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Investigation of structure, specific heat and superconducting transition in Mg1−xAlxB2(x∼0.5)
Physica C 402 (2004) 335–340 www.elsevier.com/locate/physc
Investigation of structure, specific heat and superconducting transition in Mg1xAlxB2(x 0:5) J.Y. Xiang a, D.N. Zheng
a,*
, P.L. Lang a, Z.X. Zhao a, J.L. Luo
b
a
b
National Laboratory for Superconductivity, Institute of Physics & Center for Condensed Matter Physics, Chinese Academy of Sciences, P.O. Box 603-38, Beijing 100080, PeopleÕs Republic of China Laboratory of Extreme Condition Physics, Institute of Physics & Center for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, PeopleÕs Republic of China Received 6 October 2003; received in revised form 21 November 2003; accepted 28 November 2003
Abstract We have carried out structure, magnetic and specific heat measurements on aluminum doped magnetism diboride samples Mg1x Alx B2 in order to investigate possible superconductivity at the x ¼ 0:5 concentration. A diamagnetic signal was observed in magnetization measurements accompanied by a decrease in resistivity. However, the diamagnetic signal was extremely small as compared to what expected from full diamagnetism. Also, the transition both in magnetization and resistance was very broad. We propose that the diamagnetism is due to a very small amount of superconducting phase such as MgB2 and the resistive transition is due to the percolation behavior. Furthermore, we performed specific heat measurements, which are considered as a tool to investigate the bulk nature of superconducting transition, on the x ¼ 0:5 sample to verify the existence of superconductivity. We observed no evident superconducting transition in the entire temperature region from 2 to 300 K. The undistinguishable data between 0 and 5 T magnetic fields also indicated the absence of bulk superconductivity in the x ¼ 0:5 sample. 2003 Elsevier B.V. All rights reserved. PACS: 74.70.Ad; 74.25.Bt; 74.62.Dh Keywords: MgB2 ; Al substitution; Specific heat
1. Introduction Since the discovery of superconductivity in MgB2 [1], it has attracted considerable attention worldwide due to its high transition temperature (40 K). A lot of experimental and theoretical work has been performed in order to understand
*
Corresponding author. Fax: +86-10-8264-9531. E-mail address: [email protected] (D.N. Zheng).
the underlying mechanism and to explore potential applications. The research may also give some insight on the evolution of the theoretical description from conventional superconductors to the high temperature curprate superconductors. Now it is generally recognized that superconductivity in this material can be explained within the conventional BCS framework with a strong electron–phonon coupling. Experiments such as specific heat [2–4], tunneling spectrum [5] together with first principle calculations [6] have further
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.11.017
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confirmed that MgB2 is a fully gapped superconductor with two sheets of Fermi surface that correspond to the two gaps, respectively. For a new superconductor, partial chemical substitution is regarded as a good method for the study of its properties. Unfortunately, it has been found that the substitution of other elements into MgB2 both for Mg and B atoms is very difficult [7]. This is in sharp contrast to the situation in high temperature cuprate superconductors, where chemical substitution has played an important role in evolving the nature of superconductivity. Nevertheless, Al appears to be an exception since AlB2 has the same crystal structure as MgB2 and samples with Al doping level ranging from zero to one can be made. However, a study on the Al doping samples was shown that the structure of MgB2 was remarkably modified [8]. More detailed work focused on the ÔmodifiedÕ structure indicated that a superstructure is presented in high doping level samples. The superstructure may be attributed to the structure instability observed in X-ray diffraction patterns [9]. Initially, a simple model in which the Al and Mg layers arranged orderly in an alternate fashion, i.e., a structure with Mg–B–Al– B–Mg–B–Al–B staggered in c-axis direction, was suggested [10] although subsequent TEM work showed that more complex features were associated with the superstructure [11]. The ab initio calculations further confirmed the possibility of such a structure [12]. As for the effect on superconductivity, it was found that superconductivity was destroyed as Al was introduced and bulk superconductivity vanished at about 40% Al doping level (different cutoffs at which the bulk superconductivity vanished had been reported) [8,10,13]. At the low doping levels ðx < 0:1Þ, the decrease of TC with increasing of Al is mainly attributed to the reduction in the density of state at the Fermi surface [8,9,13,14] and Al substitution for Mg does not lead to pair breaking as suggested in Ref. [15]. A theoretical calculation suggested that superconductivity vanished at 60% of Al doping [12]. On the other hand, some published experiment data has shown a diamagnetic signal in the 50% Al doping level [10,16]. Thus it has been suggested that Mg0:5 Al0:5 B2 might have properties distinct to those with higher or lower doping lev-
els, and bulk superconductivity could exist in it. although at a relatively low temperature [10]. In order to further investigate the possible superconductivity in Mg0:5 Al0:5 B2 , we made a series of Mg1x Alx B2 samples. Care was taken during the fabrication process to ensure sample quality. Specific heat measurements, which is regarded as a useful tool for obtaining the nature of superconducting transition, were performed together with XRD, magnetization and resistivity measurements.
