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DISCUSSION : DISLOCATION RELAXATIONS IN SOLIDS
L. Magalas, D. Niblett
To cite this version:
L. Magalas, D. Niblett. DISCUSSION : DISLOCATION RELAXATIONS IN SOLIDS. Journal de
Physique Colloques, 1987, 48 (C8), pp.C8-209-C8-217. �10.1051/jphyscol:1987829�. �jpa-00227133�
JOURNAL DE PHYSIQUE
Colloque C8, supplement au n 0 1 2 , Tome 48, decembre 1987
DISCUSSION :
DISLOCATION RELAXATIONS IN SOLIDS
L.B. MAGALAS and D.H. NIBLETT*
INSA d e Lyon, GEMPPM, 20 Av. A. Einstein, F - 6 9 6 2 1 Villeurbanne Cedex. France
'physics Laboratory, The University, GB-Canterbury C T 2 7 N R , Kent, Great-Britain
il&sum6: Dans c e t a r t t c l e . nous p r g s e n t o n s 1 e s c o n t r i b u t i o n s s-es aux deux s e s s i o n s D i s l o c a t i o n s . Une b r s v e d i s c u s s i o n accompagne l e r a p p e l des i d 6 e s p r i n c i p a i e s de chaque c o n t r i b u t i o n s u r l a base de 1 ' a n a l yse des r e 1 a x a t i o n s dans l e s m6taux C . C . e t c . f . c . a i n s i que dans l e s a u t r e s m a t g r i a u x .
R b r t r a c t : T h i s r e v i e w i n t r o d u c e s t h e a a p e r s c o n t r i b u t e d t o t h e
--
two s e s s i o n s on D i s l o c a t i o n s . The main i d e a s o f t h e s e c o n t r i - b u t i o n s t o o u r u n d e r s t a n d i n g o f d i s l o c a t i o n r e i a x a t i o n s i n bcc , n e t a l s . f c c m e t a l s and o t h e r m a t e r i a l s a r e b r i e f l y d i s c u s s e d .1 . D i s l o c a t i o n K e i a x a t i o n s i n bcc M e t a l s
The i n t r i n s i c d i s l o c a t i o n r e l a x a t i o n s i n bcc m e t a l s have been s t u d i e d i n t e n s i v e l y d u r i n g t h e l a s t decade. I t i s g e n e r a l l y a c c e p t e d t h a t under a p p r o p r i a t e con- d i t i o n s t h e movement o f d i s l o c a t i o n s t a k e s p l a c e b y t h e g e n e r a t i o n o f k i n k - p a i r s and t h e movement o f g e o m e t r i c a l k i n k s . B o t h k i n k - o a i r g e n e r a t i o n (KPG) and g e o m e t r i c a l k i n k m i g r a t i o n (GKM) g i v e r i s e t o i n t e r n a l f r i c t i o n ( I F ) r e l a x a t i o n peaks w h i c h o c c u r , f o r a g i v e n frequency. a t a temperature determined b y t h e h e i g h t of t h e P e i e r l s b a r r i e r . I f i t i s assumed t h a t GKM on non-screw ( 7 1 0 ) d i s l o c a t i o n s s i n c e i t i n v o l v e s t h e s m a i i e s t P e i e r l s b a r r i e r . o c c u r s a t t h e l o w e s t temperature.
t h e n . s t a r t i n g a t t h e l o w e s t t e m p e r a t u r e . one e x p e c t s t o o b s e r v e GKM on non-screw d i s l o c a t i o n s , GKM on screw d i s l o c a t i o n s , KPF ( o e a K a ) on non-screw d i s l o c a t i o n s and KPF (peak y) on screw d i s l o c a t i o n s , i n t h a t o r d e r b u t w i t h no g u a r a n t e e t h a t t h e f i r s t t h r e e p r o c e s s e s do n o t o v e r l a p . Moreover. i n t h e bcc m e t a l s a s a group one e x p e c t s t h e s e r e l a x a t i o n s t o o c c u r a t i n c r e a s i n g t e m p e r a t u r e s as t n e m e l t i n g p o i n t i n c r e a s e s . C o n s i d e r a b l e e f f o r t has a l s o been made t o c l a r i f y t h e i n t e r - a c t i o n o f d i s l o c a t i o n s w i t h m o b i l e o o i n t d e f e c t s . . i n s p i t e o f t h i s , a consensus has n o t y e t been reached on t h e r e l a x a t i o n mechanisms f o r t h e hydrogen
Snoek-Koster [ s - ~ ( t l ) ] r e i a x a t i o n , t h e d i s l o c a t i o n - e n h a n c e d Snoek e f f e c t
[DESE ( C . N . 0 ) I and t h e S-K(C.N,O) r e l a x a t i o n . I n t h i s r e s p e c t i t i s i n t e r e s t i n g t o c o n s i d e r t h e oapers c o n t r i b u t e d t o t h i s c o n f e r e n c e (TC) by R i t c h i e (TC) and b y San Juan e t a l . (TC). d e a l i n g w i t n t h e hydrogen p r o b l e m i n b c c m e t a l s . and t h e vrork o f Rubisnes e t a l . (TC) d e v o t e d t o DESEiC) i n Fe-C a l l o y s .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987829
C8-210 JOURNAL
DE
PHYSIQUE1.1 Hydrogen Induced D i s l o c a t i o n Relaxations i n bcc Metals
