ZENER RELAXATION IN SINTERED SUPERCONDUCTOR BaPb0.75Bi0.25O3

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ZENER RELAXATION IN SINTERED

SUPERCONDUCTOR BaPb0.75Bi0.25O3

M. Tanaka, R. Yoshizaki, T. Suzuki

To cite this version:

M. Tanaka, R. Yoshizaki, T. Suzuki. ZENER RELAXATION IN SINTERED

SUPERCONDUC-TOR BaPb0.75Bi0.25O3.

Journal de Physique Colloques, 1985, 46 (C10), pp.C10-715-C10-718.

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JOURNAL DE PHYSIQUE

Colloque C10, supplement a u n012, T o m e 46, dbcembre 1 9 8 5 p a g e C10-715

ZENER RELAXATION IN SINTERED SUPERCONDUCTOR BaPbo.,,Bio.2,0,

M. TANAKA, R. YOSHIZAKI AND T. SUZUKI

Institute of Applied Physics, University of Tsukuba, Sakura. Ibaraki 305, Japan

Abstract

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The internal friction in the polycrystalline sintered specimen BaPb0.75Bi0.2503 (BPB) was measured as a function of temperature between 4.2 K

and 25 K and magnetic field up to 5 T. The internal friction is proposed to reflect indirectly the electron-phonon interaction through the thermo-mechanical relaxation-Zener relaxation-in the polycrystalline specimen.

I. INTRODUCTION

The sintered superconductor BaPbl-xBixOg with x in the vicinity of x=0.25 (BPB) is drawn public attenuation because of the superconduction transition temperature as high as 12 K in spite of its relatively low carrier density of the order of 10" cm-3 11-6/. Some unknown but very effective mechanism must be working for the formation of the Cooper pairs. Hence, it is desirable to obtain experimental information pertinent to the electron-phonon interaction by measuring. the change in the ultrasonic attenuation due to the formation of Cooper pairs.

The ultrasonic pulse echo study of the sintered BPB has been carried out at 10 MHz and 30 MHz by Fukami, Inoue and Mase in the vicinity of the superconducting transition temperature as the function of temperature as well as the magnetic field in the superconducting state /6/. They have found that the ultarasonic attenuation d

or the internal friction Q-' (d=d~-', where is the angular frequency of the ultrasonic wave) in BPB at 10 MHz and 30 MHz shows little dependence on the magnetic field in the superconducting state. Thus they have concluded that the major part of the observed ultrasonic attenuation is not due to the interaction between the ultrasonic wave and the conduction electron.

We wish to report here that although we have measured the internal friction &-I at lower frequency than 10 MHz, between 100 kHz and 300 kHz, we have observed as appreciable dependence of the internal friction in BPB on the magnetic field as well as on temperature. Because our measurement is carried out at much lower frequency than 10 MHz, the direct interaction between the ultrasonic wave and the conduction eleetron must be smaller than that at 10 MHz. Hence, the internal friction measured between 200 kHz and 300 kHz cannot be due to the direct interaction of the ultrasonic wave with the conduction electron. An alternative explanation based on the thermo- mechanical relaxation-Zener relaxation-is proposed in the present paper.

The internal friction was measured by use of the apparatus shown in Fig. 1. The specimen is carefully placed between the two piezoelectric transducers of lead zirco-

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C10-716 JOURNAL DE PHYSIQUE

nium titanate (PZT) by using a micrometer-head. A damper (KRYTOX by Du Pont) is placed between the PZT and the mechanical holder. The apparatus shown in Fig. 1 is placed in a cryostat, whose temperature is controlled with the stability of 50.2

K

by a cryogenic temperature controller. The cryostat is in turn placed into the superconducting magnet which can produce the magnetic field up to 6 T.

One of the transducers is excited by a sinusoidal electric signal from a frequency synthesizer. The output signal from the other transducer is preamplified and detected by a high frequency lock-in amplifier (Model 5202 of Princeton Applied Re- search). When the excitation frequency is equal to one of the resonance frequencies which are determined by the elastic constants, geometrical shape and size of the specimen, the amplitude of the output signal shows a resonance peak. In the present experiment, the specimen of a spherical shape with the diameter of about 5 mm is used.

