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Flux pinning behaviors of Ti and C co-doped MgB2 superconductors
Physica C 468 (2008) 1202–1205
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Physica C journal homepage: www.elsevier.com/locate/physc
Flux pinning behaviors of Ti and C co-doped MgB2 superconductors Y. Yang a, D. Zhao a, T.M. Shen a, G. Li a, Y. Zhang a, Y. Feng c,d, C.H. Cheng a,b, Y.P. Zhang a, Y. Zhao a,b,* a
Key Laboratory of Magnetic Levitation Technologies and Maglev Trains (Ministry of Education of China), Superconductivity R&D Center (SRDC), Mail Stop 165#, Southwest Jiaotong University, Chengdu, Sichuan 610031, China School of Materials Science and Engineering, University of New South Wales, Sydney 2052, NSW, Australia c Northwest Institute for Nonferrous Metal Research, P.O. Box 51, Xian, Shaanxi 710016, China d Western Superconductivity Technology Company, Xian, China b
a r t i c l e
i n f o
Article history: Available online 23 May 2008 PACS: 74.60.Jg 74.60.Ge 74.60.Ec Keywords: MgB2 Critical current density Flux pinning C and Ti doping
a b s t r a c t Flux pinning behavior of carbon and titanium concurrently doped MgB2 alloys has been studied by ac susceptibility and dc magnetization measurements. It is found that critical current density and irreversibility field of MgB2 have been significantly improved by doping C and Ti concurrently, sharply contrasted to the situation of C-only-doped or Ti-only-doped MgB2 samples. AC susceptibility measurement reveals that the dependence of the pinning potential on the dc applied field of Mg0.95Ti0.05B1.95C0.05 has been deter1:5 mined to be UðBdc Þ / B1 dc compared to that of MgB2 UðBdc Þ / Bdc . As to the U(J) behavior, a relationship of U(J) / J0.17 is found fitting well for Mg0.95Ti0.05B1.95C0.05 with respect to U(J) / J0.21 for MgB2. All the results reveal a strong enhancement of the high field pinning potential in C and Ti co-doped MgB2. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The discovery of superconductivity at 39 K in MgB2 offers the possibility of wide engineering applications in a temperature range of 20–30 K, where the conventional superconductors cannot play any roles because of low Tc. Great effort has been done to further improve the critical field and current-carried ability of MgB2 superconducting materials to fulfill practical applications. Alloying with carbon is found to be the most effective to improve the Hc2 by shorting the mean free length of electron, or selective tuning of impurity scattering of p and r band according to the two-gap model of Hc2 of Gurevich [1,2]. For untextured carbon-doped filaments fabricated by a chemical vapor deposition (CVD) method, Wilke et al. [3] showed that, for carbon levels bellows 8%, the transition temperature are depressed by about 0.5 K/% C and Hc2(0) increased by about 2.5 T/% C, achieving upper critical fields in excess of 30 T at 4.2 K. Senkowicz et al. [4] have reported that milling C with MgB2 can produce Hc2(0) in excess of 32 T and critical current density approaching 106 A/cm2.
* Corresponding author. Address: Key Laboratory of Magnetic Levitation Technologies and Maglev Trains (Ministry of Education of China), Superconductivity R&D Center (SRDC), Mail Stop 165#, Southwest Jiaotong University, Chengdu, Sichuan 610031, China. Tel.: +86 28 87600786; fax: +86 28 87600785. E-mail address: [email protected] (Y. Zhao). 0921-4534/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2008.05.032
However, the critical current density, Jc, of MgB2 bulks sintered at ambient pressure is still inferior to the conventional A15 compound or NbTi superconductors due to a poor connection between grains and the lack of flux pinning centers in the materials. As reported previously, Ti doping could highly improve the critical current density of MgB2 in low field by controlling the microstructure of MgB2 [5,6]. The combination C and Ti may be a better approach to improve both Hc2 and Jc of MgB2 simultaneously, thus further improving its performance, especially in the higher magnetic field regime. In this paper, we present the results which demonstrate that the combination effect of C and Ti co-doping in MgB2 can fulfill the tasks of improving both Jc and Hc2.
