Symmetry Degeneracy of Statistical Models of Complex Ordering Alloys

A statistical model is described for alloys with a bcc lattice ordered according to the type of substitution and penetration, taking account only of pair interactions having higher symmetry than crystallographic. This leads totheoretical predictions and also to a description of a domain phase with various spatial symmetries. The latter occurs even for a simple stoichiometric state. General criteria are found for calculating the minimum number of particles necessary for interactions resulting in the symmetry being reduced to crystallographic. An example is given in which this is achieved by means of four-particle interactions.