ELASTIC AFTER EFFECT STUDIES OF MOLYBDENUM AFTER ELECTRON IRRADIATION AT 4.7 K

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ELASTIC AFTER EFFECT STUDIES OF

MOLYBDENUM AFTER ELECTRON IRRADIATION AT 4.7 K

H. Jacques, K.-H. Robrock

To cite this version:

H. Jacques, K.-H. Robrock. ELASTIC AFTER EFFECT STUDIES OF MOLYBDENUM AFTER

ELECTRON IRRADIATION AT 4.7 K. Journal de Physique Colloques, 1981, 42 (C5), pp.C5-723-

C5-728. �10.1051/jphyscol:19815111�. �jpa-00220980�

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E L A S T I C AFTER EFFECT STUDIES OF MOLYBDENUM AFTER ELECTRON I R R A D I A T I O N AT 4.7 K

H. Jacques and K.-H. Robrock

I n s t i t u t fiir Festkiirperforschung, Kemzforschungsanlage JiiZich, D-5170 JiiZich, F. R. G.

A b s t r a c t . - The s e l f - i n t e r s t i t i a l i n bcc Mo i s expected t o have t h e <110>

dumbbell c o n f i g u r a t i o n . These dumbbells should t h e r e f o r e b e a b l e t o r e - o r i e n t and e-rentually migrate simultaneously s i m i l a r t o < 100> dumbbells i n t h e fcc-metals. Because of t h e l a r g e shape parameters 6A of t h e s e l f - i n t e r s t i t i a l i n Mo a s determined from Huang-scattering experiments, t h e y should g i v e r i s e t o a l a r g e a n e l a s t i c r e l a x a t i o n p r o c e s s . The i d e n t i f i c a - t i o n of t h i s p r o c e s s was t h e main aim o f t h e p r e s e n t work.

A r e l a x a t i o n p r o c e s s with t h e expected p r o p e r t i e s h a s however not been found a f t e r low temperature e l e c t r o n i r r a d i a t i o n . I t i s concluded t h a t t h e s e l f - i n t e r s t i t i a l s i n Mo undergo a two dimensional m i g r a t i o n w i t h o u t r e o r i e n t a t i o n .

I n t r o d u c t i o n . - The mechanical r e l a x a t i o n spectrum of Mo i r r a d i a t e d with f a s t neu- t r o n s shows two dominant peaks a t 8K and 2 6 ~ a t 2 min r e l a x a t i o n t i m e , which were a t t r i b u t e d t o t h e r o t a t i o n without m i g r a t i o n of t h e <110> dumbbell s e l f - i n t e r s t i - t i a l and of t h e d i i n t e r s t i t i a l , r e s p e c t i v e l y / I / . No r e l a x a t i o n p r o c e s s i n d i c a t i n g t h e simultaneous m i g r a t i o n and r e o r i e n t a t i o n of a dumbbell l i k e t h a t of t h e < l o o >

dumbbell i n e l e c t r o n i r r a d i a t e d Al 121 could be d e t e c t e d . The shape parameter (A1-X2) and

( F

1 ( A + A )-A ) deduced f o r t h e

8K

peak and ;he 2 6 ~ peak a r e a b o u t o n e

1 2 3

o r d e r of magnitude s m a l l e r t h a n t h o s e determined f o r t h e s e l f ' - i . n t e r s t i t i a 1 atoms i n e l e c t r o n i r r a d i a t e d Mo from Huang-scattering experiments.

The p r e s e n t e l a s t i c a f t e r e f f e c t s t u d i e s on e l e c t r o n i r r a d i a t e d Mo were i n i t i a t e d i n o r d e r t o f i n d o u t whether d i f f e r e n c e s i n t h e damage p a t t e r n a f t e r f a s t neutron and e l e c t r o n i r r a d i a t i o n could account f o r t h e s e d i s c r e p a n c i e s and whether i n e l e c - t r o n i r r a d i a t e d Mo a p r o c e s s Cue t o t h e s i x u l t a n e o u s m i g r a t i o n and r e o r i e n t a t i o n jump of t h e 1 1 00> dumbbell would occur.

