JOURNAL DE PHYSIQUE
Colloque C4, supplément a u n04, Tome 46, avril 1985 page C4-141
R. Hoel, H.-U. ~ a b e r m e i e r + and M. Rühle
Max-PZanck-Institut f ü r MetaZZforschung, I n s t i t u t f ü r Werkstoffwissenschaften, S e e s t r a s s e 92, 0-7000 S t u t t g a r t 1, F.R.G.
+ ~ a x - ~ Z a n c k - l n s t i t u t für Festkti~-perforsehung, H e i s e n b e r g s t r a s s e 1, 0-7000 S t u t t g a r t 80, F . R . G.
Resume. On a f a i t c r o i t r e de fapon é p i t a x i a l e avec une o r i e n t a t i o n cube-cube des i l o t s d ' o r s u r nn s u b s t r a t de MgO. La t h d o r i e d a refseau-0 p r é v o i t l a formation p a r l e s d i s l o c a t i o n s de d i s c o r d a n c e , d'un r é s e a u c a r r é de d i s l o c a t i o n s c o i n s e s p a c é e s d e 9.9 nm e t aveo un v e c t e u r de Bnrgers de 112 Les images s u r fond c l a i r e t aveo f a i s c e a u x de f a i b l e i n t e n s i t é
~ 4 ~ ~ r h e l g l a présence de c e s d i s l o c a t i o n s . I n d i r e c t e m e n t . nlanmoins ~ 1 0 ~ ~ s l a c r é a t i o n d e s d i s l o c a t i o n s de d i s c o r d a n c e s e m a n i f e s t e p a r une f a i b l e d i s t o r t i o n en r o t a t i o n d e s i l o t s ; e t l ' i n t e r f a c e p e u t ê t r e c o n s i d e r é e comme constitne'e de zones c o h é r e n t e s l i é e s p a r d e s bandes i n c o h k r e n t e s .
A b s t r a c t . Gold i s l a n d s have been grown e p i t a x i a l l y on an Mg0 s u b s t r a t e i n a cube-cube o r i e n t a t i o n . Applying t h e O - l a t t i c e theory, m i s f i t d i s l o c a t i o n s a r e p r e d i c t e d t o form a square network of e d g e - d i s l o c a t i o n s spaced 9.9 nm a p a r t , and w i t h a Burgers v e c t o r of 112.a <110>. B r i g h t - f i e l d and weak-beam images d i d not r e v e a l t h e presence o f such d i s l o c a t i o n s . I n d i r e c t l y , however, t h e c r e a t i o n of m i s f i t d i s l o c a t i o n s i s shown t o m a n i f e s t i t s e l f throngh a s l i g h t r o t a t i o n a l d i s t o r t i o n of t h e i s l a n d s i and t h e i n t e r f a c e can be regarded a s c o n s i s t i n g of c o h e r e n t domains bonnded by i n c o h e r e n t bands.
1. I n t r o d u c t i o n . The CSL and O - l a t t i c e g r a i n boundary models [ I l have p r e v i o n s l y been shown t o be widely a p p l i c a b l e t o cubic m e t a l s , and more r e c e n t l y t o i o n i c s o l i d s C21. Work d e s c r i b e d by Bonnet and Durand 131 a l s o shows t h a t t h e DSC-lattice c o n s t r u c t i o n can be nsed t o o b t a i n t h e Burgers v e c t o r s of phase boundary d i s l o c a t i o n s .
The o b j e c t of t h e work p r e s e n t e d here i s t o e s t a b l i s h i f such geometrical models a r e a p p l i c a b l e t o a metal-ceramic i n t e r f a c e where Au i s l a n d s a r e grown e p i t a x i a l l y on Mg0 (cube-cube o r i e n t a t i o n ) . The o b s e r v a t i o n s w i l l a l s o be compared t o t h e lock-in mode1 d e s c r i b e d by Fecht and G l e i t e r 141.