The i n f l u e n c e o f hydrogen on i n t r i n s i c d i s l o c a t i o n r e l a x a t i o n s and d i s l o c a t i o n s t r u c t u r e i n bcc metals i s presented by R i t c h i e (TC) from t h e p o i n t o f view o f h y d r i d e p r e c i p i t a t i o n . Hydride p r e c i p i t a t i o n i n V, Nb and Ta has f r e q u e n t l y been i n v e s t i g a t e d by means o f e i t h e r low o r h i g h frequency I F , g i v i n g r i s e i n both cases t o a " p r e c i p i t a t i o n " I F peak. The e s s e n t i a l p r o p e r t i e s o f t h e low-frequency hydride p r e c i p i t a t i o n peak r e p o r t e d by Yoshinari and ~ o i w a l are explained by the model f o r t h e t r a n s i e n t component o f t h e low-frequency hydride p r e c i p i t a t i o n peak proposed by R i t c h i e . It should be p o i n t e d o u t t h a t t h e p r e c i p i t a t i o n peak i s accompanied by a u t o t w i s t i n g ( z e r o - p o i n t d r i f t o f t h e t o r s i o n pendulum which can be simultaneously detected d u r i n g an I F experiment) caused by t h e movement o f m i s f i t d i s l o c a t i o n s induced by t h e process o f h y d r i d e p r e c i p i t a t i o n . R i t c h i e ' s model i s based on t h e model o f Astie', i n which l o n g s t r a i g h t screw d i s l o c a t i o n s i n i r o n show thermal i n s t a b i l i t y , which manifests i t s e l f by a u t o t w i s t i n g . i n t h e temperature range o f t h e r e l a x a t i o n . Thus t h e low-frequency p r e c i p i t a t i o n peak i s erplained, according t o R i t c h i e , i n terms o f t h e S-K(H) r e l a x a t i o n on u n s t a b l e
screw
h y d r i d e m i s f i t d i s l o c a t i o n s . The c a l c u l a t i o n s made according t o t h i s model c o n f i r m t h a t the h e i g h t o f t h e p r e c i p i t a t i o n peak i s p r o p o r t i o n a l t o the h e a t i n g r a t e and i n v e r s e l y p r o - p o r t i o n a l t o t h e frequency o f v i b r a t i o n . I n f a c t , according t o t h e t h e o r e t i c a l model2 f o r t h e S-K r e l a x a t i o n i n bcc metals, one can expect t o observe t h e S-K(H) r e l a x a t i o n connected w i t h non-screw d i s l o c a t i o n s ( t h e c l a s s i c a l S-K(H) peak) and a l s o w i t h screw d i s l o c a t i o n s . I n t h e case o f V, Nb and T.a, t h e S-K(H) peak on screw d i s l o c a t i o n s overlaps t h e temperature range o f t h e t e r m i n a l s o l i d s o l u b i l i t y o f hydrogen and a t r u n c a t e d S-K(H) peak on screw d i s l o c a t i o n s i s observed, which has been r e f e r r e d t o as a " p r e c i p i t a t i o n " peak. The S-K(H) r e l a x a t i o n on screw d i s l o c a t i o n s i n i r o n has n o t y e t been c l e a r l y demonstrated because t h i s peak can be masked by two o t h e r phenomena:( i ) t h e i n s t a b i l i t y o f t h e screw o r i e n t a t i o n , which s t a r t s as low as 200
-
220K, w e l l below t h e temperature of t h e Y r e l a x a t i o n ( % 300K a t 1 Hz);( i i ) t h e existence o f t h e By r e l a x a t i o n a t about 330K. which i s connected w i t h t h e i n t e r a c t i o n o f r e s i d u a l carbon atoms w i t h t h e m o b i l e non-screw d i s l o c a t i o n s 3 9 4 .
I t can be concluded t h a t the S-K(H) r e l a x a t i o n on
screw
d i s l o c a t i o n s i n bcc metals can be expected from t h e t h e o r e t i c a l p o i n t o f view. b u t t h a t i t i s d i f f i c u l t t o assure s u i t a b l e experimental c o n d i t i o n s t o observe t h i s r e l a x a t i o n .According t o San Juan e t a l . (TC), t h e S-K(H) r e l a x a t i o n i n i r o n c o n s i s t s o f two peaks b u t t h r e e component mechanisms are advocated: t h e S-Kl(H) peak due t o KPF on non-screw d i s l o c a t i o n s c o n t r o l l e d by t h e d i f f u s i o n o f hydrogen i n t e r s t i t i a l atoms, t h e S-K2(H) peak due t o KPF on non-screw d i s l o c a t i o n s c o n t r o l l e d by t h e d i f f u s i o n o f diatomic hydrogen c l u s t e r s , p l u s another component due t o t h e i n t e r a c t i o n o f geometrical k i n k s on
screw
d i s i o c a t i o n s w i t h diatomic hydrogen c l u s t e r s r e f e r r e d t o as t h e S-K1(H) peak. San Juan e t a l . conclude t h a t t h e i n t e r a c t i o n o f geometrical k i n k s on screw d i s l o c a t i o n s w i t h hydrogen atoms i s zero. T h i s p o i n t needs f u r t h e r d i s c u s s i o n because, i n t h e long-range i n t e r a c t i o n concept, geometrical k i n k s on screw d i s l o c a t i o n s i n i r o n have a small w i d t h and are abnormally hign5; such k i n k s have a s t r o n g edge component and t h e i rh y d r o s t a t i c s t r e s s f i e l d should l e a d t o n e a r l y t h e same l e v e l o f i n t e r a c t i o n w i t h a hydrogen atom as i n t h e case o f geometrical k i n k s on non-screw (71°)
d i s l s c a t i o n s .
Much e x c i t i n g work remains t o be done t o see how important t h e short-range i n t e r a c t i o n between geometrical k i n k s and hydrogen atoms i s . However, a s e l f - c o n s i s t e n t p i c t u r e o f t h e i n t e r a c t i o n problem can o n l y be obtained i n a combined treatment o f t h e long and s h o r t range i n t e r a c t i o n aspects. Since such a t h e o r e t i c a l treatment i s n o t y e t a v a i l a b l e , we must r e l y on t h e long-range i n t e r a c t i o n concept and can s t a t e t h a t t h e i n t e r a c t i o n o f geometrical k i n k s on screw d i s l o c a t i o n s w i t h hydrogen atoms i s , a t l e a s t , n o t n e g l i g i b l e .
