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Comparative AC susceptibility analysis on Bi–(Pb)–Sr–Ca–Cu–O high-Tc superconductors
Physica C 316 Ž1999. 251–256
Comparative AC susceptibility analysis on Bi– žPb / –Sr–Ca–Cu–O high-Tc superconductors Selahattin C¸ elebi
)
Department of Physics, Faculty of Science and Arts, Karadeniz Technical UniÕersity, 61080 Trabzon, Turkey Received 8 March 1999; accepted 8 April 1999
Abstract We discuss the comparative AC susceptibility analysis on rectangular bar shaped high-temperature Bi– ŽPb. –Sr–Ca–Cu–O superconductors prepared by the liquid ammonium nitrate method and the solid state reaction method. Five samples used in this study were obtained from different starting compositions. The analysis for comparison is based on Ži. how much rapidly the relative peak temperature ŽTc y Tp . in x Y ŽT . increases with increasing fields; Žii. the suppression degree of the diamagnetic behavior with respect to fields; Žiii. the sharpness of the transition of x X ŽT . for intergranular component for the same field amplitude; Živ. the steepness of the data of x Y ŽT s 55 K. vs. the field amplitude. We also qualitatively discuss experimental results in the framework of the critical state model, estimate the effective volume fraction of the grains and determine the temperature dependence of the critical current density by means of the best fit of the calculated data for the experimental matrix susceptibility. q 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 7460Ge; 7472Fq Keywords: Bi– ŽPb. –Sr–Ca–Cu–O high-Tc superconductors; AC susceptibility; Critical current density
1. Introduction AC susceptibility measurements x s x X q i x Y are very useful for characterizing the high-temperature superconductors ŽHTS. w1–10x. The sharp decrease in the real part x X ŽT . below the critical temperature Tc is a manifestation of diamagnetic shielding and the peak in the imaginary part x Y ŽT . represents the AC losses. The shapes of x X ŽT . and x Y ŽT . are
)
Tel.: q90-462-325-8244; Fax: q90-462-325-3195; E-mail: [email protected]
strongly influenced by Ži. the classes of compounds, Žii. the fabrication process, Žiii. the thermal treatments, Živ. the morphologies of the samples: bulk, thin films, wires, tapes, single crystals, and Žv. the measuring conditions Žthe presence and orientations of DC field along with AC field amplitudes. w6x. The discovery of HTS offered a great promise of future applications. However, soon was released that there was an undesirable limitation on the transport critical current density, jc , of the HTS. One of the reasons for this low jc is the granular nature of sintered HTS. Such a low jc corresponds to small full penetration field H U , in a magnetized sample.
0921-4534r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 2 8 4 - 1
252
S. C¸ elebi r Physica C 316 (1999) 251–256
Hence, low field AC susceptibility measurements are very important both for the characterization of the samples and the promotion or modification of the critical state models. In this article, we present comparative analysis of AC susceptibility measurements on five different Bi– ŽPb. –Sr–Ca–Cu–O superconducting samples in terms of intergranular critical current density, the volume fraction of the grains and transition temperature.
2. Experimental details Samples A and B were fabricated by the liquid ammonium nitrate technique with the stoichiometric composition Bi 1.84 Pb 0.34 Sr1.91Ca 2.03 Cu 3.06 O10 and Bi 1.4 Pb 0.6 Sr2 Ca 2 Cu 3 O12 , respectively, using the nearly same route. The details of fabrication and characterization w11x and the frequency dependent AC susceptibility study w9x of sample A and the AC losses analysis w10x of sample B can be found elsewhere. The dimensions of samples A and B for the AC susceptibility measurements are 1.25 = 3 = 13 mm3 and 1.85 = 2.55 = 13.05 mm3 , respectively. Samples C, D and E were prepared with the nominal composition Bi 1.6 Pb 0.4 Sr2 Ca 3 Cu 4yx Ag xO 12 Žwhere x s 0, 0.1 and 0.4, respectively. using the conventional solid-state reaction technique. The details of the fabrication process and magnetic behaviour are given in the previous communication w12x. The dimensions of the samples for the AC susceptibility measurements do not change with the sample and are 2 = 2.5 = 12 mm3. The AC susceptibility measurements were done with a 7130 AC Susceptometer of Lake Shore with a closed cycle refrigerator. The details of the measuring system of the AC susceptibility were described in a previous work w10x.