2. Experimental Mg1xTixB2yCy alloys of four typical compositions have been paid intensive attention. These samples include Mg0.95Ti0.05B2 (denoted as Ti-doped); MgB1.95C0.05 (denoted as C-doped); Mg0.95Ti0.05B1.95C0.05 (denoted as C–Ti-doped), and undoped MgB2 (denoted as undoped). Pellets of all these samples were synthesized by a solid state reaction, at ambient pressure with the starting materials of amorphous B powder (99.99%), Mg powder (99.9%). The mean particle sizes of magnesium and boron were approximately 1 lm and 200 nm, respectively. Mixtures of magnesium, boron, graphite and/or Ti powders were well ground in a
Y. Yang et al. / Physica C 468 (2008) 1202–1205
glove box for 1 h and then uniaxially pressed into pellets of a diameter of 10 mm, sealed in iron tubes, sintered at 800 °C for 1 h in flowing high purity Ar. Then the samples were quenched to room
1203
temperature in the air. In order to increase the solubility of carbon in MgB2 without increasing the reaction temperature and reaction time, high energy milling (HEM) was employed in the preparation
Fig. 1. Jc(H) behavior at T = 20 K for the undoped, Ti-doped, C-doped, and C–Ti-doped samples. For the sake of comparison, the Jc results of nano-carbon-doped MgB2 [7] and CNT-doped-MgB2 [8] are plotted in the figure. Inset: The temperature dependent magnetization at 50 Oe for the undoped, Ti-doped, C-doped, and C–Ti-doped samples.
Fig. 2. Temperature dependence of ac susceptibility in various ac and dc applied fields at various frequencies for pure MgB2 (left column) and Mg0.95Ti0.05B1.95C0.05 (right column).
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Y. Yang et al. / Physica C 468 (2008) 1202–1205
the samples. Except for the high energy milling of 1 h, the reaction temperature and reaction time for the samples prepared with HEM technique are the same as employed for other samples in this study. Crystalline structure of the samples was investigated by powder X-ray diffraction (XRD) using an X’Pert MRD diffractometer with Cu Ka radiation. The microstructure was analyzed at scanning electron microscope (SEM). All the samples were cut to the same size of 1.0 1.5 2.8 mm3 from as-sintered pellets. The ac and dc magnetization of samples was measured using a 9-T Physical Property Measurement System (Quantum Design). A magnetic Jc was derived from the width of the magnetization loop DM based on the extended Bean model: Jc = 20DM/[a(1 a/3b)].
3. Results and discussion Fig. 1 shows the temperature dependence of dc magnetization for the undoped, Ti-doped and C–Ti-doped MgB2 samples (inset of Fig. 1) and the Jc(H) curves for the typical samples at T = 20 K. For the undoped and Ti-doped samples, their Tc values are almost the same, about 37.8 K. For the samples doped with carbon including MgB1.95C0.05 and Mg0.95Ti0.05B1.95C0.05, Tc is depressed by 0.6 K for the samples without HEM, but by 1.3 K for those with HEM, compared to the Tc of carbon-free samples. In this study, the focus will be the improvement of superconducting performance at 20 K because at this temperature, the conventional superconductors, such as Nb3Sn and NbTi alloy can no longer be used due to a lower Tc. As shown in Fig. 1, the in-field critical current densities
Fig. 3. ln f versus U(T)/KT at different ac magnetic filed for: (a) MgB2 and (b) Mg0.95Ti0.05B1.95C0.05. The solid lines are linear fits for the data.