T a k i t a and Sakamoto6 and K r o n m l l l e r e t a1.7 c l e a r l y demonstrated i n I F and magnetic a f t e r - e f f e c t experiments t h e existence o f a broad S-K(H) peak which emerged a f t e r H-charging a t t h e expense o f t h e a peak. Subsequently two well-separated peaks were r e p o r t e d by many authors a f t e r s t r o n g H-charging o r s u i t a b l e annealing treatments o f H-charged samples. The h i g h temperature p a r t o f t h e S-K(H) r e l a x a t i o n remains c o n t r o v e r s i a l . I t has been a t t r i b u t e d by V e t t e r e t a1 .8 t o t h e movement o f geometrical k i n k s on screw d i s l o c a t i o n s c o n t r o l l e d by H atoms bound i n the d i s l o c a t i o n core. Also, as p o i n t e d o u t by
KG
e t a1.9, the S-KZ(H) component should be connected w i t h l e s s mobile hydrogen c l u s t e r s . I n general, i t seems t h a t , as f a r as t h e r e l a t i o n s h i p between t h e S-K(H) and a/al peak i s concerned, San Juan e t a1.
(TC) have confirmed e a r l i e r r e s u l t s o f KronmUller e t a1.7 and ~ i b a l a lo. I n f a c t , t h e separation o f t h e a and a ' components r e p o r t e d by KronmUller e t a l . and Gibala c o n s t i t u t e t h e most obvious experimental separations so f a r reported. I t should be mentioned t h a t t h e o r e t i c a l m o d e l l i n g of the i n t e r a c t i o n between hydrogen atoms and geometrical k i n k s on screw and non-screw d i s l o c a t i o n s has been r e p o r t e d by Ogurtani and seeget-11. They showed t h a t , under a p p r o p r i a t e experimental c o n d i t i o n s , t h e i n t e r a c t i o n between i s o t r o p i c hydrogen atoms and geometrical k i n k s i n i r o n can l e a d t o an I F r e l a x a t i o n which i s i n f a c t t h e hydrogen dislocation-enhanced Snoek e f f e c t [DESE(H)]. The h i g h temperature S-K(H) peak r e p o r t e d by San Juan e t a l . (TC, F i .3) resembles a Debye peak. A s i m i l a r suggestion was made by KG e t a1. 8 .
Since t h e DESE i n bcc metals i s o f t e n n e a r l y a Debye peak3, t h e S-K1(H) peak a t 150K can be i n t e r p r e t e d i n terms o f t h e hydrogen motion i n t h e s t r e s s f i e l d o f o s c i l l a t i n g geometrical k i n k s and can be i d e n t i f i e d as the DESE(H). To c a s t one more doubt on t h e s i t u a t i o n , we may note t h a t t h e shape o f t h e h i g h temperature p a r t o f the S-K(H) peak r e p o r t e d by San Juan e t a l . (TC) i s d i f f e r e n t t o t h a t r e p o r t e d e a r l i e r by San Juan e t a112. Thus i t i s d e s i r a b l e t o c o n f i r m t h a t t h e S-K'(H) peak a t 150K i s n o t a s i d e e f f e c t . The existence o f t h e S-K8(H) peak should a l s o be v e r i f i e d by o t h e r workers. I n an attempt t o g a i n some f u r t h e r under- standing o f t h e S-K(H) r e l a x a t i o n and t h e peak a ' i n i r o n , a d d i t i o n a li n v e s t i g a t i o n s a r e c l e a r l y d e s i r a b l e ( h i g h frequency I F i s recommended f o r t h e i n v e s t i g a t i o n o f t h e a/al complex).
1.2 D i s l o c a t i o n Relaxations i n I r o n (DESE)
The i n t e r a c t i o n between moving d i s l o c a t i o n s o f non-screw o r i e n t a t i o n and heavy f o r e i g n i n t e r s t i t i a l atoms ( F I A ) leads, a t the temperature o f t h e corresponding Snoek e f f e c t , t o t h e DESE i n bcc metals3. Although t h r e e p o s s i b l e r e l a x a t i o n mechanisms t o account f o r the DESE have been considered3s4, the f i n a l i n t e r - p r e t a t i o n i s n o t y e t e s t a b l i s h e a . The DESE i n i r o n doped w i t h d i f f e r e n t carbon concentrations has been s t u d i e d by Rubianes e t a l . (TC). This paper confirms previous r e s u l t s obtained by ~ a ~ a l a s 3 , 4 * ~ ~ , who considers t h a t t h e r e l a x a t i o n s t r e n g t h o f t h e OESE(C,N) i n i r o n i s d i r e c t l y p r o p o r t i o n a l t o t h e concentration o f FIAs i n t h e Snoek atmosphere. Thus t h e r e l a x a t i o n s t r e n g t h o f t h e DESE can reach a s a t u r a t i o n vatue i n t h e case o f a s a t u r a t e d Snoek atmosphere. Hence i t is s a f e t o conclude t h a t , depending on t h e experimental c o n d i t i o n s , the r e l a x a t i o n s t r e n g t h o f t h e DESE(C,N) i n i r o n can be s t r o n g l y i n f l u e n c e d by:
JOURNAL DE PHYSIQUE
( i ) t h e c o n c e n t r a t i o n o f FIAs i n s o l i d s o l u t i o n and the concentration o f FIAs which can be released from
d i s l o c a t i o n s , g r a i n boundaries and destroyed p r e c i p i t a t e s a f t e r p l a s t i c deformation o f f r e s h l y - s a t u r a t e d i r o n o r a f t e r a d d i t i o n a l c o l d work o f a1 ready s t r a i n - a g e d sample$;
( i i ) t h e amount o f p l a s t i c deformation a t room temperature (below t h e s a t u r a t i o n l e v e l );
( i i i ) t h e s t a t e o f t h e sample.
