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AC losses and determination of some superconducting parameters of Ag2O added Bi2223 superconductors
Physica C 436 (2006) 93–98 www.elsevier.com/locate/physc
AC losses and determination of some superconducting parameters of Ag2O added Bi2223 superconductors _ Karaca b, A. O _ Du¨zgu¨n a, I. ¨ ztu¨rk c, S. C ¸ elebi I.
c,*
a
Department of Physics, Rize Faculty of Science and Arts, Karadeniz Technical University, 53100 Rize, Turkey b Department of Physics, Faculty of Science and Arts, Nigde University, 51200 Nigde, Turkey c Department of Physics, Faculty of Science and Arts, Karadeniz Technical University, 61080 Trabzon, Turkey Received 31 October 2005; received in revised form 26 January 2006; accepted 6 February 2006
Abstract The effects of Ag2O addition on electromagnetic properties in a Bi2223 superconductor have been investigated by means of AC susceptibility measurements and theoretical analysis. Intergranular critical current density was found to be decreased with increased amount of Ag2O addition (0, 15, 30 wt.%). The effective volume fractions of the grains were estimated as a function of Ag2O amount. The field and temperature dependence of the intergranular critical current density for each sample has been accounted by the function p J cm ðT Þ ¼ Ba0n 1 TTcm , where a0 denotes the pinning strength parameter at T = 0. The field exponent n, temperature exponent p, and maximum intergranular loss peaks, which are determined from the comparison of the experimental and calculated curves, increased with increasing amount of Ag2O addition. Experimental isothermal hysteresis losses as a function of field amplitude are also seen to adequately be reproduced by model calculation using the same fitting parameters as for AC susceptibility v00 (T) data. 2006 Elsevier B.V. All rights reserved. Keywords: Ag2O addition; Bi2223 superconductor; Critical current density; AC loss
1. Introduction AC loss is one of the most important parameters in determining the commercial effectiveness of technological applications. In some applications, the energy cost and efficiency is crucial, in other applications the reduction of AC loss is more important than other factors. Therefore, a vital part in the commercialization of high-Tc superconductor applications is the development of affordable conductors carrying high currents and having the minimum loss in the operating environment [1]. It is evident that any experimental or theoretical work to analyse the parameters effecting AC loss will make crucial contribution to the literature. It is well established that the largest contribution to AC losses comes from hysteresis loss. Hysteresis loss is the manifestation of hysteretic motion of flux lines. The loss *
Corresponding author. Tel.: +90 462 3772557; fax: +90 462 3253195. E-mail address: [email protected] (S. C ¸ elebi).
0921-4534/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2006.02.003
depends on the amount of flux penetration into the sample. There are various techniques for measuring the energy losses of superconductors [2]. One of the most common ones is to measure AC susceptibility (see for example [3– 5]) or DC magnetization [6]. Silver (Ag) has been found to be the only metal element among the noble metals that is non-poisoning to ceramic superconductors [7]. This non-poisoning feature of Ag is of significant technical importance in the fabrication of Ag-superconductor composites such as wires and tapes in order to overcome the physical and mechanical shortcomings of brittle ceramic superconductors. Some workers have investigated the effects of silver on microstructure and physical properties in BiA(Pb)ASrACaACuAO system (Refs. [8,9], see also references therein). Chen et al. [4] reported an increase in fg values, volume fraction of the grains, with field amplitude in YBCO system. While there are some papers reporting that fg remains nearly constant with field amplitude [10–12] and decreases
with increasing field amplitude in BSCCO system [13] where it is suggested that the average grain size and decoupling field effects might be key parameters controlling fg variation of their investigated superconducting samples. In this article we report on the effects of Ag2O addition to Bi2223 superconductor on AC losses as well as the field and temperature dependence of the intergranular critical current density. It has been shown that the theoretical calculations based onthe critical p state model using the func tion J cm ðT Þ ¼ Ba0n 1 TTcm can reproduce experimental data quite well.
χ''
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
0.2 0.0 -0.2
χ'
94
BSCCO f=20 Hz From right to left Hac=8,40,80,200,400,800 A/m
-0.4
800 400
-0.6
200 80
-0.8
40 8 A/m
-1.0 50
2. Experimental
60
70
80
90
100
110
T (K)
0.2 0.0 -0.2
χ'
BSCCO+15%Ag2O 800
f=20 Hz
-0.4
400 200
-0.6
80 40
-0.8
8 A/m
-1.0 50
60
70
80
90
100
110
T (K)
(b)
χ ''
0.2 0.0 -0.2
BSCCO+30%Ag2O
χ'
Details on preparation and microstructural analysis can be found in our previous communication [9]. However, brief description might be useful to identify the samples studied in this paper. The powder of nominal Bi1.84Pb0.34Sr1.91Ca2.03Cu3.06O10 compound was synthesized by a wet-technique using high purity (>99.99%) Bi2O3, PbO, SrCO3, CaCO3, and CuO, twice as much. Furthermore, the powder was calcined at 750 C for 10 h, pressed into pellets with 225 MPa and sintered at 848 C for 100 h. After regrinding, various amounts of Ag2O (15, 30 wt.%) were added into the samples. The ultimate powders were pressed into pellets and annealed at 830 C for 100 h. The AC susceptibility of the samples was measured with a commercial Lake Shore susceptometer model 7000. The dimensions of the samples P (BSCCO), 15A (BSCCO + 15%Ag2O), 30A (BSCCO + 30%Ag2O), for AC susceptibility measurements are 1.61 · 2.56 · 9.60 mm3, 1.73 · 2.01 · 11.45 mm3, and 1.71 · 2.24 · 11.88 mm3, respectively. The sample was mounted such that its length was along the direction of the magnetic field. The temperature variation was enhanced using a closed cycle helium cryostat equipped with a temperature controller. The signals due to the in-phase and out-of-phase magnetization were taken simultaneously.
