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Concurrent doping effect of Ti and nano-diamond on flux pinning of MgB2
Physica C 470 (2010) 1096–1099
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Physica C journal homepage: www.elsevier.com/locate/physc
Concurrent doping effect of Ti and nano-diamond on flux pinning of MgB2 Y. Zhao a,b,*, C. Ke a, C.H. Cheng b, Y. Feng c,d, Y. Yang a, P. Munroe b a Key Laboratory of Magnetic Levitation and Maglev Trains (Ministry of Education of China), Superconductivity R&D Center (SRDC), Mail Stop 165#, Southwest Jiaotong University, Chengdu, Sichuan 610031, China b Superconductivity Research Group, 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
a r t i c l e
i n f o
Article history: Available online 31 May 2010 Keywords: MgB2 Nano-diamond doping Critical current density Flux pinning
a b s t r a c t Nano-diamond and titanium concurrently doped MgB2 nanocomposites have been prepared by solid state reaction method. The effects of carbon and Ti concurrent doping on Jc–H behavior and pinning force scaling features of MgB2 have been investigated. Although Tc was slightly depressed, Jc of MgB2 have been significantly improved by the nano-diamond doping, especially in the high field region. In the mean time, the Jc value in low field region is sustained though concurrent Ti doping. Microstructure analysis reveals that when nano-diamond was concurrently doped with titanium in MgB2, a unique nanocomposite in which TiB2 forms a thin layer surrounding MgB2 grains whereas nano-diamond particles were wrapped inside the MgB2 grains. Besides, nano-diamond doping results in a high density stress field in the MgB2 samples, which may take responsibility for the Dj pinning behavior in the carbon-doped MgB2 system. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Since the discovery of superconductivity at 39 K in MgB2 [1], significant progress has been made in improving the performance of MgB2 materials. However, the realization of large-scale application for MgB2-based superconductivity technology essentially relies on the improvement of the pinning behavior of MgB2 in high magnetic fields. Among many methods to improve the performance of the material, alloying with carbon seems to be the most effective to improve the Hc2 by shorting the mean free length of electron [1,2], and by introducing extra pinning centers if nanodiamond was used as the carbon source [3,4]. However, the advantage of carbon doping was partially balanced by the grain boundary (GB) weak-link problem caused by the segregation of carbon in the GB area, leading to the decreasing of Jc in low field region [5]. In order to solved problem mentioned above, Ti and carbon concurrent doping was developed [6,7]. The experimental results clearly reveal that carbon and Ti concurrent-doping is largely cooperative in improving the performance of MgB2 in the high magnetic fields (>3 T) and at high temperature (>20 K). A mechanism is consequently proposed that carbon doping improves the electron scattering, thus enhances Hc2 of MgB2, and at the same time, Ti doping improve the MgB2 grain connection. This explanation sounds rea* Corresponding author at: Key Laboratory of Magnetic Levitation 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 87600787. E-mail address: [email protected] (Y. Zhao). 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.05.045
sonable, but experimental evidence is necessary to confirm the real mechanism, especially from both the physical behavior and the microstructure analyses. For this purpose, Ti and nano-diamond are used as dopants to concurrently dope the MgB2, and the flux-pinning behavior is then investigated. Microstructure analysis reveals that nano-diamond and titanium concurrently doped MgB2 form a unique nanocomposites in which TiB2 forms a thin layer surrounding MgB2 grains whereas nano-diamond particles were wrapped inside the MgB2 grains. The nano-diamond doping also leads to the formation of the high density stress field in the MgB2 samples, which may be the main reason for the Dj pinning behavior for the carbon-doped MgB2 material. 2. Experimental details Experimental results showed that the optimum doping level of nanocarbon in improving the Jc and Hirr of MgB2 is 5 at.% [8,9]. In order to reveal the cooperative doping effect of Ti and C in MgB2, Mg1xTixB2yCz alloys of four typical compositions have been paid intensive attention. These samples include Mg0.95Ti0.05B2 (denoted as Ti-doped), MgB1.95C0.07 (denoted as C-doped), Mg0.95Ti0.05B1.95C0.07 (denoted as C–Ti-doped), and undoped MgB2. Pellets of all these samples were synthesized by a solid state reaction, which has been previously described in detail [7], at ambient pressure with the starting materials of amorphous B powder (99.9%), Mg powder (99.9%), Ti powder (99.99%), and nano-diamond (99.9%). The mean particle sizes of magnesium and boron were approxi-
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mately 1 lm and 50 nm, respectively; the Ti powder is in sub-micron, and the nano-diamond is about 10–20 nm. Mixtures of magnesium, boron, nano-diamond, and/or Ti powders were well ground in a glove box for 1 h and then uniaxially pressed into pellets of a diameter of 10 mm, sealed in iron tubes, and sintered at 750 °C for 1 h in flowing high purity Ar. Then the samples were quenched to room temperature in liquid nitrogen. The content of nano-diamond was chosen to be 7% other than 5% in order to achieve both carbon doping and carbon addition effects in the samples. The crystal structure was investigated by powder X-ray diffraction (XRD) using an X’pert MRD diffractometer with Cu Ka radiation. Microstructure was analyzed with a Philips field emission gun transmission electron microscope (FEGTEM). DC magnetization measurements were performed in a Physical Properties Measurement System (PPMS, Quantum Design). Sample with a size of 2 2 1 mm3 were shaped for magnetic measurements. Critical current density, Jc, values were deduced from the hysteresis loop using the Bean model. The values of the irreversibility field, Hirr, were determined from the closure of hysteresis loops with a criterion of 102 A/cm2.