3. Results and discussion Since the demagnetizing correction would cause x X s y1 for low enough temperature, we normalized
Y X Fig. 1. Plot of imaginary Ž x . vs. real Ž x . components of AC susceptibility nature at f s1 kHz and Hac s80 Arm Žrms. for all samples.
experimental AC susceptibility data x Y ŽT . and x X ŽT . to the < x X < at the lowest temperature and the lowest field amplitude for each sample. It is useful to plot the x Y Ž x X . graph in order to grasp the characteristics of critical currents. Fig. 1 shows the x Y Ž x X . data for all the samples measured at Hac s 80 Arm Žrms. and f s 1 kHz. There are two contributions to the experimental AC susceptibility data. The principle of the separation of the contribution from grains and the coupling matrix has been described by Clem w13x and many workers w1,2x have extensively used it. The experimental matrix susceptibilities xmY and xmX can be extracted from the measured susceptibilities x Y and x X employing the following equations w2x:
x Y s Ž 1 y fg . xmY .
Ž 1.
x X s yfg q Ž 1 y fg . xmX .
Ž 2.
We need to know the values of fg for each sample in order to determine the matrix susceptibilities xmY and
Y Fig. 2. Extracted matrix susceptibility xm vs. temperature at Hac s 80 Arm Žrms. and f s 1 kHz for all samples. Solid line is for theoretical calculations.
S. C¸ elebi r Physica C 316 (1999) 251–256
253
S. C¸ elebi r Physica C 316 (1999) 251–256
254
xmX from Eqs. Ž1. and Ž2.. The volume fraction of the grains fg in the samples can be estimated from Figs. 1 and 2. We believe that the onset value Žindicated by an arrow in Fig. 1. of x Y Ž x X . is roughly shows the value of fg for each sample. Chen et al. w7x used the critical state model of Kim et al. w14x to calculate AC susceptibility and determine the volume fraction of the grains for BiPbSrCaCuO superconductors. Their calculated value for fg seems to be consistent with the estimated value from the high temperature portion of the x X ŽT . curves. Hence, we used the fg value determined by the above procedure for the calculation of the matrix susceptibility. Sample A ŽB. has the highest Žlowest. value of fg Žsee Table 1.. Y We have calculated xm,max and xmX ŽTp . and tabulated in Table 1 for all the samples, where f s 1 kHz, Hac s 80 Arm. For the samples of cylinder shape, according to the Bean model w15x, the theoretY ical value of xmax is equal to 0.212 and the corresponding value of x X is y0.333. The extracted Y values of xm,max and xmX ŽTp . for all samples differ slightly from the theoretical values for the Bean-cylinder case Žsee Table 1.. Consequently, we concluded that all these samples can be treated in the framework of the Bean model. When the flux lines fully penetrate the material, i.e., when Hm Ž Hm corresponds to '2 Hac Žrms.. is equal to the first full penetration field H U , the losses reach a maximum w13x. Consequently, one can estimate the temperature dependence of the critical current density using the Bean model. According to the Bean model, the critical current density at the peak temperature Tp ,
Table 1 List of the samples and some superconducting parameters Samples
A
B
C
D
E
Y xma x x X ŽTp .