The behaviour o f t h e DESE i s s u b s t a n t i a l l y d i f f e r e n t i n deformed t r e s h l y - s a t u r a t e d i r o n o r i n deformed i r o n t h a t has been aged ( a f t e r s a t u r a t i o n treatment) a t h i g h temperatures o r subjected t o a high-
temperature s t r a i n - a g e i n g treatment; s a t u r a t i o n temperature can a l s o p l a y an important r o l e i n t h e r e d i s t r i b u t i o n o f FIAs i n i r o n 3 .
The existence o f t h e DESE has been confirmed by Rubianes e t a l . (TC) and Magalas and co-workers3*4*13 i n Fe-C a l l o y s and i t has a l s o been observed394
i n Fe-N a l l o y s and i n Armco i r o n o f t e c h n i c a l p u r i t y . Needless t o say, t h e DESE should be a general phenomenon f o r t h e bcc metals. However, t h e existence o f the DESE(0) i n Nb-0 and Ta-0 a l l o y s has been contested by Guangyi e t a1 .I4. Mol i n a s e t a1
.
(TC) have confirmed t h a t t h e enhancement o f t h e oxygen Snoek peak, p r e v i o u s l y r e l a t e d t o t h e DESE(0) due t o the i n f l u e n c e o f t h e mobile d i s l o c a t i o n s l 5 , should be r e l a t e d t o oxygen pick-up from t h e r e s i d u a l atmosphere i n s i d e the t o r s i o n pendulum. Nevertheless. f u t u r e work on Nb-0 and Ta-0 a l l o y s should s e t up s u i t a b l e experimental c o n d i t i o n s t o develop the DESE(0) i n these a l l o y s . I n f a c t , the DESE(C,N) i n i r o n was a l s o over- looked, i n t h e s t u d i e s o f the i n f l u e n c e o f p l a s t i c deformation on t h e Snoek e f f e c t , f o r more than 40 years u n t i l i t s existence was c o n v i n c i n g l y demonstrated i n systematic work 3 9 4 3 1 3 .1.3 D i s l o c a t i o n Relaxations i n Niobium and Tantalum
Lauzier e t a l . (TC) r e p o r t I F measurements on nisbium and tantalum s i n g l e c r y s t a l s a t a frequency o f about 1100Hz. A pronounced r e l a x a t i o n peak was found a t 60K f o r niobium and a t 50K f o r tantalum and was i d e n t i f i e d as t h e a-peak due t o KPF on non-screw (710) d i s l o c a t i o n s . I n a d d i t i o n , they c a r r i e d o u t an i n t e r e s t i n g i n v e s t i g a t i o n o f p o i n t d e f e c t p i n n i n g e f f e c t s i n cold-worked tantalum between about 4 and 20K, i n v o l v i n g i n s i t u c o l d work and e l e c t r o n i r r a d i a t i o n . They discuss the p o s s i b i l i t i e s o f hydrogen o r i n t r i n s i c i n t e r s t i t i a l s as t h e mobile d e f e c t s which p i n t h e d i s l o c a t i o n s i n t h i s temperature range; more work i s necessary t o c l a r i f y the s i t u a t i o n . 2 . D i s l o c a t i o n Relaxations i n f c c Metals
D i s l o c a t i o n r e l a x a t i o n s i n f c c metals have been s t u d i e d f o r n e a r l y 40 years since t h e i n i t i a l discovery by ~ o r d o n i l 6 o f a low-temperature r e l a x a t i o n peak i n several cold-worked f c c metals. N i b l e t t and w i l k s 1 7 i d e n t i f i e d t h e existence o f two separate r e l a x a t i o n peaks and i t i s g e n e r a l l y agreed t h a t these a r e due t o KPF on non-screw (60°) and screw d i s l o c a t i o n s , as o r i g i n a l l y proposed by
~ e e g e r ~ * * ~ ~ . Most o f t h e e a r l y work on the Bordoni peaks was conrentrated on copper, b u t more r e c e n t l y a t t e n t i o n has been devoted t o aluminium i n order t o study t h e r o l e o f s t a c k i n g f a u l t energy i n t h e Bordoni r e l a x a t i o n . I F and u l t r a s o n i c a t t e n u a t i o n (UA) measurements on aluminium r e p o r t e d a t t h i s
conference are concerned w i t h both t h e Bordoni r e l a x a t i o n s and o t h e r d i s l o c a t i o n processes observed a t higher temperatures.
2.1 U l t r a s o n i c A t t e n u a t i o n Studies i n Aluminium
Two papers, by Alnaser and N i b l e t t (TC) and Zein (TC), r e l a t e t o UA measurements a t 10 MHz on aluminium o f 99.999% p u r i t y . Zein measured 5N aluminium s i n g l e c r y s t a l s o f d i f f e r e n t o r i e n t a t i o n s and found t h a t t h e temperature a t which t h e Bordoni peak occurs i s independent o f t h e o r i e n t a t i o n o f t h e c r y s t a l , t h u s c o n f i r m i n g e a r l i e r measurements by ~randchamp20 fo r g o i d and Brown and N i b l e t t 2 1 f o r copper and s i l v e r a t k i l o h e r t z frequencies and by N i b l e t t and ~ e i n 2 2 f o r copper a t 10 MHz. A comparison o f these two papers shows t h a t t h e Bordoni peaks observed by Zein (TC) f o r h i s s i n q l e c r y s t a l s are considerably l a r g e r than those found by Alnaser and N i b l e t t (TC) f o r p o l y c r y s t a l l i n e aluminium o f s i m i l a r p u r i t y . There i s a l s o a s u r p r i s i n g d i f f e r e n c e o f about twenty degrees between t h e
temperatures o f t h e peaks r e p o r t e d i n these two papers, f o r heavily-deformed specimens, although t h e same frequency was used. Further work i s needed t o r e s o l v e t h i s discrepancy. A p a r t i c u l a r problem i n making UA measurements w i t h q u a r t z transducers i s t o d i s t i n g u i s h a t t e n u a t i o n due t o r e l a x a t i o n processes from o t h e r losses, e s p e c i a l l y those due t o quartz-sample deformation as i l l u s t r a t e d by Becker e t a l . (TC), b u t t h i s should n o t be s i g n i f i c a n t f o r t h e h e a v i l y - deformed specimens.
