On the growth of an intermediate phase in coherently stressed thin plates Original Research Article

Cahn–Hilliard type equations are derived to study the competitive growth of three isostructural phases in a binary, stressed, thin-plate diffusion couple when the lattice parameter depends either linearly or quadratically on the composition. Compositional stresses change qualitatively and quantitatively the evolution of the intermediate phase with respect to the stress-free case. Growth kinetics depend critically on whether the plate is free to bend or is affixed to a rigid substrate. The thickness of the intermediate phase is proportional to the square root of time for the rigid substrate case, but can depend on plate thickness and exceed a linear dependence on time for other conditions. Compositional strains can stabilize a non-equilibrium phase, prevent the growth of an equilibrium phase, and give rise to the stable coexistence of three coherent phases, in contradiction to the Gibbs phase rule for hydrostatically stressed systems.