Statistical Theory of Ferroelectricity Based on the Concept of Ferroelectric Modes of Lattice Vibration

Abstract

For a crystal which is of displacement type in its ferroelectric phase, the concept of “ferroelectric modes” of lattice vibration is introduced which is different from and more basic than that introduced by Cochran and called in the same name by Landauer and Thomas. On the basis of this concept, a statistical theory of ferroelectricity is developed. Two cases are distinguished according to whether the crystal has only one or more ferroelectric modes of lattice vibration. The bulk of the present paper deals with the former case. An examination is made not only of ferroelectric phase transitions and the susceptibility to a static electric field but also of the susceptibility to electric fields alternating in high frequencies. Incidentally, a deduction is made of the complete expression for the temperature dependence of the frequency of the Cochran and others’ ferroelectric mode of lattice vibration in the vicinity of the Curie temperature.