A numerical method for deriving shape functions of nanoparticles for pair distribution function refinements. Issue 4 (6th June 2018)

• Record Type: Journal Article
• Authors: Usher, Tedi-Marie; Olds, Daniel; Liu, Jue; Page, Katharine
• Is Part Of: Acta crystallographica. Volume 74:Issue 4(2018:Jul.)
• Page Start: 322
• Page End: 331
• Publication Date: 2018-06-06
• Subjects: nanoparticles -- shape function -- pair distribution function -- total scattering; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S2053273318004977
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : A numerical method for generating shape functions of non‐spherical nanoparticles for use in small‐box refinements of pair distribution function data is presented and implemented on several sets of simulated and experimental data. With this approach, physically relevant size parameters for simple and complex nanoparticle shapes can be refined from the data. Abstract : In the structural refinement of nanoparticles, discrete atomistic modeling can be used for small nanocrystals (< 15 nm), but becomes computationally unfeasible at larger sizes, where instead unit‐cell‐based small‐box modeling is usually employed. However, the effect of the nanocrystal's shape is often ignored or accounted for with a spherical model regardless of the actual shape due to the complexities of solving and implementing accurate shape effects. Recent advancements have provided a way to determine the shape function directly from a pair distribution function calculated from a discrete atomistic model of any given shape, including both regular polyhedra ( e.g. cubes, spheres, octahedra) and anisotropic shapes ( e.g. rods, discs, ellipsoids) [Olds et al. (2015). J. Appl. Cryst. 48, 1651–1659], although this approach is still limited to small size regimes due to computational demands. In order to accurately account for the effects of nanoparticle size and shape in small‐box refinements, a numerical or analytical description is needed. This article presents a methodology to derive numerical approximations of nanoparticle shape functions by fitting to a training set of known shape functions; the numerical approximations can then be employed on larger sizes yielding a more accurate and physically meaningful refined nanoparticle size. The method is demonstrated on a series of simulated and real data sets, and a table of pre‐calculated shape function expressions for a selection of common shapes is provided.