8/14/2019 electron variation.pdf

1/4

Model for f lux creep in h ighTc sup ercon du ctorsD . D e w H u g h e sDe p a r tm e n t o f En g in e e r i n g Sc ie n ce Pa rks Ro a d O x fo r d O X l 3 P J UKA mo d e l f o r f l u x c r e e p i n h i g h Tc superconductors i s d e ve lo p e d T h e mo d e l p r e d i c t s th a tassocmted w=th th e f l u x c r e e p r e g ime ~s a r e s i s ta n ce w h i c h sh o ws a h n e a r va r i a t i o n w t tha p p h e d m a g n e t i c f i e l d I t is d e mo n s t r a te d th a t t h e mo d e l Js co n s i s te n t w i th t h e h mJ te de xp e r ime n ta l d a ta a va d a b leK e y w o r d s h = g h Tc s u p e r c o n d u c t i v i ty f l u x c r e e p m o d e l

S u p e r c o n d u c t o r s f i n d a p p h c a t l o n b o t h m p o w e r e n gi -n e e r i ng a n d e l e c t ro m c s p r i m a r i l y o n a c c o u n t o f th e i ra b l h t y t o s u s t a i n e x t r e m e l y h i g h c u r r e n t d e n s i ti e s W i t ht h e e x c e p t i o n o f t h i n f il m s , t h e r e p o r t e d v a l u e s o f c n h c a lc u r r e n t d e n s i t y , Jc , in t h e n e w h i g h T c c e r a m m o x i d e s u p e r -c o n d u c t o r s a r e d i s a p p o i n t i n g l y l o w a n d a r e , i n f a c t , w e l lb e l o w t h e v a l u e s t h a t w o u l d a l l o w t h e ir e c o n o m i c e x p l o i -t a t i o n m d e v i c e s a t a t e m p e r a t u r e o f 4 2 K , l e t a l o n e 7 7K I n t he e x c i te m e n t a n d e n t h u s i a s m r i g h tl y g e n e r a te db y t h e d i s c o v e r y o f t h e se m a t e r i a l s o n e f a c t o r w h i c h m a yl i m i t J ~ a t t e m p e r a t u r e s a b o v e t h a t o f l i q u i d h e l i u m ,p e r h a p s t o a n e x t e n t w h i c h w o u l d r e n d e r a n y r o o mt e m p e r a t u r e s u p e r c o n d u c t o r v i r t u a l l y u s e l e s s a t r o o mt e m p e r a t u r e , h a s b e e n I g n o r e d T h i s f a c t o r i s t h e r m a l l ys t i m u l a t e d f l u x c r e e p I F l u x c r e e p w a s f i r st p r e d i c t e d a sa p o s s l b d ] t y b y A n d e r s o n 2' 3 a n d i n v e s t i g a t e d b y B e a s le y ,L a b u s c h a n d W e b b 4 I t c a n b e , a n d g e n e r a l l y Is , i g n o r e df o r s tr o n g - p i n n i n g , h i g h c u r r e n t d e n s i ty s u p e r c o n d u c t o r s ,s u c h a s t h o se u s e d i n c o m m e r c m l d e v i c es w h e n o p e r a t i n ga t 4 2 K H o w e v e r , a t m u c h h i g h e r t e m p e r a t u r e s i t i s h k e l yt o h a v e a s i g n i f i c an t e f f e ct u p o n t h e o v e r a l l f l u x - p r u n i n gs i t u a t i o n a n d c r i t ic a l c u r r e n t d e n s i t y m e v e n s t r o n g -p i n n i n g m a t e r i a l s I t i s t h e p u r p o s e o f t h l s P a p e r t o m o d e lf l u x c r e e p a n d t o e s t i m a t e t h e i n f l u e n c e i t w d l h a v e u p o nt h e p e r f o r m a n c e o f h i g h T~ s u p e r c o n d u c t o r s

