THE STABILITY OF THE MOVING BOUNDARY IN SPHERICAL AND PLANAR GEOMETRIES AND ITS RELATION TO NUCLEATION AND GROWTH

摘要

Coupled heat and mass diffusion equations are set up and solved for various Stefan numbers. A stability criterion is developed for the moving interface. The general MBP is of importance in many fields, particularly in directional solidification. The analysis is applied to the homogenous nucleation and growth of a spherical particle. Traditional analyses have relied on energy balances between surface and volumetric energy. An exact solution is analyzed for appropriate boundary conditions here. The present derivation presents unpublished analyses using perturbation and consideration of the unknown moving boundary of the nucleating particle. Only certain solutions for the MBP are known and it is difficult to find solutions for the general case due to the extreme non-linear nature of the problem because of discontinuous material properties across the liquid and solid regions, and the unknown position of the liquid solid phase boundary. These concepts are applied to nucleation and phase field theory for homogenous nucleation with application to amorphous alloy formation.