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A model for six-fold ribbon in layered structure materials
Mat. Res. Bull. Vol. 14, pp. 233-236, 1979. Printed in the USA. 0025-5408/79/020233. 452.00/0 Copyright (c) Pergamon Press, Ltd.
A M O D E L FOR S I X - F O L D R I B B O N IN L A Y E R E D S T R U C T U R E M A T E R I A L S J.G. A n t o n o p o u l o s Physics Department, U n i v e r s i t y of T h e s s a l o n i k i Thessa loniki, Greece
(Received December 1, 1978; Communicated by S. Amelinckx)
ABSTRACT Based on a c o m b i n a t i o n of B u r g e r s v e c t o r s of d i s l o c a tions lying in s u c c e s s i v e c planes of a layered struc t u r e material, a model for six fold r i b b o n f o r m a t i o n is p r e s e n t e d . Partial d i s l o c a t i o n s a p p e a r to have the same B u r g e r s v e c t o r s Such r i b b o n s were o b s e r v e d in GaSe.
Introduction
Layered structure materials have received considerable attention
in r e c e n t years, m a i n l y b e c a u s e of their a n i s o t r o p i c physical p r o p e r t i e s related to their s t r u c t u r a l a n i s t o t r o p y (I). T h e s e m a t e r i a l s c a n be d e s c r i b e d as solids c o n t a i n i n g m o l e c u l e s w h i c h in two d i m e n s i o n s extend to i n f i n i t y and w h i c h are loosely stacked on top of each o t h e r to form t h r e e - d i m e n s i o n a l crystals. M a t e r i a l s of this s t r u c t u r e are, a m o n g others, carbon, a n t i m o n y and bismuth, the d i - and trihalides, the t r a n s i t i o n metal dic h a l c o g e n i d e s and the III-VI and IV-VI compounds. An i n t e r e s t i n g phenomenon, w h i c h o f t e n o c c u r s in substances w i t h this type of structure, is that of p o l y t y p i s m . T h e y crystallize into m o r e than one m o d i f i c a t i o n s w i t h the same c h e m i c a l comp o s i t i o n but d i f f e r e n t number and m a n n e r of s t a c k i n g layers in the unit cell. This is a n i n d i c a t i o n that their s t a c k i n g fault e n e r g y is small, t h e r e f o r e d i s l o c a t i o n s formed in these m a t e r i a l s should be w i d e l y s e p a r a t e d into partials. This is a s t u a l l y the c a s e , and the p a r t i a l s a r e forming d i f f e r e n t types of the
233
234
J . G . ANTONOPOULOS
Vol. 14, No. 2
so-called "dislocation ribbons", w h i c h a r e m a i n l y c k i n g fault e n e r g y d e t e r m i n a t i o n (2).
used for sta-
In this p a p e r we a d v a n c e a p o s s i b l e e x p l a n a t i o n c o n c e r n i n g the f o r m a t i o n of s i x - f o l d ribbons, r e f e r i n g to the specific ex a m p l e s o b s e r v e d in GaSe s p e c i m e n s . This e x p l a n a t i o n is based on the a s s u m p t i o n of s u p e r p o s i t i o n of d i s l o c a t i o n s l y i n g in succ e s s i v e c layers. Experimental
Results
D i f f e r e n t types of d i s l o c a t i o n r i b b o n s h a v e b e e n reported in the literature, from i s o l a t e d single r i b b o n s (3,4)up to ten-fold o n e s (5).To our knowledge, in a m u l t i - r i b b o n case, the partials w h i c h a r e g r o u p e d to form the r i b b o n h a v e not the same B u r g e r s vectors, w i t h the e x e p t i o n for the c a s e of three fold ribbons,
(a)
(b)
~0
B
(c)
(d) FIG.
