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

Acta Cryst. (2009). A65, 232–239 (

[Simulation of gold nanoparticles] Top: Simulated diffraction patterns from gold nanoparticles in the form of F(Q) = Q[S(Q) − 1], the reduced structure function. The violet and gold lines indicate the small-angle and wide-angle scattering, respectively. Bottom: The resulting PDFs obtained by Fourier transforming the data in the top panel. Normally, nanoparticle PDFs are determined by excluding the SAS (gold), in which case they have a non-linear baseline that is characteristic of the nanoparticle's shape and size and can be reconstructed by measuring the SAS (purple).
The atomic-pair distribution function (PDF) is emerging as a powerful tool for studying structure on the nanoscale. Small-angle scattering (SAS) also yields information about nanoscale density fluctuations in materials. This article presents a complete re-derivation of the PDF equations revealing the formal connection to the SAS equations and facilitating the combination of these methods. The SAS information is of particular value when modeling discrete nanoparticles as it yields the shape of the PDF baseline.
C.L. Farrow and S.J.L. Billinge