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Y211 composites
Physica C 470 (2010) S1009–S1010
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Influence of the Y211 phase on anisotropic transport properties and vortex dynamics of the melt-textured Y123/Y211 composites J. Mucha a,*, K. Rogacki a, H. Misiorek a, A. Jezowski a, A. Wisniewski b, R. Puzniak b a b
Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Wroclaw, Poland Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, PL-02-668 Warsaw, Poland
a r t i c l e
i n f o
Article history: Accepted 26 January 2010 Available online 4 February 2010 Keywords: Thermal conductivity YBaCuO Magnetothermal resistivity Anisotropy
a b s t r a c t Thermal conductivity, jðTÞ, electrical resistivity, qðTÞ, and magnetization, MðHÞ, of the melt-textured Y123/Y211 (YBa2Cu3O7d/Y2BaCuO5) composites have been studied in the ab plane and along the c axis in normal and superconducting states. Detailed measurements of these quantities have been performed in the temperature range between 4 and 300 K and at fields from 0 to 9 T, for samples with about 0, 20, 33, and 47 wt.% of the Y211 phase. By fitting the experimental jðTÞ curves at low temperature with the Debye model we have determined the mean free path of phonons to be 12 and 0.3 lm, for the samples with lower (20% and 33%) and higher (47%) content of the Y211 phase, respectively. For composites with larger amount of the Y211 phase, the total thermal conductivity decreases substantially, whereas the irreversibility line changes only marginally. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The thermal conductivity, j, both in the normal and superconducting state, is an important parameter which characterizes the interaction between phonons and charge carriers [1–3]. For materials being examined for prospective high-current applications, the thermal conductivity is a fundamental quantity for an estimation of the heat transport and the cooling power required for the stabilization of the superconducting phase. In the present communication, we report on the results of the investigation of the thermal conductivity and vortex states of single-grain melt-textured Y123/Y211 (YBa2Cu3O7d/Y2BaCuO5) composites with several contents of the Y211 phase. The presence of randomly distributed Y211 grains in a Y123 matrix results in various defects which decrease j, however increases the flux pinning force [4]. Thus, such composites exhibit high critical currents and are very interesting for power applications. 2. Experimental details Materials with the 20, 33 and 47 wt.% of the Y211 phase were prepared by the Bridgman growth technique as described in Ref. [5]. The samples of approximate dimensions of 1 1 4 mm3 were cut from the bars to obtain the ab plane parallel or perpendicular to the largest sample dimension. The samples were called: S1/ 20ab, S2/20c, S3/33ab, S4/33c, S5/47ab, and S10/20ab30°. For * Corresponding author. E-mail address: [email protected] (J. Mucha). 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.01.063
example, S1/20ab describes the sample with 20% of the Y211 phase in the Y123 matrix and with the length oriented parallel to the ab plane. S10/20ab30° means that the sample length forms a 30° angle with the ab plane. The thermal conductivity was measured using the stationary heat flux method in the temperature range 5–300 K as it was described in Ref. [6]. The irreversibility field ðHirr Þ has been determined in magnetic fields up to 9 T and in the geometry Hjjab plane (samples S1/20ab and S3/33ab) and Hjjc axis (samples S2/20c and S4/33c). All these samples show similar transition temperature to the superconducting state equal to 91 K, as obtained from the onset of a diamagnetic response. 3. Results and discussion We analyze the low-temperature behavior (below T c ¼ 91 K) of the heat transport considering the total thermal conductivity (tot) as the sum of the contributions from phonons (ph) and conduction electrons (e), i.e. jtot ¼ jph þ je [7]. Fig. 1 shows the temperature dependence of jtot in the direction parallel to the ab plane for the samples S3/33ab and S5/47ab, and at the angle of 30° to the ab plane for the sample S10/20ab30°. The temperature dependence of the electronic thermal conductivity je ðTÞ was estimated assuming the validity of the Wiedemann–Franz law: je ðTÞ ¼ L0 T=qðTÞ, where L0 denotes the Lorenz number ðL0 ¼ 2:44 108 W X K2 Þ and qðTÞ is the electrical resistivity. The resulting je ðTÞ values are about 30% of the jtot at 300 K and about 10% at T c for all samples. In the superconducting state, quasiparticles partially condense into Cooper pairs and thus je additionally decreases. Therefore, we assume that below T c the phonon component is
S1010
J. Mucha et al. / Physica C 470 (2010) S1009–S1010
80
5
Irreversibility Field (kOe)
Thermal conductivity (W/Km)
6
4 3 o
S10/20ab30 S3/33ab S5/47ab Debye model
2 1
60 20%
S1/20ab S2/20c S3/33ab S4/33c S4/33c 33%
40
33% 20%
20
0
0 0
50
100
150 200 250 Temperature (K)
300
68
350
Fig. 1. Total thermal conductivity along the ab plane and at the angle of 30° to the ab plane versus temperature for Y123/Y211 composites.
