Symmetries in the Paraelectric Phase-Transformations of Ferroelectric Crystals

Abstract

It has been found that the ferroelectrics are classified into 19 regular and 11 irregular kinds in accordance with their point groups, Bravais lattices, and types of state transition. Upon this new cognizance, a systematic investigation is made into the problem of symmetries in the paraelectric phase-transformations of ferroelectric crystals. It is known that one of the two stable states of a ferroelectric is obtained by performing upon the other any of certain operations (F-operations) belonging to the rotation group. The phase transformation is referred to as being “primitive” and “complex,” respectively, when the symmetry elements of the paraelectric phase comprise those of the ferroelectric phase and the F-operations alone, and when they include some extra symmetry elements in addition. Comments are made upon the significance of primitive and of complex phase transformations. It is expected that phase transformations being neither primitive nor complex are exceptional. On the assumption of primitiveness of the phase transformation, the tables are presented which give the point group (or space group) of the paraelectric phase when the kind alone (or both the kind and space group) of the ferroelectric crystal is specified. These tables are also useful for complex phase transformations.