Numerical modeling for peritectic solidification of RE123 high T c oxide superconductors
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I. INTRODUCTION SOLIDIFICATION microstructure largely influences on the material properties of bulk high Tc RE1Ba2Cu3Ox superconductors (123 or RE123, RE: rare earth metals, Y, Sm, Nd. . .). The critical current density, Jc is especially determined by the microstructure and improvement of the Jc property is crucially attributed to the microstructure control. During the semisolid process, the superconductive 123 phase forms from the nonsuperconductive RE2Ba1Cu1O5 (211) phase and the liquid phase via the peritectic reaction. In order to understand the microstructure formation, many directional solidification models have been proposed.[1–7] Most of them include an assumption of the liquid diffusion control and the quasi-steady-state approximation. However, because the 123 phase grows with a faceted interface, the liquid diffusion would not be a dominant rate limiting process, and because the reaction is essentially a non-steady-state process, the quasi-steady-state assumption may let our understanding be qualitative. “Modeling” is helpful in understanding the natural phenomena, and numerical modeling for the solidification of the faceted materials is of recent topics of current studies. Shunguan and Hunt[8,9] analyzed the pattern formation of the directional growth of silicon arrays. Mori and Ogi[5] made a numerical simulation of the directional microstructure formation of the Y-Ba-Cu-O superconductor. The bridge formation model was proposed by Schumitz et al.[10] based on the microstructure observation of melt-textured Y-Ba-CuO. The latter group observed directly this kind of peritectic MASAKI SUMIDA, Proposal-Based Researcher, New Energy and Industrial Technology Development Organization, Tokyo, the Department of Metallurgy, Graduate School of Engineering, The University of Tokyo, 7-3-1, Hongo, Bankyo-ku, Tokyo, 113-8656 Japan. Present address: Physical Metallurgy Laboratory, Department of Materials Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland. TAKATERU UMEDA, Professor, the Department of Metallurgy, Graduate School of Engineering, The University of Tokyo. Present address: the Department of Metallurgical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, 10330 Thailand. Manuscript submitted February 29, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
solidification using a transparent organic material (Salicylic acid-Acetamide) and made visible the dissolution of the high-temperature phase (Salicylic acid) in front of the growing peritectic phase (Salicylic acid-Acetamide, 1:1 phase).[11] They further analyzed the peritectic solidification of Y-BaCu-O using the phase-field method,[12,13] including the motion of the 211 particles at the 123 growth front.[14] In this article, a numerical model for the peritectic solidification of the 123 phase from the 211 ⫹ L mixture is proposed. The diffusion model, which is of the assumption of the liquid diffusion control and the quasi-steady-state approximation, proposed by the present author,
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