RECOVERY AND DIFFUSION ON GRAIN BOUNDARIES IN ALUMINIUM

(1)

HAL Id: jpa-00230355

https://hal.archives-ouvertes.fr/jpa-00230355

Submitted on 1 Jan 1990

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

RECOVERY AND DIFFUSION ON GRAIN BOUNDARIES IN ALUMINIUM

J. Kwieci�ski, J. Wyrżykowski

To cite this version:

J. Kwieci�ski, J. Wyrżykowski. RECOVERY AND DIFFUSION ON GRAIN BOUND- ARIES IN ALUMINIUM. Journal de Physique Colloques, 1990, 51 (C1), pp.C1-557-C1-562.

�10.1051/jphyscol:1990187�. �jpa-00230355�

(2)

RECOVERY AND DIFFUSION ON GRAIN BOUNDARIES IN ALUMINIUM

J. K W I E C I ~ S K I and J. W. W Y R ~ Y K O W S K I

Institute of Materials Science and Engineering, Warsaw University o f Technology, Narbutta 85, 02-524 Warsaw, Poland

A b s t r a c t

-

I n v e s t i g a t i o n s of r e c o v e r y and d i f f u s i o n on G r a i n Boundari es C GB> i n p01 y c r y s t a l l i n e a1 umi n i um a t l ow t e m p e r a t u r e s w e r e performed u s i n g t h e d i s l o c a t i o n s p r e a d i n g method. The k i n e t i c s of i s o t h e r m a l GB r e c o v e r y was d e t e r m i n e d . The r e s u l t s o b t a i n e d show t h a t t h e l o g a r i t h m i c l a w of r e c o v e r y o b t a i n s , which i s c h a r a c t e r i s t i c s of r e c o v e r y of mechanical p r o p e r t i e s . The d i s t r i b u t i o n f u n c t i o n s of GB d i f f u s i v i t y w e r e d e t e r m i n e d and t h e y s e r v e d , a s a b a s i s f o r c a l c u l a t i n g t h e p a r a m e t e r s of GB s e l f -di f f u s i on : p r e e x p o n e n t i a 1 f a c t o r and a c t i v a t i o n e n e r g y . I t was f o u n d t h a t GB s e l f - d i f f u s i o n i s t h e r a t e c o n t r o l l i n g f a c t o r of t h e r e c o v e r y p r o c e s s . The e f f e c t of thermp-mechanical t r e a t m e n t on b o t h t h e k i n e t i c s of GB r e c o v e r y and t h e d i s t r i b u t i o n s o f GB d i f f u s i o n p a r a m e t e r s w a s p r e s e n t e d . The d i s t r i b u t i o n s o f GB d i f f u s i o n p a r a m e t e r s c a n b e u s e d a s GB c h a r a c t e r i s t i c s of p o l y c r y s t a l .

l. I NTRODUCTI ON

Recovery of t h e m i c r o s t r u c t u r e of p01 y c r y s t a l s , a p a r t f r o m i n t r a - g r a i n mechanisms, c a n a l s o t a k e p l a c e by means of a n n i h i l a t i o n o f p o i n t d e f e c t s C l 1 and d i s l o c a t i o n s C21 o n G r a i n B o u n d a r i e s CGBs3

,

a s w e l l a s by means of o r d e r i n g of GB s t r u c t u r e C31. A n n i h i l a t i o n i n GBs which l e a d s t o t h e d e c r e a s e of t h e t o t a l d e n s i t y of d e f e c t s i s a t h e r m a l l y a c t i v a t e d mechanism c o n t r o l l e d by g r a i n boundary d i f f u s i o n .

The method t h a t was employed i n t h e p r e s e n t work c o n s i s t e d i n s t u d y i n g GB d i s l o c a t i o n s p r e a d i n g . I t a l l o w s t o d e t e r m i n e t h e k i n e t i c s of r e c o v e r y on G B s i n p o l y c r y s t a l s C21 and t o s t u d y GB d i f f u s i o n C4.51. I f a s l i d i n g l a t t i c e d i s l o c a t i o n e n c o u n t e r s a GB, t h e n t h e i r i n t e r a c t i o n r e s u l t s i n a f o r m a t i o n of t h e s o - c a l l e d Trapped L a t t i c e D i s l o c a t i o n C TLD3. A t e l e v a t e d t e m p e r a t u r e s Cwhich i n t h e c a s e of aluminium i s a l s o room t e m p e r a t u r e , as i t e x c e e d s 0.3 Tm3 TLDs undergo d i s s o c i a t i o n i n 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 CEGB-3 and as a r e s u l t t h e s t r e s s f i e l d s of TLDs a r e r e l a x e d w i t h t h e k i n e t i c s d e p e n d e n t on t e m p e r a t u r e and t i m e C4-91. The p r o c e s s d u r i n g which t h e d i s s o c i a t i o n p r o d u c t s s p r e a d o u t a l o n g GB i s u s u a l l y c a l l e d EGBD s p r e a d i n g . Because EGBD spreading i s a mechanism by means of which GBs c a n a c t am m i c r o s t r u c t u r a l s i n k s f o r l a t t i c e d i s l o c a t i o n s , h e n c e , s p r e a d i n g i s

