2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94851The structures of the liquid surface and the liquid-solid interface of sodium have been characterized with extensive first-principles molecular dynamics simulations. Friedel oscillations in the electronic charge density at the free surface were found to persist across the solid-to-liquid melting transition, with a small but distinctive electronic layering that remains decoupled from the atomic positions. Strong ionic layering was observed both at the liquid surface and at the liquid-solid interface, notwithstanding the absence of Friedel oscillations or under-coordinated atoms in the latter case. Confinement effects at these soft or hard boundaries drive the atoms into quasi-close-packed layers; even for this prototypical free-electron metal Friedel oscillations are not relevant to ordering.4 pages, 4 figures, submitted to Physical Review LettersMaterials Sciencetext