Landau phenomenological model for the alpha-INC (incommensurate)-beta transition in quartz

Abstract

The temperature dependence of the order parameters eta (alpha-phase) and xi (INC - incommensurate phase) are calculated in the presence of the electric field for the alpha-INC-beta transition in quartz by the Landau mean field theory. Landau phenomenological model with the linear (eta xi) and quadratic (eta(2)xi(2)) coupling is introduced to investigate mainly the nature of the INC phase between alpha (ordered) and beta (disordered) phases in quartz. The temperature dependence of the inverse susceptibilities (chi(-1h)(eta) and chi(-1)(xi)) of the order parameter is also predicted at constant electric fields studied for the alpha-INC-beta transition in quartz. Additionally, the E-T phase diagram for the transitions of the alpha-INC and INC-beta in quartz is constructed from the Landau phenomenological model by using the literature data. Our predictions for the order parameters (eta and xi) and the inverse susceptibilities (chi(-1)(eta) and chi(-1)(xi)) can be compared with the experimental measurements for the alpha-INC-beta transition in quartz.