Temperature Dependences of Linear Electro-Incommensurate Constants in the Vicinity of the Transition from a Prototypic Phase to a Simultaneously Incommensurate and Ferroelectric Phase

Abstract

The material constants that characterize simultaneously incommensurate and ferroelectric phases are linear electro-incommensurate constants, such as d h /d E , d q 1 /d E and d q n /d E , where E denotes an electric field applied in the direction of spontaneous polarization, h the wavenumber of the first harmonic (the fundamental wave) in Q (any one of the order parameters), q 1 the amplitude of the first harmonic, and q n the amplitude of the n th harmonic (a high harmonic). One typical case is investigated, namely the P \bar4 b 2-(1/2, 0, 0) case. In this case, a ferroelectric incommensurate phase of the absolute type is possible. The transition between this phase and the prototypic phase can be second order. The expressions of the temperature dependences of almost all linear electro-incommensurate constants in the vicinity of the mentioned transition are presented.