A Finite Element-Phase Field Study of Solid State Phase Transformation: Coarsening of Coherent Precipitates and Instability of Multilayer Thin Films

Governing equations for solid state phase transformation are derived by coupling Cahn-Hilliard type of phase field model to elasticity equations. The governing equations include 2nd order partial differential equations for elasticity coupled with a 4th order evolution partial differential equation for the conserved phase field variable. A mixed order finite element model is developed for the computations with C0 interpolation functions for displacement and C1 interpolation functions for the phase field variable. Developed finite element-phase field model is used to study coarsening of systems of coherent particles and also investigate morphological instabilities of multilayer thin films in solid state binary systems. It was shown that compositional mismatch elastic stresses in precipitates-matrix systems and multilayer thin films significantly affect the instability of these systems and alter the kinetics of transformations