strongly dominant. According to the Debye model, jph is the function of the inverse relaxation time:
jph ¼ GT 3
Z 0
H=T
x
4
s1 sinh2 ðx=2Þ
dx
ð1Þ
where x ¼ hx=kB T (where hx is the phonon energy), H is Debye temperature, G is constant, s1 is the sum of inverse relaxation P 1 times for various phonon scattering processes: s1 ¼ si , where si ¼ sb ; se ; sd ; sN ; sU denote the relaxation times for phonon scattering on grain boundaries, on conduction electrons, on defects, and for N (normal) and U (umklapp) processes of phonon scattering, respectively. Simple dependences of the relaxation times on x 1 1 4 1 and T are assumed, namely, s1 b ¼ B; se ¼ xE; sd ¼ Dx ; sph ¼ 3 1 2 PðxTÞ and sU ¼ U x Texp½a=T, where B, E, D, P, U and a are constants [8]. In Fig. 1 we illustrate how Eq. (1) fits our experimental data (dashed curves). The agreement of the Debye model with the data is excellent in the temperature range 5–100 K. The mean free paths of the phonons scattered by grain boundaries ðKb Þ were determined from sb and mph ðKb ¼ sb mph Þ to be equal to 12 lm for the sample S10/20ab30° and S3/33ab and to 0.3 lm for the sample S5/47ab. Below 60 K the plot jph ðTÞ for the sample S10/20ab30° resembles that for S3/33ab and therefore the fitting parameters for these samples are the same. At higher temperatures the influence of the phase Y211 on jph ðTÞ becomes notable and the thermal conductivity for S10/20ab30° is lower than the corresponding value for S3/33ab. Since the sample S10/20ab30° was cut at 30° angle to the ab plane, the influence of the thermal conductivity anisotropy may manifest itself in this temperature region. At 200 K the magnitude of the anisotropy can be expressed by the ratio:jðabÞ= jðab30 Þ ¼ 1:12. The influence of the Y211 phase on the thermal conductivity of Y123 is noticeable for the sample S5/47ab (Fig. 1). At T ’ 60 K the thermal conductivity of this sample is twice smaller than that of S10/20ab30° and S3/30ab. The irreversibility field data are shown in Fig. 2. We found that for all samples, Hirr ðTÞ is well described by a power-law dependence according to ð1 T=T c Þn with n very close to 3/2. This n value is typical for high-T c superconductors with moderate anisotropy [9]. Essentially identical position of the irreversibility line for the samples with different amount of the Y211 phase indicates that the introduced pinning centers, which increase the critical current density considerably, are very similar. A
72
76 80 84 Temperature (K)
88
92
Fig. 2. Irreversibility line of the Y123/Y211 composites with 20% (S1/20ab and S2/ 20c) and 33% (S3/33ab and S4/33c) of the Y211 phase for Hjjab plane (full symbols) and Hjjc axis (open symbols). Stars show the characteristic temperature obtained for the in field thermal conductivity measurements.