3. Results and discussion Fig. 1 shows the Jc(H) curves at 20 K for these four MgB2 samples. The mid-point superconductivity transition temperatures, Tc, for these four samples are 37.8, 37.2, 35.1, and 34.8 K, respectively for the undoped, Ti-doped, C-doped, and Ti–C-doped MgB2. The undoped sample has a highest zero-field Jc(0) but a smallest irreversibility field, Hirr about 4 T. After doped with Ti, the Jc(0) is slightly decreases but the Hirr increases to about 5 T. For the nano-diamond-doped MgB2, the Jc–H behavior is further improved with higher Jc in high magnetic field and higher irreversibility field. Compared with the 5% C-doped MgB2 [10], the present sample with 2% extra nano-diamond has better performance, due to the concurrent effects of carbon doping and carbon addition. However, the Jc in the low field is drastically suppressed due to the possible weak-link grain boundaries [5] as well as the suppression effect on Tc of carbon doping. The more interesting is for the Ti and C codoped MgB2: not only have the high-field Jc and Hirr been significantly improved, but also does the low-field Jc maintain a high-level value similar to that of the Ti-doped MgB2. At 20 K, the bulk
Fig. 1. Field dependence of Jc at 20 K for the four types of the samples. Inset: variation of the pinning force density with the applied field for these four types of the samples.
pinning force density, Fp(H) = l0HJc(H), reaches 2.3 G N m3 (see the inset of Fig. 1) for the undoped MgB2 and 1.9 G N m3 for Ti– C-doped one. The Fp(H) values are 1.2 and 1.6 G N m3 for the Cdoped and Ti-doped MgB2, respectively. The scaling behavior of the Fp(H) will be analyzed later in the paper. The Hirr–T relations for the four MgB2 samples are shown in Fig. 2. The Hirr(T) curves get steeper with dopant changes from Ti, to nano-diamond, and to the concurrent doping of both Ti and nano-diamond. For a comparison, the upper critical fields for the carbon doped and the non-carbon-doped MgB2 are very different. This difference is almost independent of the Ti doping, indicating that carbon affects the electron scattering in MgB2 but Ti only affects the flux-pinning behavior [7]. Fig. 3 shows the scaling behavior of Fp(H/Hirr)/Fp,max H/Hirr for these four samples. Generally, all of these four samples have a similar scaling behavior to the Kramer theory [11], which gives:
F p;Kramer ðhÞ ¼ F p =F p;max / h
1=2
ð1 hÞ2 ;
ð1Þ
where h = H/Hirr is the reduced field, Fp/Fp,max is the normalized pinning force density, and Fp,max is the maximum pinning force density. However, quantitatively, the scaling behavior for each sample has a deviation from the Kramer theory to a different degree. In order to understand the mechanism of the difference between these samples, we use the direct summation of elementary pinning forces [12] to analyze their scaling behavior. According to Dew–Hughes theory [12], the general expression for the normalized pinning force density is expressed as: p
F p ðhÞ ¼ F p =F p;max / h ð1 hÞq ;
ð2Þ
where parameters p and q are material constants. There are six different pinning cases describing the elementary pinning force using Eq. (2) with: (1) p = 0, q = 2: normal core pinning, volume pins, the peak position is at hp = 0; (2) p = 1, q = 1: Dk-pinning, volume pins, the peak position is at hp = 0.5; (3) p = 1/2, q = 2: normal core pinning, surface pins, the peak position is at hp = 0.2; (4) p = 3/2, q = 1: Dk-pinning, surface pins, the peak position is at hp = 0.6; (5) p = 1, q = 2: normal core pinning, point pins, the peak position is at hp = 0.33; and (6) p = 2, q = 1: Dk-pinning, point pins, the peak position is at hp = 0.67. Case (3) is predicted by Kramer [11] in the case of surface pins.