I
(a), (b) and (c) a r e b r i g h t field i m a g e s of the same area under d i f f e r e n t d i f f r a c t i n g c o n d i t i o n s , s h o w n in the insets. (d) is a c o r r e c t l y o r i e n t e d diagran~) e x p l a i n i n g the n o t a t i o n used in the text. which result planes.
from the f u s i o n of two
single
ribbons
in s u c c e s s i v e
G a S e is a h e x a g o n a l l a y e r e d s t r u c t u r e m a t e r i a l and d i s l o c a t i o n c o n f i g u r a t i o n s in it have a l r e a d y b e e n r e p o r t e d (6). F i g u re I shows b r i g h t field i m a g e s of p a r a l l e l d i s l o c a t i o n lines of
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235
the same a r e a in a G a S e s p e c i m e n . T h e i n s e t s a r e the c o r r e s p o n ding diffraction pattern, correctly oriented. The curvature of the l i n e s in some r e g i o n s a r e d u e to the p r e s e n c e of d i r t o n the s u r f a c e of the s p e c i m e n , w h i c h i n f l u e n c e s t h e i r s t r e s s - f i e l d . D i s l o c a t i o n s 2 , 9 , 1 1 , 1 4 a r e v i s i b l e in (a)_and (c) a n d i n v i s i b l e in (b), w h e r e ~ = I~I0. B e c a u s e of the g.b = 0 c r i t e r i o n , I t h e s e a r e e d g e p a r t i a l s w i t h B u r g e r s v e c t o r b = + C o = + ~ [1070]. The r e m a i n i n g d i s l o c a t i o n s a r e v i s i b l e in (a) a n d (b) a n d i n v i s i b l e in (c), w h e r e ~ = 5 1 1 0 . T h e r e f o r e , t h e s e a r e m i x e d p a r t i a l I d i s l o c a t i o n s w i t h 5 = + A o = + ~ [ 0 1 ~ 0 ] . D i s l o c a t i o n s 12 a n d 13 , w h i c h h a v e the same B u r g e r s vector, lie o n d i f f e r e n t p l a n e s sep a r a t e d b y a d i s t a n c e v e r y l i k e l y to be e q u a l to the t h i c k n e s s of o n e G a S e l a y e r (6). T h e i n t e r e s t i n g f e a t u r e in Fig. I is the g r o u p of dislocatio n s 3 , 4 , 5 , 6 , 7 , 8 . T h e y a l l p a r t i a l s w i t h the same B u r g e r s v e c t o r . T h e r e f o r e , w e c a n say t h a t t h e y f o r m a six fold d i s l o c a t i o n ribb o n . O f c o u r s e , w e c a n t h i n k of two s u c c e s s i v e three fold ribbons. The i n t e r p r e t a t i o n c o u l d be c o r r e c t , b u t the d i s t a n c e between a l l p a r t i a l s a r e a b s o l u t e l y equal, w h i c h w o u l d n o t be the c a s e if t h e r e w e r e two s e p a r a t e r i b b o n s . I n the next, a m o d e l for a six fold r i b b o n w i l l be d i s c u s s e d .
Discussion In the h e x a g o n a l s t r u c t u r e , d i s s o c i a t i o n in s u c c e s s i v e c p l a n e s t a k e s p l a c e in a d i f f e r e n t s u c c e s s i o n . If in o n e plane FIG. 0 Ao
.IL. oC
Oo
oC
O aB
edge
.L
aU Ca O So
A p o s s i b l e i n t e r p r e t a t i o n of the p a r t i a l s of Fig. 1 . T h e p r o p o s e d a r r a n g e m e n t of d i s l o c a t i o n s in o r d e r to f o r m s i x - f o l d ribbon is s h o w n w i t h i n the s o l i d lines.
