Environmental Engineering Reference
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the entire range of applied electric fields, and that the difference between the maxima
(around E
z
0) is only about 0.002 eV/
˚
2
(0.04 J/m
2
). Interestingly, the maxima are
not exactly at E
z
¼ 0, but are slightly shifted to positive E
z
values. This reflects the fact
that, without an electrode potential, there is still a surface dipole at the electrode sur-
face, which requires the potential of zero charge, f
pzc
, to be compensated. Although
the applied electric field induces relatively small variations in the surface free energy,
there are major effects on the surface structure. Table 1.1 summarizes the surface
charge density and layer distances for three different electrode potentials. At
E
z
¼+3.85 V/
˚
, the excess surface charge density s
e
is around +0.02 e/
˚
2
,
which means an additional charge per surface atom of around +0.15 e. Without an
electric field, the layer distances increase from 2.052
˚
between the first two surface
layers to 2.076
˚
between the second and third layers and 2.085
˚
between the third
and fourth layers. The behavior is different in the presence of an external electric field.
At the upper and lower electric field limits given in Table 5.1, the additional positive or
negative surface charge causes repulsion between the surface layers. Consequently,
d
12
increases to 2.106
˚
for E
z
¼ 3.85 V/
˚
and even 2.155
˚
for E
z
¼ 23.85 V/
˚
.
The behavior of the other layer spacings is comparable. Because of its relevance as
the ground state, the hexagonal reconstructed surface is certainly more interesting.
Without an external electric field, the additional surface atom per unit cell already
leads to an overall buckled surface, with d
12
in the range of 2.051 - 2.851
˚
. On apply-
ing an electric field, the buckling is even more pronounced, and the upper limit of d
12
increases to over 3
˚
. This might already indicate a destabilization of the hexagonal
surface layer and a lifting of the surface reconstruction.
However, as Fig. 5.7 shows, there is no crossing between the curves over the entire
range of applied external electric fields, which would be necessary for a change in the
preferred surface structure. This is because, instead of g
0
(Df), which depends on the
electrode potential and therefore allows comparison with experiments, we have used
g
0
(E
z
) from (5.22). As already mentioned, to solve this problem, we can use exper-
imental information. While from our calculations we can extract the excess surface
charge density as a function of the applied electric field s
e
(E
z
), integration of the
experimental capacity measurements (Fig. 5.6) gives the same quantity, but as a func-
tion of the electrode potential s
e
(Df). By equating the calculated and experimental
surface charge densities, we can extract a relation between the electric field applied
in
the
calculations
and
the
experimentally
applied
electrode
potential,
giving
TABLE 5.1 Calculated Excess Charge Densities and Layer Separations for the
Unreconstructed and Reconstructed Au(100) Surfaces; In Each Case, the Values for
Three Different Electric Fields are Given: 23.85, 0.00, and 3.85 V/
˚
System
Au(100)-(1
1)
Au(100)-hex
E
z
(V/
˚
)
23.85
0.00
3.85
23.85
0.00
3.85
s
e
(e/
˚
2
)
20.022
0.00
0.021
20.019
0.00
0.018
d
12
(
˚
)
2.155
2.052
2.106
2.07323.026
2.05122.851
2.06123.067
d
23
(
˚
)
2.132
2.076
2.149
2.126
2.057
2.148
d
34
(
˚
)
2.135
2.085
2.149
2.133
2.071
2.161
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