Three-dimensional anisotropic and isotropic grain growth simulations with comparisons to experiment

A 3D phase field model has been developed which takes into account the underlying anisotropy inherent in crystalline materials. It has been specifically formulated for systems with cubic anisotropy and accounts for all five macroscopic degrees of freedom of a grain boundary. The approach decouples the misorientation dependence of the grain boundary energy from that of the normal dependence. Specifically, the gradient energy coefficient is a function of misorientation, whereas higher order gradient terms in the free energy density are rotated into the respective grain's crystallographic frame of reference in order to determine the dependence of the grain boundary energy on the grain boundary normal. In an analogous manner, the kinetic coefficient has been made a function of the order parameters to allow for anisotropy in the mobility of particular grain boundaries.;Highly anisotropic grain morphologies with missing orientations are possible. For this anisotropic model increasing the misorientation reduces the regions of localized high curvature along the grain boundaries. We find that cubic shapes develop with low-energy interfaces that align along either the {111} or {100}. Additionally, features such as boundaries containing wave-like interfaces and tri-junctions that are not 120° angles are observed.;To bridge the gap between simulation and experiment the code has subsequently been parallelized and a sparse data structure algorithm has been implemented in an effort to simulate large polycrystalline samples. A comparison with an experimental study was performed to validate the predictive capabilities of the model. We employ an in-situ x-ray tomography dataset (courtesy of Erik Lauridsen et al.) as an initial condition in our simulation. Since the x-ray tomography data is collected in-situ it is possible to compare the morphology of individual grains computed at a later time with that observed experimentally.;Despite all the complex physical phenomenon that occur during grain growth, a one-to-one comparison with an isotropic phase field simulation reveals clear evidence of regions where the simulated and experimental structures have excellent agreement. Most importantly we find poor agreement in other regions of the system, confirming that anisotropy of the grain boundary energy and mobility has an important influence on grain evolution.