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Density functional theory, density functional perturbation theory, and the Debye model have been used to investigate the structural, elastic, sound velocity, and thermodynamic properties of AlN with cubic rock-salt structure under high pressure, yielding the equilibrium structural parameters, equation of state, and elastic constants of this interesting material. The isotropic shear modulus, Pugh ratio, and Poisson’s ratio were also investigated carefully. In addition, the longitudinal, transverse, and average elastic wave velocities, phonon contribution to the thermal conductivity, and interesting thermodynamic properties were predicted and analyzed in detail. The results demonstrate that the behavior of the elastic wave velocities under increasing hydrostatic pressure explains the hardening of the corresponding phonons. Based on the elastic stability criteria under pressure, it is found that AlN with cubic rock-salt structure is mechanically stable, even at pressures up to 100 GPa. Analysis of the Pugh ratio and Poisson’s ratio revealed that AlN with cubic rock-salt structure behaves in brittle manner.

A pseudopotential plane wave method based on the density functional theory has been employed to study some thermodynamic properties of copper chloride (CuCl) and copper bromide (CuBr) compounds under the effect of temperature and pressure. The phase transition pressure, the unit cell volume, the isothermal bulk modulus, the constant volume heat capacity, the entropy, the Debye temperature, the Gruneisen parameter and the volumetric thermal expansion coefficient are studied in the pressure range 0–10 GPa, and for temperatures ranging from 0 K up to 650 K and 750 K for CuCl and CuBr, respectively. The phase transition pressure is found to be around 7.8 and 6.95 GPa for CuCI and CuBr, respectively. These values are respectively in reasonably good agreement with the experimental ones of 8.2 GPa and 6.8 GPa reported in the literature. Moreover, at room temperature and zero pressure, the heat capacity at constant volume and the Gruneisen parameter of both compounds of interest are found to be in good agreement with the available experimental and theoretical data. The information gathered from the present investigation may be useful for the study of the behavior of the fundamental properties of CuCI and CuBr under the influence of high temperature and pressure.