Fig. 2. Irreversibility lines for the four types of the samples in this study.
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Fig. 3. The reduced flux-pinning force density as a function of reduced magnetic field for the four types of the samples in this study. The fitting curve with Cheng’s mode is done at p0 = 3/2, q0 = 1, Dh = 0.1, and w = 0.10. Inset shows the shape changes of Fp/Fp,max–h curve with different combination of second type of pinning mechanism, in which the line 4 is Kramer theory.
For MgB2 system, there are may be several doping effects coexistence, which affects the pinning behavior in an intrinsically different way. For example, the main pining source in MgB2 is the surface pinning [13–15]. When carbon is doped in MgB2 the Hc2 will be significantly enhanced, which consequently enhances the Hirr. The increase of Hirr may push the peak of Fp(hr)/Fp,max–h curve shifting towards the smaller h value. In addition, nanoscale pinning centers may works as another strong pinning source, which may shift the peak of Fp(hr)/Fp,max–h curve towards higher h value. The two effects may compensate each other to a certain extend. Cheng et al. [10] have developed a model to comprehensively understand the combination of these effects, which gives: p0
F p ðhÞ / wF p;Kramer ðh þ DhÞ þ ð1 wÞh ð1 hÞq
0
0
wF p;Kramer ðhÞ þ wDhF p;Kramer ðhÞ p0
q0
þ ð1 wÞh ð1 hÞ ðwith Dh < h < 1 DhÞ ðnÞ F p;Kramer ðhÞ 0
dn dxn
mechanism. With a fixed Dh of 0.05, when the contribution weight of the extra pinning strength, (1 w), increase from 0.1 to 0.5, the Fp(h)/Fp,max–h curve described by Eq. (3) shifts from left to right, in which the curve with (1 w) = 0.25 fits the Kramer theory best. This indicates that the contribution weight of the extra pinning strength must reach to about 25% in order to compensate the peak-shift toward left caused by the effect of 5% increase of Dh. Therefore, when Dh is large, the deviation of the Fp(h)/Fp,max–h curve from the Kramer theory is hard to be compensated by another type of pinning mechanism. In order to further understand the mechanism of the experimental results mentioned above, we investigated the microstructure of these samples. Fig. 4 shows the typical TEM picture for the nano-diamond-doped MgB2 samples, which mainly consists of two kinds of nanoparticles: MgB2 grains with a size of 50– 100 nm and diamond particles with a size of 10–20 nm. This may be attributed to the nano-diamond-additive effect [4] which forms a typical nanocomposite material. The nano-diamond particles are inserted into the MgB2 grains. As the ab-plane coherence length of MgB2 is about 6–7 nm [16], these 10- to 20-nm-sized diamond inclusions, with a high density, are ideal flux pinning centres and are responsible for the better performance in the samples. Fig. 5 gives high resolution TEM results for these samples. In undoped MgB2, the typical lattice structure looks almost perfect (see Fig. 5a). For the carbon-doped sample, local lattice distortion can be found (see Fig. 5b). Near the nano-diamond particles inserted in the MgB2 matrix, high density of stress field is observed. Both the lattice distortion and stress field may be the source of the Dj pinning since they will lead to strong electron scattering in the system. For Ti–C-doped sample, it is observed that TiB2 forms a thin layer surrounding MgB2 sub-grain. This is very similar to the nano-composite structure which was first found in the Ti-doped MgB2 [14]. All of these together reveal that when nano-diamond was concurrently doped with titanium in MgB2, a unique nanocomposites in which TiB2 forms a thin layer surrounding MgB2 grains whereas carbon-doping-induced stress or nano-diamond particles were wrapped inside the MgB2 grains. The observed high density stress field in the MgB2 samples may take responsibility for the Dj pinning behavior in these carbon-doped MgB2 system.