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990187

(3)

Cl-558 COLLOQUE DE PHYSIQUE

o n e of t h e mechanisms o f r e c o v e r y .

S p r e a d i n g of d i s l o c a t i o n s i n GBs m a n i f e s t s i t s e l f by a n i n c r e a s e of t h e w i d t h of d i s l o c a t i o n image. which c a n b e o b s e r v e d by e l e c t r o n microscopy.

when TLD c o n t r a s t f a d i n g c a n b e s e e n . The r a t e o f s p r e a d i n g depends on t h e s t r u c t u r e and chemical c o m p o s i t i o n of GBs, which means t h a t t h i s p a r a m e t e r i s a c h a r a c t e r i s t i c GB p r o p e r t y C101. D i s l o c a t i o n s p r e a d i n g i n GBs i n v o l v e s mass t r a n s p o r t a l o n g GB T6.71 a n d c a n b e u s e d t o s t u d y GB d i f f u s i o n C4.51.

I n v e s t i g a t i o n s of d i s l o c a t i o n s p r e a d i n g g i v e i n f o r m a t i o n a b o u t l o c a l d i f f u s i o n . I n t h e c a s e o f aluminium it is s p e c i a l 1 y u s e f u l b e c a u s e of a l a c k of a n a p p r o p r i a t e t r a c e r .

The a i m of t h i s p a p e r i s t o show how t h e s p r e a d i n g method c a n b e u s e d f o r d e t e r m i n i n g t h e k i n e t i c s of r e c o v e r y p r o c e s s on GBs and f o r i n v e s t i g a t i o n s o f GB s e l f -di f f u s i o n i n p01 y c r y s t a l l i n e a1 umini um.

F u r t h e r m o r e , t h e k i n e t i c s o f GB r e c o v e r y and d i s t r i b u t i o n f u n c t i o n s of GB d i f f u s i o n a l p a r a m e t e r s depend on t h e thermo-mechanical t r e a t m e n t and a s s u c h may form GB c h a r a c t e r i s t i c s f o r p o l y c r y s t a l l i n e m a t e r i a l s .

2. MATERIAL

I n v e s t i g a t i o n s w e r e performed on p01 y c r y s t a l l i n e 4 N a 1 umi n i um whose chemical c o m p o s i t i o n is p r e s e n t e d i n t a b l e I . The d e t a i l e d d e s c r i p t i o n of t h e m a t e r i a l i s p r e s e n t e d i n r e f . Cl1 l . I n o r d e r t o d e t e r m i n e t h e i n f l u e n c e of thermo-mechani c a l t r e a t m e n t on GB c h a r a c t e r i s t i c s i n p01 y c r y s t a l t h e m a t e r i a 1 w a s p r e p a r e d by means of h y d r o s t a t i c e x t r u s i o n and s u b s e q u e n t r e c r y s t a l l i z a t i o n a n n e a l i n g a t two t e m p e r a t u r e s : 878 K C s t a t e S3 and 623 K C s t a t e G> i n o n e h o u r . T h i s y i e l d e d two P o l y c r y s t a l s S and G w i t h mean g r a i n

sizes of 4 and 22 pm, r e s p e c t i v e l y . I n e a r l i e r i n v e s t i g a t i o n s i t w a s e s t a b l i s h e d t h a t P o l y c r y s t a l S i s c h a r a c t e r i z e d by a h i g h e r f r a c t i o n of GBs w i t h o r d e r e d s t r u c t u r e t h a n P o l y c r y s t a l G C101.