G e n e r a l f o r m a l i s m o f s t r e s s -a s s t s te dt h e r m a l a c t i v a t i o nI t i s a s s u m e d t h a t s o m e e n h t y , w h e t h e r i t b e a d i f f u si n ga t o m , a c r y s t a l d i s l o c a t i o n o r , as i n t h i s c a s e , a q u a n t l z e df lux vo r t e x (he re ina f t e r r e fe r re d to a s a f lux - l ine ) , s i t s a tt h e b o t t o m o f a p o t e n t i a l w e l l o f d e p t h U U is t h ed i f f e re n c e i n th e G i b b s F u n c t i o n o f t h e s y s t e m b e t w e e nw h e n t h e e n t i t y i s i n t h e w e l l a n d w h e n i t i s m o v e d a w a yf r o m I t I n t h e a b s e n c e o f a n y i m p o s e d s t r e ss t h e e n t i t yc a n , b y t h e r m a l a c t i v a t i o n , h o p o u t o f t h e w e l l a t t h ef o l lo w i n g r a t e (f o r b o t h f o r w a r d a n d b a c k w a r d d i r e ct i o n s)R = f Z o e x p ( - U/kT) (1)* P a p e r p r e s e n te d a t C r m c a l C u r r e n t s m H i g h T , S u p e r c o n d u c t o r sB ~ r m m g h a m , U K 1 6 M a y 1 98 80 0 11 2 2 7 5 / 8 8 / 1 0 0 6 7 4 - 0 4 0 3 0 0,~, 1988 B u t t e r w o r t h & C o ( P ubhs he r s ) L t d6 7 4 C r y o g e m c s 1 9 8 8 V o l 2 8 O c t o b e r

w h e r e Qo i s t h e f r e q u e n c y w i t h w h m h t h e e n t l t y t r i e s t oe s c a p e f r o m t h e w e l l I n t h e c a s e o f d i f f u s io n t h i s w o u l db e t h e f r e q u e n c y o f a t o m m v i b r a t i o n ( . .~ 1 0 1 3 A s theh o p p i n g r a t e s a r e t he s a m e m b o t h d i r e c t i o n s n o n e tm o t i o n o f t h e e n t i ty i s o b s e r v e d W h e n a s t re s s is im p o s e di n s u c h a w a y a s t o f a v o u r h o p p i n g m o n e d i r e c t i o n ,w h i c h n o w c a n b e i d e n t i f i e d a s t h e f o r w a r d d i r e c t i o n , a tt h e e x p e n se o f th e b a c k w a r d d l r e c h o n , t h e r a t e s o f th ef o r w a r d , R f , a n d b a c k w a r d , R b, h o p p i n g b e c o m eR f = f Z o e x p [ - U - AW)/kT] (2)a n dR b = f ~ o e x p [ - V + AW)/kT] (3)w h e r e A W i s t h e w o r k d o n e b y t h e i m p o s e d s t re s s inm o v i n g t h e e n t i t y f r o m i t s e q u i l i b r i u m p o s i t i o n a t t h eb o t t o m o f t h e w e ll t o t h e n e xt e q u l h b r l u m p o s i t i o n T h e r ei s n o w a n e t f o r w a r d r a t e o f h o p p i n g g i v en b y t h e

f f e r e n c e b e t w e e n t h e s e t w o e x p r e s s i o n sRne = 2 Q o e x p ( - U/LT)smh AW/kT) (4)

I t t s p o s s i b l e t o c o n s i d e r t w o c a s e s1 w h e n AW>>kT t ha t I s e i the r a t ve ry h igh l e ve l s o fi m p o s e d s t re s s o r a t v e r y l o w t e m p e r a t u r e s W h e n x isl a r g e , s l n h x = e x p ( x ) / 2 , t h u s , t h e n e t r a t e o f h o p p i n g

b e c o m e sRne = f ~ o e x p ( A W - U)/kT (5)

