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Dependence of peak effect on the particle size in superconducting SmBa2Cu3O7−δ powder samples
Physica C 338 Ž2000. 115–120 www.elsevier.nlrlocaterphysc
Dependence of peak effect on the particle size in superconducting SmBa 2 Cu 3 O 7yd powder samples Y. Takahama a,b, H. Suematsu a , T. Matsushita a,c , H. Yamauchi a,b,) a Materials and Structures Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan Department of InnoÕatiÕe and Engineered Materials, Interdisciplinary Graduate School, Tokyo Institute of Technology, Yokohama 226-8502, Japan Faculty of Computer Science and Systems Engineering, Kyusyu Institute of Technology, 680-4 Kawazu, Iizuka 820-8502, Japan b
c
Abstract The dependence of peak effect in the critical current density Ž Jc . vs. applied magnetic field Ž H . characteristics on the particle size in superconducting SmBa 2 Cu 3 O 7y d single-phase powder samples was investigated. The sintered pellets were crushed and the powder was sorted into three categories by means of elutriation and sieving. The samples of the three categories were characterized with respect to particle size and superconducting properties. The Jc values were calculated utilizing Bean’s model. As far as the normalized critical current density, Jc Ž H .rJc Ž0. vs. H curves were concerned, the ‘‘peak’’ was more prominent as the average particle size of the sample increased. On the other hand, quantity Jcpeak defined as the ‘‘peak’’ contribution to the total Jc depended little on the average particle size. Thus, contradiction was recognized to exist among different models for vortex pinning concerning the dependence of ‘‘apparent’’ peak effect on the particle size. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Peak effect; Particle size; SmBa 2 Cu 3 O 7y d
1. Introduction The critical current density Ž Jc . is crucially important in application of high-temperature superconductors and much effort has been made to increase their Jc values. The peak effect in the Jc vs. applied magnetic field Ž H . characteristics has been often
)
Corresponding author. Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan. Tel.: q81-45-924-5315; fax: q81-45-9245365. E-mail address: [email protected] ŽH. Yamauchi..
observed and paid attention for making the Jc value increase in the vicinity of the peak field. Many reports have been published on the peak effect in RE-123 ŽRE: Y, Sm and Nd. single crystals w1–17x and melt-grown bulks w18–26x. However, only a few works have been reported for the peak effect in polycrystallinerpowder samples w27,28x. Actually, the origin of the peak effect has not yet been elucidated, but various models have been proposed assuming certain crystalrlattice defects such as twin boundaries w7,12,15x, oxygen-deficient regions w1,11,20x, cation inter-substitution regions w8,13,16x, etc. Moreover, there has been a general belief that the strength of the peak effect depends on the average grainrparticle size. However, no work on the
0921-4534r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 0 0 . 0 0 2 1 2 - 4
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correlation between the peak effect and the particle size has been reported. In this work, we study the particle-size dependence of the peak effect in cation-stoichiometric SmBa 2 Cu 3 O 7y d ŽSm-123. powder samples. A fully oxygenated Sm-123 pellet that exhibits the peak effect is crushed and divided into three powder samples with different particle sizes. The Jc –H characteristics are compared for elucidating the correlation between peak effect and average particle size.
O 2 –Ar gas. Post-annealing was performed for the pellet samples at 3508C for 40 h in O 2 gas flow. In order to obtain samples consisting of grains with different average particle sizes, an elutriation technique was employed. The sintered pellet sample was crushed and the resultant powder was put into a beaker filled with dehydrated ethanol. After being stirred for few minutes, the powdered sample suspended in ethanol was left to stand for a certain time so that each powder grain might fall with the velocity n determined by Stokes’ equation:
2. Experimental
ns
The samples were synthesized by a liquid-phase sintering technique starting with powders of Sm 2 O 3 , BaCO 3 and CuO. The powders were mixed to the atomic ratios of Sm:Ba:Cus 1:9.1:9.9, referring to the phase diagram proposed for the Nd–Ba–Cu–O system w31x such that the liquid-phase sintered sample might be of the single-phase Sm-123. The powder mixture was prepared in an agate mortar with ethanol and then calcined at 9008C in air for 24 h. After regrinding, the powder was pressed into pellets that were sintered at 9508C for 40 h in flowing 0.1%
where d is the grain size, r the density of the solvent, rs the density of the grain, h the viscosity of the solvent, and g the gravitational constant. The powder that settled at the bottom of the beaker was removed and transferred to another beaker. The remaining solvent containing finer-sized particles was evaporated in a dry box to obtain a refined powder. The average particle size in this powder sample Žwhich was named Sample 3. as calculated by Eq. Ž1. was less than 10 mm. The coarse powder previously separated from the finer one was sieved twice.