χ ''
(a)
f=20 Hz
-0.4
800 400
-0.6
3. Results and discussion
200 80
-0.8
In Fig. 1, we display the temperature variation of the experimental AC susceptibility curves v00 (T, Hac) and v 0 (T, Hac) measured on our BSCCO samples for (a) BSCCO (b) BSCCO + 15%Ag2O and (c) BSCCO + 30%Ag2O where f = 20 Hz. The diamagnetic onset temperatures of the superconducting transition for three samples are about 108 K. The diamagnetic onset temperature remains constant at different fields. As shown in real part of AC susceptibility, the curves of v 0 versus T shows two step process which reflects the flux penetration into and between the grains, as T decreases, respectively. When the samples are at just below Tc, the superconducting grains first shield the applied magnetic field. This is measured as a negative v 0 . At low enough temperature, intergranular component of v 0 appears. At the very low temperatures, the entire volume of the sample is expected
40
8 A/m
-1.0 50
(c)
60
70
80
90
100
110
T (K)
Fig. 1. AC susceptibility as a function of temperature and AC field amplitude for the samples (a) sample P, (b) sample 15A and (c) sample 30A, where f = 20 Hz.
to be shielded by the supercurrent circulating around the sample along the grains and through the matrix and hence the v 0 –T curve saturates. We note that losses because of flux penetration into the grains seem to be negligible for the field less than 800 A/m. Therefore, the peak in v00 versus T mainly corresponds to the intergranular component. However, as the applied field increases the intragranular peaks are expected to be visible due to the field penetration into the grains. As the field amplitude increases, the peaks
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
where a0 is the pinning strength parameter at T = 0, Tcm is the transition temperature for matrix and Bn the field dependence of the intergranular (matrix) current density. Note that this expression is used in the Maxwell’s equation ~ H ~ ¼~ r jc ðB; T Þ
1000
15A 30A P
f=20 Hz
80 A/m, 15A 400 A/m, 15A 80 A/m, 30A 400 A/m, 30A 80 A/m , P 400 A/m , P
0.20
0.15
0.10
0.05
0.00
(a)
ð2Þ
80
90
100
80
90
100
110
0.0
-0.2
-0.4
χ'
assuming the current density in a critical state [14]. Comparing any two samples the larger the shift in the maxima of v00 , the weaker the pinning and hence the smaller the intergranular critical current Jcm. It is noted that addition of Ag2O amount changed the pattern of AC susceptibility as shown in Figs. 1–3. Fig. 2 depicts the semi-log plot of the AC loss peak temperatures, Tp, as a function of various AC field amplitudes, for three different samples. The peaks shift to the lower temperature with increased amount of Ag2O addition (15, 30 wt.%) resulting in a decrease of intergranular critical current density, since the dimensions of the samples are nearly the same. This conclusion can also be drawn from the interpretation of the shielding behavior of the samples. In Fig. 3, we display the AC susceptibility versus temperature graph for three samples at selected two field amplitudes. It is evident that Ag2O addition has an effect on both AC loss peaks and shielding behavior of the superconducting BSCCO samples. It is well established that the field exponent n and temperature exponent p defined in the expression of critical current density play a major role in the pattern of v00 (T) curves. Hence, we can determine these parameters by comparison of experimental and theoretical curves as shown in Fig. 5.
Hac (A/m)
0.25
χ"
of v00 (T) shift to lower temperatures and broadens. The amount of the shift as a function of the field amplitude is proportional to the magnitude or strength of the pinning force. The width of each peak is manifestation of temperature exponent p of the intergranular critical current density in the expression p a0 T J cm ðT Þ ¼ n 1 ð1Þ T cm B
95
-0.6
-0.8
-1.0
(b)
110
T (K)
Fig. 3. AC susceptibility (a) imaginary part v00 and (b) real part v 0 as function of temperature at Hac = 80, 400 A/m and f = 20 Hz for three samples.