2. Experimental Al doped MgB2 samples were fabricated using a traditional solid-state reaction method. Powders of Al, Mg, B with nominal composition Mg1x Alx B2 were well mixed and pressed into pellets with 13 mm in diameter and about 1 g in weight. The pellets wrapped with a Ta foil were put into a cylinder made of high temperature stainless steel. The cylinder was sealed with a lid and a piece of Mg flake was also put inside to avoid Mg deficiency. The samples were then sintered in a tube furnace at 900 C for two hours and then cooled down to the room temperature. The process was repeated after grinding. The sintering was carried out in an H2 / Ar2 (4%/96%) atmosphere. The microstructure of the samples were characterized by XRD and found predominantly single phase with low level of MgB4 , B2 O3 and a minor amount of MgO as secondary phases. Oxygen contamination in the x ¼ 0:5 Al doping level sample is much less than that in the x ¼ 0 sample. It appears possible to avoid oxygen contamination by adopting such a fabrication process. The samples were then cut into rectangular bars with dimensions 12 · 3 · 3 mm3 . Magnetization measurements were carried out in a superconducting quantum interference device (SQUID) magnetometer (MPMS5, Quantum Design). A standard four-probe method was used for resistivity measurements. The current density used in the resistivity measurement was about 0.1 A/cm2 . The same piece of sample was used in both magnetization and resistivity measurements. The specific heat measurements were carried out in a Quantum Design PPMS system in which a relaxation technique was employed.
J.Y. Xiang et al. / Physica C 402 (2004) 335–340
3. Results and discussion Fig. 1 shows the X-ray diffraction patterns for the x ¼ 0 and 0.5 samples. The (0 0 2) and (1 1 0) peaks can be well fitted using the Lorenz distribution function as shown by the solid line in Fig. 1.
Fig. 1. (0 0 2) and (1 1 0) peak in the X-ray diffraction patterns of MgB2 with x ¼ 0 and 0.5 Al doping levels. The solid line is a Lorentz fitting for these peaks. Inset shows the 2h scan patterns from 20 to 80 of the two samples.
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The inset in Fig. 1 is the (h–2h) scan from 20 to 80. It indicates that both samples are predominantly single phase. Shown in Fig. 2 is the magnetization and resistivity data below 50 K as a function of temperature of the x ¼ 0:5 sample. The magnetization curve was obtained in a 1 mT magnetic field using zero field cooling. A weak diamagnetic signal appeared at about 38 K that could be attributed to the MgB2 impurity phase beyond the detection of XRD. The diamagnetic signal drops faster as the temperature decreased to about 10 K, indicates the possible appearances of superconductivity in this material, as suggested in Refs. [12,17]. However we noticed that the superconducting volume is much smaller than that in the x ¼ 0 sample as shown in the inset of Fig. 2. It is only about 0.04% of the superconducting volume of the x ¼ 0 sample at 4.5 K. Fig. 2 also shows the resistivity as a function of temperature. There is a small drop in the curves begin at about 13 K, and the change of resistivity from 13 K to roughly 4.6 K is approximately 2% of the value at 15 K. The magnitude of the resistivity drop varies between samples. In some cases, resistivity shows a rather large drop. The data above 15 K can be well
Fig. 2. The magnetization and resistivity as a function of temperature of the x ¼ 0:5 Al doped sample. Magnetization was measured in 1 mT magnetic field using zero field cooling (ZFC) procedure. The right side inset shows the full resistivity transition. The open circle is the experiment, data and the solid line is the fitted data using an expression a þ bT 2 (see the text). For a comparison, the magnetization curve of undoped MgB2 is also shown in the left side inset.
