Symmetry relations at phase transitions

Abstract

Phase transitions in the solid state are classified as being continuous or discontinuous. According to Landau theory, continuous phase transitions require that there is a group-subgroup relation between the space groups of the involved crystal structures. They are driven by certain vibrational modes (soft modes) that must satisfy certain symmetry conditions. A phase transition which involves a symmetry reduction can often result in a topotactic texture consisting of domains. These are twin domains if there is a translationengleiche group-subgroup relation between the space groups of the phases, and antiphase domains if it is a klassengleiche relation. The index of the symmetry reduction determines how many kinds of domains may appear. Reconstructive phase transitions cannot proceed via a hypothetical intermediate phase whose symmetry is an assumed common subgroup of the two involved space groups.