Chemistry Reference
In-Depth Information
TABLE 6.3
Er hcp(0001) Slab Surface Work Function
Φ
and
Surface Relaxation
Φ
(eV)
‾
d
12
(%)
‾
d
23
(%)
‾
d
34
(%)
‾
d
45
(%)
k
.=.12.×.12
3.layers
3.28
−1.83
—
—
—
5.layers
3.25
−2.11
+1.10
—
—
7.layers
3.25
−1.98
+0.90
+0.12
—
9.layers
3.25
−1.90
+0.80
+0.22
−0.08
11.layers
3.25
−1.86
+0.91
+0.30
−0.02
13.layers
3.25
−1.88
+0.91
+0.30
−0.04
15.layers
3.25
−1.88
+0.92
+0.29
−0.04
17.layers
3.25
−1.87
+0.92
+0.29
−0.04
19.layers
3.25
−1.88
+0.92
+0.29
−0.04
21.layers
3.25
−1.88
+0.92
+0.29
−0.04
Bulk.limit
k
.=.8.×.8
3.26
−1.93
+0.81
+0.46
−0.06
k
.=.10.×.10
3.25
−1.82
+0.98
+0.24
−0.07
k
.=.12.×.12
3.25
−1.87
+0.92
+0.30
−0.04
k
.=.14.×.14
3.25
−1.89
+1.02
+0.27
−0.06
k
.=.16.×.16
3.25
−1.86
+0.93
+0.29
−0.06
The.changes.in.distances.
d
uv
.between.layers.
u
.and.
v
.from.the.bulk.separation.
are.given.as.a.percentage.of.the.bulk.layer.separation.
c
/2.
slab.calculation.are.presented..The.separation.between.the.irst.and.second.layers,.
d
12
,. shrinks. by. 1.9%. and. the. separation. between. the. second. and. third. layers,.
d
23
,.
increases.by.∼0.9%,.with.deeper.layers.exhibiting.minimal.relaxations..This.magni-
tude.of.relaxation.is.typical.of.close-packed.surfaces..Somewhat.larger.relaxations.
are.common.on.more.open.surfaces..These.geometry.relaxations.converge.quickly.
with.slab.thickness.for.Er(0001).and.with.surface.BZ.sample,.just.as.the.formation.
energy.did.
The.work.function,.Φ,.a.commonly.measured.physical.quantity.at.metal.surfaces,.
is.extracted.from.a.DFT.slab.calculation.as.the.Fermi.level.of.the.slab.with.respect.
to. vacuum.. This. last. caveat. is. important,. SEQQUEST. automatically. rescales. the.
self-consistent.potential.so.that.the.vacuum.potential.is.zero,.but.the.reported.Fermi.
level.in.other.codes.may.need.to.be.adjusted.manually.by.the.vacuum.level.to.obtain.
the.correct.work.function..With.a.polarized.slab.with.a.surface.dipole,.it.is.crucial.
to.have.appropriately.applied.boundary.conditions,.as.described.earlier,.in.order.to.
properly.identify.a.vacuum.potential.
The.work.function. is.very.sensitive. to.the.attenuation. of.the.density.at.the.sur-
face,.and.so.the.use.of.FOs.in.LCAO.code.is.crucial.to.getting.good.values..This.is.
a. delicate. undertaking,. as. in. conventional. DFT. codes,. because. the. work. function.
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