small difference in the position of the irreversibility line for samples S1/20ab and S3/33ab may be caused by a possible difference in texture. For the sample S4/33c, jtot ðTÞ has been studied in magnetic fields as well. The data show a systematic decrease of jtot with increasing field, particularly in the superconducting state. A notable change of the slope of jtot ðTÞ has been observed well below T c . The characteristic temperature where the change occurs decreases with increasing field and reminds the behavior of Hirr ðTÞ, as shown in Fig. 2. This suggests that the thermal conductivity can be influenced by the vortex state and thus by vortex dynamics. 4. Conclusions We summarize with the conclusion that phonons are dominant thermal energy carriers in the Y123/Y211 composites. The mean free paths of phonons Kb in the samples S10/20ab30° and S3/ 33ab are the same and equal to 12 lm in the low temperature range ðT < T c Þ. For all the samples we have studied, the experimental results can be well described in the frame of the Debye model. Acknowledgements We are very indebted to Dr. T. Puig and Dr. X. Obradors from the Institut de Ciencia de Materials de Barcelona, CSIC, for providing the Y123/Y211 samples. This work was partially supported by the Polish National Scientific Network ‘‘Materials with Strong Correlated Electrons” and by the Polish Ministry of Science and Higher Education within the research project for the years 2007–2009 (Grant No. N N202 4132 33). References [1] [2] [3] [4] [5] [6] [7] [8] [9]
A. Jezowski et al., Physica B 284–288 (2000) 1015. N. Wendling et al., Physica C 235 (1994) 1517. M. Ikebe et al., Cryogenics 34 (1994) 57. B. Martinez et al., Phys. Rev. B 58 (1998) 15198. F. Sandiumenge et al., Supercond. Sci. Technol. 10 (1997) A93. J. Mucha et al., Cryogenics 44 (2000) 145. R. Berman, Thermal Conduction in Solids, Clarendon, Oxford, 1976. J. Callaway, Phys. Rev. 113 (1959) 1046. A. Schilling et al., Phys. Rev. B 46 (1992) 14253.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Influence of the Y211 phase on anisotropic transport properties and vortex dynamics of the melt-textured Y123/Y211 composites J. Mucha a,*, K. Rogacki a, H. Misiorek a, A. Jezowski a, A. Wisniewski b, R. Puzniak b a b
Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Wroclaw, Poland Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, PL-02-668 Warsaw, Poland
a r t i c l e
i n f o
Article history: Accepted 26 January 2010 Available online 4 February 2010 Keywords: Thermal conductivity YBaCuO Magnetothermal resistivity Anisotropy
a b s t r a c t Thermal conductivity, jðTÞ, electrical resistivity, qðTÞ, and magnetization, MðHÞ, of the melt-textured Y123/Y211 (YBa2Cu3O7d/Y2BaCuO5) composites have been studied in the ab plane and along the c axis in normal and superconducting states. Detailed measurements of these quantities have been performed in the temperature range between 4 and 300 K and at fields from 0 to 9 T, for samples with about 0, 20, 33, and 47 wt.% of the Y211 phase. By fitting the experimental jðTÞ curves at low temperature with the Debye model we have determined the mean free path of phonons to be 12 and 0.3 lm, for the samples with lower (20% and 33%) and higher (47%) content of the Y211 phase, respectively. For composites with larger amount of the Y211 phase, the total thermal conductivity decreases substantially, whereas the irreversibility line changes only marginally. