Sains Malaysiana 40(8)(2011): 913–919

Simple Calculation of the Anisotropic Factor for Minimum Current Path in MgB₂ Material Using the Extrapolated Kramer Field as priori Parameter

(Pengiraan Ringkas Faktor Ketakisotropan Untuk Lintasan Arus Minimum dalam Bahan

MgB2 Menggunakan Medan Kramer Unjuran Sebagai Parameter Priori)

M.I. Adam*

Dept of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia

M.F.M. Aris & S.K. Chen

Dept of Physics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM, Serdang,

 Selangor, Malaysia

S.A. Halim

Institute For Mathematical Research (INSPEM), Universiti Putra Malaysia,

43400 UPM , Serdang, Selangor, Malaysia

Diserahkan: 24 Mac 2010 / Diterima: 17 Januari 2011

ABSTRACT

The volume flux pinning force density of MgxB2 (x = 0.8, 1.0 and 1.2) materials was calculated for grains boundary and point pinning potentials. Stoichiometric Mg0.8, MgB2, and Mg1.2B2 samples were prepared by the conventional solid state reaction method. Three pellets were annealed at temperature range of 650-800°C. Structural analysis revealed large values for FWHM at (hkl) (110)(°) which indicates distortion in the boron plane of these specimens. The a and c – axis lattice parameters showed respective contraction and elongation with the increase in processing temperature. The low crystallinity found in Mg0.8B2 and Mg1.2B2 specimens was concluded to be due to structural defects, which act as flux pinning centres. Experimental anisotropic factor and the minimum fraction for current path, obtained from the framework of current percolation theory were used to explain the strong field dependence of the critical current density, Jc in the specimens. The summit of the maximum pinning force density was shifted to lower magnetic field position with the increase of anisotropy. The scaling laws were employed in a Kramer– like field in order to identify the dominant pinning mechanism correspondence to the summit of maximum pinning. For MgB2 specimens however, a renormalization field based on the current percolation exposition is considered for the identification of their dominant pinning since it is very difficult to account for the flat behaviour of the pinning force in the weakened current region of these specimens.

Keywords: Anisotropy; current percolation; grain boundary pinning

ABSTRAK

Ketumpatan daya pengepin isipadu fluks dalam bahan MgxB2 (x = 0.8, 1.0, 1.2) dikira untuk keupayaan pengepinan titik dan sempadan butiran. Bahan berstoikiometri Mg0.8, MgB2, dan Mg1.2B disediakan melalui kaedah tindak balas keadaan pepejal. Tiga pelet disepuhlindap dalam julat suhu 650-800°C. Analisis struktur menzahirkan nilai ‘FWHM’ yang besar pada (hkl) (110)(°) yang menunjukkan herotan pada satah boron bahan tersebut. Pemalar kekisi paksi-a dan c menunjukkan pengecutan dan pemanjangan apabila suhu meningkat. Kerendahan ciri kehabluran dalam bahan Mg0.8B2 and Mg1.2B2 adalah disebabkan oleh kecacatan struktur yang bertindak sebagai pusat pengepin fluks. Faktor ketakisotroban uji kaji dan pecahan minimum yang diperoleh daripada rangka kerja teori perkolasi laluan arus digunakan untuk menjelaskan kebergantungan yang kuat ketumpatan arus genting Jc dalam bahan. Ketumpatan daya pengepin maksimum tersesar ke kedudukan rendah dengan penambahan ketakisotroban. Hukum penskalan digunakan dalam medan bak-Kramer untuk mengenalpasti mekanisme pengepinan dominan yang sepadan dengan puncak maksimum pengepinan. Walau bagaimanapun, untuk bahan MgB2 suatu medan ternormal berdasarkan kedudukan arus perkolasi diambil kira untuk penentuan pengepinan dominan kerana adalah agak sukar untuk menentukan sifat daya pengepinan yang mendatar dalam daerah arus yang lemah di dalam bahan.

Kata kunci: Anisotropi; arus perikolasi; pengepinan sempan butiran

RUJUKAN

Chen, D.X. & Goldfarb, R.B., 1989. Kim model for magnetization of type – II Superconductors. Journal of Applied Physics 66: 2489-2500.

