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AMPLITUDE-DEPENDENT INTERNAL FRICTION IN HIGH PURITY MOLYBDENUM SINGLE
CRYSTALS IN THE TEMPERATURE RANGE 5.9 - 300 K
H. Kaufmann, P. Pal-Val, D. Schulze, V. Startsev
To cite this version:
H. Kaufmann, P. Pal-Val, D. Schulze, V. Startsev. AMPLITUDE-DEPENDENT INTERNAL FRICTION IN HIGH PURITY MOLYBDENUM SINGLE CRYSTALS IN THE TEMPERA- TURE RANGE 5.9 - 300 K. Journal de Physique Colloques, 1981, 42 (C5), pp.C5-55-C5-60.
�10.1051/jphyscol:1981507�. �jpa-00220964�
JOURNAL DE PHYSIQUE
CoZZoque C5, suppZ6rnent au nolO, Tome 4 2 , octobre 1982 page ~ 5 - 5 5
AMPLITUDE-DEPENDENT INTERNAL F R I C T I O N I N H I G H P U R I T Y MOLYBDENUM SINGLE CRYSTALS I N THE TEMPERATURE RANGE 5.9
-
3 0 0 K*
x*
H.J. Kaufmann , P.P. Pal-Val, D. Schulze and V.I. Startsev
Physico-TeehnicaZ I n s t i t u t e o f Low [Pemperatures, Academy of Sciences of t h e Ukr
.
SSR, Kharkov, USSRA b s t r a c t .
-
?lmplitude and t e a p e r a t u r e dependences o f i n t e r n a l f r i c t i o n i n niolybdenum s i n g l e c r y s t a l s of tiie o r i e n t a t i o n s( l o o ) ,
<110), (111),
<941) a r e s u d i e d . rl'iie r e s i d u a l r e s i s t a n c ef
r a t i o of t h e samp:Les i s ( 1 - 2 ) x l O
.
Ti;e measurements a r e c a r r i e d o u t a t t h a f r e q u e n c y of d S kHz i n t h e t e m p e r a t u r e r a n g e 5.9- -
30,:-
A. I t h a s been estab1isi;ed t h a t a t h i g h te!nperatures t h e a n p l i t u d e - d e p e n d e n t i n t e r n a l f r i c t i o n i s due t o t h e p r o c e s s of t h e r m a l l y a c t i v a t e d d i s l o c a t i o n u n p i n n i n g from t h e p i n n i n g cea- t r e s . A t low t e m p e r a t u r e s a maxiizun i s f o u n d i n t h e a m p l i t u d e dependences t h e h e i g h t of which d e c r e a s e s w i t h d e c r e a s i n g teun- p e r a t u r e , b u t i t s ~ o s i t i o n d o e s n o t depend on t h e t e m p e r a t u r e . I n t h e same a x ? l . i t u d e r a n g e a s a t u r a t i o n re,gion a n - j e a r s i n t l ~ e modulus d e f e c t a m p l i t u d e dependences. Such a S e h s v i o u r of t l i e h i g h - a m p l i t u d e i n t e r n e l f r i c t i o n a t low t e i m e r a t u r e s c a n n o t be e:cplaiiied i n t h e framework of tile t h e o r i e s p r e s e n t .1
.
I n t r o d a c t i o n .-
The i n v a s t i g a t i o n of tile amplitude-dependen t i n t e r - n a l f r i c t i o n i n h i g h p u r i t y p e r f e c t s i n g l e c r y s t a l s i s of ? a r t i c u l a r i n t e r e s t a s d i s l o c a t i o n s y s t e m of s u c h c r y s t a l s a r e c h a r a c t e r i z e 3 by low d i s l o c a t i o n d e n s i t y and l o n g seg3ie:lts because of a s r n a l l number of p i n n i n g c e n t r e s .I n t h e p r e s e a t 2aper t % e a n a l i t x d o dci)enrlences o f i n t e r n a l f r i c t i o n have been s t u d i e d i n h i g h ~ a u r i t y molybdenum s i n z l e c r y s t a l s i n a wide t e m p e r a t u r e r a n g e i n c l u d i n r ; h e l i u m t e m p e r a t u r e s . Such i n - v e s t i g a t i o n s a 1 l . o ~ u s t o o b t a i n new d a t a on tiie te:cgerafure e i ' f e c t on
t h e d i s l o c a t i o n u n p i n n i n g p r o c e s s i n t h e low t e ~ ? p e r a t u r c r a n g e s t u - d i e d i n s u f f i c i e n t l y .
