Numerical computation of shape factor for pair distribution function of nanoparticles using atomistic model

TL;DR

This paper introduces a numerical method to compute the shape factor for nanoparticle pair distribution functions using atomistic models, addressing challenges in analytical formulations for anisotropic shapes.

Contribution

It presents a novel numerical approach for calculating shape factors of nanoparticles and a fitting method to relate these to analytical forms for various geometries.

Findings

Numerical shape factors successfully computed for multiple geometrical shapes.

Fitting formulation effectively maps numerical results to analytical shape factors.

Method enhances accuracy of nanoparticle PDF analysis.

Abstract

The atomic pair distribution function (PDF) for nano-particles has to be corrected with a shape factor, also known as form factor, in order to take size and shape effects into consideration. For most anisotropic shapes an analytical formulation of the shape factor is a challenge. In this paper, we present a new method to numerically compute the shape factor using atomistic model. This numerical method to calculate PDF for a wide range of geometrical shapes is demonstrated. In addition, a fitting formulation, which effectively converts the numerical shape factors for some selected geometrical shapes to the analytical forms, is presented.