112
4 Changes in Surface Stress Associated with Underpotential …
According to surface X-ray scattering (SXS) study of the Pb-UPD on Au (111)
electrode by Toney et al. [23], the Pb-UPD monolayer with compressive and incommensurate hcp structure is rotated from the gold substrate
01 ¯
1
direction by R = 2.5
o
at potentials lower than −0.11 V (SHE), but not rotated (i.e., R = 0
o ) at potentials
higher than −0.08 V (SHE). The humps of surface stress in Fig. 4.3 were initially
ascribed to the relaxation of compressive surface stress caused by the rotation of the
incommensurate hcp structure from R = 0
◦ to 2.5° [10–12]. Nevertheless, Stafford
and Bertocci [13] claimed that the stress hump is not associated with the rotation of the
incommensurate hcp monolayer but with the coalescence of the hcp Pb islands since
the potential at which the rotation of the incommensurate hcp monolayer takes place
is more negative by about 0.07 V than the potential at which the surface stress hump
is observed. The more detailed study by Shin et al. [15] implied that the stress hump
is associated with the phase transformation between the incommensurate hcp monolayer and surface alloy of
√
3 ×
√
3
R30
◦ . Scanning tunnel microscopic (STM)
observation during Pb-UPD on Au (111) [24] indicated that the hcp Pb islands are
slowly transformed to the alloy structure of
√
3 ×
√
3
R30
◦ only at a low coverage
of Pb, θ Pb ≈ 0.25. The transformation between the hcp island and surface alloy
structure has been also observed during the Pb-UPD or Tl-UPD on Ag (111) [25].
The alloy structure is usually more thermodynamically stable than the hcp structure at a low Pb coverage [15]. The phase transformation provides an additional
shift of surface stress toward compressive direction since Pb atoms with large radius
compared to Au atoms are embedded into the Au lattice. The alloy structure develops
accompanying the changes in surface stress toward compressive direction in the
cathodic potential scan until the Au (111) electrode surface is fully covered with the
alloy structure. The full coverage of the surface alloy
√
3 ×
√
3
R30
◦ on a smooth
Au (111) surface corresponds theoretically to θ Pb = 0.333. In contrast, in the case
where θ Pb exceeds the full coverage of surface alloy, the hcp Pb overlayer would
become more stable than the alloy structure because the further embedding of Pb
atoms in the alloy phase needs a positive interface energy [15]. Consequently, when
the coverage of surface alloy exceeds θ Pb = 0.333, the dealloying process corresponding to the transformation from the alloy structure to the hcp Pb overlayer may
occur spontaneously accompanying the relaxation of surface stress toward tensile
direction. The surface alloying and dealloying process during the growth of the PbUPD layer on Cu (111) has been confirmed by the STM observation [26] in which
the full coverage of alloy structure
√
3 ×
√
3
R30
◦ is about θ Pb = 0.4 and the alloy
structure is transformed to the hcp Pb overlayer at θ Pb > 0.4. As proposed by Shin
et al. [15], it is the most reliable that the stress hump observed during the growth of
the Pb-UPD layer on the Au (111) electrode is caused by the transformation between
the surface alloy and the incommensurate hcp Pb monolayer.
Figure 4.5 shows the nearest-neighbor distance a nn of the hcp Pb monolayer on
Au (111) electrode obtained as a function of potential from the SXS measurements
by Toney et al. [23]. The value of a nn = 0.35 nm for bulk Pb is taken at −0.05 V
(SHE) which is more positive by 0.19 V than the equilibrium potential (−0.24 V) for
4 Changes in Surface Stress Associated with Underpotential …
According to surface X-ray scattering (SXS) study of the Pb-UPD on Au (111)
electrode by Toney et al. [23], the Pb-UPD monolayer with compressive and incommensurate hcp structure is rotated from the gold substrate
01 ¯
1
direction by R = 2.5
o
at potentials lower than −0.11 V (SHE), but not rotated (i.e., R = 0
o ) at potentials
higher than −0.08 V (SHE). The humps of surface stress in Fig. 4.3 were initially
ascribed to the relaxation of compressive surface stress caused by the rotation of the
incommensurate hcp structure from R = 0
◦ to 2.5° [10–12]. Nevertheless, Stafford
and Bertocci [13] claimed that the stress hump is not associated with the rotation of the
incommensurate hcp monolayer but with the coalescence of the hcp Pb islands since
the potential at which the rotation of the incommensurate hcp monolayer takes place
is more negative by about 0.07 V than the potential at which the surface stress hump
is observed. The more detailed study by Shin et al. [15] implied that the stress hump
is associated with the phase transformation between the incommensurate hcp monolayer and surface alloy of
√
3 ×
√
3
R30
◦ . Scanning tunnel microscopic (STM)
observation during Pb-UPD on Au (111) [24] indicated that the hcp Pb islands are
slowly transformed to the alloy structure of
√
3 ×
√
3
R30
◦ only at a low coverage
of Pb, θ Pb ≈ 0.25. The transformation between the hcp island and surface alloy
structure has been also observed during the Pb-UPD or Tl-UPD on Ag (111) [25].
The alloy structure is usually more thermodynamically stable than the hcp structure at a low Pb coverage [15]. The phase transformation provides an additional
shift of surface stress toward compressive direction since Pb atoms with large radius
compared to Au atoms are embedded into the Au lattice. The alloy structure develops
accompanying the changes in surface stress toward compressive direction in the
cathodic potential scan until the Au (111) electrode surface is fully covered with the
alloy structure. The full coverage of the surface alloy
√
3 ×
√
3
R30
◦ on a smooth
Au (111) surface corresponds theoretically to θ Pb = 0.333. In contrast, in the case
where θ Pb exceeds the full coverage of surface alloy, the hcp Pb overlayer would
become more stable than the alloy structure because the further embedding of Pb
atoms in the alloy phase needs a positive interface energy [15]. Consequently, when
the coverage of surface alloy exceeds θ Pb = 0.333, the dealloying process corresponding to the transformation from the alloy structure to the hcp Pb overlayer may
occur spontaneously accompanying the relaxation of surface stress toward tensile
direction. The surface alloying and dealloying process during the growth of the PbUPD layer on Cu (111) has been confirmed by the STM observation [26] in which
the full coverage of alloy structure
√
3 ×
√
3
R30
◦ is about θ Pb = 0.4 and the alloy
structure is transformed to the hcp Pb overlayer at θ Pb > 0.4. As proposed by Shin
et al. [15], it is the most reliable that the stress hump observed during the growth of
the Pb-UPD layer on the Au (111) electrode is caused by the transformation between
the surface alloy and the incommensurate hcp Pb monolayer.
Figure 4.5 shows the nearest-neighbor distance a nn of the hcp Pb monolayer on
Au (111) electrode obtained as a function of potential from the SXS measurements
by Toney et al. [23]. The value of a nn = 0.35 nm for bulk Pb is taken at −0.05 V
(SHE) which is more positive by 0.19 V than the equilibrium potential (−0.24 V) for