2. m e r i m e n t a 1 . - The dependences o f tfie decrement 6 ai2:f modulus de- f e c t ~ N i / i y l on t h e v i b r a t i o n a m p l i t u d e &, a r e s t a d i e d i n t h e ternaera- t u r e r a n g e 5.9
-
3C0 K. ?he ineasuranents a r z made by t h e two coapo- n e n t o s c i l l a t o r t e c h n i q u e a t t h e f r e q u e n c y o f 6 3 kF1z / I / . The r e s i -"Akademie d e r Wissenschaften d e r DDR, Z e n t r a l i n s t i t u t fiir F e s t k a r p e r - physik und Werkstofforschung, Dresden, DDR
i P r e s e n t a d d r e s s : Akademie d e r Wissenschaften d e r DDR, Otto-Nuschke- S t r a s s e 2 2 / 2 3 , 1 0 8 0 B e r l i n , DDR
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981507
C5-56 JOURNAL DE PHYSIQUE
d u a l r e s i s t a n c e r a t i o ( R R R ) of molybdenum s i n g l e c r y s t a l s r a n g e s from 1 x 1 0 ~ t o 2x1 05. T i e samples have been o b t a i n e d by s p a r k c u t t i n g f r o 2 c y l i n d r i c a l as-grown c r y s t a l s . The wave v e c t o r of t h e l o n g i t u d i - n a l s t a n d i n g u l t r a s o u n d waves c o i n c i d e s w i t h one of t h e c r g s t a l l o g r a - p h i c d i r e c t i o n s < 1 5 0 ) , < ? l o ) , < I l l ) and (941) w i t h an a c c u r a c y of
2'. T i e measurements have been made w i t h f o u r s e t s of samples of t h e o r i e n t a t i o n s mentioned.
3. R e s u l t s . - The d a t a o b t a i n e d w i t h t h e samples of d i f f e r e n t s e t s have no s u f f i c i e n t q u a l i t a t i v e d i f f e r e n c e s . L a t e r on, t h e q u a n t i t a - t i v e d i f f e r e n c e s i n t h e d a t a f o r d i f f e r e n t s e t s w i l l be d i s c u s s e d s p e c i a l l y . F o r t h e s a k e of comparison we g i v e h e r e t h e r e s u l t s ob- t a i n e d i n / 1 / f o r t h e Mo-samples o f t h e same p u r i t y and t h e o r i e n t a - t i o n ( 1 1 0 ) ( i n t h e p r e s e n t p a p e r we d e n o t e them a s
t
P i g s . l a , b show t h e dependences 6 ( Eo)Y- and AM/M( E o ) f o r t h e samples o f t h e
0 7
L
LO o r i e n t a t i o n ( 1 1 0 ) . It i s s e e n t h a t t h e
5 dependences 5 ( E o ) measured have sec-
t i o n s of t k e a m p l i t u d e independent
3 (Si) and a m p l i t u d e dependent
(SH)
de-crements. X i t h d e c r e a s i n g t e m p e r a t u r e t h e c r i t i c a l a m p l i t u d e Eoc of t h e be- g i n n i n g of t h e s e c t i o n 611 s h i f t s t o
Eo- h i g h e r a m p l i t u d e s i n t h e whole tempe-
F i g . l a r a t u r e range s t u d i e d . Zvery s e t of
, I I I I
0 - _ c u r v e s h a s s u f f i c i e n t l y wide tempera-
12 - t u r e r a n g e where t h e c u r v e s 6 ( Eo) i n
-2 - semilog c o o r d i n a t e s s h i f t p a r a l l e l t o
$
(1 10) - themselves. I n t h e same amplitude-4
E - o r a n g e t h e a m p l i t u d e dependences mea-
130
-6 170 s u r e d f o r samples of d i f f e r e n t o r i e n -
210 250
-8 \ 300
o t h e r . I n t h i s c a s e Eoc i n c r e a s e s a t
;dB
io-7 ,;-6 lo-5,>
t h e s u c c e s s i v e t r a n s i t i o n from (1 00)Fe ----' t o (941>, < 1 1 0 > , <111> sample o r i e n t a -
Pig. Ib t i o n s .
