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Enhancement of flux pinning and Anderson–Dew-Hughes pinning analysis in Bi1.6Pb0.5Sr2−x TbxCa1.1Cu2.1O8+δ superconductor
Journal of Alloys and Compounds 477 (2009) L13–L16
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Letter
Enhancement of flux pinning and Anderson–Dew-Hughes pinning analysis in Bi1.6 Pb0.5 Sr2−x Tbx Ca1.1 Cu2.1 O8+ı superconductor S. Vinu a , P.M. Sarun a , R. Shabna a , A. Biju b , U. Syamaprasad a,∗ a b
National Institute for Interdisciplinary Science and Technology (CSIR), Trivandrum 695019, India M.E.S. College, Nedumkandam 685553, Kerala, India
a r t i c l e
i n f o
Article history: Received 9 September 2008 Accepted 4 October 2008 Available online 21 November 2008 PACS: 74.72.Hs 74.25.Qt Keywords: Superconductor Flux pinning and creep
a b s t r a c t The effect of substitution of rare-earth (RE), Tb on the critical current density (JC ), pinning potential (U0 ) and flux pinning properties of (Bi,Pb)-2212 superconductor was studied. The XRD and EDS analyses show that Tb-atoms are successfully substituted into the (Bi,Pb)-2212 system. The critical temperature (TC ), self-and in-field JC of Tb-substituted samples are found to be highly enhanced for optimum doping levels. The sample with x = 0.075 shows the maximum flux pinning force (FP ) of 275 × 104 N m−3 and the peak position of FP shifts to higher fields (0.84 T) as against 3.0 × 104 N m−3 and 0.12 T for the pure-sample. In addition, the values of self-field JC and U0 , calculated using Anderson’s function are maximum for this sample (x = 0.075). The Dew-Hughes pinning analysis shows that the main pinning mechanism is due to the point-defects brought about by the substitution of Tb-atoms at the Sr-site. The enhancements in JC (B) characteristics, values of U0 , irreversibility field (Birr ) and FP are of great scientific and technological significance and are explained on the basis of hole optimization and formation of point-defects due to the substitution of Tb at Sr-site of (Bi,Pb)-2212 system. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The effect of substitution of cations on the superconducting properties of Bi-2212 system has been a subject of great interest for both technologists and theoreticians. This is because doping is an effective method for improving the structural, transport, superconducting and flux pinning properties of Bibased superconductors and to make the material suitable for the application at higher-temperature and magnetic-fields. In Bi-2212, the 2D pancake vortices are easily de-pinned causing flux-flow and energy dissipation during transport-current flow. In order to sustain high non-dissipative transport-currents at higher temperatures and magnetic-fields the vortices must be pinned. Therefore, the introduction of suitable pinning-centers is required for further improvement of pinning-strength. The experimental results showed that the Pb-substituted Bi-2212 has shown slightly enhanced JC s in applied-fields, compared to the Pb-free Bi-2212 system [1,2]. Similarly, there are a few reports on the substitution of RE in Bi-2212 at Ca-site, and these studies have concluded that even though RE substitution improves the structural stability of Bi-2212, the superconducting properties and the flux pinning properties show degrading trend with increase in dopant concentration [3–5].
In this letter, we report the highly enhanced self-and in-field JC s, U0 , FP and irreversibility field (Birr ) in Tb-substituted (Bi,Pb)-2212 at its Sr-site. The U0 values were calculated by Anderson’s method and the normalized FP (FP /FPmax ) curves were theoretically fitted using Dew-Hughes function. This is the first report of its kind, giving highly enhanced superconducting and flux pinning properties for Tb-substituted (Bi,Pb)-2212 superconductor. 2. Experimental Tb-substituted (Bi,Pb)-2212 superconductors with a general stoichiometry of Bi1.6 Pb0.5 Sr2−x Tbx Ca1.1 Cu2.1 O8+ı [where x = 0.000(Tb000), 0.025(Tb025), 0.050(Tb050), 0.075(Tb075), 0.100(Tb100), 0.125(Tb125), 0.150(Tb150) and 0.175(Tb175)] were prepared by solid-state method using high purity oxides and carbonates (Aldrich > 99.9%). The ingredients were mixed and ground using a planetary ball-mill (FRISCH Pulversette-6) and subjected to a three-stage calcination process in air, at 800 ◦ C/15 h + 820 ◦ C/40 h + 840 ◦ C/60 h. Intermediate grinding was done between each stages of calcination. Samples were then pelletized under a force of 60 kN. The pellets were heat-treated at 845 ◦ C/60 h + 848 ◦ C/60 h, with one intermediate pressing under the same stress. Phase analysis of the samples was done using XRD (Philips X’pert-Pro), and elemental analysis by EDS (JEOL-JSM-5600LV). The JC in self-and applied-fields were measured at 64 K using the four-probe method with the standard criterion of 1 V/cm and field ranging from 0.0 to 1.4 T.
