Heat transfer and solidification processes of alloy melt with undercooling: II. Solidification model

The solidification process of undercooled alloy melts has been clarified experimentally in Part I of this paper. In the present paper, using the experimental evidence, a solidification model linking macroscopic heat transfer and microscopic solidification is presented. The model reflects the microscopic solidification phenomena occurring until the thermodynamically unstable field shifts to equilibrium, consisting of three fundamental processes: (first stage) free growth, (second stage) crystal expansion with relaxation, and (third stage) equilibrium solidification. Based on this model, a numerical simulation is carried out for the temperature change, interface movement, and solute concentration distribution during the solidification of an undercooled Bi-Sn melt. Theoretical predictions of the temperature changes involving the recalescence, terminal time of the relaxation process, and microsegregation for the solidified texture agree quantitatively with experimental observations.