Pig. 2 r e p r e s e n t s t h e c u r v e s
6
( E o ) f o r t h e samples of a l l s e t s measured a t 60 K.I n t h e low t e m p e r a t u r e r a n g e t h e b e h a v i o u r of t h e dependences 8( Eo) and A&I/M( Eo) changes e s s e n t i a l l y . A s t h e t e m p e r a t u r e decrea- s e s , i n the c u r v e s 6 ( Eo) a w e l l - d e f i n e d maximum a p p e a r s i n t h e h i g h a m p l i t u d e range. The a m p l i t u d e a t which t h e maximum i s observed does n o t depend p r a c t i c a l l y on t h e temperature. A t t h e same time t h e maxi-
mum h e i g h t d e c r e a s e s r a t h e r r a p i d l y w i t h d e c r e a s i n g temperature. Somewhat d i f f e r e n t i s t h e behaviour of t h e de-
0
gendences AIG/P( E o ) . I n t h e low tempe-
3
5 -f o e s
r a t u r e r a n g e t h e modulus d e f e c t L -
t o a p l a t e a u a t t h e a m p l i t u d e s where
3 -
t h e maximum i s found. Maxima a r e n o t
observed i n t h e dependences AM/M( E o ) . - 4-t t h e t e m p e r a t u r e s of a b o u t 6 K 1 -
t h e a m p l i t u d e dependences 6 and A X/Ll
a r e v e r y weak i n t h e samples of t h e lo-"
Eo-
o r i e n t a t i o n ( 1 1 1 ) . I n t h e samples of
(110) even a s m a l l d e c r e a s e of
s
i s Fig. 2n o t e d i n t h e h i g h r e g i o n of E o ,
t i ~ o u g h i n t h i s c a s e t h e s i g n of t h e change of AM/M remains p r e v i o u s . B e s i d e s t h e amplitude dependences 6 and AI&/XI, t h e t e m p e r a t u r e decrement and resonance f r e q u e n c y dependences of samples a r e measured a t t h e f i x e d v a l u e E o = 4 . 5 ~ 1
oW8
chosen i n such a way t h a t i t would c o r r e s p o n d t o t h e amplitude independent r e g i o n of t h e c u r v e s 6 ( Eo) and AM/MtE$he dependences Zi(T) and (fr/frGK- 1 ) ( T ) f o r t h e samplest I I I I I of d i f f e r e n t o r i e n t a t i o n a r e
( 1 0 0 ~ g i v e n i n E'ig,3a,b. It i s seen - t h a t t h e dependences 6 i ( ~ )
have q u a l i t a t i v e l y l i k e tempe-
- r a t u r e run. In t h e h i g h tempe- r a t u r e r a n g e broad maxima a r e
200 300
- observed i n a l l samples e x c e p t
0 100
T(K)
-
t h e o r i e n t a t i o n (11 1 ) . The ma-P i g . 3a ximum p o s i t i o n s a r e approxima-
t e l y t h e f o l l o w i n g : < l o o )
-
9-
t
0 -L I?
2
% *
r!
\ cc L
-1
-2
I I I I 230-240 K, < ? l o )
-
190-200 K ,-
(941 )-
250-260 K. I n t h e low t e m p e r a t u r e range a t T 1 2 5 K -t h e dependences 6 ( T ) have a
- s h a r p r i s e which t u r n s o u t t o
E = o be t h e h i g h e s t f o r t h e o r i e n t a - t i o n (110) and t h e l e a s t f o r
(100).