2 w he n A W

8/14/2019 electron variation.pdf

2/4

magnetic induction, B, and the temperature, T Providedthat the lnducUon is sufficiently large that each pruningparticle ~s intersected by a flux-hne, then the pruningenergy per unit volume is U N p The distance moved bythe flux-line during the unpinning process is the inter-flux-hne spacing, a o ( = 1 07[C~o/B]l/2), and the pinningforce per unit volume isJ o B = U N p a o (7)where Jo is what the critical current density wouldbe in the absence of any flux creepThe actual current flowing exerts a Lorentz forceon the flux-hne latnce, this is J x B per unit v olumewhere J is the actual cu rrent density and is less thanJo The work d one if a volume, I v , of flux latticemoves a dista nce 6y is J B a v a y When a flux-line becomesunpinned it alone will not move, nelghbourlng flux-lineswill move along with it It is reasonable to assume thatthe entire volu me of flux lattice associated with onepruning centre will on average mo ve each time a flux-lineis unpinned, l e a t = 1 N p This volume of lattme, whmh~s the eqmvalent of Anderson's flux bundle, will move tothe next equlhbrlum position, which will be when thefollowing flux-line now intersects the particle The dis-tance moved, , will thus be one mter-flux-hne spacing,ao, andA W = J B a o / N p = J U , J o (8)It should be noted that when J = J o , A W = UAs the flux moves it generates an electric field, E,given by = vB (9)where v is the average velocity of the flux-hne-lattmeIn the absence of any collaborative effects each pinnedlength of flux-hne can become un pinned at the same rateand, on average, the entire lattice is able to move throughone lattice spacing at the net hoppin g rate, R.~, Theaverage velocity is, therefore, R.etao, and the electric fieldis given byE = R n ~ ta o B = 2aoB~oexp(- U / k T ) s l n h ( A W / k T ) (10)

If ~t may be supposed that case 1 above obtains,le , AW>> LT, which also lmphes that U >>l~T, thenE = a o B ~ o e x p [ ( A W - U ) / k T]

= a o B ~ ) o e x p [ U ( J - J o )/ J oI , T ] (11)andJ = Jo[1 + ( l , T / U ) l n ( E / a o B ~ o ) ] (12)where f),, ~s some characte ristic frequenc y of the flux-hnevibration, unknown in detail but assumed to he in thera ng el 0 s 10 lls ~ At an induction of 10T, ao =1 5n mIf the usual sup ercondu cting magnet builder's criterionof a max imum accepta ble electric field of 10 -5 Vm-~ isused, then ~t can be seen that the loganthmm term issmall and negative, and the critical current densityJ~ < Jo The a ctual value of the critical curre nt de pendsonly weakly upo n the chos en criterion for E used to definecrmca llty The possibility of thermally ac tivated fluxcreep may be, in this case, ignoredIfAW

8/14/2019 electron variation.pdf

3/4

Mo de l fo r f l ux c reep D Dew Hughe sm e c h a n i s m w h o s e s t r e n g t h i n c re a s e s l in e a r ly w i t h a p p l i e dm a g n e t i c f ie ld T h i s c a n h a p p e n w h e n p i n n i n g a r i s e sb e t w e e n r e g i o n s o f t h e s u p e r c o n d u c t o r w i t h d i ff e re n tup pe r c r i t i c a l f i e ld s A s the a pp l i e d f i e ld i s i nc re a s e d , t hed i f f e re n c e i n re v e r s i b l e m a g n e u z a t l o n b e t w e e n t h e r e g i o n sw i ll in c r e a s e , r e s u l t i n g m a n i n c r e a s e i n t h e p i n n i n g f o r c et o c o u n t e r a c t t h e i n c r e a s e i n th e L o r e n t z f o r c e I t is n o ty e t c l e a r a s t o w h i c h m l c r o s t r u c t u r a l f e a t u r e s a r e a b l e t og e n e r a t e t h i s p i n n i n g m e c h a n i s m i n o x i d e s u p e r c o n d u c -t o r sT h e c r i t i c a l c u r r e n t d e n s i t y a t 4 K m t h e m a t e r i a lu s e d b y K u p f e r et al h a s a v a lu e o f 2 5 x 1 0 9 A m - 2o v e r m o s t o f t h e f ie l d r a n g e I f i t c a n b e a s s u m e d t h a ta t t h i s t e m p e r a t u r e t h e r e i s n o f l u x c r e e p , t h e n t h i sc a n b e e q u a t e d t o J o a n d u s e d t o e s ti m a t e s o m e o ft h e p a r a m e t e r s r e q u i re d b y th e a b o v e m o d e l F o r p i n n i n gb y a n o r m a l p r e c i p i t a t e o f d i a m e t e r D , U i s g i v e n b y 13U = ~ ~oD B~(I b) /4 oB~2 (17 )t~ DB(1 - b) /2~ o =B e i s n o t y e t k n o w n w i t h a n y c e r t a i n t y f o r Y B a 2 C u 3 0 7H o w e v e r , t h e v a l u e f o r c l e a n N b 3 S n i s 0 6 T 14, a n dw i th a f i ve t ime s h igh e r To, a va lue o f 3 T i s a r e a so na b lee s t i m a t e f o r Y B a 2 C u 3 0 7 B e2 ( 4 2 K ) i s a n l s o t r o p l c b u t1 00 T m a y b e t a k e n a s a r e a s o n a b l e a v e r a g e v a l u e a n d ,t h e r e f o r e , t h e p i n n i n g e n e r g y m a y b e e s t i m a t e d t o b e3 7 1 0 - 1 1 D 1 - b ) J

