2019 Volume 60 Issue 5 Pages 726-731
Single crystals are widely applied in semiconductors and turbine blades and manufactured by directional solidification. The solidification control parameters such as the withdrawal rate, axial temperature gradient and cooling rate are the key parameters in directional solidification. Through a mathematical analysis, we derive the explicit relationships between the solidification control parameters and the physical and geometrical parameters. The accuracy of these relationships is high which is proven by the comparisons between the accurate values and the approximate values. These relationships give deep understanding into the directional solidification process. Moreover, they provide guidance for the manufacturing of directionally solidified crystals. Additionally, these relationships establish a connection between the microstructure and the physical and geometrical parameters.