0.140 y0.56 0.29 0.20 y0.38 107.5 104 85.6
0.242 y0.43 0.07 0.26 y0.39 108 103 96.5
0.217 y0.45 0.14 0.25 y0.36 108 104 93
0.197 y0.47 0.15 0.23 y0.38 108 104 91
0.168 y0.46 0.14 0.20 y0.37 108 104 82.5
3.57
1.61
2.10
2.22
2.38
fg Y xm,max xmX ŽTp . Tc Tcm Tp Žfor 20 Arm. p
and the imaginary part of the AC susceptibility for cylindrical geometry w16x can be written as jcm Ž Tp . s H U rR f H U r'ab , Hm
2
Hm
xYs
ž / ž /
xYs
ž / ž /
4
4
H
y2
U
HU
y2
Hm
H
U
3p 2
HU Hm
1
1 3p
Ž 3. ,
for H U G Hm ,
,
for H U F Hm
Ž 4. where the cross-section of the rectangular bar shaped sample is 2 a = 2 b. In the calculations for the best fit of the theoretical and experimental temperature dependent matrix susceptibility xmY , two different possible temperature dependences for the matrix Žintergranular. critical current density jcm ŽT . have been exploited, namely,
ž
jcm Ž T . s jcm 0 1 y
T Tcm
p
/
, jcm 0 1 y
T
ž / Tcm
2
. Ž 5.
Y value can range from Kim’s theoretical xm,max 0.21 to 0.4 w2x. The Bean model w15x predicts the Y xm,max value to be 0.212 for infinite cylinder and 0.238 for infinite slab geometry w16x. The values of Y observed in all samples are close to that for xm,max the Bean model. Therefore, we have used the Bean model for xmY vs. Hm and determined the temperature dependence of intergranular critical current density hence pinning strength parameter. The best fit of the calculated data Žsolid line. in Fig. 2a–e for experimental matrix susceptibility yields the exponent p and the matrix critical temperature Tcm in Eq. Ž5. which are tabulated in Table 1. For completeness, we presented xmX ŽTp . values for each sample in Table 1. Chen et al. w2x calculated xmX ŽTp . for the samples with a rectangular cross-section of 2 a = 2 b and an infinite length. For bra s 2 and 1, the values of xmX ŽTp . varies from y0.34 to y0.29 and from y0.31 to y0.27, respectively. The values of xmX ŽTp . for all the samples are very close to the lowest limit of y0.34. The values of Tp Žfor 80 Arm. in Table 1 shows the peak temperature used for calculation. Fig. 3 shows the imaginary part of the experimenY as a function of tal AC susceptibility at 55 K x 55
S. C¸ elebi r Physica C 316 (1999) 251–256
Fig. 3. Imaginary part of the experimental AC susceptibility at 55 Y K x 55 as a function of field amplitude Žrms. for all samples, where f s1 kHz.
field amplitude for all samples, where f s 1 kHz. It is well known that for an infinite slab when the field amplitude Hm is less than the full penetration field H U , the imaginary part Žfundamental. of the AC susceptibility is given by
xYs
2 Hm 3p H U
.
Ž 6.
Y In the plot of x 55 as a function of field amplitude Žrms., the slope of the straight line is inversely proportional to the full penetration field, hence, the critical current density Ž H U s jcm R .. Therefore, the shallower the straight line, the larger the critical current density. According to this criteria, sample B has the largest and sample E has the lowest critical current density. As a measure of the diamagnetic suppression, hence, the magnitude of the critical current density, we show the real part of the AC X susceptibility x 55 at 55 K and 1 kHz as a function of the applied field amplitude Žrms. in Fig. 4. The above conclusion can be also drawn from Fig. 4. Fig. 5 displays the curves of x X vs. T showing two step process which reflects the shielding of flux from and between the grains, as T decreases. When the samples are just below Tc , the superconducting grains first shield the applied magnetic field. This is measured as a negative x X . At low enough temperature, intergranular component of x X appears. At
255
X Fig. 4. Real Ž x . parts of AC susceptibility as a function of the field amplitude Žrms. measured in all samples at f s1 kHz and T s 55 K.
extremely low temperatures, the whole volume of the sample expected to be shielded by the supercurrent circulating in the sample and, hence, the curve of x X vs. T saturates. The transition of x X for the intergranular component for sample B is sharper than that of the other samples confirming our conclusions above. The diamagnetic onset temperatures of the superconducting transition are listed in Table 1 as
Fig. 5. Plot of x Arm.
