DensEst: un método empírico automatizado basado en potenciales para determinar las densidades de materiales...

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 extended structure, 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 AIASSE 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%.