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DEFECTS IN METALS
K.-H. Robrock
To cite this version:
K.-H. Robrock. MECHANICAL RELAXATION STUDIES OF POINT DEFECTS IN METALS.
Journal de Physique Colloques, 1981, 42 (C5), pp.C5-709-C5-720. �10.1051/jphyscol:19815109�. �jpa-
00220977�
JOURNAL DE PHYSIQUE
Colloque C 5 , supple'ment au nOIO, Tome 4 2 , ocbobre 2981 page c5-709
MECHANICAL R E L A X A T I O N S T U D I E S OF P O I N T DEFECTS I N METALS
K.-H. Robrock
I n s t i t u t fi;x Fes-bklirperforschung, KernforschungsanZage JiiZick, 0-5170 Jiil?:ch, I'. H. C.
A b s t r a c t . - T h i s r e v i e w f o c u s s e s on t h r e e main t o p i c s . F i r s t , s e l E - i n t e r s t i t i a l atoms i n p u r e A 1 ( f c c ) and p u r c Mo ( b c c ) . The emphasis l i e s on a comparison between m e c h a n i c a l r e l a x a t i o n (MR) measurements and d i f f u s c X-ray s c a t t e r i n g
(DxS) e x p e r i m e n t s . Second, s e l f - i n t e r s t i t i a l atom s o l u t e - a t o m complexes i n d i l u t e a l l o y s and t h i r d , Zener re1axs:ion i n Ag-Zn i n t h e r m a l e q u i l i b r i ~ m and d u r ~ n g i r r a d i a t i o n w i l l b e d i s c u s s e d .
1 . S e i f - i n t e r s t i t i a l atoms i n A 1 and Mo: A comparison bctwecn MR and DXS.- The JW of point. d e f ' e c t s i s d e s c r i b e d b y t h e e l a s t i c d i p o l e t e n s o r ,
2,
which i s a meaourc o f t h c l o n e r a n g e disp1.acement f i e l d s e t up i n t h e c r y s t a l by t h e p o i n t d e - f e c t s . Tile d i p o l e t e n s o r i s d e f i n e d a s t h e s t r e s s e s ,gd,
induced by t h c d e f e c t s p e r u n i t volume c o n c e n t r a t i o n , p , of d e f c c t s ar.d h a s t h e u n i t o f an e n e r g y . I t h a s s i x i n d e p e n d e n t components. T h e r e i s a n equivalent d e f i n i t i . o n which i s <;he s t r a i n ,5
d,
n e t up i n t h e c r y s t a l by t h e d e f e c t s p e r u n i t g a t o m i c ? r a c t i o n , c , and t h i s i s c a l l e d t h e A-tensor. -
I n c u b i c c r y s t a l s t h e r e e x i s t t h r e e i n d e p e n d e n t e l a s t i c def'orrnatiowwhich can be chosen a s a h y d r o s t a t i c compression and two p u r e s h e a r derormations.'l'he p a r a e l a s - t i c r e s p o n s e o f a d e f c c t t o an e x t e r n a l l y a p p l i e d e l ~ s t i c f i e l d i s 3 e s c r i b e d by t h e modulus changes / 1 , 2 /
?'he q u a n t i t i e s i I j 2 ) a n d 11(3) a s d e f i n e d above d e t e r m i n e a l s o t h e i n t e n s i t y o f t h e DXS, i . e . H u a n g - s c a t t e r i n g I ( K ) : T h i s i s due t o t h e f a c t t h a t t h e l o n g r a n g e s t r a i n
h -
f i e l d i s imaged c l o s e t o t h e Bragg p e a k s i n t h e s c a t t e r i n g p a t t e r n .
I ~ ( K ) =
...
(j(1).,(1)+j(2).n(2)+j(3).n(3)( K )
and
n
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815109
I
(k)t
Since Huang-scattering measures t h e same de- f e c t p r o p e r t i e s a s t h e MR it i s an i d e a l method f o r comparison and c r o s s checks. T h i s k i n d of double measurements h a s worked o u t w e l l i n t h e case of H and 0 i n N'b and a l s oi n t h e c a s e of e l e c t r o n i r r a d i a t e d Al.
k=h k
The p r o p e r t i e s of t h e s i n g l e s e l f - i n t e r - s t i t i a l atom i n A 1 determined from MK mea- F i g . l : S c a t t e r e d X-ray i n t e n s i t y~ ( k )
a s a f u n c t i o n o f s c a t - surements /3/ and Huang s c a t t e r i n g/4/
a r e t e r i n g v e c t o r k_( 1
t
0 . 3 ) eV from MR]A-BI
=( 3
+
3 ) eV from DXSI n a d d i t i o n t h e MR measurements have shown t h a t t h e m i g r a t i o n of t h e s e s e l f - i n t e r - s t i t i a l atoms o c c u r s simultaneously with t h e i r r e o r i e n t a t i o n with an a c t i v a t i o n energy of 0.115 eV. A l l t h e s e o b s e r v a t i o n s a r e i n agreement with t h e p r o p e r t i e s ex- p e c t e d f o r <loo>-dumbbells. I n f i g . 2 t h e b a s i c jump p r o c e s s o f t h i s <loo>-dumbbell i s shown. One r e c o g n i z e s t h a t simultaneously with t h e m i g r a t i o n jump a r o t a t i o n by 90' of t h e dumbbell o c c u r s .