X
vs. temperature at f s1 kHz and Hac s80
256
S. C¸ elebi r Physica C 316 (1999) 251–256
lar critical current density. The small deviation between experimental and calculated data can be attributed to the multiple phase of BiPbSrCaCuO superconducting systems as well as the fact that we have used crude but simple approximation. In the comparative analysis, we determine the quality of the samples by various methods. Sample B Žfabricated by the liquid ammonium nitrate technique with the stoichiometric composition Bi 1.4 Pb 0.6 Sr2 Ca 2 Cu 3 O 12 . has the highest intergranular critical current among the samples studied for comparative analysis.
Acknowledgements
Fig. 6. Plot of ŽTc yTp .r Tc vs. field amplitude Žrms. at f s1 kHz.
108 K for the samples B, C, D, and E and 107.5 K for sample A. We display ŽTc y Tp .rTc vs. field amplitude in Fig. 6, in order to make possible comparison with various experimental data. As the field amplitude increases, the peak of x Y ŽT . shifts to lower temperatures. The amount of the shift as a function of the field amplitude is proportional to the magnitude or strength of the pinning force. The larger the shift in the maxima of x Y , the weaker the pinning and hence the smaller jcm . Once again, this implies that sample B has strongest interconnectivity of the grains among the samples studied.
This work was supported by the Research Fund of Karadeniz Technical University, Trabzon, Turkey, under grant contract 98.111.001.2.
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x
4. Conclusions From this comparative analysis and determination of some parameters, the following conclusions can be drawn. After estimation of the volume fraction of the grains from AC susceptibility data, we calculated the temperature dependent AC matrix susceptibility for all samples. The best fit to the experimental data using the Bean’s critical state model gives the information of temperature dependence of the intergranu-
w11x w12x w13x w14x w15x w16x
K.H. Muller, Physica C 159 Ž1989. 717. ¨ D.X. Chen, J. Nogues, K.V. Rao, Cryogenics 29 Ž1989. 800. T. Ishida, R.B. Goldfarb, Phys. Rev. B 41 Ž1990. 8937. K. Yamamoto, H. Mazaki, H. Yasuoka, S. Katsuyama, K. Kosuge, Phys. Rev. B 46 Ž1992. 1122. B. Loegel, D. Bolmont, A. Mehdaoui, J. Appl. Phys. 66 Ž1989. 1497. B. Loegel, D. Bolmont, A. Mehdaoui, Physica C 179 Ž1991. 15. D.X. Chen, Y. Mei, H.L. Luo, Physica C 167 Ž1990. 317. C.Y. Lee, Y.H. Kao, Physica C 241 Ž1995. 167. S. C¸ elebi, I. Karaca, E. Aksu, A. Gencer, Physica C 309 Ž1998. 131. S. C¸ elebi, S. Nezir, A. Gencer, E. Yanmaz, M. Altunbas¸, J. Alloys Compd. 255 Ž1997. 4. ¨ ¨ S. Nezir, J. Alloys Compd. S. C¸ elebi, I. Karaca, A. Ozturk, 268 Ž1998. 256. E. Yanmaz, J. S. Bolat, S. C¸ elebi, A. Gencer, H. Comert, ¨ Alloys Compd. 269 Ž1998. 1. J.R. Clem, Physica C 153 Ž1988. 50. Y.B. Kim, C.F. Hemstead, A.R. Strnad, Phys. Rev. Lett. 9 Ž1962. 306. C.P. Bean, Rev. Mod. Phys. 36 Ž1964. 31. R.B. Goldfarb, M. Lelental, C.A. Thompson, in: R.A. Hein, T.L. Francavilla, D.H. Liebenberg ŽEds.., Magnetic Susceptibility of Superconductors and Other Spin Systems, Plenum, New York, 1991.
