An evaluation of methods of diffraction-line broadening analysis applied to ball-milled molybdenum

A comparison has been carried out of different methods of X-ray diffraction-line profile analysis for the determination of crystallite sizes and microstrains, namely the integral breadth method and three methods based on Fourier analysis of diffraction lines, namely the Warren–Averbach method, an `alternative method' and a profile synthesis strain field method. The analyses have been applied to Mo powder ball milled in two types of mills: an attritor and a planetary mill. Using the Williamson–Hall integral breadth method, the line broadening at moderate deformation is attributed solely to microstrain,i.e.practically no size broadening is detected. The three methods based on the Fourier coefficients of diffraction lines yield comparable values for crystallite sizes and microstrains. With the profile synthesis strain field method, if a size effect is included, it is possible to fit the experimental Fourier coefficients over the entire range of the relevant scale of correlation distances. The line profile shape due to microstrains, as derived with the strain field method, exhibits a systematic dependence on the integral breadth. With increasing breadth, the shape changes from a Cauchy type to a Gaussian type, suggesting a change of the dislocation arrangement with increasing plastic deformation of molybdenum powders.