Structure of Liquid Metal Surfaces: A First Principles Perspective - Metallic Systems: A Quantum Chemist's Perspective - page 140

formation.of.layers.at.free.liquid.surfaces.to.the.situation.occurring.at.the.interface.
between.a.liquid.and.a.solid.[3];.at.such.an.interface,.the.formation.of.layers.in.the.
liquid.part.occurs.naturally.due.to.geometrical.coninement.of.the.liquid.atoms.by.
the.solid.atoms.

5.2.2.2 Geometrical Rearrangement to Increase Density at the Surface
Following.the.effective.Hamiltonian.simulations.of.Rice,.studies.were.made.on.liq-
uid.Au.surfaces.using.glue.model.potentials.by.Iarlori.et.al..[40].and.on.Pb.and.Au.
using.the.same.method.by.Di.Tolla.[41].and.Celestini.et.al..[42]..In.these.simulations,.
the.surface.densities.showed.oscillatory.proiles.that.were.explained.as.occurring.so.
that.the.undercoordinated.atoms.near.the.surface.regain.some.of.the.favorable.coor-
dination.they.would.have.in.the.bulk.liquid..This.increased.density.in.the.outermost.
part.of.the.surface.means.that.there.is.an.overcoordination.in.the.next.layer,.which.
is.mitigated.by.a.decrease.in.density.in.the.next.layer..This.alternating.increase.and.
decrease.in.density.continues.in.successive.layers.moving.from.the.surface.toward.
the.bulk,.and.is.consistent.with.the.layers.seen.in.the.density.proile.
The. spirit. of. this. proposed. mechanism—that. there. is. a. rearrangement. of. the.
surface. to. partially. recover. the. bulk. coordination. environment—is. similar. to. the.
explanation.proposed.by.Fabricius.et.al..[43].based.on.full.density.functional.theory.
(DFT).simulations.of.liquid.Si.surfaces.at.high.temperature.(at.the.temperature.con-
sidered,.1800.K,.Si.behaves.as.a.metal)..They.proposed.that.there.is.a.rotation.of.the.
bonds.(considerable.covalent.character.is.retained.in.the.high.temperature.state.of.Si).
at.the.surface.driven.by.a.requirement.to.recover.the.bulk.density.close.to.the.surface.
that.results.in.the.observed.oscillating.transverse.density.proiles.

5.2.2.3 Friedel Oscillations in Electronic Density Proile
A. third. explanation. is. that. Friedel. oscillations. [44]. in. the. electronic. density. may.
drive. the. atomic. layers.. Friedel. oscillations. in. the. valence. electron. density. would.
electrostatically.drive.the.atoms.toward.favorable.locations.and.away.from.unfavor-
able.ones,.giving.rise.to.the.appearance.of.layers.in.the.atomic.density..Motivation.
for. this. explanation. was. provided. by. a. set. of. DFT. calculations. on. solid. Mg(10 ¯ 0).
surfaces.by.Cho.et.al..[45],.which.indicated.that.the.ine.rearrangements.in.the.inter-
layer. relaxations. were. driven. by. the. changes. in. the. valence. electron. density. upon.
formation.of.a.surface..The.electronic.charge.density.at.the.surface.was.subtracted.
from.the.density.of.a.bulk.system;.the.difference.in.charge.density,.indicating.the.
rearrangement.of.charge.upon.formation.of.the.surface,.contained.deinite.Friedel.
oscillations..These.damped.oscillations.are.expected.to.appear.in.the.response.of.the.
valence. electrons. in. a. metallic. system. to. the. addition. of. a. localized. defect. (e.g.,. a.
surface,.or.inclusion.of.a.point.charge).and.correspond.to.a.potential. V ( r ).of.the.form

( ) ~ cos(

2
3

k r )

F

V r . (5.2)

r

.

where
r .is.the.distance.from.the.defect.(in.this.case,.the.surface)
k F .is.the.Fermi.wave.vector