Structure of Liquid Metal Surfaces: A First Principles Perspective - Metallic Systems: A Quantum Chemist's Perspective - page 148

3.0

(a) (b)

2.5

2.0

1.5

1.0

0.5

0.0

(c) (d)

2.5

2.0

1.5

1.0

0.5

0.0

-5 0 5 10 15 20 25 -5 0 5 10 15 20 25 30

z (Å) z (Å)

FIGURE 5.5 Density.proiles.obtained.for.free.liquid.sodium.surfaces.[70-74]..Black.lines.
give. the. atomic. density. proiles,. red. lines. the. valence. electron. densities.. The. simulations.
are.(a). T .=.500.K,.(001).cell;.(b). T .=.500.K,.(111).cell;.(c). T .=.400.K,.(001).cell;.(d). T .=.400.K,.
(001). cell.. (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.)

average. layer. spacings. extracted. from. the. density. proiles. are. slightly. smaller.
in.the.surface.layer.compared.to.the.inner.layers.(suggesting.coninement.in.the.
outermost.layers);.within.the.quoted.uncertainties,.the.average.layer.spacings.for.
the.two.different.simulation.cell.cross-sections.are.consistent.(indicating.that.no.
inite-size. effects. are. playing. an. important. role).. The. layer. spacings. at. the. liq-
uid. surfaces. are. uncorrelated. with. the. layer. positions. that. would. be. seen. at. a.
solid. surface. (i.e.,. in. the. surface. simulations,. the. numbers. of. atomic. layers. and.
their.spacings.are.independent.of.those.in.the.initial.bulk.simulation.cells.before.
they.were.melted);.furthermore,.the.layer.positions.are.not.greatly.affected.by.the.
temperature.

5.3.3.1.1 Assessment of Finite-Size Effects in Ab Initio
DFT MD Free Surface Simulations
Careful.examination.of.the.independence.of.the.surfaces.on.either.side.of.the.slabs.
was. made.. The. density-density. autocorrelation. functions. (see. Equation. 5.1. of.