Structure of Liquid Metal Surfaces: A First Principles Perspective - Metallic Systems: A Quantum Chemist's Perspective - page 153

6.0

3.0

0.0

-3.0

0 5 10 15 20 0 5 10 15 20

(a) z (Å) (b) z (Å)

FIGURE 5.10 Friedel.oscillations.in.valence.charge.density.redistributions.at.solid.sodium.
surfaces.[70,73]..Panel.(a).is.for.the.(001).surface.and.panel.(b).the.(111).surface..The.dotted.
vertical.lines.show.the.positions.of.the.underlying.layers.of.atoms..(Adapted.from.Walker,.
B.G..et.al.,. J. Chem. Phys .,.124,.174702,.2006;.Walker,.B.G..et.al.,. J. Phys. Condens. Matter ,.
18,. L269,. 2006;. Walker,. B.G.,. Ab Initio Molecular Dynamics Studies of Liquid Metal
Surfaces ,.PhD.thesis,.University.of.Cambridge,.2004..With.permission.)

each.to.form.a.surface..Then,.the.charge.density.was.calculated.for.this.newly.formed.
surface..The.density.determined.for.this.newly.created.surface.was.subtracted.from.
the.density.for.the.original.bulk.snapshot,.to.determine.the.redistribution.of.charge.
that.would.occur.upon.surface.formation.(no.relaxation.of.the.atomic.positions.in.the.
snapshot.is.made.when.the.surface.is.formed.by.addition.of.the.vacuum.region)..The.
charge.densities.for.selected.snapshots.from.the.bulk.liquid.simulation.are.plotted.in.
Figure.5.11,.as.well.as.the.charge.density.differences.between.the.bulk.and.surface.
charge.density.proiles.for.the.liquid.snapshots..It.is.clear.that.although.the.valence.
charge. densities. in. different. snapshots. are. rather. different. (relecting. the. fact. that.
the.atoms. in. the.liquid. move. considerably),. when.the.redistribution.proiles. of. the.
valence.charge.upon.surface.formation.are.determined.they.are.remarkably.uniform.
for.the.different.snapshots..The.charge.redistributions.are.relatively.uncoupled.from.
the.underlying.ionic.positions..Furthermore,.the.redistribution.proiles.indicate.the.
presence. of. strong. Friedel. oscillations. upon. surface. formation,. even. for. the. liquid.
snapshots,.where.there.are.no.atomic.layers..The.difference.in.the.forces.between.the.
atoms.in.the.bulk.and.surface.snapshots.are.given.in.the.bottom.panel.of.Figure.5.11..
The. atoms. that. become. the. surface. atoms. when. vacuum. regions. are. added. to. the.
bulk. simulation. snapshots. have. larger. forces. on. them. than. those. that. are. near. the.
center.of.the.slabs.of.atoms.created..The.forces.induced.upon.surface.formation.do.
not.correlate.with.the.Friedel.oscillations.observed.in.the.valence.charge.redistribu-
tion.proiles.
The.Friedel.oscillation.wavelengths.obtained.from.these.calculations.are.approxi-
mately.3.Å.(see.Table.6.7.of.Ref..[70]),.which.agree.well.with.the.expected.Friedel.
oscillation.wavelength.for.sodium.(3.4.Å).[44]..Comparing.these.numbers.with.the.
layer.spacings.calculated.for.the.free.Na.liquid.surfaces.in.Table.5.2.shows.them.to.
be.quite.similar..This.means.that.the.importance.of.Friedel.oscillations.cannot.be.
assessed. solely. on. the. basis. of. compatibility. of. the. layer. spacings. and. the. Friedel.
oscillation. wavelength.. However,. based. on. the. combination. of. the. persistence. of.
Friedel.oscillations.upon.formation.of.liquid.surfaces.and.the.strong.layer.formation.