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RADIATION RESISTANCE THEORY OF PERSPECTIVE HIGH TEMPERATURE
SUPERCONDUCTORS
A. Alexandrov, V. Elesin, M. Kazeko
To cite this version:
A. Alexandrov, V. Elesin, M. Kazeko. RADIATION RESISTANCE THEORY OF PERSPECTIVE HIGH TEMPERATURE SUPERCONDUCTORS. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-421-C1-423. �10.1051/jphyscol:1984186�. �jpa-00223742�
JOURNAL DE PHYSIQUE
Colloque C l , supplément au n° 1, Tome 45, janvier 1984 page Cl-421
RADIATION RESISTANCE THEORY OF PERSPECTIVE HIGH TEMPERATURE SUPERCONDUCTORS
A.S. Alexandrov, V.F. Elesin and M.P. Kazeko
Institute of Engineering-Physios, Kashivskoe Shosse SI, 115 409 Mosoow, U.S.S.R.
Résumé - Une m é t h o d e u n i v e r s e l l e de calcul de l'effet de ra- diation sur la t e m p é r a t u r e critique des i n t e r m é t a l l i q u e s ayant la s t r u c t u r e A-15 est p r o p o s é e .
Abstract - A u n i v e r s a l technique of c a l c u l a t i n g the r a d i a t i o n e f f e c t on the A-15 i n t e r m e t a l l i c compounds c r i t i c a l tempera- t u r e i s proposed.
High c r i t i c a l superconductive parameters i n t e r m e t a l l i c A-15 compo- unds a t t r a c t a t t e n t a t i o n b o t h t o t h e p h y s i c a l n a t u r e of t h e i r unique p a r a m e t e r s and t o t h e p o s s i b i l i t y of t h e i r p r o s p e c t i v e usage i n f u s i o n and a c c e l e r a t o r s .
I n t h i s p a p e r a u n i v e r s a l t e c h n i q u e o f c a l c u l a t i n g t h e r a d i a t i o n e f f e c t on t h e A - 1 5 i n t e r m e t a l l i c compounds e l e c t r o n p a r a m e t e r s i s p r o p o s e d . I t i s b a s e d on t h e i d e a o f e x i s t e n c e o f f i n e s t r u c t u r e i n t h e e l e c t r o n d e n s i t y o f s t a t e s and i t ' s s m e a r i n g due t o r a d i a - t i o n - i n d u c e d d e f e c t s f i e l d .
I - '£HE BEESO'I! OF ftAKUSSLON-IMDUgBD D£ffBCri!S ON SHE DKMSIEC 01 S'l'AliES. '.
The interaction with radiation-induced defects brings about a change in the dispersion law £? , i.e. a change in the form and the width of a narrow electron d-band. In / 1 / it is shown that the correspon- ding change in the density of states may be calculated in the elec- tron-impurity scattering ladder approximation / 2 / even if the cha- racteristic electron wavelength is of the order of the mean free path length. This is due to the fact that the "crossed" diagrams are numerically negligeble.
As a result the electron density of states in an irradiated sample N(£) may be expressed in terms of the density of states in a per- fect one H0(£)j
v- v x T j ' ri°(i') •
tf(i) = -£fa £(£•)', (2)
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984186
Cl-422 JOURNAL DE PHYSIQUE
2 -1
where x=3;JO CdJ i s t h e d i m e n s i o n l e s s d e f e c t s c o n c e n t r a t i o n , Cd i s t h e d e f e c t s c o n c e n t r a t i o n , ro i s t h e m a t r i x element of a d e f e c t po- t e n t i a l /'I/.
The peak i n t h e e l e c t r o n d e n s i t y o f s t a t e s i s approximated by
h e r e No i s a dimension f a c t o r , 1T.C i s a n energy-independent back- ground d e n s i t y o f s t a t e s , d/ i s ?he peak w i d t h &,, i s t h e d e n s i t y o f s t a t e s maximum p o s i t i o n . E x p r e s s i o n (3), (1) a n d ( 2 ) a l l o w a n a n a l i t i c a l c a l c u l a t i o n o f t h e smearing o f t h e e l e c t r o n d e n s i t y o f s t a t e s f i n e s t r u c t u r e by t h e d e f e c t s a n d t h e c r i t i c a l t e m p e r a t u r e Tc dependence on t h e d e f e c t s c o n c e n t r a t i o n .
