Landau phenomenological model for the α-INC (incommensurate)-β transition in quartz

ABSTRACT

The temperature dependence of the order parameters η (α-phase) and ξ (INC – incommensurate phase) are calculated in the presence of the electric field for the α-INC-β 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 α (ordered) and β (disordered) phases in quartz. The temperature dependence of the inverse susceptibilities (${\chi }_{\eta }^{-1}$ and ${\chi }_{\xi }^{-1}$) of the order parameter is also predicted at constant electric fields studied for the α-INC-β transition in quartz. Additionally, the E−T phase diagram for the transitions of the α-INC and INC-β in quartz is constructed from the Landau phenomenological model by using the literature data. Our predictions for the order parameters (η and ξ) and the inverse susceptibilities (${\chi }_{\eta }^{-1}$ and ${\chi }_{\xi }^{-1}$) can be compared with the experimental measurements for the α-INC-β transition in quartz.

KEYWORDS:

• Incommensurate phase
• quartz
• Landau model

Disclosure statement

No potential conflict of interest was reported by the author(s).