Residual stress and strain-free lattice-parameter depth profiles in a γ′-Fe4N1-x layer on an α-Fe substrate measured by x-ray diffraction stress analysis at constant information depth

Abstract

The residual stress and lattice-parameter depth profiles in a γ′-Fe4N1-x layer (6-μm thickness) grown on top of an α-Fe substrate were investigated using x-ray diffraction stress analysis at constant penetration depths. Three different reflections (220, 311, and 222) were recorded at six different penetration depths using three different wavelengths. At each penetration depth, x-ray diffraction stress analysis was performed on the basis of the sin2ψ method. As a result, the residual-stress depth profile was obtained from the measured lattice strains. The lattice spacings measured in the strain-free direction were used to determine the (strain-free) lattice-parameter depth profile. The nitrogen-concentration depth profile in the layer was calculated by applying a relationship between the (strain-free) γ′ lattice parameter and the nitrogen concentration. It was found that the strain-free lattice-parameter depth profile as derived from the 311 reflections is best compatible with nitrogen concentrations at the surface and at the γ′/α interface as predicted on the basis of local thermodynamic equilibrium. It could be shown that the 311 reflection is most suitable for the analysis of lattice-parameter and residual stress depth profiles because the corresponding x-ray elastic constants exhibit the least sensitivity to the type of and changes in grain interaction. The depth-dependence of the grain interaction could be revealed. It was found that the grain interaction changes from Voigt-type near the surface to Reuss-type at the layer/substrate interface.