T a b l e I . The c h e m i c a l c o m p o s i t i o n i n 4 N Al Cp. p. m. 3

3. EXPERIMENTAL

Two methods c a n b e used t o d e t e r m i n e t h e s p r e a d i n g k i n e t i c s o f d i s l o c a t i o n s o n GBs. The f i r s t is b a s e d o n i n v e s t i g a t i o n s of s p r e a d i n g when a n n e a l i n g i s c o n d u c t e d i n i s o t h e r m a l c o n d i t i o n s and t h i s method was u s e d i n t h e p r e s e n t work. The s e c o n d i s b a s e d on i s o c h r o n a l a n n e a l i n g s a t v a r i o u s t e m p e r a t u r e s C 41

.

S p r e a d i n g was o b s e r v e d on t h i n f o i 1s b y means of t h e P h i l i p s e l e c t r o n m i c r o s c o p e w i t h a n a c c e l e r a t i n g v o l t a g e o f 100 k V . The o b s e r v a t i o n s i n Pol y c r y s t a l G were performed a t f o u r t e m p e r a t u r e s : 293, 343, 373 and 403 K, and i n Pol y c r y s t a l S a t 293, 373 and 403 K. I n t h i s work t h e e x p e r i m e n t a l p r o c e d u r e was a p p l i e d which i s d e s c r i b e d i n d e t a i l i n r e f . C21.

I n o r d e r t o c h a r a c t e r i z e t h e p r o c e s s o f r e c o v e r y on GBs i n a g i v e n s a m p l e , c h a n g e s i n t h e number of GBs w i t h and f r e e of TLDs were d e t e r m i n e d a s a f u n c t i o n o f a n n e a l i n g t i m e a t a g i v e n t e m p e r a t u r e . For e a c h m e a s u r i n g t i m e - t e m p e r a t u r e p o i n t t h e f r a c t i o n X o f GBs f r e e o f TLDs was d e t e r m i n e d a f t e r o b s e r v i n g 3 t o S f o i l s and a t l e a s t 50 b o u n d a r i e s .

R e g a r d l e s s o f t h e s p r e a d i n g model C6,7,121 t h e s p r e a d i n g t i m e t d a t t e m p e r a t u r e T i s i n v e r s e l y p r o p o r t i a n a l t o t h e GB d i f f u s i o n c o e f f i c i e n t Db

(4)

where C i s t h e n u m e r i c a l . c o n s t a n t , V is t h e a t o m i c volume, G is t h e s h e a r modulus. S m i s t h e d i s l o c a t i o n c o r e w i d t h when TLD c o n t r a s t d i s a p p e a r s d u r i n g TEM o b s e r v a t i o n s . According t o J o h a n e s s o n a n d Tholen C61 S m i s equal t o t h r e e e x t i n c t i o n d i s t a n c e s and t h i s was c o n f i r m e d by V a r i n and Romanowska C131. The v a l u e of c o n s t a n t C = 20 was assumed a f t e r r e f . C131.

Dependence of t h e f r a c t i o n of GBs w i t h TLDs C 1

- ^{X >}

on t h e t i m e of a n n e a l i n g a t 2 9 3 up t o 1 5 0 0 h f o r Pol y c r y s t a l s ^Gand S i s p r e s e n t e d a t F i g . l .

t l h l

F i g . l , 2. Curves o f i s o t h e r m a l r e c o v e r y on GBs i n p o l y c r y s t a l l i n e aluminium f o r s t a t e s S and G.

F i g . 2 p r e s e n t s d a t a f o r P o l y c r y s t a l G a t 293, 343, 373 and 403 K and f o r P o l y c r y s t a l S a t 293. 3 7 3 and 4 0 3 K , t i m e up t o 1 0 0 h. The e x p e r i m e n t a l r e s u l t s of i n v e s t i g a t i o n s c o n c e r n i n g c h a n g e s i n t h e f r a c t i o n of GBs w i t h TLDs C l - X > a s a f u n c t i o n of t i m e c a n b e a p p r o x i m a t e d b y e q u a t i o n :

where X - t h e f r a c t i o n o f GBs f r e e f r o m TLDs, t d - r e c o v e r y t i m e i n s e c o n d s , A and B

-

c o n s t a n t s f o r a g i v e n t e m p e r a t u r e . The s a m e dependence is r e g a r d e d a s c h a r a c t e r i s t i c of t h e r e c o v e r y o f mechanical p r o p e r t i e s and i t i s u s u a l 1 y c a l l e d t h e l o g a r i t h m i c r e c o v e r y l a w C141.

