Type II and IV twins with irrational twin boundaries are studied by high-resolution transmission electron microscopy in two plagioclase crystals. The twin boundaries in these and in NiTi are found to relax to form rational facets separated by disconnections. The topological model (TM), amending the classical model, is required for a precise theoretical prediction of the orientation of the Type II/IV twin plane. Theoretical predictions also are presented for types I, III, V, and VI twins. The relaxation process that forms a faceted structure entails a separate prediction from the TM. Hence, faceting provides a difficult test for the TM. Analysis of the faceting by the TM is in excellent agreement with the observations.
Keywords: disconnections; dislocations; phase transformations; twins.