e two domains observed, d i f f e r i n g only by a small r e l a t i v e displacement of 0.023 nm normal t o t h e boundary.

However, recent observations [19,22] on t w i n boundaries have shown t h a t the s t r a i n contrast associated with these l i n e a r features i s unexpectedly-strong. In order t o study t h e i r t r u e nature, the l i n e a r features v i s i b l e on the (130) boundary, Z5 f i g . (4a,b) of a recent paper by Bacmann [19l, .have been investigated using STBM. Four extra pictures w i t h a common d i f f r a c t i n g vector have been kindly supplied by Dr Bac- mann w i t h a l l t h e i r geometric and crystallographic c h a r a c t e r i s t i c s , and a seventh picture has been taken by t h e present author by replacing Bacmann's original f o i l i n the microscope and using STBM. The comparison, f i g . 2, of the experimental (column a ) and computed images (column b ) , shows unambiguously t h a t a t a resolution of 2nm the l i n e a r feature v i s i b l e t o the r i g h t of f i g . 4 a,b of Bacmann [I91 is a composite dis- location. I t s Burgers vector is (1/10 [00311 t (1/10) [215]1, where the subscript 1 r e f e r s t o l e f t c r y s t a l , f i g . 2 column a. The vector (1/10) [215] i s t h e Burgers vector of a DSC dislocation. The other feature v i s i b l e on the 1eFt of f i g . 4a,b of Bacmann [I91 has been s i m i l a r l y i d e n t i f i e d as being a composite dislocation w i t h a r e s u l t a n t Burgers vector (1/10)[003] 1 + (1/10) 11301 1. The measured Burgers vector components a r i s i n g from the analysis of t h e a f r i n g e s , i .e. (1/10) 100311, a r e i s good agreement w i t h those derived by Bacmann 1191 from a model of t h e C5 boundary, assuming four atomic neighbours f o r each atom of germanium i n t h e boundary, as in the bulk c r y s t a l . Indeed, t h i s model leads t o the components (l/lO)[0,0,5/2]1.

The above composite dislocations can interact.. between themselves as shown fig.3a.

Fig: 3b d e t a i l s the Burgers vectors of the defects, found from STBM. Such cgmposite dislocations a r e a l s o part of t h e i n t r i n s i c s t r u c t u r e of t i l t boundaries (130)1, axis C0011, only s l i g h t l y misoriented w i t h respect t o the C5 coincidence, as shown i n f i g . 4. The astonishing f a c t is t h a t the imperfect dislocations have never been obser- ved alone

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they have been i n combination with other DSC dislocations. In passing, i t is worth reporting t h a t our examination of t h e C5 boundaries i n Ge have not con- firmed any presence of imperfect dislocations of the king (1/4) [ I l l ] suggested as a p o s s i b i l i t y by Bacmannet a l . [231.

I1

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^{PHASE BOUNDARY} STRUCTURES

The s t r u c t u r e s of phase boundaries are not easy t o observe a t the atomic s c a l e , except i n very p a r t i c u l a r cases e.g. f o r Si/NiSie [21]. However, l a t t i c e imaging i s e a s i e r and allows i n t e r e s t i n g r e s u l t s t o be obtained, e.g. t h e s t e p s t r u c t u r e s a t the interfaces between Al'matrix and 8' plates i n A1-5 w t % Cu [24]. The STBM can also be used i n cases where t h e i n t r i n s i c dislocations a r e separate from each other.

Fig. 5a,b,c i l l u s t r a t e 3 such cases concerning phase boundaries separating a nickel based phase ( f . c . c . Bravais l a t t i c e ) and a phase based on the i n t e r m e t a l l i c compound Ni3A1 (simple cubic Bravais l a t t i c e ) . Theses boundaries have been obtained a f t e r annealing an i n d u s t r i a l alloy t h r e e weeks a t 1100°C. These figures i l l u s t r a t e