3. Result and discussion ∗ Corresponding author. Tel.: +91 471 2515373; fax: +91 471 2491712. E-mail address: [email protected] (U. Syamaprasad). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.10.033
The XRD patterns (Fig. 1(a)) show that all samples contain only (Bi,Pb)-2212 phase and no secondary phase containing Tb or any
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Letter / Journal of Alloys and Compounds 477 (2009) L13–L16
Fig. 1. (a) XRD patterns of pure and Tb-substituted (Bi,Pb)-2212 after last stage heat treatment and (b) resolved view of the XRD peaks for the (0 0 8) plane.
other cation could be detected. This indicates that the reactants phases are fully converted into (Bi,Pb)-2212 and the substituted Tb is incorporated into the crystal lattice of (Bi,Pb)-2212. In addition, Fig. 1(a) shows that when the Tb-content increases, the peak height corresponding to the (0 0 l) planes systematically decreases. In order to bring out the decrease in peak height of the (0 0 l) planes, the typical peaks of (0 0 8) plane of all samples are shown, with better resolution in Fig. 1(b). This shows that the texturing decreases with increase of Tb-content. This figure also shows that the peaks systematically shift towards higher-angle [maximum ı(2) = 0.30◦ ] with Tb-substitution, which indicates that c-axis length of the Tbsubstituted samples decreases with increase in Tb-content. The
Fig. 2. (a) Variation of normalized JC (B) as a function of magnetic-field (inset—variation of self-field JC with Tb-content) and (b) variation of normalized FP as a function of magnetic-field (EXP—experimental data points denoted by legends and THE—theoretical fit using Eq. (1) denoted by solid lines).
EDS analysis (spot analysis) show the presence of Tb in the Tbsubstituted (Bi,Pb)-2212 grains with a corresponding reduction in Sr. The decreased c-axis length and the EDS results support that the Tb-atoms are successfully substituted at the Sr-site of (Bi, Pb)2212. The variation of TC with Tb-content is given in Table 1. It is interesting to note that the Tb-substituted (Bi,Pb)-2212 show much higher TC values compared to the pure-sample (Tb000) and Tb175 shows the maximum TC . Fig. 2(a) shows the JC (B)/JC (0) characteris-
Table 1 TC , FPmax , U0 , Birr and the fitting parameters of pure and Tb-substituted (Bi,Pb)-2212. Samples
Tb000 Tb025 Tb050 Tb075 Tb100 Tb125 Tb150 Tb175
TC (K)
80.1 84.8 86.4 88.2 90.4 92.2 94.8 96.8
At field B (T)
Reduced field B/Birr at which FPmax occurs
Pinning potential U0 (±0.001 eV)
×104 N m−3
At 0.32 T
At 0.64 T
3.0 13.9 81.0 275.2 169.5 103.1 51.3 31.7
0.12 0.24 0.56 0.84 0.76 0.64 0.48 0.36
0.293 0.333 0.348 0.354 0.353 0.331 0.322 0.349
0.077 0.129 0.264 0.470 0.368 0.346 0.242 0.175
Nil 0.096 0.228 0.345 0.321 0.273 0.189 0.139
Value of FPmax
A × 104 (N m−3 )
p
q
Birr (T)
10.4 52.3 256.5 1270.3 843.9 544.4 283.5 180.8
0.61 0.65 0.70 0.77 0.82 0.85 0.88 0.90
1.45 1.51 1.58 1.69 1.74 1.80 1.83 1.85
0.41 0.72 1.61 2.37 2.15 1.93 1.49 1.03
Letter / Journal of Alloys and Compounds 477 (2009) L13–L16
L15