portisis
J" oC
O oB
2
Ca
O Ba
O oA
six - fold
- J" aC
O Aa
.l. aC
O Aa
O Aa
I aC
the d i s s o c i a t i o n p r o d u c e p o s i t i v e s t a c k i n g f a u l t b e t w e e n the p a r tials, the d i s s o c i a t i o n in the n e x t w i l l p r o d u c e a n e g a t i v e stac k i n g f a u l t . A l s o , s i n g l e r i b b o n s in two p l a n e s s e p a r a t e d by a d i s t a n c e ( 2 n + I ) c / 2 c a n c o m b i n e to p r o d u c e m o r e c o m p l e x r i b b o n s . Based o n t h e s e ideas, w e t h o u g h t of the f o l l o w i n g r e a c t i o n s to take p l a c e in s u c c e s s i v e c p l a n e s . AC CB BC CB BA
--~' --~ --~ -~ -~
Ao oB BO OB Bo
+ + + + +
aC Co oC Co oA
(Positive (Negative (Positive (Negative (Positive
fault) " ) " ) " ) " )
236
J.G. A N T O N O P O U L O S
Vol. 14, No. 2
In Fig. 2, w i t h i n the solid lines, the a r r a n g e m e n t of the partial d i s l o c a t i o n s proposed for the model is shown. The two vertic a l l y lined dislocations, w i t h Burgers vectors + Co and + Bo, can combine, since these a t t r a c t each other , to-produce _+-oA a c c o r d i n g to the reaction. Co + Bo ~
oA
or
oC + oB - - ÷ Ao
Then, the group a p p e a r s with all six d i s l o c a t i o n s having the same Burgers vector + oA and forming a six-fold ribbon. The rest of the d i s l o c a t i o n s of Fig. I are also d r a w n in Fig. 2. Distances b e t w e e n d i s l o c a t i o n s are not in scale and the d i s t r i b u t i o n in d e p t h is rather speculative, but this is inevitable, because there is no s t e r e o - p h o t o g r a p h of this p a r t i c u l a r region. Such photographs, a v a i l a b l e for other regions, have shown that the d i s l o c a t i o n s are in d i f f e r e n t depths. In conclusion, it was shown that six fold ribbons, with all partial d i s l o c a t i o n s having the same Burgers vectors, can be formed as a result of s u p e r p o s i t i o n of d i s l o c a t i o n s lying in succ e s s i v e c planes. Ac k n o w l e d @ e m e n t s The a u t h o r wishes to a c k n o w l e d g e stions of Prof. S. Amelinckx.
the d i s c u s s i o n s
and
sugge-
References I. 2. 3. 4. 5. 6.
"Physics and C h e m i s t r y of M a t e r i a l s w i t h L a y e r e d Structures", Vol. I-5, D. Reidel Publish. Co, Dordrech, Holland (1976-77). S.Amelinckx, "The D i r e c t O b s e r v a t i o n s of Dislocations", Acad. Press, New York (1964). P . D e l a v i g n e t t e and S.Amelinckx, J.Nucl. Mater., 5, 17 (1962). P . G r i g o r i a d i s and J.Stoemenos, J.Mat. Science, ~ . 483 (1978). E.Ruedl, P . D e l a v i g n e t t e and S.Amelinckx, Phys. Shat. Sol., 2_88, 305 (1968). Z.S.Basinski, D.B.Dovel and E.Mooser, J.Appl. Phys. 3_44, 469 (1963).
A M O D E L FOR S I X - F O L D R I B B O N IN L A Y E R E D S T R U C T U R E M A T E R I A L S J.G. A n t o n o p o u l o s Physics Department, U n i v e r s i t y of T h e s s a l o n i k i Thessa loniki, Greece
(Received December 1, 1978; Communicated by S. Amelinckx)
ABSTRACT Based on a c o m b i n a t i o n of B u r g e r s v e c t o r s of d i s l o c a tions lying in s u c c e s s i v e c planes of a layered struc t u r e material, a model for six fold r i b b o n f o r m a t i o n is p r e s e n t e d . Partial d i s l o c a t i o n s a p p e a r to have the same B u r g e r s v e c t o r s Such r i b b o n s were o b s e r v e d in GaSe.
Introduction
Layered structure materials have received considerable attention
in r e c e n t years, m a i n l y b e c a u s e of their a n i s o t r o p i c physical p r o p e r t i e s related to their s t r u c t u r a l a n i s t o t r o p y (I). T h e s e m a t e r i a l s c a n be d e s c r i b e d as solids c o n t a i n i n g m o l e c u l e s w h i c h in two d i m e n s i o n s extend to i n f i n i t y and w h i c h are loosely stacked on top of each o t h e r to form t h r e e - d i m e n s i o n a l crystals. M a t e r i a l s of this s t r u c t u r e are, a m o n g others, carbon, a n t i m o n y and bismuth, the d i - and trihalides, the t r a n s i t i o n metal dic h a l c o g e n i d e s and the III-VI and IV-VI compounds. An i n t e r e s t i n g phenomenon, w h i c h o f t e n o c c u r s in substances w i t h this type of structure, is that of p o l y t y p i s m . T h e y crystallize into m o r e than one m o d i f i c a t i o n s w i t h the same c h e m i c a l comp o s i t i o n but d i f f e r e n t number and m a n n e r of s t a c k i n g layers in the unit cell. This is a n i n d i c a t i o n that their s t a c k i n g fault e n e r g y is small, t h e r e f o r e d i s l o c a t i o n s formed in these m a t e r i a l s should be w i d e l y s e p a r a t e d into partials. This is a s t u a l l y the c a s e , and the p a r t i a l s a r e forming d i f f e r e n t types of the
233
234
J . G . ANTONOPOULOS
Vol. 14, No. 2
so-called "dislocation ribbons", w h i c h a r e m a i n l y c k i n g fault e n e r g y d e t e r m i n a t i o n (2).
