Pressure-dependent elastic constants and sound velocities of wurtzite SiC, GaN, InN, ZnO, and CdSe, and their relation to the high-pressure phase transition: A first-principles study

Abstract

Elastic constants and sound velocities calculated from first principles as function of pressure are presented for wurtzite SiC, GaN, InN, ZnO, and CdSe. The ${C}_{11}$ and ${C}_{33}$ elastic constants, which are involved in longitudinal sound waves along symmetry directions, are found to monotonically increase with pressure. The shear moduli ${C}_{44}$ and ${C}_{66}$, which are involved in transverse sound waves along symmetry directions, either decrease with increasing pressure or initially increase from zero pressure but then turn over and start decreasing. Of special interest is the pressure at which the ${C}_{44}$ and ${C}_{66}$ elastic constants cross. At this pressure, the transverse acoustic waves in the basal plane, which are shown to be closely related to the symmetry breaking strain component that leads to the phase transition, become easier to excite than the ones with displacement along the $c$ axis. It is found that this crossover pressure is an upper limit to the actual phase transition pressure. The average of the calculated equilibrium transition pressure and the crossover pressure is proposed as a good estimate for the actual transition pressure in cases where the transition is strongly kinetically hindered by an enthalpy barrier between the two phases. This occurs for SiC and GaN and is confirmed with literature data for AlN. For the remaining materials, all these pressures are close to each other. The trends of the elastic constants and sound velocities with the materials' Phillips scale ionicity are also reported.