Quantitative process design of 1-D crystallization for pure melt

A 1-D crystallization process has been analyzed for thermal diffusion by solving the Fourier equation. The expressions of thermal fields indicate that the temperature decreases as the crystal grows and the temperature decreases in the solid phase as the crystal growth rate decreases. The trend of temperature variation is the opposite in the liquid phase. Meanwhile the temperature gradient decays along the crystal growth direction in both the solid and liquid phases. An obvious temperature layer gradually appears as the crystal growth rate increases when the crystal grows in an undercooled melt. According to these results, the following guidelines are suggested for the quantitative process design of the 1-D crystallization at a constant crystal growth rate: (1) the heater temperature must be decreased as the crystal grows along a route established using a formula, (2) the linear simplification of temperature distribution is applicable to the process design of crystallization only below a high growth rate limit, and (3) in order to keep the crystal growing in a non-undercooled melt, its growth rate cannot exceed a maximum.