Quantitative analysis of grain size in bimodal powders by x-ray diffraction and transmission electron microscopy

Abstract

In most studies related to milled powders, the grain size¹ is analyzed via X-ray diffraction (XRD) experiments, and a transmission electron microscopy (TEM) image with high magnification, if provided, is used primarily to confirm the results obtained by XRD experiments. This widely used approach is reasonable in light of the difficulties associated with TEM sample preparation. The present study, however, addresses the hypothesis that such an approach may not be valid when there is an inhomogeneous distribution of grains present. TEM examination, carried out in carefully prepared Al-7.5 wt% Mg samples, in which a global region is observable by TEM, provided the opportunity for quantitative analysis of grain size in cryomilled powders having an inhomogeneous distribution of grain sizes. The cryomilled Al-7.5 wt% Mg had a bimodal grain microstructure of 77% (area fraction) fine grains in the range of 10 to 60 nm and 23% coarse grains of approximately 1 μm. The results show that the XRD analysis yields a grain size that is close to that present in the fine-grained regions (i.e., 10–60 nm). The present study also systematically investigated the influence of the nine possible combinations of the Cauchy (C) and the Gaussian (G) approximations on the calculated grain size value, and the results show that the CC-CC approximation resulted in the largest calculated grain size, the GG-GG generated the smallest one, and the CG-CG, the approximation recommended by Klug and Alexander [1], led to a calculated grain size that is approximately equal to the average one from the CC-CC and GG-GG approximations. The maximum possible fluctuation of grain size values stemming from the various approximations is 38%.