were enhanced by Ti doping, particularly in lower fields. At 20 K, the maximum zero field value Jc(0) was achieved in Mg0.95Ti0.05B2 sample, a Jc value in self-field at 20 K was improved from 2.1 105 A/cm2 of non-doped sample to 3.1 105 A/cm2. This result is consistent with our previous report on Ti-doped MgB2 bulk superconductor, where Jc(0) was improved by refining MgB2 grains and forming a strongly-coupled nanoparticle structure [6]. For C–Ti-doped sample, the Jc of this sample is lower than that of Ti-doped sample in magnetic field from 0 to 2 T, but, in higher magnetic fields (>2 T), it is significantly improved and much higher than the Jc of Ti-doped sample. The in-field Jc of this sample is also higher than carbon-only-doped samples, including nano-carbon-doped-MgB2 [7] and CNT-doped MgB2 [8], in the high magnetic field region. At temperature of 20 K, the Jc reaches 1 104 A/cm2 in 4 T, and 4 103 in 5 T; and the irreversibility field determined from the closure of hysteresis loops with a criterion of 102 A/cm2 exceeds 6 T. The improvement of Jc and pinning behavior at 10 K and 5 K are also observed. Our results clearly show that the concurrently doping Ti and C in MgB2 is a feasible and effective route to further improve the superconducting performance of MgB2, especially at higher temperatures (20 K) and in higher fields (>3 T). In order to understand the pinning mechanism behind the enhanced Jc in the carbon-doped MgB2, the influence of ac and dc applied fields at various frequencies on the v0 (T) and v00 (T) has been studied and the results are illustrated in Fig. 2 for both the undoped and Ti-C-doped MgB2 samples. The superconducting transition temperature decreases with augmenting ac or dc field amplitude and the transition width broadens. On contrary, the transition undergoes a shift towards high temperature region upon augmenting the driven frequency as display in Fig. 2. By varying the dc applied field, the ac field amplitude as well as the driven
Fig. 4. ln U(j) versus ln Bac at different dc magnetic fields for: (a) MgB2 and (b) Mg0.95Ti0.05B1.95C0.05. The solid are linear fits for the data.
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Y. Yang et al. / Physica C 468 (2008) 1202–1205
while for Mg0.95Ti0.05B1.95C0.05, U(J) / j0.17. A reduction of c value reveals an enhanced performance in field ad demonstrated previously. The dependence of the pinning potential on dc applied field can be derived by using the relationship obtained in Fig. 4, the result in shown in Fig. 5. A UðBdc Þ / B0:96 dependence has been obtained for dc MgB2 co-doped by Ti and C, compared to UðBdc Þ / B1:41 in MgB2. It dc is known that in REBCO MTG samples, a UðBdc Þ / B0:5 dependence dc has been obtained, which demonstrated a relatively poor in field behaviour of MgB2 samples. However, strong enhancement of the high field pinning potential suggested largely ameliorated flux pinning behavior by the cooperation of Ti and C, which is in good agreement with the Jc H behavior shown in Fig. 1. According to the results shown in Figs. 3–5, the pinning potential for both pure and C–Ti-doped MgB2 can be described as: " UðT;j;Bdc Þ ¼ U 0 1 " UðT;j;Bdc Þ ¼ U 0 1
T T irr
T T irr
2 #2 ðBdc Þ
1:41
ðjÞ
ðBdc Þ
0:96
ðjÞ
2 #2
0:21
ðfor MgB2Þ;
0:17
ðfor Mg0:95 Ti0:05 B1:95 C0:05 Þ:
4. Conclusion
Fig. 5. ln U(B) versus ln Bdc at different ac magnetic field for: (a) MgB2 and (b) Mg0.95Ti0.05B1.95C0.05. The solid lines are linear fits for the data.
frequency, are able to investigate doping influence on the flux pinning potential, govern by Bdc, Bac and f. In flux dynamics, an approach has been proposed based on the Anderson-Kim flux creep model [9]. According to Blatter et al. [10], the relation can be written in the following form:
UðTÞ UðjÞUðBdc Þ ¼ ln f ln t; KT
ð1Þ
where U represents the pinning potential, T is the peak temperature in the imaginary part of ac susceptibility, K is the Bolzman constant, f is the driven frequency, t is the time scale. As obtained by Qin et al. [11], the dependence of the pinning potential on different variables can be summarized in the following form:
" UðT; j; Bdc Þ ¼ U 0
T 1 T irr
2 #a b c B j ; B0 j0
T UðTÞ ¼ 1 T irr
ð2Þ
2 #2 ;
Acknowledgements The authors are also grateful to the financial support of Australian Research Council (under Contract Nos. DP0559872, DP0452522, DP0881739). This work was also supported by National Natural Science Foundation of China (under Contract Nos. 50372052, and 50588201). References
where for MgB2, a = 2, i.e.