gd 2 Ž rs y r . 18h
,
Fig. 1. XRD patterns for Sm-123 polycrystalline samples with different average particle sizes, d.
Ž 1.
Y. Takahama et al.r Physica C 338 (2000) 115–120
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The mesh sizes of the sieves were 150 and 32 mm, respectively. The two yielded powder samples were called Sample 1 and Sample 2 containing particles in the range of, respectively, 32–150 and 10–32 mm. In order to identify the compound phases contained, powder X-ray diffractometry ŽXRD. analysis was carried out. Samples 1, 2 and 3 were all characterized using a superconducting quantum interference device ŽSQUID. magnetometer in terms of superconducting properties and a scanning electron microscope ŽSEM. with respect to the particle size. In the present SQUID measurements, the powder sample was mixed with Y2 O 3 powder by six times in weight of the sample so that the inter-particle superconducting current might be totally avoided. To calculate Jc values, Bean’s model was employed: Jc s 30
D Mob d
,
Ž 2.
where D Mob indicates the magnetic hysteresis width at a magnetic field, H, at a fixed temperature as measured by SQUID and d indicates the average particle size measured by SEM.
3. Results and discussions XRD patterns for Samples 1, 2 and 3 are given in Fig. 1, showing that all the samples are essentially single-phase. The superconductivity transition temperatures ŽTc . for all the samples were the same, being at 94 K. Histograms of the particle size for the three samples are shown in Fig. 2. The average values of the particle size, d, were 49.8Ž"15.4. mm, 24.3Ž"10.8. mm and 7.5Ž"5.0. mm for Samples 1, 2 and 3, respectively. Thus, single-phase samples having the same Tc value but different particle sizesrdistributions were successfully obtained. The Jc –H curves measured at 60 and 77 K are given in Fig. 3Ža. and Žb.. It can be seen that each sample exhibits peak effect with a common peak field for each temperature: ; 3.2 and ; 1.2 T at 60 and 77 K, respectively. At both temperatures, a clear tendency is observed that the Jc Ž0. value is the higher for the finer-sized particle sample. This would mean that the degree of flexibility of vortex lines to meet
Fig. 2. Particle size distribution for Ža. Sample 1, Žb. Sample 2, and Žc. Sample 3.
the pinning sites is higher at near zero fields for the finer-sized particle sample, because the density of pinning sites is supposed to be the same in the three samples. Also note that the same tendency extends into the region of field up to ; 5 T at 60 K and ; 0.7 T at 77 K. This result is consistent with those of previous works w32,33x on the thickness dependence of the Jc –H curve. To take into account the difference in the degree of flexibility of vortex lines at near zero fields, the Jc Ž H . data were normalized by Jc Ž0. as shown in Fig. 4Ža. and Žb.. It is observed that as the average particle size becomes larger, the higher is the nor-
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Jc Ž Jcback . is assumed, based on the Kim–Anderson w29,30x model, to be given by: b Jcback Ž H . s q c. Ž 3. aqH To determine constants, a, b and c, the 0–2 T portion of the Jc –H curve was fitted by Eq. Ž3. under the condition that Jcback Ž Hirr . s 0 at the irreversibility field that had been determined by extrapolating the Jc –lnŽ H . curve to Jc s 0 w34x. The Hirr values determined were 12.1, 12.3 and 11.9 T at 60 K and 5.7, 5.0 and 4.7 T at 77 K for Samples 1, 2 and 3, respectively. Then: Jcpeak Ž H . s Jc Ž H . y Jcback Ž H . .