F i g . 2: The diffusion-jump of t h e 11002 - dumbbell
F i g . 3: The <llO>-dumbbell i n t h e bcc l a t t i c e and i t s r e s o n a n t modes:
I. L i b r a t i o n a l I s=& L i b r a t i o n a l I1
t r a n s l a t i o n a l
The s e l f - i n t e r s t i t i a l atoms i n Mo ( b c c ) a r e expected t o p o s s e s s t h e s t r u c t u r e of a
<llO>-dumbbell, which i s shown i n f i g . 3. T h i s f i g u r e shows a l s o t h r e e c h a r a c t e r i s - t i c v i b r a t i o n s which t h e dumbbell can undergo and which p o s s e s s t h e l a r g e s t ampli- t u d e s f o r a given t h e r m a l e x c i t a t i o n . I n c a l c u l a t i o n s u s i n g t h e a-Fe p o t e n t i a l of Johnson
/7/
t h e l i b r a t i o n a v i b r a t i o n i n t h e]
1101-plane ( l i b r a t i o n a l I ) p o s s e s s e s t h e l a r g e s t amplitude of t h e t h r e e modes f o r a given thermal e x c i t a t i o n .The e x p e r i m e n t a l r e s u l t s on Mo can be summarized a s f o l l o w s : 1 . ) The d i p o l e t e n s o r i s according t o t h e DXS / h / :
20 1 1 0 P =
l o
11 20 0 3 8 ) lev12 . ) Measurements of t h e d i f f u s e X-ray s c a t t e r i n g
/4/,
recovery of e l e c t r i c a l r e s i s - t i v i t y / 5 / and MiiBbauer measurements on Mo c o n t a i n i n g ~ e ~ ~ /6/ have shown t h a t t h e m i g r a t i o n of t h e Mo s e l f - i n t e r s t i t i a l atoms occurs i n a temperature regime between30K and 40K.
3 . ) If t h e m i g r a t i o n o c c u r s w i t h a simultaneous r e o r i e n t a t i o n o r i f t h e dumbbells undergo an in-place r e o r i e n t a t i o n b e f o r e t h e i r m i g r a t i o n a r e l a x a t i o n e f f e c t i s expected f o r t h e MR. S i n c e t h e d i f f e r e n c e , f o r i n s t a n c e , between t h e elements of t h e d i a g o n a l i s about 18 eV which i s 18 times l a r g e r t h a n t h e corresponding value d e t e r n i n e d f o r t h e <loo>-dumbbells i n Al, a MR-process i s expected i n Mo which i s more t h a n 2 o r d e r s of magnitude l a r g e r t h a n t h e corresponding one i n A l . E l a s - t i c a f t e r e f f e c t measurements have been performed i n t h e temperature regime from 4K t o about 100K on e l e c t r o n i r r a d i a t e d Mo by H . Jacques /8/ and i n a s i m i l a r manner by S . Okuda and J . Mizubayashi / 2 2 / a f t e r neutron i r r a d i a t i o n i n s e a r c h f o r t h i s l a r g e r e l a x a t i o n e f f e c t . The r e s u l t i s shown i n f i g . 4 . The r e s p e c t i v e upper c u r v e s i n f i g . ha and
41:
a r e t h o s e curves which a r e expected i f d i p o l e t e n - s o r components a r e assumed a s determined from DXS. I n t h i s s c a l e t h e a c t u a l l y measured c u r v e s a r e e s s e n t i a l l y z e r o f o r both c a s e s r e p o r t e dThe expected l a r g e r e l a x a t i o n p r o c e s s caused by t h e <llO>-dumbbells does not e x i s t i n Mo. This means, t h e <?lo>-dumbbells n e i t h e r undergo an in-place r o t a t i o n
DXS P E W nor do t h e y r e o r i e n t e d u r i n g t h e i r m i g r a t i o n . I t could be s p e c u l a t e d t h a t t h e dumbbe1.ls m i - g r a t e one-dimensionally a l o n g a <110> d i r e c t i o n v i a a pure t r a n s l a t i o n a l . mode. The s a d d l e m m o a
p o i n t f o r t h i s d i f f u s i o n a l . jump would be t h e
.
am lr-,a o c t a h e d r a l c e n t e r . An i n t e r s t i t i a l i n t h e oc-' 0 m w m n,.
- !.
muf.d I* 11 s ah. t a h e d r a l c e n t e r h a s however a formation energy
* *..uk,-%
21 " XuM whicn i s about 1.1 eV h i g h e r t h a n t h a t of a
<llO>-dumbbell / 7 / . This v a l u e would be approxi-
*
1
mately t h e m i g r a t i o n energy f o r t h e t r a n s l a -~m
-
- O X S t i o n a l jump and i s much t o o l a r g e i n o r d e r t oI.DWI.d
.
on* r-ba account f o r a m i g r a t i o n which t a k e s p l a c e a tOO m m m
. -,
about 30K t o 40K. H . Jacques e t a 1 / 8 / have1- 1.1
r e c e n t l y proposed n model which e x p l a i n s t h e F i g .
4
: EAE and DXS i n Mo 99.99 low a c t i v a t i o n energy a s w e l l as t h e f a c t t h a t-
a f t e r e l e c t r o n i r r a d i a t i o n t h e m i g r a t i o n of t h e <IlO>-dumbbell o c c u r s ( 3 M ~ v ) . cFD = 300 ppm
without r e o r i e n t a t i o n ( s e e f i g . 5 ) . The jump
initial final
o c c u r s v i a t h e l i b r a t i o n a l mode I which i sposit ion
expec+;ed t o p o s s e s s t h e l a r g e s t a m p l i t u d e o f a l l r e s o n a n t v i b r a t i o n s . l%e e s t i m a t c o f t h e m i g r a t i o n e n e r g y i s 0 . 3 eV from t h e computer c a l c u l a t i o n s/'[/.