"
Flux pinning behavior of carbon and titanium concurrently doped MgB2 alloys has been studied by ac susceptibility and dc magnetization measurements. It is found that critical current density and irreversibility field of MgB2 have been significantly improved by doping C and Ti concurrently, sharply contrasted to the situation of C-only-doped or Ti-only-doped MgB2 samples. AC susceptibility measurement reveals that the dependence of the pinning potential on the dc applied field of Mg0.95Ti0.05B1.95C0.05 has been determined to be UðBdc Þ / B1 dc compared to that of MgB2 UðBdc Þ / B1:5 dc . As to the U(J) behavior, a relationship of U(J) / J0.17 is found fitting well for Mg0.95Ti0.05B1.95C0.05 with respect to U(J) / J0.21 for MgB2. All the results reveal a strong enhancement of the high field pinning potential in C and Ti co-doped MgB2.
ð3Þ
where Tirr represents the irreversible temperature. The relationship ln f U/KT is obtained by using this method, as shown in Fig. 3. As in Fig. 3, a linear fit has be conducted for both samples, according to which U(Bdc) U(j) can be determined at Bdc = 0.5 T. By varying the applied filed U(Bdc) U(j) was then derived. Fig. 4 displays the results of the calculations from Fig. 3. The linearity of In U(j) ln Bac, given the linearity between j and Bac, demonstrates an exponential dependence of U(j) on j at different dc applied field. A relationship U(J) / j0.21 has been found for MgB2 pure sample,
[1] A. Gurevich, Phys. Rev. B 67 (2003) 184515. [2] A. Gurevich, S. Patnaik, V. Braccini, K.H. Kim, C. Mielke, X. Song, L.D. Cooley, S.D. Bu, D.M. Kim, J.H. Choi, L.J. Belenky, J. Giencke, M.K. Lee, W. Tian, X.Q. Pan, A. Siri, E.E. Hellstrom, C.B. Eom, D.C. Larbalestier, Supercond. Sci. Technol. 17 (2004) 278. [3] R.H.T. Wilke, S.L. Bud’ko, P.C. Canfield, D.K. Finnemore, Phys. Rev. Lett. 92 (2004) 217003. [4] B.J. Senkowicz, J.F. Giencke, S. Patnaik, C.B. Com, E.E. Hellstrom, D.C. Larbalestier, Appl. Phys. Lett. 86 (2005) 202502. [5] Y. Zhao, Y. Feng, C.H. Cheng, L. Zhou, Y. Wu, T. Machi, Y. Fudamoto, N. Koshizuka, M. Murakami, Appl. Phys. Lett. 79 (2001) 154. [6] Y. Zhao, D.X. Huang, Y. Feng, C. Cheng, T. Machi, N. Koshizuka, M. Murakami, Appl. Phys. Lett. 80 (2002) 1640. [7] S. Soltanian, J. Horvat, X.L. Wang, P. Munroe, S.X. Dou, Physica C 390 (2003) 85. [8] S.X. Dou, W.K. Yeoh, J. Horvat, M. Ionescu, Appl. Phys. Lett. 83 (2003). [9] P.W. Anderson, Y.B. Kim, Rev. Mod. Phys. 36 (1964) 39. [10] B. Blatter, M.V. Feigel’man, V.B. Geshkenbein, A.I. Larkin, V.M. Vinokur, Rev. Mod. Phys. 66 (1994) 1125. [11] M.J. Qin, X.L. Wang, S. Soltanian, A.H. Li, H.K. Liu, S.X. Dou, Phys. Rev. B 64 (2001) 060505.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Flux pinning behaviors of Ti and C co-doped MgB2 superconductors Y. Yang a, D. Zhao a, T.M. Shen a, G. Li a, Y. Zhang a, Y. Feng c,d, C.H. Cheng a,b, Y.P. Zhang a, Y. Zhao a,b,* a
Key Laboratory of Magnetic Levitation Technologies and Maglev Trains (Ministry of Education of China), Superconductivity R&D Center (SRDC), Mail Stop 165#, Southwest Jiaotong University, Chengdu, Sichuan 610031, China School of Materials Science and Engineering, University of New South Wales, Sydney 2052, NSW, Australia c Northwest Institute for Nonferrous Metal Research, P.O. Box 51, Xian, Shaanxi 710016, China d Western Superconductivity Technology Company, Xian, China b
a r t i c l e
i n f o
Article history: Available online 23 May 2008 PACS: 74.60.Jg 74.60.Ge 74.60.Ec Keywords: MgB2 Critical current density Flux pinning C and Ti doping
