Phenomenological theory of successive phase transitions in TMATC-Zn

Abstract

The (N(CH₃)₄)₂ ZnCl₄ crystal possesses commensurate-incommensurate phase transitions. To describe them the phenomenological free-energy expansion which contains only the second- and fourth-order invariants, has been derived. The model is based on the assumption of two branches of symmetry T^(k,4) of which one is acoustic and the second is related with spontaneous polarisation of the crystal. The periodic modulation in the crystal is described in terms of harmonics. The minimum set of harmonics which completely defines the commensurate modulation is established. Commensurate phases characterised by the wavevectors k/b*=0, 1/2, 1/3, 2/5 and n/m where n, m are any integers, arise from the second- and fourth-order Umklapp terms usually of higher harmonics. Phases specified by n even and m odd are ferroelectric.