For an ideally isotropic and spherical specimen, the single resonance peak with the lowest frequency is known to be assigned to the pure shear vibration / 7 / . The resonance spectra of the BPB specimen observed between 25 and 4.2 K is shown in Fig. 2. The spectra consist of many adjacent resonance peaks instead of a single peak, indicating the deviation from the ideal elastic isotropy and uniformity. Because of the overlapping between the trails of the neighboring resonance peaks, the internal friction cannot be estimated from the width of a resonance peak. Hence, the change in the height of the resonance peak is recorded as the quantity to represent the behav- ior of the inverse of the internal friction.

Figure 3 shows the variation of the ratio, of the resonance peak height in BPB with temperature. Hence, Is is the resonance peak height at the temperature lower than 25 K and the height at 25 K. The ratio remains approximately constant in the temperature region above 15 K. It increases drastically with the decrease of temperature below Tc-the superconducting transition-5em~erature.

Figure

4

shows the variation of the rati0~~1,(1~'of the resonance peak height

in

BPB with

ma

netic field at

4.2

K.

Here, I is the resonace peak height at the magnetic field of 5 T. The ratio decreasesnwith the increase of the magnetic field. The decrease is appreciable only when the magnetic field higher than Hc2 is applied. The upper critical field Hc2 of BPB is about 3.1 T at 4.2 K

/4/.

111. DISCUSSION

While the dependence of the internal friction or the resonance peak height in BPB on the temperature and the magnetic field cannot be interpreted in terms of the direct phonon-electron interaction as mentioned in the introduction, the internal friction in BPB is found to be critically dependent on temperature Tc as well as on the magnetic field. As a mechanism for the internal friction in the sintered polycrystalline specimen of BPB, the thermoelastic relaxation-Zener relaxation-is adopted here /8/. The Zener relaxation in the polycrystalline specimen is given by

Here,

R

is a factor of the order of 1, which indicates the friction of the total strain energy associated with the relaxation. C,-C, is the difference between the specific heat capacity at constant pressure andrthat at constant volume. The coupling between the acoustic wave and the thermal phonog is represented'phenomenologically by the factor Cp-CV, which is related to the Gr'keisen parameter. The relaxation frequency fo is glven by fo = vslp/~;, where lp is the mean free path of thermal phonon, V, the sound velocity, LC the mean diameter of the single crystal grain in the sintered polycrystalline specimen.

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t h e s i n g l e c r y s t a l g r a i n i n t h e specimen used i n t h e p r e s e n t experiment i s e s t i m a t e d t o be 1 0 p m from t h e e l e c t r o n microscope photograph. I f t h e phonon mean f r e e p a t h i s of t h e o r d e r of 200 A, f o i s e s t i m a t e d t o be 6 . 8 ~ 1 0 ~ Hz, which i s h i g h e r t h a n t h e frequency f i n t h e p r e s e n t experiment. The phonon mean f r e e p a t h of a t y p i c a l i n s u l a - t o r such a s NaCl and q u a r t z i s of t h e o r d e r of 200 A a t 77 K. The phonon mean f r e e p a t h i n BPB a t 4.2 K w i t h r e l a t i v e l y low c a r r i e r c o n c e n t r a t i o n should be expected t o be l o n g e r t h a n 200 A. Hence, it can be assumed t h a t t h e c o n d i t i o n f o > > f i s f u l f i l l e d i n t h e p o l y c r y s t a l l i n e specimen i n t h e p r e s e n t experiment and t h e measurement of t h e i n t e r n a l f r i c t i o n a t low frequency i n t h e range of 200 kHz p r o v i d e u s w i t h a new means t o measure t h e change i n t h e phonon mean f r e e path. On t h e o t h e r hand, t h e u l t r a s o n i c a t t e n u a t i o n o r t h e i n t e r n a l f r i c t i o n measured a t high frequency i n t h e range of 10 MHz i s expected t o be r a t h e r i n s e n s i t i v e t o t h e change i n t h e t h e r m a l phonon mean f r e e path, because of t h e p r o x i m i t y of f t o f o and because of t h e s t a t i s - t i c a l d i s t r i b u t i o n of g r a i n s i z e LC.

