A phenomenological approach for construction theoretical phase diagrams with multiple phase transitions including incommensurate transitions is developed for the case when a special triple point, a Lifshitz-type point, is assumed to be present in the experimental diagram for {N(CH 3 ) 4 } 2 ZnCl 4 crystal family. The theoretical temperature-pressure phase diagram for {N(CH 3 ) 4 } 2 ZnCl 4 is plotted and is found to be in agreement with the experimental phase diagram. The approximations and assumptions made in the construction of the diagrams are discussed.

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The main theoretical concepts of phenomenological approach to constructing temperature -pressure phase diagrams for TMA -family crystals are presented. The phase diagram is calculated successfully for {N(CH 3 ) 4 } 2 CuCl 4 .Keywords: Phase diagram; Devil's staircase; incommensurate phase A theoretical method is developed for a constructing the temperature-pressure (T-P) phase diagrams of different crystals of tetramethylammonium tetrahalogenometalic compounds, {N(CH 3 ) 4 } 2 MX 4 , where M and X are divalent metals and halogens, respectively (see, e.g. reviews [1-3]).The method is based on the phenomenological description of a Devil's staircase [4]. We assume that all phases, observed on the T-P phase diagram in experiment for each crystal, are produced by a single soft optical branch of the normal vibration spectrum of the crystal. This branch in TMA-crystals has, in some range of parameters, two minima:the first at the center and the second at an arbitrary point of the Brillouin zone (Fig. 1). Due to this special feature, the TMA crystals differ from other crystals with the same space group D 2h 16 of the initial phase C, such as, e.g., K 2 SeO 4 , SC(NH 2 ) 2 , BCCD, the soft optical branch for which has only one minimum. As a result, a triple point of a new type, called the Lifshitz-type (LT) point, appears on the T-P phase diagrams. This point was previously predicted theoretically [5]. The LT-point can be observed in the T-P phase diagram at a given wave number q=q TL . At qq TL the C-IC phase transition occurs (IC is the incommensurate phase). Thus, the LT-point separates the transitions from the C phase to the C 0/1 and IC phases. The Lifshitz (L) point separates the same transitions [6]. But the L-point can be observed on the T-P phase diagrams at q=0.Therefore a specific feature of the T-P phase diagrams for the TMA-crystals is just the absence of the L-point.We use two theoretical approaches for description of the sequence of phase transitions