It is well known that there are two different contributions to magnetic response of granular superconductors, namely intergranular or matrix and intragranular contribution. Detailed description of this subject can be found in Ref. [15]. To separate these contribution, one has to know the effective volume fraction of the grains fg. Method of calculations for fg is reported by several workers, see for example Refs. [4,11–13]. C ¸ elebi [16] suggested and some workers [17] adopted that in the v00 (T) versus v 0 (T) graph the onset or extrapolated onset value of v 0 can provide the estimation of fg. Applying the same procedure, we estimated the values of fg in the uncertainty of ±0.05 for each sample, see Table 1. It should be noted that Ag2O addition process slightly increased the values of fg and that increas-
100
Table 1 Some superconducting parameters for three samples BSCCO
10
75
80
85
90
95
100
105
Tp (K) Fig. 2. Displays the variation of Hac as a function of peak temperature extracted from Fig. 1 for each sample.
fg (for 400 A/m) v00m;max Tcm (K) n H*0 (A/m) p
BSCCO + 15%Ag2O BSCCO + 30%Ag2O
0.12 0.14 0.232 0.264 102 103 0.11 0.27 8800 8000 1.4 1.8
0.18 0.267 100 0.28 7600 1.9
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
96
ing AC field amplitude in low field range are seen not to change significantly the estimated values of fg for each sample studied, see Fig. 4. We have extracted and displayed the intergranular contribution v00m to the experimental AC loss peaks v00 for three samples in Fig. 5 where Hac = 400 A/m, using the following equation:
v00 ¼ ð1 fg Þv00m
ð3Þ
In Fig. 5, we also present the calculations for three samples using the power law model for critical state given in Eq. (1). For idealized cylindrical geometry, Eq. (2) leads to dB=dr ¼ l0 aðT Þ=Bn
ð4Þ
0.25 0.25 80 A/m P 800 A/m
0.20
0.20
0.15
χ"
χ"m
0.15
0.10 0.10
0.05
Experimental Calculation, n=0.11, H*0=8800 A/m, p=1.4, Tcm=102 K
0.05
-fg 0.00 0.00 -1.0
75 -0.9
-0.8
-0.7
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0.0
80
85
(a)
90
95
100
95
100
105
T (K)
χ'
(a)
0.30 0.25 80 A/m 15A 800 A/m
0.25
0.20
0.20
χ"
χ''m
0.15
0.15
0.10
0.10
0.05
0.05
Experimental Calculation, n= 0.27, H*0=8000 A/m, p=1.8, Tcm=103 K
0.00 0.00 -1.0
75 -0.9
-0.8
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-0.6
-0.5
-0.4
-0.3
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80
85
(b)
90
105
T (K)
χ'
(b)
0.30
0.25 80 A/m 30A 800 A/m
0.25
0.20 0.20
χ"
χ''m
0.15
0.15
0.10
0.10
0.05
0.05
Experimental Calculation, n=0.28, H*0=7600 A/m, p=1.9, Tcm=100 K
0.00
0.00 -1.0
75
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
χ'
(c) 00
0
Fig. 4. v versus v for three samples studied, where we present two different AC field amplitudes for comparison.
(c)
80
85
90
95
100
105
T (K)
Fig. 5. Displays v00m , the imaginary part of AC susceptibility versus temperature at Hac = 400 A/m and a frequency of 20 Hz for (a) sample P, (b) sample 15A and (c) sample 30A.
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
Simple expressions can be obtained integrating Eq. (4) for the variety of flux density profiles B(r) encountered as the applied field Ha is made to vary through a complete cycle. Integration of these profiles over the radius leads to analytic formulae for hBi, the spatial average of B(r), for each value selected for Ha. Therefore, hysteresis loops 2e+5 Experimental Calculation
2e+5 2e+5
f=20 Hz, T=97 K
W (a.u.)
1e+5 1e+5 1e+5 8e+4 6e+4 4e+4 2e+4 0
1
10
100
1000
10000
1000
10000
Hac (A/m)
(a) 2e+5 Experimental Calculation
2e+5 2e+5
f=20 Hz, T=94 K
1e+5
W (a.u.)
1e+5 1e+5 8e+4
6e+4 4e+4 2e+4 0
1
10
100
Hac (A/m)
(b) 1.8e+5 Experimental Calculation
1.6e+5 1.4e+5
f=20 Hz, T=91 K
W (a.u.)
