Diffraction line broadening due to lattice-parameter variations caused by a spatially varying scalar variable: its orientation dependence caused by locally varying nitrogen content in [epsilon]-FeN_0.433

The diffraction line broadening due to lattice-parameter variations caused by a position-dependent (spatial) scalar variable (e.g. the composition) was analysed theoretically. It was shown that the anisotropy of the resulting microstrain-like line broadening depends on the symmetry of the crystal system of the phase concerned. This model provides a physical basis for a special case of a previously reported phenomenological description of anisotropic microstrain broadening [Stephens (1999). J. Appl. Cryst. 32, 281–289], which is widely used in Rietveld refinement. The model presented was used to analyse the hkl dependence of the X-ray diffraction line broadening of a sample of hexagonal [epsilon]-iron nitride, FeN_y0 with the average N content y₀ = 0.433. The observed anisotropy of the line broadening was shown to be compatible with the known composition dependencies of the lattice parameters a(y) and c(y). From the extent of the line broadening, the standard deviation of y₀ could be determined very well, as 0.008.