I1
-
RADIATION-INDUCPD AE;GRADATIOLT U D BOOST OF T,,The c r i t i c a l t e m p e r a t u r e dependence on t h e d e f e c t s c o n c e n t r a t i o n a n d f l u e n c e was o r i g i n a l l y c a l c u l a t e d i n t e r m s o f t h e BCS t h e o r y . According t o t h i s t h e o r y t h e c r i t i c a l t e m p e r a t u r e is d e r i v e a from f h e f o l l o w ir:g e q u a t i o n
E ? + ~ D E
%zc
,i = v 0
dcd(6) J (4)r - p
where V is t h e BCS p o t e n t i a l , en is t h e Debye temperacur, E is t h e 2 e r g i e n e r g y i n a m a t e r i a l w i t h d e f e c t s . b h i l e c a l c u l a t i 6 . g t h e c r i t i c a l t e m p e r a t u r e dependence on f i u e n c a 9
,
t h e d e f e c t s concen- t r a t i o n was assumed t o b e d i r e c t l y p r o p o r t i o n a l t o g.The ~ e s u l t s o f c a l c u l a t i o n a p p e a r e d t o depend e s s e n t i a l l y on t h e Fezmi energy p o s i t i o n E r e l a t i v e t o t h e peak i n t h e e l e c t r o n den- s i t y o f s t a t e s . ( s e e ~ i g . ?).
t h e Tc L5-
- 7~0
0.5 0
a e f e c t s
4.a:=%$;r t 0' .O
a
With Ifp-E,\ 2 b/ t h e e f f e c t o r b o o s t o r T i s p o s s i b l e , c o n d i t i o n e d by t h e i n c r e a s e of i i i ~ ~ ) w h i l e t h e f l u e g c e (and, c o n s e q u e n t l y , Cd) i s small.
012 a 2d s Eig. 1
-
Reduced c r i t i c a l t e m p e r a t u r e dedendence c o n c e n t r a t i o n s f o r cliff r e n t.
Big. 2 r e p r e s e n t s t h e n u m e r i c a l r e s u l t s o f t h e s o l u t i o n o f t h e s y s -
t e a ( 1 )
-
(4) a n d t h e comparison w i t h t h e e x p e r i m e n t a l d a t a f o r LYb3Sn i r r a d i a t e d by 2 IuleV h e l i u m i o n s /$/ a n d oxygen i o n s /4/.Pig. 2
-
&educed c r i t i c a l t e m p e r a t u r e dependence on t h e f l u e n c e6 S o l i d l i n e
-
t h e o r y f o r 2 MeV h e l i u m i o n s , 0-
e x p e r i m e n t ; d a s h e d l i n e-
t h e o r y f o r 25 MeV oxygen i o n s , @-
e x p e r i m e n t . ) Note t h a t i f t h e form o f N ( E ) is more c o m p l i c a t e d , Tc m a y a l s o i n c r e a s e at h i g h f l u e n c e a f t e r i n i t i a l d e c r e a s e /I/.The r e s u l t s may b e g e n e r a l i z e d f o r t h e c a s e o f s t r o n g - c o u p l i n g . The c r i t i c a l t e m p e r a t u r e was d e t e r m i n e d f r o m t h e E l i a s h b e r g - t y p e e q u a t i o n s , t h e f i n e s t r u c t u r e o f N(€) h a v i ~ g been t a k e n i n t o ac- count. The r e s u l t s d i f f e r from t h e c a s e o f weak-coupling by s e v e r a l p e r c e n t .
To c o n c l u d e i t s h o u l d be mentioned, t h a t i n t h e t h e o r y p r o p o s e d t h e r a d i a t i o n e f f e c t on t h e c r i t i c a l t e m p e r a t u r e is d e t e r m i n e d by t h e s i n g l e d i m e n s i o n l e s s p a r a m e t e r X ( s e e ( 2 ) ) . which f o r suaU a n d i n t e r m i d e a t e f l u e n c e s may b e c o n s i d e r e d t o be d i r e c t l y p r o p o r t i o n a l t o t h e f l u e n c e /1,5/. The v a l u e o f X a l s o dependes on t h e chacac- t e r i s t i c e n e r g y s c a l e o f t h e d e n s i t y o f s t a t e s a n d t h e magnitude o f t h e i n t e r a c t i o n w i t h t h e s i n g l e d e f e c t f i e l d .
/'I/ UXANDROV A . S . , ELXSIN V.B., W X K 0 M.P., P i e . Tverd. T e l a 21 (1979) 2062.
/2/ a-RIKOSOV A.A., GOIII(OV L.P., DZYBLOSHINSKI I.E., Methods o f Quantum F i e l d Theory i n S t a t i s t i c a l P h y s i c s ( P r e n t i c e H a l l , Jinglewood C l i f f s , N. J. , 1963).
/3/ POATE J.M.
,
DYNXC ROC*,
TESTARDY LOR., W O N D R.H.,
Phys. Rev.L e t t . 37 (1976) 1308.
/4/ B E S S L E ; ~ ~ ~ B., ISC2UNI(O Qi, KLATJMUNLEdI S. e t . a l e , Phys.
L e t t * (1978) 49.
/5/ UUANDROV A . S . ? DJSGTYARUXKO N.N., EIiESIN V.F.
,
-0 M.P.,SKkLDIN A.L., PLZ. P e t . i Met. (1981) 505.