On the frequency of occurrence of tilt and twist grain boundaries

Abstract

Homophase grain boundaries are frequently classified into twist, tilt and mixed-type boundaries. With small deviations from pure twist and tilt allowed, there are finite probabilities of occurrence of these particular boundary types in a set of random boundaries. These probabilities are determined for the case of cubic crystal symmetry. If the limit on the deviations is 3°, then 3.9% of random boundaries have near-twist character, and as many as 84.0% of random boundaries are near-tilt boundaries.