Relationship between the atomic pair distribution function and small angle scattering: implications for modeling of nanoparticles

TL;DR

This paper clarifies the relationship between atomic pair distribution functions and small angle scattering, revealing how baseline features in PDFs relate to nanoparticle shape and size, thus enhancing nanoparticle modeling techniques.

Contribution

It explicitly links PDF and SAS functions, explaining the origin of baseline features and their relation to nanoparticle shape and size.

Findings

Baseline in PDFs originates from neglected SAS intensity.

Non-linear baseline in nanoparticles encodes shape and size information.

The relationship aids in improved nanoparticle modeling.

Abstract

Here we show explicitly the relationship between the functions used in the atomic pair distribution function (PDF) method and those commonly used in small angle scattering (SAS) analyses. The origin of the sloping baseline, $-4\pi r\rho_0$, in PDFs of bulk materials is identified as originating from the SAS intensity that is neglected in PDF measurements. The non-linear baseline in nanoparticles has the same origin, and contains information about the shape and size of the nanoparticles.