2. Geometricallv P r e d i c t e d Boundarv S t r u c t u r e . The O - l a t t i c e , and consequently t h e m i s f i t d i s l o c a t i o n s t r u c t u r e of t h e phase boundary, can be obtained a s follows. According t o Bollmann Cl1 t h e t r a n s l a t i o n v e c t o r s , Lx0], g i v i n g t h e p o s i t i o n s of p o i n t s of good f i t ( i . e . t h e O - l a t t i c e ) a r e g i v e n by
-1 -1 lx0] = I I - A 1 Cxl
where t h e v e c t o r s [XI d e f i n e t h e p r i m i t i v e r e f e r e n c e l a t t i c e ce11 ( s e e Pig. l a ) . Prom Pig. l a i t can a l s o be s e e n (choosing t h e Mg0 l a t t i c e a s r e f e r e n c e ) t h a t t h e a p p r o p r i a t e two-dimensional r e f e r e n c e m a t r i x i s g i v e n by
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985417
JOURNAL DE PHYSIQUE
F i a . 1. a ) An and Mg0 hard sphere s t r n c t u r e s , and b) (110) l a t t i c e p l a n e s viewed along t h e [ I l 0 1 d i r e c t i o n .
( w i t h a ' = l a t t i c e c o n s t a n t of Mg01 and t h e t r a n s f o r m a t i o n matrix. A. i s t h e prodnct of a r o t a t i o n m a t r i x , and a m a t r i x d e s c r i b i n g t h e d i s t o r t i o n n e c e s s a r y t o t r a n s f o r m t h e u n i t ce11 of t h e r e f e r e n c e l a t t i o e i n t o t h e u n i t ce11 of t h e o t h e r l a t t i c e . For t h e p r e s e n t c a s e t h i s d i s t o r t i o n i s simply t h e r a t i o of t h e l a t t i c e parameters, and t h e r o t a t i o n i s 0'. Hence
cos o0 - s i n o0
A = . [
-
s i n o0 cos o0 1
w i t h a = n ' ' / a ' (a" = l a t t i c e c o n s t a n t of Au).
This g i v e s
and
Hence
a '
w i t h a' = - 2(1-a) = 7.0 nm f o r t h e Au-Mg0 i n t e r f a c e .
I n t e r f a c e m i s f i t d i s l o c a t i o n s a r e e x p e c t e d t o r u n a l o n g t h e b o u n d a r i e s of t h e Wigner-Seitz ce11 of t h e O - l a t t i c e . i . e . a l o n g <110> d i r e c t i o n s w i t h a s p a c i n g e q u a l t o 7.0 n m = 9.9 nm.
F i g . l a shows a h a r d s p h e r e mode1 of t h e Mg0 and Au s t r u c t u r e s . One p o s s i b l e i n t e r f a c e s t r u c t u r e c o n f i g u r a t i o n i s d e p i c t e d i n F i g . l b . The f i g u r e shows how l a t t i c e p l a n e s g e t g r a d u a l l y more and more o u t o f r e g i s t e r , u n t i l midway between p o i n t s o f n e a r c o i n c i d e n c e a 1 1 2 . a ' <110> edge m i s f i t d i s l o c a t i o n i s accommodated. (The l a t t i c e p l a n e s a r e assnmed c o n t i n n o u s a c r o s s t h e i n t e r f a c e . ) Snch a d i s l o c a t i o n s t r u c t u r e i s c o n s i s t e n t w i t h t h e DSC l a t t i c e c a l c u l a t i o n s f o r f c c / f c c systems ( P i e r a g g i [ S I ) . Thus t h e i n t e r f a c e would c o n s i s t o f c o h e r e n t . s q u a r e domains bounded by p u r e e d g e - d i s l o c a t i o n s . Such d i s l o c a t i o n s s h o u l d b e r e s o l v e d on b r i g h - f i e l d a s w e l l a s on weak-beam images.
