DYNAMIC DISLOCATION DAMPING IN METALS

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DYNAMIC DISLOCATION DAMPING IN METALS

V. Al’Shits, N. Kobelev, Ya. Soifer

To cite this version:

D Y N A M I C DISLOCATION D A M P I N G IN METALS

V . I . A l l S h i t s , N.P. ~ o b e l e v * and Ya.M. s o i f e r *

I n s t i t u t e o f CrystaZZography, Academy of Sciences o f t h e USSR, Moscow, USSR " ~ n s t i t u t e o f Solid S t a t e Physics, Academy of Sciences o f t h e USSR,

ChernogoZovka, Moscow d i s t r i c t , USSR

A b s t r a c t .

-

The s i m u l t a n e o u s measurements of t h e a m p l i t u d e i n d e p e n d e n t damping and modulus d e f e c t i n t h e copper a n d lead s i n g l e c r y s t a l s a r e performed w i t h i n t h e t e m p e r a t u r e r a n g e from 4 , 2 K t o 300 K (Cu) and from 4 , 2 K t o 1 0 K (Pb) a t 5+15 MHz. It i s found t h a t t h e d i s l o c a t i o n i n t e r n a l f r i c t i o n i n copper

i s d e t e r m i n e d by t h e s u p e r p o s i t i o n of two e n e r g y l o s s c o n t r i - b u t i o n s : dynamic l o s s caused by t h e v i s c o u s d i s l o c a t i o n d r a g and t h e r e l a x a t i o n one caused by t h e r m o a c t i v a t e d d i s l o c a t i o n motion. The dynamic l o s s c o n t r i b u t i o n was s i n g l e d o u t , and t h e t e m p e r a t u r e dependence of t h e damping c o n s t a n t B is o b t a i n e d . The B(T) dependence i n Cu i s d i s c u s s e d i n - t e r m s of t h e e x i s t i n g models of t h e dynamic d i s l o c a t i o n damping. B u s i n g t h e super- c o n d u c t i n g t r a n s i t i o n i n l e a d t h e s t r o n g a v i x e n c e l e o b t a i n e d

t h a t t h e damping c o n s t a n t B a t low t e m p e r a t u r e s i s d e t e r m i n e d by t h e e l e c t r o n - d i s l o c a t i o n i n t e r a c t i o n ,

I n t r o d u c t i o n ,

-

According t o t h e t h e o r e t i c a l p r e d i c t i o n s , t h e d i s l o - c a t i o n dynamic damping i n m e t a l s , c h a r a c t e r i z e d by t h e damping cons- t a n t B, i s determined by t h e p h o n o n - d i s l o c a t i o n and e l e c t r o n - d i s l o c a - t i o n i n t e r a c t i o n s . To o b t a i n t h e v a l u e of B t h e a m p l i t u d e independent d i s l o c a t i o n i n t e r n a l f r i c t i o n i s u s u a l l y measured, and t h e r e s u l t s a r e a n a l y z e d i n t h e t e r m s of t h e Granato-Lucke s t r i n g model [l]

.

A t

p r e s e n t t h e r e i s a number of mechanisms proposed t o d e s c r i b e t h e d i s l o c a t i o n i n t e r a c t i o n s w i t h phonons and e l e c t r o n s . The b e s t way f o r t e s t i n g t h e t h e o r i e s i s t o s t u d y t h e d i s l o c a t i o n damping under c o n d i t i o n s of c o n t r o l l a b l e v a r y i n g of t h e e l e m e n t a r y e x c i t a t i o n den- s i t y i n c r y s t a l . F o r example, one c a n change t h e phonon d e n s i t y by t h e t e m p e r a t u r e v a r y i n g , and t h e f r e e e l e c t r o n s d e n s i t y by means of t h e s u p e r c o n d u c t i n g t r a n s i t i o n . However, t h e e x p e r i m e n t a l r e a l i z a t i o n of t h a t programme h a s met some d i f f i c u l t i e s ( s e e , e.g. i n c a s e of Cu