tics of all samples, at 64 K and field upto 1.4 T. The inset of this figure shows the variation of self-field JC as a function of Tb-content. At 64 K, the values of self-field JC are 1460 kA m−2 and 18070 kA m−2 for Tb000 and Tb075, respectively. Substitution of Tb-atoms at Srsite supplies additional electrons to the system due to the higher valence state of Tb, which reduces the number of holes and thus shifts the system from the ‘over-doped’ to ‘optimally doped’ condition, as far as the hole-density is concerned. The attainment of optimum hole-concentration is responsible for the enhancement of TC and hence the JC values. Also the JC (B) characteristics of the Tb-substituted samples are found to be much better than that of the pure-sample. That is, the deterioration of JC due to the magneticfield is significantly reduced because of Tb-substitution. This shows that the substitution of Tb at the Sr-site enhances the flux pinning strength of (Bi,Pb)-2212 superconductor. The crystal-defects created due to the Pb-substitution are mainly confined in the Bilayer, but the defects produced by Tb-substitution are mainly in the Sr-layer. The vortices are confined in the Cu–O2 layers, which are closer to the Sr-layer than the Bi-layers. Thus, it is likely that the strongly coupled vortices in the Cu–O2 layer are effectively pinned by the defects in the near by Sr-layer than the defects produced in the distant Bi-layer. This is attributed to the enhanced pinning and the unusually high JC (B) performance of Tb-substituted (Bi,Pb)2212. The flux pinning strength of a superconductor can be determined by measuring the pinning force density FP = JC × B) [6]. The normalized FP as a function of applied-field is shown in Fig. 2(b) and all sets of data is found to fit well (Fig. 2(b)) with the Dew-Hughes equation [7] given by, FP FPmax
B P
=A
Birr
1−
B Birr
q
(1)
where A is a numerical parameter and for normal point-pins, p = 1 and q = 2. The fitting parameters for different samples are given in Table 1. For Tb000, the values of p and q are 0.61 and 1.45, respectively. It is found that with increasing Tb-content, the values of p and q gradually increases and for Tb175, p = 0.90 and q = 1.85 are obtained. Also according to Dew-Hughes model, for point pinning the peak position of FP is appeared at a reduced-field value, B/Birr = 0.33. In our case, for all samples we get B/Birr = 0.33 ± 0.03 (Table 1) which shows that the main pinning mechanism is that due to point-defects aroused out of the substitution of Tb-atoms at Srsite. Tb075 shows the maximum flux pinning strength among all the Tb-substituted samples, which implies that a Tb-substituted sample of x = 0.075 makes the optimum defects concentration for attaining the maximum pinning strength. Consequently, the peak position of FP /FPmax of Tb075 shifts to a maximum field of 0.84 T, and FP attains a maximum value of 275 × 104 N m−3 . Tb000 has the weakest pinning effect with a minimum peak position of FP /FPmax at 0.12 T, and the FP value of only 3.0 × 104 N m−3 (Table 1). The thermally activated flux creep model proposed by Anderson [8] can be used to calculate the pinning-potential of the superconductor. According to Anderson’s model, R(T,H) = Ro e−(U0 /kB T )
(2)
where R(T,H) is the resistance as a function of temperature and magnetic field, Ro is the normal-state resistance and kB is the Boltzmann’s constant. The value of U0 (H) for the samples can be calculated from the slopes of ln R versus T−1 plots. In Fig. 3(a) and (b) the plots taken at 0.32 T and 0.64 T are shown. These plots are almost linear over a wide range, which indicates that the resistance tails are caused by thermally activated process. The variation of U0 (H) with Tb-content is given in Fig. 3(c), exhibits peaking of U0 (H) for Tb075 at 0.32 T and 0.64 T. This shows that
Fig. 3. (a) The ln R versus T−1 curves measured at 0.32 T, (b) at 0.64 T and (c) variation of pinning-potential as a function of Tb-content.
