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REARRANGEMENTS IN THE SYSTEM OF GRAIN BOUNDARY DISLOCATIONS AND MIGRATION OF
GRAIN BOUNDARIES
M. Imayev, L. Fionova
To cite this version:
M. Imayev, L. Fionova. REARRANGEMENTS IN THE SYSTEM OF GRAIN BOUNDARY DIS-
LOCATIONS AND MIGRATION OF GRAIN BOUNDARIES. Journal de Physique Colloques, 1990,
51 (C1), pp.C1-513-C1-517. �10.1051/jphyscol:1990180�. �jpa-00230348�
REARRANGEMENTS IN THE SYSTEM OF GRAIN BOUNDARY DISLOCATIONS AND MIGRATION OF GRAIN BOUNDARIES
M.F. IMAYEV and L.K. FIONOVA'
Institute of Metals Superplasticity Problems, URSS Academy of Sciences, frfa 450001, U.R.S.S.
Institute for Microelectronics Technology, URSS Academy of Sciences, Moscow-Chernogolovka 142432, U.R.S.S.
A b s t r a c t
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The d i s l o c a t i o n s t r u c t u r e and b e h a v i o u r o f g r a i n b o u n d a r i e s i n a low s t r a i n e d n i c k e l a l l o y u n d e r s l o w and f a s t c o n t i n u o u s h e a t i n g was s t u d i e d . It i s e s t a b l i s h e d t h a t t h e p r o c e s s e s o f g r a i n boundary m i g r a t i o n a n d d i s s o c i a t i o n o f g r a i n b o u n d a r i e s s t a r t ( o n a m a c r o s c a l e ) n o t w i t h t h e d i s a p p e a r a n c e o f e l e c t r o n c ~ i c r o - s c o p i c c o n t r a s t due t o e x t r i n s i c g r a i n boundary d i s l o c a t i o n s , b u t a t h i g h e r tempe- r a t u r e s c o r r e s p o n d i n g t o a c t i v e r e a r r a n g e m e n t s o f l a t t i c e d i s l o c a t i o n s w i t h i n t h s g r a i n volume. B o u n d a r i e s o f a n o m a l o u s l y c o a r s e g r a i n s a r e c h a r a c t e r i z e d by an i n t a n - s i v e t w i n n i n g d u r i n g t h e i r motion and t h e m o t i v e f o r s e o f boundary d i s s o c i a t i o n i s a s s o c i a t e d w i t h t h e p r e s e n c e o f t h e p r o d u c t s o f d i s s o c i a t i o n o f t h e e x t r i n s i c g r a i n boundary d i s l o c a t i o n s i n t h e boundary. kJith t h e growth o f t h e r a t e o f c o n t i n u o u s h e a t i n g t h e p r o c e s s e s o f d i s l o c a t i o n r e a r r a n g e m e n t s b o t h i n t h e g r a i n b o u n d a r i e s and w i t h i n t h e g r a i n s would s h i f t i n t h e h i g h - t e m p e r a t u r e a r e a and t h e anomalous g r a i n growLh i s s u p p r e s s e d .1
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INTRODUCTIONMhen low s t r a i n e d p o l y c r y s t a l s a r e h e a t e d t h e y d e m o n s t r a t e an anomalous growth o f g r a i n s which a t t r i b u t e d i n l i t e r a t u r e w i t h t h e g r a d i e n t o f t h e volume d e n s i t y o f l a t t i c e d i s l o c n - t i o n s (LD) /l/, a s w e l l a s t o t h e h i g h m o b i l i t y o f g r a i n b o u n d a r i e s d u r i n g t h e a b s o r p t i m o f e x t r i n s i c g r a i n boundary d i s l o c a t i o n s (EGBO) / 2 / . The growth o f t h e r a t e o f c o n t i n u o u s h e a t i n g s t o p s t h e anomalous g r a i n growth a f t e r c r y t i c a l s t r a i n / 3 / . A t t h e same t i m e t h e s t r u c t u r a l r e a s o n s f o r - t h i s phenonlenon a r e n o t c l e a r . The i n v e s t i g a t i o n o f t h e e v o l u t i o n o f d i s l o c a t i o n s t r u c t u r e w i t h i n t h e g r a i n s and i n g r a i n b o u n d a r i e s would b e h e l p f u l i n t h e u n d e r s t a n d i n g o f p r o c e s s e s which a r e e f f e c t i v e u n d e r s u c h h e a t t r e a t m e n t s . T h a t is why t h i s p a p e r i s c o n c e r n e d w i t h t h e i n v e s t i g a t i o n o f t h e v a r i a t i o n s o f t h e d e n s i t y o f LD and EGBD a s w e l l a s b e h a v i o u r o f g r a i n b o u n d a r i e s d e p e n d i n g on t h e t e m p e r a t u r e - t i m e c o n d i t i o n s o f h e a t i n g .