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fitted by an expression qðT Þ ¼ a þ bT 2 , as the solid line shown in the inset, of Fig. 2, with a ¼ 451 and b ¼ 0:0089, respectively. The appearance of resistivity drop and diamagnetic signal appears to suggest the existence of superconductivity. Indeed, in Refs. [10,16], the authors proposed that MgAlB4 phase is superconducting. Also, other properties such as Raman spectra show that MgAlB4 is different from others [10,13,17]. The consistency of the data below 20 K between the magnetization measurement and transportation measurement may be explained as the possible existence of superconductivity. However, the magnitude of the diamagnetic signal is so small and the absence of zero-resistance makes such claimant doubtful. One possible explanation is that the superconducting grains are not well connected and the grain boundaries are weak-links or even non-superconducting. In such cases, if the grain size is small as compared to the penetration depth, the diamagnetic signal would be very small. The absence of zero-resistivity could be attributed to the porosity and weak-link nature of in this sample. On the other hand, there could be other explanations. The very small diamagnetic signal might imply that the superconducting phase have a very small volume fraction and is not the major phase. In other words, the Mg0:5 Al0:5 B2 phase is not superconducting. The resistivity drop is probably caused by the percolation effect. We have performed resistivity measurements with different applied currents in order to check if the resistivity drop shift to lower temperatures as would be expected from the percolation effect explanation. However, we did not observe such a shift. This could be due to the fact that the non-superconducting Mg0:5 Al0:5 B2 phase is metallic and shows a resistivity value comparable with MgB2 . In order to further confirm the properties of the x ¼ 0:5 sample, we carried out specific heat measurements on the samples, i.e., the x ¼ 0 and 0.5 samples. If the x ¼ 0:5 phase is superconducting of bulk nature, we would expect changes in specific heat. Fig. 3 shows the total specific heat as a function of temperature for the x ¼ 0 and 0.5 samples. A clear jump can be seen near 38 K for the x ¼ 0 sample, while no evident anomaly is ob-
Fig. 3. The total specific heat as a function of temperature for the (a) x ¼ 0 and (b) x ¼ 0:5 Al doped MgB2 samples at zero magnetic field. A clear jump can be seen in the x ¼ 0 sample, while no abnormality could be seen in the x ¼ 0:5 sample. The dash dot line is the Debye model plus an Einstein term fitting (Eq. (2)) and the solid line is the multiple Einstein optic vibration modes fitting (Eq. (3)). Inset of (a) is the low temperature part of specific heat data as a function of temperature, in which the phonon contribution fitted using different models was subtracted. The solid line is the results from Debye model, the solid square is representative of the fitting results using the multiple Einstein modes and the solid circle is the data in which the data of the x ¼ 0:5 sample have been subtracted.
served in the entire temperature range from 2 to 210 K for the doped sample. Furthermore, we performed measurements in a 5 T magnetic field on the x ¼ 0:5 sample and the results are shown in Fig. 4. The two sets of data are overlapped to each other very well. The inset of Fig. 4 shows the low temperature data. We calculated the difference of the 0 and 5 T data and found no difference within the experimental resolution between the specific heat data measured in the 0 and 5 T magnetic field. These results appear to further suggest that there is
J.Y. Xiang et al. / Physica C 402 (2004) 335–340
Fig. 4. The specific heat as a function of temperature square of MgB2 of the x ¼ 0:5 sample in 0 and 5 T magnetic fields. Inset shows the low temperature part of specific heat of 0 and 5 T magnetic field versus temperature square. The solid line in the graph represents the multiple Einstein vibration modes fitted data.
