Surface Effect of Small Nanocrystals on the Accuracy of Structural Parameters Obtained by Pair Distribution Function Analysis

Abstract

The effect of the nanocrystal surface on the accuracy of average lattice parameters, crystal sizes, and mean square atom displacements (MSDs) obtained from pair distribution function (PDF) analysis of powder X-ray diffraction is investigated. A computational workflow is developed where atomistic models of gold nanocrystals with sizes between 5 and 30 nm are created by molecular dynamics simulations, diffraction data sets are computed by the Debye scattering equation over a temperature interval of 0–300 K, and PDF refinement is performed on the diffraction data by the DiffpyCMI algorithm. The accuracy of refined parameters is evaluated against real space calculations performed directly on the atomic coordinates. Results show that the performance of PDF refinement on diffraction data is temperature-dependent, and higher temperatures favor improved accuracy in refined lattice parameters, crystal sizes, and dynamic mean square atom displacements. The surface structure of nanocrystals leads to underestimated crystallographic parameters with up to 0.16, 6.6, and 15% deviation from the true lattice parameters, crystal size, and MSDs, respectively, for 5 nm gold nanocrystals at 0 K. However, with increasing crystal size and temperature, all deviations diminish such that for 30 nm gold nanocrystals at 300 K, they are calculated as 0.021, 1.67, and 11.16%.

A benchmark analysis of pair distribution function (PDF) refinement of X-ray diffraction data from small (5−30 nm) gold nanocrystalline powders over a temperature interval of 0−300 K is provided. The accuracy of refined crystallographic parameters, i.e., lattice parameters, crystal sizes, and mean square atom displacements, is shown to degrade with a decreasing nanocrystal size and temperature.