84
3 Potential- or Adsorbate-Induced Changes in Surface Stress …
where Y I and d are the biaxial modulus and thickness of the iodine adlayer, respectively. The value of Y I = 39.1 GPa for the
p ×
√
3
iodine adlayer on Au (111) is
estimated by substituting (g) = −0.63 J m
−2 , ε = −0.065, and d = 0.248 nm
for iodine adlayer into Eq. (3.5). The biaxial moduli of any iodine adlayers on noble
metals have not been reported so far. The value of Y I = 39.1 GPa for the
p ×
√
3
iodine adlayer on Au (111) is less than Y Pb(111) = 58.4 GPa for the hexagonal closepacked (hcp) underpotential deposition (UPD) layer of Pb on Au (111) and Y Bi =
77.1 GPa for the UPD layer of Bi with the same
p ×
√
3
structure on Au (111)
(see Sects. 4.3.1 and 4.3.2 of Chap. 4).
3.4 Surface Stress versus Surface Charge Density
or Potential versus Surface Elastic Strain
3.4.1 Surface Stress–Surface Charge Density Coefficient ζ g,q
The value of ζ g,q = −0.91 V obtained by Haiss et al. [22] from the slope of the
linear relationship between g and q for the unreconstructed, textured-(111) Au
thin-film electrode in 0.1 M HClO 4 solution is consistent with that (ζ g,q = −0.86 V)
obtained by Ibach [24]. Smetanin et al. [35] measured the changes in surface stress
of a (111)-textured Au thin-film electrode in 7 × 10
−3 M NaF and 0.01 M HClO 4
solutions and found the linear relationship between g and q near E pzc . The value
of E pzc = 0.20 V (SCE) in 0.01 M HClO 4 solution determined from the capacity
minimum in the measured differential capacity versus potential curve [35] is close
to E pzc = 0.23 V (SCE) in 0.01 M HClO 4 solution reported for the unconstructed Au
(111) surface [36], confirming that the (111)-textured Au thin-film electrode used
for the measurement of changes in surface stress is unreconstructed. The surface
stress–surface charge density coefficients obtained from the linear slopes [35] are
ζ g,q = −1.95 V for 7 × 10
−3 M NaF solution and −2.0 V for 0.01 M HClO 4 solution,
which are larger by a factor of two than those obtained by Haiss et al. [22] and by
Ibach [24], while they are in good agreement with the results (ζ g,q = −1.86 V) of
ab initio calculations for Au (111) in vacuum [37].
It has been reported [38] that ζ g,q in 0.1 M HClO 4 solution for a fresh and clean Au
(111) surface is close to −2.0 V. The value of ζ g,q may be influenced by the contamination of the Au (111) surface. At present, however, the causes for the discrepancy
of ζ g,q between the researchers have not been made clear. The value of ζ g,q obtained
from the slope of the linear relationship between g and q is not sensitive to potential
since it is an average value over the specified potential region. We discuss the results
obtained by a potential-sensitive technique of ζ g,q in the next pages.
3 Potential- or Adsorbate-Induced Changes in Surface Stress …
where Y I and d are the biaxial modulus and thickness of the iodine adlayer, respectively. The value of Y I = 39.1 GPa for the
p ×
√
3
iodine adlayer on Au (111) is
estimated by substituting (g) = −0.63 J m
−2 , ε = −0.065, and d = 0.248 nm
for iodine adlayer into Eq. (3.5). The biaxial moduli of any iodine adlayers on noble
metals have not been reported so far. The value of Y I = 39.1 GPa for the
p ×
√
3
iodine adlayer on Au (111) is less than Y Pb(111) = 58.4 GPa for the hexagonal closepacked (hcp) underpotential deposition (UPD) layer of Pb on Au (111) and Y Bi =
77.1 GPa for the UPD layer of Bi with the same
p ×
√
3
structure on Au (111)
(see Sects. 4.3.1 and 4.3.2 of Chap. 4).
3.4 Surface Stress versus Surface Charge Density
or Potential versus Surface Elastic Strain
3.4.1 Surface Stress–Surface Charge Density Coefficient ζ g,q
The value of ζ g,q = −0.91 V obtained by Haiss et al. [22] from the slope of the
linear relationship between g and q for the unreconstructed, textured-(111) Au
thin-film electrode in 0.1 M HClO 4 solution is consistent with that (ζ g,q = −0.86 V)
obtained by Ibach [24]. Smetanin et al. [35] measured the changes in surface stress
of a (111)-textured Au thin-film electrode in 7 × 10
−3 M NaF and 0.01 M HClO 4
solutions and found the linear relationship between g and q near E pzc . The value
of E pzc = 0.20 V (SCE) in 0.01 M HClO 4 solution determined from the capacity
minimum in the measured differential capacity versus potential curve [35] is close
to E pzc = 0.23 V (SCE) in 0.01 M HClO 4 solution reported for the unconstructed Au
(111) surface [36], confirming that the (111)-textured Au thin-film electrode used
for the measurement of changes in surface stress is unreconstructed. The surface
stress–surface charge density coefficients obtained from the linear slopes [35] are
ζ g,q = −1.95 V for 7 × 10
−3 M NaF solution and −2.0 V for 0.01 M HClO 4 solution,
which are larger by a factor of two than those obtained by Haiss et al. [22] and by
Ibach [24], while they are in good agreement with the results (ζ g,q = −1.86 V) of
ab initio calculations for Au (111) in vacuum [37].
It has been reported [38] that ζ g,q in 0.1 M HClO 4 solution for a fresh and clean Au
(111) surface is close to −2.0 V. The value of ζ g,q may be influenced by the contamination of the Au (111) surface. At present, however, the causes for the discrepancy
of ζ g,q between the researchers have not been made clear. The value of ζ g,q obtained
from the slope of the linear relationship between g and q is not sensitive to potential
since it is an average value over the specified potential region. We discuss the results
obtained by a potential-sensitive technique of ζ g,q in the next pages.