Phase stability, magnetism, elastic properties and hardness of binary iron nitrides from first principles

• The properties of binary iron nitrides are calculated by employing first principles.
• The linear relation ΔHf = −65.912x − 11.154 kJ mol−1 are found.
• The relations between the properties and electronic structure are discussed.

First-principles calculations were performed to investigate the phase stability, magnetism, elastic properties and hardness of four main binary iron nitrides: FeN, ζ-Fe2N, ε-Fe3N and γ′-Fe4N. The linear relation ΔHf = −65.912x − 11.154 kJ mol−1 was found between the formation enthalpies and their nitrogen content x. Based on this linear approximation, the formation enthalpies of ε-Fe3N1.1, ε-Fe3N1.3 and γ″-FeN0.91 were estimated as −28.95, −31.59 and −42.56 kJ mol−1, respectively. The values were consistent with the experimental results. The calculated elastic constants indicated that the FeN and γ′-Fe4N phases were significantly anisotropic, the ζ-Fe2N exhibited some anisotropy to a certain degree. While the ε-Fe3N showed a relatively strong isotropic character. The ratios of bulk modulus (B) to shear modulus (G), 3.41 for FeN, 2.69 for ζ-Fe2N, 2.39 for ε-Fe3N and 3.09 for γ′-Fe4N, indicated their ductile nature. Magnetism calculations showed that the FeN was antiferromagnetic, the ζ-Fe2N, ε-Fe3N and γ′-Fe4N were paramagnetic. Besides, the Vickers hardness of these iron nitrides were calculated, and the strong Fe–N covalent bonds were found to play important roles in the hardness of iron nitrides.