t h e extreme s e n s i t i v i t y o f t h e geometry o f t h e d i s l o c a t i o n networks t o t h e l o c a l i n - t e r f a c e o r i e n t a t i o n s and t h e important e f f e c t o f s l i g h t m i s o r i e n t a t i o n s from p a r a l l e - l i s m o f t h e d i r e c t i o n s <loo> o f both cubic phases. Since t h e two phases have l a t t i c e parameters d i f f e r i n g o n l y by a few 10-5 nm, i t i s n o t easy t o e x t r a c t from t h e p a t t e r n , t h e exact r o l e o f t h e m i s o r i e n t a t i o n , t h e order o f magnitude,of which i s l e s s than 10-1 degree according t o t h e observation o f K i k u c h i l i n e d i f f r a c t i o n p a t t e r n s . The f i r s t step i s t o determine t h e p o s s i b l e Burgers v e c t o r s o f these i n t r i n s i c G.B.D.'s by c o n s t r u c t i o n t h e DSC-1 and DSC-2 l a t t i c e s , a procedure a l r e a d y given by t h e author [25,26,271. According t o t h i s procedure, t h e two near-coincident c e l l s M1 and M2 are t h e cubic c e l l s o f both phases, and t h e DSC-1 l a t t i c e i s i d e n t i c a l w i t h t h e f.c.c.

l a t t i c e o f t h e nickel-based phase. The i n t r i n s i c phase boundary d i s l o c a t i o n s o f f i g . 5a,b,c have thus Burgers vectors (112) <110> o r perhaps <100>. The STBM can then be a p p l i e d t o i d e n t i f y t h e t r u e Burgers vectors, p r o v i d e d t h a t a s u f f i c i e n t number o f d i f f e r e n t b r i g h t f i e l d images i s taken ( t h e c o n t r a s t e f f e c t s o f t h e v e r y s l i g h t d i f - ference i n l a t t i c e parameters are here n e g l i g i b l e ) . Fig. 6 allows a comparison t o be made between experimental and computed images o f d i s l o c a t i o n segments w i t h a Burgers v e c t o r (1/2)[1011. N o t i c e t h a t f o r t h e upper image, t h e d i s l o c a t i o n c o n t r a s t i s q u i t e v i s i b l e , d e s p i t e g.b ⁼ 0.

For t h e lower image, i b i s however seen t h a t t h e c o n t r a s t o f t h e d i s l o c a t i o n seg-

~ i l e n t j u s t a t t h e emerging p o i n t o f t h e f r e e surfaces i s n o t w e l l reproduced by image matching. Such an e f f e c t c o u l d be due, f o r instance, t o a l o c a l s p l i t t i n g o f t h e d i s -

l o c a t i o n 1281.

Fig. 3

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I n t e r a c t i o n o f composite d i s l o c a t i o n s i n t h e C5 boundary. The micrograph ( a ) i s provided by Bacmann and correspondsto i t s f i g u r e 2 C201. A p p l i c a t i o n o f t h e STBll leads t o t h e i d e n t i f i c a t i o n o f t h e l i n e a r f e a t u r e s described i n (b). They a r e a l l composite d i s l o c a t i o n s with_-Burgers vectors-$ A - I , B + I, C + I where

A = ( 1 / 1 0 ) ~ 3 1 0 1 ~ , 6 = (1/10)121511, C = (l/lO)[L2511, I = (1/10)[00311. I n ( b ) , T denotes t h e upper p a r t o f t h e boundary.

C4-66 JOURNAL DE PHYSIQUE

Fig. 4

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Aspect of the Z5 boundary when both c r y s t a l s are very s l i g h t l y misoriented around t h e common axis C001I1. I n t r i n s i c edge GBD's a r e produced on the two boundary domains, w i t h Burgers vectors (1/10) 11301 1 and directions [001] 1. Two adjacent do- mains arp limited by composite dislocations with Burgers vectors

( l / l O ) [ 1 3 0 1 ~ ¹ (1/10)[00311. The dislocation network i s hence non periodic around such composite dislocations, due t o complex e l a s t i c interactions between t h e dislo- cations (Work i n progress w i t h Bacmann).

Fig. 5

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Typical aspects of i n t r i n s i c dislocations a t interfaces separating a nickel- based crystal and an Ni3Al-based i n t e r m e t a l l i c compound. Assuming two parallel cubic c r y s t a l s w i t h no l a t t i c e m i s f i t , t h e micrographs a,b,c a r e taken for-a f o i l normal [I341 ; the d i f f r a c t i n g vectors aye respectively (111) f o r a,b and (200) f o r c. For a and b, t h e boundary normal is C1,1,111 while the electron beam i s 11341.

The geometry of t h e i n t e r f a c i a l features i s very s e n s i t i v e t o t h e orientation para- meters of t h e boundaries,l ike f o r low angle grain boundaries.

Fig. 6 - Image matching for the dislocation segments of fig. 5a running from the top left to the bottom right. The diffracting vectors are, towards bottom, (Ill), (Ill), (200), (113), (113). The Burgers vector is (1/2) [loll. Note that g.b = 0 for line a.