the irreversibility-line of Tb-substituted samples shifts to highertemperatures and magnetic-fields compared to the pure-sample, and the flux pinning strength of (Bi,Pb)-2212 significantly increases with Tb-substitution at the Sr-site. 4. Conclusion The critical current density (JC ) and flux pinning properties of Tb-substituted (Bi,Pb)-2212 superconductor have been investigated. It is found that the values of self-and in-field JC , U0 calculated by Anderson’s function and flux pinning strength of Tb-substituted samples are highly enhanced for samples with x = 0.075–0.100. The enhancement of flux pinning properties is evident from the improved JC (B) characteristics and the pinningpotential values. Dew-Hughes pinning analysis shows that the enhanced flux pinning is mainly due to point-defects produced by the substituted Tb-atoms at the Sr-site. The enhancements of TC and JC of (Bi,Pb)-2212 are attributed to the optimization of hole concentration and the formation of point-defects due to the sub-
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Letter / Journal of Alloys and Compounds 477 (2009) L13–L16
stitution of Tb-atoms at the Sr-sites, which act as flux pinning centers. Acknowledgements The authors SV, RS and PMS acknowledge University Grants Commission and Kerala State Council for Science, Technology and Environment (India) for Junior Research Fellowships and Council of Scientific and Industrial Research (India) for Senior Research Fellowship, respectively.
References [1] I. Chong, Z. Hiroi, M. Izumi, J. Shimoyama, Y. Nakayama, K. Kishio, T. Terashima, Y. Bando, M. Takano, Science 276 (1997) 770–773. [2] T. Motohashi, Y. Nakayama, T. Fujita, K. Kitazawa, J. Shimoyama, K. Kishio, Phys. Rev. B 59 (1999) 14080–14086. [3] S. Singh, Phys. C 294 (1998) 249–256. [4] H. Jin, J. Kotzler, Phys. C 325 (1999) 153–158. [5] C.A.M. dos-Santos, G.S. Pinto, B. Ferreira, A.J.S. Machado, Phys. C 354 (2001) 388–390. [6] M.R. Koblischka, M. Murakami, Supercond. Sci. Technol. 13 (2000) 738–744. [7] D. Dew-Hughes, Philos. Mag. 30 (1974) 293–305. [8] P.W. Anderson, Phys. Rev. Lett. 9 (1962) 309–311.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Letter
Enhancement of flux pinning and Anderson–Dew-Hughes pinning analysis in Bi1.6 Pb0.5 Sr2−x Tbx Ca1.1 Cu2.1 O8+ı superconductor S. Vinu a , P.M. Sarun a , R. Shabna a , A. Biju b , U. Syamaprasad a,∗ a b
National Institute for Interdisciplinary Science and Technology (CSIR), Trivandrum 695019, India M.E.S. College, Nedumkandam 685553, Kerala, India
a r t i c l e
i n f o
Article history: Received 9 September 2008 Accepted 4 October 2008 Available online 21 November 2008 PACS: 74.72.Hs 74.25.Qt Keywords: Superconductor Flux pinning and creep
a b s t r a c t The effect of substitution of rare-earth (RE), Tb on the critical current density (JC ), pinning potential (U0 ) and flux pinning properties of (Bi,Pb)-2212 superconductor was studied. The XRD and EDS analyses show that Tb-atoms are successfully substituted into the (Bi,Pb)-2212 system. The critical temperature (TC ), self-and in-field JC of Tb-substituted samples are found to be highly enhanced for optimum doping levels. The sample with x = 0.075 shows the maximum flux pinning force (FP ) of 275 × 104 N m−3 and the peak position of FP shifts to higher fields (0.84 T) as against 3.0 × 104 N m−3 and 0.12 T for the pure-sample. In addition, the values of self-field JC and U0 , calculated using Anderson’s function are maximum for this sample (x = 0.075). The Dew-Hughes pinning analysis shows that the main pinning mechanism is due to the point-defects brought about by the substitution of Tb-atoms at the Sr-site. The enhancements in JC (B) characteristics, values of U0 , irreversibility field (Birr ) and FP are of great scientific and technological significance and are explained on the basis of hole optimization and formation of point-defects due to the substitution of Tb at Sr-site of (Bi,Pb)-2212 system. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The effect of substitution of cations on the superconducting properties of Bi-2212 system has been a subject of great interest for both technologists and theoreticians. This is because doping is an effective method for improving the structural, transport, superconducting and flux pinning properties of Bibased superconductors and to make the material suitable for the application at higher-temperature and magnetic-fields. In Bi-2212, the 2D pancake vortices are easily de-pinned causing flux-flow and energy dissipation during transport-current flow. In order to sustain high non-dissipative transport-currents at higher temperatures and magnetic-fields the vortices must be pinned. Therefore, the introduction of suitable pinning-centers is required for further improvement of pinning-strength. The experimental results showed that the Pb-substituted Bi-2212 has shown slightly enhanced JC s in applied-fields, compared to the Pb-free Bi-2212 system [1,2]. Similarly, there are a few reports on the substitution of RE in Bi-2212 at Ca-site, and these studies have concluded that even though RE substitution improves the structural stability of Bi-2212, the superconducting properties and the flux pinning properties show degrading trend with increase in dopant concentration [3–5].