3. S ~ e c i m e n P r e ~ a r a t i o n . Specimens s u i t a b l e f o r face-on T M o b s e r v a t i o n s o f t h e i n t e r f a c e were p r e p a r e d a s f o l l o w s . 3 mm Mg0 d i s c s were p o l i s h e d t o o p t i c a l f l a t n e s s on one s i d e , t h e n dimpled and ion-beam t h i n n e d t o e l e c t r o n t r a n s p a r a n c y on t h e o t h e r . The p o l i s h e d f a c e was c l e a n e d by a glow d i s c h a e p r i o r t o e-beam c o a t i n g . B e f o r e and d u r i n g d e p o s i t i o n t h e vacuum r a s 7.10-SgPa and 7 - 1 0 - ~ Pa.
r e s p e c t i v e l y . The Au was d e p o s i t e d a t a r a t e of 0.05 nmls u n t i l a n a v e r a g e t h i c k n e s s of 25 nm was reached. The s u b s t r a t e t e m p e r a t u r e of 6 5 0 ' ~ was r e t a i n e d f o r 5 mins a f t e r c o a t i n g . Some samples were s u b s e q u e n t l y tempered f o r 2 h o n r s a t 350 C and a i r . T h i s a n n e a l i n g d i d n o t a f f e c t t h e r e s u l t s d i s c u s s e d below. O
4. R e s n l t s and D i s c u s s i o n . F i g . 2 a shows a t y p i c a l Au i s l a n d w i t h Moire f r i n g e s which a r e c h a r a c t e r i s t i c o f e p i t a x i a l cube-cube growth. The dimensions of t h e i s l a n d s s t u d i e d were (120 9 0 ) nm, and t h e f o l l o w i n g imaging c o n d i t i o n s were nsed i n s e a r c h i n g f o r t h e m i s f i t d i s l o c a t i o n s : ( i ) i l l u m i n a t i o n a l o n g t h e [O011 zone a x i s , and g two-beam b r i g h t f i e l d imaging, and ( i i i ) ( g , 4g) weak-beam imI:::2?$ith g g2?200) o r g = ( 2 2 0 ) ) . F i g . 2 shows examples o f s u c h images. The two most n o t i c a b l e f e a t u r e s observed a r e :
1 ) The p r e d i c t e d r e g u l a r a r r a y o f m i s f i t d i s l o c a t i o n s i s net d i r e c t l y observed. T h i s c a n b e i n t e r p r e t e d a s f o l l o w s . ( i ) The s t r a i n s u r r o u n d i n g t h e d i s l o c a t i o n s i s s o s m a l l t h a t no a p p r e c i a b l e c o n t r a s t c a n b e s e e n . ( i i ) The s p a c i n g of t h e d i s l o c a t i o n i s s o s m a l l t h a t i n d i v i d u a l d i s l o c a t i o n s c a n n o t b e r e s o l v e d , and ( i i i ) no d i s l o c a t i o n s a r e p r e s e n t a t a l l . F o r r e a s o n s d i s c u s s e d below. ( i i i ) i s n o t r e g a r d e d a s a p l a u s i b l e e x p l a n a t i o n f o r t h e p r e s e n t c a s e .
2) The Moire p a t t e r n s a r e r o t a t e d ( 7 . 5 9 . ~ ) ~ w.r.t. t h e Mg0 r e f e r e n c e l a t t i c e . T h i s c o r r e s p o n d s t o a i e a l r o t a t i o n of ( 0 . 2 2 0 . 0 7 ) ' of t h e Au i s l a n d s . The u n c e r t a i n t y i s n o t caused by e x p e r i m e n t a l e r r o r s ( t h e a c c u r a c y i n a n a l y z i n g t h e d i f f r a c t i o n p a t t e r n i s +0.7'),but b y s c a t t e r i n g f o r d i f f e r e n t e x p e r i m e n t s . S i x measurements were done f o r t h r e e d i f f e r e n t i s l a n d s which r e s u l t e d i n t h e
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Fin. 2. a) shows 2 0 0 Moire cross-fringes (spacing 7.0 nm). illumination along 10011. b) g two-beam bright-field image (fringe spacing 7.0 nm), gZZO two-bea brigk?-field (fringe spacing 4.9 nm), and d) a weak-beam image, s = 0.02 A-T. Only weak thickness fringes are seen.