1.2e+5 1.0e+5
97
of hBi versus Ha, and the area they enclose, can be easily computed. It is well known that the theoretical imaginary part of the susceptibility vhys can be written [18], vhys ¼ W =pl0 H 2ac
ð5Þ 7
where l0 = 4p · 10 T m/A this area, and W denotes the enclosed area by the hysteresis loop and measures the hysteresis losses per unit volume per cycle. Hence, comparing the maximum of the experimental matrix susceptibility with theoretical imaginary part of the susceptibility provides us the field exponent n in Eq. (1). The other fitting parameters p, Tcm and H*m0 used for each sample are given in the legend of Fig. 5, where H*m0 represents the full penetration field at T = 0. We note that H*m0 decreased from 8800 A/m to 7600 A/m, which is consistent with a decrease in the intergranular critical current density, with addition of 30% Ag2O into Bi2223 superconductor. Detailed description for calculations can be found elsewhere [14]. Some superconducting parameters are summarized for each sample in Table 1. It is evident that the field exponent n, maximum intergranular loss peaks and temperature exponent p, which are determined from the comparison of the experimental and calculated curves, increased with increasing amount of Ag2O addition. We can attribute the variations in the parameters to the multiphase and granular structure of these ceramic superconductors, and also heat treatment due to the fact that the addition of Ag causes a decrease in the melting point compared with the values when Ag is not added [19]. We note that the same heat treatment (at 830 C for 100 h) has been used for the samples studied to investigate the effect of the amount of Ag addition in the form of Ag2O on the superconducting properties of Bi2223 system at the same heat treatment. It is well known that heat treatment is one of the main factors playing role in the pinning mechanism. We also note that calculations of isothermal hysteresis losses for each sample using these parameters give quite a good fit to experimental data, shown in Fig. 6. We can conclude that temperature and field dependence of the critical current density given in Eq. (1) can account for both YBCO and Bi2223 superconductors. In our analysis we did not take into account flux flow or flux creep losses which are frequency dependent. Detailed measurements and calculations including frequency dependent terms are intended to be done in the future.
8.0e+4
4. Summary and conclusion
6.0e+4 4.0e+4 2.0e+4 0.0 1
(c)
10
100
1000
10000
Hac (A/m)
Fig. 6. Displays isothermal hysteresis losses W versus field amplitude Hac at a frequency of 20 Hz for (a) sample P, (b) sample 15A and (c) sample 30A. Solid lines are for calculations using the parameters given in Table 1.
We have measured AC susceptibility in a high-Tc superconductor, sintered BSCCO sample with 0%, 15%, 30% Ag2O added, as a function of temperature T, for several amplitudes of applied AC fields 8 6 Hac 6 800 A/m, at a frequency f = 20 Hz. Exploiting the critical-state concept, p
with jcm ðT Þ ¼ Ba0n 1 TTcm to describe the intergranular critical current, and Maxwell’s equation for idealized cylinder geometry we develop expressions for the evolution of
98
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
the configurations of the flux density profiles B(r) and their spatial average hBi for the different sweeps of applied field Ha at different temperatures. Integration of the area enclosed inside the hysteresis loops of hBi versus Ha yields W, the hysteresis loss per cycle per unit volume, hence a calculated susceptibility of v00 = vhys = W/pl0 (Hac)2. The theoretical curves generated by this simple model are seen to reproduce the measured curves of both v00 versus T and W versus Hac. Some quantities such as the field exponent n, temperature exponent p, and maximum intergranular loss peaks are found to increase, while intergranular critical current density Jcm are seen to decrease, with increasing amount of Ag2O addition in Bi2223 system. Acknowledgement This work was supported by the Research Fund of Karadeniz Technical University. References [1] C.M. Friend, in: Studies of High Temperature Superconductors, vol. 32, edited by Narlikar Nova Science Publishers, New York, 2000, pp. 1–61.
[2] I. Hlasnik, M. Majoros, L. Jansak, in: B. Seeber (Ed.), Handbook of Applied Superconductivity, vol. 1, IOP Publishing, Bristol, 1998, p. 344. [3] K.H. Mu¨ller, Physica C 159 (1989) 717. [4] D.-X. Chen, J. Nogues, K.V. Rao, Cryogenics 29 (1989) 800. [5] T. Ishida, R.B. Goldfarb, Phys. Rev. B 41 (1990) 8937. [6] S. Jin, R.C. Sherwood, T.H. Tiefel, G.W. Kammlott, R.A. Fastnacht, M.A. Davis, S.M. Zahurak, Appl. Phys. Lett. 52 (1988) 1628. [7] M. Polak, L. Krempasky, Physica C 357–360 (2001) 1144. [8] A. Sobha, R.P. Aloysius, P. Guruswamy, K.G.K. Warrier, U. Syamaprasad, Physica C 307 (1998) 277. _ Karaca, S. C [9] I. ¸ elebi, A. Varilci, A.I. Malik, Supercond. Sci. Technol. 16 (2003) 100. [10] S. Ravi, V.S. Bai, Phys. Rev. B 49 (1994) 13082. [11] S. Ravi, Physica C 295 (1998) 277. [12] D.X. Chen, A. Sanchez, T. Puig, L.M. Martinez, J.S. Munoz, Physica C 168 (1990) 652. [13] A. Sedky, M.I. Youssif, Physica C 403 (2004) 297. ¨ ztu¨rk, S. C [14] A. O ¸ elebi, M.A.R. LeBlanc, Supercond. Sci. Technol. 18 (2005) 1029. [15] J.R. Clem, Physica C 153 (1988) 50. [16] S. C ¸ elebi, Physica C 316 (1999) 251. [17] A. Amira, P. Molinie´, M.F. Mosbah, A. Leblanc, J. Magnet. Magnet. Mater. 292 (2005) 186. [18] J.R. Clem, in: R.A. Hein, T.L. Francavilla, D.H. Liebenberg (Eds.), Magnetic Susceptibility of Superconductors and Other Spin Systems, Plenum Press, New York, 1992, p. 260. [19] K. Yoshida, Y. Sano, Y. Tomii, Supercond. Sci. Technol. 8 (1995) 329.
