Direct determination of amorphous number density from the reduced pair distribution function

The inference of amorphous bulk density, while straightforward for nonporous, soluble materials, may present a formidable challenge in some of the most important classes of industrial applications, involving melts, porous solids, and non-soluble organic pharmaceuticals, with varied implications depending on the material's level of technological interest. Within nanotechnology and the life sciences in particular, accurate determination of amorphous true density is a frequent requirement and a regular puzzle, when, e.g., neither the Archimedean principle nor gas pycnometry may be applied, the former being only applicable to insoluble compounds, while the latter yielding skeletal density - an overestimate of true density to the extent of blind pores - and its efficiency is affected by the choice of the gas medium. In these cases, it is feasible to infer amorphous density from diffraction experiments through the use of the reduced Pair Distribution Function (PDF). Although an estimate of crystalline density has been known to be possible via the PDF shape, here we outline a new method extending this facility to include the estimation of amorphous density. Amorphous density may be inferred from the position of a local minimum of the reduced PDF profile, the latter extracted via a Fourier transformation of collected diffraction intensity. The PDF minimum is located within the PDF range bounded by r(min)=2 pi/Q(max) and the position of the first coordination peak, where Q(max) is the maximum length of the scattering vector achieved in the diffraction experiment. Amorphous density is calculated as the ratio of the value of the reduced PDF at the local minimum, divided by the term 4 pi r, where r is the real space coordinate of the local minimum. (C) 2019 The Author(s). Published by Elsevier B.V.