Comparison of X-ray analysis methods used to determine the grain size and strain in nanocrystalline materials

The Warren-Averbach (WA) analysis of X-ray Bragg-peak broadening, as well as simplified methods, are employed in the characterization of a set of nanocrystalline Fe powder samples with a wide range of grain sizes. In the WA analysis. the hook effect present at short times is attributed to small-angle grain boundaries. A universal relationship between grain size and rms strain is observed for all samples. For subtraction of instrumental peak broadening, a parabolic relation is found to yield the closest approximation to iterative convolution. Among the integral breadth methods, assuming that both strain and grain size broadening result in a Cauchy peak shape yields the largest grain size and smallest strain. Assuming that both contributions result in Gaussian peaks does the opposite, providing the closest approximation of the WA volume-averaged grain size. The Scherrer equation shows fortuitous agreement with the WA area-averaged grain size. The simplified methods can lead to severe systematic errors when the peak shape varies between samples.