no bulk superconductivity in the Mg0:5 Al0:5 B2 sample. In order to obtain more information on how Al doping affects the properties in MgB2 , we also analyzed the specific heat data to make estimations on some important parameters such as Dybe temperature and the normal state electronic specific heat coefficient. It is known that the measured specific heat data consist of electronic and lattice vibration contributions. To separate these two contributions, we employed three approaches reported in the literature, in which the phonon contribution is described by a simplified Debye model [2], Debye term plus an Einstein term [18] and multi-Einstein-mode [3], respectively. The corresponding equations are: CðT Þ ¼ cn T þ bT 3 þ dT 5 ; HD HE CðT Þ ¼ cn T þ 3RfD þ f 3RfE ; T T CðT Þ ¼ cn T þ 3R
8 X 0
pi fE
x i
T
;
ð1Þ ð2Þ
ð3Þ
Rx 2 where fD ðxÞ ¼ 3x3 0 y 4 ey ðey 1Þ dy and fE ðxÞ ¼ 2 2 x x x e ðe 1Þ . Here cn is the normal state elec-
339
tronic specific heat coefficient, HD and HE is the Debye and Einstein temperature, respectively. b, d, f and pi are the fitting parameters. The parameter f in Eq. (2) was used to adjusts the ratio between the two Pterms. A limitation condition for pi in Eq. (3) is i pi ¼ 1. In Eq. (2), an Einstein term in addition to the usual Debye term accounts for the contribution of an optical mode in MgB2 as indicated by a theoretical calculations [19]. The fitting results are shown for both x ¼ 0 and 0.5 samples in Fig. 3. For the x ¼ 0 sample, the specific heat after the substraction of the phonon contribution (as modeled by using Eqs. (2) and (3)) are shown in the inset of Fig. 3(a) represented by the solid line and solid square, respectively. One can see that the fitting using Eq. (3) overlaps with the experimental data in a wider temperature region. We take some estimations based on this fitting results. The specific heat jump DC at TC and the ratio DC=cnTC estimated from the data are 32.8 mJ gat1 K1 and 0.92, respectively, which are consistent with the results reported previously [2– 4,20]. For the x ¼ 0 sample, the fitted normal state specific heat coefficient is 0.92 mJ gat1 K2 and used the calculated density of states at the Fermi surface N ðEF Þ 0:72 eV1 [21], the average mass enhancement of the conduction electrons m =m is estimated to be 1.61 using a relation cn ¼ 2=3p3 kB2 N ðEF Þ m =m. For the x ¼ 0:5 sample, the fitting results yields cn ¼ 0:36 mJ gat1 K2 , and thus m =m is estimated to be 2.77, with N ðEF Þ 0:33 eV1 [12,22]. The electron–phonon coupling constant k ¼ ðm =mÞ 1 (taking no account of the other many-body effects) is estimated to be 0.61 for the x ¼ 0 sample which indicates the strong coupling between the phonon and electron as reported in Ref. [3]. For the x ¼ 0:5 sample, however, k is estimated to be 1.77, this may indicate a very strong coupling between phonons and electrons in such a system as suggested in Ref. [17]. We notice that the difference of the specific heat between the x ¼ 0:5 and 0 sample above the superconducting transition temperature is very small, this may be due to the small change after the partial substitution of Al atoms for Mg atoms. Thus, we propose to use the Al doped sample as a reference sample used in the differential specific heat measurement technique, in which a sample
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has a similar contribution of lattice vibration to the total specific heat was used. The solid circles in the inset of Fig. 3(a) are the data points of the x ¼ 0 sample, in which the lattice contributions represented by the data of the x ¼ 0:5 sample, has been directly substracted. We can see that the data do display the expected temperature dependence of the electronic specific heat Cel in the temperature region below TC . In summary, we have studied the structure, superconducting and specific heat properties of Al doped MgB2 samples. Our results showed that although diamagnetic signal and resistivity drop was observed in the x ¼ 0:5 sample the sample with Mg0:5 Al0:5 B2 composition is unlikely to possess of bulk superconductivity. We suggested that the previous reports about superconductivity in the sample could be explained by percolation effect. In addition, we estimated the Debye temperature, electronic specific heat coefficient and other parameters for the samples. Acknowledgements The authors would like to give thanks to Dr. J. Zhang for the discussions in the started specific heat measurement. This work was supported by the National Natural Science foundation of China (10174093, 10221002) and the Ministry of Science and Technology (NKBRSF-G19990646). References [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Nature (London) 63 (2001) 401. [2] F. Boquet, R.A. Fisher, N.E. Phillips, D.G. Hinks, J.D. Jorgensen, Phys. Rev. Lett. 87 (2001) 047001. [3] Y.X. Wang, T. Plackowski, A. Junod, Physica C 355 (2001) 179.