I I I I I The t e m p e r a t u r e dependen-
0 100 200 300
T(K)- c e s of (fr/fr6-1) a l s o have a q u a l i t a t i v e l y l i k e t e m p e r a t u r e Fig. 3b
run. B i t h d e c r e a s i n g tempera-
C5-58 JOURNAL DE PHYSIQUE
t u r c t h e m o n o t o n i c a l i n c r e a s e o f a r e s o n a n c e f r e q u e n c y of' a sample w i t h g o i n g t o tile c l a t e a u t a k e s p l a c e i n t h e t e m p e r a t u r e r a n g e 1 3 C K . The a b s o l u t e v a l u e o f tlie maximun r e l a t i v e v a r i a t i o n i n c r e a s e s a-t tlie s u c c e s s i v e t r a n s i t i o n from (111) t o ( I I O ) , ( 3 4 1 )
,
(IOc').3. D i s c u s s i o n . - The p e c u l i a r i t i e s of t h e degundences 8 ( Eo) and A?;;/::( Eo) d - e s c r i b e d a l l o w u s t o c o n c l u d e t k a t i n t h e h i g h tempera-
t u r e r a n g e tiicy a r e due t o t h e mechanisms of t h e r m a l l y a c t i v a t e d d i s - l o c a t i o n h y s t e r e s i s d e v e l o ~ e d i n t h e o r i e s o f Granato-S;ic!re-Teutonic0 / 2 , 3 / and Indenborn-Ciicrnov / 4 / . The drair~bacir or^ t h e t h e o r c t i c a l con- s i d e r a t i o n s / 2 , 3 / c o n s i s t s i n t h e d i f f i c u l t y o f t h e q u a n t i t a t i v e cornparison o f tlle t h e o r y w i t h e x p e r i m e n t a l d a t a . i n / 4 j a more gcne- r a l a ? p r o a c h is u s e d and b e s l d e s , t h e main c o n c l u s i o n s o f t h e tiieory :nay be co::ipared r a t h e r e a s i l y w i t h t h e d a t a on amplitude-depondent i n t e r n a l f r i c t i o n .
une of t h e main c r i t e r i a o f t h e a p p l i c a b i l i t y o f t h e t h e o r y /4/ i s t h e a a r a l l . e l s h i f t o f t h e a n p l i t u d e d e c r e m e n t dependences i n t h e s e n i l o g c o o r d i n a t e s a s t h e t e m p e r a t u r e ckanges. As i t i s s h o r n i n i'ig. l a , s u c h a s h i f t i s i n d e e d o b s e r v e d i n wide t e m p e r a t u r e and a m o l i t u d e r a n g e s . ]:!oreover, t h e c u r v e s o f t h e dapendences measured f o r d i f f e r e n t o r i e n t a t i o n s ( 3 i g . 2 ) s h i f t p a r a l l e l . Such a n a g r e e - ment o f t h e t h e o r y w i t h t h e e x p e r i m e n t a l l o w s u s t o o b t a i n t h e i m - p o r t a n t c h a r a c t e r i s t i c s of t h e p r o c e s s o f d i s l o c a t i o n overcoming t h e p i n n i n g c e n t r e s , i . e . a c t i v a t i o n e n e r g y and a c t i v a t i o n volume dependences on t h e d e f o r m a t i o n a m p l i t u d e , tlle d i s t r i b u t i o n f u n c t i o n o f d i s l o c a t i o n segment l e n g t h s , t h e f o r c e law o f d i s l o c a t i o n i n t e r a c - t i o n w i t h p i n n i n g c e n t r e s f o r t k i s t e m p e r a t u r e r a n g e . The a c t i v a t i o n volume v a r i e s f roin
-
5 b f o r tile s h o ~ t 3 u n p i n n i n g s e p i e n t s and d e f o r - m a t i o n a i p l i t u d e Eo z 5x1 o - ~ t o 6xi o3b3 f o r t h e l o n g e s t segments and E~ r 5r10-'.
