On the theory of ferroelectric transition in the crystal LiNbO3

A simple model for ferroelectric transition in the crystal LiNbO3 is proposed. It is considered that one of two optical branches of vibrations of the system of crystal planes in the direction of trigonal c-axis (on which the ions Li+, Nb5+ and O2- are distributed) plays the role of the "soft mode" at the ferroelectric transition in LiNbO3. The dynamic problem of these plane vibrations is solved. For frequencies of optical modes the analytical expressions depending on coordinates, charges and weights of ions are obtained. It is shown, that the frequency of one of these two optical modes, under a certain condition, tends to zero (soft mode). This condition enables one to find with high accuracy the dispositions of ions in both ferroelectric and paraelectric phases and gives an opportunity to follow the changes of these dispositions at the phase transition. Then, it is assumed that the reason of a ferroelectric transition is the thermal expansion of crystal. On the basis of this assumption the thermal shifts of ions and the Curie-Weiss law for the square of the frequency of SM are obtained. (C) 1999 Elsevier Science B.V.