Comparative AC susceptibility analysis on Bi– žPb / –Sr–Ca–Cu–O high-Tc superconductors Selahattin C¸ elebi
)
Department of Physics, Faculty of Science and Arts, Karadeniz Technical UniÕersity, 61080 Trabzon, Turkey Received 8 March 1999; accepted 8 April 1999
Abstract We discuss the comparative AC susceptibility analysis on rectangular bar shaped high-temperature Bi– ŽPb. –Sr–Ca–Cu–O superconductors prepared by the liquid ammonium nitrate method and the solid state reaction method. Five samples used in this study were obtained from different starting compositions. The analysis for comparison is based on Ži. how much rapidly the relative peak temperature ŽTc y Tp . in x Y ŽT . increases with increasing fields; Žii. the suppression degree of the diamagnetic behavior with respect to fields; Žiii. the sharpness of the transition of x X ŽT . for intergranular component for the same field amplitude; Živ. the steepness of the data of x Y ŽT s 55 K. vs. the field amplitude. We also qualitatively discuss experimental results in the framework of the critical state model, estimate the effective volume fraction of the grains and determine the temperature dependence of the critical current density by means of the best fit of the calculated data for the experimental matrix susceptibility. q 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 7460Ge; 7472Fq Keywords: Bi– ŽPb. –Sr–Ca–Cu–O high-Tc superconductors; AC susceptibility; Critical current density
1. Introduction AC susceptibility measurements x s x X q i x Y are very useful for characterizing the high-temperature superconductors ŽHTS. w1–10x. The sharp decrease in the real part x X ŽT . below the critical temperature Tc is a manifestation of diamagnetic shielding and the peak in the imaginary part x Y ŽT . represents the AC losses. The shapes of x X ŽT . and x Y ŽT . are
)
Tel.: q90-462-325-8244; Fax: q90-462-325-3195; E-mail: [email protected]
strongly influenced by Ži. the classes of compounds, Žii. the fabrication process, Žiii. the thermal treatments, Živ. the morphologies of the samples: bulk, thin films, wires, tapes, single crystals, and Žv. the measuring conditions Žthe presence and orientations of DC field along with AC field amplitudes. w6x. The discovery of HTS offered a great promise of future applications. However, soon was released that there was an undesirable limitation on the transport critical current density, jc , of the HTS. One of the reasons for this low jc is the granular nature of sintered HTS. Such a low jc corresponds to small full penetration field H U , in a magnetized sample.
0921-4534r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 2 8 4 - 1
252
S. C¸ elebi r Physica C 316 (1999) 251–256
Hence, low field AC susceptibility measurements are very important both for the characterization of the samples and the promotion or modification of the critical state models. In this article, we present comparative analysis of AC susceptibility measurements on five different Bi– ŽPb. –Sr–Ca–Cu–O superconducting samples in terms of intergranular critical current density, the volume fraction of the grains and transition temperature.
2. Experimental details Samples A and B were fabricated by the liquid ammonium nitrate technique with the stoichiometric composition Bi 1.84 Pb 0.34 Sr1.91Ca 2.03 Cu 3.06 O10 and Bi 1.4 Pb 0.6 Sr2 Ca 2 Cu 3 O12 , respectively, using the nearly same route. The details of fabrication and characterization w11x and the frequency dependent AC susceptibility study w9x of sample A and the AC losses analysis w10x of sample B can be found elsewhere. The dimensions of samples A and B for the AC susceptibility measurements are 1.25 = 3 = 13 mm3 and 1.85 = 2.55 = 13.05 mm3 , respectively. Samples C, D and E were prepared with the nominal composition Bi 1.6 Pb 0.4 Sr2 Ca 3 Cu 4yx Ag xO 12 Žwhere x s 0, 0.1 and 0.4, respectively. using the conventional solid-state reaction technique. The details of the fabrication process and magnetic behaviour are given in the previous communication w12x. The dimensions of the samples for the AC susceptibility measurements do not change with the sample and are 2 = 2.5 = 12 mm3. The AC susceptibility measurements were done with a 7130 AC Susceptometer of Lake Shore with a closed cycle refrigerator. The details of the measuring system of the AC susceptibility were described in a previous work w10x.