Tiie e s t i m a t i o n of t h e b i n d i n g e n e r g y o f a d i s l o c a t i o n w i t h p i n n i n g c e n t r e s g i v e s t h e v a l u e o f Lo = 9.6 eY. The d i s t r i b u t i o n f u n c t i o n o f t h e d i s l o c a t i o n seginent l e n g t h s a p 7 e a r s t o be e x p o n e n t i a l w i t h t h e exponent c l o s e t o -6. These d a t a t u r n o u t t o be i d e n t i c a l f o r t h e s a n p l e s o f a l l o r i e n t a t i o n s and v e r y c l o s e t o t1:ose o b t a i n e de a r l i e r / l / f o r 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 p u r i t y of t h e o r i e n t a - t i o n (110). I t a l l o w s u s t o c o n c l u d e t h a t i n a l l s a r r p l e s ( a t l e a s t , i n t h e t e m p e r a t u r e r e g i o n mentioned) t h e t h e r m a l l y a c t i v a t e d u n p i n - n i n g o f d i s l o c a t i o n s (of one t y p e mainly) from t h e p i n n i n g c e n t r e s h a v i n g a s m a l l s p r e a d of b i n d a n g e n e r g y w i t h d i s l o c a t i o n s t a k e s place.
The i n c r e a s e o f Eoc shown i n Yig. 2 i s a p p a r e n t l y c o n n e c t e d w i t h t h e change o f t k e Schmid f a c t o r s f o r a c t i n g s l i p systelns a t t h e t r a n s i t i o n f r o m one o r i e n t a t i o n t o a n o t h e r .
The b e h a v i o u r of t h e dependences
5 (
E o ) and A!;;/!:( E o ) a t lowt e m p e r a t u r e s Where t h e i m p o s s i b i l i t y o f t h e i n t e r p r e t a t i o n o f expe- r i m e n t a l d a t a i n t h e framework o f Indenboa-Chernov t h e o r y i s q u i t e e v i d e n t , i s of c o n s i d e r a b l e i n t e r e s t . The a p ? e a r a n c e o f a maximun i n t h e dependences
b (
Eo) i n t h e h i g h a m p l i t u d e r e g i o n i s p r e d i c t e d by d o g e r s i n /5/. It i s c o n n e c t e d w i t h t h e a c h i e v e m e n t of s u c h E o a t which t h e u n p i n n i n g of a l n o s t a l l d i s l o c a t i o n segments o c c u r s , Such a s i t u a t i o n i s p o s s i b l e f o r d i s l o c a t i o n s y s t e m s w i t h l o n g segments.S i m i l a r s y s t e m s a r e formed e i t h e r a t low t e c i p e r a t u r e c r y s t a l d e f o r - m a t i o n / 6 , 7 / o r i n t h e c a s e of h i g h p u r i t y of t h e samples s t u d i e d a s i t i s i n t h e p r e s e n t i n v e s t i g a t i o n . The f a c t t h a t t h e p u r i t y of t t e c r y s t a l s f a v o u r s t h e f i n d i n g o u t of t h e n o ~ r l o n o t o n i c c h a r a c t e r o f t h e dependence g( Eo) i s s e e n when comparing t h e low t e m p e r a t u r e beha- v i o u r of t h e c u r v e s o b t a i n e d i n t h i s work f o r t h e samples w i t h ERR
5 3
=I0 w i t k t h a t of R I L i i = 1 0 i n / I / . I n t h e s a m p l e s w i t h RHR-
l o 3
t h e maximum i n t h e c u r v e s 6 ( Eo) i s n o t o b s e r v e d up t o h e l i u m temperatu- r e s .The Rogers t h e o r y /5/ d e s c r i b e s t h e n o n - a c t i v a t e d p r o c e s s o f d i s l o c a t i o n u n p i n n i n g , i . e . i t i s p r a c t i c a l l y t r u e a t 0 K. But t h i s t h e o r y d o e s n o t t a k e i n t o a c c o u n t t h e change of damping p r o p e r t i e s i n which d i s l o c a t i o n s move when c h a n g i n g t e m p e r a t u r e ( t h i s drawback i s a l s o i n t r i n s i c t o t h e t h e o r y /4/). T h a t ' s why, a t ~ r e s c n t we have no p o s s i b i l i t y t o a n a l y s e c o r r e c t l y s u c h p e c u l i a r i t i e s of t h e b e h a v i o u r o f t h e maximum o b s e r v e d as t h e r a p i d d e c r e a s e o f i t s h e i g h t and t h e s t a b i l i t y o f i t s p o s i t i o n w i t h r e s p e c t t o t h e a x i s Eo when d e c r e a s i n g T. The o n l y f a c t i s e v i d e n t t h a t w h i l e d e c r e a s i n g T, t h e l o s s e s con- n e c t e d w i t h t h e d i s l o c a t i o n u n p i n n i n g from t h e p i n n i n g c e n t r c s de- c r e a s e s h a r p l y .