Experiment.- The e l a s t i c a f t e r e f f e c t measurements (Em) were c a r r i e d o u t on s i n g l e c r y s t a l l i n e c y l i n d r i c a l specimen i n a t o r s i o n a l pendulum, Two d i f f e r e n t l y o r i e n t e d s o r t s of specimen were used, with t h e cubic <ill> a x i s and t h e <110> a x i s along t h e t o r s i o n a x i s o f t h e sample, r e s p e c t i v e l y . The a n g u l a r displacements were measured with a l a s e r i n t e r f e r o m e t e r system with a r e s o l u t i o n of 6$ = 10 -8 r a d . The e l e c t r o n i r r a d i a t i o n s were performed a t t h e low t e x p e r a t u r e i r r a d i a t i o n f a c i l i t y o f KFA J i i l i c h . The r a d i a t i o n induced d e f e c t c o n c e n t r a t i o n s were monitored by s i m u l t a n e o u s l y

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815111

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JOURNAL DE PHYSIQUE

i r r a d i a t e d e l e c t r i c a l r e s i s t i v i t y samples

R e s u l t s . - The r e s u l t s a r e shown i n condensed form i n f i g . 1 . The upper p a r t ( l a ) shows t h e schematic r e l a x a t i o n spectrum, where t h e r e l a x a t i o n s t r e n g t h s i s p l o t t e d v e r s u s t h e measuring temperature f o r a < l l O > - o r i e n t e d sample. Four d i f f e r e n t r e - l a x a t i o n p r o c e s s e s have been i d e n t i f i e d i n a narrow temperature regime between 22K and 28K a f t e r t h e e l e c t r o n i r r a d i a t i o n a t 300 ppm d e f e c t c o n c e n t r a t i o n . They a r e i n d i c a t e d by t h e

4

b a r s i n f i g . l a , whose p o s i t i o n i s a t temperatures where t h e r e l a x a t i o n time

r

= 100s and whose h e i g h t s a r e given by t h e observed r e l a x a t i o n s t r e n g t h s . The o r i e n t a t i o n dependence i n d i c a t e s a <110> orthorhombic d e f e c t s t r u c - t u r e f o r p r o c e s s e s 2 and 3 , and a < l o o > - t e t r a g o n a l s t r u c t u r e f o r p r o c e s s e s 1 and 4 . The a c t i v a t i o n e n e r g i e s and p r e e x p o n e n t i a l f a c t o r s a r e i n a range expected f o r jump p r o c e s s e s o f s e l f - i n t e r s t i t i a l s .

M O (110) The next f i g u r e , f i g . l b , shows

hrgh dose

'

² ₁ C . = 300 ppm t h e a n n e a l i n g of t h e e l e c t r i c a l r e -

a

'Lk

L _ _ - L - _ _ 2 s i s t i v i t y d u r i n g t h e i s o c h r o n a l

measurdng temperature T I K I

tempering t r e a t m e n t . The d i f f e r e n t i a l

-

c u r v e , which shows t h e a n n e a l i n g

s t a g e s more c l e a r l y , h a s been taken b ⁴a

o L

I---l-- o n from r e f .

/ 4 /

because of i t s b e t t e r

1 p r e c i s i o n t h a n t h e p r e s e n t one.

C F i n a l l y , t h e f o u r lowest curves

f i g . lc-f show t h e behaviour of t h e 4 peaks d u r i n g t h e a n n e a l i n g t r e a t -

c

e

i \ LA--

--,- ^L ,-- 3 --, d i s c u s s i o n given i n t h e i n t r o d u c t i o n ment. I n r e s p e c t t o t h e p o i n t s under

100 r

t h e f o l l o w i n g i t e m s a r e i m p o r t a n t : f

20 30 40 50

anneolmg femperoture T I K I F i g . 1

F i g . l a : Schematic view of t h e mechanical r e l a x a t i o n spectrum a t r = 100s f o r e l e c - t r o n i r r a d i a t e d Mo. AG i s t h e maximum r e l a x a t i o n s t r e n g t h o b t a i n e d d u r i n g a 10 min i s o c h r o n a l a n n e a l i n g t r e a t m e n t . No p r o c e s s e s below 2OK and b e t - ween 5 0 K and 5OOK o c c u r .

P i g . l b : Recovery o f t h e r e s i d u a l e l e c t r i c a l r e s i s t i v i t y ( l e f t s c a l e ) and d i f - f e r e n t i a l r e c o v e r y curve ( r i g h t s c a l e ) taken from r e f .

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F i g . lc-.Recovery of t h e d i f f e r e n t r e l a x a t i o n peaks 1-4 o b t a i n e d i n t h e i s o c h r o n a l F i g . I f ' a n n e a l i n g program.