Ž 4.
The Jcpeak –H curves at 60 and 77 K calculated by Eq. Ž4. are shown in Fig. 5Ža. and Žb.. It is clearly
Fig. 3. The Jc – H characteristics at Ža. 60 K and Žb. 77 K for Samples 1–3 with different average particle sizes.
malized peak height at the both temperatures, though more clearly seen at 60 K. In this representation of the data, i.e. the Jc Ž H .rJc Ž0. –H curve, the peak effect looks more prominent as the grain size is larger. This may be explained by an enhancement of the degree of flexibility of the vortex lines to meet the pinning sites at the magnetic field where a transitional change would occur to affect the elastic property of the vortex lines w14x. At this transition, the vortex lines with the less degree of flexibility Žat low fields in the larger-sized particle sample. would acquire more flexibility to yield the results given in Fig. 4Ža. and Žb.. It is possible to extract the absolute ‘‘peak’’ contribution from the Jc Ž H . data, i.e. Jcpeak Ž H ., as in the following manner. First of all, the background
Fig. 4. Jc normalized by the Jc value at zero field vs. applied field H at Ža. 60 K and Žb. 77 K for Sm-123 polycrystalline samples with different particle sizes.
Y. Takahama et al.r Physica C 338 (2000) 115–120
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Fig. 5Ža. and Žb. may be explained by a model in which at least two different types of pinning sites exist: one works effectively at near zero fields and the other is weak at low magnetic fields but becomes effective for the transitioned vortex system at high magnetic fields. Thus, at the moment, no unique explanation can be presented for the appearance of peak effect only based on the presently obtained data. To make this situation clear, further experimental data are required for the region of the particle size less than the longitudinal correlation length, l 44 . 4. Conclusion
Fig. 5. The Jcpeak – H curves at Ža. 60 K and Žb. 77 K for Sm-123 polycrystalline samples with different particle sizes. w Jcpeak is defined in Eq. Ž4..x
The dependence of the peak effect on the particle size in SmBa 2 Cu 3 O 7y d single-phase powder samples was investigated. Single-phase powder samples with the same Tc value but different average particle sizes were successfully prepared. Each sample exhibited peak effect. In the Jc Ž H .rJc Ž0. –H plot, the peak was more prominent as the average particle size was larger. On the other hand, Jcpeak wthe absolute contribution to peak effect as defined by Eq. Ž4.x was little dependent on the particle size. Thus, different particle-size dependencies of the ‘‘apparent’’ peak effect were concluded for different vortex pinning models.
Acknowledgements Jcpeak
seen that the peak field where shows a maximum depends on temperature: the higher the temperature is, the lower is the peak field. That is, the peak field was at 3.2 and 1.2 T at 60 and 77 K, respectively. This clearly excludes models based on the vortex lattice matching. Quantity Jcpeak is nearly the same for the three samples at both temperatures Žthough that for Sample 3 at 60 K is rather larger than the other two.. This might mean that the critical current density is simply of an additive nature with respect to the contributions from pinning sites of different types, and also, that upon a transitional change in the vortex property, quantity Jcpeak originates from a contribution to vortex pinning which may be ‘‘weak’’, being different from those effective at near zero fields. Thus, the results given in
The authors acknowledge Dr. S. Lee for his helpful suggestions. We also wish to express our gratitude to Dr. Y. Ohba for her valuable suggestions on experiments and Prof. T. Yano for his help in SEM observations.
