Theoretical Hardness of Zr₃N₄ Films

The structures, energetics and properties for orthohombic Zr₃N₄ and cubic Zr₃N₄ are calculated by first−principles calculations. The agreement between the predicted properties with available experimental data is excellent. The cubic phase has a smaller volume (by 11.2%) and a slightly higher total energy (by 0.3 eV/pair), in comparison to the orthohombic phase. We elucidate the effects of stress on hardness of Zr₃N₄ films. The results show that the hardness of c−Zr₃N₄ increases up to 23% as the stress increases to 15 GPa.