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EXPERIMENTAL PROCEDURE AND MATERIALS.A n i c k e l a l l o y of t h e f o l l o w i n y ! c o n p o s i t i o n : 0.01% C , 0.10% Mn, 0,63% S i , 0.003% P ,
0.003% S, 21.53% C r , 0,3S% F e , 0,06% A l , 0,005% T i , b a l s n s e N i was u s o d . 100 mm l o n g s p e c i - mens were c u t o u t o f a w i r e deformed by d r a w i n g from t h e d i a m e t e r o f 6 . 2 mm t o t h e d i a m e t e r - o f 4.5 mm a t room t e m p e r a t u r e . The i n i t i a l r e c r y s t a l l i z e d s t r u c t u r ~ w i t h a mean g r a i n s i z e
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o f 5 pm was o b t a i n e d by t h e 2 h o u r a n n e a l i n g a t 760°C and g u e n c h i n g i n w a t e r . To o b t a i n
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990180
Cl-514 COLLOQUE DE PHYSIQUE
p r e l i m i n a r y cold-working, t h e specimens were 5% t e n s i x ? s t r a i n e d a t room temperature.
Then t h e specimens were subjected t o continuous heatings up t o a v a r i e t y o f temperatures a t two r a t e s . Slow h e a t i n g a t t h e r a t e o f 0.2 O/s was e f f e c t u a t e d w i t h t h e furnace, f a s t h e a t i n g a t t h e r a t e o f 500°/s was conducted on s p e c i a l u n i t w i t h passing c u r r e n t . A f t e r t h o r e q u i r e d temperature was achieved a t a c e r t a i n r a t e o f heating, t h e specimens were immedia- t e l y quenched i n t h e 10% water s o l u t i o n o f NaCl w i t h o u t any i s o t h e r m i c h o l d i n g .
M i c r o s t r u c t u r e was s t u d i e d a f t e r t h e e l e c t r o l y t i c e t c h i n g i n t h e 10% s o l u t i o n o f s u l p h u r i c a s i d i n e t h a n o l and a d d i t i o n a l chemical e t c h i n g i n t h e a s i d s o l u t i o n : 30 m1 n i t r i c asid, 28 m 1 h y d r o c h l o r i c a c i d , 8 m1 orthophosphoric a c i d and 40 m 1 a c e t i c a c i d . Chemical e t c h i n g was used f o r a more p r e c i s e determination o f t w i n boundaries s i n s e a f t e r t h e e l e c t r o l y t i c e t c h i n g they were almost i n v i s i b l e . While counting
d
using t h e method o f secants 200 o r more g r a i n were taken.The d e n s i t y o f LD was assessed by means o f t h e method o f secants using e l e c t r o n microscopy and t h e d e n s i t y o f EGBD was determined by t h e r a t i o o f t h e number o f d i s l o c a t i o n s i n t h e boundary t o t h e , l e n g t h o f t h e g i v e n p o r t i o n o f t h e boundary.
