Flux compression in hard superconductors

Volume 10, number 1

PHYSICS

FLUX

COMPRESSION

LETTERS

IN HARD

15 May 1964

SUPERCONDUCTORS

H. J. GOLDSMID and J. M. CORSAN T/¢ General Electric Company Limited, Central Research Laboratories, Hirst Research Centre, Wem bley, England Received 6 April 1964

W e h a v e r e c e n t l y s t u d i e d the m a g n e t i s a t i o n at 4.2OK of s u p e r c o n d u c t i n g t u b e s m a d e f r o m s i n t e r e d Nb3Sn c o m p a c t s of low d e n s i t y (~ 4.5 g / c m 3 ) . T h e m a g n e t i s a t i o n c u r v e s f o r f i e l d s up to 54 kG h a v e b e e n found to be c o n s i s t e n t with the r e l a t i o n g i v e n by K i m et al. 1), J =~ Bo+B'

mEFORE

COMPRESSION

(1)

w h e r e J is the c r i t i c a l c u r r e n t d e n s i t y in a l o c a l m a g n e t i c f i e l d B, and ~ and B o a r e c o n s t a n t s f o r a g i v e n s a m p l e . A n o t a b l e f e a t u r e of our e x p e r i m e n t s h a s b e e n the a l m o s t c o m p l e t e a b s e n c e of flux j u m p s w h e n the e x t e r n a l f i e l d h a s b e e n c h a n g e d as r a p i d l y as 4 k G / m i n e v e n , in s o m e c a s e s , w i t h a d i f f e r e n c e of up to about 50 kG b e t w e e n the e x t e r n a l f i e l d and the f i e l d i n s i d e the tube. It is thought that the a b s e n c e of flux j u m p s m a y be a s s o c i a t e d with the high p o r o s i t y of our s a m p l e s w h i c h f a c i l i t a t e s c o o l i n g of the tube w a l l s . T h e f a c t that o u r Nb3Sn t u b e s h a v e b e e n so w e l l - b e h a v e d h a s e n c o u r a g e d us to e x a m i n e the p o s s i b i l i t i e s of flux c o m p r e s s i o n u s i n g s u p e r c o n d u c t i n g p i s t o n s as d e s c r i b e d by S w a r t z and R o s n e r 2). It is a p p a r e n t that the a s s u m p t i o n that the flux p e n e t r a t i o n w i t h i n the w a l l s is n e g l i g i b l e is inv a l i d for h a r d s u p e r c o n d u c t o r s in high m a g n e t i c f i e l d s . W e h a v e , t h e r e f o r e , c a l c u l a t e d the b e h a v i o u r to be e x p e c t e d f o r a flux c o m p r e s s o r of s i m p l e g e o m e t r y t a k i n g into a c c o u n t the p e n e t r a t i o n of flux into the w a l l s . T h e c o m p r e s s o r c o n s i s t s of a s u p e r c o n d u c t i n g tube, of i n t e r n a l and e x t e r n a l r a d i i r 2 and r 3 , r e s p e c t i v e l y , into w h i c h can be i n s e r t e d a s u p e r c o n d u c t i n g p i s t o n of r a d i u s ~'~,~ It is s u p p o s e d that the tube is f i r s t m a g n e t i s e d so a s to h a v e an i n t e r n a l f i e l d B 1 and t h a t , a f t e r i n s e r t i o n of the p i s t o n , the s p a c e b e t w e e n the w a l l s r e a c h e s a f i n a l f i e l d B 2. F i g . 1 s h o w s s c h e m a t i c a l l y the v a r i a t i o n with p o s i t i o n of the m a g n e t i c f i e l d b e f o r e and a f t e r c o m p r e s s i o n . It is a s s u m e d t h a t the t h i c k n e s s ( r 3 - r 2) of the tube

AFTER COMPRESSION r= __ r t

_

B

l,

k I

~ m

I 1 I

I I )

I I

( I I

I

D,ST~Ct

~tSTANCE

Fig. 1. Schematic diagram showing variation of m a g netic field with position before and after flux c o m p r e s sion. w a l l is g r e a t enough to p r e v e n t l o s s of flux d u r i n g the c o m p r e s s i o n and that the r a d i u s r 1 of the p i s ton is l a r g e enough to k e e p the f i e l d e q u a l to z e r o at the axis. T h e n e c e s s a r y c o n d i t i o n s a r e found to be BoB 2 + ~B 2 2 r 3 - r 2 >~ k~ ~< r l ' (2) w h e r e k = 4n × 10 -4 kG c m / A , m a g n e t i c f i e l d s b e i n g e x p r e s s e d in kG, a in k G A / c m 2 and the r a d i i in c m . A s s u m i n g , then, that the t o t a l flux is the s a m e b e f o r e and a f t e r c o m p r e s s i o n , it can be shown u s i n g eq. (1) that (r22 - r l 2 ) B 2

B22 ( r 1 + r 2) (3B o + 2B2) 3k~ B 2 = r 2 2 B 1 + ~ 1 - {h~r~(3B +2B~) 3(k~)2 z o 1 +

+ B o 2 B 1 + ~BoB12 + ~B13} .