ð3Þ
where ¼ F p;Kramer jx¼h is the nth derivative of Fp,Kramer(h); p0 and q take the value not the same as what in the Kramer theory; w (0 6 w 6 1) represents the relative contribution of Kramer-type pinning and other type of pinning mechanism; Dh is the increase of h by the second pinning independent of the Kramer-type surface pinning. In the case of point pins with Dj pinning, p0 and q0 take 2 and 1, respectively. As shown in Fig. 3, the Fp(h)/Fp,max–h data for the undoped MgB2 can be well fitted with the Kramer theory. The data for the Tidoped one can be well fitted with Cheng’s model of Eq. (3) with p0 = 3/2, q0 = 1, Dh = 0.1, and w = 0.10, i.e., the combination of Kramer-type pinning with the Dj surface pinning. For the nano-diamond-doped and Ti–C-doped samples, the deviation from the Kramer theory is so large and may not be described by the Cheng’s model which is based on the small perturbation (Dh h). We attribute the large deviation from the Kramer theory in the nanodiamond-doped and Ti–C-doped samples to a relatively large enhancement of Hirr. This may significantly distort the shape of the Fp(h)/Fp,max–h curve from the Kramer theory, which cannot be easily compensated by considering another type of pinning mechanism as proposed by Cheng et al. [10]. In order to understand the compensation of Dh effect with the additional pinning effect, we made a calculation based on a series of combination of Dh and w values (see the inset of Fig. 3). In this calculation we also chose p0 = 3/2, q0 = 1, i.e., the Dj surface pinning as the addition pinning
4. Conclusions In this work, nano-diamond and titanium concurrently doped MgB2 nanocomposites have been prepared by solid state reaction method. The effects of carbon and Ti concurrent doping on Jc–H
Fig. 4. FEGTEM micrographs for Ti–C-doped MgB2.
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Fig. 5. HRTEM micrographs for the typical samples used in this study: (a) undoped MgB2; (b) nano-diamond-doped MgB2; (c) stress field near the nano-diamond particles in Ti–C-doped MgB2; and (d) sub-grain structure in Ti–C-doped MgB2.
behavior and pinning force scaling features of MgB2 have been investigated. It is observed that Jc of MgB2 have been significantly improved in the high field region by nano-diamond doping, and a good value of Jc in low field region is sustained by Ti doping. The microstructure analysis reveals that when nano-diamond was concurrently doped with titanium in MgB2, a unique nanocomposite in which TiB2 forms a thin layer surrounding MgB2 grains (EDS analysis reveals that Ti mainly exists in the grain boundary region, not shown here) whereas nano-diamond particles were wrapped inside the MgB2 grains. Besides, nano-diamond doping results in a high density stress field in the MgB2 samples, which may take responsibility for the Dj pinning behavior in the carbon-doped MgB2 system. Acknowledgements This work was supported by the National Natural Science Foundation of China (Nos. 50588201 and 50872116), National High-Tech Research Program of China (863 program, No. 2007AA03Z203), the PCSIRT of the Ministry of Education of China (IRT0751), the Specialized Research Fund for the Doctoral Program of Higher Education (200806130023), the Australian Research Council (Nos. DP0559872 and DP0881739), and the University of New South Wales (Goldstar Award).
