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

Abstract

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.

Acknowledgements

The authors are greatful to Mr. Jürgen Köhler for his help with the nitriding experiments and to Dr Ewald Bischoff for performing the EBSD measurements. We also wish to thank Mr. Peter Kobold and Dr Peter van Aken for TEM analysis. Special thanks go to Dr Shunli Shang (Pennsylvania State University, Pennsylvania, USA) for calculating the elastic constants of ε-Fe₃N and to Dr Michael Knapp (CELLS, Barcelona, Spain), who assisted during the measurements at the beamline B2, DESY, Hasylab (Hamburg, Germany).

Notes

¹ χ is the angle of rotation of the sample around the axis defined by the intersection of the diffraction plane and sample surface, i.e. perpendicular to the θ/2θ plane; χ coincides in χ mode with the angle ψ.

² Small changes δa(j) = a(j)–a(j–1) and δc(j) = c(j)–c(j–1) with respect to a(j–1) and c(j–1), as well as linear dependence on depth of a and c within the sublayers leads to a practical linear dependence on depth of (z) and d_hkl (z) within each sublayer.

³ Application of calculated hkl-dependent XECs (used as and in equation (3a)) recognizing the slight anisotropy of the SECs and calculated using different methods for grain interactio 33, 34 did not lead to an improvement of the fitting results described in section 4.3.

⁴ If one imposes in the fitting procedure the one-to-one relations between composition and the lattice parameters 17, 18 an unacceptable description of the experimental data occurs.

⁵ The isotropic coefficient of thermal expansion α_ε was assumed to vary linearly with concentration and the values used for α_ε at the surface and at the ε/γ′-interface were obtained by inter- and extrapolation, respectively, at nitrogen content values pertaining to the surface and the ε/γ′ interface (see table 1).