The structural and elastic properties of the recently-discovered wⅡ- and δ-Si_3N_4 are investigated through the plane-wave pseudo-potential method within ultrasoft pseudopotentials.The elastic constants show that wⅡ- and δ-Si_3N_4 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-Si_3N_4 are also obtained.Some interesting features are found in these properties.δ-Si_3N_4 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-Si_3N_4.
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 pseudopotential. 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 β→P61 phase transition is very likely to occur at 42.9 GPa and 300 K. The reason why the β→P61→δ phase transitions had never been observed is also discussed.
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 orthorhombic Ge_3N_4.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 Ge_3N_4 are brittle solids at 0 GPa,while they behave in ductile manners in the pressure range of 5-25 GPa.t- and o-Ge_3N_4 are hard materials but anisotropic.m-Ge_3N_4 has the largest ductility among the three phases.The results reveal that m-Ge_3N_4 belongs to an indirect band gap semiconductor,while t- and o-Ge_3N_4 have direct band gaps.For the thermal properties,several interesting features can be observed above 300 K.o-Ge_3N_4exhibits the largest heat capacity,while m-Ge_3N_4 shows the highest Debye temperature.The results predicted in this work can provide reference data for future experiments.