I n t h e c a s e u n d e r c o n s i d e r a t i o n , U i n c r e a s e s r a t h e rt h a n d e c r e a s e s w i t h i n c r e a s i n g m a g n e t i c i n d u c t i o n , a se x p l a i n e d a b o v e , a n d w i ll b e le s s t h a n t h e a b o v e e s t i m a t eG i v i n g D a v a l u e o f 5 0 n m , r e m o v i n g t h e d e p e n d e n c e o nb a n d r e d u c i n g t h e m a g n i t u d e b y a f a c to r o f l 0 t o a c c o u n tf o r t h e f a c t t h a t p i n n i n g i s n o t b y n o r m a l p a r t i c l e s b u tb y le s s s t r o n g l y s u p e r c o n d u c t i n g p a r t i c le s , s u g g e s t s t h a ta r e a s o n a b l e v a l u e f o r U m i g h t b e 1 8 x l 0 - 1 9 J N o t et h a t t h is i s i n d e e d v e r y m u c h g r e a t e r t h a n t h e m a g n i t u d eo f kT, 5 5 x 1 0 - 2 3 J F r o m E q u a t i o n (7 ) It IS poss ib l e t oe s t i m a t e N p t o b e a b o u t 2 1 0 1 9 m - 3 , w i t h a n a v e r a g es e p a r a t i o n o f a p p r o x i m a t e l y 0 4 m T h e s e v a l u e s s e e mt o b e e n t i r e l y r e a s o n a b l e a n d c o n s i s t e n t w i t h w h a t i so b s e r v e d i n t he m i c r o s t r u c t u r e o f t he s e a n d o t h e r s u p e r -c o n d u c t o r sR a i s i n g t h e t e m p e r a t u r e f r o m 4 t o 8 0 K i s e x p e c t e dt o r e d u c e b o t h B c a n d BeE b y a f a c t o r o f a b o u t 1 0F o r e x a m p l e , i n t h e m a t e r i a l u s e d b y K u p f e r et alB e 2 s e e m s , f r o m Jc versus B c u r v e s , t o b e 8 T T h i sr e d u c t i o n i n v a l u e s o f c r i ti c a l fi e ld s p r o d u c e s a f a c t o ro f 1 0 r e d u c t i o n i n U , a n d w o u l d b e e x p e c t e d t o p r o d u c ea c o n c o m i t a n t r e d u c t i o n , b y th e s a m e f a ct o r , m J c I nf a c t, in K u p f e r et al 's s a m p l e , J a t 8 0 K , i n t h e m i d - f i e l dr a n g e , i s l 0 T A m - z , t h i s c o r r e s p o n d s t o a f a c t o r o f 2 5 0r e d u c t i o n N o t e t h a t U a t 1 8 x 1 0 - z J i s n o w a p p r o a c h -i n g t h e m a g n i t u d e o f k T , 1 1 x 1 0 - 2 1 J , a n d A W w i ll n o wb e l e s s t h a n k T T h u s , f l ux c r e e p i s e x p e c t e d t o i n f l u en c eJ a t t h i s t e m p e r a t u r eT a k i n g f~ o = 1 07 s - 1 , u s i n g t h e s a m e v a l u e f o r N _a s be fo re (2 1019) , a n e l e c t r i c f i e ld c r i t e r io n o f 10 -gV m - 1 ( a l t h o u g h i t is n o t a t a l l c le a r w h a t v a l u e o ff i e l d c r i t e r i o n s h o u l d b e a s c r i b e d t o c r i t i c a l c u r r e n t se s t i m a t e d f r o m m a g n e t i z a t i o n m e a s u r e m e n t s ) a n d t h ev a l u e f o r U d e d u c e d a t 8 0 K , i t i s p o s s i b l e t o e s t i m a t ef r o m E q u a t i o n ( 1 6 ) t h e c r i t i c a l c u r r e n t d e n s i t y i n am a g n e t i c I n d u c t i o n o f 2 T t o b e a p p r o x i m a t e l y 3 x l 0 7A m - 2 a t 8 0 K T h i s c o m p a r e s w e l l w i t h th e e x p e r i m e n t a lv a l u e o f 1 07 A m - 2 o b t a i n e d b y K u p f e r et al A n a r b i t r a r y