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RESULTSM e t a m h y . The dependence o f
d
( b o t h w i t h and w i t h o u t t w i n boundaries) on t h e tempe- r a t u r e o f low h e a t i n g i s shown i n F i g . 1.0 " m 900 Ilum IIW
t , O c
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F i g . 1
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Dependence o f t h e mean g r a i n s i z ed
on t h e temperaturet
o f low continuous hea- t i n g : 1 , 2 - w i t h o u t t w i n boundaries; 3,4 - w i t h g r a i n boundaries; 1,3-
5% pre- s t r a i n i n g ; 2,4 - nondeformed specimens.I n t h e deformed and nondeformed s t a t e s t h e g r a i n growth becomes pronounced above 800°C. I n nondeformed specimens, no matter what i s t h e method o f counting used, a normal g r a i n growth i s observed, i . e . t h e r e a r e no g r a i n s w i t h p r e f e r e n c i a l growth c o n d i t i o n s . I n deformed spe- cimens when t w i n boundaries are taken i n t o account, no anomalous g r a i n growth takes p l a s e and
d
c o i n s i d e i n b o t h s t a t e s . At t h e same t i m e , whend
i s counted w i t h o u t t h e considera- t i o n o f t w i n boundaries, p r e f e r e n t i a l growth o f c e r t a i n g r a i n s which w i t h t h e r i s e o f tem- p e r a t u r e grow t o anomalously l a r g e s i z e s becomes pronounced i n t h e deformed s t a t e above 830°C. At t h e 950°C t h e r e a r e p r a c t i c a l l y no f i n e g r a i n s l e f t i n t h e s t r u c t u r e o f deformed specimens. Note t h a t according t o p r e l i m i n a r y experiments t h e l a r g e s t g r a i n s a t slow-
h e a t i n g w i l l grow a f t e r t h e 5% s t r a i n , i . e . t h i s s t r a i n l e v e l i s c r y t i c a l . At llOO°C
d
i n b o t h s t a t e s become equal.The anomalous g r a i n growth i s accompanied by an abrupt growth o f t h e f r a c t i o n o f t w i n boun- d a r i e s ( g ) i n t h e o v e r - a l l l e n g t h o f boundaries ( F i g . 2 ) . T h i s parameter grows up t o 950 'C and t h e n decreases w i t h f u r t h e r heating. At llOO°C
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8 i n b o t h s t a t e s a r e equal.Under f a s t heating, k i n both s t a t e s s t a r t growing a t 920°C and c o i n c i d e throughout t h e temperature i n t e r v a l up t o t h e m e l t i n g p o i n t . I n t h e deformed specimens t h e anomalous g r a i n growth i s suppressed and g r a i n s grow normally.
E l e c t r o n microscopy. I n t h e i n i t i a l s t a t e , b e f o r e deformation, t h e r e are p r a c t i c a l l y no -daries. After t h e 5% p l a s t i c deformation EGBD a r e found p r a c t i c a l l y i n
a l l boundaries ( F i g . 3). Under slow h e a t i n g t h e density o f L0 i n t h e f i n e - g r a i n e d deformed m a t r i x s t a r t decreasing above 600°C, b u t i t s value drops most a b r u p t l y b e f o r e t h e s t a r t and
t h e d e n s i t y o f L0 i n t h e a l l o y d e c r e a s e s t o t h e i n i t i a l l e v e l which c o r r e s p o n d s t o t h e non- d e f o r ~ n s d s t a t e .
F i g . 2
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The v a r i a t i o n o f t h e f r a c t i o n o f t w i n b o u n d a r i e s (d
) i n t h e o v e r - a l l l e n g t h o f b o u n d a r i e s d e p e n d i n g on t h e t e m p e r a t u r e , t , o f t h e c o n t i n u o u s h e a t i n g : 1 , 2-
s l o w h e a t i n g ; 3 , 4-
f a s t h e a t i n g ; 1 , 3-
5% p r e - s t r a i n i n g ; 2 , 4-
nondeformed s p e c i m e n s .F i g . 3
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The s t r u c t u r e o f t h e a l l o y a f t e r t h e 5% s t r a i n i n g a t room t e m p e r a t u r e . Arrows p o i n t a t EGBD.During t h e s t u d y o f t h e a b s o r p t i o n p r o p e r t i e s o f g r a i n b o u n d a r i e s it was e s t a b l i s h e d t h a t t h e r e a r e two c h a r a c t e r i s t i c c u s p s on t h e c u r v e o f t h e t e m p e r a t u r e dependence o f t h e f r a c - t i o n o f b o u n d a r i e s (
