Group-Theoretical Analysis for the Ferroelastic Domain Walls

Abstract

By the group-theoretical method, the permissible domain walls for all 94 ferroelastic species were analyzed. This method is not only consistent with wall equations using Sapriel's strain tensor method, but also provides additional information such as the types of wall, the point groups of each domain, and the configurations of twin structures. The permisible domain walls for a given domain pair were characterized by one or more symmetry elements which are defined as the set of wall characterizing elements (WCE). We found that the Sapriel's W wall was characterized by mirror plane or two or more symmetry elements, while the W^′ wall by only one rotational symmetry element. With the help of the crystallographic consideration, the group-theoretical analysis showed that all permissible domain walls are crystallographically prominent planes with fixed indices. They are represented by W_m, W_b, W_f, or combinations of them, depending on the WCE. Most notably, the existence of a four-fold wall, W_f, is suggested for the first time.