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DISLOCATION AMPLITUDE DEPENDENT
ULTRASOUND ABSORPTION IN NORMAL AND
SUPERCONDUCTING LEAD CONTAINING
DIVERSE VALENCY IMPURITIES
L. Pal-Val, V. Platkov, A. Roshchupkin
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque C5, suppZdment au nO1O, Tome 4 2 , octobre 1981 page ~ 5 - 2 5 3
DISLOCATION AMPLITUDE DEPENDENT ULTRASOUND ABSORPTION IN NORMAL AND SUPERCONDUCTING LEAD CONTAINING DIVERSE VALENCY IMPURITIES
Y
L.N. Pal-Val, V.Ya. Platkov and A.M. Roshchupkin
Physico-TechnicaZ I n s t i t u t e of Low Temperatures, Kharkov, U . S . S. R.
-X.
Voronezh PoZytechnicaZ I n s t i t u t e , Voronezh, U.S.S.R.
A b s t r a c t . - iLrllpli t u d e deeendence o f u l t r a s o n i c a b s o r p t i o n &(&I
f o l l o w i n g i m p u r i t i e s : 11, Sn, B i , Sd, Sb. C r i t i c a l a m p l i t u d e o f t h e b e g i n n i n g o f E, dependence on
d.
i n c r e a s e d i n tlicd
h a s been s t u d i e d i n l e a d s i n g l e c r y s t a l s c o n t a i n i n g one oft
e g o i n g from %$l t o Sb i n t h e above i m p u r i t y s e r i e s . A t S-n t r a n - s i t i o n&,
i n c r e a s e d by 2 5 t o 3570. The c 1 l r ; r a c t e r i s t i c s t r e s s l e v e l v a l u e s of d i s l o c a t i o n u n p i n n i n g from i m p u r i t i e s were o b t a i n e d and t h e i r change a t t h e s u p e r c o n d u o t i n g t r a n s i t i o n was i d e n t i f i e d . l f i t h t h e aim t o d e f i n e c o n t r i b u t i o n s o f d i f f e - r e n t p h y s i c a l n a t u r e t o t h e t o t a l v a l u e of i n t e r a c t i o n between d i s l o c a t i o n s snd i r n p r i t y atoms a n approach f o r e x p e r i m e n t a l d a t a t r e a t m e n t i s o f f e r e d and tile q u a n t i t a t i v e i n f ormotion of t h e s e c o n t r i b u t i o n s i s obtained.The change o f a t n-S t r a n - s i t i o n i s e x p l a i n e d by t h e v a r i a t i o n of d i s l o c a t i o n l o o p s ,lN,
overdamping d e g r e e l e a d i n g t o t h e i n c r e a s e i n i n t e r n a l f r i c t i o n . , > e c h a n i c a l p r o 2 e r t i e s of a r e a l c r y s t a l de7end on c o n c e n t r a t i o n o f i m ? u r i t g atoms a l o n g t h e d i s l o c a t i o n l i n e and on i t s e n e r g y of i n t e r a c t i o nv
w i t h t h e s e atoms.The f u l lV
v a l u e i s determined by some c o n t r i b u t i o n s o f d i f f e r e n t p h y s i c a l n a t u r e . S e p a m t i o n of i n - d i v i d u a l c o n t r i b u t i o n s may be accomplfshed by t h e s t u d y o f a r n ~ l i t u d e de_sendent i n t e r n a l f r i c t i o n s i n c e i t i s due t o t h e p r o c e s s o f d i s l o - c a t i o n unpinning.To e s t a b l i s h t h e r o l e of some t y p e s of i n t e r a c t i o n s i n v e s t i g a t i o n s and a n a l y s i s o f a m p l i t u d e dependent i n t e r n a l f r i c t i o n were c a r r i e d o u t i n Pb c o n t a i n i n g i m p u r i t i e s d i f f e r i n g f i r s t of a l l i n v a l e n c y u n d e r c o n d i t i o n s ( a r a t h e r h i g h f r e q u e n c y and lost tem- p e r a t u r e r a n g e ) when i t i s expected t h a t t h e 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 w i l l be athermal.The n e x t aim was t o c l e a r t h e mechanismt h a t i s r e s p o n s i b l e f o r t h e change i n h i g h f r e q u e n c y a m p l i t u d e depen- d e n t i n t e r n a l f r i c t i o n a t 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 .
