A phase-field model for polycrystalline thin film growth

Abstract

In this work we introduce and apply a diffuse interface model to the problem of polycrystalline evolution in zeolite thin film growth. The phase-field model is based on a Ginzburg–Landau free energy functional, where a set of non-conserved order parameters is used to capture geometry and temporal evolution of the solid grains and the liquid phase. Special attention is given to the modelling of anisotropic interface properties resulting in a growth shape which corresponds to experiments for hydrothermally grown MFI zeolites. The model parameters used in the simulations are determined from available physical data, taking into account the experimental length and energy scales. To produce sound results with a minimum of seed crystals, a method to cover the unit sphere in three dimensions with angularly equidistant grain orientations is developed. Simulations in 2D and 3D are carried out to study competitive growth of equisized seeds with randomly distributed orientations on a flat substrate. In each case, the evolution of the orientation distribution leads to a fibre texture, selecting the direction of fastest growth perpendicular to the substrate. The dynamics of front growth velocity and of the average grain diameter is evaluated and compares well to experimental and theoretical findings. No significant differences in the competitive growth process using either solid–liquid interface energy anisotropy or anisotropy in the kinetic coefficient were found. This allows the conclusion that under the imposed conditions no major effect of interface energy balances at triple junctions on structure evolution is present, as it is the case for grain growth. The simplifying assumptions imposed in the modelling of the process are discussed, and possible refinements of the phase-field model are proposed.