D5 X-ray Diffraction (Crystallite Size)

Topic

X-ray diffraction from this nanostructure—characterized by a crystallite size typically below one hundred nanometers—relies on the same Bragg's law used to describe X-ray diffraction in metals; here, too, the law identifies the angles at which the nanostructure's diffraction peaks appear, thereby revealing its internal crystalline structure. Because the nanostructure possesses a specific crystalline structure, Bragg's law dictates that its diffraction peaks emerge at angles characteristic of that structure—just as they would for the same material in its bulk form.

However, at this nanoscale, the Scherrer equation—also adapted from metallurgy models—plays a far more significant role than it does for bulk materials. In this nanostructure, the crystallite size itself (being under one hundred nanometers) is almost invariably the primary cause of diffraction peak broadening, with microstrain making a negligible contribution by comparison. Since peak broadening is thus dominated by crystallite size rather than microstrain, the Scherrer equation alone—without the need for the Williamson-Hall analysis required in other instances—can reliably estimate the crystallite size. For this reason, this model—which begins by employing Bragg's law and the Scherrer equation—adapts to the nanoscale the same experimental method used to describe a different set of materials (specifically, metals), without requiring any changes to the instrument or measurement procedure; the only real difference is that, in this case, the crystallite size yielded by the Scherrer equation corresponds much more directly to the actual size of the entire nanostructure, rather than to the size of a grain within a much larger object.

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