b u t i n f o r m e d c h o i c e h a s b e e n m a d e f o r m a n y o f th ep a r a m e t e r s i n t h e a b o v e e x e r c i s e s T h e c h o i c e is j u s t i f ie db y t h e c o n s i s t e n c y o f t h e r e s u l ts I n h i s s t u d ie s o n f l uxp i n n i n g i n t h in f il m s o f Y B a E C u 3 0 7, K e s h a s r e p o r t e de f f ec t s a t 7 7 K w h i c h c a n b e e x p l a i n e d b y t h e o c c u r r e n c eof f lux c ree p 15

I t is in t e r e s t i n g t o n o t e t h a t i f a n e w s u p e r c o n d u c t -i n g m a t e r i a l w e r e d i s c o v e r e d , w i t h a t r a n s i t i o n t e m -p e r a t u r e s u f f ic i en t ly a b o v e r o o m t e m p e r a t u r e t h a t Ua t , s a y , 3 0 0 K w a s e q u a l t o t h a t o f th e Y B a E C U 3 0 7s a m p l e c o n s i d e r e d a b o v e a t 8 0 K , t h en b y t h e s a m ec r i t e r i a a s u s e d a b o v e t h e c r i t i c a l c u r r e n t d e n s i t y w o u l db e o n l y a b o u t 1 25 0 A m - ' T h i s is a p p r o x i m a t e l y 2 0 00t i m e s le s s c u r r e n t t h a n i s n o r m a l l y c a r r i e d b y u n c o o l e dc o p p e r v

E q u a t i o n ( 1 3 ) p r e d i c t s l i n e a r v o l t a g e versus c u r r e n tc u r v e s f o r s u p e r c o n d u c t o r s i n t h e f l u x c r e e p r e g i m eS u c h c u r v e s h a v e b e e n s e en o n s a m p l e s o f Y B a / C u 3 0 7t e s t e d a t 7 7 K T h e y h a v e b e e n I n v e s t i g a t e d I n d e t a i lb y E k l n et a116 A l s o , a s p r e d i c t e d , t h e s l o p e o f t h e s ec u r v e s i n c r e a s e s w i t h i n c r e a s i n g a p p l i e d m a g n e t i c i n d u c -t i on ( se e R e fe re nc e 16 , F ig u re s 2 a nd 3 ) Eq ua t io n (15 )p r e d i c t s a l i n e a r r e l a t i o n b e t w e e n f l ux f l o w r es i s t i v it y a n dm a g n e t i c i n d u c t i o n , i f t h e v a r i a t i o n w i t h m d u c U o n o f Ui s i g n o r e d A g a i n t h i s p r e d i c t i o n i s c o n f i r m e d b y t h er e s u l t s o f E k l n et al ( R e f e r e n c e 1 6, F i g u r e 4) T h e s l o p eo f t h is l a t t e r c u r v e is a p p r o x i m a t e l y I 0 ~ f ~ m T - 1 I n s e r t -m g t h e p a r a m e t e r s u s e d m t h e a b o v e a n a l y s is o f K u p f e ret al 's m a t e r i a l a t 8 0 K i n t o E q u a t i o n ( 15 ) g i v e s a v a l u e o f1 8 x 1 0 - i 3 f l m T - l , a m i ll i o n t i m e s s m a l l e r t h a n e x p e r i -m e n t U n f o r t u n a t e l y E k l n et al s s a m p l e s c a r r i e d m u c hl o w e r c u r r e n t d e n s i t i es t h a n t h o s e c o n s i d e r e d a b o v e , a n da d i r e c t c o m p a r i s o n i s n o t p o s s i b l e , b u t t h e l o w e r c u r r e n td e n s i t y w o u l d l e a d t o a h i g h e r r e s i s t i v i t y