In this letter, we report the highly enhanced self-and in-field JC s, U0 , FP and irreversibility field (Birr ) in Tb-substituted (Bi,Pb)-2212 at its Sr-site. The U0 values were calculated by Anderson’s method and the normalized FP (FP /FPmax ) curves were theoretically fitted using Dew-Hughes function. This is the first report of its kind, giving highly enhanced superconducting and flux pinning properties for Tb-substituted (Bi,Pb)-2212 superconductor. 2. Experimental Tb-substituted (Bi,Pb)-2212 superconductors with a general stoichiometry of Bi1.6 Pb0.5 Sr2−x Tbx Ca1.1 Cu2.1 O8+ı [where x = 0.000(Tb000), 0.025(Tb025), 0.050(Tb050), 0.075(Tb075), 0.100(Tb100), 0.125(Tb125), 0.150(Tb150) and 0.175(Tb175)] were prepared by solid-state method using high purity oxides and carbonates (Aldrich > 99.9%). The ingredients were mixed and ground using a planetary ball-mill (FRISCH Pulversette-6) and subjected to a three-stage calcination process in air, at 800 ◦ C/15 h + 820 ◦ C/40 h + 840 ◦ C/60 h. Intermediate grinding was done between each stages of calcination. Samples were then pelletized under a force of 60 kN. The pellets were heat-treated at 845 ◦ C/60 h + 848 ◦ C/60 h, with one intermediate pressing under the same stress. Phase analysis of the samples was done using XRD (Philips X’pert-Pro), and elemental analysis by EDS (JEOL-JSM-5600LV). The JC in self-and applied-fields were measured at 64 K using the four-probe method with the standard criterion of 1 V/cm and field ranging from 0.0 to 1.4 T.
3. Result and discussion ∗ Corresponding author. Tel.: +91 471 2515373; fax: +91 471 2491712. E-mail address: [email protected] (U. Syamaprasad). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.10.033
The XRD patterns (Fig. 1(a)) show that all samples contain only (Bi,Pb)-2212 phase and no secondary phase containing Tb or any
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Letter / Journal of Alloys and Compounds 477 (2009) L13–L16
Fig. 1. (a) XRD patterns of pure and Tb-substituted (Bi,Pb)-2212 after last stage heat treatment and (b) resolved view of the XRD peaks for the (0 0 8) plane.
other cation could be detected. This indicates that the reactants phases are fully converted into (Bi,Pb)-2212 and the substituted Tb is incorporated into the crystal lattice of (Bi,Pb)-2212. In addition, Fig. 1(a) shows that when the Tb-content increases, the peak height corresponding to the (0 0 l) planes systematically decreases. In order to bring out the decrease in peak height of the (0 0 l) planes, the typical peaks of (0 0 8) plane of all samples are shown, with better resolution in Fig. 1(b). This shows that the texturing decreases with increase of Tb-content. This figure also shows that the peaks systematically shift towards higher-angle [maximum ı(2) = 0.30◦ ] with Tb-substitution, which indicates that c-axis length of the Tbsubstituted samples decreases with increase in Tb-content. The
Fig. 2. (a) Variation of normalized JC (B) as a function of magnetic-field (inset—variation of self-field JC with Tb-content) and (b) variation of normalized FP as a function of magnetic-field (EXP—experimental data points denoted by legends and THE—theoretical fit using Eq. (1) denoted by solid lines).