F o r f u r t h e r d e t a i l s o f t h i s junip mechilnisrn s e e t h e c o n t r i b u t i o n or' H . J a c q u e s c t a l . /8/ t o t , h i s c o n f e r e n c e . I t s h o u l d b e p o l n t e d o u t t h a t t h i s jump c a u s e s F i g . 5: J ~ u n p v i a l i b r a t i o n a l T mode a two-dimensional d i f f u s i 3 1 1 o f t h e s e l f - i n -t e r s t i t i a l atoms i n a [ I 1 3 ] - ~ l a n e and be- c a u s e o f t h i s e x p l a i n s a l s o t h e p e c u l i a r b c h a v i o u r o f r e s i s t i v i t y r e c o v e r y and or' t h e MoDbauer e f f e c t i n Lhc a n n e a l i n g r a n g e o r s t a g e I
/5,6/ .
2 . S e l f - I n t e r s t i t i r l l Atoms ( 3 1 ~ ) - S o l u t e - A t o m ( S A )
-
(:omplexcs.-S1A-SA-complexes which a r e formed by t r a p p i n g o f m i g r a t i n g SIA at irnmobi1.e SA p l a y a predominant r o l e i n t h e b ~ h a v i o u r or' n e t a l s d u r i n g i r r a d i a t i o n . S e l f - i n t e r s t i t i a l atoms may b e p r e s e r v e d i n t h e Torn! o f s u c h complexes ttnd a c t a s a d d i t i . o n a 1 r e a c t i o n p z r t n e r s a t h i g n e r t e m p e r a t . ~ r e s f o r m i g r a t i n g v a c a n c i e s . T h i s i s t h e b a s i c mechanism which l e a d s t o t h e r e d u c t i o n ol' v o i d swel.ling. Tklc & i f f u s i o n o f SIA-SA-complexes a s a u n i t l c a d s t o a p r e f e r e n t i a l n a s s - t r a n s p o r t . which i s o b s e r v e d i n r a d i a t i o n induced s e g r e g a t i o n and p o s s i b l y i n f a s t d i f f u s i o n phenomena. 'ihc main p o i n t s o f i n t e r e s t w i t h r e s p e c t t o t h e s c phenomena a r e : t2le b i n d i n g e n e r g i e s , E ~ , t h e migra- t i o n e n e r g i e s , E?., M and t h e c o n f i g u r a t i o n s .
The p h y s i c a l o r i g i n o f t h e b i i i d i n g o f s e l f - i n t e r s t i t i a l atoms a t s o l u t e atoms i s n o t y e t u n d e r s t o o d i n f u l l d e t a i l . A p r o b a b l y v e r y i m p o r t a n t c o n t r i b u t i o n t o t h i s b i n d i n g can b e s e e n by t h e a i d of t h e Yellowing model ( f i ~ . 6 ) . The r a t h e r h i g h
f o r m a t i o n e n e r g y o f t h e s e l f - i n t e r s t i t i a l atom i n t h e f c c l a t t i c e i s a consequence of t h e h i g h amount o f s t r a i n e n e r g y a s s o c i a t e d w i t h t h e compressed a t o m i c arrangement around t h e s e l f - i n t e r s t i t i a l atom. B i n d i n g F i z .
6 :
For e x p l a n a t i o n s e e t e x tof s e l f - i n t e r s t i t i a l atoms a t s o l u t e atoms would o c c u r , i f t h e s o l u t e atoms c o u l d b e i n c o r p o r a t e d i n s u c h a manner t h a t p a r t cf t h i s s t r a i n e n e r a can b e r e g a i n e d a g a i n . T h i s i s p o s s i b l e f o r s o l u t e atoms w i t h n s m a l l e r ion.ic c o r e t h a n t h e h o s t a t o m s , j f one of' t h e dumbbell atoms i s repl.aced by t h e s m a l l e r s o l u t e atom a s shown i n f i g .
6 .
I n t h i s way a mixed eumbbell i s c r e a t e d . On t h e o t h e r hand s o l u t e atoms w i t h a l a r g e r i o n i c c o r e c a n s l s o b e i n c o r p o r a t e d i n t h e neighbourhood o f Lhe dumb- b e l i w i t h e n e r g y gained. {is shown i n r i g . 7 . T h i s i s d ~ e t o t h c f a c t t h a t t h e r i n g o f atoms Xo. 1-4 i s opened up by t h e d i s p l s c e n i e n t f i e l d s u r r o u n d i n g t h e dumbbell a s i n d i c a t e d by t h e a r r o w s . S i n c e t h e n e a r e s t n e i ~ h b o u r No. 5 i s l o c a t e d c l o s e t ot h i s r i n g a n o v e r s i z e d s o l u t e a.tom can b e accomnodated h e r e .
As a measure f'or t h e s i z e of' t h e s o l u t e atoms it h a s b e e n proposed t o t a k e t h e r e l a x a t i o n volume o f s c l u t c atoms j.n d i l u t e s o l i d s o l u t i o n which c a n b e determined from l a t t i c e p a r e m e t e r measurement,s / 7 , 9 /
1 a a a i s t i e l a t t i c e p a r m e t e r , and r = - . -
0 a acgA cSA t h e a t o m i c f r a c t i o n o f s o l u t e a t o m s . r i s usua1;y c a l l e d t h e m i s f i t .
I f ro i s n e g a t i v e s o l u t e atoms a r e c o n s i d e r e d t o b e imcicr- s i z e d w i t h r e s p e c t t o t h e h o s t atoms and o v e r s i z e d i f r F i g . 7 : F o r e x p l a n a t i o n
s e e t e x t i s p o s i t i . v e
.
D e t a i l e d computer s i m u l a t i o n s t u d i e s have been shorn t h a t u n d e r s i z e d s o l u t e atoms may b e i n c o r p o r a t e d i n d i f f e r e n t w a j s as shown i n f i g .