AC losses and determination of some superconducting parameters of Ag2O added Bi2223 superconductors _ Karaca b, A. O _ Du¨zgu¨n a, I. ¨ ztu¨rk c, S. C ¸ elebi I.
c,*
a
Department of Physics, Rize Faculty of Science and Arts, Karadeniz Technical University, 53100 Rize, Turkey b Department of Physics, Faculty of Science and Arts, Nigde University, 51200 Nigde, Turkey c Department of Physics, Faculty of Science and Arts, Karadeniz Technical University, 61080 Trabzon, Turkey Received 31 October 2005; received in revised form 26 January 2006; accepted 6 February 2006
Abstract The effects of Ag2O addition on electromagnetic properties in a Bi2223 superconductor have been investigated by means of AC susceptibility measurements and theoretical analysis. Intergranular critical current density was found to be decreased with increased amount of Ag2O addition (0, 15, 30 wt.%). The effective volume fractions of the grains were estimated as a function of Ag2O amount. The field and temperature dependence of the intergranular critical current density for each sample has been accounted by the function p J cm ðT Þ ¼ Ba0n 1 TTcm , where a0 denotes the pinning strength parameter at T = 0. The field exponent n, temperature exponent p, and maximum intergranular loss peaks, which are determined from the comparison of the experimental and calculated curves, increased with increasing amount of Ag2O addition. Experimental isothermal hysteresis losses as a function of field amplitude are also seen to adequately be reproduced by model calculation using the same fitting parameters as for AC susceptibility v00 (T) data. 2006 Elsevier B.V. All rights reserved. Keywords: Ag2O addition; Bi2223 superconductor; Critical current density; AC loss
1. Introduction AC loss is one of the most important parameters in determining the commercial effectiveness of technological applications. In some applications, the energy cost and efficiency is crucial, in other applications the reduction of AC loss is more important than other factors. Therefore, a vital part in the commercialization of high-Tc superconductor applications is the development of affordable conductors carrying high currents and having the minimum loss in the operating environment [1]. It is evident that any experimental or theoretical work to analyse the parameters effecting AC loss will make crucial contribution to the literature. It is well established that the largest contribution to AC losses comes from hysteresis loss. Hysteresis loss is the manifestation of hysteretic motion of flux lines. The loss *
Corresponding author. Tel.: +90 462 3772557; fax: +90 462 3253195. E-mail address: [email protected] (S. C ¸ elebi).
0921-4534/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2006.02.003
depends on the amount of flux penetration into the sample. There are various techniques for measuring the energy losses of superconductors [2]. One of the most common ones is to measure AC susceptibility (see for example [3– 5]) or DC magnetization [6]. Silver (Ag) has been found to be the only metal element among the noble metals that is non-poisoning to ceramic superconductors [7]. This non-poisoning feature of Ag is of significant technical importance in the fabrication of Ag-superconductor composites such as wires and tapes in order to overcome the physical and mechanical shortcomings of brittle ceramic superconductors. Some workers have investigated the effects of silver on microstructure and physical properties in BiA(Pb)ASrACaACuAO system (Refs. [8,9], see also references therein). Chen et al. [4] reported an increase in fg values, volume fraction of the grains, with field amplitude in YBCO system. While there are some papers reporting that fg remains nearly constant with field amplitude [10–12] and decreases
with increasing field amplitude in BSCCO system [13] where it is suggested that the average grain size and decoupling field effects might be key parameters controlling fg variation of their investigated superconducting samples. In this article we report on the effects of Ag2O addition to Bi2223 superconductor on AC losses as well as the field and temperature dependence of the intergranular critical current density. It has been shown that the theoretical calculations based onthe critical p state model using the func tion J cm ðT Þ ¼ Ba0n 1 TTcm can reproduce experimental data quite well.
χ''
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
0.2 0.0 -0.2
χ'
94
BSCCO f=20 Hz From right to left Hac=8,40,80,200,400,800 A/m
-0.4
800 400
-0.6
200 80
-0.8
40 8 A/m
-1.0 50
2. Experimental
60
70
80
90
100
110
T (K)
0.2 0.0 -0.2
χ'
BSCCO+15%Ag2O 800
f=20 Hz
-0.4
400 200
-0.6
80 40
-0.8
8 A/m
-1.0 50
60
70
80
90
100
110
T (K)
(b)
χ ''
0.2 0.0 -0.2
BSCCO+30%Ag2O
χ'
Details on preparation and microstructural analysis can be found in our previous communication [9]. However, brief description might be useful to identify the samples studied in this paper. The powder of nominal Bi1.84Pb0.34Sr1.91Ca2.03Cu3.06O10 compound was synthesized by a wet-technique using high purity (>99.99%) Bi2O3, PbO, SrCO3, CaCO3, and CuO, twice as much. Furthermore, the powder was calcined at 750 C for 10 h, pressed into pellets with 225 MPa and sintered at 848 C for 100 h. After regrinding, various amounts of Ag2O (15, 30 wt.%) were added into the samples. The ultimate powders were pressed into pellets and annealed at 830 C for 100 h. The AC susceptibility of the samples was measured with a commercial Lake Shore susceptometer model 7000. The dimensions of the samples P (BSCCO), 15A (BSCCO + 15%Ag2O), 30A (BSCCO + 30%Ag2O), for AC susceptibility measurements are 1.61 · 2.56 · 9.60 mm3, 1.73 · 2.01 · 11.45 mm3, and 1.71 · 2.24 · 11.88 mm3, respectively. The sample was mounted such that its length was along the direction of the magnetic field. The temperature variation was enhanced using a closed cycle helium cryostat equipped with a temperature controller. The signals due to the in-phase and out-of-phase magnetization were taken simultaneously.
