Effects of Quantum Fluctuations and Deformability Parameter on Structural Phase Transitions for Ferroelectric Materials with Deformable Double-Well Potentials

Abstract

We investigate the features of a ferroelectric one-dimensional lattice model, with a class of symmetric deformable double-well substrate potentials and harmonic interaction, that exhibits structural phase transitions. The mean-field theory (MFT) is developed for this model, whose substrate potential shape varies in several manners as a function of a shape parameter. The temperature dependence of the structural order parameter is studied over a large temperature interval and then, the behavior of structural phase transitions is modified by the influence of quantum fluctuations and the shape parameter µ, particularly at low temperatures. Its effect on the phase diagram of temperature versus shape parameter is described and leads to highly nonlinear phase boundaries Tc(µ) in (Tc, µ) space. Also, the general phase diagram characteristics are derived from the order parameter saturation, leading to a more extensive survey of the order parameter, which is responsible for the structural transitions, and which becomes temperature independent below a saturation temperature θs. An application of the model to KH2PO4-type crystals and comparison of the model calculations with the experimental critical temperatures for KH2PO4 (KDP) and KD2PO4 (DKDP) yield satisfactory agreement. In the small-values limit, an approximate general Landau-type expression for the Gibbs free energy is given including the effects of order parameter saturation and which leads to the study of a tricrital phase transition and displacive limit case.