[4] H.D. Yang, J.Y. Lin, H.H. Li, F.H. Hsu, S.C. Li, R.C. Yu, C.Q. Jin, Phys. Rev. Lett. 87 (2001) 167003. [5] A. Sharoni, I. Felner, O. Millo, Phys. Rev. B 63 (2001) 220508. [6] H.J. Choi, D. Roundy, H. Sun, M.L. Cohen, S.G. Louie, Nature (London) 418 (2002) 758. [7] R.J. Cava, H.W. Zandbergen, K. Inumaru, Physica C 385 (2003) 8. [8] J.S. Slusky, N. Rogado, K.A. Regan, M.A. Hayward, P. Khalifah, T. He, K. Inumaru, S. Loureiro, M.K. Haas, H.W. Zandbergen, Nature (London) 410 (2001) 343. [9] J.Y. Xiang, D.N. Zheng, J.Q. Li, L. Li, P.L. Lang, H. Chen, C. Dong, G.C. Che, Z.A. Ren, H.H. Qi, H.Y. Tian, Y.M. Ni, Z.X. Zhao, Phys. Rev. B 65 (2002) 214536. [10] J.Q. Li, L. Li, F.M. Liu, C. Dong, J.Y. Xiang, Z.X. Zhao, Phys. Rev. B 65 (2002) 132505. [11] H.W. Zandbergan, M.Y. Wu, H. Jiang, M.A. Hayward, M.K. Haas, R.J. Cava, Physica C 366 (2002) 221. [12] S.V. Barabash, D. Stroud, Phys. Rev. B 66 (2002) 012509. [13] P. Postorino, A. Congeduti, P. Dore, A. Nucara, A. Bianconi, D. Di Castro, S. De Negri, A. Saccone, Phys. Rev. B 65 (2001) 020507 (R). [14] J.B. Neaton, A. Perali, cond-mat/0104098, 2001; S. Suzuki, S. Higai, K. Nakao, J. Phys. Soc. Jpn. 70 (2001) 1206; G. Satta, G. Profeta, F. Bernardini, A. Continenza, S. Massidda, Phys. Rev. B 64 (2001) 104507. [15] H. Kotegawa, K. Ishida, Y. Kitaoka, T. Muranaka, N. Nakagawa, H. Takagiwam, J. Akimitsu, cond-mat/ 0201578, 2002. [16] S. Margadonna, K. Prassides, I. Arvanitidis, M. Pissas, G. Papavassiliou, A.N. Fitch, Phys. Rev. B 66 (2002) 014518. [17] B. Renker, K.B. Bohnen, R. Heid, D. Ernst, H. Schober, M. Koza, P. Adelmann, P. Schweiss, T. Wolf, Phys. Rev. Lett. 88 (2002) 067001. [18] C. Kittel(Ed.), Introduction to Solid State Physics, Sixth ed. John Eiley & Sons Inc., New York, p. 107. [19] J. Kortus, I.I. Mazin, K.D. Belashchenko, V.P. Antropov, L.L. Boyer, Phys. Rev. Lett. 86 (2001) 4656. [20] S.L. BudÕko, G. Lapertot, C. Pertrovic, C.E. Cunningham, N. Anderson, P.C. Canfield, Phys. Rev. Lett. 86 (2001) 1877. [21] J. Kortus, I.I. Mazia, K.D. Belashchenako, V.P. Antropov, L.L. Boyer, Phys. Rev. Lett. 86 (2001) 4366. [22] O. De la Pe~ na, A. Aguaya, R. de Coss, Phys. Rev. B 66 (2002) 012511.
Investigation of structure, specific heat and superconducting transition in Mg1xAlxB2(x 0:5) J.Y. Xiang a, D.N. Zheng
a,*
, P.L. Lang a, Z.X. Zhao a, J.L. Luo
b
a
b
National Laboratory for Superconductivity, Institute of Physics & Center for Condensed Matter Physics, Chinese Academy of Sciences, P.O. Box 603-38, Beijing 100080, PeopleÕs Republic of China Laboratory of Extreme Condition Physics, Institute of Physics & Center for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, PeopleÕs Republic of China Received 6 October 2003; received in revised form 21 November 2003; accepted 28 November 2003
Abstract We have carried out structure, magnetic and specific heat measurements on aluminum doped magnetism diboride samples Mg1x Alx B2 in order to investigate possible superconductivity at the x ¼ 0:5 concentration. A diamagnetic signal was observed in magnetization measurements accompanied by a decrease in resistivity. However, the diamagnetic signal was extremely small as compared to what expected from full diamagnetism. Also, the transition both in magnetization and resistance was very broad. We propose that the diamagnetism is due to a very small amount of superconducting phase such as MgB2 and the resistive transition is due to the percolation behavior. Furthermore, we performed specific heat measurements, which are considered as a tool to investigate the bulk nature of superconducting transition, on the x ¼ 0:5 sample to verify the existence of superconductivity. We observed no evident superconducting transition in the entire temperature region from 2 to 300 K. The undistinguishable data between 0 and 5 T magnetic fields also indicated the absence of bulk superconductivity in the x ¼ 0:5 sample. 2003 Elsevier B.V. All rights reserved. PACS: 74.70.Ad; 74.25.Bt; 74.62.Dh Keywords: MgB2 ; Al substitution; Specific heat
1. Introduction Since the discovery of superconductivity in MgB2 [1], it has attracted considerable attention worldwide due to its high transition temperature (40 K). A lot of experimental and theoretical work has been performed in order to understand
*
Corresponding author. Fax: +86-10-8264-9531. E-mail address: [email protected] (D.N. Zheng).
