On the analysis of grain size in bulk nanocrystalline materials via x-ray diffraction

The Warren-Averbach (WA) analysis and other simplified methods that are commonly used to determine the grain size of nanocrystalline materials are discussed in terms of accuracy and applicabilities. The nanocrystalline materials used in the present study are prepared by cryomilling of A1 powders and subsequent consolidation (hot isostatic pressing and extrusion). Transmission electron microscopy observations of the as-extruded nanocrystalline A1 reveal a bimodal distribution of grain sizes centered around 50 to 100 nm and 250 to 300 nm. It is shown that the grain size determined by the WA analysis agrees with the lower bound grain size (e.g., 50 to 100 nm) observed experimentally. In the case of the integral method, it is useful to use a parabolic (Cauchy-Gaussian (CG)) relationship to approximate instrumental broadening and separate the intrinsic broadening. Compared to the Cauchy-Cauchy (CC) and Gaussian-Gaussian (GG) approximations, this is shown to give the best results. In addition, the reliability of the Scherrer equation is also discussed.