kfeasurements were c a r r i e d o u t u s i n g t h e u l t r a o o n i c p u l s e method a t a f r e q u e n c y of
7.5
kHz i n Pb s i n g l e c r y s t a l s c o n t a i n i n g one o f t h e f o l l o w i n g i m ~ u r i t i e s : T1, Sn, B i , Cd, Sb,which w a s i n t r o d u c e d i n a n-3
e q u a l amount o f 8x10 at.%. A l l s i n g l e c r y s t a l s were o f t h e same o r i - e n t a t i o n . D i r e c t i o n of t h e sound wave p r o p a g a t i o n c o i n c i d e d w i t 1 1 t h e c r y s t a l l o g r a p h i c d i r e c t i o n [IOO~. F o r e a c h t y o e of i m ~ u r i t y measure- ments were c a r r i e d o u t on f i v e i d e n t i c a l sample8 p r e p a r e d of one
C5-254 JOURNAL DE PHYSIQUE
s i n g l e c r y s t a l .
The
&
(&a) depenc-lences were i n v e s t i g a t e d i n t h e n- and S - s t a t e~t 4.2 ;i ( , ' i g s , l a and b ) . The a v e r a g e d &C v a l u e s and c o r r e s ~ o n d i n g
c r i t i c a l s t r e s s e s
TC
i n n- and S - s t a t e s a r e g i v e n i n I'able 1. Thed
(60)
de3enqence i s d e t e r l i n e d by t h e p r o c e s s of ? i n n i n g c e n t e r s u r - mounting by d i s l o c a t i o n . Lack of tile i n f l u e n c e of t e m p e r a t u r e c h a n g e by a f a c t o r of 2.5 (from 1.3 t o 4.2K) i n tjle n - s t a t e o b s e r v e d e x 2 e r i - a e n t a l l g i n d i c a t e s t h e a t h e r m a l c h a r a c t e r of u n p i n n i n g . 2 h i s e n a b l e s -t o a n a l i z e d a t a i d tire f rane o f Cranato-LLiclce a t h e r m e 1 t h e o r y [l]. The
&(E,) d e p e n d e n c i e s Gerc p r e s e n t e d i n Grsnato-Liicke c o o r d i n a t e s . The sl;raig!lC l i n e s l o p e s i n t h o s e c o o r d i n a t e s a r e p r o ~ > o i q t i o n a l t o t h e
c h a r a c t e r i s t i c s t r e s s l e v e l
r
.
illable 1 p r e s e n t s t!le a v e r a g e dr
va-l u e s i n n- c i ~ d S-stctt-es. A t tlle s u c c e s s i v e c o n s i d e r a t i o n i n t i l e fra-
r ~ e s o f s t r i n g model t u r n o s t o be[2] e q u a l t o
T\ .L?
.<!here f b i s t i l e maximum b i n d i n g f o r c e between t h e d i s l o c a t i o n and
t h e pinnin:; c e n t e r , b i s tile 3 u r g e r s v e c t o r , lc i s tl:e mean l e n g t h
o f d i s l o c a t i o n se-ment.