Vincent e t a l . (TC) r e p o r t UA measurements performed d u r i n g room temperature creep t e s t s i n t e r r u p t e d by successive s t r e s s r e d u c t i o n s . I n t h e course o f creep t e s t i n g , a decrease o f UA was recorded d u r i n g creep time which i s due t o d i s l o c a t i o n p i n n i n g . Unloading was accompanied by an increase o f UA which i s accounted f o r i n terms o f breakaway, Nevertheless, a c o m p e t i t i o n between breakaway and dragging processes i s p o s s i b l e . This c o m p e t i t i o n can be s t r o n g l y i n f l u e n c e d by experimental c o n d i t i o n s : creep temperature, s t r e s s decrement, amount o f p r e s t r a i n , time e t c . An e s s e n t i a l d i f f e r e n c e was, however, observed d u r i n g the f i r s t s t r e s s r e a u c t i o n provided t h a t p l a s t i c deformation exceeded 0.4%. Under these c o n d i t i o n s an anomalous decrease of UA was detected d u r i n g unloading. It seems reasonable t h a t t h i s phenomenon can be accounted f o r i n terms o f t h e change o f t h e mobile
d i s l o c a t i o n d e n s i t y , i e . t h e a n n i h i l a t i o n o f screw d i s l o c a t i o n s by c r o s s - s l i p . Even though t h i s i n t e r p r e t a t i o n i s borne o u t by t h e i n f l u e n c e o f creep r a t e on the amount o f t h e anomalous decrease o f UA, i t would be worthwhile t o v e r i f y t h e i n f l u e n c e of temperature on the anomalous decrease o f UA d u r i n g t h e f i r s t unloading.
An up-dated k i n e t i c d i s l o c a t i o n model i s s u c c e s s f u l l y used by S h i o i r i and Sakino (TC) t o describe t h e dynamic behaviour o f d i s l o c a t i o n s i n deformed 5N p o l y c r y s t a l l i n e aluminium a t h i g h s t r a i n r a t e s . T h i s model a l s o p r e d i c t s t h e experimental r e l a t i o n s h i p between the f l o w s t r e s s and the s t r a i n r a t e a t v e r y h i g h s t r a i n r a t e s (above 104 s-1).
2.2 Medium Temperature Relaxations i n High P u r i t y Aluminium
One o f t h e most severe d i f f i c u l t i e s emerging from t h e i n t e r p r e t a t i o n o f t h e r e l a x a t i o n peaks a t around 0.5 Tm i n h i g h - p u r i t y aluminium i s t h e l a c k o f r e p r o d u c i b i l i t y o f t h e I F peaks r e p o r t e d by v a r i o u s workers. Agreement w i l l o n l y be a t t a i n e d i f samples of s t r i c t l y - c o n t r o l l e d p u r i t y and well-known d i s l o c a t i o n s t r u c t u r e are used by t h e d i f f e r e n t groups working i n t h i s f i e l d . Esnouf e t a l . (TC) r e p o r t measurements o f these r e l a x a t i o n s i n aluminium specimens doped w i t h d i f f e r e n t i m p u r i t i e s . They found t h a t t h e doped samples show a
higher a c t i v a t i o n energy than f o r 6N aluminium and discuss whether the peaks f o r t h e d i f f e r e n t p u r i t i e s r e s u l t from t h e same mechanism o r from d i f f e r e n t mechanisms.
N6 e t a l . (TC) present t h e r e s u l t s o f I F measurements a t 1Hz on 6N aluminium.
They r e p o r t two peaks:
( i ) P1 peak (H = 1.1 eV, i e . H
=
0.7Hv, V 1000b, Tmax"
450K),accounted f o r i n terms o f the g l i d e o f screw d i s l o c a t i o n s c o n t r o l l e d by j o g c l i m b i n g a s s i s t e d by vacancy p i p e - d i f f u s i o n ;
C8-214 JOURNAL DE PHYSIQUE
( i i ) P I ' peak (H = 0.8 eV, i e . H ~ 0 . 5 Hv, V -1000b, Tmax z350K), t h e analogue o f t h e P1 peak b u t w i t h mixed d i s l o c a t i o n s .