L2,3] ) which h a s n o t allowed one t o make unambiguous c o n c l u s i o n a b o u t d i s l o c a t i o n i n t e r a c t i o n mechanisms involved. These d i f f i c u l t i e s have been overcome i n [ 4 , 5 1 . The a u t h o r s showed, t h a t t h e i n e x p l i - c a b l e b e h a v i o r of B(T) o b s e r v e d i n

p,3]

f o r Cu was d u e t o t h e f a c t t h a t t h e h i g h f r e q u e n c y d i s l o c a t i o n a m p l i t u d e i n d e p e n d e n t damping was d e t e r m i n e d n o t o n l y by t h e dynamic, as h a s been a c c e p t e d p r e v i -

o u s l y , b u t r a t h e r by t h e combination of t h e dynamic and r e l a x a t i o n

C5-346 JOURNAL DE PHYSIQUE

t y p e s of d i s l o c a t i o n damping.

The p a p e r r e p o r t s on t h e d e t a i l e d e x p e r i m e n t a l i n v e s t i g a t i o n of t h e damping c o n s t a n t B t e m p e r a t u r e dependences i n t h e c o p p e r and l e a d s i n g l e c r y s t a l s under t h e c o n t r o l l a b l e c o n d i t i o n s .

E x p e r i m e n t a l Nethod.

-

The s i m u l t a n e o u s measurements of t h e a m p l i t u d e independent d i s l o c a t i o n damping and modulus d e f e c t i n t h e copper and l e a d s i n g l e c r y s t a l s a r e c a r r i e d o u t w i t h i n t h e t e m p e r a t u r e r a n g e from 4 , 2 K t o 300 K a t 5+100 MHz f o r Cu and w i t h i n 4 , 2 K t o 1 0 K a t

5+15 MHz f o r Pb by t h e r e s o n a n c e t e c h n i q u e

161

.

I n o r d e r t o i n t r o - duce f r e s h d i s l o c a t i o n s t h e Cu specimens w i t h [III] o r i e n t a t i o n were c o m p r e s s i v e l y deformed by 0,1 t o 0,Yo i n a t e s t i n g machine t h r o u g h t h e s p e c i a l d e v i c e t o keep t h e specimen f a c e s p a r a l l e l . To s t a b i l i z e t h e d i s l o c a t i o n s t r u c t u r e t h e measurements were performed i n 1,5-2

h o u r s a f t e r t h e deformation. Then t h e specimen was p l a c e d i n t o t h e c r y o s t a t where t h e measurements of s a n d

F

were c a r r i e d out. To s i n g l e o u t t h e d i s l o c a t i o n c o n t r i b u t i o n i n t h e t o t a l energ;y l o s s

8

t h e specimen was

8

- i r r a d i a t e d from co60 up t o t h e d o s e 8.10 t h a t c o r r e s p o n d s t o t h e complete pinning. I t i s shown, t h a t t h e

r(

- i r r a d i a - t i o n d o s e a p p l i e d d o e s n o t i n f l u e n c e t h e n o n - d i s l o c a t i o n c o n t r i b u t i - ons t o t h e t o t a l l o s s . The d i s l o c a t i o n c o n t r i b u t i o n i n

g

and

%

i s d e t e r m i n e d a s a d i f f e r e n c e between t h e v a l u e s o f

8

and

a

befo-

b

9

'

r e and a f t e r s u c h - i r r a d i a t i o n . The damping c o n s t a n t B i s d e f i n e d %rom t h e measurements of a m p l i t u d e i n 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 by

t h e wellknown Granato-Lucke r e l a t i o n f o r

( ~ ~ 4 4 ' 1

,

where

Z=

BLZh2~

:

3

Y ~ N .

'

S

~ = K , N ~ ~ ~ , & = K , N L '

B =

-r-

Y

(A*/$

'

(1)

where

K,

and & a r e t h e c o n s t a n t s ; t h e r e s t n o t a t i o n s a r e t h e same

as Granato-Lucke used [l]

.