I n t h e experiment i n BPB a s shown i n Fig. 3 and Fig. 4, t h e change of t h e i n t e r n a l f r i c t i o n i s i n t e r p r e t e d t o r e p r e s e n t t h e d e c r e a s e of t h e t h e r m a l pnonon mean f r e e p a t h due t o t h e d e c r e a s e of t h e Cooper p a i r s by t h e i n c r e a s e , o f t h e t e m p e r a t u r e of by t h e a p p l i c a t i o n o f t h e magnetic f i e l d . The r a t i o of t h e u l t r a s o n i c a t t e n u a t i o n of t h e high frequency phonon i n t h e s u p e r c o n d u c t i v i t y s t a t e d , t o t h a t i n t h e normal s t a t e d n i s given by i n t e r m s of t h e superconducting energy gap 26 a s f o l l o w s

I f t h e r a t i o of t h e i n t e r n a l f r i c t i o n a t 4.2 K t o 25 K shown i n Fig. 3 i s assumed t o be e n t i r e l y due t o t h e change i n t h e a t t e n u a t i o n , i.e. t h e mean f r e e path, of t h e t h e r m a l phonons, Eq. 3.2 g i v e s t h e e n e r g y g a p o f 24=1.0 meV a t 4.2 K. A l t h o u g h t h i s i s n o t unreasonable v a l u e f o r t h e superconducting energy gap, it cannot be t a k e n a s a q u a n t i t a t i v e e s t i m a t e f o r t h e energy gap. The f a c t o r which c o n t a i n s Cp-Cv i n Eq. 3.1 i s a l s o dependent on t e m p e r a t u r e and d e c r e a s e s a p p r e c i a b l y w i t h t h e d e c r e a s e of t h e temperature. This i s r e f l e c t e d i n t h e f a c t t h a t t h e change i n t h e i n t e r n a l f r i c t i o n a s s o c i a t e d w i t h t h e d e s t r u c t i o n of t h e superconducting s t a t e by t h e magnetic f i e l d a t 4.2 K i s s m a l l e r t h a n t h e superconducting change by t h e i n c r e a s e of t h e temperature.

The main p r o p o s a l of t h i s paper t h a t t h e i n t e r n a l f r i c t i o n i n t h e s i n t e r e d p o l y c r y s t a l l i n e specimen p r o v i d e s u s w i t h t h e means t o measure t h e t h e r m a l phonon mean f r e e p a t h i s a l s o supported by f u r t h e r experiment i n t h e BaPb03 specimen, which i s n o t superconducting a t 4.2 K. This r e s u l t w i l l be published elsewhere.

The a u t h o r would l i k e t o acknowledge t h e s t i m u l a t i n g d i s c u s s i o n s w i t h Drs. Y. Hiki, T. Sakudo, T. I s h i g u r o and K. Kajimura. They a r e a l s o indebted t o Messrs. T. Hikata, J. Shiozawa a n d ~ . F u j i t ~ f o r t h e i r a s s i s t a n c e i n t h e c o u r s e of t h e p r e s e n t experiment.

A. W. S l e i g h t , J. L. G i l l s o n , a n d P. E. B i e r s t e d t , S o l i d S t a t e Commun. 1 7 , ( 1 9 7 5 ) 27.

T. I t o h , K. K i t a g a w a , and S. Tanaka, J. Phys. Soc. Jpn. 53, (1984) 2668. L. F. M a t t h e i s s and D. R. Hamann, Phys. Rev. B 26, ( 1 9 8 2 ) 2686.

T. D. Thanh, A. Koma, and S. Tanaka, Appl. Phys. 2 2 , ( 1 9 8 0 ) 205.

C. E. M e t h f e s s e l , G. R. S t e w a r t , B. T. M a t t h i a s , and C. K. N. P a t e l , Proc. N a t i o n . Acad. S c i . 77, ( 1 9 8 4 ) 6307.

T. Fukami, N. I n o u e , and S. Mase, J. Phys. Soc. Jpn. 5 3 , ( 1 9 8 4 ) 4322. D. B. F r a s e r and R. C. LeCraw, Rev. S c i . I n s t r . 3 5 , (1964) 1113.

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JOURNAL DE PHYSIQUE 4 MICROMETER W 0 a U W a a S A M P L E 1

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1 0 15 30

Fig. 1 Schematic view of t h e sample TEMPERATURE ( K 1 h o l d e r of s p h e r e resonance metho'd. _{Fig. 3 Temperature dependence of t h e r a t i o}

of t h e s p h e r e resonance amplitude of BaPb0.75Bi0.2503. The l i n e i s a g u i d e f o r e y e s . I I 0 3 6 I MAGNETIC FIELD ( T ) T=24.5

e . z 3

Fig. 4 Magnetic f i e l d dependence of t h e r a t i o

of t h e s p h e r e resonance amplitude of

200 250 300 BaPb0.75Bi0a2503. The l i n e i s a g u i d e f o r eyes. FREQUENCY (

kHz

)