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p r o c e s s between 50K and 500K.

2 . ) None o f t h e f o u r p e a k s d i s a p p e a r s i n a u n i q u e a n n e a l i n g s t a g e . Such a s t a g e would i n d i c e t e t h a t t h e d e f e c t r e s p o n s i b l e f o r t h i s p r o c e s s m i g r a t e s o r d i s s o -

c i a t e s i t s e l f a t t h a t t e m p e r a t u r e . A p p r e n t l y a l l 4 peaks a r e d e c r e a s e d p a r - t i a l l y by t h e d e f e c t s r e s p o n s i b l e f o r t h e r e s i s t i v i t y r e c o v e r y peak a t 28K, and t h e i r f i n a l decay i s c o r r e l a t e d w i t h t h e r e c o v e r y o c c u r i n g between 35K and 42K.

2.) I n o r d e r t o compare t h e r e l a x a t i o n - s t r e n g t h s w i t h t h o s e e x p e c t e d from t h e shape p a r a m e t e r s o b s e r v e d i n t h e H u a n g - s c a t t e r i n g measurements, t h e sum o f t h e r e l a x a - t i o n s t r e n g t h s of a l l

4

p r o c e s s e s i s c a l c u l a t e d and n o r m a l i z e d t o t h e i n i t i a l . F r e n k e l - p a i r c o n c e n t r a t i o n . The c o r r e s p o n d i n g q u a n t i t y c a n b e ca1cu:ated from t h e H u a n g - s c a t t e r i n g r e s u l t s / 3 , 5 / . Both a r e g i v e n i n t a b l e 1 f o r c o m p a r i s o n , t o g e t h e r w i t h t h e c o r r e s p o n d i n g d a t a from t h e n e u t r o n i r r a d i a t e d Mo / I / .

p r e s e n t Ern

n - i r r a d .

Euang / 3 / EAE / I /

A1(C) and

A ~ ( c ' )

a r e t h e p a r t i a l . r e l a x a t i o n s t r e n g t h s f o r < l o o > - and <1102-shear d e f o r m a t i o n , r e s p e c t i v e l y . C i s t h e t o t a l d e f e c t c o n c e n t r a t i o n .

D i s c u s s i o n . - 1 . ) There i s a c l e a r d i f f e r e n c e between t h e EAE-spectra o f e l e c t r o n arid f a s t n e u t r o n i r r a d i a t e d Mo: The

8K

peak i s m i s s i n g i n t h e e l e c t r o n i r r a d i a t e d Mo, and i n s t e a d o f one u n i q u e peak a t 2 6 ~ a s p e c t r u m o f f o u r s i m i l a r l y l a r g e peaks i s fo.md around 2 6 ~ . Because of t h e m i s s i n g 8K peak t h e p r e s e n t measurernents a r e n o t c o n s i s t e n t w i t h t h e i n t e r p r e t a t i o n of t h i s peak i n t e r m s o f a r e o r i e n t a t i o n p r o c e s s of' s i n g l e <110-. dumbbells a s proposed by Mizubayashi / I / .

I r r e s p e c t i v e of' q u e s t i o n w h e t h c r t h e r e o r i e n t a t i o n o f t h e 1110> dumbbell o c c u r s w i t h o r w i t h o u t i t s s i m u l t a n e o u s m i g r a t i o n , i f one o f t h e p r o c e s s e s c o u l d b e a t t r i - b u t e d t o t h e r e o r i e n t a t i o n of t h e <110> dumbbell, i t s h o u l d a n n e a l i n a s t a g e l i k e manner a t t h e t e m p e r a t u r e where t h e dumbbell m i g r a t e s . T h i s h a s n o t b e e n o b s e r v e d . The 6K and 2 6 ~ - p e a k i n t h e n - i r r a d i a t e d Mo a s w e l l a s t h e p r e s e n t 4 peaks a n n e a l a l l i n a wide t e m p e r a t u r e regime and n o t i n a u n i q u e s t a g e .

2 . ) The shape p a r a m e t e r s a s d e t e r m i n e d by t h e X u a n g - s c a t t e r i n g measurements a r e al-

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most one o r d e r o f magnitude l a r g e r t h a n t h o s e d e t e r m i n e d from t h e p r e s e n t EAE- measurements, d e s p i t e t h e f a c t t h a t b o t h measurements were made a f t e r e l e c t r o n i r r a - d i a t i o n o f a l m o s t i d e n t i c a l c o n d i t i o n s . T h i s can o n l y mean t h a t t h e dominant d e f e c t s s e e n i n t h e Huang s c a t t e r i n g measurements a r e n o t o r a t most a minor f r a c t i o n o f them s e e n i n t h e EAE-experiments.

