Kinetics of phase growth in stressed systems with non-equilibrium interfaces

A numerical model is developed to study the effects of misfit strains and applied stress on the one-dimensional microstructural evolution of a multi-phase, binary-diffusion couple for which the interfaces are in not in local thermodynamic equilibrium. The interfaces are treated as sharp, planar and coherent. No excess quantities are associated with the interface. Elastic deformation can result from misfit strain, applied stresses or substrate induced strain compositional strains are not considered.; The finite difference method employed solves the coupled elastic and mass diffusion equations using a fine grid overlay in the region of each interface that tracks the interface, while using a coarser grid over the remainder of the material. The competitive growth of several phases can be simulated, and kinetic barriers can be associated with any interface. Physical parameters of the system such as diffusivity, elastic constants, misfit strain, applied stress, and solution thermodynamics, as well as the initial compositions and phase fractions can be varied in each phase.; Numerical simulations and analytic approximations predict exponential movement of a single interface with time for large misfit strain for a free-standing system, as compared to the $t12$ movement for stress-free systems. The interface position is approximated as where K₂ is a function of stress-free physical constants and K₁ is a function of the elastic constants, misfit strains, and other system parameters. The qualitative change is a result of the non-linear effect of elasticity on the interfacial boundary conditions.; In the absence of all stress effects, but in the presence of interfacial kinetic barriers, the numerical simulations predict three regimes of growth for a single intermediate phase. The first is a period of no intermediate phase growth, the second is growth of the intermediate phase proportional to time, and the third regime of growth is parabolic with time and approaches the growth rate expected when the interfaces are in local thermodynamic equilibrium. A wide range of behavior is predicted in the absence of stress, but when interfacial kinetic barriers are present. A chemically stable intermediate phase initially present can dissolve and then grow at later times. Dissolution of chemically stable deposited layers has been reported experimentally.; The evolution of a single intermediate phase in the presence of stress is shown to depend on the initial conditions, in particular, the initial thickness of the intermediate phases. A critical initial thickness was identified, above which the intermediate phase grew, and below which the intermediate phase dissolved. The competitive growth of two intermediate phases possessing traction boundary conditions show that a misfit strain in one of the terminal phases produces behavior similar to the sequential growth of phases seen in thin film systems. Numerical simulations showed that one intermediate phase can grow and nearly dissolve the adjacent terminal phase, while the other intermediate phase shrinks (or dissolves) from its initial thickness. After the terminal phase adjacent to the growing intermediate phase is nearly-dissolved, the other intermediate phase begins to grow.; The competitive growth of two intermediate phases is compared to the growth trajectories predicted. The trajectories predicted by Johnson and Martin [JM90] using a quasi-static approximation are shown to underestimate the influence of the kinetic barriers on interface motion. This is due to the quasi-static approximation assuming no gradient in the terminal phases.