Ionic and electronic structures of liquid aluminium from the quantal hypernetted-chain equations combined with the molecular dynamics method

Abstract

Liquid aluminium is a simple metal which can be modelled as an electron-ion mixture with pairwise interparticle interactions. On the basis of the density functional theory, the quantal hypernetted-chain (QHNC) formulation for the electron-ion mixture provides exact expressions for the electron-ion and ion-ion radial distribution functions (RDF), and shows that this electron-ion mixture can be treated as a quasi-one-component liquid interacting only through a pairwise interaction without many-body forces. Using the approximation that the exchange-correlation effect of the conduction electrons in the mixture is represented by the local-field correction (LFC) of the jellium model, the QHNC formulation offers a procedure for performing a first-principles molecular dynamics (MD) simulation where the effective ion-ion interaction is determined self-consistently with its liquid structure. Using the Geldart-Vosko (GV) LPC the structure factor of liquid aluminium near its melting point is calculated by this procedure (QHNC-MD) and is in fairly good agreement with experiment, in conjunction with the bridge function and the direct correlation function. The calculated ion-ion RDF exhibits a significant dependence on which kind of LFC is adopted in the QHNC-MD method in contrast with what is found in the case of liquid alkali metals where the LFC of the GV type and of the local-density-approximation type yield almost the same structure factors. The effective ion-ion potential from the QHNC-MD method with the GV LFC becomes a deep negative well where the potential of Dagens, Geldart and Taylor has a positive minimum. The electron-ion RDF is obtained in a consistent way with the density profile rho (r) of a neutral pseudoatom. The Ashcroft model potential with core radius rc=1.12aB produces an electron density distribution rho (r) and ion-ion RDF almost identical with the QHNC-MD results.