Both p o i n t s , t h e m i s s i n g u n i q u e a n n e a l i n g s t a g e o f a r e l a x a t i o n p r o c e s s and t h e small r e l a x a t i o n s t r e n g t h a s compared t o t h e Huang s c a t t e r i n g e x p e r i m e n t s l e a d t o t h e c o n c l u s i o n , t h a t t h e r e o r i e n t a t i o n o f t h e <IlO>-dumbbells i n Mo i s n o t o b s e r v e d by EAE-measurements.

S e v e r a l arguments may b e i n v o l v e d t o a c c o u n t f o r t h i s r e s u l t : ( i ) The <llO>-dumb- b e l l n e e d s l e s s t h a n 1 jump i n o r d e r t o d i s a p p e a r . I n t h i s c a s e , a l s o EAE-meesure- ments would f a i l t o o b s e r v e t h i s p r o c e s s . No such jump mechanism h a s however been p r o p o s e d s o f a r . ( i i ) A s u p p r e s s i o n o f t h e e x p e c t e d r e l a x a t i o n p r o c c s s by m u t u a l i n t e r a c t i o n o f <110>-dumbbells may b e e x c l u d e d b e c a u s e t h i s p r o c e s s i s a l s o m i s s i n g i n a sample i r r a d i a t e d t o a F r e n k e l p a i r c o n c e n t r a t i o n o f 10 ppm, a t which concen- t r a t i o n t h e i n t e r a c t i o n s h o u l d be n e g l i g i b l y s m a l l . ( i i i ) The <llO>-dumbbell i n t e r -

s t i t i a l atoms may p e r f o r m a m i g r a t i o n a l jump w i t h o u t

~ n ~ t ~ o l f ~ n a l r e o r i e n t a t i o n . Among t h e jump p r o c e s s e s proposed s o postt1on

f a r

/G/

t h e r e i s o n l y t h e s o c a l l e d p u r e t r a n s l a -

.-Ma

t i o n a l jump ( f i g . 2 ) which f u l f i l l s t h i s r e q u i r e - ment i n p r i n c i p l e . The a c t i v a t i o n e n e r g y IiM f o r t h i s jump i s r a t h e r h i g h . F o r t h e a - F e - p o t e n t i a l r i g . 2: P u r e t r a n s l a t i o n a l o f Johnson

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it i s about 1 eV a c c o r d i n g t o t h e

jump o f t h e <110>- c a l c u l a t i o n s o f D e d e r i c h s / 8 / . I t a p p e a r s r a t h e r in the

u n l i k e l y t h a t t h i s jump c o u l d have s u c h a low va- l a t t i c e

l u e a s

HM 2

0 . 1 eV i n Mo a s r e q u i r e d t o a c c o u n t f o r a m i g r a t i o n o c c u r i n g a t a b o u t 30K t o 40K / 1 2 , 1 3 / .

I n s p i t e o f che l a c k o f a s u i t a b l e jump p r o c e s s we have reexamined t h e b a s i c , c h a r a c t e r i s t i c r e s o n a n t v i b r a t i o n s which t h e <IlO>-dumbbell may p e r f o r m . As shown

i n f i g . 3 t h e r e i s one t r a n s l a t i o n a l r e s o n a n t mode, which g i v e s r i s e t o t h e t r a n s l a t i o n a l jump, and t h e r e a r e two l i b r a t i o n a l modes. A d i f f e r e n t k i n d of jump whereby a m i g r a t i o n w i t h o u t r e o r i e n - t a t i o n o f t h e dumbbell c a n o c c u r may r e s u l t from t h e s t i m u l a t i o n o f t h e l i b r a t i o n a l I mode.

T h i s new jump model i s shown i n f i g .

4 .

I f t h e F i g . 3: Resonant v i b r a t i o n s

o f t h e < I lo>-dumbbeli a m p l i t u d e o f t h e l i b r a t i o n a l 1 mode i s s u f f i - l i b r a t i o n a l I mode c i e n t l y l a r e e , one of t h e dumbbell atoms may :.: . . . ..:: ::<,..

.

