Ab initio studies of layering behavior of liquid sodium surfaces and interfaces

We have studied the liquid surface of sodium with extensive ab initio molecular dynamics simulations based on ensemble density-functional theory. We find clear evidence of layering in the direction perpendicular to the surface that persists to temperatures more than 100 K above the melting point. We also observe clear Friedel oscillations in the electronic density response to the presence of a surface, but their direct effect on atomic layering is ruled out. A careful finite-size effect analysis accompanies our results, showing that liquid slabs 20-25 A thick capture the essential details of the surface structure. We conclude that geometrical confinement is the common cause for layer formation, which is similar to what happens at a liquid-solid interface: at a free liquid surface, the rapid decay of the electronic density from the bulk liquid value to zero in the vapor forms a hard wall against which the atoms pack. Finally, we predict x-ray reflectivities from ab initio molecular dynamics data that include some of the large surface-normal wave vector-transfer regions that, for alkali metals, are not accessible to experiments