(3)

W h e n B 1 is s m a l l it is a good a p p r o x i m a t i o n to n e g l e c t the flux in the w a l l s of the tube before i n s e r t i o n of the p i s t o n , in which c a s e the s e c o n d t e r m on the r i g h t - h a n d s i d e of eq. (3) d i s a p p e a r s . 39

Volume 10, number 1

PHYSICS LETTERS

F o r r a t h e r higher v a l u e s of B1, it is a b e t t e r app r o x i m a t i o n if this t e r m is not n e g l e c t e d but r e p l a c e d by B12r2(3Bo + 2B1)/3km We have p e r f o r m e d a c o m p r e s s i o n e x p e r i m e n t using a piston of r a d i u s r 1 = 0.442 cm and a tube with an i n t e r n a l r a d i u s r 2 = 0.475 cm. M a g n e t i s a tion e x p e r i m e n t s on s i m i l a r l y p r e p a r e d s a m p l e s of Nb3Sn have y i e l d e d v a l u e s of B o and ks equal to about 4 kG and 2.5 × 103 k G 2 / c m , r e s p e c t i v e l y . Table 1 Theoretical and experimental values for B2. B 1 (k.G)

B2 (theor} (kG)

B2 (exp) (kG)

3.0 16

9.9 22.7

8.5 23.5

THE ANGULAR SOME TYPE

DEPENDENCE I AND TYPE

15 May 1964

The t h e o r e t i c a l and m e a s u r e d values of B 2 a r e c o m p a r e d in table 1. It will be seen that the ex p e r i m e n t a l r e s u l t s a g r e e r e a s o n a b l y well with the t h e o r e t i c a l p r e d i c t i o n s . We have p l e a s u r e in thanking Mr. G.W. C o l e s and Mr. A. G. Buxton for the p r e p a r a t i o n of the s a m p l e s and Mr. N. J. Lyon for a s s i s t a n c e in p e r f o r m i n g the e x p e r i m e n t s .

References 1) Y.B.Kim, C.F.Hempstead and A.R.Strnad, Phys. Rev. 129 (1963) 528. 2) P.S.Swartz and C.H.Rosner, J. Appl. Phys. 33 (1962) 2292.

OF SURFACE II L E A D B.ASED

SUPERCONDUCTIVITY SUPERCONDUCTORS

IN *

H. R. HART J r . and P. S. SWARTZ General Electric Research Laboratory, Schenectady, New York

Received 6 April 1964

We have found additional e v i d e n c e 1-3) f o r sup e r c o n d u c t i v i t y above the t h e r m o d y n a m i c c r i t i c a l fie ld H c and the A b r i k o s o v 4) c r i t i c a l field Hc2 in type I and type II lead b a s e d s u p e r c o n d u c t o r s . B e c a u s e of the a g r e e m e n t of the c r i t i c a l field HT of this r e m n a n t s u p e r c o n d u c t i v i t y with the theory of s u r f a c e s u p e r c o n d u c t i v i t y of S a i n t - J a m e s and De Gennes 5), and b e c a u s e of the dependence of H T on s u r f a c e r o u g h n e s s , we a tt r ib u t e its o r i g i n to a s u p e r c o n d u c t i n g s u r f a c e l a y e r . We find, as have o t h e r s 2), that H T is s e n s i t i v e to the angle 6 between the m a g n e t i c field and the plane of the s u r f a c e , being a m a x i m u m at ~ = 0. We find in addition that the n o r m a l i s e d angular dependence of H T is independent of c o m p o s i t i o n for the e n t i r e r a n g e of the l e a d - t h a l l i u m type H s u p e r c o n d u c t o r s that we tested. In the type I s u p e r c o n d u c t o r s t e s t ed, p u r e lead and Pb0.99T10.01, we find evidence f or s u r f a c e s u p e r c o n d u c t i v i t y (ref. 3) above H c when ~ is s m a l l . Beyond an angle ~c, HT b e c o m e s l e s s than Hc and is not e x p e r i m e n t a l l y defined. * The research described in this letter was supported by the United States Air Force under Contra~t No. AF-33(657)-11722. 40

H o w e v e r , for 0 ~< • < 0c the n o r m a l i s e d angular dependence of H T is the s a m e as for the type II superconductors. The s a m p l e s w e r e c h e m i c a l l y polished s h e e t s (~< 0.05 cm X 2.5 cm × 2.5 cm) which had been annealed in vacuo for 40 h o u r s at 10-30°C below t h e i r m el t i n g t e m p e r a t u r e . The s u p e r c o n d u c t i n g t o - n o r m a l t r a n s i t i o n (4.2oK) was obtained by m e a s u r i n g the t r a n s m i s s i o n of a s m a l l a l t e r n a t ing magnetic field (~ 0.01 Oe at 104 c / s ) through the c e n t r a l p o r t i o n of the sheet as a function of applied steady m a g n e t i c field and angle ~. C a r e was taken to m i n i m i s e the a l t e r n a t i n g field n e a r the edges of the sheet. The breadth of the t r a n s i tion was typically 1%-3% of the steady field. HT(~) , defined as the midpoint of the t r a n s i t i o n , was found to change l e s s than 1% upon v a r y i n g the ac field o v e r a f a c t o r of 100. Our c u r v e s of HT(6 ) a r e q u a l i t a t i v e l y s i m i l a r to, but not identical with, t h o se m e a s u r e d using other methods 2,3). We identify HT(0O ) with Hc3 and HT(90o ) with Hc2. A cco r d i n g to S a i n t - J a m e s and De Gennes 5) Hc3/Hc 2 = 1.695; our r a t i o s (see table 1) a r e in f a i r l y good a g r e e m e n t . (For Pb0.97T10.03 and Pb0.70T10.30 the t r a n s i t i o n