9 i s l o c a t i o n a l s t r u c t u r e , ~ . v h i c h i s r e s ~ o n s i b l e f o r t h e a p g e a r a n c e
of h y s - t e r e s i s l o s s e s i - k i l e :*lcasurin,- by u l - t r a s o n i c y l s e method i n
t h e lzeliurn t e ~ x p e r a t u r e
ranee
i s f o n i ~ e d d u r i n g t h e sample d e f o r m a t i o nby a q u a r t z c e l l b e c a u s e of d . i f f e r e n c e i n t i l e i r l i n e a r e x p a n s i o n
c o e f i " i c i e n t s . In .t!~is c a s e lc i s de-termined by[2]
i . l :
6,
j e p e n d s n c e of i n Fb c o n t a i n i n g d i f f e r e n t i m p u r i -t i c s a t 4.2 K. a
-
n - s z r t e , b-
S - s t a t e .h e r e U b is t n e b i n d i n g energy between t h e d i s l o c a t i o n and i m p u r i t y
atom, CO = ~ b ~ / 2 i s t h e e l a s t i c energy of d i s l o c a t i o n of b l e n g t h ,
G i s t h e s h e a r modulus. Taking i n t o account t h a t
Tcw
l;', (2: nay bev e r i f i e d through experimental d a t a on c dependence of
5,
, F o r Pb+Sbr e s u l t s i n l g - l g c o o r d i n a t e s f a l l on a s t r a i g h t l i n e w i t h a s l o p e of 2 / 3 , t h u s c o n f i m i n g ( 2 ) .
E'rom t h e P e i e r l e s - 9 a b a r m model i t f o l l o w s t h a t fb=j\ljSud /8d
where d i s t h e h a l f w i d t h of d i s l o c a t i o n l i n e and i s equal t o b. Sub- s t i t u t i n g e x p r e s s i o n s f o r lc and f b i n t o ( 1 ) a r a t i o i s o b t a i n e d
which c o n n e c t s
r
w i t h t h e b i n d i n g energywhere
ro
= 3 v ~ c ' / ~ / 1 6,
t h a t a t t h e c s e l e c t e d and Pb g i v e s2
604.3 g/mm
.
I n t h e frames of Peierles-Kabarro model Ub between t h e d i s l o c a ~
t i o n and an i m p u r i t y atom l o c a t e d j u s t i n i t s s l i p plane i s d e f i n e d
where H = 3kVh(l-2 1) )/2% (1-
3
),
9
i s t h e P o i s s o n l s r a t i o , k i st h e modulus of d i l a t a t i o n , Vh i s t h e volume of m a t r i x atom. h t h e
c a s e of 18ad Ijpb = 1.45
eV.
The d i m e n s i o n l e s s parameter i n t r o d u c e dh e r e
'Itot
= t
+ d z
+p2
z
-a.z2
( 5 )
c h a r a c t e r i z e s t h e "power" of p o i n t d e f e c t taking i n t o account i t s
charge.Eere
)I
= l / a da/dc i s t h e f a c t o r of dimensional i n c o n s i s t e n -c y , Z i s t h e r e l a t i v e valency of m a t r i x and i m p u r i t y ,
d
, /S
and 2'a r e c o n s t a n t s c h a r a c t e r i z i n g ( r e s p e c t i v e l y ) f i r s t o r d e r e l t c t r o s t a t i c interaction,electrodimensional i n t e r a c t i o n and second o r d e r e l e c t r i - c a l i n t e r a c t i o n between t h e d i s l o c a t i o n and i m p u r i t y atom.Pormula ( 3 ) r e w r i t t e n a s
a l l o w s , p r o c e e d i n g from t h e experimental d a t a on , t o determine U
d i r e c t l y . T a b 1 e 2 g i v e s t h e
I
UbI
v a l u e s found i n t h i s way.I
blJOURNAL DE PHYSIQUE
s i n c e i t does n o t de-?end on t h e o r e t i c a l e n t i t n a t i o n s of go and Fo. Talcing Sn a s a s t a n d a r d ira.surity atom f o r .i~hich Z = 0 znd t h u s
I
= = 0.071, and u s i n g t h e e x n e r i n e n t a l r : v z l u e s1
t o t t o tc a n be determined by
( 7 )
f o r t h e r e c t i l ~ l ~ u s i t i c s ( s e c > a b l e 2 ) . - 2 0 , : -i n g t h e e x p e r i m e n t a l v a l u e s o f [iib/ and
11
.,e can f i n d .i-
-
cxp
S 1.32 eV by ( 4 ) , t h a t b e i n g o n l y by 10% d i f f e r e n t frorn 11 t i l e o r =1.45 eV.
