On identification of symmetric and improperly quasi-symmetric grain boundaries

Symmetric and improperly quasi-symmetric grain boundaries have special geometric features. They are important reference boundaries in quantitative studies of boundary networks. Methods for identification of symmetric and improperly quasi-symmetric boundaries used so far, which are based on distance functions defined in the space of boundary parameters, are computationally complex and inefficient. In this article, new parameters that approximate the distances to the nearest symmetric and improperly quasi-symmetric boundaries are defined to simplify and speed up the analyses. Very strong correlations between the new parameters and the corresponding distances validate these new parameters to be a suitable replacement for the distances. Distributions of the introduced parameters may serve as characteristics of boundary networks. As an example, the new parameters are applied to the studies of symmetric and improperly quasi-symmetric characters of boundaries in three-dimensional microstructure data collected from a nickel-based superalloy.