the underlying mechanism and to explore potential applications. The research may also give some insight on the evolution of the theoretical description from conventional superconductors to the high temperature curprate superconductors. Now it is generally recognized that superconductivity in this material can be explained within the conventional BCS framework with a strong electron–phonon coupling. Experiments such as specific heat [2–4], tunneling spectrum [5] together with first principle calculations [6] have further
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.11.017
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J.Y. Xiang et al. / Physica C 402 (2004) 335–340
confirmed that MgB2 is a fully gapped superconductor with two sheets of Fermi surface that correspond to the two gaps, respectively. For a new superconductor, partial chemical substitution is regarded as a good method for the study of its properties. Unfortunately, it has been found that the substitution of other elements into MgB2 both for Mg and B atoms is very difficult [7]. This is in sharp contrast to the situation in high temperature cuprate superconductors, where chemical substitution has played an important role in evolving the nature of superconductivity. Nevertheless, Al appears to be an exception since AlB2 has the same crystal structure as MgB2 and samples with Al doping level ranging from zero to one can be made. However, a study on the Al doping samples was shown that the structure of MgB2 was remarkably modified [8]. More detailed work focused on the ÔmodifiedÕ structure indicated that a superstructure is presented in high doping level samples. The superstructure may be attributed to the structure instability observed in X-ray diffraction patterns [9]. Initially, a simple model in which the Al and Mg layers arranged orderly in an alternate fashion, i.e., a structure with Mg–B–Al– B–Mg–B–Al–B staggered in c-axis direction, was suggested [10] although subsequent TEM work showed that more complex features were associated with the superstructure [11]. The ab initio calculations further confirmed the possibility of such a structure [12]. As for the effect on superconductivity, it was found that superconductivity was destroyed as Al was introduced and bulk superconductivity vanished at about 40% Al doping level (different cutoffs at which the bulk superconductivity vanished had been reported) [8,10,13]. At the low doping levels ðx < 0:1Þ, the decrease of TC with increasing of Al is mainly attributed to the reduction in the density of state at the Fermi surface [8,9,13,14] and Al substitution for Mg does not lead to pair breaking as suggested in Ref. [15]. A theoretical calculation suggested that superconductivity vanished at 60% of Al doping [12]. On the other hand, some published experiment data has shown a diamagnetic signal in the 50% Al doping level [10,16]. Thus it has been suggested that Mg0:5 Al0:5 B2 might have properties distinct to those with higher or lower doping lev-
els, and bulk superconductivity could exist in it. although at a relatively low temperature [10]. In order to further investigate the possible superconductivity in Mg0:5 Al0:5 B2 , we made a series of Mg1x Alx B2 samples. Care was taken during the fabrication process to ensure sample quality. Specific heat measurements, which is regarded as a useful tool for obtaining the nature of superconducting transition, were performed together with XRD, magnetization and resistivity measurements.
2. Experimental Al doped MgB2 samples were fabricated using a traditional solid-state reaction method. Powders of Al, Mg, B with nominal composition Mg1x Alx B2 were well mixed and pressed into pellets with 13 mm in diameter and about 1 g in weight. The pellets wrapped with a Ta foil were put into a cylinder made of high temperature stainless steel. The cylinder was sealed with a lid and a piece of Mg flake was also put inside to avoid Mg deficiency. The samples were then sintered in a tube furnace at 900 C for two hours and then cooled down to the room temperature. The process was repeated after grinding. The sintering was carried out in an H2 / Ar2 (4%/96%) atmosphere. The microstructure of the samples were characterized by XRD and found predominantly single phase with low level of MgB4 , B2 O3 and a minor amount of MgO as secondary phases. Oxygen contamination in the x ¼ 0:5 Al doping level sample is much less than that in the x ¼ 0 sample. It appears possible to avoid oxygen contamination by adopting such a fabrication process. The samples were then cut into rectangular bars with dimensions 12 · 3 · 3 mm3 . Magnetization measurements were carried out in a superconducting quantum interference device (SQUID) magnetometer (MPMS5, Quantum Design). A standard four-probe method was used for resistivity measurements. The current density used in the resistivity measurement was about 0.1 A/cm2 . The same piece of sample was used in both magnetization and resistivity measurements. The specific heat measurements were carried out in a Quantum Design PPMS system in which a relaxation technique was employed.
J.Y. Xiang et al. / Physica C 402 (2004) 335–340
3. Results and discussion Fig. 1 shows the X-ray diffraction patterns for the x ¼ 0 and 0.5 samples. The (0 0 2) and (1 1 0) peaks can be well fitted using the Lorenz distribution function as shown by the solid line in Fig. 1.
Fig. 1. (0 0 2) and (1 1 0) peak in the X-ray diffraction patterns of MgB2 with x ¼ 0 and 0.5 Al doping levels. The solid line is a Lorentz fitting for these peaks. Inset shows the 2h scan patterns from 20 to 80 of the two samples.
