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EPITAXIAL RELATIONSHIPS BETWEEN f.c.c. AND b.c.c. CRYSTALS
M. Kato, M. Wada, M. Shibata-Yanagisawa, T. Mori
To cite this version:
M. Kato, M. Wada, M. Shibata-Yanagisawa, T. Mori. EPITAXIAL RELATIONSHIPS BETWEEN f.c.c. AND b.c.c. CRYSTALS. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-849-C1-854.
�10.1051/jphyscol:19901133�. �jpa-00230044�
COLLOQUE DE PHYSIQUE
Colloque C l , supplement au n o l , Tome 51, j a n v i e r 1990
EPITAXIAL RELATIONSHIPS BETWEEN
f.c.c.
AND b . c . c . CRYSTALSM. KATO, M. WADA, M. SHIBATA-YANAGISAWA and T. MORI
D e p a r t m e n t
of Materials Science and
E n g i n e e r i n g , T o k y oI n s t i t u t e of
T e c h n o l o g y , 4259 N a g a t s u t a , M i d o r i - k u , Y o k o h a m a 227,Japan
A b s t r a c t
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On t h e b a s i s o f v a r i o u s e x p e r i m e n t a l r e s u l t s f o r t h e e p i t a x i a l r e l a t i o n s h i p s between f . c . c . and b . c . c . s u b s t r a t e / d e p o s i t s y s t e m s , s i m p l e g e o m e t r i c a l c r i t e r i a a r e proposed t o p r e d i c t f a v o r a b l e e p i t a x i a l r e l a t i o n s h i p s i n a g i v e n system w i t h any s u b s t r a t e p l a n e o r i e n t a t i o n . It i s found t h a t t h e p r e s e n t c r i t e r i a a r e e x c e l l e n t l y a p p l i c a b l e t o t h e u n d e r s t a n d i n g o f e x p e r i m e n t a l l y observed e p i t a x i a l r e l a t i o n s h i p s f o r t h e Fe/Cu system w i t h low- and high-index s u b s t r a t e o r i e n t a t i o n s .1
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INTRODUCTIONThe c r y s t a l l o g r a p h y of a t h i n c r y s t a l d e p o s i t e d o n t o a n o t h e r c r y s t a l s u b s t r a t e h a s been exam- i n e d f o r many f . c . c . 1 b . c . c . s y s t e m s . Most s t u d i e s s o f a r conducted have focused on t h e o b s e r - v a t i o n of e p i t a x i a l r e l a t i o n s h i p s (ERs) r e a l i z e d on s u b s t r a t e s w i t h low-index c r y s t a l l o g r a p h i c p l a n e s . For example, such e p i t a x i e s d e s c r i b e d by p a r a l l e l r e l a t i o n s h i p s between s u b s t r a t e and d e p o s i t p l a n e s a s ( l l l ) f / / ( l O 1 ) b , (OOl)f//(OO1)b, (lO1)f//(OO1)b and (OO1)f//(lO1)b a r e among t h e most f r e q u e n t l y observed ones. ( I n t h i s s t u d y , t h e s u b s c r i p t s f and b s t a n d f o r f . c . c . and b . c . c . c r y s t a l s , r e s p e c t i v e l y . )
Simple g e o m e t r i c a l c r i t e r i a have been proposed t o p r e d i c t whether t h e Kurdjumov-Sachs o r Nishiyama o r i e n t a t i o n r e l a t i o n s h i p i s f a v o r e d f o r t h e ( l l l ) f / / ( l O l ) b e p i t a x y depending o n t h e s u b s t r a t e / d e p o s i t c o m b i n a t i o n s / l - 4 1 . Moreover, t h e r e l a t i v e f a v o r a b i l i t i e s between (001)'//
( 0 0 1 ) ~ and ( 0 0 1 ) ~ / / ( 1 0 1 ) ~ e p i t a x i e s on a g i v e n (OO1)s s u b s t r a t e p l a n e have a l s o been d i s c u s s e d 15-101. (The s u p e r s c r i p t s s and d s t a n d f o r s u b s t r a t e and d e p o s i t c r y s t a l s , r e s p e c t i v e l y . )