χ ''
(a)
f=20 Hz
-0.4
800 400
-0.6
3. Results and discussion
200 80
-0.8
In Fig. 1, we display the temperature variation of the experimental AC susceptibility curves v00 (T, Hac) and v 0 (T, Hac) measured on our BSCCO samples for (a) BSCCO (b) BSCCO + 15%Ag2O and (c) BSCCO + 30%Ag2O where f = 20 Hz. The diamagnetic onset temperatures of the superconducting transition for three samples are about 108 K. The diamagnetic onset temperature remains constant at different fields. As shown in real part of AC susceptibility, the curves of v 0 versus T shows two step process which reflects the flux penetration into and between the grains, as T decreases, respectively. When the samples are at just below Tc, the superconducting grains first shield the applied magnetic field. This is measured as a negative v 0 . At low enough temperature, intergranular component of v 0 appears. At the very low temperatures, the entire volume of the sample is expected
40
8 A/m
-1.0 50
(c)
60
70
80
90
100
110
T (K)
Fig. 1. AC susceptibility as a function of temperature and AC field amplitude for the samples (a) sample P, (b) sample 15A and (c) sample 30A, where f = 20 Hz.
to be shielded by the supercurrent circulating around the sample along the grains and through the matrix and hence the v 0 –T curve saturates. We note that losses because of flux penetration into the grains seem to be negligible for the field less than 800 A/m. Therefore, the peak in v00 versus T mainly corresponds to the intergranular component. However, as the applied field increases the intragranular peaks are expected to be visible due to the field penetration into the grains. As the field amplitude increases, the peaks
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
where a0 is the pinning strength parameter at T = 0, Tcm is the transition temperature for matrix and Bn the field dependence of the intergranular (matrix) current density. Note that this expression is used in the Maxwell’s equation ~ H ~ ¼~ r jc ðB; T Þ
1000
15A 30A P
f=20 Hz
80 A/m, 15A 400 A/m, 15A 80 A/m, 30A 400 A/m, 30A 80 A/m , P 400 A/m , P
0.20
0.15
0.10
0.05
0.00
(a)
ð2Þ
80
90
100
80
90
100
110
0.0
-0.2
-0.4
χ'
assuming the current density in a critical state [14]. Comparing any two samples the larger the shift in the maxima of v00 , the weaker the pinning and hence the smaller the intergranular critical current Jcm. It is noted that addition of Ag2O amount changed the pattern of AC susceptibility as shown in Figs. 1–3. Fig. 2 depicts the semi-log plot of the AC loss peak temperatures, Tp, as a function of various AC field amplitudes, for three different samples. The peaks shift to the lower temperature with increased amount of Ag2O addition (15, 30 wt.%) resulting in a decrease of intergranular critical current density, since the dimensions of the samples are nearly the same. This conclusion can also be drawn from the interpretation of the shielding behavior of the samples. In Fig. 3, we display the AC susceptibility versus temperature graph for three samples at selected two field amplitudes. It is evident that Ag2O addition has an effect on both AC loss peaks and shielding behavior of the superconducting BSCCO samples. It is well established that the field exponent n and temperature exponent p defined in the expression of critical current density play a major role in the pattern of v00 (T) curves. Hence, we can determine these parameters by comparison of experimental and theoretical curves as shown in Fig. 5.
Hac (A/m)
0.25
χ"
of v00 (T) shift to lower temperatures and broadens. The amount of the shift as a function of the field amplitude is proportional to the magnitude or strength of the pinning force. The width of each peak is manifestation of temperature exponent p of the intergranular critical current density in the expression p a0 T J cm ðT Þ ¼ n 1 ð1Þ T cm B
95
-0.6
-0.8
-1.0
(b)
110
T (K)
Fig. 3. AC susceptibility (a) imaginary part v00 and (b) real part v 0 as function of temperature at Hac = 80, 400 A/m and f = 20 Hz for three samples.
