Analysis of morphological stability in ternary two-phase diffusion couples

It has been established that, under certain conditions, the flat interphase boundary separating two ternary phases can be become morphologically unstable during the interdiffusion process. By a direct analogy with the constitutional supercooling criterion in alloy solidification, it has been proposed that the instability in ternary two-phase diffusion couples occurs when either or both diffusion paths enter into the two-phase region of the phase diagram. In this work a linear stability analysis of the diffusion problem is performed and the conditions for stability are expressed in terms of the diffusion coefficients, the slopes of the concentration profiles at the interface, and the system free energy as a function of composition. Through the use of a model ternary system, various examples of unstable interfaces are illustrated. It is found that the crossing of a diffusion path into the two-phase coexistence region is a necessary, but not sufficient condition for instability.