A Phase-Field - Finite Element Model for Instabilities in Multilayer Thin Films

摘要

Cahn-Hilliard type of phase-field (PF) model coupled with elasticity equations is used to study the instabilities in multilayer thin films. The governing equations of the solid state phase transformation include a 4th order partial differential equation representing the evolution of the conserved PF variable (concentration) coupled to 2nd order partial differential equations representing the mechanical equilibrium. A mixed order Galerkin finite element (FE) model is used including C~0 interpolation functions for the displacement, and C~1 interpolation functions for the concentration. It is shown that quadratic convergence, expected for conforming elements, is achieved from this coupled mixed-order FE model. Using the PF -FE model, first, we studied the effect of compositional strain on the PF interface thickness and the results of simulations are compared with the analytical solutions of an infinite thin film diffusion couple with a flat interface. Morphological instabilities in binary multilayer thin films are investigated. The alloys with and without intermediate phase are considered, as well as the cases with stable and meta-stable intermediate phase. Maps of transformations in multilayer systems are carried out considering the effects of initial thickness of layers, compositional strain, and growth of a stable/unstable intermediate phase on the instability of the multilayer thin films. It is shown that at some cases phase transformation, intermediate phase nucleation and growth, or deformation of layers due to high compositional strain can lead to the coarsening of the layers which can result in different mechanical and materials behaviors of the original designed multilayer.