^. l i b r a t i o n a l I1 mode jump o v e r t o t h e n e a r e s t n e i g h b o u r atoms w i t h

t r a n s l a t i o n a l mode which it forms a new dumbbell. T h i s dumbbell

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position t o a two dimensional longe range d i f f u - s i o n of t h e <llO>-dumbbells i n a (110)- p l a n e without r e o r i e n t a t i o n . From t h e c a l c u l a t i o n s of Dederichs

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i t i s

...

p o s s i b l e t o g i v e an e s t i m a t e f o r t h e ac- t i v a t i o n energy of t h i s jump: s i n c e t h e Fig.

4:

Diffusion jump o f t h e 1 1 0 -dumb- s a d d l e p o i n t c o n f i g u r a t i o n is very c l o s e

b e l l without r e o r i e n t a t i o n v i a t h e c o n f i g u r a t i o n of t h e < I l l > - d u m b b e l l , t h e l i b r a t i o n a l I mode

one can t a k e t h e d i f f e r e n c e of t h e f o r - mation e n e r g i e s of t h e < I l l > - and t h e

< ? l o > - d u m b b e l l s a s a crude e s t i m a t e . This d i f f e r e n c e i s 0.28 eV f o r a-Fe

181.

This v a l u e appears t o be I-easonably c l o s e t o H~ 0 . 1 eV r e q u i r e d by t h e experiments i n s p i t e of t h e a m b i g u i t i e s a r i s i n g from t h e use of an a-Pe p o t e n t i a l i n o r d e r t o make an e s t i m a t e f o r Mo.

I f t h e <ill>-dunhbell were t h e t r u e ( s t a t i c ) s a d d l e p o i n t c o n f i g u r a t i o n , t h e p r e s e n t jump would only o c c ~ u - with a p r o b a b i l i t y of 113 and jumps o u t of t h e par- t i c u l a r { l l O ) - p l a n e with a p r o b a b i l i t y of 213 due t o t h e t r i g o n a l symmetry of t h e 11 1-axis. Because of t h e displacement p a t t e r n of t h e v i b r a t i o n a l I mode, where a l s o t h e next n e a r e s t neighbours a r e d i s p l a c e d s t r o n g l y i n t h e (110)-plane, t h e jumps i n t h i s p l w e may be h i g h l y favoured over t h e jumps o u t of t h e p l a n e 191.

Such dynamic31 e f f e c t s i n d i f f u s i o n phenomena a r e n o t unknown /10,11/. The p r e s e n t e x p e r i m e n t a l o b s e r v a t i o n s r e q u i r e t h a t t h e jumps w i t h i n t h e {llO]-plane occur with a p r o b a b i l i t y of about 0.98. A t h e o r e t i c a l e s t i m a t e whether such a h i g h de- g r e e of' d i P f u s i o n - a n i s o t r o p y i s r e a l i s t i c i s not a v a i l a b l e a t p r e s e n t . F u t u r e computer-simulation s t u d i e s may be a p o s s i b i l i t y t o give i n s i g h t i n t o such a n i - s o t r o p i c d i f f u s i o n phenomena.

The p r e s e n t l y proposed new jump model e x p l a i n s a l s o t h e u n u s u a l b e h a v i o u r of r e s i s t i v i t y a n n e a l i n g observed i n Mo i n s t a g e I /12/ and of t r a p p i n g o f s e l f - i n t e r s t i t i a l atoms a t ~ e ~ - ' - ~ 8 1 3 b a u e r atoms 1131 on t h e b a s i s of t h e two dimensional m i g r a t i o n . Therefore t h e s e o b s e r v a t i o n s a r e a n o t h e r support o f t h e p r e s e n t jump model.

Conclusion.- The comparison of EAE experiments on neutron i r r a d i a t e d Mo / I / and of t h e p r e s e n t ones on e l e c t r o n i r r a d i a t e d Mo with Huang-scattering measurements on e l e c t r o n i r r a d i a t e d Mo /3/ l e a d s t o t h e c o n c l u s i o n , t h a t t h e <IlO>-dumbbell s e l f - i n t e r s t i t i a l atom i n Mo does n o t r e o r i e n t b e f o r e o r d u r i n g i t s m i g r a t i o n . T h i s o b s e r v a t i o n i s e x p l a i n e d by a model of a jump p r o c e s s which l e a d s t o a two dimen- s i o n a l m i g r a t i o n of <llO>-dumbbells i n { l l O > - p l a n e s without r e o r i e n t a t i o n .

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