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Journal of Superconductivity Vo l. 9 No. 1 1996

Est imation of Intragrain Magnet ic Flux Motion Viscos i ty inHigh Temperature SuperconductorsA A K o r d y u k ~ a n d V V N e m o s h k a l e n k o ~

Received 5 January 1995A simple method for evaluation of the lower limit of intragrain magnetic flux motion viscosityis presented. We have also shown that in our experiment the energy loss in an alternatingmagnetic field in a granular YBa2Cu3Ov x superconductor prepared by the standard sinteringmethod is determined by thermally assisted magnetic flux flow into superconducting grainsand does not depend on the intergrain space.KEY WORDS: Granular superconductors; flux motion; energy losses; levitation.

1. INTRODUCTIONThe study of the macroscopic magnetic proper-ties of high-temperature superconductors HTSC) has

attr acted the interest o f researchers [ 1 . This is under-standable since such fundamental parameters as thecoherence length, the magnetic field penetrationdepth, and information on pinning and magnetic fluxmotion, namely critical currents and viscosity, maybe obtained. Determination of the values of theseparameters is necessary both for construction oftheoretical models and for the successful practicalapplication of HTSC.In the study of the magnetic flux dynamics inHTSC, vibromechanical methods of research areespecially convenient. These methods combine theadvantages of noncontac t methods with the simplicityof interpretation of experimental results. It is possiblehere to divide the method into two classes: i)methods using a HTSC vibrating in a magnetic fieldwith high-Q mechanical oscillator [2], vibration reed

experiments [3], and oscillator studies of ceramicsuperconductors [4]) ; ii) metho ds using a stationaryHTSC sample and a vibrating permanent magnet[5,6].In our previous papers [7-11] a simple from thepoint of view of experimental realization) system,~Institute of Metal Physics, National Academy of Science ofUkraine, Vernadsky pr. 36, 252680 Kiev 142, Ukraine.

where the permanent magnet PM) was freely sus-pended above the HTSC sample, was investigated.The many parameters of such a system that can befound experimentally permits one to obtain extensiveinformation on the properties of the HTSC samplesstudied. In [7,8] we described the observable proper-ties of such a system, and in [10,11] their dependenceon the HTSC structure [9] and the magnetic proper-ties of the grains were determined.In this paper, with the help of such a PM-HTSCsystem we have shown that in our experiment theenergy losses in an alternating magnetic field in thegranular YBa2Cu307-x superconductor prepared bythe standard sintering method are determined byintragrain magnetic flux motion. We have also evalua-ted the lower limit of intragrain flux motio n viscosity.Its large value may be considered as the independentconfi rmation of the existence o f thermal ly assisted fluxflow TAFF) [12,13] in the HTSC grains.

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2 E X P E R I M E N T A LIn this work we focused on the granular

YBazCu307-x superconductor prepared by the stan-dard sintering metho d [ 14]. Typical dimensions of thecomponent grains were 10-12pm. Two types ofsamples were used in our experiments, ceramicsamples and composite samples. All samples were0.8 cm thick pellets o f 4 cm diameter. The first ones

0896-1107/96/0200-0077509.50/0 9 1996 PlenumPublishingCorporation

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8 Kordyuk and Nemoshkalenko

were cut from sintered superconductor. The compos-ite samples were formed from dispersed grains ofsuperconductors in an insulating paraffin. The disper-sed grains were obtained by grinding a piece of Y-superconductor. The volume fraction of the ceramicgrains was 62%. The absence of electrical contactsbetween grains was verified by resistance measure-ments. For comparison we have also investigated cer-amic and composite samples made of(Pb0.16Bi0.84)2Sr2Ca2Cu~Oy superconductor [ 15].We investigated our samples using the methodof permanent magnet (PM) forced oscillations. Thismetho d was described in detail in [7]. The PM ofSmCo5 had the shape of a spheroid with massm ~0.021 g an d magnetic moment/~ ~ 1.2 G. cm3. Itlevitated above the HTSC sample at a height ofx0~0.10 0.25cm with r oriented parallel to theHTSC surface. PM forced oscillations with frequency~o were excited by an alternating magnet ic field gener-ated by an AC coil. The amplitude of the PM oscilla-tions was determined by a microscope with 4 mprecision. As the sample sizes were much greater thanx0 which was greater t han the PM size, we could con-sider the PM as a point magnetic dipole above aninfinite HTSC surface [8].

