Accuracy Limits of Pair Distribution Function Analysis in Structural Characterization of Nanocrystalline Powders by X-ray Diffraction

Abstract

We report the minimum errors of structural parameters, namely lattice parameter, crystallite size, and atomic displacement parameters, expected from Pair Distribution Function (PDF) analysis of nanocrystalline gold powders for the first time by a self-consistent computational methodology. Although PDF analysis has been increasingly used to characterize nanocrystalline powders by X-rays, the current literature includes no established error bounds to be expected from the resulting structural parameters. For accurate interpretation of X-ray diffraction data, these error bounds must be determined, and the obtained structural parameters must be cleared from them. Our novel methodology includes: 1) simulation of ideal powder diffraction experiments with the use of the Debye scattering equation, 2) pair distribution function analysis of the diffraction data with the Diffpy-CMI analysis software, and 3) determination of the errors from PDF analysis of the simulated diffraction data by comparing them with real-space analysis of spherical gold nanocrystals that are 30 nm size and smaller. Our results show that except for the lattice parameters and even with an ideal crystalline powder sample and ideal diffraction data, the extracted structural parameters from PDF analysis diverge from their true values for the studied nanopowder. These deviations are dependent on the average size of the nanocrystals and the energy of the X-rays selected for the diffraction experiments, where lower X-ray energies and small-sized nanocrystalline powders lead to greater errors.