The grain-boundary structural unit model redux

Properties of grain boundaries (GBs) and their underlying structures are key to understanding polycrystalline material phenomena. The most widely used model for GB structure is the structural unit model (SUM), introduced ∼ 50 years ago. The SUM represents GB structure as a combination of structural units (SUs); this combination evolves systematically with GB misorientation. Despite its successes, many observations suggest the SUM does not completely describe the GB structure; its utility for predicting GB properties is limited. There has been a growing realization that, even for fixed misorientation, multiple stable/metastable structures are common (corresponding to different microscopic degrees of freedom). We generalize the SUM by considering the effect of such metastable structures. While the SUM can describe GB structure evolution between a pair of delimiting boundaries, there will be many such evolutionary paths, corresponding to SUs associated with the metastable structure of the delimiting boundaries. The equilibrium GB energy vs. misorientation does not necessarily correspond to one of these paths, but will have contributions from many. Recognizing this, we propose a new approach to predict GB structure and energy, allowing for accurate determination of the GB energy vs. misorientation based on a very small number of atomistic simulations. For example, we predict the GB energy vs. misorientation for [100] and [111] symmetric tilt boundaries in BCC tungsten over the entire misorientation range to a mean error of <2 % based on atomistic simulations at only three or four misorientations. Our approach allows for the trade-off between computational cost and prediction accuracy.