Infinite Lifshitz point in incommensurate type-I dielectrics

Abstract

The phenomenological analysis of the pressure-temperature $(P\ensuremath{-}T)$ phase diagram of ${[\mathrm{N}(\mathrm{C}\mathrm{H}}_{3}{)}_{4}{]}_{2}{\mathrm{CuCl}}_{4}$ (TMATC-Cu) crystals is presented. It is shown that serious disagreement between the experimental results and theory may be removed assuming that the coefficient of the Landau free energy expansion $\ensuremath{\kappa}$ at the gradient term ${(dq/dz)(dq}^{*}/dz)$ changes the sign in the experimental range of pressures. The phase diagram in the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\kappa}$ phase plane is characterized by infinite Lifshitz point (at $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\kappa}}\ensuremath{\infty})$ in which both lines of the phase transitions into the incommensurate phase merge together, whereas the incommensurate wave vector approaches its zero value. The triple point ${(P}_{K}\ensuremath{\approx}55\mathrm{MPa},$ ${T}_{K}\ensuremath{\approx}304\mathrm{K})$ observed in these crystals may be considered as an artificial point, which results from the limitation of experimental resolution. Therefore, even above ${P}_{K}$ there still exist two very close (unresolved) lines of the incommensurate phase transitions.