a b s t r a c t Flux pinning behavior of carbon and titanium concurrently doped MgB2 alloys has been studied by ac susceptibility and dc magnetization measurements. It is found that critical current density and irreversibility field of MgB2 have been significantly improved by doping C and Ti concurrently, sharply contrasted to the situation of C-only-doped or Ti-only-doped MgB2 samples. AC susceptibility measurement reveals that the dependence of the pinning potential on the dc applied field of Mg0.95Ti0.05B1.95C0.05 has been deter1:5 mined to be UðBdc Þ / B1 dc compared to that of MgB2 UðBdc Þ / Bdc . As to the U(J) behavior, a relationship of U(J) / J0.17 is found fitting well for Mg0.95Ti0.05B1.95C0.05 with respect to U(J) / J0.21 for MgB2. All the results reveal a strong enhancement of the high field pinning potential in C and Ti co-doped MgB2. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The discovery of superconductivity at 39 K in MgB2 offers the possibility of wide engineering applications in a temperature range of 20–30 K, where the conventional superconductors cannot play any roles because of low Tc. Great effort has been done to further improve the critical field and current-carried ability of MgB2 superconducting materials to fulfill practical applications. Alloying with carbon is found to be the most effective to improve the Hc2 by shorting the mean free length of electron, or selective tuning of impurity scattering of p and r band according to the two-gap model of Hc2 of Gurevich [1,2]. For untextured carbon-doped filaments fabricated by a chemical vapor deposition (CVD) method, Wilke et al. [3] showed that, for carbon levels bellows 8%, the transition temperature are depressed by about 0.5 K/% C and Hc2(0) increased by about 2.5 T/% C, achieving upper critical fields in excess of 30 T at 4.2 K. Senkowicz et al. [4] have reported that milling C with MgB2 can produce Hc2(0) in excess of 32 T and critical current density approaching 106 A/cm2.
* Corresponding author. Address: Key Laboratory of Magnetic Levitation Technologies and Maglev Trains (Ministry of Education of China), Superconductivity R&D Center (SRDC), Mail Stop 165#, Southwest Jiaotong University, Chengdu, Sichuan 610031, China. Tel.: +86 28 87600786; fax: +86 28 87600785. E-mail address: [email protected] (Y. Zhao). 0921-4534/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2008.05.032
However, the critical current density, Jc, of MgB2 bulks sintered at ambient pressure is still inferior to the conventional A15 compound or NbTi superconductors due to a poor connection between grains and the lack of flux pinning centers in the materials. As reported previously, Ti doping could highly improve the critical current density of MgB2 in low field by controlling the microstructure of MgB2 [5,6]. The combination C and Ti may be a better approach to improve both Hc2 and Jc of MgB2 simultaneously, thus further improving its performance, especially in the higher magnetic field regime. In this paper, we present the results which demonstrate that the combination effect of C and Ti co-doping in MgB2 can fulfill the tasks of improving both Jc and Hc2.
2. Experimental Mg1xTixB2yCy alloys of four typical compositions have been paid intensive attention. These samples include Mg0.95Ti0.05B2 (denoted as Ti-doped); MgB1.95C0.05 (denoted as C-doped); Mg0.95Ti0.05B1.95C0.05 (denoted as C–Ti-doped), and undoped MgB2 (denoted as undoped). Pellets of all these samples were synthesized by a solid state reaction, at ambient pressure with the starting materials of amorphous B powder (99.99%), Mg powder (99.9%). The mean particle sizes of magnesium and boron were approximately 1 lm and 200 nm, respectively. Mixtures of magnesium, boron, graphite and/or Ti powders were well ground in a
Y. Yang et al. / Physica C 468 (2008) 1202–1205
glove box for 1 h and then uniaxially pressed into pellets of a diameter of 10 mm, sealed in iron tubes, sintered at 800 °C for 1 h in flowing high purity Ar. Then the samples were quenched to room
1203
temperature in the air. In order to increase the solubility of carbon in MgB2 without increasing the reaction temperature and reaction time, high energy milling (HEM) was employed in the preparation
Fig. 1. Jc(H) behavior at T = 20 K for the undoped, Ti-doped, C-doped, and C–Ti-doped samples. For the sake of comparison, the Jc results of nano-carbon-doped MgB2 [7] and CNT-doped-MgB2 [8] are plotted in the figure. Inset: The temperature dependent magnetization at 50 Oe for the undoped, Ti-doped, C-doped, and C–Ti-doped samples.
