On the existence of a nonmonotone surface ion density in liquid metals: Perturbative introduction of discrete ions into jellium

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Abstract
We show that at the surface of a liquid metal oscillations are induced in the positions of ion planes by the Friedel oscillations of the electron density. This conclusion, derived from a discrete ion model via a perturbative pseudopotential analysis, is the same as reached earlier by Allen and Rice in a study of self‐consistently relaxed jellium. In the present work the surface of a liquid is modeled by close packed planes of cubic lattices. For either a face centered cubic lattice whose surface has been formed by cleavage perpendicular to the (111) direction, or a body centered cubic lattice cleaved perpendicular to the (110) direction, we find that when rs is less than about 3 only the first lattice plane relaxes; it moves away from the second plane by about 0.5% to 1% of the bulk interplanar spacing. When rs is greater than about 3, we find that the first two planes move nearer to one another than the bulk spacing (by about 0.5% to 1.5%) in such a way that the distance between the second and third lattice planes is greater than the bulk spacing by about 0.3%. This trend holds whether we use the step boundary electron distributions of Lang and Kohn or the author’s relaxed jellium electron distributions. The changes in ion plane positions are in qualitative agreement with the oscillations found for the continuum ion charge distributions of relaxed jellium.