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 a s simplified methods, are employed in the characterization of a set of nano crystalline Fe powder samples with a wide range of grain sizes. In the WA a nalysis. the hook effect present at short times is attributed to small-angl e grain boundaries. A universal relationship between grain size and rms str ain is observed for all samples. For subtraction of instrumental peak broad ening, a parabolic relation is found to yield the closest approximation to iterative convolution. Among the integral breadth methods, assuming that bo th strain and grain size broadening result in a Cauchy peak shape yields th e largest grain size and smallest strain. Assuming that both contributions result in Gaussian peaks does the opposite, providing the closest approxima tion of the WA volume-averaged grain size. The Scherrer equation shows fort uitous agreement with the WA area-averaged grain size. The simplified metho ds can lead to severe systematic errors when the peak shape varies between samples.