Diffraction-line broadening due to strain fields in materials; Fundamental aspects and methods of analysis

Broadening of (X-ray) diffraction lines is often due to the distortion fields associated with lattice defects as dislocations. A generally applicable flexible model for distributions of lattice defects and their distortion fields is presented. The model allows a straightforward calculation of diffraction-line profiles. Parameters of the model are the average distance between the defects, the extent of the distortion fields and the mean-squared strain. The order dependence of the shape and width of line profiles is studied as a function of these model parameters. The adequacy for practical application of two methods frequently used to analyse X-ray diffraction-line broadening (the Warren-Averbach analysis and the Williamson-Hall analysis) is investigated by applying them to calculating hue profiles. The 'size' and 'strain' parameters deduced by the methods mentioned are discussed with reference to the strain-field model parameters. It is concluded that only in limiting cases can the results be related directly to the microstructure. Experimental line profiles taken from a ball-milled tungsten powder are used to show that the line profiles calculated on the basis of the strain-field model pertain to realistic situations. It is shown that, in principle, an interpretation of measured line broadening is possible directly in terms of strain-held parameters.