Facet and energy predictions in grain boundaries: Lattice matching and molecular dynamics

Many material properties can be traced back to properties of their grain boundaries. Grain boundary energy (GBE), as a result, is a key quantity of interest in the analysis and modeling of microstructure. A standard method for calculating grain boundary energy is molecular dynamics (MD); however, on-the-fly MD calculations are not tenable due to the extensive computational time required. Lattice matching (LM) is a reduced-order method for estimating GBE quickly; however, it has only been tested against a relatively limited set of data, and does not have a suitable means for assessing error. In this work, we use the recently published dataset of Homer et al. (2022) to assess the performance of LM over the full range of GB space, and to equip LM with a metric for error estimation. LM is used to generate energy estimates, along with predictions of facet morphology, for each of the 7,304 boundaries in the Homer dataset. The relative and absolute error of LM, based on the reported MD data, is found to be 5%-8%. An essential part of the LM method is the faceting relaxation, which corrects the expected energy by convexification across the compact space (S2) S 2) of boundary plane orientations. The original Homer dataset did not promote faceting, but upon extended annealing, it is shown that facet patterns similar to those predicted by LM emerge.