Static and dynamic atom displacements in nanocrystalline powders from diffraction analysis at finite temperature

Abstract

We evaluate the accuracy of x-ray diffraction analysis performed by Rietveld refinement in extracting the static and dynamic atomic displacement parameters of spherical gold nanocrystals with sizes of 30 nm and below and within a temperature interval of 10–300 K. A self-consistent computational workflow composed of real- and reciprocal- space analyses is designed for this purpose. We obtain average lattice parameters, static and thermal atomic displacements as well as their temperature and particle size dependence in an ideally monodispersed and realistic nanocrystalline powder generated by molecular dynamics simulations. Then, we compare crystallographic parameters obtained from real- and reciprocal- space analyses to evaluate the accuracy of diffraction analysis. We also extend the comparison to local variations of crystallographic parameters in the nanocrystals and show how Rietveld refinement relates to the average parameters of the core and surface regions separately. We show that 1) average lattice parameters obtained from Rietveld refinement are greater than the mean lattice parameter of small nanocrystals and converge to the core lattice parameter with increasing particle size, 2) Rietveld refinement significantly underestimates static atom displacements of surface atoms in small nanocrystals, 3) dynamic atomic displacements in nanocrystalline gold powders are reliably obtained within 5 % error by Rietveld refinement, provided that thermal diffuse scattering is adequately removed from the diffraction data, 4) the discrepancy between real- and reciprocal-space analysis increases for the smallest gold nanocrystal.