About the existence of a Lifshitz point on the phase diagram of Sn₂P₂(Se_xS_1–x)₆solid solutions: acoustic and optical studies

On the critical exponent of order parameter in Sn2P2S6 and Sn2P2(Se0.28S0.72)6 crystals

“…It is equal to 0.24 0.02  (see Table 2). This value corresponds to the conditions of the tricritical point and agrees well with the conclusions drawn in our earlier work [5]. We have shown (see [5]) that a change in the phase transition order from the second-order one (at x < 0.28) to the first-order one (at x > 0.28) should occur in the solid solutions with x = 0.28.…”

“…Then the tricritical point should appear somewhere in the vicinity of x = 0.28. This conclusion agrees perfectly with the results of our earlier study [5].…”

“…Notice that the mentioned value of  exactly corresponds to the tricritical point. However, as shown in [4,5], the tricritical point appears on the (x, T)-diagram at x = 0.28, while for the pure Sn 2 P 2 S 6 crystals we have that point on the (P, T)-diagram at P = 4.3 kbar and T = 259 K. Moreover, a reliable value of the critical exponent for Sn 2 P 2 S 6 obtained using the optical birefringence is equal to 0.3 [15]. The disagreement between the critical exponent and the coordinates of the tricritical point can be caused by the fact that the  value mentioned above has been obtained using the assumption that the angle between the a axis and the spontaneous polarisation vector is equal to 13 deg at the room temperature [16].…”

“…Many authors have noticed that the phase transition in Sn 2 P 2 S 6 is close to a number of specific polycritical points on the (x, T)-phase diagram of Sn 2 P 2 (Se x S 1-x ) 6 solid solutions, namely a tricritical point (see, e.g., the recent work [2][3][4][5]), a Lifshitz point [1,3,6], or a tricritical Liftshitz point [7]. The results of our recent work [5] have testified that, at x = 0.28, the tricritical point should occur on the (x, T)-phase diagram of Sn 2 P 2 (Se x S 1-x ) 6 rather than the Lifshitz one, whereas the triple point characterised by the appearance of incommensurately modulated phase should occur at some higher concentrations of selenium (e.g., at 0.4 x  ). It is known that, according to the mean-field theory of phase transitions, the behaviour of physical properties of crystals can be characterised by a number of critical exponents, which acquire different values for different polycritical points on the phase diagram.…”

Acoustooptic figure of merit for Sn2P2S6 crystals and the temperature dependences of acoustic wave velocities

“…1a). In our recent studies [13,14], we have shown that such a temperature behaviour of the acoustic wave velocities in Sn 2 P 2 S 6 is caused by a closeness of those crystals to the tricritical point on their Nonetheless, the velocities of the longitudinal waves show some anomalies at the Curie temperature and a corresponding increase in the AOFM can indeed occur. However, the mentioned velocities are higher than those peculiar of the transverse waves, and so the relevant AOFMs will be much lower than the values measured in the work [8].…”