JOURNAL DE PHYSIQUE

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[I41 HASHIMOTO, S., EBERHARDT, A . , and BAUDELET, B . , J . Crystal Growth 49 (1980) 410.

1151 MAHESWARAN, P., Thesis on "the formation of i n t e r f a c e s between d i s s i m i l a r f.c.

c. metals", Univ. of Surrey (feb. 1982).

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[18] BALLUFFI, R.W., p r i v a t e communication.

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[251 BONNET, R., and DURAND, F., Phil. Mag. 32 (1975) 997.

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C281 BURSILL, L.A., and BLANCHIN, M.G., Phil. Mag. A49 (1984) 365.

DISCUSSION

N e w :

P. Does t h e p o s i t i o n of t h e phase boundary away from t h e neck correspond t o t h e p o s i t i o n which can be calculated from t h e volume f r a c t i o n s of phase from t h e phase diagram?

R. Bonnet: It was impossible t o measure t h e volume f r a c t i o n o f t h e phases a f t e r annealing because of t h e rough surface of t h e s i l v e r b a l l , see f i g . 4 of a paper by A. Laffont and myself (Acta Met. 3 (1982) 763). This seems probably due t o t h e occurence of i n t e n s e vacancy movements, a s surface h o l e s a r e .appearing on Ag b a l l s .

M. Hoftnann: I n W-W-spheres annealed i n t h e presence of N i , g r a i n boundaries were formed i n t h e neck of t h e two spheres. They migrate i n t o one of t h e spheres

forming d i f f e r e n t k i n d s o f f a c e t s . Is t h i s a l s o observed a t i n t e r f a c e s i n t h e Ag-Cu system and is it p o s s i b l e t h a t even i n t h e c a s e of random o r i e n t a t i o n r e l a t i o n s h i p , t h e s e i n t e r f a c e d g r a i n boundaries have planes o f low i n d i c e s a f t e r migration?

R. Bonnet: The phase boundary f a c e t t i n g was never observed f o r t h e Ag/Cu boundaries. The o r i e n t a t i o n r e l a t i o n s h i p o f t h e two b a l l s were a p p a r e n t l y random, and t h u s may be r e l a t e d t o t h e p a r a l l e l i s m o f some low index p l a n e s between t h e phases.

M. Are t h e r e s u l t s o f t h e STBM r e a l l y unique, which means t h a t t h e observable c o n t r a s t s cannot be explained by a n o t h e r p o s s i b l e c o n f i g u r a t i o n ?

R . Bonnet: STBM is s a f e t o apply provided t h a t t h e Burgers vector o f t h e d i s l o c a t i o n , o r t h e modulus o f t h e r i g i d body t r a n s l a t i o n , is ( i ) s u f f i c i e n t l y l a r g e , t y p i c a l l y l a r g e r than * 0.01 nm, ( i i ) d i f f e r e n t than a l l t h e o t h e r p o s s i b l e Burgers v e c t o r s i n l e n g t h (-0.01 nm) o r a n g u l a r d i r e c t i o n . Uniqueness o f t h e s o l u t i o n found by i n t e g r a t i n g t h e Howie-Whelan equation i s r e a l i z e d , f o r a s i n g l e d i s l o c a t i o n , a s soon a s t h r e e d i f f e r e n t computed images, obtained with t h r e e d i f f e r e n t and non coplanar d i f f r a c t i n g v e c t o r s , reproduce t h e c o n t r a s t d e t a i l s o f t h e experimental images, a s shown t h e o r e t i c a l l y by Head.

From a number o f previous papers, it appears t h a t i n g e n e r a l t h r e e o r f o u r p i c t u r e s a r e s u f f i c i e n t t o i d e n t i f y t h e Burgers v e c t o r . Extra p i c t u r e s a r e however always taken f o r complementary confirmation.

M. Rljhle: I n your i n t e r e s t i n g r e s u l t s on t h e s t r u c t u r e o f t h e i n t e r f a c e between Cu and Ag you assume t h a t t h e r e is s t e p function-like c o n c e n t r a t i o n p r o f i l e (no Ag i n Cu and v i c e v e r s a ) . 1s this assumption c o r r e c t ? I s n ' t it p o s s i b l e t h a t a

"diffuset1 i n t e r f a c e ( s e v e r a l l a t t i c e planes) w i l l change and i n f l u e n c e t h e s t r u c t u r e o f i n t e r f a c e ?