3. Results and discussion Since the demagnetizing correction would cause x X s y1 for low enough temperature, we normalized
Y X Fig. 1. Plot of imaginary Ž x . vs. real Ž x . components of AC susceptibility nature at f s1 kHz and Hac s80 Arm Žrms. for all samples.
experimental AC susceptibility data x Y ŽT . and x X ŽT . to the < x X < at the lowest temperature and the lowest field amplitude for each sample. It is useful to plot the x Y Ž x X . graph in order to grasp the characteristics of critical currents. Fig. 1 shows the x Y Ž x X . data for all the samples measured at Hac s 80 Arm Žrms. and f s 1 kHz. There are two contributions to the experimental AC susceptibility data. The principle of the separation of the contribution from grains and the coupling matrix has been described by Clem w13x and many workers w1,2x have extensively used it. The experimental matrix susceptibilities xmY and xmX can be extracted from the measured susceptibilities x Y and x X employing the following equations w2x:
x Y s Ž 1 y fg . xmY .
Ž 1.
x X s yfg q Ž 1 y fg . xmX .
Ž 2.
We need to know the values of fg for each sample in order to determine the matrix susceptibilities xmY and
Y Fig. 2. Extracted matrix susceptibility xm vs. temperature at Hac s 80 Arm Žrms. and f s 1 kHz for all samples. Solid line is for theoretical calculations.
S. C¸ elebi r Physica C 316 (1999) 251–256
253
S. C¸ elebi r Physica C 316 (1999) 251–256
254
xmX from Eqs. Ž1. and Ž2.. The volume fraction of the grains fg in the samples can be estimated from Figs. 1 and 2. We believe that the onset value Žindicated by an arrow in Fig. 1. of x Y Ž x X . is roughly shows the value of fg for each sample. Chen et al. w7x used the critical state model of Kim et al. w14x to calculate AC susceptibility and determine the volume fraction of the grains for BiPbSrCaCuO superconductors. Their calculated value for fg seems to be consistent with the estimated value from the high temperature portion of the x X ŽT . curves. Hence, we used the fg value determined by the above procedure for the calculation of the matrix susceptibility. Sample A ŽB. has the highest Žlowest. value of fg Žsee Table 1.. Y We have calculated xm,max and xmX ŽTp . and tabulated in Table 1 for all the samples, where f s 1 kHz, Hac s 80 Arm. For the samples of cylinder shape, according to the Bean model w15x, the theoretY ical value of xmax is equal to 0.212 and the corresponding value of x X is y0.333. The extracted Y values of xm,max and xmX ŽTp . for all samples differ slightly from the theoretical values for the Bean-cylinder case Žsee Table 1.. Consequently, we concluded that all these samples can be treated in the framework of the Bean model. When the flux lines fully penetrate the material, i.e., when Hm Ž Hm corresponds to '2 Hac Žrms.. is equal to the first full penetration field H U , the losses reach a maximum w13x. Consequently, one can estimate the temperature dependence of the critical current density using the Bean model. According to the Bean model, the critical current density at the peak temperature Tp ,
Table 1 List of the samples and some superconducting parameters Samples
A
B
C
D
E
Y xma x x X ŽTp .