I n o r d e r t o b e c o n f i d e n t t h a t t h e r e l a - t i o n W C 4 4

1

i s f u l f i l l e d , t h e measurements a t t h e d i f f e r e n t f r e q u e n - c i e s were made, and t h e l i n e a r dependence

s/

v e r s u s C3 id-checked. The t e m p e r a t u r e dependence of B d e f i n e d i n t h e manner d e c r i b e d above

i s shown i n t h e Fig.1 and 2. I n Fig.1, t h r e e E(T) c u r v e s a r e shown f o r t h e c a s e of t h e same specimen w i t h v a r i o u s mean l o o p l e n g t h s

Z

of a d i s l o c a t i o n . I n o r d e r t o o b t a i n i n t h e same specimen v a r i o u s t h e specimen was s p e c i a l l y i r r a d i a t e d by t h e d i f f e r e n t small d o s e s o f

8

- i r r a d i a t i o n . The measurements were made a t 15 WXz. I n Fig. 2 f o u r B(T) c u r v e s a r e shown f o r t h e c a s e of t h e specimen w i t h t h e same

c,

b u t measured a t d i f f e r e n t f r e q u e n c i e s . A s it s e e n from F i g s . 1 and 2,B(T) c u r v e s a r e n o t monotonous and depend on

L

and f r e q u e n c y of t h e measurements. The most d i f f e r e n c e s a r e s e e n t o o b s e r v e i n t h e r a n g e of 40-100 K. A t t h e same t e m p e r a t u r e r a n g e a s t e p w i s e @ change

c a l c u l a t e d from t h e % and 44/54

measurements i n t h e same copper specimen with,the d i f f e r e n t mean l o o p l e n g t h (L) of a d i s l o c a t i o n a r i s e d a f t e r t h e c o r r e s ~ o n d i n n sgall-doses of

&'

- i r r a d i a t i o n ' - (L,

>

~ ~ 7 % ~ ) . f

= l 5

XHz. 1 1 , 2 , w i t h o u t ta- k i n g i n t o account- t h e r e l a x a t i o n damping compo.nent 4,5,6 t h e same r e s u l t s o b t a i n e d by t h e e x c l u d i n g of t h e r e l a x a - t i o n damping component.

F

: The t e m p e r a t u r e depen- ence of t h e damping c o n s t a n t B c a l c u l a t e d from t h e

8

and A ~ / w

measurements i n t h e same cop'cer specimen a t t h e d i f f e r e n t f r e - quencies. The numbers by t h e c u r v e s d e n o t e t h e measurement f r e q u e n c i e s . The p o i n t s (1 t o 4) a r e o b t a i n e d w i t h o u t t a k i n g i n t o a c c o u n t t h e r e l a x a t i o n damping component. The p o i n t s

(5-8)

a r e o b t a i n e d by t h e e x c l u d i n g of t h e r e l a x a t i o n damping component. i s found, t h a t i s t y p i c a l f o r t h e r e l a x a t i o n t y p e i n t e r n a l f r i c t i o n . T h i s i s confirmed by t h e s h i f t of t h e

431

s t e p towards t h e h i g h e r

F

iiemperature when t h e measurement f r e q u e n c y i s i n c r e a s e d . Assuming t h e s h i f t of t h e 6 E ( T ) i s t h e r m a l l y a c t i v a t e d , one can e s t i m a t e t h e

_-v

a c t i v a t i o n p a r a m e t e r s of t h e p r o c e s s i n v o l v e d : H=0,035 e v ,

caz

10'1° s e c . These a r e t y p i c a l f o r d i s l o c a t i o n r e l a x a t i o n p r o c e s s i n Cu

f

7 3

.