8.
F i g . 8 a shows a < l o o > - d u m b b e l l , where a s o l u t e atom repl.aces a r e g u l a r, - -
~i
h o s t atom i n t h e d d b e l l . There a r e 1 s i x e q u i v a l e n t 2 c s i t i o n s f o r i h c s a - l u t e a t o r w i t h i n t h e c c t a h e d r a l c e l l .f:
I n e a c h s o l u t e a t o r p c s i t i o n t h e dumbbell. h a s a d i f ' f e r e n t o r i e n t a t i o n . Jurnps o f t h e s o l u t e etom f r o n one! a ) ( b ( C p o s i t i o n t o a n o t h e r l e a d t o e r e o r i e n - F i g . 8: P o s s i b l e c o n f i g u r a t i o n s o f SIA-SA t a t i o n o f t h e n i x e d dumbbell.. S i n c e
complexes c o n t a i n i n g u n d e r s i z e d SA
t h e s e p a r a t i o n between t h e s e p o s i - t i o n s i s r ~ l t h e r s h o r t , t h e j ~ u n p s can bc e x p e c t e d t o o c c u r w i t h a 1 . o ~ ac- t i v a t i o n e n e r a . T n e r e f o r e , one e x p e c t s a r e l a x a t i o n e f f e c t from t h e s e n i x e d durnb- b e l l s which o c c u r s a t low t e m p e r a t u r e s .
Depending on t h e m i s f i t r o r d e p e n d i n g on s l i g h t e s t d e s t o r t i o n s i n t h e i n t e r - a t o m i c i n t e r a c t i o n p o t e n t i a l , o t h e r catqes may b e p o s s i b l e . An exmp1.e i s s!iowi i n f l g . Ob. I n t h i s c a s e t h e dumbbell i s t i l t e d s l i g h t l y o f f t h e < l o o > - d i r e c t i o n and t h e r e a r e now 24 e q u i v e l e n t p o s i t i o n s f o r t h e s o l u t e atom. Two d i f f c r e n l ; jrunp modes may o c c u r w i t h t h i s c a g e . F i r s t , t h e s o l u t e atom n a y jump w i t h a Yrequcncg v ' w i t h i n e a c h of t h e s q u a r e s . Thesc jumps, however, do n o t l e a d t c t r e n s i t i o n s from one s q u a r e t o t h e o t h e r . Such jumps c c c u r v i a a second node a t f r e ~ w n c y v 2
.
T h e r e f o r e t h i s cage p r o v i d e s a model f o r i complex, hlhich g i v e s r i s e t o two i n t e r - n a l f r i c t i o n p e a k s which a r e s e p a r a t e d on a f r e q u e n c y o r t e x p e r a t u r e s c a l e . T h i s i s c a l l e d f r o z e n - f r e e - s p l i t phenomena i n t h e l i t e r a t u r e / I / . Tne computer c a l c u l a - t i o n s show t h a t w i t h i n c r e a s i n g m i s f i t r t h e s q u a r e s become l e r g e r and l a r g e r and a t t h e same t i m e t h e t r i a n g l e s c o n n e c t i n g t h e s q u a r e s become s n a l l e r u r l t i l f j n a l l y
t h e t r i a n g l e s d e g e n e r a t e i n t o one p o i n t . Then t h e c o n f i g u r a t i o n shown i n f i g . 8c i s a r r i v e d a t . This i s a cube l i k e cage where t h e r e i s no mixed dumbbell anymore, but t h e s o l u t e atom p o s s e s s e s t h r e e e q u i v a l e n t neighbouring h o s t atoms.
Independent of t h e p a r t i c u l a r cage s t r u c t u r e , however, a l l o f t h e s e cages should give r i s e t o i n t e r n a l f r i c t i o n peaks a t low t e m p e r a t u r e s , i . e . with s m a l l a c t i v a t i o n e n e r g i e s , due t o l o c a l i z e d d i f f u s i o n of t h e s o l u t e atom i n a narrow cage.
S e l f - i n t e r s t i t i a l atoms bound t o an o v e r s i z e d i m p u r i t y atom should a l s o give r i s e t o i n t e r n a l f r i c t i o n peaks Cue t o t h e f a c t t h a t t h e r e a r e twelve e q u i v a l e n t position^
f o r t h e dumbbell bound a t t h e i m p u r i t y atom a s shown i n f i g . 7 and f i g .
9:
Since i n t h i s c o n f i g u r a t i o n , a r e g u l a r h o s t atom dumbbell i s bound t o t h e s o l u t e atom, t h e s e dumbbells perform a s i m i l a r jump a s t h e f r e e dumb- b e l l i n o r d e r t o come from one of t h e p o s i t i o n s t o t h e o t h e r s only t h a t t h e motion i s r e s t r i c t e d t o t h e twelve p o s i t i o n s . T h e r e f o r e , one can ex- p e c t a mechanical r e l a x a t i o n p r o c e s s a t a tem- p e r a t u r e where a l s o t h e m i g r a t i o n of t h e f r e e s e l f - i n t e r s t i t i a l atom dumbbell o c c u r s .
Mechanical r e l a x a t i o n measurements, with t h e aim t o s t u d y t h e v i b r a t i o n a l behaviour of SIA-SA- complexes, have been performed i n a number of F i g . 9 : The twelve e q u i v a l e n t a l l o y s c o n t a i n i n g u n d e r s i z e d a s w e l l a s o v e r s i z e d
p o s i t i o n s of a dumbbell
s o l u t e atoms i n s o l u t i o n . These r e s u l t s a r e shown bound a t an o v e r s i z e d
S A i n f i g . 10.