3. RESULTS AND DISCUSSIONThere are five modes of PM oscillations in sucha PM-HTSC system: three translation and two rota-

tion (or torsion) oscillations. The parameteters ofthese modes, such as the resonance fi'equency co andthe damping 5 for PM amplitude A~0, have beenpresented in [9] and [10] for Y and Bi samples, respec-tively. In [10] we have also presented the characterist icamplitude dependences of these parameters for allmodes for Y and Bi samples. The interesting featureof the 5(A) dependence is the distinct plateau forA

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E s t i m a t i o n o f I n tr a g r ai n M a g n e t i c F l u x M o t i o n V i s c o s i t y 9

F r o m t h e a b o v e , i t i s p o s s i b l e t o e v a l u a t e t h er a n g e o f v i sc o s it ie s o f t h e i n t r a g r a i n f l u x m o t i o n . T h el i n e a r v i s c o s i t y r / t i s t h e p r o p o r t i o n a l i t y f a c t o rb e t w e e n t h e v i s c o u s f r i c t i o n a l f o r c e p e r v o r t e x l e n g t ha n d t h e v o r t e x v e l o c i t y : fv = ~ tv . W e m a y a l s o w r i t ethe vo lum e v i scos i ty 77 v = r/ tB/c~o [ 7 ] , wher e B i s them a g n e t i c f i e l d i n t h e s u p e r c o n d u c t i n g g r a i n s a n d q~ois t h e m a g n e t i c f l ux q u a n t u m . T h e e n e r g y l o s s d u r i n gt h e p e r i o d m a y b e o b t a i n e d b y i n t e g r a t i o n o f th e w o r kd o n e b y f r i c t i o n a l f o r c e o v e r t h e p e r i o d a n d i t s s u m -m a t i o n w i t h r e s p e c t t o a l l v o r t i c e s [ 7 ] : W - -Tor /l co ( a 2 ) V o B / c ) o . H e r e ( a 2 ) i s t h e m e a n s q u a r e o s c il -l a t i o n a m p l i t u d e o f v o r t i c e s a n d V o i s t h e v o l u m e o ft h e s u p e r c o n d u c t o r i n w h i c h t h e m a i n e n e r g y di s si p a -t i o n o c c u r s . C o m p a r i n g t h i s e q u a t i o n w i t h ( 1 ) w eo b t a i n

2m~b0~r / j V~ 2 (2)wh er e a 2 = ( a 2 ) / A 2. F o r e s t i m a t i n g t h e v i s c o s i t y d u et o t h e s t e e p l y d e c r e a s i n g d i p o l a r m a g n e t i c f i e ld o f th eP M , H o c l / x 3 , w e m a y w r i t e V o ~ x 3 [ 7] . We wi l l con-s i d e r t h e v e r t i c a l t r a n s l a t i o n m o d e o f t h e P M o s c i ll a -t i o n s . T h e n , a s s u m i n g B ~ H ~ / x 3 a n d t a k i n g i n t oa c c o u n t t h e e x p e r i m e n t a l v a l u e o f ~ = 3 .8 s -1 [ 10 ], w em a y w r it e 7 b ~ 2 / ~ b 0 ~ / / z a 2 ~ ( 1 . 3 x 1 0 - a / a 2 ) g / c m . s.F o r q u a n t i t a t i v e e s t i m a t i o n o f r /l w e s h o u l d k n o w t h em e c h a n i s m o f v o r t e x p e n e t r a t i o n i n t o t h e g r a in , b u tw e m a y e s t i m a t e t h e l o w e r l i m i t o f r /l i f w e r e p l a c e( a 2 ) b y a o , i ts m a x i m u m v a l u e : a (c o , r ) 3 x 1 0 - 4 g / c m 9 s( o r r / v > 1 0 5 g / c m 3 9 s ), w h i c h e x c e e d s t h e f l u x f l o wv i s c o s i t y r/FF~ 1 0 7 g / c m " S [7 ] b y m o r e t h a n t h r e eo r d e r s o f m a g n i t u d e . S u c h a g r e a t v i s c o si t y m a y b ee x p l a i n e d b y o t h e r m e c h a n i s m o f v i sc o u s f lu x m o t i o n ,n a m e l y T A F F [ 12 ,1 3 ].4 . C O N C L U S I O N S

I n t h i s w o r k w e h a v e o b t a i n e d a n i n d e p e n d e n tc o n f i r m a t i o n o f t h e e x i s te n c e o f T A F F p r o c es s e s i n

H T S C g r a in s a n d e v a l u a t e d t h e l o w e r l im i t o f i n t r a-g r a i n f l u x m o t i o n v i s c o s i t y . I t i s a l s o s h o w n t h a t t h ed y n a m i c p r o p er ti e s o f a P M - H T S C s y st e m , r e so n a n c ef r e q u e n c y a n d d a m p i n g , a r e d e t e r m i n e d b y t h e i n t e r -a c t i o n o f th e P M f ie ld w i th g r a in s a n d d o n o t d e p e n do n t h e i n t e r g r a i n s p a c e . S u c h a s i m p l e s y s t e m a l l o w so n e t o i n v e s ti g a t e th e i n t r a g r a i n d y n a m i c s o f m a g n e t i cf lu x in g r a n u l a r H T S C .

I n s u m m a r y , w e n o t e t h a t s t u d i e s o f t h e d y n a m i cp r o p e r t i e s o f a l l f iv e m o d e s o f P M o s c i l l a t io n s a r ep r o m i s i n g s i n ce t h e y g i v e in f o r m a t i o n o n t h e m e c h a -n i s m s o f m a g n e t i c fl u x d y n a m i c s a n d p e n e t r a t i o n a n dt h e i r d e p e n d e n c e s o n f r e q u e n c y , a m p l i t u d e , a n d o r ie n -t a t i o n o f t h e a l t e r n a t i n g m a g n e t i c f i e l d c a n b eo b t a i n e d .

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