The evolution and morphological stability of a particle in a binary alloy melt

Abstract

The evolution and morphological stability of a particle in a binary alloy melt is re-examined using the asymptotic method. The resulting asymptotic solution of the dynamics model of the particle reveals that the temporal evolution and morphological stability of the particle vary continuously as functions of solute concentration. In particular, (1) the critical nucleation radius of the particle in the binary alloy melt is determined. When solute is rejected from solid phase to liquid phase, the initial concentration increases the critical nucleation radius and depresses the growth velocity of the particle. When solute is incorporated into the solid, the initial concentration decreases the critical nucleation radius. (2) The absolute and relative stability criteria of the particle in the binary alloy melt are shown on the basis of Mullins and Sekerka’s work in the pure melt. The critical stability radii for the absolute and relative stability criteria of the particle in the binary alloy melt are determined. The growth ratio of the critical stability radius to the critical nucleation radius in the binary melt does not exceed that in the pure melt. (3) When the segregation coefficient is less than one, with the growth of the particle, the initial concentration in the binary alloy melt first suppresses and then enhances the morphological stability of the particle. There exists a minimum solute concentration in the binary alloy melt such that when the initial concentration is lower than the minimum solute concentration, the stability of the particle decreases with the increase of solute concentration, whereas when the initial concentration is higher than the minimum solute concentration, the stability of the particle increases with the solute concentration. As the initial concentration increases, the critical stability radius first decreases to the minimum solute concentration at a certain solute concentration, and then increases with the solute concentration. This may control the morphological stability of particles by changing the addition of solute in the alloy melt.