References [1] A. Gurevich, Phys. Rev. B 67 (2003) 184515. [2] A. Gurevich, S. Patnaik, V. Braccini, K.H. Kim, C. Mielke, X. Song, L. DCooley, 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] Y. Zhao, C.H. Cheng, X.F. Rui, H. Zhang, P. Munroe, H.M. Zeng, N. Koshizuka, M. Murakami, Appl. Phys. Lett. 83 (2003) 2916. [4] C.H. Cheng, H. Zhang, Y. Zhao, Y. Feng, X.F. Rui, P. Munroe, H.M. Zeng, N. Koshizuka, M. Murakami, Supercond. Sci. Technol. 16 (2003) 1182. [5] A. Matsumoto, H. Kitaguchi, H. Kumakura, Supercond. Sci. Technol. 21 (2008) 065007. [6] Y. Zhao, Y. Feng, T.M. Shen, G. Li, Y. Yang, C.H. Cheng, J. Appl. Phys. 100 (2006) 123902. [7] T.M. Shen, G. Li, C.H. Cheng, Y. Zhao, Supercond. Sci. Technol. 19 (2006) 1219. [8] S. Soltanian, J. Horvat, X.L. Wang, P. Munroe, S.X. Dou, Physica C 390 (2003) 185. [9] S.X. Dou, W.K. Yeoh, J. Horvat, M. Ionescu, Appl. Phys. Lett. 83 (2003) 996. [10] C.H. Cheng, Y. Yang, P. Munroe, Y. Zhao, Supercond. Sci. Technol. 20 (2007) 296. [11] E.J. Kramer, J. Appl. Phys. 44 (1973) 1360. [12] D. Dew-Hughes, Philos. Mag. 30 (1974) 293. [13] Y. Zhao, Y. Feng, C.H. Cheng, L. Zhou, Y. Wu, T. Machi, Y. Fudamoto, N. Koshizuka, M. Murakami, Appl. Phys. Lett. 79 (2001) 1154. [14] Y. Zhao, D.X. Huang, Y. Feng, C. Cheng, T. Machi, N. Koshizuka, M. Murakami, Appl. Phys. Lett. 80 (2002) 1640. [15] Y. Zhao, Y. Feng, T. Machi, C.H. Cheng, D.X. Huang, Y. Fudamoto, N. Koshizuka, M. Murakami, Europhys. Lett. 57 (2002) 437. [16] M. Xu, H. Kitazawa, Y. Takano, J. Ye, K. Nishida, H. Abe, A. Matsushita, N. Tsujii, G. Kido, Appl. Phys. Lett. 79 (2001) 2779.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Concurrent doping effect of Ti and nano-diamond on flux pinning of MgB2 Y. Zhao a,b,*, C. Ke a, C.H. Cheng b, Y. Feng c,d, Y. Yang a, P. Munroe b a Key Laboratory of Magnetic Levitation and Maglev Trains (Ministry of Education of China), Superconductivity R&D Center (SRDC), Mail Stop 165#, Southwest Jiaotong University, Chengdu, Sichuan 610031, China b Superconductivity Research Group, 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
a r t i c l e
i n f o
Article history: Available online 31 May 2010 Keywords: MgB2 Nano-diamond doping Critical current density Flux pinning
a b s t r a c t Nano-diamond and titanium concurrently doped MgB2 nanocomposites have been prepared by solid state reaction method. The effects of carbon and Ti concurrent doping on Jc–H behavior and pinning force scaling features of MgB2 have been investigated. Although Tc was slightly depressed, Jc of MgB2 have been significantly improved by the nano-diamond doping, especially in the high field region. In the mean time, the Jc value in low field region is sustained though concurrent Ti doping. Microstructure analysis reveals that when nano-diamond was concurrently doped with titanium in MgB2, a unique nanocomposite in which TiB2 forms a thin layer surrounding MgB2 grains whereas nano-diamond particles were wrapped inside the MgB2 grains. Besides, nano-diamond doping results in a high density stress field in the MgB2 samples, which may take responsibility for the Dj pinning behavior in the carbon-doped MgB2 system. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Since the discovery of superconductivity at 39 K in MgB2 [1], significant progress has been made in improving the performance of MgB2 materials. However, the realization of large-scale application for MgB2-based superconductivity technology essentially relies on the improvement of the pinning behavior of MgB2 in high magnetic fields. Among many methods to improve the performance of the material, alloying with carbon seems to be the most effective to improve the Hc2 by shorting the mean free length of electron [1,2], and by introducing extra pinning centers if nanodiamond was used as the carbon source [3,4]. However, the advantage of carbon doping was partially balanced by the grain boundary (GB) weak-link problem caused by the segregation of carbon in the GB area, leading to the decreasing of Jc in low field region [5]. In order to solved problem mentioned above, Ti and carbon concurrent doping was developed [6,7]. The experimental results clearly reveal that carbon and Ti concurrent-doping is largely cooperative in improving the performance of MgB2 in the high magnetic fields (>3 T) and at high temperature (>20 K). A mechanism is consequently proposed that carbon doping improves the electron scattering, thus enhances Hc2 of MgB2, and at the same time, Ti doping improve the MgB2 grain connection. This explanation sounds rea* Corresponding author at: Key Laboratory of Magnetic Levitation 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 87600787. E-mail address: [email protected] (Y. Zhao). 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.05.045