The o b s e r v a t i o n of t h e s t e p w i s e b e h a v i o r of t h e

Y

( T ) s u g g e s t s t h a t t h e d i s l o c a t i o n a m p l i t u d e independent i n t e r n a l r i c t i o n a t h i g h f r e q u e n c i e s i s determined by t h e s u p e r p o s i t i o n of dynamic and r e l a - x a t i o n t y p e s of d i s l o c a t i o n damping. Knowing t h e t e m p e r a t u r e depen- dence o f

bS1

,

one can r e s t o r e t h e r e l a x a t i o n c o n t r i b u t i o n i n

g

a t

9''

t h e d i f f e r e n t f r e q u e n c i e s . It a l l o w s one t o s i n g l e o u t t h e dynamic c o n t r i b u t i o n t o t h e damping and c a l c u l a t e t h e new v a l u e s of D(T) un- d e r t h e assumption t h a t b o t h c o n t r i b u t i o n s a r e a d d i t i v e . The B(T) c u r v e s o b t a i n e d by e x c l u d i n g t h e r e l a x a t i o n damping c o n t r i b u t i o n

C5-348 JOURNAL DE PHYSIQUE

t h e t e m p e r a t u r e and i s c o n n e c t e d w i t h t h e p h o n o n - d i s l o c a t i o n i n t e r - a c t i o n , t h e second one i s t e m p e r a t u r e i n d e 2 e n d e n t and can be a s s o c i a - t e d w i t h e l e c t r o n - d i s l o c a t i o n i n t e r a c t i o n . S i n c e B=Bph+Bel, a n d Bel

i s c o n s i d e r e d t o be t e m p e r a t u r e i n d e p e n d e n t

L81

one can c a l c u l a t e Bph a s a d i f f e r e n c e between t h e v a l u e of E(T) and t e m p e r a t u r e i n d e - p e n d e n t p a r t of B. The c o r r e s p o n d i n g p l o t of B i s shown i n F i g . 3 ph ( t h e p o i n t s a r e i n d i c a t e d by t r i a n g l e s ) . The t h e o r e t i c a l c u r v e of B ph shown i n F i g . 3 ( s o l i d l i n e ) i s p l o t t e d f o r t h e c a s e

6,

= 0 , 4 , w h e r e b i s t h e e x p e r i m e n t a l l y d e t e r m i n e d v a l u e t h a t c h a r a c t e r i z e s t h e r e l a t i - v e c o n t r i b u t i o n of 'Blow phonon r e l a x a t i o n t t m e c h a n i s m t o B compared

Ph

w i t h t h e "phonon wind" mechanism L 9 3

.

I n t h e same f i g u r e t h e d a t a of B (T) o b t a i n e d by t h e d i r e c t measurements of d - i s l o c a t i o n m o b i l i t y

~O]':re shown. Comparison of t h e s e r e s u l t s w i t h t h e p r e s e n t o n e s f i t t e d . : The t e m p e r a t u r e depen- &%?of Eph n o r m a l i s e d by t h e Debye t e m p e r a t u r e

9 .

S o l i d l i n e i s a t h e o r e t i c a l c u r v e f o r t h e c a s e of

A

= 0 , 4 c 9 1

.

l ( A

) t h e p r e s e n t r e s u l t s ,

2

( a )

t h e r e - s u l t s of J a s s b y andYeeeland[l0]. E s t i m a t i o n af Bel from t h e e x p e r i m e n t a l d a t a g i v e ~ , ~ 1 . 5 . 1 0 - ~ dyI3*a/cm2 t h a t a g r e e s w e l l w i t h t h e o r e t i c a l v a l u e of Del f o r Cu

La,

111

.

However, t h e s t r o n g e r e v i d e n c e m i g h t be t h e e x p e r i m e n t s i n which one c o u l d show t h a t t h e v a r i a t i o n i n t h e e l e c t r o n i c s y s t e m l e a d s

t o t h e c o r r e s p o n d i n g c h a n g i n g i n B. It can be performed by t h e super- c o n d u c t i n g t r a n s i t i o n , U n f o r t u n a t e l y , t h e t e m p e r a t u r e of t h e X-S t r a n s i t i o n i n c o p p e r c r y s t a l s i s v e r y low, t h e r e f o r e s u c h k i n d expe- r i m e n t s a r e c o n v e n i e n t t o c a r r y o u t i n t h e l e a d s i n g l e c r y s t a l , where t h e c r i t i c a l t e m p e r a t u r e i s a b o u t 7 , 2 K. Thus, t h e a m p l i t u d e indepen- d e n t d a m p i n g and modulus d e f e c t ; i s i n v e s t i g a t e d i n t h e 99,99975 p u r e ( r e s i s t i v i t y r a t i o ~ J =4.