R e c e n t l y , Kato and Mishima used a h i g h e r - i n d e x s u b s t r a t e p l a n e / l l / : They d e p o s i t e d Fe on t h e (112)f p l a n e of a Cu-Ni a l l o y and found a new ER d e s c r i b e d a s ( 1 1 2 ) ~ / / ( 2 1 3 ) : and [ 1 1 0 1 f / / [ ~ I T J ~ . Wada e t a l . d e p o s i t e d Fe on a s p h e r i c a l s u b s t r a t e of Cu a t t h e t i p o f a n e e d l e - l i k e specimen f o r f i e l d i o n microscopy (FIM)/12-131. B e f o r e t h e Fe d e p o s i t i o n , a n FIM image of t h e s p h e r i c a l Cu s u r f a c e showed t h e exposure of many p o l e s of atomic p l a n e s . A f t e r Fe was depos- i t e d , p a r a l l e l r e l a t i o n s h i p s between f . c . c . and b . c . c . p o l e s such a s ( l l l ) f / / (101)g, ( 1 0 2 ) f / / (111)f and ( 1 1 3 ) f / / ( 1 1 2 ) ~ were r e c o g n i z e d . These s t u d i e s i n d i c a t e t h a t t h e r e i s a p o s s i b i l i t y o f f i n d i n g c e r t a i n ERs even when high-index p l a n e s a r e u s e d a s s u b s t r a t e o r i e n t a t i o n s .
The p u r p o s e of t h e p r e s e n t s t u d y i s t w o f o l d . F i r s t , s i m p l e c r i t e r i a f o r t h e p r e d i c t i o n o f f a v o r a b l e ERs w i l l be d e r i v e d on t h e b a s i s of t h e p r e v i o u s e x p e r i m e n t a l r e s u l t s . Secondly, t h e a p p l i c a b i l i t y of t h e c r i t e r i a w i l l b e i n v e s t i g a t e d e x p e r i m e n t a l l y f o r t h e c a s e o f h i g h e r - i n d e x s u b s t r a t e o r i e n t a t i o n s . The main f o c u s i s p l a c e d o n t h e Fe/Cu ( i n some c a s e s , Fe/Ni a s w e l l ) system; one a s a s u b s t r a t e and t h e o t h e r a s a d e p o s i t .
2
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BRIEF SURVEY OF PREVIOUS STUDIES ON THE Fe/Cu SYSTEMMatthews and J e s s e r / l 4 / and Olsen and J e s s e r / l 5 / d e p o s i t e d Fe on (OO1)f N i and (OO1)f Cu sub- s t r a t e s , r e s p e c t i v e l y . They found t h a t Fe i n i t i a l l y d e p o s i t e d pseudomorphically o n Cu ( o r Ni) a s f . c . c . y-Fe and t h a t when t h e t h i c k n e s s of a n Fe o v e r l a y e r exceeded about 2 nm, t h e d i f f u - s i o n l e s s y + a t r a n s f o r m a t i o n caused t h e f o r m a t i o n of a-Fe v a r i a n t s w i t h c e r t a i n ERs t o t h e Cu (Ni) s u b s t r a t e s . By a n a l y z i n g t h e e x p e r i m e n t a l r e s u l t s , Olsen and J e s s e r concluded t h a t t h e m i s f i t s t r e s s caused by t h e l a t t i c e mismatch between Cu (Ni) and y-Fe h e l p e d t h e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19901133
Cl-850
COLLOQUE DE PHYSIQUE< i i ~ > ~ / / < i i i > ~ N (with 12 v a r i a n t s ) : { l l l } f / / { l l O } b
< i i 2 > f ~ / < i i o > b P (with 12 v a r i a n t s ) : {OO1}f//{llO}b
TO>^
B (with 3 v a r i a n t s ) : {OO1}f//~OO1}b
< 1 i 0 > ~
With t h e s e observed r e s u l t s , simple u n i f i e d c r i t e r i a f o r t h e p r e d i c t i o n of E R s on given s u b s t r a t e p l a n e s w i l l be d i s c u s s e d .
