Domain-wall orientations in ferroelastics

The orientations of domain walls in ferroelastic materials are theoretically investigated. The procedure followed is based on the same criterion of spontaneous strain compatibility defined by Fousek and Janovec for ferroelectric crystals. Two given domains in a ferroelastic are found to be separated by a planar wall whose orientation belongs to a set of two mutually perpendicular orientations. Domain walls are not always crystallographically prominent planes of fixed indices ($W$ planes) and can instead be determined by the relative magnitude of the components of the second-rank tensor representing the spontaneous strain ($W^{\prime }$ walls). In the latter case the orientation is expected to be temperature dependent. It is also shown that symmetry considerations are sufficient to find all $W$ planes. According to the considered ferroelastic species the pair of permissible walls between two domains can be two $W$ planes, or a $W$ plane and a $W^{\prime }$ plane, or two $W^{\prime }$ planes. The situation where no permissible walls are expected is of particular interest and is examined in known crystals. The predicted orientations of walls are given for the 94 species of full ferroelastics. Available experimental data of the literature are all consistent with our results.