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

Highlights: • The properties of binary iron nitrides are calculated by employing first principles. • The linear relation ΔH_f = −65.912x − 11.154 kJ mol⁻¹ are found. • The relations between the properties and electronic structure are discussed. - Abstract: 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 ΔH_f = −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-Fe₃N_1.1, ε-Fe₃N_1.3 and γ″-FeN_0.91 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