Definition of a Transcendental Order Parameter for Reconstructive Phase Transitions

Abstract

We propose a generalization of the Landau theory of phase transitions which applies to reconstructive transitions. For the first time an order parameter is defined for this category of transition. This order parameter is shown to be a transcendental function of the large atomic displacements arising at the transition. The absence of a group-subgroup relationship between the symmetries of the phases is proved to be the consequence of specific displacements. The approach is introduced through examples of reconstructive transitions found in crystals of the elements.