used for sta-
In this p a p e r we a d v a n c e a p o s s i b l e e x p l a n a t i o n c o n c e r n i n g the f o r m a t i o n of s i x - f o l d ribbons, r e f e r i n g to the specific ex a m p l e s o b s e r v e d in GaSe s p e c i m e n s . This e x p l a n a t i o n is based on the a s s u m p t i o n of s u p e r p o s i t i o n of d i s l o c a t i o n s l y i n g in succ e s s i v e c layers. Experimental
Results
D i f f e r e n t types of d i s l o c a t i o n r i b b o n s h a v e b e e n reported in the literature, from i s o l a t e d single r i b b o n s (3,4)up to ten-fold o n e s (5).To our knowledge, in a m u l t i - r i b b o n case, the partials w h i c h a r e g r o u p e d to form the r i b b o n h a v e not the same B u r g e r s vectors, w i t h the e x e p t i o n for the c a s e of three fold ribbons,
(a)
(b)
~0
B
(c)
(d) FIG.
I
(a), (b) and (c) a r e b r i g h t field i m a g e s of the same area under d i f f e r e n t d i f f r a c t i n g c o n d i t i o n s , s h o w n in the insets. (d) is a c o r r e c t l y o r i e n t e d diagran~) e x p l a i n i n g the n o t a t i o n used in the text. which result planes.
from the f u s i o n of two
single
ribbons
in s u c c e s s i v e
G a S e is a h e x a g o n a l l a y e r e d s t r u c t u r e m a t e r i a l and d i s l o c a t i o n c o n f i g u r a t i o n s in it have a l r e a d y b e e n r e p o r t e d (6). F i g u re I shows b r i g h t field i m a g e s of p a r a l l e l d i s l o c a t i o n lines of
Vol. 14, No. 2
LAYERED STRUCTURE MATERIALS
235
the same a r e a in a G a S e s p e c i m e n . T h e i n s e t s a r e the c o r r e s p o n ding diffraction pattern, correctly oriented. The curvature of the l i n e s in some r e g i o n s a r e d u e to the p r e s e n c e of d i r t o n the s u r f a c e of the s p e c i m e n , w h i c h i n f l u e n c e s t h e i r s t r e s s - f i e l d . D i s l o c a t i o n s 2 , 9 , 1 1 , 1 4 a r e v i s i b l e in (a)_and (c) a n d i n v i s i b l e in (b), w h e r e ~ = I~I0. B e c a u s e of the g.b = 0 c r i t e r i o n , I t h e s e a r e e d g e p a r t i a l s w i t h B u r g e r s v e c t o r b = + C o = + ~ [1070]. The r e m a i n i n g d i s l o c a t i o n s a r e v i s i b l e in (a) a n d (b) a n d i n v i s i b l e in (c), w h e r e ~ = 5 1 1 0 . T h e r e f o r e , t h e s e a r e m i x e d p a r t i a l I d i s l o c a t i o n s w i t h 5 = + A o = + ~ [ 0 1 ~ 0 ] . D i s l o c a t i o n s 12 a n d 13 , w h i c h h a v e the same B u r g e r s vector, lie o n d i f f e r e n t p l a n e s sep a r a t e d b y a d i s t a n c e v e r y l i k e l y to be e q u a l to the t h i c k n e s s of o n e G a S e l a y e r (6). T h e i n t e r e s t i n g f e a t u r e in Fig. I is the g r o u p of dislocatio n s 3 , 4 , 5 , 6 , 7 , 8 . T h e y a l l p a r t i a l s w i t h the same B u r g e r s v e c t o r . T h e r e f o r e , w e c a n say t h a t t h e y f o r m a six fold d i s l o c a t i o n ribb o n . O f c o u r s e , w e c a n t h i n k of two s u c c e s s i v e three fold ribbons. The i n t e r p r e t a t i o n c o u l d be c o r r e c t , b u t the d i s t a n c e between a l l p a r t i a l s a r e a b s o l u t e l y equal, w h i c h w o u l d n o t be the c a s e if t h e r e w e r e two s e p a r a t e r i b b o n s . I n the next, a m o d e l for a six fold r i b b o n w i l l be d i s c u s s e d .
