First-principles study on the electronic, elastic and thermodynamic properties of three novel germanium nitrides

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 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 Ge₃N₄ are brittle solids at 0 GPa, while they behave in ductile manners in the pressure range of 5-25 GPa. t- and o-Ge₃N₄ 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-Ge₃N₄ 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.