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-diagonal terms in the diffusion matrix. The Gibbs-Thompson equation in a ternary system undergoing coarsening reveals that the concentrations at the particle/matrix interface are dependent on the far-field supersaturations as well as on the particle radius. In addition, the capillary length depends on the diffusivities of the two components. An asymptotic 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 limit; however, the amplitudes of the power laws are modified. We find that the trajectory of the matrix supersaturation must lie along a tie-line, but the trajectory of the particle composition does not. An expression for the effect of dilute ternary additions to the coarsening rate of a binary alloy is also given.