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The thermal conductivity, j, both in the normal and superconducting state, is an important parameter which characterizes the interaction between phonons and charge carriers [1–3]. For materials being examined for prospective high-current applications, the thermal conductivity is a fundamental quantity for an estimation of the heat transport and the cooling power required for the stabilization of the superconducting phase. In the present communication, we report on the results of the investigation of the thermal conductivity and vortex states of single-grain melt-textured Y123/Y211 (YBa2Cu3O7d/Y2BaCuO5) composites with several contents of the Y211 phase. The presence of randomly distributed Y211 grains in a Y123 matrix results in various defects which decrease j, however increases the flux pinning force [4]. Thus, such composites exhibit high critical currents and are very interesting for power applications. 2. Experimental details Materials with the 20, 33 and 47 wt.% of the Y211 phase were prepared by the Bridgman growth technique as described in Ref. [5]. The samples of approximate dimensions of 1 1 4 mm3 were cut from the bars to obtain the ab plane parallel or perpendicular to the largest sample dimension. The samples were called: S1/ 20ab, S2/20c, S3/33ab, S4/33c, S5/47ab, and S10/20ab30°. For * Corresponding author. E-mail address: [email protected] (J. Mucha). 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.01.063
example, S1/20ab describes the sample with 20% of the Y211 phase in the Y123 matrix and with the length oriented parallel to the ab plane. S10/20ab30° means that the sample length forms a 30° angle with the ab plane. The thermal conductivity was measured using the stationary heat flux method in the temperature range 5–300 K as it was described in Ref. [6]. The irreversibility field ðHirr Þ has been determined in magnetic fields up to 9 T and in the geometry Hjjab plane (samples S1/20ab and S3/33ab) and Hjjc axis (samples S2/20c and S4/33c). All these samples show similar transition temperature to the superconducting state equal to 91 K, as obtained from the onset of a diamagnetic response. 3. Results and discussion We analyze the low-temperature behavior (below T c ¼ 91 K) of the heat transport considering the total thermal conductivity (tot) as the sum of the contributions from phonons (ph) and conduction electrons (e), i.e. jtot ¼ jph þ je [7]. Fig. 1 shows the temperature dependence of jtot in the direction parallel to the ab plane for the samples S3/33ab and S5/47ab, and at the angle of 30° to the ab plane for the sample S10/20ab30°. The temperature dependence of the electronic thermal conductivity je ðTÞ was estimated assuming the validity of the Wiedemann–Franz law: je ðTÞ ¼ L0 T=qðTÞ, where L0 denotes the Lorenz number ðL0 ¼ 2:44 108 W X K2 Þ and qðTÞ is the electrical resistivity. The resulting je ðTÞ values are about 30% of the jtot at 300 K and about 10% at T c for all samples. In the superconducting state, quasiparticles partially condense into Cooper pairs and thus je additionally decreases. Therefore, we assume that below T c the phonon component is
S1010
J. Mucha et al. / Physica C 470 (2010) S1009–S1010
80
5
Irreversibility Field (kOe)
Thermal conductivity (W/Km)
6
4 3 o
S10/20ab30 S3/33ab S5/47ab Debye model
2 1
60 20%
S1/20ab S2/20c S3/33ab S4/33c S4/33c 33%
40
33% 20%
20
0
0 0
50
100
150 200 250 Temperature (K)
300
68
350
Fig. 1. Total thermal conductivity along the ab plane and at the angle of 30° to the ab plane versus temperature for Y123/Y211 composites.
