Group theory description of transformation pathway degeneracy in structural phase transformations

Pathway degeneracy of structure transformations with symmetry breaking underpins the functionalities of a broad class of smart materials - the ferroics. Despite of its significance, there has been a lack of rigorous theoretical description of pathway degeneracy, leading to several case-dependent treatments which are not generally correct. In this work, we incorporate lattice correspondence into group theory to define and determine pathway degeneracy during structural transformations. In particular we show that a stabilizer can be determined by taking into account either the deformation relationship (under a given lattice correspondence) or the orientation relationship, through which deformation variant is defined rigorously and distinguished clearly from orientation variant. Such a definition provides a theoretical foundation for investigating the formation of domain and defect structures arising from symmetry breaking during structural phase transformations.