Fig. 2. Temperature dependence of ac susceptibility in various ac and dc applied fields at various frequencies for pure MgB2 (left column) and Mg0.95Ti0.05B1.95C0.05 (right column).
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Y. Yang et al. / Physica C 468 (2008) 1202–1205
the samples. Except for the high energy milling of 1 h, the reaction temperature and reaction time for the samples prepared with HEM technique are the same as employed for other samples in this study. Crystalline structure of the samples was investigated by powder X-ray diffraction (XRD) using an X’Pert MRD diffractometer with Cu Ka radiation. The microstructure was analyzed at scanning electron microscope (SEM). All the samples were cut to the same size of 1.0 1.5 2.8 mm3 from as-sintered pellets. The ac and dc magnetization of samples was measured using a 9-T Physical Property Measurement System (Quantum Design). A magnetic Jc was derived from the width of the magnetization loop DM based on the extended Bean model: Jc = 20DM/[a(1 a/3b)].
3. Results and discussion Fig. 1 shows the temperature dependence of dc magnetization for the undoped, Ti-doped and C–Ti-doped MgB2 samples (inset of Fig. 1) and the Jc(H) curves for the typical samples at T = 20 K. For the undoped and Ti-doped samples, their Tc values are almost the same, about 37.8 K. For the samples doped with carbon including MgB1.95C0.05 and Mg0.95Ti0.05B1.95C0.05, Tc is depressed by 0.6 K for the samples without HEM, but by 1.3 K for those with HEM, compared to the Tc of carbon-free samples. In this study, the focus will be the improvement of superconducting performance at 20 K because at this temperature, the conventional superconductors, such as Nb3Sn and NbTi alloy can no longer be used due to a lower Tc. As shown in Fig. 1, the in-field critical current densities
Fig. 3. ln f versus U(T)/KT at different ac magnetic filed for: (a) MgB2 and (b) Mg0.95Ti0.05B1.95C0.05. The solid lines are linear fits for the data.
were enhanced by Ti doping, particularly in lower fields. At 20 K, the maximum zero field value Jc(0) was achieved in Mg0.95Ti0.05B2 sample, a Jc value in self-field at 20 K was improved from 2.1 105 A/cm2 of non-doped sample to 3.1 105 A/cm2. This result is consistent with our previous report on Ti-doped MgB2 bulk superconductor, where Jc(0) was improved by refining MgB2 grains and forming a strongly-coupled nanoparticle structure [6]. For C–Ti-doped sample, the Jc of this sample is lower than that of Ti-doped sample in magnetic field from 0 to 2 T, but, in higher magnetic fields (>2 T), it is significantly improved and much higher than the Jc of Ti-doped sample. The in-field Jc of this sample is also higher than carbon-only-doped samples, including nano-carbon-doped-MgB2 [7] and CNT-doped MgB2 [8], in the high magnetic field region. At temperature of 20 K, the Jc reaches 1 104 A/cm2 in 4 T, and 4 103 in 5 T; and the irreversibility field determined from the closure of hysteresis loops with a criterion of 102 A/cm2 exceeds 6 T. The improvement of Jc and pinning behavior at 10 K and 5 K are also observed. Our results clearly show that the concurrently doping Ti and C in MgB2 is a feasible and effective route to further improve the superconducting performance of MgB2, especially at higher temperatures (20 K) and in higher fields (>3 T). In order to understand the pinning mechanism behind the enhanced Jc in the carbon-doped MgB2, the influence of ac and dc applied fields at various frequencies on the v0 (T) and v00 (T) has been studied and the results are illustrated in Fig. 2 for both the undoped and Ti-C-doped MgB2 samples. The superconducting transition temperature decreases with augmenting ac or dc field amplitude and the transition width broadens. On contrary, the transition undergoes a shift towards high temperature region upon augmenting the driven frequency as display in Fig. 2. By varying the dc applied field, the ac field amplitude as well as the driven
Fig. 4. ln U(j) versus ln Bac at different dc magnetic fields for: (a) MgB2 and (b) Mg0.95Ti0.05B1.95C0.05. The solid are linear fits for the data.