p r e f e r e n t i a l formation of c e r t a i n a-Fe v a r i a n t s on t h e y -+ a t r a n s f o r m a t i o n of Fe ( t h e m i s f i t s t r e s s e f f e c t ) / l 6 / . I n o t h e r words, t h e p r e f e r e n t i a l l y formed a-Fe v a r i a n t s were i d e n t i f i e d a s t h o s e which possessed n e g a t i v e i n t e r a c t i o n e n e r g i e s between t h e m i s f i t s t r e s s and t h e Bain deformation.
L a t e r , Kato e t a l . examined more thoroughly t h e crystall.ography of a-Fe d e p o s i t s on ( 0 0 1 ) f , (lO1)f and Cu and N i s u b s t r a t e s / l 7 , 1 8 / . The m i s f i t s t r e s s between y-Fe and Cu h a s a d i f f e r e n t s i g n from t h a t between y-Fe and X i . Therefore, i f t h e m i s f i t s t r e s s e f f e c t i s predominant i n determining t h e e p i t a x y of a-Fe, t h e p r e f e r e n t i a l l y formed a-Fe v a r i a n t s on Cu would be completely d i f f e r e n t from t h o s e on N i . However, t h e experimental r e s u l t s showed t h a t many a-Fe v a r i a n t s were commonly observed on a given s u b s t r a t e p l a n e r e g a r d l e s s of t h e sub- s t r a t e c r y s t a l s / l 8 / . As an e x t e n t i o n of t h e s e s t u d i e s , Kato e t a l . a l s o interchanged t h e r o l e s of Fe and Cu/19/: a-Fe was used a s s u b s t r a t e s and Cu was d e p o s i t e d on them. I n t h i s c a s e , t h e d e p o s i t e d Cu c o n s i s t e d of many f i n e i s l a n d s which were considered t o be formed a s s m a l l f . c . c . c r y s t a l s from t h e e a r l y s t a g e of t h e d e p o s i t i o n . Therefore, t h e m i s f i t s t r e s s e f f e c t should be a b s e n t . N e v e r t h e l e s s , c e r t a i n ERs were observed between Cu and Fe depending on t h e o r i e n t a t i o n of t h e s u b s t r a t e s / l 9 / .
Table 1 l i s t s t h e r e p o r t e d p a r a l l e l r e l a t i o n s h i p s between s u b s t r a t e and d e p o s i t p l a n e s a t t h e i n t e r f a c e s f o r t h e Fe/Cu (Fe/Cu-Ni) system. Among t h e Kurdjumov-Sachs (KS), Nishiyama(N), P i t s c h (P) and Bain (B) r e l a t i o n s h i p s , t h e
r a t i o n a l ( n e a r e s t ) ones t o approximately Table 1
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The p a r a l l e l r e l a t i o n s h i p s between d e s c r i b e t h e r e s p e c t i v e ERs a r e a l s o shown f . c . c . and b.c.c. p l a n e s i n observed ERs f o r t o g e t h e r w i t h t h e r e f e r e n c e s . The above four Fe/Cu and Fe/Cu-NiP B N P KS, N
KS B KS, N
N r e l a t i o n s h i p s a r e expressed a s
KS (with 24 v a r i a n t s ) : { l l l } f / / { l l O } b
3
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SIMPLE CRITERIA FOR FAVORABLE EPITAXIESS u b s t r a t e Deposit R e l a t i o n s h i p Reference
I
Although some of t h e following c r i t e r i a have a l r e a d y been adopted t o e x p l a i n t h e observed ERs l i s t e d i n Table 1 , we w i l l r e c o n s i d e r and g e n e r a l i z e them h e r e . From Table 1 , i t i s recog- n i z e d t h a t a s f a r a s t h e Fe/Cu (Fe/Cu-Ni) system i s concerned, t h e f . c . c . 1 b . c . c . i n t e r f a c e p l a n e s always conform t o t h e well-known Bain correspondence. One of t h e c r y s t a l l o g r a p h i c a l l y e q u i v a l e n t forms of t h e Bain correspondence between (hkR)f and ( ~ q r ) ~ p l a n e s i s w r i t t e n a s
Our f i r s t c r i t e r i o n can now be s t a t e d : (I)
The f.c.c. and b.c.c. planes to form an interface are related to each other
bythe Bain correspondence.