It is well known that there are two different contributions to magnetic response of granular superconductors, namely intergranular or matrix and intragranular contribution. Detailed description of this subject can be found in Ref. [15]. To separate these contribution, one has to know the effective volume fraction of the grains fg. Method of calculations for fg is reported by several workers, see for example Refs. [4,11–13]. C ¸ elebi [16] suggested and some workers [17] adopted that in the v00 (T) versus v 0 (T) graph the onset or extrapolated onset value of v 0 can provide the estimation of fg. Applying the same procedure, we estimated the values of fg in the uncertainty of ±0.05 for each sample, see Table 1. It should be noted that Ag2O addition process slightly increased the values of fg and that increas-
100
Table 1 Some superconducting parameters for three samples BSCCO
10
75
80
85
90
95
100
105
Tp (K) Fig. 2. Displays the variation of Hac as a function of peak temperature extracted from Fig. 1 for each sample.
fg (for 400 A/m) v00m;max Tcm (K) n H*0 (A/m) p
BSCCO + 15%Ag2O BSCCO + 30%Ag2O
0.12 0.14 0.232 0.264 102 103 0.11 0.27 8800 8000 1.4 1.8
0.18 0.267 100 0.28 7600 1.9
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
96
ing AC field amplitude in low field range are seen not to change significantly the estimated values of fg for each sample studied, see Fig. 4. We have extracted and displayed the intergranular contribution v00m to the experimental AC loss peaks v00 for three samples in Fig. 5 where Hac = 400 A/m, using the following equation:
v00 ¼ ð1 fg Þv00m
ð3Þ
In Fig. 5, we also present the calculations for three samples using the power law model for critical state given in Eq. (1). For idealized cylindrical geometry, Eq. (2) leads to dB=dr ¼ l0 aðT Þ=Bn
ð4Þ
0.25 0.25 80 A/m P 800 A/m
0.20
0.20
0.15
χ"
χ"m
0.15
0.10 0.10
0.05
Experimental Calculation, n=0.11, H*0=8800 A/m, p=1.4, Tcm=102 K
0.05
-fg 0.00 0.00 -1.0
75 -0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
80
85
(a)
90
95
100
95
100
105
T (K)
χ'
(a)
0.30 0.25 80 A/m 15A 800 A/m
0.25
0.20
0.20
χ"
χ''m
0.15
0.15
0.10
0.10
0.05
0.05
Experimental Calculation, n= 0.27, H*0=8000 A/m, p=1.8, Tcm=103 K
0.00 0.00 -1.0
75 -0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
80
85
(b)
90
105
T (K)
χ'
(b)
0.30
0.25 80 A/m 30A 800 A/m
0.25
0.20 0.20
χ"
χ''m
0.15
0.15
0.10
0.10
0.05
0.05
Experimental Calculation, n=0.28, H*0=7600 A/m, p=1.9, Tcm=100 K
0.00
0.00 -1.0
75
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
χ'
(c) 00
0
Fig. 4. v versus v for three samples studied, where we present two different AC field amplitudes for comparison.
(c)
80
85
90
95
100
105
T (K)
Fig. 5. Displays v00m , the imaginary part of AC susceptibility versus temperature at Hac = 400 A/m and a frequency of 20 Hz for (a) sample P, (b) sample 15A and (c) sample 30A.
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
Simple expressions can be obtained integrating Eq. (4) for the variety of flux density profiles B(r) encountered as the applied field Ha is made to vary through a complete cycle. Integration of these profiles over the radius leads to analytic formulae for hBi, the spatial average of B(r), for each value selected for Ha. Therefore, hysteresis loops 2e+5 Experimental Calculation
2e+5 2e+5
f=20 Hz, T=97 K
W (a.u.)
1e+5 1e+5 1e+5 8e+4 6e+4 4e+4 2e+4 0
1
10
100
1000
10000
1000
10000
Hac (A/m)
(a) 2e+5 Experimental Calculation
2e+5 2e+5
f=20 Hz, T=94 K
1e+5
W (a.u.)
1e+5 1e+5 8e+4
6e+4 4e+4 2e+4 0
1
10
100
Hac (A/m)
(b) 1.8e+5 Experimental Calculation
1.6e+5 1.4e+5
f=20 Hz, T=91 K
W (a.u.)
1.2e+5 1.0e+5
97
of hBi versus Ha, and the area they enclose, can be easily computed. It is well known that the theoretical imaginary part of the susceptibility vhys can be written [18], vhys ¼ W =pl0 H 2ac
ð5Þ 7
where l0 = 4p · 10 T m/A this area, and W denotes the enclosed area by the hysteresis loop and measures the hysteresis losses per unit volume per cycle. Hence, comparing the maximum of the experimental matrix susceptibility with theoretical imaginary part of the susceptibility provides us the field exponent n in Eq. (1). The other fitting parameters p, Tcm and H*m0 used for each sample are given in the legend of Fig. 5, where H*m0 represents the full penetration field at T = 0. We note that H*m0 decreased from 8800 A/m to 7600 A/m, which is consistent with a decrease in the intergranular critical current density, with addition of 30% Ag2O into Bi2223 superconductor. Detailed description for calculations can be found elsewhere [14]. Some superconducting parameters are summarized for each sample in Table 1. It is evident that the field exponent n, maximum intergranular loss peaks and temperature exponent p, which are determined from the comparison of the experimental and calculated curves, increased with increasing amount of Ag2O addition. We can attribute the variations in the parameters to the multiphase and granular structure of these ceramic superconductors, and also heat treatment due to the fact that the addition of Ag causes a decrease in the melting point compared with the values when Ag is not added [19]. We note that the same heat treatment (at 830 C for 100 h) has been used for the samples studied to investigate the effect of the amount of Ag addition in the form of Ag2O on the superconducting properties of Bi2223 system at the same heat treatment. It is well known that heat treatment is one of the main factors playing role in the pinning mechanism. We also note that calculations of isothermal hysteresis losses for each sample using these parameters give quite a good fit to experimental data, shown in Fig. 6. We can conclude that temperature and field dependence of the critical current density given in Eq. (1) can account for both YBCO and Bi2223 superconductors. In our analysis we did not take into account flux flow or flux creep losses which are frequency dependent. Detailed measurements and calculations including frequency dependent terms are intended to be done in the future.