P o l y c r y s t a l s G and S d i f f e r d i s t i n c t l y as f a r a s t h e c o u r s e of r e c o v e r y i s concerned CFigs. 1 and 2 ) . The r a t e of r e c o v e r y i s much h i g h e r i n P o l y c r y s t a l G t h a n i n S. The r a t e of r e c o v e r y i n b o t h p o l y c r y s t a l s i n c r e a s e s markedly w i t h t e m p e r a t u r e . Recovery r a t e d e c r e a s e s w i t h i n c r e a s i n g e x t e n t of r e c o v e r y .

On t h e b a s i s of t h e o b t a i n e d d a t a t h e a c t i v a t i o n e n e r g y of t h e p r o c e s s was d e t e r m i n e d f r o m t h e e q u a t i o n :

where C - c o n s t a n t f o r a g i v e n f r a c t i o n . 8 - r e c o v e r y a c t i v a t i o n e n e r g y . P l o t t i n g t h e g r a p h I n t d v e r s u s 1/T f o r a c o n s t a n t f r a c t i o n , from t h e s l o p e of t h e l i n e t h e v a l u e s of Q c o r r e s p o n d i n g t o f r a c t i o n s f r o m t h e r a n g e 0 . 2 -

(5)

Cl-560 COLLOQUE DE PHYSIQUE

0.8 Cl-X3 c o v e r e d by t h e measurements w e r e o b t a i n e d f o r b o t h p o l y c r y s t a l s . The v a l u e s o b t a i n e d a r e p r e s e n t e d i n F i g . 3.

A c t i v a t i o n e n e r g y of r e c o v e r y Q c h a n g e s l i n e a r l y w i t h t h e f r a c t i o n of GBs w i t h TLDs Cl-XI, t h e r a n g e of t h e c h a n g e s b e i n g d i f f e r e n t f o r t h e two p01 y c r y s t a l s . The l i n e a r dependence of a c t i v a t i o n e n e r g y on t h e f r a c t i o n

60

3

E

⁵⁰

\ 9

E,

& 40

Cwhere QO

.

^b

^-

c o n s t a n t s 3 was o b s e r v e d . Such dependence i s c h a r a c t e r i s t i c of r e c o v e r y p r o c e s s e s f o r which t h e l o g a r i t h m i c l a w o b t a i n s C141. As Q i s d e p e n d e n t on r e c o v e r y f r a c t i o n , i t i s a l s o a f u n c t i o n of t i m e , which means t h a t 8 c h a n g e s d u r i n g r e c o v e r y . The Q v a l u e s o b t a i n e d r e v e a l t h a t r e c o v e r y a c t i v a t i o n e n e r g y i n c r e a s e s w i t h t h e d e g r e e t o which r e c o v e r y h a s advanced.

T h i s means t h a t r e c o v e r y , b e i n g a t h e r m a l l y a c t i v a t e d p r o c e s s , b e g i n s on more d i s o r d e r e d b o u n d a r i e s , i

.

e . on b o u n d a r i e s w i t h lower a c t i v a t P o n e n e r g y .

For e a c h ti me-temperature p o i n t t h e d i f f u s i v i t y v a l u e w a s c a l c u l a t e d u s i n g e q u a t i o n C l > . N e x t t h e d i s t r i b u t i o n f u n c t i o n s of GB d i f f u s i v i t y w e r e d e t e r m i n e d a t d i f f e r e n t t e m p e r a t u r e s and t h e y a r e p r e s e n t e d i n F i g . 4 and 5.

l ' l 7 l 7 1 '

log

(dob I

F i g . 3. P l o t o f a c t i v a t i o n e n e r g y of r e c o v e r y Qr a s a f u n c t i o n of

-

t h e f r a c t i o n of GBs w i t h TLDs

- i n P o l y c r y s t a l s G and S

-

^S

-

Lpm

G - 22pm

- -

F i g . 4 , 5. D i s t r i b u t i o n f u n c t i o n s of GB d i f f u s i v i t y i n aluminium f o r P o l y c r y s t a l s G and S, r e s p e c t i v e l y .

