DShaper: an approach for handling missing low-Q data in pair distribution function analysis of nanostructured systems

This article discusses the potential problems and currently available solutions in modeling powder-diffraction-based pair distribution function (PDF) data from systems where morphological feature information content includes distances in the nanometre length scale, such as finite nanoparticles, nanoporous networks and nanoscale precipitates in bulk materials. The implications of an experimental finite minimum Q value are reviewed by simulation, which also demonstrates the advantages of combining PDF data with small-angle scattering data. A simple Fortran90 code, DShaper, is introduced, which may be incorporated into PDF data fitting routines in order to approximate the so-called `shape function' for any atomistic model.