Table 1 shows t h a t t h e observed ERs a r e always c l o s e t o one of t h e f o u r well-known o r i e n t a t i o n r e l a t i o n s h i p s , KS, N , P and B. Since a l l of t h e s e r e l a t i o n s h i p s can be regarded a s s l i g h t l y r o t a t e d v e r s i o n s of t h e Bain r e l a t i o n s h i p , not only f . c . c . 1 b . c . c . i n t e r f a c e p l a n e s but a l s o f . c . c . and b.c.c. d i r e c t i o n s on t h e i n t e r f a c e should be r e l a t e d t o each o t h e r by t h e Bain correspondence, although t h e corresponding d i r e c t i o n s on t h e i n e e r f a c e a r e not necessa- r i l y p a r a l l e l . Using t h e r e c i p r o c a l m a t r i x of t h e m a t r i x i n e q u a t i o n ( l ) , t h e Bain corre- spondence between [ a b c I f and [uvwIb d i r e c t i o n s can be expressed a s
Cl-851
Table 2
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The Bain correspondence between f.c.c. and b.c.c. interface planes and directionsWhen a substrate plane is given, candidate deposit planes can be found from equation (l).
Kato and Mishima have shown that two mutually perpendicular directions,
sf
and $f, on the f.c.c. side of the interface can be found uniquely so that they are related to two mutually perpendicular directions,itb
and 3b, on the b.c.c. side of the interface by the Bain corre- spondence of equation (2)/11/. Table 2 shows the f.c.c. and b.c.c. planes and directions which are related by the Bain correspondence, equations (1) and (2). For convenience, two cases, i.e., f.c.c. substrate/b.c.c. deposit and b.c.c. substrate1f.c.c. de osit, are shown separately. It should be noted that ?if and$
are perpendicular toFf
and yb, respectively.S
The directional correspondence in Table 2 assures that a rectangular region defined by the two vectors
gf
andTf
contain the same number of atoms as in the rectangular region defined byzb
and
Tb.
Let us consider the case of the f .c.c. substrate1b.c.c. deposit. Then, by knowing sf,
+
yf, xb and yb, the atomic arrangement of the b.c.c. interface plane can be obtained by an ++
affine transformation of the atomic arrangement of the f.c.c. interface plane as
where 111 (=j$lab/lgf ]af) and
n2
( = l ~ ~ l a ~ / l 3 ~ l a ~ ) are principal distortions and af and ab are the lattice parameters of the f.c.c. and b.c.c. crystals, respectively. According to the invariant-line criterion by Dahmen/20/, the optimum matching of two crystals at a given inter- face is realized when the atomic arrangements of the two crystals match perfectly along at least one particular direction (the invariant-line direction) on the interface. Dahmen has shown that this situation is realized when the deposit plane is rotated with respect to the substrate plane about the interface normal so that the angle 8 between?if
andzb
directions satisfies(h, k,
Of
U ((h-k)/2, (h+k)/2,$lb
-+ 2 2 2 2
xf=[hll, kg, -(h +k
)If
++ zb=[(h-k)~, (h+k)ll, -(h +k)lb
-+ -+
yf'[-k. h, Olf ++ y b =[-(h+k). (h-k), Olb (P, q, r)b
+
(P-9. ~ + q , rIf-+ 2 2 2 2
xb=[pr, qr, -(p +q
)lb *
zf=[(p-q)r/2, (p+q)r/2, -(P +q)If
+ +
yb'[-9, P, ++ yf'[-(p+q)/2, (p-q)/2, Olf f .c.c.
