Domain average engineering in ferroics

In a domain average engineered sample of a multidomain ferroic, the sample is divided into a very large number of domains, representing m domain states where m is less than the theoretically allowed maximum number n of domain states. The response to external fields is described by tensorial properties averaged over all the involved domain states. We have developed a program to classify subsets of m < n domain states which can arise in a ferroic phase transition. We calculate properties of these subsets of domain states, including the symmetry of the subset, the subset domain polarizations and magnetizations, and, if they exist, the poling directions which gives rise to the subsets of domain states.