0.140 y0.56 0.29 0.20 y0.38 107.5 104 85.6
0.242 y0.43 0.07 0.26 y0.39 108 103 96.5
0.217 y0.45 0.14 0.25 y0.36 108 104 93
0.197 y0.47 0.15 0.23 y0.38 108 104 91
0.168 y0.46 0.14 0.20 y0.37 108 104 82.5
3.57
1.61
2.10
2.22
2.38
fg Y xm,max xmX ŽTp . Tc Tcm Tp Žfor 20 Arm. p
and the imaginary part of the AC susceptibility for cylindrical geometry w16x can be written as jcm Ž Tp . s H U rR f H U r'ab , Hm
2
Hm
xYs
ž / ž /
xYs
ž / ž /
4
4
H
y2
U
HU
y2
Hm
H
U
3p 2
HU Hm
1
1 3p
Ž 3. ,
for H U G Hm ,
,
for H U F Hm
Ž 4. where the cross-section of the rectangular bar shaped sample is 2 a = 2 b. In the calculations for the best fit of the theoretical and experimental temperature dependent matrix susceptibility xmY , two different possible temperature dependences for the matrix Žintergranular. critical current density jcm ŽT . have been exploited, namely,
ž
jcm Ž T . s jcm 0 1 y
T Tcm
p
/
, jcm 0 1 y
T
ž / Tcm
2
. Ž 5.
Y value can range from Kim’s theoretical xm,max 0.21 to 0.4 w2x. The Bean model w15x predicts the Y xm,max value to be 0.212 for infinite cylinder and 0.238 for infinite slab geometry w16x. The values of Y observed in all samples are close to that for xm,max the Bean model. Therefore, we have used the Bean model for xmY vs. Hm and determined the temperature dependence of intergranular critical current density hence pinning strength parameter. The best fit of the calculated data Žsolid line. in Fig. 2a–e for experimental matrix susceptibility yields the exponent p and the matrix critical temperature Tcm in Eq. Ž5. which are tabulated in Table 1. For completeness, we presented xmX ŽTp . values for each sample in Table 1. Chen et al. w2x calculated xmX ŽTp . for the samples with a rectangular cross-section of 2 a = 2 b and an infinite length. For bra s 2 and 1, the values of xmX ŽTp . varies from y0.34 to y0.29 and from y0.31 to y0.27, respectively. The values of xmX ŽTp . for all the samples are very close to the lowest limit of y0.34. The values of Tp Žfor 80 Arm. in Table 1 shows the peak temperature used for calculation. Fig. 3 shows the imaginary part of the experimenY as a function of tal AC susceptibility at 55 K x 55
S. C¸ elebi r Physica C 316 (1999) 251–256
Fig. 3. Imaginary part of the experimental AC susceptibility at 55 Y K x 55 as a function of field amplitude Žrms. for all samples, where f s1 kHz.
field amplitude for all samples, where f s 1 kHz. It is well known that for an infinite slab when the field amplitude Hm is less than the full penetration field H U , the imaginary part Žfundamental. of the AC susceptibility is given by
xYs
2 Hm 3p H U
.
Ž 6.
Y In the plot of x 55 as a function of field amplitude Žrms., the slope of the straight line is inversely proportional to the full penetration field, hence, the critical current density Ž H U s jcm R .. Therefore, the shallower the straight line, the larger the critical current density. According to this criteria, sample B has the largest and sample E has the lowest critical current density. As a measure of the diamagnetic suppression, hence, the magnitude of the critical current density, we show the real part of the AC X susceptibility x 55 at 55 K and 1 kHz as a function of the applied field amplitude Žrms. in Fig. 4. The above conclusion can be also drawn from Fig. 4. Fig. 5 displays the curves of x X vs. T showing two step process which reflects the shielding of flux from and between the grains, as T decreases. When the samples are just below Tc , the superconducting grains first shield the applied magnetic field. This is measured as a negative x X . At low enough temperature, intergranular component of x X appears. At
255
X Fig. 4. Real Ž x . parts of AC susceptibility as a function of the field amplitude Žrms. measured in all samples at f s1 kHz and T s 55 K.
extremely low temperatures, the whole volume of the sample expected to be shielded by the supercurrent circulating in the sample and, hence, the curve of x X vs. T saturates. The transition of x X for the intergranular component for sample B is sharper than that of the other samples confirming our conclusions above. The diamagnetic onset temperatures of the superconducting transition are listed in Table 1 as
Fig. 5. Plot of x Arm.