Substrate and b.c.c.
Deposit b.c.c.
Substrate and f.c.c.
Deposit
Then, the angle a between the invariant-line direction and
?if
becomes/ll/2 2 112
tancl = C(l-r1~)/(11~- 1))
.
(5)Planes
Directions
Planes
Directions
The invariant-line criterion has been found successful in explaining the observed ERs listed in Table 1/11,17-191. Therefore, our second criterion is: (11)
The directional corre- spondence of the two crystals at an interface is also described by the
Baincorrespondence.
The parallel relationship between directions is determined by the invariant-line criterion.
It should be noted from equations (4) and (5) that for the invariant line to exist, either
?l< 1 < n 2 or " 2 l < n l must be satisfied. However, this is not always the case for a given mterface. The (OO1)f//(OO1)b interface with nl=n2 is one of the examples for the invalidity of the invariant-line criterion. In such a case, 8 = 0 has been conventionally assigned/lO/.
For a substrate orientation other than two or three planes exist as candidate deposit planes satisfying the Bain correspondence. For example, (001)f corresponds to both
(OO1)b and (lO1)b and (101)f corresponds to both (OO1)b and (112)b, as shown in Table 1. To judge the relative favorabilities of different correspondences, the following M parameter has been proposed/lO/
Cl-852 COLLOQUE DE PHYSIQUE
where c l = q1 - 1 and c 2 = q 2 - 1 . T h i s p a r a m e t e r i s e s s e n t i a l l y a f a c t o r p r o p o r t i o n a l t o t h e e l a s t i c s t r a i n energy of t h e d e p o s i t c r y s t a l owing t o t h e l a t t i c e mismatch between s u b s t r a t e and d e p o s i t p l a n e s . We t h e r e f o r e a s s i g n o u r t h i r d c r i t e r i o n : (111)
The smaller the M value, the more favorable an epitaxy becomes.
I n f a c t , t h e r e l a t i v e f a v o r a b i l i t i e s between (001)S//( 0 0 1 ) ~ and ( 0 0 1 ) ~ / / ( 1 0 1 ) ~ e p i t a x i e s i n v a r i o u s c u b i c s u b s t r a t e / d e p o s i t s y s t e m s have been e x p l a i n e d e x c e l l e n t l y by t h e M p a r a m e t e r / l O / . I t s h o u l d b e n o t e d , however, t h a t two o r more ERs w i t h d i f f e r e n t M v a l u e s have sometimes been o b s e r v e d o n a g i v e n s u b s t r a t e p l a n e , s u c h a s t h o s e on (001); Cu and (101): Cu i n T a b l e 1. T h e r e f o r e , a l a r g e M v a l u e d o e s n o t n e c e s s a r i l y mean t h a t t h e c o r r e s p o n d i n g ER c a n n e v e r be r e a l i z e d . Even i f t h e e l a s t i c s t r a i n e n e r g y , o r t h e M v a l u e , i s l a r g e , i t c a n be reduced s i g n i f i c a n t l y by t h e g e n e r a t i o n o f a r r a y s of m i s f i t d i s l o c a t i o n s a t t h e i n t e r f a c e / 3 , 9 , 2 1 , 2 2 / .
The above proposed c r i t e r i a a r e p u r e l y g e o m e t r i c a l a n 3 do n o t t a k e i n t o account t h e atom s p e c i e s . However, a s f a r a s t h e Fe/Cu system i s concerned, t h e above c r i t e r i a have been suc- c e s s f u l l y a p p l i e d t o e x p l a i n t h e o b s e r v e d ERs i n T a b l e 1. I n t h e n e x t s e c t i o n , E R s on high- i n d e x p l a n e s w i l l be examined t o d i s c u s s t h e a p p l i c a b i l i t y o f t h e proposed c r i t e r i a .