A l l o f t h e s e curves were ob-
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s e r v e d a f t e r t h e samples have been i r r a d i a t e d w i t h e l e c t r o n s a t low t e m p e r a t u r e s and t h e m i g r a t i o n of t h e f r e e s e l f - i n t e r s t i t i a l atoms had occured s o t h a t t h e y had t h e p o s s i b i l i t y t o r e a c t w i t h t h e so- l u t e atoms p r e s e n t i n t h e m a t e r i a l . The o r i g i n a l c o n c e n t r a t i o n of so- l u t e atoms i n t h e s e a l l o y s was o f t h e o r d e r of 200 atppm and t h e s e l f - i n t e r s t i t i a l atom c o n c e n t r a t i o n s produced by t h e e l e c t r o n i r r a d i a t i o n was of t h e o r d e r of 40 atppm o r l e s s . The most important f e a t u r e s F i g . 10: I F - s p e c t r a i n d i l u t e a l l o y s f o r t h e p r e s e n t concern are t h e
( c s ~ = 1 0 0 .
.
.300 ppm; cSI=40 ppm) f o l l o w i n g : a f t e r e - - i r r a d i a t i o n and SI-migrationa ) I n e a c h a l l o y s e v e r a l d i f f e r e n t r e l a x a t i o n p e a k s have b e e n f o u n d which grow and d e c a y upon a n n e a l i n g a t d i f f e r e n t t e m p e r a t u r e s a s shown i n F i g . 1 1 . I f d e f e c t s c a u s i n g d i f f e r e n t i n t e r n a l f r i c t i o n p e a k s grow o r a n n e a l a t d i f f e r e n t t e m p e r a t u r e s , it means b y n e c e s s i t y t h a t t h e y have d i f f e r e n t c o n f i g u r a t i o n s . T h i s means t h a t i n a l l o f t h e a l l o y s s e v e r a l d i f f e r e n t c o n f i g u r a t i o n s of SIA-SA-complexes a r e p r e s e n t s i m u l t a n e o u s l y i n t h e sample d e s p i t e t h e low s e l f - i n t e r s t i t i a l atom and s o l u t e - a t o m c o n c e n t r a t i o n s . S e v e r a l r e a s o n s may a c c o u n t f o r t h i s o b s e r v a t i o n . F ' i r s t , a complex c o n t a i n i n g one s e l f - i n t e r s t i t i a l atom and one s o l u t e - a t o m may b e p r e s e n t i n s e v e r a l d i f f e r e n t m e t a - s t a b l e c o n f i g u r a t i o n s . Second, s e v e r a l d i f f e r e n t l y s i z e d complexes, i . e . one s o l u t e atom w i t h o n e , t w o , t h r e e and s o on s e l f - i n t e r s t i t i a l a t o m b o u n d t o i t may a l s o a c c o u n t f o r t h e s e d i f f e r e n t c o n f i g u r a t i o n s . F o r t h e c a s e o f Cu-In f o r i n s t a n c e , K o l l e r s /13/ h a s s h o r n t h a t t h e e x i s t e n c e o f f i v e i n t e r n a l f r i c t i o n peaks i s i n a c c o r d a n c e w i t h t h e a s s u m p t i o n t h a t a p o i s s o n d i s t r i b u t i o n o f d i f f e r e n t l y s i z e d SIA-SA-complexes i s p r e s e n t i n t h e sample.
b ) I n e a c h of t h e a l l o y s c o n t a i n i n g u n d e r s i z e d s o l u t e atoms low t e m p e r a t u r e p e a k s a r e f o u n d . T h i s i s i n agreement w i t h t h e p i c t u r e o f l o c a l i z e d d i f f u s i o n i n c a g e s . However, low t e m p e r a t u r e p e a k s a r e n o t u n i q u e o n l y t o s u c h c a g e s b u t a l s o o c c u r f o r t r a p p e d d i - i n t e r s t i t i a l s i n v o l v i n g o v e r s i z e d s o l u t e atoms a s r e c e n t l y shown by K o l l e r s / 1 3 / .