Chen, S.K., Serquis, A., Serrano, G., Yates, K.A., Blamire, M.G., Guthrie, D., Cooper, J., Wang, H., Margadonna, S.M. & MacManus – Driscoll, J.L. 2008. Structural and superconducting property variations with nominal Mg non-stoichiometry in MgxB2 and its enhancement of upper critical field. Advanced Functional Materials 18: 113-20.

Cheng, C.H., Yang, Y., Munroe, P. & Zhao, Y. 2007. Comparison between Nano–diamond and carbon nanotube doping effects on critical current density and flux pinning in MgB2. Superconductor Science & Technology 20: 296-301.

Eisterer, M., 2008. Calculation of the volume pinning force in MgB2 superconductors. Physical Review B 77: 144524-1-5.

Eisterer, M., Robert, S.K., Webber H.W., Sumption, M.D. & Bhatia, M. 2007. Neutron irradiation of SiC doped magnesium rich MgB2 wires. IEEE Transactions in Applied Superconductivity 17: 2814-17.

Eisterer, M., Zehetmayer, M. & Weber, H.W., 2003. Current percolation andanisotropy in polycrystalline MgB2. Physical Review Letters 90: 247002-1-4.

Kramer, E.J. 1973. Scaling laws for flux pinning in hard superconductors. Journal of Applied Physics. 44: 1360 -70.

Kramer, E.J. 1978. Fundamental fluxoid–defect interactions in irradiate superconductors. Journal of Nuclear Materials 72: 5-33.

Larbalestier, D.C., Rikel, M.O., Cooley, L.D., Polyanskii, A.A., Jiang, J.Y., Patniak, S., Cai, X.Y., Feldmann, D.M., Gurevich, A., Squitieri, A.A., Naus, M.T., Eom, C.B. & Hellstrom, E.E. 2001. Strongly linked current flow in polycrystalline forms of the superconductor MgB2. Nature 410: 186-89.

Matsushita, T., Kiuchi, M., Yamamoto, A., Shimoyama, J. & Kishio, K. 2008. Critical current density and flux pinning in superconducting MgB2. Physica C 568: 1833-35.

Mikheenko, P., Martinez, E., Bevan, A., Abell, J.S. & MacManus – Driscoll, J.L., 2007. Grain boundaries and pinning in bulk MgB2. Superconductor Science & Technology 20: S264-70.

Oh, Sangjun. & Kim, Keeman. 2006. A Consistent description of scaling laws for flux pinning in Nb3Sn strands based on the Kramer Model. IEEE Transactions in Applied Superconductivity 16: 1216-19.

Pol, Vilas Ganpat., Pol, Swati Vilas., Felner, Israel & Gednaken, Aharon. 2006. Critical current density in the MgB2 nanoparticles prepared under autogenicpressure at elevated temperature. Chemistry & Physics Letters 433: 115-19.

Qu, B., Sun, X.D., Li, J.G., Xiu, Z.M., Liu, S.H. & Hue, C.P. 2009. Significant improvement of critical current density in MgB2 doped with ferromagneticFe3O4 nanoparticles. Superconductor Science & Technology 22: 015-027.

Stauffer, D. & Aharony, A. 1998. Introduction to Percolation Theory. Taylor & Francis PA 19106.

Tilley, D.R. 1965. The Ginsburg – Landau equations for anisotropic alloys. Proceedings of the Royal Physical Society 86: 289-95.

Yamamoto, A., Shimomya, J., Kishio, K. & Matsushta, T. 2007. Limiting factors of normal – state conductivity in superconducting MgB2: an application of mean – field theory for a site percolation problem. Superconductor Science & Technology 20: 658-66.

Yamamoto, A., Shimoyama, J., Ueda, S., Katsura, Y., Iwayama, I., Horii, S. & Kishio, K. 2006. Crystallinity and flux pinning properties of MgB2 bulks. Physica C 445-448: 806-10.

*Pengarang untuk surat-menyurat; email: miadam@um.edu.my