T h i s i n t e r p r e t a t i o n becomes more c l e a r i f we review, v e r y b r i e f 1 y, t h e p e r t i n e n t d a t a f o r t h e PI and P i ' peaks: b o t h peaks can o n l y be d e t e c t e d when a t a n g l e d d i s l o c a t i o n s t r u c t u r e i s observed a f t e r p l a s t i c deformation; these peaks disappear a f t e r creep o r p o l y g o n i z a t i o n . Thus t h e K6 g r a i n boundary model can be e a s i l y r u l e d o u t . F u r t h e r s u p p o r t i n g evidence f o r t h i s i n t e r p r e t a t i o n i s p r o v i d e d by t h e amplitude dependence and t h e absence o f any e f f e c t o f s t a t i c b i a s s t r e s s on t h e P I and P I 1 peaks. However, t h e i n t e r p r e t a t i o n o f t h e i n f l u e n c e o f doping on j o g movement remains c o n t r o v e r s i a l . As p o i n t e d o u t by
N6
e t a1. ,
t h e r e i s ample experimental evidence t h a t t h e P I and P I ' peaks can occur over a wide range o f temperatures, w i t h a p o s s i b l e v a r i a t i o n o f peak temperature o f about 60 degrees, depending on experimental c o n d i t i o n s . T h i s may mean t h a t some o f t h e wide v a r i e t y o f I F peaks r e p o r t e d ( a t l e a s t seven peaks i n 5N and 6N aluminium: PI, P I ' , P2, P3, K2, KG peak, m a c r o c r y s t a l l i n e o r "bamboo boundary" peak 23-26) may be e l i m i n a t e d and perhaps j u s t two r e l a x a t i o n phenomena w i l l be i d e n t i f i e d .2.3 C y c l i c Bias Stress Measurements i n Aluminium and Copper
Important r e c e n t proaress i n t h e study o f d i s l o c a t i o n dynamics has r e s u l t e d from t h e development o f t h e c y c l i c b i a s s t r e s s technique, f i r s t i n t r o d u c e d by
Gremaud and B e n o i t 2 7 9 2 8 , i n which t h e a t t e n u a t i o n o f u l t r a s o n i c waves i s measured i n a sample w h i l e i t i s subjected t o a low-frequency c y c l i c b i a s s t r e s s . Quenet e t a l . (TC) used t h i s technique t o study t h e Bordoni r e l a x a t i o n i n 5N and 6N aluminium. They obtained v e r y d i f f e r e n t " s i g n a t u r e s " f o r t h e two d i f f e r e n t p u r i t i e s , which t h e y i n t e r p r e t w i t h a modified v e r s i o n o f t h e KPG model i n terms o f t h e d i f f e r e n t l o o p l e n g t h s and t h e d i f f e r e n t i n t e r n a l s t r e s s e s a c t i n g on t h e d i s l o c a t i o n s i n t h e two cases. I t would be i n t e r e s t i n g t o know whether d i f f e r e n t deformations on specimens o f t h e same p u r i t y can produce s i m i l a r changes t o those produced by d i f f e r e n t p u r i t i e s .
It seems t h a t t h i s technique i s a m i l e s t o n e i n t h e f i e l d of t h e i n v e s t i g a t i o n o f d i s l o c a t i o n - o b s t a c l e i n t e r a c t i o n , since i t provides an exhaustive d e s c r i p t i o n o f t h e i n t e r a c t i o n between d i s l o c a t i o n s and mobile o r immobile obstacles29 and t h e time-dependent e v o l u t i o n o f t h i s i n t e r a c t i o n can a l s o be obtained. Becker e t a l . (TC) have used t h e technique t o study d i s l o c a t i o n p i n n i n g i n copper doped w i t h v a r i o u s elements o f d i f f e r e n t atomic s i z e and s o l u b i l i t y . The s t r i k i n g f e a t u r e o f t h e b u t t e r f l y curves presented i s t h e r e d u c t i o n o f t h e b u t t e r f l y h y s t e r e s i s around 550
-
700K f o l l o w e d by t h e r e t u r n o f L( ) h y s t e r e s i s above 750K. This phenomenon i s a m a n i f e s t a t i o n o f d i f f e r e n t d i s l o c a t i o n - p o i n t d e f e c t i n t e r a c t i o n s t r e n g t h s :( i ) weak p i n n i n g
-
small b u t t e r f l y h y s t e r e s i s due t o p i n n i n g by vacancy-foreign atom complexes;( i i ) s t r o n g p i n n i n q
-
considerable h y s t e r e s i s due t o p i n n i n g by f o r e i g n atoms ( r e l e a s e d from t h e annealed vacancy-foreign atom complexes).2.4 D i s l o c a t i o n s i n F a t i g u e
Most o f t h e i n v e s t i g a t i o n s devoted t o f a t i g u e i n metals have been m a i n l y observ- a t i o n a l . I n s p i t e of an e v i d e n t development i n our understanding o f metal fatigue30, t h e t h e o r i e s so f a r proposed a r e s t i 11 i n s u f f i c i e n t t o account f o r a1 1
t h e experimental observations. Thus i t i s i n t e r e s t i n g t o note an a p p l i c a t i o n o f UA measurements t o the i n v e s t i g a t i o n o f t h e f a t i g u e s a t u r a t i o n range i n 5N aluminium by Fougeres e t a l . (TC). This technique i s somewhat s i m i l a r t o c y c l i c b i a s s t r e s s measurements, b u t i n t h i s case t h e c y c l i c b i a s s t r e s s i s i n t h e p l a s t i c range. A close r e l a t i o n s h i p between UA and t h e $J parameter introduced by Fougzres e t a l . ( VJ describes t h e c a p a c i t y o f c e l l w a l l s t o e m i t o r absorb d i s l o c a t i o n s ) bears o u t t h e p r i n c i p a l assumptions o f t h e composite model i n metal f a t i g u e , and describes i n an elegant way t h e time-dependent v a r i a t i o n o f t h e c u r r e n t d e n s i t y o f mobile d i s l o c a t i o n s i n s i d e t h e c e l l s r e l a t e d t o t h e emission and absorption o f d i s l o c a t i o n s i n t h e c e l l w a l l s . It seems t h a t t h e beginning of a c o n s i s t e n t p i c t u r e o f t h e d i s l o c a t i o n dynamics i n the s a t u r a t i o n range i n aluminium i s emerging.
3. D i s l o c a t i o n Relaxations i n Other M a t e r i a l s 3.1 D i s l o c a t i o n Relaxations i n A l k a l i Halides
Brandt e t a l . (TC) r e p o r t I F measurements on pure and ~r*+-doped NaCl s i n g l e c r y s t a l s . They observed a r e l a x a t i o n peak PI w i t h an a c t i v a t i o n energy o f 0.09 eV f o r t h e pure c r y s t a l s ; i t s h e i g h t decreases and i t s temperature
increases w i t h i n c r e a s i n g dopant concentration. Since i t s f e a t u r e s resemble those o f t h e Bordoni peak i n f c c metals, t h e authors a t t r i b u t e t h i s peak t o KPF and c a l c u l a t e a v a l u e f o r t h e P e i e r l s s t r e s s which they compare w i t h values obtained from y i e l d s t r e s s measurements. A smaller peak P2 observed i n t h e doped c r y s t a l s i s thought t o be due t o i n t e r a c t i o n between d i s l o c a t i o n s and t h e imuuri t i e s .