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Y. Yang et al. / Physica C 468 (2008) 1202–1205
while for Mg0.95Ti0.05B1.95C0.05, U(J) / j0.17. A reduction of c value reveals an enhanced performance in field ad demonstrated previously. The dependence of the pinning potential on dc applied field can be derived by using the relationship obtained in Fig. 4, the result in shown in Fig. 5. A UðBdc Þ / B0:96 dependence has been obtained for dc MgB2 co-doped by Ti and C, compared to UðBdc Þ / B1:41 in MgB2. It dc is known that in REBCO MTG samples, a UðBdc Þ / B0:5 dependence dc has been obtained, which demonstrated a relatively poor in field behaviour of MgB2 samples. However, strong enhancement of the high field pinning potential suggested largely ameliorated flux pinning behavior by the cooperation of Ti and C, which is in good agreement with the Jc H behavior shown in Fig. 1. According to the results shown in Figs. 3–5, the pinning potential for both pure and C–Ti-doped MgB2 can be described as: " UðT;j;Bdc Þ ¼ U 0 1 " UðT;j;Bdc Þ ¼ U 0 1
T T irr
T T irr
2 #2 ðBdc Þ
1:41
ðjÞ
ðBdc Þ
0:96
ðjÞ
2 #2
0:21
ðfor MgB2Þ;
0:17
ðfor Mg0:95 Ti0:05 B1:95 C0:05 Þ:
4. Conclusion
Fig. 5. ln U(B) versus ln Bdc at different ac magnetic field for: (a) MgB2 and (b) Mg0.95Ti0.05B1.95C0.05. The solid lines are linear fits for the data.
frequency, are able to investigate doping influence on the flux pinning potential, govern by Bdc, Bac and f. In flux dynamics, an approach has been proposed based on the Anderson-Kim flux creep model [9]. According to Blatter et al. [10], the relation can be written in the following form:
UðTÞ UðjÞUðBdc Þ ¼ ln f ln t; KT
ð1Þ
where U represents the pinning potential, T is the peak temperature in the imaginary part of ac susceptibility, K is the Bolzman constant, f is the driven frequency, t is the time scale. As obtained by Qin et al. [11], the dependence of the pinning potential on different variables can be summarized in the following form:
" UðT; j; Bdc Þ ¼ U 0
T 1 T irr
2 #a b c B j ; B0 j0
T UðTÞ ¼ 1 T irr
ð2Þ
2 #2 ;
Acknowledgements The authors are also grateful to the financial support of Australian Research Council (under Contract Nos. DP0559872, DP0452522, DP0881739). This work was also supported by National Natural Science Foundation of China (under Contract Nos. 50372052, and 50588201). References
where for MgB2, a = 2, i.e.
"
Flux pinning behavior of carbon and titanium concurrently doped MgB2 alloys has been studied by ac susceptibility and dc magnetization measurements. It is found that critical current density and irreversibility field of MgB2 have been significantly improved by doping C and Ti concurrently, sharply contrasted to the situation of C-only-doped or Ti-only-doped MgB2 samples. AC susceptibility measurement reveals that the dependence of the pinning potential on the dc applied field of Mg0.95Ti0.05B1.95C0.05 has been determined to be UðBdc Þ / B1 dc compared to that of MgB2 UðBdc Þ / B1:5 dc . As to the U(J) behavior, a relationship of U(J) / J0.17 is found fitting well for Mg0.95Ti0.05B1.95C0.05 with respect to U(J) / J0.21 for MgB2. All the results reveal a strong enhancement of the high field pinning potential in C and Ti co-doped MgB2.
ð3Þ
where Tirr represents the irreversible temperature. The relationship ln f U/KT is obtained by using this method, as shown in Fig. 3. As in Fig. 3, a linear fit has be conducted for both samples, according to which U(Bdc) U(j) can be determined at Bdc = 0.5 T. By varying the applied filed U(Bdc) U(j) was then derived. Fig. 4 displays the results of the calculations from Fig. 3. The linearity of In U(j) ln Bac, given the linearity between j and Bac, demonstrates an exponential dependence of U(j) on j at different dc applied field. A relationship U(J) / j0.21 has been found for MgB2 pure sample,
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