sonable, but experimental evidence is necessary to confirm the real mechanism, especially from both the physical behavior and the microstructure analyses. For this purpose, Ti and nano-diamond are used as dopants to concurrently dope the MgB2, and the flux-pinning behavior is then investigated. Microstructure analysis reveals that nano-diamond and titanium concurrently doped MgB2 form a unique nanocomposites in which TiB2 forms a thin layer surrounding MgB2 grains whereas nano-diamond particles were wrapped inside the MgB2 grains. The nano-diamond doping also leads to the formation of the high density stress field in the MgB2 samples, which may be the main reason for the Dj pinning behavior for the carbon-doped MgB2 material. 2. Experimental details Experimental results showed that the optimum doping level of nanocarbon in improving the Jc and Hirr of MgB2 is 5 at.% [8,9]. In order to reveal the cooperative doping effect of Ti and C in MgB2, Mg1xTixB2yCz alloys of four typical compositions have been paid intensive attention. These samples include Mg0.95Ti0.05B2 (denoted as Ti-doped), MgB1.95C0.07 (denoted as C-doped), Mg0.95Ti0.05B1.95C0.07 (denoted as C–Ti-doped), and undoped MgB2. Pellets of all these samples were synthesized by a solid state reaction, which has been previously described in detail [7], at ambient pressure with the starting materials of amorphous B powder (99.9%), Mg powder (99.9%), Ti powder (99.99%), and nano-diamond (99.9%). The mean particle sizes of magnesium and boron were approxi-
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mately 1 lm and 50 nm, respectively; the Ti powder is in sub-micron, and the nano-diamond is about 10–20 nm. Mixtures of magnesium, boron, nano-diamond, and/or Ti powders were well ground in a glove box for 1 h and then uniaxially pressed into pellets of a diameter of 10 mm, sealed in iron tubes, and sintered at 750 °C for 1 h in flowing high purity Ar. Then the samples were quenched to room temperature in liquid nitrogen. The content of nano-diamond was chosen to be 7% other than 5% in order to achieve both carbon doping and carbon addition effects in the samples. The crystal structure was investigated by powder X-ray diffraction (XRD) using an X’pert MRD diffractometer with Cu Ka radiation. Microstructure was analyzed with a Philips field emission gun transmission electron microscope (FEGTEM). DC magnetization measurements were performed in a Physical Properties Measurement System (PPMS, Quantum Design). Sample with a size of 2 2 1 mm3 were shaped for magnetic measurements. Critical current density, Jc, values were deduced from the hysteresis loop using the Bean model. The values of the irreversibility field, Hirr, were determined from the closure of hysteresis loops with a criterion of 102 A/cm2.
3. Results and discussion Fig. 1 shows the Jc(H) curves at 20 K for these four MgB2 samples. The mid-point superconductivity transition temperatures, Tc, for these four samples are 37.8, 37.2, 35.1, and 34.8 K, respectively for the undoped, Ti-doped, C-doped, and Ti–C-doped MgB2. The undoped sample has a highest zero-field Jc(0) but a smallest irreversibility field, Hirr about 4 T. After doped with Ti, the Jc(0) is slightly decreases but the Hirr increases to about 5 T. For the nano-diamond-doped MgB2, the Jc–H behavior is further improved with higher Jc in high magnetic field and higher irreversibility field. Compared with the 5% C-doped MgB2 [10], the present sample with 2% extra nano-diamond has better performance, due to the concurrent effects of carbon doping and carbon addition. However, the Jc in the low field is drastically suppressed due to the possible weak-link grain boundaries [5] as well as the suppression effect on Tc of carbon doping. The more interesting is for the Ti and C codoped MgB2: not only have the high-field Jc and Hirr been significantly improved, but also does the low-field Jc maintain a high-level value similar to that of the Ti-doped MgB2. At 20 K, the bulk
Fig. 1. Field dependence of Jc at 20 K for the four types of the samples. Inset: variation of the pinning force density with the applied field for these four types of the samples.