3.2 D i s l o c a t i o n Relaxations i n S i l i c o n
The paper by Kaufmann e t a l . (TC) describes non-linear behaviour observed i n I F measurements on s i l i c o n s i n g l e c r y s t a l s . Asymmetric resonances associated w i t h an amplitude-dependent modulus must have been observed by many I F experimenters d u r i n g t h e p a s t 30 years. However, n o t much i n f o r m a t i o n has been p u b l i s h e d about these n o n - l i n e a r e f f e c t s and t h e authors have c o n t r i b u t e d a d e t a i l e d e x p l a n a t i o n based on t h e motion of d i s l o c a t i o n s .
Gadaud e t a l . (TC) a l s o r e p o r t measurements o f t h e damping o f s i l i c o n s i n g l e c r y s t a l s . The k i n k m i g r a t i o n energy i n c o v a l e n t m a t e r i a l s i s thought t o be so h i g h t h a t r e l a x a t i o n peaks due t o KPF w i i l n o t be observed below about
IOOOOC f o r t h e frequencies normally used i n I F measurements. Consequently, t h i s group made isothermal measurements over a wide range o f very low frequencies and t h e y were a b l e t o . i d e n t i f y t h r e e r e l a x a t i o n peaks w i t h a c t i v a t i o n energies o f 1.5, 1.95 and 2.4 eV, superimposed on a background damping which increased w i t h decreasing frequency. The t h r e e peaks a r e a t t r i b u t e d , r e s p e c t i v e l y , t o GKM, t h e n u c l e a t i o n and m i g r a t i o n o f i n t e r a c t i n g k i n k - p a i r s and t h e a c t i v a t i o n and m i g r a t i o n of n o n - i n t e r a c t i n g k i n k s on segments c o n t a i n i n g weak obstacles.
3.3 D i s l o c a t i o n Relaxations i n I 1 1
-
V CompoundsD i s l o c a t i o n s i n 111
-
V compounds are o f g r e a t i n t e r e s t because o f t h e i r e l e c t r i c a l p r o p e r t i e s and t h e i r a p p l i c a t i o n s i n e l e c t r o n i c devices. Q u d l a r d e t a l . (TC) r e p o r t two I F peaks i n deformed undoped InSb s i n g l e c r y s t a l s :( i ) t h e 570K peak (H = 1.15 eV), generated by c o l d work below t h e athermal temperature and a t t r i b u t e d t o KPF on screw d i s l o c a t i o n s ;
( i f ) t h e 640K peak ( H = 1.3 eV), generated by c o i d work above t h e athermal temperature and due t o KPF on 6 type 60°
d i s l o c a t i o n s ;
C8-216 JOURNAL DE PHYSIQUE
These r e s u l t s c o n f i r m a general b e l i e f t h a t slow screw and 60° B d i s l o c a t i o n s experience a s t r o n g P e i e r l s f r i c t i o n f o r c e ( t h e v e l o c i t y o f 60° a d i s l o c a t i o n s i s much h i g h e r ) . From t h e peak temperatures o f the i n t r i n s i c d i s l o c a t i o n
r e l a x a t i o n s i n InSb c r y s t a l s i t can be concluded t h a t t h e P e i e r l s f o r c e i s higher f o r 600 d i s l o c a t i o n s than f o r screw d i s l o c a t i o n s . However, no evidence o f d i f f e r e n t v e l o c i t i e s f o r screw and 600 B d i s l o c a t i o n s was provided by TEM studies31. I n a d d i t i o n , t h e concept o f t h e m o b i l i t y o f screw and
B
type 600 d i s l o c a t i o n s c o n t r o l l e d by the 300 p a r t i a l B d i s l o c a t i o n s has n o t been addressed i n the i n v e s t i g a t i o n o f d i s l o c a t i o n s i n 111-
V compounds. Also t h e r e a r e no data y e t a v a i l a b l e on t h e secondary P e i e r l s p o t e n t i a l i n I 1 1-
V compounds.4. I n t e r n a l F r i c t i o n and the Portevin-Le C h a t e l i e r (P-L) E f f e c t
The P-L e f f e c t has been s u c c e s s f u l l y s t u d i e d by means o f I F measurements i n the k i l o h e r t z frequency range on A1-Mg and Cu-A1 a1 l o y s by ~chwarz32. I t i s a l s o intended by B e r t l i n g - B e r r e n s e t a l . (TC) t o use low-frequency ( 1 Hz) I F i n t h e i n v e s t i g a t i o n o f d i s l o c a t i o n - p o i n t d e f e c t i n t e r a c t i o n i n commercial A1-Mg-Si a l l o y s . Taking i n t o account t h e s i g n i f i c a n c e o f t h e time-dependent s o l u t e hardening component, high-frequency I F provides u s e f u l i n f o r m a t i o n . I n c o n t r a s t , low-frequency I F and modulus measurements can be used t o d e t e c t the temperature range o f d i f f e r e n t p i n n i n g stages. I n f a c t , such an approach i s presented by B e r t l i n g - B e r r e n s e t a l . However, a t present, no d e f i n i t e conclusions can be drawn by t h e authors from the complicated behaviour o f the I F . The c o r r e l a t i o n between t h e P-L e f f e c t and t h e measurements o f I F needs f u r t h e r e l a b o r a t i o n . We suggest t h a t t h e r e may be a close c o r r e l a t i o n between t h e P-L e f f e c t i n i r o n i n t e r s t i t i a l a l l o y s and t h e DESE (C,N) i n i r o n .
