Irregular Ferroelectrics

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Abstract
The ferroelectrics are divided into the regular and the irregular ferroelectrics. The regular ferroelectrics crystallographically must belong to the polar groups. The irregular ferroelectrics are divided into those belonging to the polar groups and those belonging to the noncentrosymmetrical groups except the polar groups. The latter irregular ferroelectrics are scarcely expected to exist. All of the hitherto discovered irregular ferroelectrics belong to the former. This paper deals with the former irregular ferroelectrics exclusively and refers to them as simply the "irregular ferroelectrics." In the first place the classification of the irregular ferroelectrics is attempted. It is found that the irregular ferroelectrics are divisible into 11 kinds in accordance with their point groups, Bravais lattices, and types of state transition. A new symbol is given to each of these kinds. Secondly, it is systematically shown how the tensorial properties of each kind of irregular ferroelectrics should be changed with the state transition. The kinds of tensors considered are the polar and axial tensors of ranks two, three, and four. This study is aimed to serve not only for predicting the manners of change of the tensorial properties in the irregular ferroelectrics, but also for identifying the kind of an irregular ferroelectric and for judging regularity or irregularity of a ferroelectric. Lastly, the gyroelectricity and hypergyroelectricity in the irregular ferroelectrics are examined. Those crystals have been referred to as being gyroelectric and hypergyroelectric whose gyration and electrogyration, respectively, are nonzero and reversed in sign by means of a suitable biasing electric field. (Electrogyration means the rate of change of the gyration with the biasing electric field at zero value of the biasing electric field.) It is found that, of the 11 kinds of irregular ferroelectrics, 2 kinds are gyroelectric, 7 hypergyroelectric, and the remaining 2 neither gyroelectric nor hypergyroelectric.