EDS analysis (spot analysis) show the presence of Tb in the Tbsubstituted (Bi,Pb)-2212 grains with a corresponding reduction in Sr. The decreased c-axis length and the EDS results support that the Tb-atoms are successfully substituted at the Sr-site of (Bi, Pb)2212. The variation of TC with Tb-content is given in Table 1. It is interesting to note that the Tb-substituted (Bi,Pb)-2212 show much higher TC values compared to the pure-sample (Tb000) and Tb175 shows the maximum TC . Fig. 2(a) shows the JC (B)/JC (0) characteris-
Table 1 TC , FPmax , U0 , Birr and the fitting parameters of pure and Tb-substituted (Bi,Pb)-2212. Samples
Tb000 Tb025 Tb050 Tb075 Tb100 Tb125 Tb150 Tb175
TC (K)
80.1 84.8 86.4 88.2 90.4 92.2 94.8 96.8
At field B (T)
Reduced field B/Birr at which FPmax occurs
Pinning potential U0 (±0.001 eV)
×104 N m−3
At 0.32 T
At 0.64 T
3.0 13.9 81.0 275.2 169.5 103.1 51.3 31.7
0.12 0.24 0.56 0.84 0.76 0.64 0.48 0.36
0.293 0.333 0.348 0.354 0.353 0.331 0.322 0.349
0.077 0.129 0.264 0.470 0.368 0.346 0.242 0.175
Nil 0.096 0.228 0.345 0.321 0.273 0.189 0.139
Value of FPmax
A × 104 (N m−3 )
p
q
Birr (T)
10.4 52.3 256.5 1270.3 843.9 544.4 283.5 180.8
0.61 0.65 0.70 0.77 0.82 0.85 0.88 0.90
1.45 1.51 1.58 1.69 1.74 1.80 1.83 1.85
0.41 0.72 1.61 2.37 2.15 1.93 1.49 1.03
Letter / Journal of Alloys and Compounds 477 (2009) L13–L16
L15
tics of all samples, at 64 K and field upto 1.4 T. The inset of this figure shows the variation of self-field JC as a function of Tb-content. At 64 K, the values of self-field JC are 1460 kA m−2 and 18070 kA m−2 for Tb000 and Tb075, respectively. Substitution of Tb-atoms at Srsite supplies additional electrons to the system due to the higher valence state of Tb, which reduces the number of holes and thus shifts the system from the ‘over-doped’ to ‘optimally doped’ condition, as far as the hole-density is concerned. The attainment of optimum hole-concentration is responsible for the enhancement of TC and hence the JC values. Also the JC (B) characteristics of the Tb-substituted samples are found to be much better than that of the pure-sample. That is, the deterioration of JC due to the magneticfield is significantly reduced because of Tb-substitution. This shows that the substitution of Tb at the Sr-site enhances the flux pinning strength of (Bi,Pb)-2212 superconductor. The crystal-defects created due to the Pb-substitution are mainly confined in the Bilayer, but the defects produced by Tb-substitution are mainly in the Sr-layer. The vortices are confined in the Cu–O2 layers, which are closer to the Sr-layer than the Bi-layers. Thus, it is likely that the strongly coupled vortices in the Cu–O2 layer are effectively pinned by the defects in the near by Sr-layer than the defects produced in the distant Bi-layer. This is attributed to the enhanced pinning and the unusually high JC (B) performance of Tb-substituted (Bi,Pb)2212. The flux pinning strength of a superconductor can be determined by measuring the pinning force density FP = JC × B) [6]. The normalized FP as a function of applied-field is shown in Fig. 2(b) and all sets of data is found to fit well (Fig. 2(b)) with the Dew-Hughes equation [7] given by, FP FPmax
B P
=A
Birr
1−
B Birr
q
(1)