8.0e+4
4. Summary and conclusion
6.0e+4 4.0e+4 2.0e+4 0.0 1
(c)
10
100
1000
10000
Hac (A/m)
Fig. 6. Displays isothermal hysteresis losses W versus field amplitude Hac at a frequency of 20 Hz for (a) sample P, (b) sample 15A and (c) sample 30A. Solid lines are for calculations using the parameters given in Table 1.
We have measured AC susceptibility in a high-Tc superconductor, sintered BSCCO sample with 0%, 15%, 30% Ag2O added, as a function of temperature T, for several amplitudes of applied AC fields 8 6 Hac 6 800 A/m, at a frequency f = 20 Hz. Exploiting the critical-state concept, p
with jcm ðT Þ ¼ Ba0n 1 TTcm to describe the intergranular critical current, and Maxwell’s equation for idealized cylinder geometry we develop expressions for the evolution of
98
_ Du¨zgu¨n et al. / Physica C 436 (2006) 93–98 I.
the configurations of the flux density profiles B(r) and their spatial average hBi for the different sweeps of applied field Ha at different temperatures. Integration of the area enclosed inside the hysteresis loops of hBi versus Ha yields W, the hysteresis loss per cycle per unit volume, hence a calculated susceptibility of v00 = vhys = W/pl0 (Hac)2. The theoretical curves generated by this simple model are seen to reproduce the measured curves of both v00 versus T and W versus Hac. Some quantities such as the field exponent n, temperature exponent p, and maximum intergranular loss peaks are found to increase, while intergranular critical current density Jcm are seen to decrease, with increasing amount of Ag2O addition in Bi2223 system. Acknowledgement This work was supported by the Research Fund of Karadeniz Technical University. References [1] C.M. Friend, in: Studies of High Temperature Superconductors, vol. 32, edited by Narlikar Nova Science Publishers, New York, 2000, pp. 1–61.
[2] I. Hlasnik, M. Majoros, L. Jansak, in: B. Seeber (Ed.), Handbook of Applied Superconductivity, vol. 1, IOP Publishing, Bristol, 1998, p. 344. [3] K.H. Mu¨ller, Physica C 159 (1989) 717. [4] D.-X. Chen, J. Nogues, K.V. Rao, Cryogenics 29 (1989) 800. [5] T. Ishida, R.B. Goldfarb, Phys. Rev. B 41 (1990) 8937. [6] S. Jin, R.C. Sherwood, T.H. Tiefel, G.W. Kammlott, R.A. Fastnacht, M.A. Davis, S.M. Zahurak, Appl. Phys. Lett. 52 (1988) 1628. [7] M. Polak, L. Krempasky, Physica C 357–360 (2001) 1144. [8] A. Sobha, R.P. Aloysius, P. Guruswamy, K.G.K. Warrier, U. Syamaprasad, Physica C 307 (1998) 277. _ Karaca, S. C [9] I. ¸ elebi, A. Varilci, A.I. Malik, Supercond. Sci. Technol. 16 (2003) 100. [10] S. Ravi, V.S. Bai, Phys. Rev. B 49 (1994) 13082. [11] S. Ravi, Physica C 295 (1998) 277. [12] D.X. Chen, A. Sanchez, T. Puig, L.M. Martinez, J.S. Munoz, Physica C 168 (1990) 652. [13] A. Sedky, M.I. Youssif, Physica C 403 (2004) 297. ¨ ztu¨rk, S. C [14] A. O ¸ elebi, M.A.R. LeBlanc, Supercond. Sci. Technol. 18 (2005) 1029. [15] J.R. Clem, Physica C 153 (1988) 50. [16] S. C ¸ elebi, Physica C 316 (1999) 251. [17] A. Amira, P. Molinie´, M.F. Mosbah, A. Leblanc, J. Magnet. Magnet. Mater. 292 (2005) 186. [18] J.R. Clem, in: R.A. Hein, T.L. Francavilla, D.H. Liebenberg (Eds.), Magnetic Susceptibility of Superconductors and Other Spin Systems, Plenum Press, New York, 1992, p. 260. [19] K. Yoshida, Y. Sano, Y. Tomii, Supercond. Sci. Technol. 8 (1995) 329.