Group-theoretical analysis for the ferroelastic domain walls

By the group-theoretical method, the permissible domain walls for all 94 fu rroelastic species were analyzed. This method is not only consistent with w all equations using Sapriel's strain tensor method. but also provides addit ional information such as the types of wall, the point groups of each domai n, and the configurations of twin structures. The permisible domain walls f or a given domain pair were characterized by one or more symmetry elements which are defined as the set of wall characterizing elements (WCE). We foun d that the Sapriel's W wall was characterized by mirror plane or two or mor e symmetry elements, while the W ' wall by only one rotational symmetry ele ment. With the help of the crystallographic consideration, the group-theore tical analysis showed that all permissible domain walls are crystallographi cally 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 exi stence of a four-fold wall, W-f, is suggested for the first time.