Optimizing Experimental Parameters for Rietveld Refinement of Powder X-ray Diffraction from Small Gold Nanocrystals

Lattice parameters, average crystal sizes and root-mean-square atom displacements obtained from Rietveld refinement of powder diffraction data from gold nanopowders of 5-30 nm size are systematically investigated. A computational workflow is introduced where atomistic models of gold nanocrystals are created, and corresponding analytical diffraction data are computed and refined. The effect of nanocrystal size, nanocrystal shape, step size of the diffraction data and refinement range on the refined parameters are separately discussed for developing an optimized Rietveld refinement strategy for accurate sample characterization. Results show that a step size no greater than 0.2° ensures stable refined lattice parameters, crystal sizes and microstrains for gold nanocrystals smaller than 30 nm. For larger nanocrystals, smaller step sizes are necessary. Accuracy of refined lattice parameters are dependent on the refinement much more strongly for smaller nanocrystals than larger ones. Depending on the shape of the nanocrystal, limited refinement range may result in over or underestimations of the lattice parameter, hence extended refinement ranges are suggested for highest accuracy. Finally, microstrains refined from ideal crystalline gold nanospheres are significantly overestimated for smaller nanocrystals than larger ones for limited refinement range. However, if the refinement range includes four to five high-intensity Bragg peaks, then the refined microstrains stabilize irrespective of the nanocrystal size.