Algorithm for systematic peak extraction from atomic pair distribution functions

Abstract

The study presents an algorithm, ParSCAPE, for model-independent extraction of peak positions and intensities from atomic pair distribution functions (PDFs). It provides a statistically motivated method for determining parsimony of extracted peak models using the information-theoretic Akaike information criterion (AIC) applied to plausible models generated within an iterative framework of clustering and chi-square fitting. All parameters the algorithm uses are in principle known or estimable from experiment, though careful judgment must be applied when estimating the PDF baseline of nanostructured materials. ParSCAPE has been implemented in the Python program SrMise. Algorithm performance is examined on synchrotron X-ray PDFs of 16 bulk crystals and two nanoparticles using AIC-based multimodeling techniques, and particularly the impact of experimental uncertainties on extracted models. It is quite resistant to misidentification of spurious peaks coming from noise and termination effects, even in the absence of a constraining structural model. Structure solution from automatically extracted peaks using the Liga algorithm is demonstrated for 14 crystals and for C60. Special attention is given to the information content of the PDF, theory and practice of the AIC, as well as the algorithm's limitations.

Recent advances in the application of total scattering methods to functional materials

“…To conclude, the increasing number of PDF-dedicated beamlines at synchrotrons around the world, together with the continuous development of user-friendly softwares by several groups [67][68][69][70][71][72][73][74][75] and the interest shown by several companies in developing laboratory-scale PDF instruments, are going to make the PDF analysis the structural characterization technique of choice in modern materials science.…”

Direct determination of amorphous number density from the reduced Pair Distribution Function

“…For these materials, the reduced PDF, symbolized as G(r), is the sum of peak information and of a straight sloping baseline expressed as À4pr 0 r and intrinsically feasible to work out from the PDF shape. However, upon increasing deviation from bulk crystallinity, this baseline becomes affected by the dominating presence of an attenuating particle shape factor, g(r), and is, then, expressed as À4pr 0 g(r)r [1]. The extreme case of linearity deviation towards high values of the real space coordinate, r, is that of completely amorphous materials [2][3][4][5][6][7], in which case r 0 may not be estimated from the tangent of the baseline as the latter is no longer a straight line [8].…”

“…In some cases, numerical estimation (i.e. the identification of PDF peaks and, as a result, of what constitutes baseline) has been cited as possible via modelling [1], but in practice this is not readily applicable to the amorphous state. Additionally, although in principle the PDF baseline may be estimated from a Fourier transform of Small Angle Scattering (SAS) data [8], the pair density function, r(r), which feeds into the calculation requires use of ab initio structural models, and we are not aware of such paradigms applied to amorphous materials in the literature.…”

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

“…For these materials, the reduced PDF, symbolized as G(r), is the sum of peak information and of a straight sloping baseline expressed as −4πρ 0 r and intrinsically feasible to work out from the PDF shape. However, upon increasing deviation from bulk crystallinity, this baseline becomes affected by the dominating presence of an attenuating particle shape factor, γ(r), and is, then, expressed as −4πρ 0 γ(r)r [1]. The extreme case of linearity deviation towards high values of the real space coordinate, r, is that of completely amorphous materials [[2], [3], [4], [5], [6], [7]], in which case ρ 0 may not be estimated from the tangent of the baseline as the latter is no longer a straight line [8].…”

“…In some cases, numerical estimation (i.e. the identification of PDF peaks and, as a result, of what constitutes baseline) has been cited as possible via modelling [1], but in practice this is not readily applicable to the amorphous state. Additionally, although in principle the PDF baseline may be estimated from a Fourier transform of Small Angle Scattering (SAS) data [8], the pair density function, ρ(r), which feeds into the calculation requires use of ab initio structural models, and we are not aware of such paradigms applied to amorphous materials in the literature.…”