337
The inset in Fig. 1 is the (h–2h) scan from 20 to 80. It indicates that both samples are predominantly single phase. Shown in Fig. 2 is the magnetization and resistivity data below 50 K as a function of temperature of the x ¼ 0:5 sample. The magnetization curve was obtained in a 1 mT magnetic field using zero field cooling. A weak diamagnetic signal appeared at about 38 K that could be attributed to the MgB2 impurity phase beyond the detection of XRD. The diamagnetic signal drops faster as the temperature decreased to about 10 K, indicates the possible appearances of superconductivity in this material, as suggested in Refs. [12,17]. However we noticed that the superconducting volume is much smaller than that in the x ¼ 0 sample as shown in the inset of Fig. 2. It is only about 0.04% of the superconducting volume of the x ¼ 0 sample at 4.5 K. Fig. 2 also shows the resistivity as a function of temperature. There is a small drop in the curves begin at about 13 K, and the change of resistivity from 13 K to roughly 4.6 K is approximately 2% of the value at 15 K. The magnitude of the resistivity drop varies between samples. In some cases, resistivity shows a rather large drop. The data above 15 K can be well
Fig. 2. The magnetization and resistivity as a function of temperature of the x ¼ 0:5 Al doped sample. Magnetization was measured in 1 mT magnetic field using zero field cooling (ZFC) procedure. The right side inset shows the full resistivity transition. The open circle is the experiment, data and the solid line is the fitted data using an expression a þ bT 2 (see the text). For a comparison, the magnetization curve of undoped MgB2 is also shown in the left side inset.
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fitted by an expression qðT Þ ¼ a þ bT 2 , as the solid line shown in the inset, of Fig. 2, with a ¼ 451 and b ¼ 0:0089, respectively. The appearance of resistivity drop and diamagnetic signal appears to suggest the existence of superconductivity. Indeed, in Refs. [10,16], the authors proposed that MgAlB4 phase is superconducting. Also, other properties such as Raman spectra show that MgAlB4 is different from others [10,13,17]. The consistency of the data below 20 K between the magnetization measurement and transportation measurement may be explained as the possible existence of superconductivity. However, the magnitude of the diamagnetic signal is so small and the absence of zero-resistance makes such claimant doubtful. One possible explanation is that the superconducting grains are not well connected and the grain boundaries are weak-links or even non-superconducting. In such cases, if the grain size is small as compared to the penetration depth, the diamagnetic signal would be very small. The absence of zero-resistivity could be attributed to the porosity and weak-link nature of in this sample. On the other hand, there could be other explanations. The very small diamagnetic signal might imply that the superconducting phase have a very small volume fraction and is not the major phase. In other words, the Mg0:5 Al0:5 B2 phase is not superconducting. The resistivity drop is probably caused by the percolation effect. We have performed resistivity measurements with different applied currents in order to check if the resistivity drop shift to lower temperatures as would be expected from the percolation effect explanation. However, we did not observe such a shift. This could be due to the fact that the non-superconducting Mg0:5 Al0:5 B2 phase is metallic and shows a resistivity value comparable with MgB2 . In order to further confirm the properties of the x ¼ 0:5 sample, we carried out specific heat measurements on the samples, i.e., the x ¼ 0 and 0.5 samples. If the x ¼ 0:5 phase is superconducting of bulk nature, we would expect changes in specific heat. Fig. 3 shows the total specific heat as a function of temperature for the x ¼ 0 and 0.5 samples. A clear jump can be seen near 38 K for the x ¼ 0 sample, while no evident anomaly is ob-
Fig. 3. The total specific heat as a function of temperature for the (a) x ¼ 0 and (b) x ¼ 0:5 Al doped MgB2 samples at zero magnetic field. A clear jump can be seen in the x ¼ 0 sample, while no abnormality could be seen in the x ¼ 0:5 sample. The dash dot line is the Debye model plus an Einstein term fitting (Eq. (2)) and the solid line is the multiple Einstein optic vibration modes fitting (Eq. (3)). Inset of (a) is the low temperature part of specific heat data as a function of temperature, in which the phonon contribution fitted using different models was subtracted. The solid line is the results from Debye model, the solid square is representative of the fitting results using the multiple Einstein modes and the solid circle is the data in which the data of the x ¼ 0:5 sample have been subtracted.
served in the entire temperature range from 2 to 210 K for the doped sample. Furthermore, we performed measurements in a 5 T magnetic field on the x ¼ 0:5 sample and the results are shown in Fig. 4. The two sets of data are overlapped to each other very well. The inset of Fig. 4 shows the low temperature data. We calculated the difference of the 0 and 5 T data and found no difference within the experimental resolution between the specific heat data measured in the 0 and 5 T magnetic field. These results appear to further suggest that there is
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Fig. 4. The specific heat as a function of temperature square of MgB2 of the x ¼ 0:5 sample in 0 and 5 T magnetic fields. Inset shows the low temperature part of specific heat of 0 and 5 T magnetic field versus temperature square. The solid line in the graph represents the multiple Einstein vibration modes fitted data.
