3.2 Surface Reconstruction
71
(100)-(hex) and -(1 × 1) surfaces in 0.01 M HClO 4 solution [11]. The solid curve in
Fig. 3.2 for the Au (100)-(hex) surface was measured during anodic potential scan
from −0.4 to 0.6 V (SCE). The value of E pzc = 0.27 V (SCE) for the Au (100)(hex) surface is obtained from the location of the differential capacity minimum in
the solid curve. The dotted curve in Fig. 3.2 for the Au (100)-(1 × 1) surface was
measured during cathodic potential scan from 0.6 to −0.4 V (SCE) after lifting of
the Au (100)-(hex) surface. The value of E pzc = 0.03 V (SCE) for the Au (100)-(1
× 1) surface is also obtained from the location of the differential capacity minimum
in the dotted curve. The difference of 0.24 V in E pzc between the Au (100)-hex and
-(1 × 1) surfaces is consistent with that obtained by Kolb [1, 2].
As explained in Sect. 1.9 of Chap. 1, the Lippmann equation:
∂γ
∂ E
T,μ i
= −q
can be used for a solid metal electrode as well as a liquid metal electrode such as
mercury. Consequently, the potential dependence of surface tension γ (E), i.e., the
electrocapillary curve (γ vs. E) for the Au (100) electrode surfaces, can be calculated
from the double integration of differential capacity c(E) with respect to potential E:
γ (E) = γ pzc −
˜ E
E pzc
c(E)dE, where γ pzc is the surface tension at E pzc . Although the
absolute value of γ pzc for the Au (100) electrode surfaces cannot be obtained from
experiments, the theoretical value of γ for zero surface charge may be available for
γ pzc . Ibach et al. [12] calculated γ (E) for the Au (100)-(hex) and -(1 × 1) surfaces
from the double integration of the differential capacity data in Fig. 3.2 by employing
the value of γ pzc = 1.25 J m
−2 obtained with first-principles calculation [13–16].
However, the value of γ pzc = 1.25 J m
−2 is rather pertinent to the Au (111)-(1
× 1) surface than the Au (100)-(1 × 1) surface [13, 14]. The surface energy of the
Au (100)-(1 × 1) surface is larger than that of the Au (111)-(1 × 1) surface since
the atomic density of the former is lower than that of the latter. The value of γ pzc
= 1.44 J m
−2 is preferable for the Au (100)-(1 × 1) surface [15]. Moreover, the
value of γ pzc of the Au (100)-(hex) surface has not been theoretically obtained but it
should be less than that of the Au (100)-(1 × 1) surface since the Au (100)-(1 × 1)
surface has the low atomic density as compared to the Au (100)-(hex) surface. The
difference in γ pzc between Au (100)-(1 × 1) and -(hex) surfaces is estimated to be
0.02–0.04 J m
−2 [17, 18].
Figure 3.3 shows the electrocapillary (γ vs. E) curves of the Au (100)-(hex) and
-(1 × 1) surfaces calculated from the differential capacity data (Fig. 3.2). In Fig. 3.3,
it is reminded that γ pzc = 1.44 J m
−2 is employed for the Au (100)-(1 × 1) surface
in place of γ pzc = 1.25 J m
−2 . Furthermore, the value of γ pzc = −0.035 J m
−2 is
chosen for the difference in γ pzc between Au (100)-(hex) and -(1 × 1) surfaces, so
that the electrocapillary curves of the Au (100)-(hex) and -(1 × 1) surfaces intersect
at 0.55 V (SCE) corresponding to the critical potential for lifting in 0.01 M HClO 4
solution, and γ (E) for the Au (100)-(1 × 1) surface becomes less than that for
the Au (100)-(hex) surface at potentials more positive than 0.55 V (SCE), which is
consistent with the results obtained by Santos and Schmickler [18]. The necessary
condition for lifting of reconstruction is that the Au (100)-(1 × 1) surface becomes
more thermodynamically stable than that the Au (100)-(hex) surface.