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) w i t h o u t EGBD ( F i g . 4 ) .F i g . 4
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The d e p e n d e n c e of LD d e n s i t y ( 1 , 2 ) and f r a c t i o n o f g r a i n b o u n d a r i e s (3
) w i t h o u t EGBD ( 3 , 4 ) on t h e t e m p e r a t u r e o f c o n t i n u o u s h e a t i n g : 1 , 3-
s l o w h e a t i n g ; 2 , 4-
f a s t h e a t i n g .Cl-516 COLLOQUE DE PHYSIQUE
The d e t e r m i n a t i o n o f g r a i n m i s o r i e n t a t i o n s h a s i n d i c a t e d t h a t i n t h e a b o v e t e m p e r a t u r e i n t e r - v a l s t h e s p r e a d i n g o f t h e e l e c t r o n m i c r o s c o p i c images o f EGBO (EGBO r e l a x a t i o n ) i n t h e random and s p e c i a l g r a i n b o u n d a r i e s . Under low h e a t i n g t h e c u s p s on t h e
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(T) c u r v e a r n o b s e r v e d i n t h e t e m p e r a t u r e i n t e r v a l s o f 250-300°C and 550-600°C. I n t w i n b o u n d a r i e s t h e EGBO images a r e p r e s e r v e d u n t i l t h o s e b o u n d a r i e s a r e a b s o r b e d by t h e f r o n t o f a n o m a l o u s l y growing g r a i n s . With t h e r i s e o f t h e t e m p e r a t u r e o f h e a t i n g , e s p e c i a l l y i n t h e i n t e r v a l o f 800-850°C, t h e EGBO s y s t e m i n some o f t h e t w i n b o u n d a r i e s becomes o r d e r e d w i t h t h e q u a s i p e r i o d i c a l r o w s and n e t w o r k s b e i n g formed.F a s t h e a t i n g s h i f t s t h e p r o c e s s e s o f t h e r e a r r a n g e m e n t o f d i s l o c a t i o n s b o t h w i t h i n t h e g r a i n s and i n g r a i n b o u n d a r i e s t o t h e i n t e r v a l o f h i g h e r t e m p e r a t u r e s ( F i g . 4 ) . T h u s , t h e t e m p e r a - t u r e s o f EGBO r e l a x a t i o n s i n random b o u n d a r i e s s h i f t by 250°C on t h e a v e r a g e , w h i l e i n s p e - c i a l b o u n d a r i e s t h e s h i f t is 180-200°C. The t e m p e r a t u r e i n t e r v a l o f t h e o r d e r i n g o f t h e EGBO s y s t e m i n t w i n b o u n d a r i e s s h i f t s by 100-150°C. A t t h e same time t h e t e m p e r a t u r e i n t e r v a l o f t h e d r o p i n t h e d e n s i t y o f LD s h i f t s o n l y by 70-100°C.
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OISCUSSIONThe growth o f g r a i n s b o t h i n t h e deformed and nondeformed s t a t e s d o e s n o t s t a r t a t t h e tempe- r a t u r e s o f EGBD r e l a x a t i o n , no m a t t e r what t h e r a t e o f h e a t i n g i s ( s e e F i g . 1 , 2 , 4 )
.
A t b o t h r a t e s o f h e a t i n g t h e s t a r t o f g r a i n g r o w t h c o r r e l a t e s w i t h t h e t e m p e r a t u r e i n t e r v a l i n which a n a b r u p t d r o p o f t h e d e n s i t y o f LD w i t h i n t h e g r a i n s t a k e s p l a c e .An i n c r e a s e o f d and
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( F i g . 1 , 2 ) i s o b s e r v e d i n t h e same t e m p e r a t u r e i n t e r v a l where t h e a b r u p t d r o p of t h e d e n s i t y LD u n d e r s l o w h e a t i n g o c c u r s ( F i g . 4 ) . The r e l a x a t i o n o f EGBD i n t h e g r a i n b o u n d a r i e s s t a r t e d s e v e r a l h u n d r e d s o f d e g r e e s below t h e t e m p e r a t u r e a t which t h e r e a r r a n g e m e n t s of LD w i t h i n t h e g r a i n s was l a u n c h e d , no boundary m i g r a t i o n b e i n g o b s e r v e d . However, b a s i n g on t h e d i f f e r e n c e o f t h e t e m p e r a t u r e s o f t h e EGBD r e l a x a t i o n and boundary m i g r a t i o n , no c o n c l u s i o n c a n be drawn on t h e a b s e n c e o f any r e l a t i o n between t h e d i s l o c a t i o n r e a r r a n g e m e n t p r o c e