OSTWALD RIPENING IN TERNARY ALLOYS

A theory of coarsening in an isothermal, ternary alloy is developed in an effort to understand the effects of a third chemical component on the ripening behavior of a two-phase system. The analysis is valid for a general, nonideal, nondilute solution, but is limited to extremely small volume fractions of the coarsening phase and neglects off-diagon al terms in the diffusion matrix. The Gibbs-Thompson equation in a ter nary system undergoing coarsening reveals that the concentrations at t he particle/matrix interface are dependent on the far-field supersatur ations as well as on the particle radius. In addition, the capillary l ength depends on the diffusivities of the two components. An asymptoti c analysis shows that the exponents of the temporal power laws for the average particle radius, number of particles per unit volume, and the matrix supersaturations are the same as that found in the binary limi t; however, the amplitudes of the power laws are modified. We find tha t the trajectory of the matrix supersaturation must lie along a tie-li ne, but the trajectory of the particle composition does not. An expres sion for the effect of dilute ternary additions to the coarsening rate of a binary alloy is also given.