热力学
材料科学
热扩散率
相(物质)
领域(数学)
合金
分配系数
二进制数
巨大的潜力
凝聚态物理
物理
化学
冶金
数学
算术
色谱法
量子力学
纯数学
作者
Seong Gyoon Kim,Won Tae Kim,Toshio Suzuki
出处
期刊:Physical review
日期:1999-12-01
卷期号:60 (6): 7186-7197
被引量:925
标识
DOI:10.1103/physreve.60.7186
摘要
We present a phase-field model (PFM) for solidification in binary alloys, which is found from the phase-field model for a pure material by direct comparison of the variables for a pure material solidification and alloy solidification. The model appears to be equivalent with the Wheeler-Boettinger-McFadden (WBM) model [A.A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phys. Rev. A 45, 7424 (1992)], but has a different definition of the free energy density for interfacial region. An extra potential originated from the free energy density definition in the WBM model disappears in this model. At a dilute solution limit, the model is reduced to the Tiaden et al. model [Physica D 115, 73 (1998)] for a binary alloy. A relationship between the phase-field mobility and the interface kinetics coefficient is derived at a thin-interface limit condition under an assumption of negligible diffusivity in the solid phase. For a dilute alloy, a steady-state solution of the concentration profile across the diffuse interface is obtained as a function of the interface velocity and the resultant partition coefficient is compared with the previous solute trapping model. For one dimensional steady-state solidification, where the classical sharp-interface model is exactly soluble, we perform numerical simulations of the phase-field model: At low interface velocity, the simulated results from the thin-interface PFM are in excellent agreement with the exact solutions. As the partition coefficient becomes close to unit at high interface velocities, whereas, the sharp-interface PFM yields the correct answer.
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