5. Discussion
During t h e Discussion session Benoit r a i s e d a general question concerning t h e measurement o f UA d u r i n g deformation o f a sample. He s a i d t h a t i n t e r p r e t a t i o n s always assumed t h a t e v e r y t h i n g was i n a s t a t i c s t a t e , eg. d i s l o c a t i o n s are assumed t o be immobile whereas i n f a c t they a r e moving d u r i n g deformation and t h i s motion might i n t r o d u c e an a d d i t i o n a l damping term. This could produce an a l t e r n a t i v e i n t e r p r e t a t i o n o f some e f f e c t s , eg. t h e systematic increase o f damping observed d u r i n g t h e i n i t i a l stages o f deformations. It i s always assumed t h a t t h i s i s a r e s u l t o f depinning, b u t he suggested t h a t i t might be a dynamic e f f e c t . Vincent r e p l i e d t h a t t h e d i s l o c a t i o n motion d u r i n g p l a s t i c deformation o r creep i s n o t a continuous motion b u t i s a j e r k y motion. Thus t h e d i s l o c a t i o n moves r a p i d l y between obstacles and then w a i t s u n t i l t h e s t r e s s i s s u f f i c i e n t t o move i t over t o t h e n e x t obstacle, so t h e d i s l o c a t i o n i s o n l y moving f o r a small f r a c t i o n o f t h e time. I n t h e UA measurements a t h i g h r a t e s o f s t r a i n by S h i o i r i and Sakino (TC), t h e p e r i o d o f t h e j e r k y motion o f the d i s l o c a t i o n s i s two orders o f magnitude smaller than the p e r i o d o f t h e u l t r a s o n i c waves. Hence, since t h e damping depends on t h e average v e l o c i t y o f t h e d i s l o c a t i o n s so t h a t we a r e concerned w i t h how t h e average v e l o c i t y changes w i t h t h e s t r e s s , t h e e f f e c t suggested by Benoit w i l l be very small.
REFERENCES
1. Yoshinari, 0. and Koiwa, M., Acta Met.,
30
(1982) 1979 and 1987.2. Seeger, A., J.de Physique.
2
(1981) C5-201.3. Magalas, L.B., i n I n t e r n a l F r i c t i o n i n S o l i d s , Proc. Summer School on I n t e r n a l F r i c t i o n i n S o l i d s , Cracow, 1984, ed. by S. Gorczyca and L.B. Magalas (Wydawnictwo AGH, Krak6w 1984), p.89.
4. Maaalas, L.B. and Gorczyca, S., J. de Physique.
46
(1985) C10-253.5. Ackermann, F., Mughrabi, H. and Seeger, A . , Acta Met.,
31
(1983) 1353.6. T a k i t a , K. and Sakamoto, K., S c r i p t a Met.,
10
(1976) 399.7. KronmGller, H., Steeb, H. and ~ o n i g , N., I 1 Nuovo Cimento,
338
(1976) 205.8. V e t t e r , K., Steeb, H. and Kronmdller, H., Proc. 2nd I n t e r . Cong. on Hydrogen i n Metals, P a r i s , Pergamon Press (1977)ZC-5.
9. K6, T.S., Kronmcller, H., Seeger, A. and Sun, Z.Q., Hydrogen E f f e c t s i n Metals, ed. by I .M. B e r n s t e i n and A.M. Thompson, The M e t a l l u r g i c a l Society o f AIME (1981) 281.
10. Gibala, R., Trans. Met. Soc. AIME,
239
(1967) 1585.11. Ogurtani, T.O. and Seeger, A., J.App1. Phys.,
57
(1985) 5127.12. San Juan, J., Fantozzi, G., Esnouf, C., Vanoni, F. and Bernalte, A., J. de Physique,
44
(1983) C9-633.13. Magalas, L.B., Moser, P. and R i t c h i e , I.G., J. de 'physique,
9
(1983) C9-645.14. Guangyi, L., Jinguan, X. and Xiaowei, W., ( t o be p u b l i s h e d ) .
15. Seeger, A., Weller, M., D i e h l , J., Pan, Z.L
.,
Zhang, J.X. and K;, T.S., Z. M e t a l l k . ,73
(1982) 1.16. Bordoni, P.G., Ric. Sci.,
19
(1949) 851.17. N i b l e t t , D.H. and Wilks, J., P h i l . Mag.,
-
2 (1957) 1427.18. Seeger, A., P h i l . Mag.. L ( 1 9 5 6 ) 651.
19. Seeger, A., J. de Physique,
2
(1971) C2-193.20. Grandchamp, P.A., J. de Physique,
32,
(1971) C2-229.21. Brown, G.R. and N i b l e t t , D.H., J.Phys.0: Appl. Phys.,
6
(1973) 809 and 1560.22. N i b l e t t , D.H. and Zein, M., J.Phys.F: Metal Phys..
10
(1980) 773.23. Woirgard, J., P h i l . Mag.,
33
(1976) 623.24. K6, T.S., Cui, P., Yan, S.C. and Huang, Q., Phys.Stat.So1 . ( a ) ,
86
( i 9 8 4 ) 593.25. Kd. T.S. and Zhang, B.S., Phys.Stat.So1 . ( a ) ,
96
(1986) 515.26. Iwasaki, K., Phys.Stat.So1 . ( a ) ,
90
(1985) K35.27. Gremaud, G . and Benoit, W., J. de Physique,
42
(1981) C5-163 ana 369.28. Gremaud, G., J. de Physique,
42
(1981) C5-1141.29. Gremaud, G., Bujard, M. and Benoit, W., J. Appl. Phys.,
61
(1987) 1795.30. Mughrabi, H., i n D i s l o c a t i o n s and P r o p e r t i e s o f Real M a t e r i a l s , The I n s t i t u t e o f Metals (1985), p.244.
31. Fnaiech, M., Reynaud, F., Couret, A. and C a i l l a r d , 0.. P h i l . Mag.
( t o be published).
32. Schwarz, R.B., J. de Physique,