k s s u ~ n i n g i n
( 5 )
Z = 0 i i e o b t a i n t h e e l a s t i c c o n s t i t u e n t of f u l l b i n d - ? a b l e 1i n g energy
fiowing if and
$
one o b t a i n s t h e n o r e e c c u r n t e (exncrimen- exp1%
v a l u e f o r a l l t h e i c ? u r i t y a t o m ( > a b l e 2 ) .-ron t h e Pb+T1 i2b+Sn Pb+Bi Ib+Cd Pb+SbI
I
w i t h(
r j b l olle call conclude a b o u t t h e r e l a t i v ecomparison o f Ub el
c o n t r i b u t i o n of e l e c t r o s t a t i c i n t e r a c t i o n t o t h e t o t a l b3.nding energy between t h e i m p u r i t y atoms and d i s l o c a t i o n s .
be n o t o n l y of t h e sa-ye o r d e r of magnitude a s t h e e l a s t i c o n e , b u t ,
a s f o r example i n t h e c a s e of S b , g r e a t l y exceed
i t .
The r e l a t i v e change of Ub i n l e a d a t n-S t r a n s i t i o n does n o t
exceed s e v e r a l p e r cent[2J, t h a t b e i n g e s s e n t i a l l y l e s s t h a n t h e
r e l a t i v e change of maximum b i n d i n g f o f c e
fnb-s/ft
30% r e w i f e &f o r t h e e x p l a n a t i o n of t h e experimental r e s u l t s o b t a i n e d . T h e r e f o r e
a n a l t e r n a t i v e mechanism i s c o n s i d e r e d , - e f f e c t of t h e e l e c t r o n v i s - c o s i t y d e c r e a s e a t t h e t r a n s i t i o n t o S - s t a t e on t h e p r o c e s s of pin- n i n g c e n t e r s surmounting by d i s l o c a t i o n s under high-frequency ampli- tude dependent i n t e r n a l f r i c t i o n .
The main r e s u l t of t h i s s t u d y i s t h e c o n c l u s i o n about t h e essen-
t i a l i n f l u e n c e of d i s l o c a t i o n l o o p s ,
h,
overdamping l e v e l on t h eamplitude dependent l o s s e s values.The overdamping l e v e l i s determin-
ed by t h e r e l a t i o n s h i p between t h e l e n g t h ,
$,
and t h e c h a r a c t e r i s -t i c l e n g t h
IfA
.p 2@7%z, where C i s t h e l i n e t e n s i o n c o e f f i c i e n t andU
B i s t h e damping c o e f f i c i e n t . A t $>>Ld d i s l o c a t i o n a l h y s t e r e s i s i s
p r i n c i p a l l y of dynamic c h a r a c t e r and t h e i n t e r n a l f r i c t i o n i s des-
c r i b e d by t h e e x p r e s s i o n
where Q-' i s t h e v a l u e of amplitude dependent i n t e r n a l f r i c t i o n
w i t h no v i s c o s i t y . A t t h e t r a n s i t i o n t o S - s t a t e t h e l o o p o v e r d m p i n g l e v e l d e c r e a s e s a n d , a s a consequence,the amplitude dependent l o s s e s i n c r e a s e . T h i s e f f e c t i s of a g r e a t enough v a l u e t o e x p l a i n t h e i n - t e r n a l f r i c t i o n changes a t t h e t r a n s i t i o n t o s - s t a t e observed expe- r i m e n t a l l y .
References
1. Granato A . ,Liicke K., J.App1. Phys.,
a,
NO. 6 , 583, 1956.2. Pal-Val L.N.,Platkov V.Ya.,Hoshchupkin A . X . , P r e p r i n t 22-1980,
FTIWT, Kharkov.