Discussion In the h e x a g o n a l s t r u c t u r e , d i s s o c i a t i o n in s u c c e s s i v e c p l a n e s t a k e s p l a c e in a d i f f e r e n t s u c c e s s i o n . If in o n e plane FIG. 0 Ao
.IL. oC
Oo
oC
O aB
edge
.L
aU Ca O So
A p o s s i b l e i n t e r p r e t a t i o n of the p a r t i a l s of Fig. 1 . T h e p r o p o s e d a r r a n g e m e n t of d i s l o c a t i o n s in o r d e r to f o r m s i x - f o l d ribbon is s h o w n w i t h i n the s o l i d lines.
portisis
J" oC
O oB
2
Ca
O Ba
O oA
six - fold
- J" aC
O Aa
.l. aC
O Aa
O Aa
I aC
the d i s s o c i a t i o n p r o d u c e p o s i t i v e s t a c k i n g f a u l t b e t w e e n the p a r tials, the d i s s o c i a t i o n in the n e x t w i l l p r o d u c e a n e g a t i v e stac k i n g f a u l t . A l s o , s i n g l e r i b b o n s in two p l a n e s s e p a r a t e d by a d i s t a n c e ( 2 n + I ) c / 2 c a n c o m b i n e to p r o d u c e m o r e c o m p l e x r i b b o n s . Based o n t h e s e ideas, w e t h o u g h t of the f o l l o w i n g r e a c t i o n s to take p l a c e in s u c c e s s i v e c p l a n e s . AC CB BC CB BA
--~' --~ --~ -~ -~
Ao oB BO OB Bo
+ + + + +
aC Co oC Co oA
(Positive (Negative (Positive (Negative (Positive
fault) " ) " ) " ) " )
236
J.G. A N T O N O P O U L O S
Vol. 14, No. 2
In Fig. 2, w i t h i n the solid lines, the a r r a n g e m e n t of the partial d i s l o c a t i o n s proposed for the model is shown. The two vertic a l l y lined dislocations, w i t h Burgers vectors + Co and + Bo, can combine, since these a t t r a c t each other , to-produce _+-oA a c c o r d i n g to the reaction. Co + Bo ~
oA
or
oC + oB - - ÷ Ao
Then, the group a p p e a r s with all six d i s l o c a t i o n s having the same Burgers vector + oA and forming a six-fold ribbon. The rest of the d i s l o c a t i o n s of Fig. I are also d r a w n in Fig. 2. Distances b e t w e e n d i s l o c a t i o n s are not in scale and the d i s t r i b u t i o n in d e p t h is rather speculative, but this is inevitable, because there is no s t e r e o - p h o t o g r a p h of this p a r t i c u l a r region. Such photographs, a v a i l a b l e for other regions, have shown that the d i s l o c a t i o n s are in d i f f e r e n t depths. In conclusion, it was shown that six fold ribbons, with all partial d i s l o c a t i o n s having the same Burgers vectors, can be formed as a result of s u p e r p o s i t i o n of d i s l o c a t i o n s lying in succ e s s i v e c planes. Ac k n o w l e d @ e m e n t s The a u t h o r wishes to a c k n o w l e d g e stions of Prof. S. Amelinckx.
the d i s c u s s i o n s
and
sugge-
References I. 2. 3. 4. 5. 6.
"Physics and C h e m i s t r y of M a t e r i a l s w i t h L a y e r e d Structures", Vol. I-5, D. Reidel Publish. Co, Dordrech, Holland (1976-77). S.Amelinckx, "The D i r e c t O b s e r v a t i o n s of Dislocations", Acad. Press, New York (1964). P . D e l a v i g n e t t e and S.Amelinckx, J.Nucl. Mater., 5, 17 (1962). P . G r i g o r i a d i s and J.Stoemenos, J.Mat. Science, ~ . 483 (1978). E.Ruedl, P . D e l a v i g n e t t e and S.Amelinckx, Phys. Shat. Sol., 2_88, 305 (1968). Z.S.Basinski, D.B.Dovel and E.Mooser, J.Appl. Phys. 3_44, 469 (1963).