Relating atomistic grain boundary simulation results to the phase-field model

A coarse-graining method for mapping discrete data to a continuous structural order parameter is presented. This method is intended to provide a useful and consistent method of utilizing structural data from molecular simulations in continuum models, such as the phase field model. The method is based on a local averaging of the variation of a Voronoi tessellation of the atomic positions from the Voronoi tessellation of a perfect crystal (the Wigner–Seitz cell). The coarse-graining method is invariant to coordinate frame rotation. The method is illustrated with a simple two-dimensional example and then applied to a three-dimensional relaxation simulation using the silicon EDIP potential of a Σ5 grain boundary. Calculated results indicate that a continuous structural parameter is obtained that has grain boundary characteristics similar to phase-field models of grain boundaries. Comparisons to other coarse-graining measures of structure are discussed as well as applications to experimental data sets.