4
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EPITAXIAL RELATIONSHIPS ON HIGH-INDEX SUBSTRATE PLANESAlthough any high-index p l a n e can be chosen a s a T a b l e 3
-
C a l c u l a t e d M v a l u e s f o r p l a n a r s u b s t r a t e p l a n e , we have chosen, i n t h e p r e s e n t c o r r e s p o n d e n c e s f o r (102)f and (112)b s t u d y , (102)F Cu and (112); Fe. A s shown i n T a b l e 1 , s u b s t r a t e s .t h e s e p l a n e s a p p e a r a s d e p o s i t p l a n e s o n t h e (111); Fe and (101)z Cu s u b s t r a t e p l a n e s , r e s p e c - t i v e l y .
Using t h e t h r e e c r i t e r i a i n t h e p r e v i o u s s e c t i o n , l e t u s f i r s t p r e d i c t t h e f a v o r a b l e ERs on t h e s e s u b s t r a t e p l a n e s . From t h e Bain correspond- e n c e i n e q u a t i o n ( l ) , w e f i n d t h a t (102)f corre- sponds t o {111)
,
{114}b and {103Ib, and (112)b c o r r e s p o n d s t o ? 1 0 1 } ~ and { 1 1 3 I f . The v a l u e s of t h e M p a r a m e t e r were c a l c u l a t e d f o r t h e s e correspond- e n c e s u s i n g t h e p r o c e d u r e i n t r o d u c e d i n t h e p r e v i o u s s e c t i o n . They a r e shown i n T a b l e 3 . The l a t t i c ep a r a m e t e r s o f Cu and Fe were a s s i g n e d a s a f = 0 . 3 6 1 n m and a -0.286nm, r e s p e c t i v e l y . From T a b l e 3 , i t i s found t h a t (102)f//(111): and (112);/l(101)gbshould be most f a v o r a b l e s i n c e t h e s e have t h e s m a l l e s t M v a l u e s ( t h e c r i t e r i o n ( 1 1 1 ) ) . T h e r e f o r e , l e t u s d i s c u s s t h e s e two e p i t a x i e s i n t h e f o l l o w i n g . Both of t h e s e e p i t a x i e s c a n s a t i s f y t h e i n v a r i a n t - l i n e c o n d i t i o n . To a p p l y o u r c r i t e r i o n ( 1 1 ) , such p a r a m e t e r s a s t h o s e shown i n e q u a t i o n s (3) and (4) must b e e v a l u a t e d . Using t h e Bain c o r r e s p o n d e n c e i n T a b l e 2 , t h e p r i n c i p a l d i r e c t i o n s ,
gf, 3f, gb
and3 yb, and t h e p r i n c i p a l d i s t o r t i o n s , "1 and "2, were found and t h e a n g l e of r o t a t i o n 8 was c a l c u l a t e d from e q u a t i o n ( 4 ) . The r e s u l t s a r e shown i n T a b l e 4 , which c o m p l e t e l y d e t e r m i n e t h e p r e d i c t e d ERs f o r t h e (102):// (111): and ( 1 1 2 ) ~ / / (101): e p i t a x i e s .
