Efficient solution of particle shape functions for the analysis of powder total scattering data

Leonardi, A.; Neder, R.; Engel, M.

doi:10.1107/S1600576722001261

Journal of Applied Crystallography Journal of Applied
Crystallography

IUCr IT WDC

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Figure 1
Modelling the shape function for a cube of edge length ∼16 nm. The shape function, $[\gamma (r )]$ , is computed by summing the CVFs, $[{\Gamma _{\hat {\bf n}}}(r )]$ , over a set of [hkl ] directions. Here the CVFs for the [100], [110] and [111] directions are shown as an example. The contribution for each direction was scaled with the area fraction, $[{\omega _{\hat {\bf n}}}]$ , of a unit-surface-area sphere divided by a tessellation for which the projections of the directions are generator centres (schematic inset). The small-angle PDF correction in equation (6)