A Thermal Fluctuation-Based Nucleation Method For Phase-Field Models

A thermal fluctuation-based nucleation model for use in a phase-field model is proposed. In the model, a normally distributed random temperature fluctuation is imposed on a calculation system, and if a given grid temperature is lower than the average, the undercooling is converted to an increase in the crystallized/precipitated phase fraction. The conversion coefficient is derived as a function of a phase-field critical value for nucleation. The idea of a threshold of nucleation for the phase field, i.e., a critical value, is introduced first in the present study. The model is applied to homogeneous nucleation during solidification in a supercooled pure metal, and a reasonable nucleation probability curve is successfully obtained from the numerical calculations. An application to the homogeneous nucleation of an Al-Cu alloy is also demonstrated.