Bishop CMCarter WC2020-10-192020-10-192002Bishop CM, Carter WC (2002). Relating atomistic grain boundary simulation results to the phase-field model. Computational Materials Science. 25(3). 378-386.0927-0256https://hdl.handle.net/10092/101143A 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. © 2002 Elsevier Science B.V. All rights reserved.enAll rights reserved unless otherwise statedcoarse-grainingphase-field modelVoronoi tessellationgrain boundaryJournal Article2020-07-15Fields of Research::40 - Engineering::4016 - Materials engineeringhttp://doi.org/10.1016/S0927-0256(02)00241-0