Possible Species of Ferroelectrics

Abstract

A ferroelectric crystal can be considered as a (slight) modification of a certain nonferroelectric ideal crystal which is referred to as the "prototype" of the ferroelectric crystal; in crystallographical symmetry, the prototype should be higher than the ferroelectric crystal and equal to the paraelectric phase if possible. With the aid of the preceding studies and by introducing a new postulate on the free energy, which is expected to be generally valid, it is shown theoretically that there are, in all, 55 possible species of ferro-electrics as distinguished according to the point group of the prototype and the total number and orientation of the equivalent unique ferroelectric directions. This theory demands, as a revision of conclusions in previous studies, that 28 (FPT222(2)A2, $\mathrm{FPT}\mathrm{mm}2\mathrm{}\left(1\right)\mathrm{}\mathrm{D}m$, and others) of the 83 species of ferro-paraelectric phase transitions must be impossible, and that three ($i1\mathrm{}$-I, $i1\mathrm{}$-II, and $\mathrm{im}$) of the 25 kinds of ferroelectrics must be impossible. These theoretical predictions do not conflict with existing observational facts. By the way, the concept of "minor species" is introduced. Some species are able, and sometimes need, to be divided into two or more minor species from a crystallographical point of view. If one minor species is counted as one species, there turn out to be, in all, 67 possible species of ferroelectrics.