The r e a c h i n g o f t h e p l a t e a u by t h e modulus d e f e c t i n h i g h - a m p l i t u d e r e g i o n b e g i n n i n g w i t h Eo a t which t h e maximum i n t h e depen- d e n c e 6 ( E o ) i s o b s e r v e d may be q u a l i t a t i v e l y e x p l a i n e d u s i n g t h e a p p r o a c h d e v e l o p e d i n /5/. However, as i n t h e c a s e o f t h e d e c r e m e n t , we c a n ' t a n a l y s e s u c c e s s i v e l y a l l e x p e r i m e n t a l d a t a o b t a i n e d .
The s h a r p i n c r e a s e o f 6 a t T ' 2 5 K r e s u l t s from t h e i n t e r a c - t i o n o f e l a s t i c u l t r a s o u n d waves w i t h c o n d u c t i o n e l e c t r o n s /9,1/. The o b s e r v a t i o n o f t h i s phenomenon a t s u c h low f r e q u e n c i e s i s e x p l a i n e d by h i g h p u r i t y o f t h e samples. R a t h e r t h e s p r e a d i n v a l u e s o f
6
a t 6 K from one sample t o a n o t h e r i s c o n n e c t e d w i t h t h e d i f f e r e n c e i n t h e o r i g i n a l p u r i t y o f s a m p l e s and i n t h e p e r f e c t i o n of t h e i r s t r u c - t u r e . F o r t h e p u r e s t samples t h e e l e c t r o n mean p a t h t u r n s o u t t o be a b o u t 1 mm. The broad maxima o b s e r v e d i n t h e c u r v e s 6 ( T ) i n t h e r a n g e of c o m p a r a t i v e l y h i g h T a r e e v i d e n t l y due t o r e l a x a t i o n p r o c e s s e s o f d i s l o c a t i o n i n t e r a c t i o n w i t h i m p u r i t y c e n t r e s /9/. T h e i r weak-pro-C5-60 JOURNAL DE PHYSIQUE
nounced c h a r a c t e r i s i n d i c a t i v e o f t h e r e l z t i v e s t a b i l i t y o f t h e d i s l o c a t i o n s t r u c t u r e s o f t h e s a m p l e s when d e c r e a s i n g T.
The d i f i e r e n c e o f t i l e t e r n p r a t u r e d e p e n d c n c s s (fr/f,61c-l) f o r d i f f e r e n t o r i e n t a t i o n s i s e x p l a i n e d by the a n i s o t r o p y of t h e tempe- r a t u r e d e p e n d e n c e s o f t h e e l a s t i c n o d u l i o f t h e m e t a l g i v e n . I n a d d i t i o n a s i t i s s e e n from t h e d a t a o b t a i n e d f o r t h e o r i e n t a t i o n
( 1 1 0 ) t h e d i s l o c a t i o n modulus 4 e f e c t f o r v a r i o u s i n i t i a l s t r u c t u r e s o f s a n p l e s p l a y s a n e s s e n t i a l r o l e i n tiiis c a s e .
l i e f e r e n c e s
---
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