Gia. 3. Shows t h e c o n v e r g e n t beam 200 r e f l e c t i o n s from Mg0 and Au, convergence a n g l e e q u a l s 0.3 mrad.
d i f f e r e n t r o t a t i o n a n g l e s . Such r o t a t i o n s c a n a l s o b e confirmed b y c o n v e r g e n t beam r e f l e c t i o n s , a s shown i n F i g . 3.
S i m i l a r r o t a t i o n s of Moire p a t t e r n s a s a r e s u l t of m i c r o s t r u c t u r a l d i s t o r t i o n s have p r e v i o u s l y been observed i n PtIAu, SnlSnTe. Ag/MoS2 and Cul N i systems ( s e e 16, 71 f o r a r e v i e w ) . F o r a s t r o n g l y bound system, a s Au/MgO, one e x p e c t s t h a t t h e r o t a t i o n i n v o l v e s a d i s t o r t i o n of t h e l a t t i c e u n i t ce11 o f t h e Au i s l a n d . Such a d i s t o r t i o n c a u s e s t h e c r e a t i o n of m i s f i t d i s l o c a t i o n s and r e l a x a t i o n of m i s f i t s t r a i n . T h e r e f o r e , m i s f i t d i s l o c a t i o n s have t o be p r e s e n t a t t h e s t u d i e d m e t a l l c e r a m i c i n t e r f a c e .
With t h i s t h e o r y i n mind, and r e f e r r i n g t o t h e model d e s c r i b e d i n t h e i n t r o d u c t i o n , t h e TEM o b s e r v a t i o n s c a n be i n t e r p r e t e d a s b e i n g a n i n d i r e c t c o n f i r m a t i o n of t h e p r e s e n c e of m i s f i t d i s l o c a t i o n s . I n t h e v i c i n i t y of t h e d i s l o c a t i o n c o r e , however, t h e r e i s a l o s s of coherency. and t h e l a t t i c e p l a n e s a r e n o t c o n t i n u o n s a s d e p i c t e d i n P i g . l b . The r e d u c t i o n i n coherency s t r a i n i s s u f f i c i e n t t o r e n d e r t h e d i s l o c a t i o n s i n v i c i b l e . The i n t e r p h a s e c a n t h e r e f o r e b e t h o u g h t o f a s c o n s i s t i n g of c o h e r e n t , however s m a l l , domains bound by i n c o h e r e n t
m.
Such o b s e r v a t i o n s a r e c o n s i s t e n t w i t h t h e l o c k - i n model d e s c r i b e d by P e c h t and G l e i t e r [41. According t o t h i s model, a low e n e r g y c o n f i g u r a t i o n i s r e a c h e d when low index p l a n e s and close-packed d i r e c t i o n s ( < 1 0 0 > , <110>) o f t h e two p h a s e s a r e p a r a l l e l . The close-packed d i r e c t i o n s on t h e s u r f a c e of t h e i o n i c c r y s t a l s a r e s e p a r a t e d b y v a l l e y s , and i t i s i n t e r e s t i n g t o n o t e from t98 h a r d s p h e r e model of F i g . l a t h a t t h e v a l l e y s d e f i n e d by t h e row of Mg i o n s running i n <110> d i r e c t i o n s a r e w i d e r t h a n t h e v a l l e y s p a r a l l e l t o t h e c l o s e r packed <100> d i r e c t i o n s . The f o u r Au atoms o f t h e p r i m i t i v e u n i t c e 1 1 may form a l o c k - i n c o n f i g u r a t i o n by s i t t i n g o n t o p of f o u r Mg lock-in atoms. As t h e Au
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i s l a n d grows i n t h e <110> d i r e c t i o n s , t h e 11101 p l a n e s p e r p e n d i c n l a r t o t h e i n t e r f a c e w i l l become more and more o n t of r e g i s t e r ( F i g . I b ) . However, a s t h e An atoms a r e capable of s l i d i n g along <110> v a l l e y s . b o t h coherency s t r a i n and t h e degree of coherency w i l l be rednced. It shonld a l s o be noted t h a t d u r i n g t h i s s l i d i n g p r o c e s s t h e Au atoms have t o overcome a c e r t a i n p o t e n t i a l b a r r i e r .
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