F i g u r e s 1 ( a ) and (b) show t h e 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 s w i t h t h e zone a x e s perpen- d i c u l a r t o (102)f and (112)b, r e s p e c t i v e l y . These d i f f r a c t i o n p a t t e r n s a r e e x p e c t e d t o b e observed when t h e above p r e d i c t e d ERs and t h e i r c r y s t a l l o g r a p h i c a l l y e q u i v a l e n t v a r i a n t s a r e a c t u a l l y formed on t h e r e s p e c t i v e s u b s t r a t e p l a n e s . I n o r d e r t o examine w h e t h e r t h e above p r e d i c t i o n i s t r u e , we have made e x p e r i m e n t a l i n v e s t i g a t i o n s . Thin f o i l specimens f o r t r a n s - m i s s i o n e l e c t r o n microscopy (TEM) w i t h d e s i r e d f l a t s u r f a c e o r i e n t a t i o n s , (102)f and (112)b, were p r e p a r e d from Cu and Fe s i n g l e c r y s t a l s , r e s p e c t i v e l y . Fe (on (102)f Cu) and Cu (on
(112)b Fe) were d e p o s i t e d on h e a t e d ( a b o u t 700K) s u b s t r a t e s under a vacuum o f about 1 0 - ~ ~ a . The a v e r a g e t h i c k n e s s o f t h e d e p o s i t e d c r y s t a l s was e s t i m a t e d t o be about 30nm. The TEM
S u b s t r a t e P l a n e
T a b l e 4
-
B a i n c o r r e s p o n d e n c e and r e l a t e d p a r a m e t e r s f o r t h e ( 1 0 2 ) ~ / / ( 1 1 1 ) ~ and ( 1 1 2 ) g / / (101): e p i t a x i e s .(112)b { l O l ) f 0.0103 {113If 0.0401 (102)f
D e p o s i t P l a n e
0.0214 { 1 1 4 j b 0.0235 {1O3Ib 0.0410
F i g . 1
-
Schematic d i f f r a c t i o n p a t t e r n s which a r e expected t o b e observed when t h e p r e d i c t e d e p i t a x i a l r e l a t i o n s h i p s , (a) ( 1 0 2 ) f / / ( 1 1 1 ) g and (b) (112)g//(101)2, a r e r e a l i z e d t o g e t h e r w i t h t h e i r c r y s t a l l o g r a p h i c a l l y e q u i v a l e n t v a r i a n t s . Open and c l o s e d symbols r e p r e s e n t r e f l e c t i o n s p o t s from d e p o s i t and s u b s t r a t e c r y s t a l s , r e s p e c t i v e l y .lal
C 0
*A
** *
- * 0 .,
Fig. 2
-
( a ) a SAD p a t t e r n and (b) a d a r k - f i e l d micrograph t a k e n by t h e s p o t A i n (a) of t h e Fe/(102)$ Cu specimen.-
@- .
F i g . 3
-
(a) a SAD p a t t e r n and (b) a d a r k - f i e l d Cu/(112){ Fe specimen.vm
micrograph t a k e n by t h e s p o t B i n ( a ) of t h e
Cl-854 COLLOQUE
DE
PHYSIQUEo b s e r v a t i o n s were made on a 200kV H i t a c h i H - 7 0 0 TEM.
F i g u r e s 2 ( a ) and (b) show a s e l e c t e d - a r e a d i f f r a c t i o n (SAD) p a t t e r n of t h e ~ e / ( 1 0 2 ) : Cu specimen and a d a r k - f i e l d micrograph of t h e d e p o s i t Fe c r y s t a l s , r e s p e c t i v e l y . A s i m i l a r s e t of photographs f o r t h e Cu/(112){ Fe specimen a r e shown i n F i g s . 3 (a) and ( b ) . It can be s e e n t h a t t h e morphology o f t h e d e p o s i t e d Fe (Fig. 2 ( b ) ) i s q u i t e d i f f e r e n t from t h a t of t h e depos- i t e d Cu ( F i g . 3 ( b ) ) . Such a d i f f e r e n c e i s c o n s i d e r e d t o r e f l e c t t h e d i f f e r e n c e i n t h e growth mode of t h e d e p o s i t c r y s t a l s , a s was d i s c u s s e d p r e v i o u s l y / l 0 , 1 9 / . What i s more i n t e r e s t i n g i s t h a t t h e o b s e r v e d SAD p a t t e r n s i n F i g s . 3 ( a ) and 4 ( a ) a r e i n e x c e l l e n t agreement w i t h t h o s e p r e d i c t e d ( F i g s . l ( a ) and ( b ) . r e s p e c t i v e l y ) . T h e r e f o r e , we c o n c l u d e t h a t t h e proposed c r i - t e r i a f o r f a v o r a b l e ERs a r e a l s o a p p l i c a b l e t o t h e c a s e of high-index s u b s t r a t e o r i e n t a t i o n s .
