Structure of Liquid Metal Surfaces: A First Principles Perspective - Metallic Systems: A Quantum Chemist's Perspective - page 155

TABLE 5.2
Layer Spacings Determined from Sodium Liquid
Surface Simulations in Refs. [70-74]
d surface (Å) d inner (Å)

T ( K ) (001) (111) (001) (111)

400 2.98.±.0.03 2.97.±.0.05 2.98.±.0.24 3.20.±.0.15

500 2.91.±.0.15 2.75.±.0.12 3.04.±.0.24 3.34.±.0.43

Source: . Adapted. with. permission. from.Walker,. B.G.,. Ab Initio
Molecular Dynamics Studies of Liquid Metal Surfaces ,.
PhD. thesis,. University. of. Cambridge,. copyright. 2004;.
Walker,.B.G..et.al.,. J. Phys. Condens. Matter ,.16,.S2575,.
copyright.2004;.Walker,.B.G..et.al.,. J. Chem. Phys .,.124,.
174702,. copyright. 2006;. Walker,. B.G.. et. al.,. J. Phys.
Condens. Matter ,. 18,. L269,. copyright. 2006;. Walker,.
B.G.. et. al.,. J. Chem. Phys .,. 127,. 134703,. copyright.
2007,.American.Institute.of.Physics.
The.labels.“(001)”.and.“(111)”.refer.to.the.simulation.cells.having.
square-. and. diamond-shaped. cross-sectional. geometries,.

respectively.

ordering,.the.atoms.are.on.average.sixfold-coordinated,.although.there.are.signii-
cant.numbers.of.atoms.with.coordination.numbers.of.5.and.7.
Experimental.work.on.liquid.lead.in.contact.with.a.solid.silicon.surface.[81].found.
evidence.for.the.existence.of.partial.icosahedral.fragments.(corresponding.to.ivefold.
local.ordering).at.the.interface.of.the.lead.with.the.Si.surface..In.considering.free.
liquid. surfaces. and. liquid-solid. interfaces,. one. can. ask. whether. this. type. of. local.
ordering.might.exist.at.those.interfaces.in.other.types.of.metal.
The. DFT-based. molecular. dynamics. simulations. of. liquid. Na. discussed. in.
Section.5.3.were.analyzed.in.relation.to.this.question.[74]..The.simulations.yielded.
indications,. although. weak,. that. there. is. a. preference. for. ivefold-. and. sixfold-
coordinated. ordering. within. the. planes. at. the. surface,. with. the. tendency. toward.
sixfold.ordering.increasing.as.the.temperature.is.lowered.
The.regions.of.the.free.surface.considered.in.examining.the.in-plane.structure.are.
indicated. in. Figure. 5.12..The. numbers. of. nearest. neighbors. in. the. various.regions.
are. shown. in. Figure. 5.13.. The. dominant. number. of. neighbors. is. 5,. though. there.
are. signiicant. weights. at. 4. and. 6.. The. proportion. of. atoms. having. 4. neighbors.
decreases.as.the.temperature.is.lowered.from.500.to.400.K..The.in-plane.structure.
can.be.further.examined.with.the.calculation.of.bond.angle.distributions;.the.bond.
angle. distributions. obtained. from. the. molecular. dynamics. simulations. appear. in.
Figure.5.14..The.bond.angle.distributions.do.not.vary.much.in.the.different.regions.
of.the.surface.at.the.same.temperature,.though.in.comparing.the.bond.angle.distribu-
tions.at. T .=.400.K.with.those.at. T .=.500.K,.a.movement.of.weight.to.higher.bond.angles.
can.be.seen.at.the.lower.temperature..It.was.suggested.[74].that.this.is.consistent.with.