The structural and elastic properties of the recently-discovered wⅡ- and δ-Si3N4 are investigated through the plane-wave pseudo-potential method within ultrasoft pseudopotentials.The elastic constants show that wⅡ- and δ-Si3N4 are mechanically stable in the pressure ranges of 0-50 GPa and 40-50 GPa,respectively.The α→wⅡ phase transition can be observed at 18.6 GPa and 300 K.The β→δ phase transformation occurs at pressures of 29.6,32.1,35.9,39.6,41.8,and 44.1 GPa when the temperatures are100,200,300,400,500,and 600 K,respectively.The results show that the interactions among the N-2s,Si-3s,3p bands（lower valence band） and the Si-3p,N-2p bands（upper valence band） play an important role in the stabilities of the wⅡ and S phases.Moreover,several thermodynamic parameters（thermal expansion,free energy,bulk modulus and heat capacity） of δ-Si3N4 are also obtained.Some interesting features are found in these properties.δ-Si3N4 is predicted to be a negative thermal expansion material.The adiabatic bulk modulus decreases with applied pressure,but a majority of materials show the opposite trend.Further experimental investigations with higher precisions may be required to determine the fundamental properties of wⅡ- andδ-Si3N4.
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.
This paper describes the results of structural, electronic and elastic properties of silicon nitride （in its high-pressure P61 and P62 phases） through the first-principles calculation combined with an ultra-soft pseudo- potential. The computed equilibrium lattice constants agree well with the experimental data and the theoretical results. The strongest chemical bond （N-Si bond） shows a covalent nature with a little weaker ionic character. P61- Si3N4 is more stable than P62-Si3N4 due mainly to the fact that the shorter N-Si bond in the P61 phase allows stronger electron hybridizations. We have also predicted the phase stability of Si3N4 using the quasi-harmonic approximation, in which the lattice vibration and phonon effect are both considered. The results show that the 13 P61 phase transition is very likely to occur at 42.9 GPa and 300 K. The reason why the β→P61→3 phase transitions had never been observed is also discussed.
First-principles calculations of the crystal structures, phase transition, and elastic properties of EuS have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as some of the existing model calculations. The dependence of the elastic constants, the aggregate elastic modulus, and the elastic anisotropy on pressure have been investigated. Moreover, the variation of the Poisson＇s ratio, Debye temperature, and the compressional and shear elastic wave velocities with pressure have been investigated for the first time. Through the quasi-harmonic Debye model, the thermal expansions, heat capacities, Grneisen parameters and Debye temperatures dependence on the temperature and pressure are obtained in the pressure range from 0 GPa to 60 GPa and temperature range from 0 K to 800 K.
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.
The ultrasoft pseudo-potential plane wave method combined with the quasi-harmonic approach have been used to study the electronic, elastic and thermodynamic properties of the tetragonal, monoclinic and or- thorhombic Ge3N4. The negative formation enthalpies, the satisfactory of Born＇s criteria and the linear variations of elastic constants with pressure indicate that the three polymorphs can retain their stabilities in the pressure range of 0-25 GPa. The three GeaN4 are brittle solids at 0 GPa, while they behave in ductile manners in the pressure range of 5-25 GPa. t- and o-GeaN4 are hard materials but anisotropic, m-Ge3N4 has the largest ductility among the three phases. The results reveal that m-Ge3N4 belongs to an indirect band gap semiconductor, while t- and o-Ge3N4 have direct band gaps. For the thermal properties, several interesting features can be observed above 300 K. o-GeaN4 exhibits the largest heat capacity, while m-Ge3N4 shows the highest Debye temperature. The results predicted in this work can provide reference data for future experiments.
