垂直Bridgman法多组元晶体生长的多场耦合模型

Improved Mathematical Model for the Multi-Field Coupling Growth Process of Multi-Compound Crystal by Vertical Bridgman Method

对垂直Bridgman法多组元晶体生长的准稳态模型所采用的Boussinesq线性密度假设进行了改进,基于密度的Taylor展开式,得到了熔体密度随温度、浓度变化的非线性函数关系并引入到模型中,改进后的准稳态模型(PSSM)能揭示晶体生长过程的非线性本质.明确了模型的边界条件,得到了晶体生长的完整数学描述.改进后的PSSM以及已获得的多组元晶体准确物性为晶体生长的多场耦合定量数值模拟研究奠定了基础.

The Boussinesq linear hypothesis used in pseudo-steady-state model（PSSM） for multicompound crystal growth by vertical Bridgman method was amended. Based on Taylor expansion of melt density, a nonlinear density function coupling with temperature and concentration was deduced. The improved PSSM can reveal the non-linear physical mechanism of crystal growth more effectively. Moreover, the boundary conditions for improved PSSM were determined clearly, and thus a completed multi-field coupling mathematical model for multi-compound crystal growth process was proposed. The improved PSSM and the exact thermal properties of multi-compound crystal obtained provide a sound foundation for quantitative multi-filed coupling numerical simulation of crystal growth process.