X
vs. temperature at f s1 kHz and Hac s80
256
S. C¸ elebi r Physica C 316 (1999) 251–256
lar critical current density. The small deviation between experimental and calculated data can be attributed to the multiple phase of BiPbSrCaCuO superconducting systems as well as the fact that we have used crude but simple approximation. In the comparative analysis, we determine the quality of the samples by various methods. Sample B Žfabricated by the liquid ammonium nitrate technique with the stoichiometric composition Bi 1.4 Pb 0.6 Sr2 Ca 2 Cu 3 O 12 . has the highest intergranular critical current among the samples studied for comparative analysis.
Acknowledgements
Fig. 6. Plot of ŽTc yTp .r Tc vs. field amplitude Žrms. at f s1 kHz.
108 K for the samples B, C, D, and E and 107.5 K for sample A. We display ŽTc y Tp .rTc vs. field amplitude in Fig. 6, in order to make possible comparison with various experimental data. As the field amplitude increases, the peak of x Y ŽT . shifts to lower temperatures. The amount of the shift as a function of the field amplitude is proportional to the magnitude or strength of the pinning force. The larger the shift in the maxima of x Y , the weaker the pinning and hence the smaller jcm . Once again, this implies that sample B has strongest interconnectivity of the grains among the samples studied.
This work was supported by the Research Fund of Karadeniz Technical University, Trabzon, Turkey, under grant contract 98.111.001.2.
References w1x w2x w3x w4x w5x w6x w7x w8x w9x w10x
4. Conclusions From this comparative analysis and determination of some parameters, the following conclusions can be drawn. After estimation of the volume fraction of the grains from AC susceptibility data, we calculated the temperature dependent AC matrix susceptibility for all samples. The best fit to the experimental data using the Bean’s critical state model gives the information of temperature dependence of the intergranu-
w11x w12x w13x w14x w15x w16x
K.H. Muller, Physica C 159 Ž1989. 717. ¨ D.X. Chen, J. Nogues, K.V. Rao, Cryogenics 29 Ž1989. 800. T. Ishida, R.B. Goldfarb, Phys. Rev. B 41 Ž1990. 8937. K. Yamamoto, H. Mazaki, H. Yasuoka, S. Katsuyama, K. Kosuge, Phys. Rev. B 46 Ž1992. 1122. B. Loegel, D. Bolmont, A. Mehdaoui, J. Appl. Phys. 66 Ž1989. 1497. B. Loegel, D. Bolmont, A. Mehdaoui, Physica C 179 Ž1991. 15. D.X. Chen, Y. Mei, H.L. Luo, Physica C 167 Ž1990. 317. C.Y. Lee, Y.H. Kao, Physica C 241 Ž1995. 167. S. C¸ elebi, I. Karaca, E. Aksu, A. Gencer, Physica C 309 Ž1998. 131. S. C¸ elebi, S. Nezir, A. Gencer, E. Yanmaz, M. Altunbas¸, J. Alloys Compd. 255 Ž1997. 4. ¨ ¨ S. Nezir, J. Alloys Compd. S. C¸ elebi, I. Karaca, A. Ozturk, 268 Ž1998. 256. E. Yanmaz, J. S. Bolat, S. C¸ elebi, A. Gencer, H. Comert, ¨ Alloys Compd. 269 Ž1998. 1. J.R. Clem, Physica C 153 Ž1988. 50. Y.B. Kim, C.F. Hemstead, A.R. Strnad, Phys. Rev. Lett. 9 Ž1962. 306. C.P. Bean, Rev. Mod. Phys. 36 Ž1964. 31. R.B. Goldfarb, M. Lelental, C.A. Thompson, in: R.A. Hein, T.L. Francavilla, D.H. Liebenberg ŽEds.., Magnetic Susceptibility of Superconductors and Other Spin Systems, Plenum, New York, 1991.