We b e l i e v e t h a t t h e e x c e l l e n t a p p l i c a b i l i t y o f t h e p r e s e n t c r i t e r i a t o t h e Fe/Cu system owes v e r y much t o t h e f a c t t h a t Fe and Cu have s i m i l a r molar volumes, 7.04~10-6m3/mol f o r Fe and 7 . 0 8 ~ 1 0 - ~ m 3 / r n o l f o r Cu. Because of t h i s , t h e Bain correspondence between Fe and Cu p l a n e s a s s u r e s t h a t a g i v e n i n t e r f a c e a r e a i s o c c u p i e d by a p p r o x i m a t e l y t h e same number of Fe and Cu atoms. I f t h e molar volumes of f . c . c . and b.c.c. c r y s t a l s a r e s i g n i f i c a n t l y d i f f e r e n t , o n t h e o t h e r hand, t h e matching between two p l a n e s r e l a t e d t o each o t h e r by t h e B a i n c o r r e s p o n d e n c e would, i n g e n e r a l , be t o o poor t o form a r e a l i s t i c i n t e r f a c e . I n such a c a s e , o u r c r i t e r i a cannot be a p p l i e d a s t h e y a r e and some m o d i f i c a t i o n s a r e n e c e s s a r y .
R e c e n t l y , some e v i d e n c e was found f o r t h e e x i s t e n c e of t h e o t h e r e p i t a x i e s shown i n T a b l e 3 , such a s ( 1 0 2 ) f / / ( 1 1 4 ) g , ( 1 1 2 ) g / / ( 1 1 3 ) $ , e t c . Very c a r e f u l and thorough TEM o b s e r v a t i o n must be made i n o r d e r t o a s c e r t a i n t h a t t h e s e ERs a c t u a l l y e x i s t . T h i s r e s e a r c h i s c u r r e n t l y u n d e r p r o g r e s s .
5
-
SUMMARYThe e p i t a x i a l r e l a t i o n s h i p s between f . c . c . and b . c . c . c r y s t a l s were examined. The Fe/Cu s y s - tem, one a s a s u b s t r a t e and t h e o t h e r a s a d e p o s i t , was mainly i n v e s t i g a t e d . Taking i n t o account (1) t h e Bain c o r r e s p o n d e n c e between f . c . c . and b . c . c . p l a n e s and d i r e c t i o n s , ( 2 ) t h e i n v a r i a n t - l i n e c r i t e r i o n , and (3) m i s f i t s t r a i n e n e r g y c o n s i d e r a t i o n , c r i t e r i a f o r t h e p r e d i c - t i o n of f a v o r a b l e e p i t a x i a l r e l a t i o n s h i p s on a g i v e n s u b s t r a t e p l a n e o r i e n t a t i o n were proposed.
It was found t h a t t h e p r e s e n t c r i t e r i a were e x c e l l e n t l y a p p l i c a b l e t o t h e e x p l a n a t i o n and p r e d i c t i o n of t h e e p i t a x i a l r e l a t i o n s h i p s which were r e a l i z e d n o t o n l y on low-index b u t a l s o on h i g h e r - i n d e x s u b s t r a t e p l a n e s .
Acknowledgment
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T h i s r e s e a r c h i s s u p p o r t e d by a Grant-in-Aid f o r S c i e n t i f i c Research from M i n i s t r y o f E d u c a t i o n , S c i e n c e and C u l t u r e under Grant No. 63550473.REFERENCES
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