The phenomenological analysis of the pressure-temperature $\mathrm{}(P-T)\mathrm{}$ phase diagram of ${\left[\mathrm{N}\right(\mathrm{C}\mathrm{H}}_3{)}_4{]}_2{\mathrm{CuCl}}_4$ (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 $\kappa$ at the gradient term ${\mathrm{}(dq/dz)(dq}^{*}/dz)$ changes the sign in the experimental range of pressures. The phase diagram in the $\alpha -\kappa$ phase plane is characterized by infinite Lifshitz point (at $\overrightarrow{\kappa }\infty )$ 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 ${(P}_K\approx 55\mathrm{MPa},$ $T_K\approx 304\mathrm{K})$ 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.

This paper presents the results of ultrasonic measurements of ${\text{LiNbO}}_3$ and ${\text{LiNbO}}_3:\text{MgO}$ crystals. The tensors of piezoelectric coefficients, elastic stiffness constants, and elastic compliances are determined for both crystals at room temperature. Combining these data with the results of piezo-optical measurements, a complete set of photoelastic tensor coefficients is also calculated. Doping of ${\text{LiNbO}}_3$ crystals by MgO does not lead to a considerable modification of their elastic and photoelastic properties. However, ${\text{LiNbO}}_3:\text{MgO}$ is characterized by a considerably higher resistance with respect to powerful light radiation, making it promising for future application in acousto-optic devices that deal with superpowerful laser radiation. Presented here are the complete tensor sets of elastic constants and photoelastic coefficients of ${\text{LiNbO}}_3$ and ${\text{LiNbO}}_3:\text{MgO}$ crystals that may be used for a geometry optimization of acousto-optical interaction providing the best diffraction efficiency of acousto-optical cells made of these materials.