Improved mathematical model for the multi-field coupling growth process of multi-compound crystal by vertical Bridgman method

The Boussinesq linear hypothesis used in pseudo-steady-state model(PSSM) for multi-compound 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.