71
(100)-(hex) and -(1 × 1) surfaces in 0.01 M HClO 4 solution [11]. The solid curve in
Fig. 3.2 for the Au (100)-(hex) surface was measured during anodic potential scan
from −0.4 to 0.6 V (SCE). The value of E pzc = 0.27 V (SCE) for the Au (100)(hex) surface is obtained from the location of the differential capacity minimum in
the solid curve. The dotted curve in Fig. 3.2 for the Au (100)-(1 × 1) surface was
measured during cathodic potential scan from 0.6 to −0.4 V (SCE) after lifting of
the Au (100)-(hex) surface. The value of E pzc = 0.03 V (SCE) for the Au (100)-(1
× 1) surface is also obtained from the location of the differential capacity minimum
in the dotted curve. The difference of 0.24 V in E pzc between the Au (100)-hex and
-(1 × 1) surfaces is consistent with that obtained by Kolb [1, 2].
As explained in Sect. 1.9 of Chap. 1, the Lippmann equation:
∂γ
∂ E
T,μ i
= −q
can be used for a solid metal electrode as well as a liquid metal electrode such as
mercury. Consequently, the potential dependence of surface tension γ (E), i.e., the
electrocapillary curve (γ vs. E) for the Au (100) electrode surfaces, can be calculated
from the double integration of differential capacity c(E) with respect to potential E:
γ (E) = γ pzc −
˜ E
E pzc
c(E)dE, where γ pzc is the surface tension at E pzc . Although the
absolute value of γ pzc for the Au (100) electrode surfaces cannot be obtained from
experiments, the theoretical value of γ for zero surface charge may be available for
γ pzc . Ibach et al. [12] calculated γ (E) for the Au (100)-(hex) and -(1 × 1) surfaces
from the double integration of the differential capacity data in Fig. 3.2 by employing
the value of γ pzc = 1.25 J m
−2 obtained with first-principles calculation [13–16].
However, the value of γ pzc = 1.25 J m
−2 is rather pertinent to the Au (111)-(1
× 1) surface than the Au (100)-(1 × 1) surface [13, 14]. The surface energy of the
Au (100)-(1 × 1) surface is larger than that of the Au (111)-(1 × 1) surface since
the atomic density of the former is lower than that of the latter. The value of γ pzc
= 1.44 J m
−2 is preferable for the Au (100)-(1 × 1) surface [15]. Moreover, the
value of γ pzc of the Au (100)-(hex) surface has not been theoretically obtained but it
should be less than that of the Au (100)-(1 × 1) surface since the Au (100)-(1 × 1)
surface has the low atomic density as compared to the Au (100)-(hex) surface. The
difference in γ pzc between Au (100)-(1 × 1) and -(hex) surfaces is estimated to be
0.02–0.04 J m
−2 [17, 18].
Figure 3.3 shows the electrocapillary (γ vs. E) curves of the Au (100)-(hex) and
-(1 × 1) surfaces calculated from the differential capacity data (Fig. 3.2). In Fig. 3.3,
it is reminded that γ pzc = 1.44 J m
−2 is employed for the Au (100)-(1 × 1) surface
in place of γ pzc = 1.25 J m
−2 . Furthermore, the value of γ pzc = −0.035 J m
−2 is
chosen for the difference in γ pzc between Au (100)-(hex) and -(1 × 1) surfaces, so
that the electrocapillary curves of the Au (100)-(hex) and -(1 × 1) surfaces intersect
at 0.55 V (SCE) corresponding to the critical potential for lifting in 0.01 M HClO 4
solution, and γ (E) for the Au (100)-(1 × 1) surface becomes less than that for
the Au (100)-(hex) surface at potentials more positive than 0.55 V (SCE), which is
consistent with the results obtained by Santos and Schmickler [18]. The necessary
condition for lifting of reconstruction is that the Au (100)-(1 × 1) surface becomes
more thermodynamically stable than that the Au (100)-(hex) surface.