Atomistic modeling based on the density functional theory combined with the quasi-harmonic approximation is used to investigate the lattice parameters and elastic moduli of the P6 and P6＇ phases of Si3N4. β-Si3N4 is set as a benchmark system since accurate experiments are available. The calculated lattice constants and elastic constants of β-Si3N4 are in good agreement with the experimental data. The crystal anisotropy, mechanical stability, and brittle behavior of P6- and P6＇-Si3N4 are also discussed in the pressure range of 30-55 GPa. The results show that these two polymorphs are metallic compounds. The brittleness and elastic anisotropy increase with applied pressure increasing. Besides, the phase boundaries of the β→P6＇→δ transitions are also analysed. The β phase is predicted to undergo a phase transition to the P6＇ phase at 40.0 GPa and 300 K. Upon further compression, the P6＇→δ transition can be observed at 53.2 GPa. The thermal and pressure effects on the heat capacity, cell volume and bulk modulus are also determined. Some interesting features are found at high temperatures.
Atomistic modeling based on the accurate first-principles method is used to investigate the lattice parameter, elastic constant, elastic modulus including bulk modulus （B） and shear modulus （G）, Poisson＇s ratio, and elastic anisotropy of Al, NiAl and NiaAl under extreme condition. The elastic constants obtained from calculations meet their mechanical stability criteria. Both NiAl and Ni3Al exhibit ductile behavior due to their high bulk mudulus to shear modulus ratios of B/G ratios. Through the full-electronic quasi-harmonic approximation, in which the mobile electrons are considered, we successfully obtain the thermo-physical properties including the thermal expansion coefficient, bulk modulus, heat capacity and entropy at simultaneously high temperatures and high pressures. The calculated quantities agree well with the available results. Some silent results are also interpreted. Several interesting features in the thermodynamic properties can also be observed.