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w4x J.L. Vargas, D.C. Larbalestier, Appl. Phys. Lett. 60 Ž1992. 1741. w5x M. Ossena, P.A.J. de Groot, S.J. Porter, Phys. Rev. B 51 Ž1994. 1389. w6x P.D. Panetta, J.E. Ostenson, D.K. Finnemore, C.L. Snead Jr., Phys. Rev. B 52 Ž1995. 570. w7x A. Zhukov, H.K. Kupfer, H. Claus, H. Wuhl, G. ¨ ¨ M. Klaser, ¨ Muller-Vogt, Phys. Rev. B 52 Ž1995. 9871. ¨ w8x T. Egi, J.G. Wn, K. Kuroda, H. Unoki, N. Koshizuka, Appl. Phys. Lett. 67 Ž1995. 2406. w9x M. Nakamura, Y. Yamada, T. Hirayama, Y. Ikuhara, Y. Shiohara, S. Tanaka, Physica C 259 Ž1996. 303. w10x H. Asaoka, Y. Kazumata, H. Takei, K. Noda, Physica C 268 Ž1996. 14. w11x A. Erb, J.Y. Genoud, M. Dhalle, E. Walker, R. Flukiger, ¨ Physica C 282–287 Ž1997. 2145. w12x H. Kutami, Y. Yamada, S. Koyama, J.G. Wen, T. Egi, Z. Nakagawa, Y. Shiohara, Jpn. J. Appl. Phys. 36 Ž1997. 674. w13x K. Kuroda, K. Abe, S. Segawa, J.G. Wen, H. Unoki, N. Koshizuka, Physica C 275 Ž1997. 311. w14x T. Nishizaki, T. Naito, N. Kobayashi, Phys. Rev. B 58 Ž1998. 11169. w15x M. Jirsa, M.R. Koblishka, T. Higuchi, M. Murakami, Phys. Rev. B 58 Ž1998. 771. w16x A.K. Pradhan, B. Chen, W. Ting, K. Kuroda, K. Nakao, N. Koshizuka, Supercond. Sci. Technol. 11 Ž1998. 408. w17x H. Kupfer, Th. Wolf, A.A. Zhukov, R. Meier-Hirmer, Phys. ¨ Rev. B 60 Ž1999. 7631. w18x U. Ullrich, D. Muller, W. Mexener, M. Steins, K. Heine¨ mann, H.C. Freyhardt, Phys. Rev. B 48 Ž1993. 7513. w19x M. Murakami, S.I. Yoo, T. Higuchi, N. Sakai, J. Weltz, N. Koshizuka, S. Tanaka, Jpn. J. Appl. Phys. 33 Ž1994. L715. w20x F. Frangi, E. Varesi, G. Ripamonti, S. Zannella, Supercond. Sci. Technol. 7 Ž1994. 103.
w21x H.H. Wen, X.S. Rong, B. Yin, G.C. Che, Z.X. Zhao, Physica C 242 Ž1995. 365. w22x B. Martınez, X. Obradors, A. Gou, V. Gomis, S. Pinol, ´ ˜ J. Fontcuberta, Phys. Rev. B 53 Ž1995. 2797. w23x I. Monot, J. Wang, M.P. Delamare, J. Provost, G. Desgardin, Physica C 267 Ž1996. 173. w24x S. Ikeda, T. Oka, Y. Yamada, M. Yoshikawa, Y. Yanagi, Y. Itoh, U. Mizutani, Jpn. J. Appl. Phys. 36 Ž1997. L345. w25x A. Andreone, C. Aruta, M.L. Russo, G.W. Crabtree, Y. DeWilde, M. Iavarone, P.C. Canfield, Supercond. Sci. Technol. 11 Ž1998. 169. w26x F. Sandiumenge, B. Martinez, N. Vilalta, R. Yu, X. Obradors, Supercond. Sci. Technol. 11 Ž1998. 165. w27x J.G. Ossandon, J.R. Thompson, D.K. Christen, B.C. Sales, H.R. Kerchner, J.O. Thomson, Y.R. Sun, K.W. Lay, J.E. Tkaczyk, Phys. Rev. B 45 Ž1992. 534. w28x M. Kawano, H. Suematsu, T. Onda, M. Hayakawa, H. Ogiwara, M. Karppinen, H. Yamauchi, Appl. Supercond. 5 Ž1997. 119. w29x M. Kambara, X. Yao, E.A. Goodilin, Y. Shiohara, J. Am. Ceram. Soc. 81 Ž1998. 2116. w30x D.P. Norton, A. Goyal, D. Budai, D.K. Christen, D.M. Kroeger, E.D. Specht, Q. He, B. Saffian, M. Paranthaman, C.E. Klabunde, D.F. Lee, B.C. Sales, F.A. List, Science 274 Ž1996. 755. w31x T. Takagi, K. Hashimoto, K. Matsumoto, T. Machi, J.G. Wen, T. Morishita, N. Koshizuka, Adv. Supercond. 10 Ž1998. 635. w32x Y.B. Kim, C.F. Hempstead, A.R. Strnad, Phys. Rev. Lett. 9 Ž1963. 306. w33x P.W. Anderson, Phys. Rev. Lett. 9 Ž1962. 309. w34x H. Yamauchi, M. Karppinen, K. Fujinami, T. Ito, H. Suematsu, K. Matsuura, K. Isawa, Supercond. Sci. Technol. 11 Ž1998. 1006.
