Structure of Liquid Metal Surfaces: A First Principles Perspective - Metallic Systems: A Quantum Chemist's Perspective - page 139

high.momentum.transfers,.with.the.density.proile.itted.to.reproduce.the.density..In.
the.case.of.the.high.surface.tension.metals,.a.complete.peak.in.the.relectivity.was.
observed,.and.thus.itting.the.surface.density.proile.was.unambiguous..In.the.case.
of.the.low.surface.tension.metals.(K.and.eutectic.Na:K.alloys),.only.the.lead.up.to.a.
peak.from.the.low. q z .side.was.seen.in.the.experimental.measurements;.this.made.the.
itting.to.determine.the.density.proiles.more.dificult..In.addition,.the.intrinsic.struc-
ture.of.the.liquid.surface.is.damped.by.thermally.excited.capillary.waves..Though.
these. are. suppressed. by. higher. surface. tension,. for. the. low. surface. tension. metals.
where. the. damping. is. not. very. signiicant,. there. is. correspondingly. an. increased.
dificulty. in. measuring. the. intrinsic. surface. structure.. In. measurements. on. liquid.
Sn.[17,18].and.Bi.[18],.a.decreased.spacing.between.the.surface.layer.and.the.second.
layer.from.the.surface.relative.to.the.spacings.of.the.subsequent.layers.was.observed.
Additional. studies. of. liquid. metal. surfaces. have. been. made. using. x-ray. tech-
niques,. including. the. structures. of. various. nonmetallic. layers. on. liquid. metal. sur-
faces.[19-23].and.the.wetting.and.segregation.at.the.surface.of.components.in.alloys,.
for.example,.Bi:Sn.[24],.Au:Si.[25,26],.Au:Sn.[27].
In.contrast.to.the.measurements.made.on.the.liquid.metals,.experimental.measure-
ments.on.the.surface.of.water.[28].showed.no.evidence.of.molecular.layer.formation.
at. the. free. surface.. Subsequent. measurements. on. the. molecular. liquid. tetrakis(2-
ethylhexoxy)silane,.an.isotropic,.dielectric.liquid.[29].showed.that.layer.formation.is.
possible.at.dielectric.liquid.surfaces.
5.2.2 S imulationS v ieWPoint
We.review.three.possible.explanations.for.the.mechanism.of.layer.formation.at.the.
free.surfaces.of.liquid.metals.coming.out.of.simulation.research..Systematic.exami-
nation.of.these.explanations.was.the.focus.of.simulations.of.free.surfaces.of.sodium.
made.using.ab.initio.molecular.dynamics,.which.we.shall.review.in.Section.5.3,.as.
well.as.supporting.computer.“experiments.”
5.2.2.1 Layering against Hard Wall
The.earliest.atomistic.simulations.of.liquid.metals.were.made.by.Rice.and.cowork-
ers. [30-39]. and. predicted. (in. fact,. before. the. experimental. techniques. were. able.
to. ascertain. deinitely). that. the. transverse. density. proiles. at. liquid. metal. surfaces.
would. display. layering. oscillations.. Their. simulations. were. made. using. an. “effec-
tive.Hamiltonian”.to.describe.the.electronic.structure,.together.with.a.Monte.Carlo.
algorithm.to.sample.atomic.conigurations..A.fairly.large.set.of.metals.were.stud-
ied.using.this.approach,.including.Na.[30,31,34],.Cs.[31],.Hg.[32],.Ga.[37],.and.Mg.
[36]..In.addition.to.these,.various.alloys.were.simulated:.Na:Cs.[33,34],.Bi:Ga.[38],.
and.Ga:Sn.[39]..The.physical.explanation.for.the.layering.mechanism.resulting.from.
this. work. is. that. the. rapid. decay. of. the. electronic. density. across. the. surface,. and.
the. strong. dependence. of. the. effective. ionic. potential. on. electron. density. (which.
accounts.for.the.“phase-transition”.from.a.metallic.system.with.the.associated.delo-
calization. of. the. electrons. in. the. liquid,. to. the. atomic. state. in. which. the. electrons.
are. localized. on. their. corresponding. nuclei). acts. like. a. rigid. wall. that. geometri-
cally.conines.the.motion.of.atoms.across.the.surface..This.explanation.connects.the.