A f u r t h e r e x p e r i m e n t a l o b s e r v a t i o n w h i c h c a n b ee x p l a i n e d i n t e r m s o f f l ux c r e e p i s t h a t o n e o f s e v e r a lw a y s m w h i c h t h e b e h a v l o u r o f t h e n e w h i g h T~ o x i d es u p e r c o n d u c t o r s d if fe rs f r o m t h a t o f c o n v e n t i o n a l s u p e r -c o n d u c t o r s i s m t h e r e s p o n s e o f t h e i r r e s is t i v e t r a n s i t i o nt o a m a g n e t i c f i e l d T h e r e s i s t i v e t r a n s i t i o n ( p l o t o fr e s i s t a n c e o r r e s i s ti v i t y o f t h e s u p e r c o n d u c t o r versust e m p e r a t u r e i n t h e w c l n l t y o f t h e c r i ti c a l t e m p e r a t u r e , T~)f o r a c o n v e n t i o n a l s u p e r c o n d u c t o r is , m g e n e r a l , m e r e l ys h i f t e d b o d i l y t o a l o w e r t e m p e r a t u r e w h e n t h e s u p e r -c o n d u c t o r ~s s u b j e c t e d t o t h e i n f l u e n c e o f a n e x t e r n a lm a g n e t i c f ie ld A n y b r o a d e n i n g o f t h e t r a n s i t i o n i s u s u a l l ys m a l l T h e c o r r e s p o n d i n g e f f e c t i n a h i g h T ~ m a t e r i a l i sq u i te d i ff e re n t T h e t r a n s m o n b e c o m e s e x t r e m e l y b r o a d ,t h e d e g r e e o f b r o a d e n i n g i n c r e a s i n g a s t h e s t r e n g t h o f t h em a g n e t i c f i e ld is ra i s e d T h e r e s i s t iv i t y n o l o n g e r r i s e ss h a r p l y f r o m z e r o t o t h e n o r m a l s t a t e v a l u e o v e r a l i m i t e dr a n g e o f t e m p e r a t u r e I n s t e a d , t h e r es i s t i v it y b e g i n s t or i se a t a t e m p e r a t u r e v e r y m u c h b e l o w t h e c r i t i ca lt e m p e r a t u r e ( i n d e e d m h i g h f i e l d s t h e r e s l s t l w t y m a yb e g i n t o r i s e a t a t e m p e r a t u r e w e l l b e l o w TJ2) a n dc o n t i n u e s t o r is e i n a f a s h i o n w h i c h a p p r o x i m a t e s t oe x p o n e n t l I u p t o th e n o r m a l s t a t e v al u e a t a te m p e r a t u r eb e l o w t h e z e r o f i e l d T T h i s b e h a v l o u r h a s b e e n s e e n i nm a n y i n v e s t ig a t i o n s o n a w i d e v a r i e t y o f ox i d e s u p e r -c o n d u c t o r s a n d i s c l e a r l y i l l u s t r a t e d in m a n y p u b l i c a t i o n sE x a m p l e s r a n g e f r o m t h e p a p e r d e s c r i b i n g t h e o r i g i n a ld i s c o v e r y o f Y B a 2 C u 3 0 7 ( s ee R e f e r e n c e 1 7) t o a r e c e n td e s c r i p t io n o f t r a n s p o r t p r o p e r t i e s m a B I S r C a C u o x i d es ing le c ry s t a l T T h i s I S j u s t t h e b e h a v l o u r p r e d i c t ed b yE q u a t i o n ( 1 5 )

