Kinetics of Coarsening of Spherical Particles in a Liquid Matrix

Abstract

The theory of particle coarsening kinetics under control by diffusion through the matrix and by phase-boundary reaction is reviewed, and extended to the case of diffusion control when the particles are closely spaced and for impurity control at the interface. For the first case, d̄=f(T,φ)t⅓, Nv=f(T,φ)t−1, where d̄ is the mean particle diameter, φ is the volume fraction solid, T is temperature, and Nv is the number of particles per unit volume. For the latter two cases, d̄=f(T)t12,Nv=f(T)t−32, the temperature-dependent functions being different for the two cases. The models are used to discuss existing kinetic data on the iron-liquid copper and oxide-liquid silicate systems. New data on the NbC-liquid iron system reveal the absence of the expected diffusion-field interaction effect when particles are close together. The role of surface-active impurities, particularly boron, on the mechanism of growth is discussed and it is shown that, while growth may be diffusion-controlled in the absence of impurities, it may become phase-boundary reaction controlled when appreciable quantities of impurities are present. The apparent coefficient of diffusion of iron in copper is calculated to be about 6.06×10−4 cm2/sec at 1120°C.