Dependence of peak effect on the particle size in superconducting SmBa 2 Cu 3 O 7yd powder samples Y. Takahama a,b, H. Suematsu a , T. Matsushita a,c , H. Yamauchi a,b,) a Materials and Structures Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan Department of InnoÕatiÕe and Engineered Materials, Interdisciplinary Graduate School, Tokyo Institute of Technology, Yokohama 226-8502, Japan Faculty of Computer Science and Systems Engineering, Kyusyu Institute of Technology, 680-4 Kawazu, Iizuka 820-8502, Japan b
c
Abstract The dependence of peak effect in the critical current density Ž Jc . vs. applied magnetic field Ž H . characteristics on the particle size in superconducting SmBa 2 Cu 3 O 7y d single-phase powder samples was investigated. The sintered pellets were crushed and the powder was sorted into three categories by means of elutriation and sieving. The samples of the three categories were characterized with respect to particle size and superconducting properties. The Jc values were calculated utilizing Bean’s model. As far as the normalized critical current density, Jc Ž H .rJc Ž0. vs. H curves were concerned, the ‘‘peak’’ was more prominent as the average particle size of the sample increased. On the other hand, quantity Jcpeak defined as the ‘‘peak’’ contribution to the total Jc depended little on the average particle size. Thus, contradiction was recognized to exist among different models for vortex pinning concerning the dependence of ‘‘apparent’’ peak effect on the particle size. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Peak effect; Particle size; SmBa 2 Cu 3 O 7y d
1. Introduction The critical current density Ž Jc . is crucially important in application of high-temperature superconductors and much effort has been made to increase their Jc values. The peak effect in the Jc vs. applied magnetic field Ž H . characteristics has been often
)
Corresponding author. Materials and Structures Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503, Japan. Tel.: q81-45-924-5315; fax: q81-45-9245365. E-mail address: [email protected] ŽH. Yamauchi..
observed and paid attention for making the Jc value increase in the vicinity of the peak field. Many reports have been published on the peak effect in RE-123 ŽRE: Y, Sm and Nd. single crystals w1–17x and melt-grown bulks w18–26x. However, only a few works have been reported for the peak effect in polycrystallinerpowder samples w27,28x. Actually, the origin of the peak effect has not yet been elucidated, but various models have been proposed assuming certain crystalrlattice defects such as twin boundaries w7,12,15x, oxygen-deficient regions w1,11,20x, cation inter-substitution regions w8,13,16x, etc. Moreover, there has been a general belief that the strength of the peak effect depends on the average grainrparticle size. However, no work on the
0921-4534r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 0 0 . 0 0 2 1 2 - 4
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correlation between the peak effect and the particle size has been reported. In this work, we study the particle-size dependence of the peak effect in cation-stoichiometric SmBa 2 Cu 3 O 7y d ŽSm-123. powder samples. A fully oxygenated Sm-123 pellet that exhibits the peak effect is crushed and divided into three powder samples with different particle sizes. The Jc –H characteristics are compared for elucidating the correlation between peak effect and average particle size.
