Elastic anisotropy of γ′-Fe₄N and elastic grain interaction in γ′-Fe₄N_1-y layers on α-Fe: First-principles calculations and diffraction stress measurements

The three independent single-crystal elastic-stiffness constants C_ij of cubic γ′-Fe₄N (face-centred cubic (fcc)-type iron substructure) have been calculated by first-principles methods using the density functional theory: C₁₁ = 307.2 GPa, C₁₂ = 134.1 GPa and C₄₄ = 46.0 GPa. The Zener elastic-anisotropy ratio, A = 2C₄₄/(C₁₁ - C₁₂) = 0.53, is strikingly less than 1, implying 〈1 0 0〉 as stiffest directions, whereas all fcc metals show A > 1. This elastic anisotropy is ascribed to the ordered distribution of N on the octahedral interstitial sites. X-ray diffraction lattice-strain measurements for a set of different h k l reflections recorded from γ′-Fe₄N_1-y layers on top of α-Fe confirmed the "abnormal" elastic anisotropy of γ′-Fe₄N_1-y. Stress evaluation, yielding a compressive stress of about -670 MPa parallel to the surface, was performed on the basis of effective X-ray elastic constants determined from the calculated single-crystal elastic constants C_ij and allowing a grain interaction intermediate between the Reuss and the Voigt models.