pinning force density, Fp(H) = l0HJc(H), reaches 2.3 G N m3 (see the inset of Fig. 1) for the undoped MgB2 and 1.9 G N m3 for Ti– C-doped one. The Fp(H) values are 1.2 and 1.6 G N m3 for the Cdoped and Ti-doped MgB2, respectively. The scaling behavior of the Fp(H) will be analyzed later in the paper. The Hirr–T relations for the four MgB2 samples are shown in Fig. 2. The Hirr(T) curves get steeper with dopant changes from Ti, to nano-diamond, and to the concurrent doping of both Ti and nano-diamond. For a comparison, the upper critical fields for the carbon doped and the non-carbon-doped MgB2 are very different. This difference is almost independent of the Ti doping, indicating that carbon affects the electron scattering in MgB2 but Ti only affects the flux-pinning behavior [7]. Fig. 3 shows the scaling behavior of Fp(H/Hirr)/Fp,max H/Hirr for these four samples. Generally, all of these four samples have a similar scaling behavior to the Kramer theory [11], which gives:
F p;Kramer ðhÞ ¼ F p =F p;max / h
1=2
ð1 hÞ2 ;
ð1Þ
where h = H/Hirr is the reduced field, Fp/Fp,max is the normalized pinning force density, and Fp,max is the maximum pinning force density. However, quantitatively, the scaling behavior for each sample has a deviation from the Kramer theory to a different degree. In order to understand the mechanism of the difference between these samples, we use the direct summation of elementary pinning forces [12] to analyze their scaling behavior. According to Dew–Hughes theory [12], the general expression for the normalized pinning force density is expressed as: p
F p ðhÞ ¼ F p =F p;max / h ð1 hÞq ;
ð2Þ
where parameters p and q are material constants. There are six different pinning cases describing the elementary pinning force using Eq. (2) with: (1) p = 0, q = 2: normal core pinning, volume pins, the peak position is at hp = 0; (2) p = 1, q = 1: Dk-pinning, volume pins, the peak position is at hp = 0.5; (3) p = 1/2, q = 2: normal core pinning, surface pins, the peak position is at hp = 0.2; (4) p = 3/2, q = 1: Dk-pinning, surface pins, the peak position is at hp = 0.6; (5) p = 1, q = 2: normal core pinning, point pins, the peak position is at hp = 0.33; and (6) p = 2, q = 1: Dk-pinning, point pins, the peak position is at hp = 0.67. Case (3) is predicted by Kramer [11] in the case of surface pins.
Fig. 2. Irreversibility lines for the four types of the samples in this study.
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Fig. 3. The reduced flux-pinning force density as a function of reduced magnetic field for the four types of the samples in this study. The fitting curve with Cheng’s mode is done at p0 = 3/2, q0 = 1, Dh = 0.1, and w = 0.10. Inset shows the shape changes of Fp/Fp,max–h curve with different combination of second type of pinning mechanism, in which the line 4 is Kramer theory.
For MgB2 system, there are may be several doping effects coexistence, which affects the pinning behavior in an intrinsically different way. For example, the main pining source in MgB2 is the surface pinning [13–15]. When carbon is doped in MgB2 the Hc2 will be significantly enhanced, which consequently enhances the Hirr. The increase of Hirr may push the peak of Fp(hr)/Fp,max–h curve shifting towards the smaller h value. In addition, nanoscale pinning centers may works as another strong pinning source, which may shift the peak of Fp(hr)/Fp,max–h curve towards higher h value. The two effects may compensate each other to a certain extend. Cheng et al. [10] have developed a model to comprehensively understand the combination of these effects, which gives: p0
F p ðhÞ / wF p;Kramer ðh þ DhÞ þ ð1 wÞh ð1 hÞq
0
0
wF p;Kramer ðhÞ þ wDhF p;Kramer ðhÞ p0
q0
þ ð1 wÞh ð1 hÞ ðwith Dh < h < 1 DhÞ ðnÞ F p;Kramer ðhÞ 0
dn dxn
mechanism. With a fixed Dh of 0.05, when the contribution weight of the extra pinning strength, (1 w), increase from 0.1 to 0.5, the Fp(h)/Fp,max–h curve described by Eq. (3) shifts from left to right, in which the curve with (1 w) = 0.25 fits the Kramer theory best. This indicates that the contribution weight of the extra pinning strength must reach to about 25% in order to compensate the peak-shift toward left caused by the effect of 5% increase of Dh. Therefore, when Dh is large, the deviation of the Fp(h)/Fp,max–h curve from the Kramer theory is hard to be compensated by another type of pinning mechanism. In order to further understand the mechanism of the experimental results mentioned above, we investigated the microstructure of these samples. Fig. 4 shows the typical TEM picture for the nano-diamond-doped MgB2 samples, which mainly consists of two kinds of nanoparticles: MgB2 grains with a size of 50– 100 nm and diamond particles with a size of 10–20 nm. This may be attributed to the nano-diamond-additive effect [4] which forms a typical nanocomposite material. The nano-diamond particles are inserted into the MgB2 grains. As the ab-plane coherence length of MgB2 is about 6–7 nm [16], these 10- to 20-nm-sized diamond inclusions, with a high density, are ideal flux pinning centres and are responsible for the better performance in the samples. Fig. 5 gives high resolution TEM results for these samples. In undoped MgB2, the typical lattice structure looks almost perfect (see Fig. 5a). For the carbon-doped sample, local lattice distortion can be found (see Fig. 5b). Near the nano-diamond particles inserted in the MgB2 matrix, high density of stress field is observed. Both the lattice distortion and stress field may be the source of the Dj pinning since they will lead to strong electron scattering in the system. For Ti–C-doped sample, it is observed that TiB2 forms a thin layer surrounding MgB2 sub-grain. This is very similar to the nano-composite structure which was first found in the Ti-doped MgB2 [14]. All of these together reveal that when nano-diamond was concurrently doped with titanium in MgB2, a unique nanocomposites in which TiB2 forms a thin layer surrounding MgB2 grains whereas carbon-doping-induced stress or nano-diamond particles were wrapped inside the MgB2 grains. The observed high density stress field in the MgB2 samples may take responsibility for the Dj pinning behavior in these carbon-doped MgB2 system.