s s e s i n g r a i n b o u n d a r i e s and m i g r a t i o n and t w i n n i n g . According t o / 4 , 5 / m i g r a t i o n and d i s s o c i a t i o n o f g r a i n b o u n d a r i e s c a n b e d e s c r i b e d by a u n i v e r s a l d i s l o c a t i o n mechanism. The f a c t t h a t n o g r a i n - b o u n d a r y d i s l o c a t i o n s r e s p o n s i b l e f o r t h e s e p r o c e s s e s were o b s e r v e d i n t h e e l e c t r o n m i c r o s c o p e may b e due t o t h e s m a l l v a l u e s o f t h e i r B u r g e r s v e c t o r s . The f o r c e s o f i n t e r a t o m i c i n t e r a c t i o n i n g r a i n b o u n d a r i e s a r e known t o b e weaker t h a n t h o s e w i t h i n t h e g r a i n / 6 , 7 / . S i n c e e v e r y s i n g l e a c t o f m i g r a t i o n must b e accompanied by a c o o p e r a - t i v e s h i f t o f a g r o u p o f a t o m s i n c l u d i n g t h e a t o m s . f r o m w i t h i n t h e g r a i n s / B / , it i s o b v i o u s t h a t a t t h e t e m p e r a t u r e s o f EGBD r e l a x a t i o n no a t o m s from w i t h i n t h e g r a i n s a r e i n v o l v e d i n t h e r e a r r a n g e m e n t o f g r a i n boundary d i s l o c a t i o n s and g r a i n boundary d i s l o c a t i o n s move t o r e - l a t i v e l y s h o r t d i s t a n c e s . The a c t u a l m i g r a t i o n i s o f a m i c r o s c o p i c c h a r a c t e r . With t h e r i s e o f t e m p e r a t u r e a t o m s w i t h i n t h e g r a i n s become more m o b i l e , which i s e x p r e s s e d i n t h e motion o f L0 ( F i g . 4 ) , and a p o s s i b i l i t y a r i s e s t o move them u s i n g t h e motion o f g r a i n boundary d i s - l o c a t i o n s . T h i s r e s u l t s i n t h e m a c r o s c o p i c development o f t h e p r o c e s s e s o f m i g r a t i o n and d i s - s o c i a t i o n o f g r a i n b o u n d a r i e s which a r e aimed a t t h e d e c r e a s e o f t h e s u r p l u s e n e r g y o f t h e b o u n d a r i e s .The p r e s e n c e o f a peak on t h e
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v s t e m p e r a t u r e c u r v e ( F i g . 2 ) i n d i c a t e s t h a t d u r i n g t h e ano- malous g r o w t h o f g r a i n s t h e p r o c e s s o f s p e c i a l g r a i n boundary d i s s o c i a t i o n accompanied w i t h t h e f o r m a t i o n o f t w i n s p r e v a i l s w h i l e a f t e r t h e g r o w t h is f i n i s h e d it i s t h e merging o f t w i n b o u n d a r i e s which p r e v a i l s .The growth o f d u r i n g h e a t i n g i s due t o t h e d i s s o c i a t i o n o f t h e b o u n d a r i e s o f anomalously c o a r s e g r a i n s . The m o t i v e f o r s e o f t w i n n i n g i n t h i s c a s e i s a s s o c i a t e d w i t h t h e p r e s e n c e o f s u r p l u s g r a i n boundary d i s l o c a t i o n s i n t h e d i s s o c i a t i n g b o u n d a r i e s , t h o s e d i s l o c a t i o n s b e i n g t h e p r o d u c t o f t h e EGBO d i s s o c i a t i o n . When t h e f i n e g r a i n e d deformed m a t r i x d i s a p p e a r s n e a r 950°C, t h e s o u r c e o f EGBD d i s a p p e a r s t o o , h e n s e , t h e m o t i v e f o r c e o f g r a i n boundary d i s s o c i a - t i o n s t a r t s d e c r e a s i n g . T h i s i s o n e o f t h e r e a s o n s f o r t h e d e c r e a s e o f
8
d u r i n g h e a t i n g a b o v e 950°C ( F i g . 