O 2 –Ar gas. Post-annealing was performed for the pellet samples at 3508C for 40 h in O 2 gas flow. In order to obtain samples consisting of grains with different average particle sizes, an elutriation technique was employed. The sintered pellet sample was crushed and the resultant powder was put into a beaker filled with dehydrated ethanol. After being stirred for few minutes, the powdered sample suspended in ethanol was left to stand for a certain time so that each powder grain might fall with the velocity n determined by Stokes’ equation:
2. Experimental
ns
The samples were synthesized by a liquid-phase sintering technique starting with powders of Sm 2 O 3 , BaCO 3 and CuO. The powders were mixed to the atomic ratios of Sm:Ba:Cus 1:9.1:9.9, referring to the phase diagram proposed for the Nd–Ba–Cu–O system w31x such that the liquid-phase sintered sample might be of the single-phase Sm-123. The powder mixture was prepared in an agate mortar with ethanol and then calcined at 9008C in air for 24 h. After regrinding, the powder was pressed into pellets that were sintered at 9508C for 40 h in flowing 0.1%
where d is the grain size, r the density of the solvent, rs the density of the grain, h the viscosity of the solvent, and g the gravitational constant. The powder that settled at the bottom of the beaker was removed and transferred to another beaker. The remaining solvent containing finer-sized particles was evaporated in a dry box to obtain a refined powder. The average particle size in this powder sample Žwhich was named Sample 3. as calculated by Eq. Ž1. was less than 10 mm. The coarse powder previously separated from the finer one was sieved twice.
gd 2 Ž rs y r . 18h
,
Fig. 1. XRD patterns for Sm-123 polycrystalline samples with different average particle sizes, d.
Ž 1.
Y. Takahama et al.r Physica C 338 (2000) 115–120
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The mesh sizes of the sieves were 150 and 32 mm, respectively. The two yielded powder samples were called Sample 1 and Sample 2 containing particles in the range of, respectively, 32–150 and 10–32 mm. In order to identify the compound phases contained, powder X-ray diffractometry ŽXRD. analysis was carried out. Samples 1, 2 and 3 were all characterized using a superconducting quantum interference device ŽSQUID. magnetometer in terms of superconducting properties and a scanning electron microscope ŽSEM. with respect to the particle size. In the present SQUID measurements, the powder sample was mixed with Y2 O 3 powder by six times in weight of the sample so that the inter-particle superconducting current might be totally avoided. To calculate Jc values, Bean’s model was employed: Jc s 30
D Mob d
,
Ž 2.
where D Mob indicates the magnetic hysteresis width at a magnetic field, H, at a fixed temperature as measured by SQUID and d indicates the average particle size measured by SEM.
3. Results and discussions XRD patterns for Samples 1, 2 and 3 are given in Fig. 1, showing that all the samples are essentially single-phase. The superconductivity transition temperatures ŽTc . for all the samples were the same, being at 94 K. Histograms of the particle size for the three samples are shown in Fig. 2. The average values of the particle size, d, were 49.8Ž"15.4. mm, 24.3Ž"10.8. mm and 7.5Ž"5.0. mm for Samples 1, 2 and 3, respectively. Thus, single-phase samples having the same Tc value but different particle sizesrdistributions were successfully obtained. The Jc –H curves measured at 60 and 77 K are given in Fig. 3Ža. and Žb.. It can be seen that each sample exhibits peak effect with a common peak field for each temperature: ; 3.2 and ; 1.2 T at 60 and 77 K, respectively. At both temperatures, a clear tendency is observed that the Jc Ž0. value is the higher for the finer-sized particle sample. This would mean that the degree of flexibility of vortex lines to meet
Fig. 2. Particle size distribution for Ža. Sample 1, Žb. Sample 2, and Žc. Sample 3.