1.0

0.6

0.4

0.2

The o b t a i n e d d i s t r i b u t i o n s g i v e t h e GB c h a r a c t e r i s t i c s of d i f f u s i o n a l p r o p e r t i e s i n a1 umi n i um p01 y c r y s t a l S and t h e y depend on t h e r mo-mechani c a l t r e a t m e n t . The r e s u l t s o b t a i n e d show t h a t t h e GB d i f f u s i v i t i e s a t a g i v e n t e m p e r a t u r e d i f f e r f r o m e a c h o t h e r by two o r d e r s of t h e magnitude o r e v e n more. F u r t h e r m o r e , t h e v a l u e s of GB d i f f u s i v i t i e s i n P o l y c r y s t a l G a r e h i g h e r i n comparison w i t h Pol y c r y s t a l S. So t h e h i g h e r d i f f u s i o n a l p r o p e r t i e s i n t h e g i v e n aluminium o n e c a n o b t a i n i n t h e c a s e of a h i g h e r r e c r y s t a l l i z a t i o n

. i d / / :

-

9 LOJK

- -

0 0 1 . I I I . I ~

-18 -27 -26 -25 -24

log

(dob

)

(6)

t h e y a r e i n a good agreement w i t h r e s u l t s of computer s i m u l a t i o n s of GB s e l f - d i f f u s i o n a t 523 K i n aluminium o b t a i n e d by B i s c o n d i I151.

I t c a n b e assumed t h a t i n log-normal c o o r d i n a t e s t h e e x p e r i m e n t a l p o i n t s a t c o n s t a n t t e m p e r a t u r e CFig. 4 and 53 c a n be a p p r o x i m a t e d by l i n e a r f u n c t i o n . I n t h i s way t h e d i s t r i b u t i o n f u n c t i o n s of t h e GB d i f f u s i v i t y t a k e a f o r m of s t r a i g h t l i n e s i n t h e e x p e r i m e n t a l a r e a . The s l o p e of t h e s e l i n e s depends weakly on t e m p e r a t u r e f o r P o l y c r y s t a l G b u t h a s a s t r o n g t e m p e r a t u r e dependence f o r P o l y c r y s t a l S. T h i s i n d i c a t e s t h a t d i s t r i b u t i o n of GB d i f f u s i o n a c t i v a t i o n e n e r g i e s i s more u n i f o r m f o r P o l y c r y s t a l G t h a n f o r P o l y c r y s t a l S. T h i s is a l s o c o n f i r m e d by a c a l c u l a t i o n of a c t i v a t i o n e n e r g l e s of GB d i f f u s i o n . Taking v a l u e s o f t h e GB d i f f u s i v i t y c o r r e s p o n d i n g t o c o n s t a n t f r a c t i o n CFig. 4 and 53 t h e A r r h e n i u s p l o t i s o b t a i n e d and f u r t h e r t h e p a r a m e t e r s of GB s e l f - d i f f u s i o n a r e c a l c u l a t e d . The p r o c e d u r e a l l o w s t o o b t a i n t h e d i s t r i b u t i o n s of GB s e l f -di f f u s i on p a r a m e t e r s i n p01 y c r y s t a l S. The o b t a i n e d p a r a m e t e r s of GB s e l f - d i f f u s i on : p r e e x p o n e n t i a 1 f a c t o r dDbO and a c t i v a t i o n e n e r g y of GB s e l f - d i f f u s i o n Qb a r e g i v e n i n t a b l e 11. These d i s t r i b u t i o n s a r e much more u n i f o r m i n Pol y c r y s t a l G t h a n i n S. The v a l u e s of GB s e l f - d i f f u s i o n p a r a m e t e r s a r e c l o s e o n e t o t h e o t h e r i n P o l y c r y s t a l G w h i l e i n P o l y c r y s t a l S t h e s e v a l u e s f a l l i n a b r o a d e r r a n g e .

Tab1 e I I

.

G r a i n boundary s e l f -di f f u s i o n p a r a m e t e r s i n a 1 umi n i um o b t a i n e d by t h e d i s l o c a t i o n s p r e a d i n g method.

The d e t e r m i n e d v a l u e s of r e c o v e r y a c t i v a t i o n e n e r g y c o r r e s p o n d t o t h e v a l u e s of GB s e l f -di f f u s i on a c t i v a t i o n e n e r g y and t h e r e f o r e i n d i c a t e that GB s e l f - d i f f u s i o n i s t h e r a t e c o n t r o l l i n g f a c t o r f o r r e c o v e r y on GBs. I n d i v i d u a l GBs i n p01 ycr y s t a l d i f f e r i n t h e i r d i f f u s i o n a l p r o p e r t i e s which r e f l e c t s t h e d i f f e r e n c e s i n t h e s t r u c t u r e and l e a d s t o t h e d i f f e r e n c e s i n r e c o v e r y k i n e t i c s . The P o l y c r y s t a l s G and S h a v e d i f f e r e n t GB c h a r a c t e r i s t i c s a s a c o n s e q u e n c e of t h e i r d i f f e r e n t thermo-mechanical t r e a t m e n t s , h e n c e t h e y d i f f e r i n k i n e t i c s o f t h e p r o c e s s .

