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.
| Original language | English |
|---|---|
| Pages (from-to) | 322-331 |
| Number of pages | 10 |
| Journal | Acta Crystallographica Section A: Foundations and Advances |
| Volume | 74 |
| Issue number | 4 |
| DOIs | |
| State | Published - Jul 2018 |
Funding
The authors acknowledge Dr Gabriel Caruntu, Benard Kavey and Swati Naik for synthesis of the BaTiO3 nanocubes and associated microscopy analysis. We acknowledge the original authors of Petkov et al. (2009) for use of the Fe2O3 data and the original authors of Liu et al. (2017) for use of the TiO2 nanoplate data. Time spent by the authors was supported through the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Early Career Research Program award KC040602. A portion of this research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. This research used resources of the Advanced Photon Source, a US DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract No. DE-AC02-06CH11357. This work benefited from the use of the SasView application, originally developed under NSF award DMR-0520547. SasView contains code developed with funding from the European Union’s Horizon 2020 research and innovation programme under the SINE2020 project, grant agreement No. 654000. Time spent by the authors was supported through the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Early Career Research Program award KC040602. A portion of this research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. This research used resources of the Advanced Photon Source, a US DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract No. DE-AC02-06CH11357. This work benefited from the use of the SasView application, originally developed under NSF award DMR-0520547. SasView contains code developed with funding from the European Union’s Horizon 2020 research and innovation programme under the SINE2020 project, grant agreement No. 654000.
Keywords
- Nanoparticles
- Pair distribution function
- Shape function
- Total scattering