The classification of phase transitions according to the permutation properties of domain states

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Abstract
We present a classification scheme of domain pairs for equitranslational phase transitions. The scheme is based on a unique characterization of a domain pair by means of the symmetry of one domain state within the pair, the twinning group and stabilizing groups of the pair. Permutational, rotational and crystallographic types of pairs are introduced. Pairs exhibiting similar tensor distinction are assigned to same rotational, or crystallographic type; the former being adequate to the continuum description the latter including the periodicity of crystals. Lastly we classify pairs by their complexity. For that purpose we employ permutational properties of the two states under operations of the twinning group, and specify the mutual relationship between the states, called the ‘twinning law', by stabilizing groups. We distinguish four kinds of such laws each defining one class of domain pairs. According to a possible occurrence of domain pairs in a distorted phase and respective twinning laws, phase transitions are divided into four classes.