Pol y c r y s t a l S C4 pm3

G C22 pm3

5. CONCLUSI ONS

1. The k i n e t i c s of r e c o v e r y by a n n i h i l a t i o n of d i s l o c a t i o n s i n GBs i n a 1 umi n i um c a n b e d e t e r rni ned by t h e d i sl o c a t i on s p r e a d i n g method and i t i s d e s c r i b e d by t h e l o g a r i t h m i c r e c o v e r y l a w .

2. The r a t e of r e c o v e r y on G B s d e p e n d s on t h e GB c h a r a c t e r i s t i c s of p01 y c r y s t a l S.

dDb0 C m3/s]

2 . 0 ~ 1

o - * ~

3. 4x1 cl0-*' 8. l *l

o - * ~

-

4. 9*l 0-*' 2.5wl0-"

F r a c t i o n C 1 - X 3 0 . 5 0 . 8 0 . 2 0 . 5 0.8

3. The d i s t r i b u t i o n s o f p a r a m e t e r s o f GB s e l f - d i f f u s i o n i n aluminium : p r e e x p o n e n t i a l f a c t o r and a c t i v a t i o n e n e r g y may b e o b t a i n e d u s i n g t h e d i s l o c a t i o n s p r e a d i n g method and t h e y c a n b e used a s GB c h a r a c t e r i s t i c s of p o l y c r y s t a l .

Qb C k J/molI 67.7 47.2 5 1 . 1 49.7 44.0

(7)

COLLOQUE DE PHYSIQUE

REFERENCES

1. R. W. B a l u f f i , P r o c . ASCM Materials S c i e n c e S e m i n a r : G r a i n B o u n d a r y S t r u c t u r e a n d K i n e t i c s . S . 297, ASM M e t a l s P a r k . O h i o . 1980

2. J . K w i e c i h s k i , J . W. W y r z y k o w s k i

.

A c t a M e t a l l . , 37 C19893, 1503 3. M. W. G r a b s k i . J . P h y s i q u e . 46 C1985>, C4-567

4. W. A. S w i a t n i c k i , W. L o j k o w s k i , M. W. G r a b s k i , A c t a M e t a l l . , 34 C19863, 599 5. W . L o j k o w s k i . J . K w i e c i h s k i . J . W. W y r z y k o w s k i , D . L . B e k e . I . G a d e n y . I n t . C o n f .

" D i f f u s i o n i n M e t a l s a n d A l l o y s " , D. L. B e k e . F. J . K e d v e s eds.

,

B a l a t o n f u r e d , H u n g a r y C 19883

6. T . J o h a n e s s o n , A. T h o l e n , M e t . Sci

.

J . , 6 C19723, 189 7. P . H. P u m p h r e y , H. G l e i t e r , P h i l

.

Mag. , 30 C19743, 593 8. S. L a r ti g u e . L. P r i e s t e r , A c t a M e t a l l .

.

31 ClQ833. 1803

Q. R.Z. V a l i e v . V. Y u . G e r t s m a n , 0. A . K a i b y s h e v . Phys. Stat. Sol. Ca3. 78 C1 9833 , 177

10. J . W. W y r z y k o w s k i , M. W. G r a b s k i , P h i l . Mag. , 53 C19863, SO5 11. J . W. W y r z y k o w s k i , M. W. G r a b s k i . M e t . Sci.

.

17 C19833. 445

12. W. L o j k o w s k i

.

^M.W. G r a b s k i i n : " D e f o r m a t i o n of Pol y c r y s t a l s : M e c h a n i s m s and M i c r o s t r u c t u r e s " ed. N. H a n s e n , 2nd R i s o I n t . S y m p . on M e t a l l u r g y and Mater. S c i . , p. 329 C19813

13. R. A. V a r i n . E. R o m a n o w s k a - H a f t e k

,

M a t . Sci

.

E n g . ,66 C 19873

,

97

14. J . G. B y r n e . " R e c o v e r y , R e c r y s t a l l i z a t i o n and G r a i n G r o w t h " , T h e M a c m i l l a n C o m p a n y , New Y o r k 1965

15. M. B i s c o n d i , i n " P h y s i c a l C h e m i s t r y of Solid S t a t e : A p p l i c a t i o n s t o M e t a l s and t h e i r C o m p o u n d s , ed. P . L a c o m b e . E l s e v i e r S c i e n c e P u b l i s h e r s B.V.. A m s t e r d a m 1984. p. 225