X-ray diffraction line-profile analysis of hexagonal ϵ -iron nitride compound layers: composition–and stress–depth profiles

Two hexagonal ε-Fe₃N_{1+ x} layers grown on α-Fe substrates by nitriding in NH₃/H₂ gas atmospheres were investigated by high-resolution X-ray powder diffraction using synchrotron radiation employing systematic tilting of the diffraction vector with respect to the specimen surface. Considering all recorded reflections simultaneously, the complicated diffraction profiles obtained were analyzed using a model incorporating hkl-dependent (anisotropic) and tilt angle (ψ)-dependent diffraction-line broadening and diffraction-line shifting. The diffraction-line broadening is mainly ascribed to the nitrogen concentration–depth profile within the layers causing depth-dependent strain-free lattice parameters, whereas the line shifts are predominantly caused by the stress–depth profile originating from the concentration-dependence of the coefficients of thermal expansion of the ε phase, with stress parallel to the surface, which is of tensile nature at the surface and of compressive nature at the ε/γ′ interface. This stress gradient additionally leads to a ψ dependence of the line broadening. Fitting of the microstructure and diffraction model led to determination of microstructure parameters, which can be related to the different sets of treatment conditions applied for the ε-iron nitride layer growth.