R. Bonnet: For t h e b i c r y s t a l experiments, o u r r e s u l t is t h a t a f t e r 50 h r s annealing a t high temperatures t h e chemical compositions o f t h e phases were t h a t o f t h e s o l i d s o l u t i o n s o f t h e Ag-Cu diagram. The measurements were made w i t h a c l a s s i c a l microprobe a n a l y s e r (CAMECA a p p a r a t u s ) . This means t h a t a t a r e s o l u t i o n o f a few microns from t h e Ag/Cu boundary, t h e c o n c e n t r a t i o m o f i l e s o f Ag and Cu a r e s t e p functions. No information i s a v a i l a b l e f o r a b e t t e r r e s o l u t i o n and, o f course, f o r t h e e x i s t e n c e o f any t t d i f f u s e t t i n t e r f a c e .

y. Ishida: The problem o f Burgers vector determination o f an i s o l a t e d g r a i n boundary d i s l o c a t i o n using your STBM method seems t o be t h e i n s e n s i t i v i t y . What is your comment t o t h e i n s e n s i t i v i t y problem?

C4-70 JOURNAL DE PHYSIQUE

R. Bonnet: It is t r u e t h a t when t h e set o f t h e p o s s i b l e burgers v e c t o r s contain almost e q u i v a l e n t DSC v e c t o r s , STBM is o f no use because o f t h e i n s e n s i t i v i t y o f t h e computed image c o n t r a s t s . However, such c a s e s can occur o n l y f o r very elongated DSC u n i t c e l l s , i .e.

,

f o r very high 2 values. Even i n t h e s e c a s e s , a m b i g u i t i e s could perhaps be removed by using t r i p l e mode j u n c t i o n s o f DSC d i s l o c a t i o n s .

conce&ing t h e l i m i t a t i o n s o f t h e weak-beam f r i n g e counting method, it is o f no use i f t h e d i f f r a c t i n g v e c t o r s i n both g r a i n s a r e n o t common and i f a 100 kV o r 200 kV e l e c t r o n microscope i s used. I n a d d i t i o n , it cannot be a p p l i e d i f

g

.

⁹ is n o t an i n t e g e r (e.g. imperfect d i s l o c a t i o n s ) .

H. G l e i t e r : My remark s u p p o r t s D r . Bonnet's conclusion about t h e energy o f i n t e r p h a s e boundaries. Recent s y s t e m a t i c s t u d i e s on t h e energy o f i n t e r p h a s e boundaries (paper by Fecht and myself) have shown t h a t t h e energy o f t h e s e boundaries depends on t h e boundary s t r u c t u r e i n t h e s e n s e t h a t low energy boundaries a r e obtained i f close-packed d i r e c t i o n s and close-packed p l a n e s i n t h e l a t t i c e s o f t h e two phases a r e p a r a l l e l .

R. Bonnet: It is a w e l l known experimental f a c t t h a t dense planes o f both phases a r e a s p a r a l l e l a s p o s s i b l e when t h e two-phase m a t e r i a l allows its i n t e r f a c e s t o choose its own 5 o r i e n t a t i o n r e l a t i o n s h i p parameters, e.g. f o r t h e A1/A12Cu d i r e c t i o n a l l y s d l i d i f i e d e u t e c t i c (see Bonnet and Durand, 1972,

Proceedings o f L a k e v i l l e Conference on Itin s i t u Compositett).

H.E. Exner; I a g r e e with your f i n a l s t a t e m e n t t h a t i n t e r f a c i a l e n e r g i e s depend upon o r i e n t a t i o n . I n many two-phase systems (e.g. A1-Si, Ag-Ni, most oxides i n i n t e r n a l l y oxidized s i l v e r a l l o y s ) t h e i n t e r f a c e s a r e c l e a r l y f a c e t t e d . I would l i k e c a u t i o n a g a i n s t drawing conclusions frbm t h e s i n t e r i n g experiments where s p h e r e s o f non-equilibrium phases a r e used a s p a r t n e r s . The chemical d r i v i n g f o r c e s a r e u s u a l l y s o much s t r o n g e r than i n t e r f a c i a l f o r c e s t h a t a t l e a s t during t h e e a r l y s t a g e s where non-equilibrium phases a r e i n c o n t a c t , a l l i n t e r f a c i a l energy e f f e c t s a r e wiped out. I n t h e l a t e r s t a g e s , i n t e r f a c i a l f o r c e s a r e n o t very a c t i v e anymore due t o t h e l a r g e necks formed.

R. Bonnet: I am pleased about t h i s important remark.