strongly dominant. According to the Debye model, jph is the function of the inverse relaxation time:
jph ¼ GT 3
Z 0
H=T
x
4
s1 sinh2 ðx=2Þ
dx
ð1Þ
where x ¼ hx=kB T (where hx is the phonon energy), H is Debye temperature, G is constant, s1 is the sum of inverse relaxation P 1 times for various phonon scattering processes: s1 ¼ si , where si ¼ sb ; se ; sd ; sN ; sU denote the relaxation times for phonon scattering on grain boundaries, on conduction electrons, on defects, and for N (normal) and U (umklapp) processes of phonon scattering, respectively. Simple dependences of the relaxation times on x 1 1 4 1 and T are assumed, namely, s1 b ¼ B; se ¼ xE; sd ¼ Dx ; sph ¼ 3 1 2 PðxTÞ and sU ¼ U x Texp½a=T, where B, E, D, P, U and a are constants [8]. In Fig. 1 we illustrate how Eq. (1) fits our experimental data (dashed curves). The agreement of the Debye model with the data is excellent in the temperature range 5–100 K. The mean free paths of the phonons scattered by grain boundaries ðKb Þ were determined from sb and mph ðKb ¼ sb mph Þ to be equal to 12 lm for the sample S10/20ab30° and S3/33ab and to 0.3 lm for the sample S5/47ab. Below 60 K the plot jph ðTÞ for the sample S10/20ab30° resembles that for S3/33ab and therefore the fitting parameters for these samples are the same. At higher temperatures the influence of the phase Y211 on jph ðTÞ becomes notable and the thermal conductivity for S10/20ab30° is lower than the corresponding value for S3/33ab. Since the sample S10/20ab30° was cut at 30° angle to the ab plane, the influence of the thermal conductivity anisotropy may manifest itself in this temperature region. At 200 K the magnitude of the anisotropy can be expressed by the ratio:jðabÞ= jðab30 Þ ¼ 1:12. The influence of the Y211 phase on the thermal conductivity of Y123 is noticeable for the sample S5/47ab (Fig. 1). At T ’ 60 K the thermal conductivity of this sample is twice smaller than that of S10/20ab30° and S3/30ab. The irreversibility field data are shown in Fig. 2. We found that for all samples, Hirr ðTÞ is well described by a power-law dependence according to ð1 T=T c Þn with n very close to 3/2. This n value is typical for high-T c superconductors with moderate anisotropy [9]. Essentially identical position of the irreversibility line for the samples with different amount of the Y211 phase indicates that the introduced pinning centers, which increase the critical current density considerably, are very similar. A
72
76 80 84 Temperature (K)
88
92
Fig. 2. Irreversibility line of the Y123/Y211 composites with 20% (S1/20ab and S2/ 20c) and 33% (S3/33ab and S4/33c) of the Y211 phase for Hjjab plane (full symbols) and Hjjc axis (open symbols). Stars show the characteristic temperature obtained for the in field thermal conductivity measurements.
small difference in the position of the irreversibility line for samples S1/20ab and S3/33ab may be caused by a possible difference in texture. For the sample S4/33c, jtot ðTÞ has been studied in magnetic fields as well. The data show a systematic decrease of jtot with increasing field, particularly in the superconducting state. A notable change of the slope of jtot ðTÞ has been observed well below T c . The characteristic temperature where the change occurs decreases with increasing field and reminds the behavior of Hirr ðTÞ, as shown in Fig. 2. This suggests that the thermal conductivity can be influenced by the vortex state and thus by vortex dynamics. 4. Conclusions We summarize with the conclusion that phonons are dominant thermal energy carriers in the Y123/Y211 composites. The mean free paths of phonons Kb in the samples S10/20ab30° and S3/ 33ab are the same and equal to 12 lm in the low temperature range ðT < T c Þ. For all the samples we have studied, the experimental results can be well described in the frame of the Debye model. Acknowledgements We are very indebted to Dr. T. Puig and Dr. X. Obradors from the Institut de Ciencia de Materials de Barcelona, CSIC, for providing the Y123/Y211 samples. This work was partially supported by the Polish National Scientific Network ‘‘Materials with Strong Correlated Electrons” and by the Polish Ministry of Science and Higher Education within the research project for the years 2007–2009 (Grant No. N N202 4132 33). References [1] [2] [3] [4] [5] [6] [7] [8] [9]
A. Jezowski et al., Physica B 284–288 (2000) 1015. N. Wendling et al., Physica C 235 (1994) 1517. M. Ikebe et al., Cryogenics 34 (1994) 57. B. Martinez et al., Phys. Rev. B 58 (1998) 15198. F. Sandiumenge et al., Supercond. Sci. Technol. 10 (1997) A93. J. Mucha et al., Cryogenics 44 (2000) 145. R. Berman, Thermal Conduction in Solids, Clarendon, Oxford, 1976. J. Callaway, Phys. Rev. 113 (1959) 1046. A. Schilling et al., Phys. Rev. B 46 (1992) 14253.