ð3Þ
where ¼ F p;Kramer jx¼h is the nth derivative of Fp,Kramer(h); p0 and q take the value not the same as what in the Kramer theory; w (0 6 w 6 1) represents the relative contribution of Kramer-type pinning and other type of pinning mechanism; Dh is the increase of h by the second pinning independent of the Kramer-type surface pinning. In the case of point pins with Dj pinning, p0 and q0 take 2 and 1, respectively. As shown in Fig. 3, the Fp(h)/Fp,max–h data for the undoped MgB2 can be well fitted with the Kramer theory. The data for the Tidoped one can be well fitted with Cheng’s model of Eq. (3) with p0 = 3/2, q0 = 1, Dh = 0.1, and w = 0.10, i.e., the combination of Kramer-type pinning with the Dj surface pinning. For the nano-diamond-doped and Ti–C-doped samples, the deviation from the Kramer theory is so large and may not be described by the Cheng’s model which is based on the small perturbation (Dh h). We attribute the large deviation from the Kramer theory in the nanodiamond-doped and Ti–C-doped samples to a relatively large enhancement of Hirr. This may significantly distort the shape of the Fp(h)/Fp,max–h curve from the Kramer theory, which cannot be easily compensated by considering another type of pinning mechanism as proposed by Cheng et al. [10]. In order to understand the compensation of Dh effect with the additional pinning effect, we made a calculation based on a series of combination of Dh and w values (see the inset of Fig. 3). In this calculation we also chose p0 = 3/2, q0 = 1, i.e., the Dj surface pinning as the addition pinning
4. Conclusions In this work, nano-diamond and titanium concurrently doped MgB2 nanocomposites have been prepared by solid state reaction method. The effects of carbon and Ti concurrent doping on Jc–H
Fig. 4. FEGTEM micrographs for Ti–C-doped MgB2.
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Fig. 5. HRTEM micrographs for the typical samples used in this study: (a) undoped MgB2; (b) nano-diamond-doped MgB2; (c) stress field near the nano-diamond particles in Ti–C-doped MgB2; and (d) sub-grain structure in Ti–C-doped MgB2.
behavior and pinning force scaling features of MgB2 have been investigated. It is observed that Jc of MgB2 have been significantly improved in the high field region by nano-diamond doping, and a good value of Jc in low field region is sustained by Ti doping. The microstructure analysis reveals that when nano-diamond was concurrently doped with titanium in MgB2, a unique nanocomposite in which TiB2 forms a thin layer surrounding MgB2 grains (EDS analysis reveals that Ti mainly exists in the grain boundary region, not shown here) whereas nano-diamond particles were wrapped inside the MgB2 grains. Besides, nano-diamond doping results in a high density stress field in the MgB2 samples, which may take responsibility for the Dj pinning behavior in the carbon-doped MgB2 system. Acknowledgements This work was supported by the National Natural Science Foundation of China (Nos. 50588201 and 50872116), National High-Tech Research Program of China (863 program, No. 2007AA03Z203), the PCSIRT of the Ministry of Education of China (IRT0751), the Specialized Research Fund for the Doctoral Program of Higher Education (200806130023), the Australian Research Council (Nos. DP0559872 and DP0881739), and the University of New South Wales (Goldstar Award).
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