676 Cryogenics 988 Vol 28 October

8/14/2019 electron variation.pdf

4/4

ConclusionsW ~ t h o u t d e t a i l e d e x p e r i m e n t a l t n v e s t t g a t ~ o n o n w e l lc h a r a c t e r i z e d s a m p l e s o f o x t d e s u p e r c o n d u c t o r s , f o rw h i c h p a r a m e t e r s s u c h a s d e n s it y , g e o m e t r y a n d s t r e n g tho f f lu x p m m n g c e n t r e s a r e i n d e p e n d e n t l y d e t e r m i n e d , t h ec a s e f o r f l ux c r e e p c a n n o t b e r e g a r d e d a s d e f i m t e l y p r o v e nH o w e v e r t h e r e s u l t s q u o t e d a b o v e a r e c o n s t s t e n t w ~ thc n t t c a l c u r r e n t s b e i n g h m ~ t e d b y f l u x c r e e p a t h q u t dm t r o g e n t e m p e r a t u r e s a n d a b o v e , a n d s u g g e s t t h a t a n yr o o m t e m p e r a t u r e s u p e r c o n d u c t o r m a y b e q m t e u s e l e s s

T h e o n s e t o f f lu x cr e e p c a n b e d e l a y e d b y m c r e a s m gt h e p l n n m g s t r e n g t h , o r m o r e p r o p e r l y b y m c r e a s m g t hep i n n i n g e n e r g y , U F o r a g t v e n p r u n i n g i n t e r a c t i o n t h ep i n n i n g s t r e n g t h , a n d h e n c e t h e n o n - f l u x c r e e p h m l t e dJ ~, is m a x t m l z e d b y a f i n e d i s p e r s i o n o f p m n m g c e n t r e sU w i ll in f a c t b e l a r g e r i f t h e l n d l w d u a l p m n m g c e n t r e sa r e a s l a r g e a s p o s s i b l e a n d t h e o p t i m u m d l s p e r s t o n o fc e n t re s w tl l b e a c o m p r o m i s e T h e n a t u r e o f t h e p l n n m gc e n t re , spe c t f i c a l ly t he d i f f e re nc e be tw e e n ~ t a nd the m a t r ix ,a l s o i n f l u en c e s t h e p m n m g s t r e n g t h I t i s u s u a l t o a s s u m et h a t t h e m a x i m u m d ~ f f e r e n c e o c c u r s w h e n t h e c e n t r e t s an o n - s u p e r c o n d u c t m g r e g io n H o w e v e r , a n e ve n g re a t ere f fe c t lS ob ta i ne d w h e n the c e n t r e ~s f e r r om a gn e t t c a9 2oA s m a n y o x i d e s a r e f e r r o m a g n e t t c i t s h o u l d b e r e l a t iv e l ye a s y to i n c o r p o r a t e m a g n e t i c i n c lu s i o n s m t o a n o x t d es u p e r c o n d u c t o r

F i n a l ly , m e n t i o n m u s t b e m a d e o f t h i n fi lm s C u r r e n td e n s i t ie s m t h i n f i l m s o f Y B a z C u 3 0 7 a t 7 7 K c a n b e a sh i g h a s 1 09 A m - 2 i n m a g n e t i c m d u c t l o n s o f 2 T s e eR e f e r e n c e 2 1) I t is b e h e v e d t h a t t h e s e f i l m s h a v e o r i e n t e dg r a i n s t r u c t u r e s , a n d t h a t f l u x - h n e s a r e p m n e d a t p l a n a ri n t e r fa c e s I f t h e f l u x - l m e s a r e p m n e d o v e r t h e i r e n t i r el e n g t h , t h e n t h e r m a l d e p l n n m g w i l l b e e x t r e m e l y d i f fi c u ltI t ~s, t h e r e f o r e , m o s t h k e l y t h a t o x i d e s u p e r c o n d u c t o r sw d l f i rs t fi n d a p p h c a t l o n i n e le c t r o n i c s m t h e f o r m o f t h i nf i lmscknow l edgemen t s