a:FT]
c ) The maximum b i n d i n g e n e r g y , c a n i n p r i n c i p l e b e d e t e r m i n e d from t h e a n n e a l i n g0
t e m p e r a t u r e , Tm, o f t h e complex w i t h t h e
'
(U h i g h e s t Tm, p r o v i d e d t h a t t h e a n n e a l i n g r e s u l t s
0 from complex d i s s o c i a t i o n and n o t from i t s
lrq]
m i g r a t i o n o r i t s r e a c t i o n wit'n a n o t h e r complex m d i f f u s i n g t h r o u g h t h e l a t t i c e . Very he1.pful-,
o i n t h i s r e s p e c t a r c comparisons w i t h t h e r e -
r 3 3 1
s u l t s o f o t h e r e x p e r i m e n t s . Such a comparison0s
-
LI . A i s shown f o r t h e p r e s e n t 5 a l l o y s i n t h e f o l - . I
0 w P W W ~ r n m m lowing t a b l e , where t h e a n n e a l i n g tempera-
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t u r e s , Tm, a r e g i v e n a.s d e t e r m i n e d from F i g . 1 1 : Normalized peak h e i g h t s m e c h a n i c a l r e l a x a t i o n measurements, i ' r o n ~ r e -
as a function of covery o f r e s i d u a l r e s i s t i v i t y , rrom damage t e m p e r a t u r e . A l l o y s a s i n
f i g . l o . r a t e - and from c h a n n e l i n g measuremenl.~ / 1 4 / . For t h e c a s e o f A].-Ye and A1-Mn t h e r c i s agreement between t h e measurements t h a t f i n a l d e t r a p p i n g o c c u r s a t a b o u t 200K, which c o r r e s p o n d s t o t h e t e m p e r a t u r e regime o f s t a g e 111. It i s r e a s o n a b l e t o assume t h a t i n t h i s c a s e d e t r a p p i n g o c c u r s by a n n i - h i l a t i o n of t h e SIA-SA-complexes by m i g r a t i n g v a c a n c i e s . T h i s meens t h a t o n l y a l o w e r bound f o r t h e b i n d i n g e n e r a c a n be e s t i m a t e d which is
0.6
eV. I r i Al-Zn peak 1d i s a p p e a r s a t 15OK. I n damage r a t e and c h a n n e l i n g s t u d i e s , however, f i n a l d e t r a p p i n e i s o b s e r v e d a t 2OOK. l ' h i s means, t h a t t h e r e a r e i n a d d i t i o n t o t h e d e f e c t s which c a u s e peak 1 i n A?.-Zn, SIA-SA-complexes must e x i s t i n t h e m a t e r i a l which a r e n o t s e e n i n t h e mechanical r e l a x a t i o n s t u d i e s . A1-Mg and Cu-In show an a n n e a l i n g beha- v i o u r which i s v e r y s i m i l a r t o t h a t oi' Cu-Ag and Cu-Au which h a s been s t u d i e d i r ~ g r e a t d e t a i l by Cannon and S o s i n / 1 5 / . T h e i r a n a l y s i s h a s shown t h a t t h e d e t r a p p i n g o b s e r v e d a t about 150K i s due t o a t r u e 3 i s s o c i a t i o n p r o c e s s o f t h e complexes. I f i n anal.ogy t h e same i s assurr.ed f o r A1-Mg and Cu-In, t h e b i n d i n g e n e r g y f o r t h e s e complexcs i n t h c s e a l l o y s i s a b o u t 0 . 3 eV.
T a b l e 1 :
d ) The d e t e r m i n a t i o n o f t h e SIA-SA-complex c o n f ' i g u r a t i o n s s o i'ar r e s u l t s mainly from c h a n n e l i n g measurements / 2 3 / . I n o r d e r t o a c h i e v e t h e s e measurements s e l f - i n t e r s t i t i a l - a t o m a s w e l l a s s o l u t e - a t o m c o n c c n t r a t i o n s o f t h e o r d e r o f 1000 atppm and more had t o be u s e d . Due t o t h e p a r t i c u l a r s e n s i t i v i t y o f MR-measurements, t h e SIA-SA-complex c o n f i g u r a t i o n s car. b e d e t e r m i n e d from t h e o r i e n t a t i o n dependence o f Em-processes a t much l o w e r I . e v e l s o f t h e o r d e r o f 50 atppm and l e s s . I n A].-Fe c l e a r e v i d e n c e f o r t h e e x i s t e n c e o f a cage motion h a s b c e n f o u n d . T h i s c a g e h a s d e f i n i t e l y n s t t h e < l o o > - t e t r a g o p a l symmetry r e q u i r e d f o r t h e <loo>-mixed dumb- b e l l . l ' h i s r r s u 1 . t h a s r e c e n t l y bcen corroborated by t h e a n a l y s i s of t h e MoBbauer s p e c t r a of an i r r a d i a t e d Al-Co a l l o y / 2 4 / . A cage model which a c c o u n t s f o r a l l pro- p e r t i e s o b s e r v e d i n t h c m e c h a n i c a l r e l a x a t i o n s t u d i e s and i n t h e MSil3bauer s t u d i e s on Al-Fe h a s however noC y e t been developed / 1 6 / . I n Al-Zn t h e u l t r a s o n i c s t u d i e s show a n o r i e n t a t i a n dependence whi.ch i s i n agreement w i t h t h e
<loo>
symmetry of t h e mixed dumbbell. I n t h i s a l 1 . o ~ t h e r e i s a l s s e v i d e n c e t h a t a t lov t e m p e r a t u r e s t h e r e o r i e n t a t i o n o f t h i s mixed dumbbell o c c u r s v i a t u r n e l i n g modes / I T / .T
1x1
from:3 . Zener r e l a x a t i o n i n AR-Zn a l l o y s i n t h e r m a l e q u i l i b r i u n ~ and under i r r a d i a t i o n . B e r r y and Orehotsky /18/ have shown many y e a r s ago t h a t Zener r e l . a x a t i o n measure- ments i n c o n c e n t r a t e d Ag-Zn a i l o y s a r e a p o w e r f u l t o o l i n o r d e r t o s t u d y t h e o r d e r i n g phenonene o b s e r v e d i n t h e s e al.!oys
.
Hal.bwac!is,
Hi1 l a i r e t and o t h e r s /19-21/ have c a r r i e d f u r t h e r t h i s method and a p p l i e d 'it i n p a r t i c u 1 . m t o a l l o y s under i r r a d i a t i o n i n o r d e r t o s t u d y d e f e c t p r o d u c t i o n and d e f e c t m o b i l i t i e s undere - l : 1nt.7..
F r i c t i o n RRR: r e c . o f r e s
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i r r a d i a t i o n i n t h e s e a l l o y s . The b a s i c e x p e r i m e n t a l o b s e r v a t i o n i s shown i n f i g . 1 2 . I n t h i s f ' i g u r e n o r m a l i z e d r e l a - x a t i o n c u r v e s a r e shown a s a f u n c t i o n of t i m e i n a l o g a r i t h m i c t i m e s c a l e . One r e - c o g n i s e s t h a t t h e r e l a x a t i o n i n t h e r m a l -1
d d d 6 e q u i l i b r i u m i s enhanced by one o r two
IhnL., -
o r d e r s o f magnitude, r e s p e c t i v e l y , d u r i n g F i g . 12: R e l a x a t i o n c u r v e s a t 1 0 0 ~ ~ .
y- or electron irradiation.
