Symmetry analysis of structural transitions between phases not necessarily group-subgroup related. Domain structures

Abstract

It is shown that, in phase transitions, a theory of symmetry can be derived in the case where there is no group-subgroup relationship assumed between space groups of both phases, provided that a condition of nondisruption is obeyed at the transition. This condition states that any one of the structures of both phases can be described in the frame of reference of the other. A classification of structural transitions, based on symmetry, is proposed. Then, consequences of the hypotheses made are derived for domain structures arising from transition. Two examples, KCl${\mathrm{O}}_{3}$ and BaTi${\mathrm{O}}_{3}$, which are known from experiment to undergo a phase transition in which there is no such a group-subgroup relationship, are discussed.