2 ) . The o t h e r r e a s o n is c o n c e r n e d w i t h t h e c o m p e t i t i v e g r a i n g r o w t h a n d a b s o r p t i o n o f some_ o f t h e g r a i n s t o g e t h e r w i t h t h e t w i n s w i t h i n t h e m . The e q u a l i t y o f t h e 8 v a l u e s and a l s o d o f t h e deformed and non-deformed s t a t e a t llOO°C i n d i c a t e s t h a t a t t h i s t e m p e r a t u r e a c e r t a i n " e q u i l i b r i u m " f r a c t i o n o f t w i n s i s a v a i l a b l e .The s e n s i t i v i t y o f t h e anomalous g r a i n growth t o t h e r a t e o f h e a t i n g show t h a t d u r i n g t h e c o n t i n u o u s h e a t i n g t h e r e i s a c o m p e t i t i o n o f t w o p r o c e s s e s l e a d i n g t o t h e d e c r e a s e o f t h e s y s t e m e n e r g y : t h e m i g r a t i o n o f t h e b o u n d a r i e s o f anomalously c o a r s e g r a i n s and r e c o v e r y w i t h i n t h e g r a i n s . Under s l o w h e a t i n g t h e p r o c e s s o f thr? m i g r a t i o n o f s u c h b o u n d a r i e s i s k i - n e t i c a l l y more p r e f e r a b l e and t h e anomalous g r o w t h o f g r a i n s i s o v e r b e f o r e t h e r e c o v e r y w i t h i n t h e g r a i n s h a s been a c c o m p l i s h e d . Under f a s t h e a t i n g t h e r e c o v e r y w i t h i n t h e g r a i n s becomes more p r e f e r a b l e and it i s o v e r b e f o r e t h e anomalous g r a i n growth h a s d e v e l o p e d . S i n c e
growth o f g r a i n s i n d i c a t e s t h a t w i t h increase o f r a t e o f h e a t i n g t h e processes o f t h e r e a r - rangement o f d i s l o c a t i o n s i n g r a i n boundaries s h i f t t o -the h i h temperature i n t e r v a l more considerable t h a n those w i t h i n t h e g r a i n s . IHowever, t h i s conc?usion i s n o t d e r i v e d d i r e c t l y from Fig. 4 s i n c e t h e r e l a x a t i o n o f EG8D i n g r a i n boundaries and rearrangement o f LD w i t h i n t h e g r a i n s s t a r t s w i t h a t d i f f e r e n t temperatures and t h e motion o f g r a i n boundary d i s l o c a - t i o n s r e s p o n s i b l e f o r t h e m i g r a t i o n o f boundaries cannot be seen i n t h e e l e c t r o n microscope because o f t h e very s m a l l Burgers vectors.
5
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CONCLUSIONS1. The temperature i n t e r v a l s o f t h e EGBD r e l a x a t i o n depend on t h e t y p e o f g r a i n boundaries.
With t h e r i s e o f t h e r a t e o f continuous h e a t i n g processes o f d i s l o c a t i o n rearrangements both w i t h i n t h e g r a i n s and i n g r a i n boundaries s h i f t t o h i g h e r temperatures, i n g r a i n boundaries t h e s h i f t being more considerable t h a n w i t h i n t h e g r a i n s .
2. I n t h e Ni-20%Cr a l l o y t h e temperatures o f t h e s t a r t o f t h e processes o f m i g r a t i o n and g r a i n boundary d i s s o c i a t i o n are h i g h e r t h a n t h e temperatures o f t h e EGBO r e l a x a t i o n . These processes s t a r t a t t h e temperatures o f t h e i n t e n s i f i c a t i o n o f L0 rearrangement w i t h i n t h e g r a i n s .
3. The anomalous g r a i n growth d u r i n g t h e annealing o f Ni-2(%Cr a f t e r c r y t i c a l s t r a i n i s accompanied w i t h t h e growth of t h e f r a c t i o n o f t w i n s i n t h e p o l y c r y s t a l . I t i s e s t a b l i s h e d t h a t t h i s i s connected w i t h t h e v a r i a t i o n o f t h e s t r u c t u r e and p r o p e r t i e s o f g r a i n bounda- r i e s due t o t h e LD trapped by them.
REFERENCES
/l/ G o r e l i k , S. S., R e c r y s t a l l i z a t i o n o f Metals and A l l o v s . Moscow: M e t a l l u r g i a Publ. (1978) ( i n Russian).
/2/ V a l i e v , R. Z., Gertsman, V. Yu., and Kaibyshev, 0. A. S c r i p t a Met. 18 (1984) 639.
/3/ Bodiako, M. N., Astapchik, S. A., Jaroshevitch, G. \ I . , Thermokineti= o f R e c r y s t a l l i z a - t i o n . Minsk: Nauka i Tekhnika Publ. (1968) ( i n Russian).
/4/ Rae, C. M. F. and Smith, D. A., P h i l . Mag. 4 1 (1980) 477.
/ 5 / And~eeva, A . V., Perevezentsev, V. N.., F i o n G a , L. K., and Shcherban, M. Yu., Poverkhnost N S (1982) 116 ( i n Russian).
/ 6 / Hashimoto, M., I s h i d a , Y., Yamamoto, R., and Doyama, D., Acta M e t a l l . 29 (1981) 617.
/7/ Imayev, M, F.. F i z i k a M e t a l l o v i Metallovedenie (FMM) 64, N 4 (1987) 8 z ( i n Russian) /8/ Bishop, G. H., Harrison, R. J . , Kwok, T., and Yip, S., J. Appl. Phys. 53 (1982) 5609.