where A is a numerical parameter and for normal point-pins, p = 1 and q = 2. The fitting parameters for different samples are given in Table 1. For Tb000, the values of p and q are 0.61 and 1.45, respectively. It is found that with increasing Tb-content, the values of p and q gradually increases and for Tb175, p = 0.90 and q = 1.85 are obtained. Also according to Dew-Hughes model, for point pinning the peak position of FP is appeared at a reduced-field value, B/Birr = 0.33. In our case, for all samples we get B/Birr = 0.33 ± 0.03 (Table 1) which shows that the main pinning mechanism is that due to point-defects aroused out of the substitution of Tb-atoms at Srsite. Tb075 shows the maximum flux pinning strength among all the Tb-substituted samples, which implies that a Tb-substituted sample of x = 0.075 makes the optimum defects concentration for attaining the maximum pinning strength. Consequently, the peak position of FP /FPmax of Tb075 shifts to a maximum field of 0.84 T, and FP attains a maximum value of 275 × 104 N m−3 . Tb000 has the weakest pinning effect with a minimum peak position of FP /FPmax at 0.12 T, and the FP value of only 3.0 × 104 N m−3 (Table 1). The thermally activated flux creep model proposed by Anderson [8] can be used to calculate the pinning-potential of the superconductor. According to Anderson’s model, R(T,H) = Ro e−(U0 /kB T )
(2)
where R(T,H) is the resistance as a function of temperature and magnetic field, Ro is the normal-state resistance and kB is the Boltzmann’s constant. The value of U0 (H) for the samples can be calculated from the slopes of ln R versus T−1 plots. In Fig. 3(a) and (b) the plots taken at 0.32 T and 0.64 T are shown. These plots are almost linear over a wide range, which indicates that the resistance tails are caused by thermally activated process. The variation of U0 (H) with Tb-content is given in Fig. 3(c), exhibits peaking of U0 (H) for Tb075 at 0.32 T and 0.64 T. This shows that
Fig. 3. (a) The ln R versus T−1 curves measured at 0.32 T, (b) at 0.64 T and (c) variation of pinning-potential as a function of Tb-content.
the irreversibility-line of Tb-substituted samples shifts to highertemperatures and magnetic-fields compared to the pure-sample, and the flux pinning strength of (Bi,Pb)-2212 significantly increases with Tb-substitution at the Sr-site. 4. Conclusion The critical current density (JC ) and flux pinning properties of Tb-substituted (Bi,Pb)-2212 superconductor have been investigated. It is found that the values of self-and in-field JC , U0 calculated by Anderson’s function and flux pinning strength of Tb-substituted samples are highly enhanced for samples with x = 0.075–0.100. The enhancement of flux pinning properties is evident from the improved JC (B) characteristics and the pinningpotential values. Dew-Hughes pinning analysis shows that the enhanced flux pinning is mainly due to point-defects produced by the substituted Tb-atoms at the Sr-site. The enhancements of TC and JC of (Bi,Pb)-2212 are attributed to the optimization of hole concentration and the formation of point-defects due to the sub-
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Letter / Journal of Alloys and Compounds 477 (2009) L13–L16
stitution of Tb-atoms at the Sr-sites, which act as flux pinning centers. Acknowledgements The authors SV, RS and PMS acknowledge University Grants Commission and Kerala State Council for Science, Technology and Environment (India) for Junior Research Fellowships and Council of Scientific and Industrial Research (India) for Senior Research Fellowship, respectively.
References [1] I. Chong, Z. Hiroi, M. Izumi, J. Shimoyama, Y. Nakayama, K. Kishio, T. Terashima, Y. Bando, M. Takano, Science 276 (1997) 770–773. [2] T. Motohashi, Y. Nakayama, T. Fujita, K. Kitazawa, J. Shimoyama, K. Kishio, Phys. Rev. B 59 (1999) 14080–14086. [3] S. Singh, Phys. C 294 (1998) 249–256. [4] H. Jin, J. Kotzler, Phys. C 325 (1999) 153–158. [5] C.A.M. dos-Santos, G.S. Pinto, B. Ferreira, A.J.S. Machado, Phys. C 354 (2001) 388–390. [6] M.R. Koblischka, M. Murakami, Supercond. Sci. Technol. 13 (2000) 738–744. [7] D. Dew-Hughes, Philos. Mag. 30 (1974) 293–305. [8] P.W. Anderson, Phys. Rev. Lett. 9 (1962) 309–311.