Evaluating nanocrystallite size distributions in doped and undoped nanocrystalline ceramics by X-ray diffractometry

Abstract

Analytical expressions are formulated that enable the lognormal distribution of nanocrystallite sizes and the mean-squared crystal lattice microstrain in both doped and undoped nanocrystalline ceramics to be routinely determined by X-ray diffractometry. Importantly, these expressions, which are also applicable to most well-annealed nanocrystalline metals/alloys, are developed under the consideration that both the experimental and instrumental X-ray diffraction peaks are modeled by split Voigt functions to account for the (hitherto widely ignored) intrinsic peak asymmetry. The general analytical expressions of this new single-peak line-broadening method are then particularized to the case of small nanocrystallites with uniform composition for which a reasonable simplification (i.e., symmetrization of the experimental peak) can be made without compromising the accuracy of the results. Next, as an example of application the method developed is applied to the characterization of a nanocrystalline ceramic powder, and the nanocrystallite sizes so-determined are validated by transmission electron microscopy. The more complete and reliable microstructural information offered by this single-peak line-broadening method could contribute towards the accurate characterization of both doped and undoped nanocrystalline ceramics, and of most well-annealed nanocrystalline metals/alloys as well, a topic of particular research interest today.