T h e m t t t a l s t i m u l u s t o t h i s w o r k w a s a n t n v t t a t ~ o n t o

Mo d e / fo r f lu x cre ep D D e w H u g h e sp a r ti c ip a t e m t h e N l jm e g e n W o r k s h o p o n H i g h M a g n e t icF i e l d s m S e p t e m b e r 1 98 7, f o r w h i c h I t h a n k t h eo r g a m z e r s T h e e n c o u r a g e m e n t o f m a n y c o ll e a gu e s , i np a r U c u l a r H a r r y J o n e s a n d P e t e r K e s , h a s b e e n a s p u rt o t h e d e v e l o p m e n t o f t h o s e ~ m p e r f ec t ly ex p r e s s e d a n de x t r e m e l y c r u d e ~ d ea s m t o t h e p r e s e n t p a p e r

References1 De w-Hughe s, D Pa pe r pre se nte d a t the Wo rkshop on H ighMagneUc Fie lds , N1jmegen, The Netherlands (1987)2 Anderson, P W Ph v s Re v Le t t (1962) 9 3093 Anderson, P W and Kim, Y B R e v M o d P h y s 11964) 36 394 Beasley, M R , Labusch, R and Webb W W Ph v s Re v (1969) 181

6825 Klm, Y B H empstead, C F and Strnad A R Ph v s Re v (1965) 13911636 H u ds on , P A , Y m , F C and Jones H I E E E T r a n ~ M a g n (1981)M A G - 1 7 1 6 4 97 Hudson, P A , Ym, F C and Jones H 1 E E E T r a n s M a g n (1983)M A G - 1 9 9 0 38 Hampshire D P , Jone s , H a nd Mi tc hel l , E J W I E E E T r an s M a g n(1985) MAG-21 2899 Kupfer, H , Apfels tedt , I , Schauer , W , Flukiger , R , Meler-HirmerR and Wuhl, H Ze l t Ph y szk (1987) 169 15910 Ya m a da, Y , Fukushim a, N , Na k a ya m a , S , Yoshm o H andMurase S J p n J Ap p l Ph y s Le t t (1987) 26 186511 Dew-Hu ghes, D Proc CE C Workshop on Htqh T~ Superconductorsand their Apphcat tons Genoa, I ta ly (1987) 6712 Hslang T Y and Finnemore D K P h y s R e v (1980) B22 15413 Dew-Hug hes, D P h d M a g (1987) B55 45914 Orlando , T P , M cNlff , E J , Foner , S and Beasley, M R P h y s R e v(1979) BI2 14715 Kes, P H P ro ~ H T S C M M S Inter laken, Switzer land (1988)16 Ekin, J W , Bra gm skl , A l , Pa nson, A J , J a no c ko, M A, Ca pone II ,D W Zaluza N J F landermeyer B de L ima O F Hong MKwo, J and Llou, S H . J Ap p l Ph v s (1987) 62 482117 Wu, M K , Ashburn , J R , Torng , C . J , Hor , P H , Me ng, R L , Ga o,L , Hua ng, Z J , Wa ng, Y Q a nd Chu, C W Ph ~ ~ Re v Le t t (1987) 5890818 T a ka gl , H , E l sa kl, H , U c hlda , S , Ma e da , A , T a j lm a , S ,Uc lnnokura , K , and Tanaka S N a t u r e (1988) 332 23619 Alden, T H . and Lmngston J D A p p l P h y s L e t t (1966) 8 620 Campbell, A M , Evetts, J E and Dew-Hughes, D P h d M a 9 (1968)18 31321 Sum l tom o Ele c t ri c Indusm e s N a t u r e (1988) 331 105

Cryogenics 988 Vol 28 October 677