the pinning sites is higher at near zero fields for the finer-sized particle sample, because the density of pinning sites is supposed to be the same in the three samples. Also note that the same tendency extends into the region of field up to ; 5 T at 60 K and ; 0.7 T at 77 K. This result is consistent with those of previous works w32,33x on the thickness dependence of the Jc –H curve. To take into account the difference in the degree of flexibility of vortex lines at near zero fields, the Jc Ž H . data were normalized by Jc Ž0. as shown in Fig. 4Ža. and Žb.. It is observed that as the average particle size becomes larger, the higher is the nor-
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Jc Ž Jcback . is assumed, based on the Kim–Anderson w29,30x model, to be given by: b Jcback Ž H . s q c. Ž 3. aqH To determine constants, a, b and c, the 0–2 T portion of the Jc –H curve was fitted by Eq. Ž3. under the condition that Jcback Ž Hirr . s 0 at the irreversibility field that had been determined by extrapolating the Jc –lnŽ H . curve to Jc s 0 w34x. The Hirr values determined were 12.1, 12.3 and 11.9 T at 60 K and 5.7, 5.0 and 4.7 T at 77 K for Samples 1, 2 and 3, respectively. Then: Jcpeak Ž H . s Jc Ž H . y Jcback Ž H . .
Ž 4.
The Jcpeak –H curves at 60 and 77 K calculated by Eq. Ž4. are shown in Fig. 5Ža. and Žb.. It is clearly
Fig. 3. The Jc – H characteristics at Ža. 60 K and Žb. 77 K for Samples 1–3 with different average particle sizes.
malized peak height at the both temperatures, though more clearly seen at 60 K. In this representation of the data, i.e. the Jc Ž H .rJc Ž0. –H curve, the peak effect looks more prominent as the grain size is larger. This may be explained by an enhancement of the degree of flexibility of the vortex lines to meet the pinning sites at the magnetic field where a transitional change would occur to affect the elastic property of the vortex lines w14x. At this transition, the vortex lines with the less degree of flexibility Žat low fields in the larger-sized particle sample. would acquire more flexibility to yield the results given in Fig. 4Ža. and Žb.. It is possible to extract the absolute ‘‘peak’’ contribution from the Jc Ž H . data, i.e. Jcpeak Ž H ., as in the following manner. First of all, the background
Fig. 4. Jc normalized by the Jc value at zero field vs. applied field H at Ža. 60 K and Žb. 77 K for Sm-123 polycrystalline samples with different particle sizes.
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Fig. 5Ža. and Žb. may be explained by a model in which at least two different types of pinning sites exist: one works effectively at near zero fields and the other is weak at low magnetic fields but becomes effective for the transitioned vortex system at high magnetic fields. Thus, at the moment, no unique explanation can be presented for the appearance of peak effect only based on the presently obtained data. To make this situation clear, further experimental data are required for the region of the particle size less than the longitudinal correlation length, l 44 . 4. Conclusion
Fig. 5. The Jcpeak – H curves at Ža. 60 K and Žb. 77 K for Sm-123 polycrystalline samples with different particle sizes. w Jcpeak is defined in Eq. Ž4..x
The dependence of the peak effect on the particle size in SmBa 2 Cu 3 O 7y d single-phase powder samples was investigated. Single-phase powder samples with the same Tc value but different average particle sizes were successfully prepared. Each sample exhibited peak effect. In the Jc Ž H .rJc Ž0. –H plot, the peak was more prominent as the average particle size was larger. On the other hand, Jcpeak wthe absolute contribution to peak effect as defined by Eq. Ž4.x was little dependent on the particle size. Thus, different particle-size dependencies of the ‘‘apparent’’ peak effect were concluded for different vortex pinning models.
Acknowledgements Jcpeak
seen that the peak field where shows a maximum depends on temperature: the higher the temperature is, the lower is the peak field. That is, the peak field was at 3.2 and 1.2 T at 60 and 77 K, respectively. This clearly excludes models based on the vortex lattice matching. Quantity Jcpeak is nearly the same for the three samples at both temperatures Žthough that for Sample 3 at 60 K is rather larger than the other two.. This might mean that the critical current density is simply of an additive nature with respect to the contributions from pinning sites of different types, and also, that upon a transitional change in the vortex property, quantity Jcpeak originates from a contribution to vortex pinning which may be ‘‘weak’’, being different from those effective at near zero fields. Thus, the results given in
The authors acknowledge Dr. S. Lee for his helpful suggestions. We also wish to express our gratitude to Dr. Y. Ohba for her valuable suggestions on experiments and Prof. T. Yano for his help in SEM observations.
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