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DensEst: an automated empirical potential-based means of determining the densities of disordered materials from total scattering data.

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Title: DensEst: an automated empirical potential-based means of determining the densities of disordered materials from total scattering data.
Authors: Daramola, Ayobami D1 (AUTHOR) adaramo2@ed.ac.uk, Parekh, Marissa N H1 (AUTHOR), Loveday, John S1 (AUTHOR), Proctor, John E2 (AUTHOR) j.e.proctor@salford.ac.uk, Ackland, Graeme J1 (AUTHOR) gjackland@ed.ac.uk, Pruteanu, Ciprian G1 (AUTHOR) cip.pruteanu@ed.ac.uk
Source: Nanotechnology. 2026, Vol. 37 Issue 9, p1-18. 18p.
Subjects: Density, Radial distribution function, Multiple scattering (Physics), Fourier transforms, Amorphous substances
Abstract: We investigate the fundamental limits of using total-scattering measurements to simultaneously determine the atomic number density (ρ) and pair distribution function (g (r)) of disordered materials. Building on rigorous Fourier-transform relationships between the structure factor S (Q) and g (r), we first show analytically that even infinitely precise, noise-free S (Q) data-spanning an unbounded Q- range-cannot uniquely specify both ρ and g (r). This non-uniqueness arises from phase information loss, finite-dimensional projections inherent in one-dimensional pair distributions, and the mathematical insensitivity of S (Q) to coordinated rescaling of density and radial distances. In addition, we highlight practical problems arising from mathematical methods aimed at extracting ρ via Fourier transform of data. Direct calculation from integrating g (r) − 1 (Yarnell method) converges badly for high density because of long-range structure in g (r), and at low density because of a bias coming from the central atom in g (r). Indirect calculation from the slope of f ⋅ [ g (r) − 1 ] (Eggert method) depends sensitively on having good quality high- Q data. To address these ambiguities, we introduce a density-sweep protocol using the empirical potential structure refinement (EPSR) within the ab initio augmented structure solving engine framework. By systematically varying trial densities around target values ( ± 5 % – 50 % ) and evaluating both the internal EPSR R -factor and an external R -factor based on final F (Q), one can identify a clear minimum bracketing the true ρ without reliance on external equations of state or arbitrary fitting ranges. We showcase the effectiveness of the method by application to supercritical krypton at multiple pressures, liquid D2O at 298 K and amorphous silica and reliably recover known densities within ± 5 % . [ABSTRACT FROM AUTHOR]
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Abstract:We investigate the fundamental limits of using total-scattering measurements to simultaneously determine the atomic number density (ρ) and pair distribution function (g (r)) of disordered materials. Building on rigorous Fourier-transform relationships between the structure factor S (Q) and g (r), we first show analytically that even infinitely precise, noise-free S (Q) data-spanning an unbounded Q- range-cannot uniquely specify both ρ and g (r). This non-uniqueness arises from phase information loss, finite-dimensional projections inherent in one-dimensional pair distributions, and the mathematical insensitivity of S (Q) to coordinated rescaling of density and radial distances. In addition, we highlight practical problems arising from mathematical methods aimed at extracting ρ via Fourier transform of data. Direct calculation from integrating g (r) − 1 (Yarnell method) converges badly for high density because of long-range structure in g (r), and at low density because of a bias coming from the central atom in g (r). Indirect calculation from the slope of f ⋅ [ g (r) − 1 ] (Eggert method) depends sensitively on having good quality high- Q data. To address these ambiguities, we introduce a density-sweep protocol using the empirical potential structure refinement (EPSR) within the ab initio augmented structure solving engine framework. By systematically varying trial densities around target values ( ± 5 % – 50 % ) and evaluating both the internal EPSR R -factor and an external R -factor based on final F (Q), one can identify a clear minimum bracketing the true ρ without reliance on external equations of state or arbitrary fitting ranges. We showcase the effectiveness of the method by application to supercritical krypton at multiple pressures, liquid D2O at 298 K and amorphous silica and reliably recover known densities within ± 5 % . [ABSTRACT FROM AUTHOR]
ISSN:09574484
DOI:10.1088/1361-6528/ae4809