Elastic anisotropy of γ′-Fe4N and elastic grain interaction in γ′-Fe4N1−y layers on α-Fe: First-principles calculations and diffraction stress measurements

Abstract: 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: C 11 =307.2GPa, C 12 =134.1GPa and C 44 =46.0GPa. The Zener elastic-anisotropy ratio, A =2C 44/(C 11 − C 12)=0.53, is strikingly less than 1, implying 〈100〉 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′-Fe4N1−y layers on top of α-Fe confirmed the “abnormal” elastic anisotropy of γ′-Fe4N1−y . Stress evaluation, yielding a compressive stress of about −670MPa 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. [Copyright &y& Elsevier]