The mechanical and electronic properties of two GaN crystals, wurtzite and zinc-blende GaN, under various hydrostatic pressures were investigated using first principles calculations. The results show that the lattice constants of the two GaN crystals calculated in this study are close to previous experimental results, and the two GaN crystals are stable under hydrostatic pressures up to 40 GPa. The pressure presents extremely similar trend effect on the volumes of unit cells and average Ga-N bond lengths of the two GaN crystals. The bulk modulus increases while the shear modulus decreases with the increase in pressure, resulting in the significant increase of the ratios of bulk moduli to shear moduli for the two GaN polycrystals. Different with the monotonic changes of bulk and shear moduli, the elastic moduli of the two GaN polycrystals may increase at first and then decrease with increasing pressure. The two GaN crystals are brittle materials at zero pressure, while they may exhibit ductile behaviour under high pressures. Moreover, the increase in pressure raises the elastic anisotropy of GaN crystals, and the anisotropy factors of the two GaN single crystals are quite different. Different with the obvious directional dependences of elastic modulus, shear modulus and Poisson’s ratio of the two GaN single crystals, there is no anisotropy for bulk modulus, especially for that of zinc-blende GaN. Furthermore, the band gaps of GaN crystals increase with increasing pressure, and zinc-blende GaN has a larger pressure coefficient. To further understand the pressure effect on the band gap, the band structure and density of states (DOSs) of GaN crystals were also analysed in this study.

For the limitation of experimental methods in crystal characterization, in this study, the mechanical, thermodynamic and electronic properties of wurtzite and zinc-blende GaN crystals were investigated by first-principles calculations based on density functional theory. Firstly, bulk moduli, shear moduli, elastic moduli and Poisson's ratios of the two GaN polycrystals were calculated using Voigt and Hill approximations, and the results show wurtzite GaN has larger shear and elastic moduli and exhibits more obvious brittleness. Moreover, both wurtzite and zinc-blende GaN monocrystals present obvious mechanical anisotropic behavior. For wurtzite GaN monocrystal, the maximum and minimum elastic moduli are located at orientations [001] and < 111 >, respectively, while they are in the orientations < 111 > and < 100 > for zinc-blende GaN monocrystal, respectively. Compared to the elastic modulus, the shear moduli of the two GaN monocrystals have completely opposite direction dependences. However, different from elastic and shear moduli, the bulk moduli of the two monocrystals are nearly isotropic, especially for the zinc-blende GaN. Besides, in the wurtzite GaN, Poisson's ratios at the planes containing [001] axis are anisotropic, and the maximum value is 0.31 which is located at the directions vertical to [001] axis. For zinc-blende GaN, Poisson's ratios at planes (100) and (111) are isotropic, while the Poisson's ratio at plane (110) exhibits dramatically anisotropic phenomenon. Additionally, the calculated Debye temperatures of wurtzite and zinc-blende GaN are 641.8 and 620.2 K, respectively. At 300 K, the calculated heat capacities of wurtzite and zinc-blende are 33.6 and 33.5 J mol^-1 K^-1, respectively. Finally, the band gap is located at the G point for the two crystals, and the band gaps of wurtzite and zinc-blende GaN are 3.62 eV and 3.06 eV, respectively. At the G point, the lowest energy of conduction band in the wurtzite GaN is larger, resulting in a wider band gap. Densities of states in the orbital hybridization between Ga and N atoms of wurtzite GaN are much higher, indicating more electrons participate in forming Ga-N ionic bonds in the wurtzite GaN.