Group-theoretical considerations concerning domain formation in ordered alloys

Domain formation in ordered alloys has been studied from the group-theoretical point of view. A method is derived to determine the number of orientation variants as well as the number of translation variants from the point groups and lattices of the ordered and disordered structures. The number of orientation variants is found to be equal to the order of the point group of the disordered phase divided by that of the ordered phase. It has been shown that under certain conditions the set of operations that produce all variants from a given original variant can be chosen so as to form a group. The operations relating the orientation variants are the elements of this group called the variant generating group. The results of the theory derived in this paper are general and can be applied to any disorder-order transformation. A few examples are worked out explicitly to illustrate the different theorems.