Coarsening in binary solid-liquid mixtures

Abstract

A theory of Ostwald ripening has been developed for a solid-liquid mixture consisting of a low volume fraction array of spherical solid particles in a liquid wherein the coarsening process proceedsvia the transport of both heat and mass. We find that the simultaneous transport of heat and mass during ripening does not alter the exponents of the temporal power laws governing the ripening process from their classical values but does alter the amplitudes of these power laws. The growth rate of the cube of the average particle radius, the rate constant, is found to depend both on the alloy solute concentration and the ratio of the thermal to solutal diffusivities. In most metallic systems, a large decrease in the rate constant can be expected with small additions of solute to a pure metal. The mean-field temperature and concentration in the liquid will vary with time during ripening and will approach their equilibrium values along a unique path which is dependent only on the materials parameters of an alloy. Possible extensions of this theory to the analogous problem of ripening in isothermal ternary alloys are also discussed.