Temperature-pressure phase diagram of deuterated tetramethylammonium tetrachlorozincate

Abstract

The pressure temperature phase diagram has been obtained in the deuterated TMATC-Zn by measuring the modulation wave vector in the range 0 to 1.8 kbar and — 5 to 36 °C. This diagram is a nice illustration of the devil's staircase. It exhibits various commensurate stairs with k = 1/3,2/5 in the ferroelectric phase, 3/7 and 1/2. At high temperatures lock-in occurs at 2/5. This phase separates two incommensurate phases, one with k > 0.4 and one with k < 0.4. There the devil's staircase is incomplete, hysteresis appears at the lock-in transitions. At low P and T the devil's staircase is complete and behaviour irreversible. In a phenomenological theory, commensurability is induced by setting the proper terms in the free energy expansion. Together with invariant powers of the principal order parameter, there are coupling terms involving a secondary order parameter. Direct coupling of the POP with polarization leads to a contribution of order 2 n for a commensurate phase of order 1/n. In order to reduce this order, coupling is examined through a secondary order parameter depending on the distortion of wave vector 3 k or 2 k. These two distortions coincide for k = 0.4. One coupling term is dominant when k > 0.4, the other one when k < 0.4. The SOP then changes its symmetry from Σ2to Σ 3