The f r a c t i o n o f n o r m a l i z e d - 1
t o t a l r e l a x a t i o n was p l o t t e d The r e l a x a t i o n r a t e , T
,
i s r e l a t e d v e r s u s t i m e :a ) w i t h no f l u x t o t h e o r d e r i n g r a t e s v*,by e q u a t i o n /21/
9 b ) under a gamma f l u x of
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S I ~ S I A ~ : I A1 . 6 ~ 1 0 1 1 e-lcm2xsec.
aV and a r e e f f e c t i v i t y f a c t o r s o f t h e ( D . B e r e t z , M . Halbwachs,
J . H i l l a i r e t ) o r d e r o f 1 , C
v
and CSIA a r e t h e a t o m i c f r a c t i o n o f v a c a n c i e s and s e l f - i n t e r s t i t i a l atoms, r e s p e c t i v e l y , I n t h e r m a l e q u i l i b r i u m o n l y v a c a n c i e s a r e p r e s e n t w i t h c o n c e n t r a t i o nCV = :C e x p
CE
F / k ~ ) F .where E 1 s t h e vecancy f o r m a t i o n e n e r a , k t h e Boltzmann f a c t o r and T t h e tempera- t u r e . F o r t h e m a t e r i a l d u r i n g i r r a d i a t i o n , t h e t i m e dependent c o n c e n t r a t i o n s o f v a c a n c i e s , C V , and o f t h e s e l f - i n t e r s t i t i a l a t o m s , CSIA, can b e c a l c u l a t e d from t h e f o l l o w i n g r a t e e q u a t i o n s 1211
where P i s t h e p r o d u c t i o n r a t e , @ t h e i r r a d i a t i o n f l u x , R t h e r e c o n b i n a t i o n t e r m , pV and pSIA t h e e f f e c t i v e s i n k d e n s i t i e s f o r v a c a n c i e s and SIA and vv and vSIA t h e jump r a t e s o f v a c a n c i e s and SIA, r e s p e c t i v e l y .
For low s i n k c o n c e n t r a t i o n s t h e t i m e e v o l u t i o n i s a s shown i n f i g . 13. A t t h e b e ~ i n n i n g o f t h e i r r a d i a t i o n d e f e c t s a r e produced and s t o r e d i n t h e l a t t i c e . As t h e i r c o n c e n t r a t i o n i n c r e a s e s , m u t u a l r e c o m b i n a t i o n s e t s i n a n d l e a d s t o a q u a s i - s t a t i o n a r y l e v e l a f t e r a c e r t a i n t i m e . I n t h e l o n g r u n t h e f a s t e r d i f f u s i n g de- f e c t s a r r i v e a t n l a r g e r r a t e a t t h e s i n k s and t h e r e f o r e t h e i r c o n c e n t r a t i o n g o e s down a g a i n . At t h e same t i m e t h e c o n c e n t r a t i o n o f t h e s l o w e r d e f e c t s i n c r e a s e s .
-
1F o r t h e r e l a x a t i o n r a t e , T
,
t h i s i m p l i e s a dependence a s shown i n t h e l o w e r p a r t o f f i g . 13. I n t h e t i m e regime where r e c o m b i n a t i o n d o m i n a t e s t h e r e l a x a t i o n-
1r a t e g o e s t h r o u g h a q u a s i s t a t i o n a r y p l a t e a u , T ~ and f o r l o n g t i m e s ~ ~ , it g o e s down a g a i n t o a s t a t i o n a r y v a l u e , 7 -1
s t '
Under s i m p l i f y i n g c o n d i t i o n s , ( v * ~ and
Inck < pSIA2pV) t h e r e l a x a t i o n r a t e s i n t h e q u a s i s t a t i o n a r y r e g i m e , T and i n t h e s t a t i o n a r y r e g i m e , T-?: ' a r e g i v e n
I s t
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I I by t h e r e l a t i o n s /21/
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where vf and v a r e t h e jump r a t e s o ft ----_-_-
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t h e f a s t e r and s l o w e r nioving s p e c i e s .r,y \..
These f o r m u l a d e m o n s t r a t e t h e powerY i n h e r e n t i n t h i s method: The m o b i l i t i e s
In t,,,
o f t h e f a s t e r and t h e s l o w e r comoonent F i g . 13: Time e v o l u t i o n o f d e f e c t - c o n -
c e n t r a t i o n s and o r d e r i n g r a t e . c a n b e d e t e r m i n e d i n d e p e n d e n t l y from
i n h e r e n t i n t h e system.
t e x t .