lo3)

~l e a d s i n g l e c r y s t a l s w i t h ~ ~ ~ , ~ ~

Q101

o r i e n t a t i o n a t 5+15 MHz. I n t h i s f r e q u e n c y r a n g e t h e r e l a t i o n

s a r y t o p o i n t o u t t h a t u n l i k e copper experiments i t i s v e r y d i f f i c u l t t o s i n g l e o u t t h e d i s l o c a t i o n c o n t r i b u t i o n t o t o t a l damping. There- f o r e t o s i n g l e o u t t h e d i s l o c a t i o n s c o n t r i b u t i o n t o t h e t o t a l damping change t h e o t h e r procedure was used.

: The a m p l i t u d e i n d e -

wt

l o g a ~ i t h m i c decrement

8

and resonance f r e q u e n c y f v e r s u s t h e v o l t a g e g i v e n ac- r o s s t h e t r a n s d u c e r i n t h e N and S s t a t e s i n t h e l e a d s i n - g l e c r y s t a l s . T=4.2 K. I O l i 0 B b: Pig.4. Xl and S1 c u r v e s r e p r e s e n t t h e dependences of r a n d 4 i n t h e

N

and - s t a t e s on t h e v o l t a g e ampli- t u d e g i v e n a c c r o s s t h e t r a n s d u c e r . From Fig.4 t h e r e g i o n of t h e ampli- t u d e independent damping i s c l e a r l y seen. It i s n e c e s s a r y t o n o t i c e t h a t

g

i n t h e X-state i s much l a r g e r t h a n i n t h e S s t a t e whereas f i s p r a c t i c a l l y independent of t h e s t a t e . The c u r v e s N2 and S 2 correspond t o t h e same specimen but s u b j e c t e d t o a a d d i t i o n a l deformation. The magnitude of t h e d i s l o c a t i o n c o n t r i b u t i o n t o t h e damping i s p r o p o r t i - o n a l t o t h e d i f f e r e n c e between corresponding v a l u e s b e f o r e and a f t e r a d d i t i o n a l deformation. One can s e e t h a t t h e modulus d e f e c t does n o t change a t t h e N-S t r a n s i t i o n , whereas t h e v a l u e of t h e d i s l o c a t i o n damping i n t h e N-state l a r g e r t h a n i n t h e S - s t a t e . According t o ( 1 ) i t

Fig.

5

: The t e m p e r a t u r e de- pendence of t h e damping con- s t a n t P i n l e a d s i n g l e c r y s t a l g i n t h e N and S s t a - t e s ( f = 5 RKz).

C5-350 JOURNAL DE PHYSIQUE

the predictions of the Kravchenko theory proposed to explain the mechanism of the electron-dislocation interaction C111

.

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3

(1956) 583, 789. 2. T.Kaneda: J.Phys.Soc. Jap.

3

(1970) 1205.

3.

H.R.Kaufmann, D.Lenz, K.LCcke: Internal Friction and Ultrasonic Attenuation in Crystalline Solids (Aachen 1973), v.11, Springer- Verlag, Berlin (1975) p.177.

4. H.Araki, T.Ninomiya: Internal Friction and Ultrasonic Attenuation in Solids (Tokio 1977), University of Tokio Press (1977) p.

509.

5.

N.P.Kobelev, Ya.M.Soif er, V. I.Al 'shits: Fiz.Tverd.Tela

21

(1979)

1172.

6. N.P.Kobelev, Ya.K.Soifer: Piz.Tverd.Tela

g

(1979) 1362.

7. Ya.M.Soif er, V.G.Steinberg: Phys.Stat.Sol.(a) (1977) H87.

8. M.I.Kaganov, V.Ya.Kravchenko, V.D.Natsik: Usp.Fiz.Nauk

III

(1973)

655-