no bulk superconductivity in the Mg0:5 Al0:5 B2 sample. In order to obtain more information on how Al doping affects the properties in MgB2 , we also analyzed the specific heat data to make estimations on some important parameters such as Dybe temperature and the normal state electronic specific heat coefficient. It is known that the measured specific heat data consist of electronic and lattice vibration contributions. To separate these two contributions, we employed three approaches reported in the literature, in which the phonon contribution is described by a simplified Debye model [2], Debye term plus an Einstein term [18] and multi-Einstein-mode [3], respectively. The corresponding equations are: CðT Þ ¼ cn T þ bT 3 þ dT 5 ; HD HE CðT Þ ¼ cn T þ 3RfD þ f 3RfE ; T T CðT Þ ¼ cn T þ 3R
8 X 0
pi fE
x i
T
;
ð1Þ ð2Þ
ð3Þ
Rx 2 where fD ðxÞ ¼ 3x3 0 y 4 ey ðey 1Þ dy and fE ðxÞ ¼ 2 2 x x x e ðe 1Þ . Here cn is the normal state elec-
339
tronic specific heat coefficient, HD and HE is the Debye and Einstein temperature, respectively. b, d, f and pi are the fitting parameters. The parameter f in Eq. (2) was used to adjusts the ratio between the two Pterms. A limitation condition for pi in Eq. (3) is i pi ¼ 1. In Eq. (2), an Einstein term in addition to the usual Debye term accounts for the contribution of an optical mode in MgB2 as indicated by a theoretical calculations [19]. The fitting results are shown for both x ¼ 0 and 0.5 samples in Fig. 3. For the x ¼ 0 sample, the specific heat after the substraction of the phonon contribution (as modeled by using Eqs. (2) and (3)) are shown in the inset of Fig. 3(a) represented by the solid line and solid square, respectively. One can see that the fitting using Eq. (3) overlaps with the experimental data in a wider temperature region. We take some estimations based on this fitting results. The specific heat jump DC at TC and the ratio DC=cnTC estimated from the data are 32.8 mJ gat1 K1 and 0.92, respectively, which are consistent with the results reported previously [2– 4,20]. For the x ¼ 0 sample, the fitted normal state specific heat coefficient is 0.92 mJ gat1 K2 and used the calculated density of states at the Fermi surface N ðEF Þ 0:72 eV1 [21], the average mass enhancement of the conduction electrons m =m is estimated to be 1.61 using a relation cn ¼ 2=3p3 kB2 N ðEF Þ m =m. For the x ¼ 0:5 sample, the fitting results yields cn ¼ 0:36 mJ gat1 K2 , and thus m =m is estimated to be 2.77, with N ðEF Þ 0:33 eV1 [12,22]. The electron–phonon coupling constant k ¼ ðm =mÞ 1 (taking no account of the other many-body effects) is estimated to be 0.61 for the x ¼ 0 sample which indicates the strong coupling between the phonon and electron as reported in Ref. [3]. For the x ¼ 0:5 sample, however, k is estimated to be 1.77, this may indicate a very strong coupling between phonons and electrons in such a system as suggested in Ref. [17]. We notice that the difference of the specific heat between the x ¼ 0:5 and 0 sample above the superconducting transition temperature is very small, this may be due to the small change after the partial substitution of Al atoms for Mg atoms. Thus, we propose to use the Al doped sample as a reference sample used in the differential specific heat measurement technique, in which a sample
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has a similar contribution of lattice vibration to the total specific heat was used. The solid circles in the inset of Fig. 3(a) are the data points of the x ¼ 0 sample, in which the lattice contributions represented by the data of the x ¼ 0:5 sample, has been directly substracted. We can see that the data do display the expected temperature dependence of the electronic specific heat Cel in the temperature region below TC . In summary, we have studied the structure, superconducting and specific heat properties of Al doped MgB2 samples. Our results showed that although diamagnetic signal and resistivity drop was observed in the x ¼ 0:5 sample the sample with Mg0:5 Al0:5 B2 composition is unlikely to possess of bulk superconductivity. We suggested that the previous reports about superconductivity in the sample could be explained by percolation effect. In addition, we estimated the Debye temperature, electronic specific heat coefficient and other parameters for the samples. Acknowledgements The authors would like to give thanks to Dr. J. Zhang for the discussions in the started specific heat measurement. This work was supported by the National Natural Science foundation of China (10174093, 10221002) and the Ministry of Science and Technology (NKBRSF-G19990646). References [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimitsu, Nature (London) 63 (2001) 401. [2] F. Boquet, R.A. Fisher, N.E. Phillips, D.G. Hinks, J.D. Jorgensen, Phys. Rev. Lett. 87 (2001) 047001. [3] Y.X. Wang, T. Plackowski, A. Junod, Physica C 355 (2001) 179.
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