By d o p i n g t h e m a t e r i a l w i t h t h e f a s t e r o r t h e s l o w e r component i t i s a l s o p o s s i b l e t o d e t e r m i n e what s p e c i e s is f a s t e r and what s p e c i e s i s s l o w e r , vacancy o r i n t e r s t i t i a l . A s s h o r n i n t h e l o w e r p a r t o f f i g . 13 by c u r v e ( x ) d o p i n g w i t h t h e f a s t e r component l e a d s t o a n enhancement o f o r d e r i n g and t h u s t o a n enhancement o f t h e r e l a x a t i o n r a t e . Doping w i t h t h e s l o w e r component c u r v e (xx) e n h a n c e s r e c o m b i n a t i o n and t h e r e f o r e r e d u c e s t h e r e l a x a t i o n r a t e . The r e s u l t o f such a d o p i n g experiment i s shown i n f i g . 1 4 . Here t h e r e l a x a t i o n r a t e i s shoun as a f u n c t i o n of i r r a d i a t i o n t i m e f o r a w e l l a n n e a l e d s m p l e o f Ag-Zn and a sample which was doped w i t h v a c a n c i e s b e f o r e i r r a d i a t i o n . I t i s s e e n t h a t vacancy d o p i n g l e a d s t o a c o n s i d e r a b l e i n c r e a s e i n t h e r e l a x a t i o n r a t e . According t o f i g . 13 t h i s means t h a t t h e v a c a n c i e s a r e t h e f a s t s p e c i e s and t h u s f a s t e r moving t h a n t h e i n - t e r s t i t i a l atoms. Once t h i s i d e n t i f i c a t i o n i s done it i s now p o s s i b l e on t h e b a s i s o f p r e c e d i n g e q u a t i o n s t o d e t e r m i n e t h e a c t i v a t i o n e n e r a f o r t h e m i g r a t i o n o f t h e v a c a r ~ c i e s and of t h e i n t e r s t i t i a l atoms from t h e t e m p e r a t u r e dependence o f t h e q u a s i s t a t i o n a r y z e l a x a t i o n r a t e and t h e s t a t i o n a r y r e l a x a t i o n r a t e . The r e s u l t i s shown i n f i g . 15.
A c t i v a t i o n e n e r g i e s o f 0.56 eV and 0 . 8 2 eV f o r t h e d i f f u s i o n a l jumps o f va- c a n c i e s and S I A , r e s p e c t i v e l y , a r e d e t e r m i n e d . Both f i g u r e s show a l s o t h e c u r v e o b s e r v e d i n t h e r m a l e q u i l i b r i m . The v a l u e o f 1 . 4 4 eV d e t e r m i n e d from t h e s l o p e o f t h e s e c u r v e s c o r r e s p o n d s t o t h e a c t i v a t i o r , e n e r g y f o r s e l f d i f f u s i o n i n Ag-Zn.
F i g . 14: R e l a x a t i o n r a t e s i n annecrled F i g . 15: V a r i a t i o n of r e l a x a t i o n r a t e s with
and vacancy doped Ag-Zn /20/ temperature 1211
The production r a t e s w i t h which f r e e m i g r a t i n g vacancies and s e l f - i n t e r s t i t i a l atoms a r e produced under i r r a d i a t i o n by photons, e l e c t r o n s , n e u t r o n s ,
...
can a l s o be determined from t h e s e Zener r e l a x a t i o n s t u d i e s . The e v a l u a t i o n r e q u i r e s a more d e t a i l e d a n a l y s i s of t h e o r i g i n a l r a t e e q u a t i o n s which i s beyond t h e scope of t h e p r e s e n t review. The r e a d e r i s r e f e r r e d t o t h e o r i g i n a l paper /21/ and t o t h e con- tribu:ion by D . Beretz e t a l . :o t h i s conference.Conclusions.
1 . S e l f - i n t e r s t i t i a l atoms: I n N , t h e s e l f - i n t e r s t i t i a l atoms have t h e configura- t i o n of <loo>-dumbbells and t h e i r d i p o l e t e n s o r i s o n l y s l i g h t l y a n i s o t r o p i c . S i - multaneously w i t h t h e i r d i f f u s i o n a l jump t h e y r e o r i e n t with an a c t i v a t i o n energy o f 0.115 eV. T h i s m i g r a t i o n occurs i n s t a g e I . I n Mo, t h e DXS measurements show t h a t s e l f - i n t e r s t i t i a l atoms have t h e form of <llO>-dumbbells. From t h e absence of a corresponding r e l a x a t i o n e f f e c t it h a s been concluded t h a t t h e s e dumbbells migrate without r e o r i e n t a t i o n . A model h a s been proposed which i m p l i e s t h a t t h e dumbbells migrate two dimensionally i n I1 l ~ l - ~ l a n e s .
2 . SIA-SA-complexes: The mechanical r e l a x a t i o n p r o c e s s e s observed i n i r r a d i a t e d d i - l u t e a l l o y s support t h e q u a l i t a t i v e view t h a t undersized s o l u t e atoms a r e i n c o r - p o r a t e d a s a member o f t h e dumbbell, and t h a t t h e i r motion i s confined t o a cage ( l o c a l i z e d d i f f u s i o n ) . Oversized s o l u t e atoms b i n d with a r e g u l a r dumbbell a t a n e a r e s t neighbour p o s i t i o n and t h i s dumbbell may jump around t h e s o l u t e atom l i k e on a l e a s h . Even a t low c o n c e n t r a t i o n s of s e l f - i n t e r s t i t i a l atoms and s o l u t e atoms of t h e o r d e r of 50 atppm many d i f f e r e n t c o n f i g u r a t i o n s o f SIA-SA-complexes a r e ob- s e r v e d . T h i s c o n t r a d i c t s t h e i n t e r p r e t a t i o n of channeling measurements 1231 where one c o n f i g u r a t i o n i s assumed f o r t h e d a t a e v a l u a t i o n .
3. Zener r e l a x a t i o n : Ordering i n Zener a l l o y s can be c o n s i d e r a b l y enhanced by i r r a - d i a t i o n . Vacancies and s e l f - i n t e r s t i t i a l atoms c o n t r i b u t e both t o o r d e r i n g . Va- c a n c i e s i n Ag-Zn a r e f a s t e r rnoving t h a n s e l f - i n t e r s t i t i a l atoms. Such measurements a r e a v a l u a b l e t o o l i n o r d e r t o determine t h e m o b i l i t i e s of v a c a n c i e s o r s e l f - i n t e r s t i t i a l atoms i n t h e r m a l e q u i l i b r i u m a s w e l l a s d u r i n g i r r a d i a t i o n .
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