3.2 Surface Reconstruction
77
Au (111)-(1 × 1) surface, and thereby the Au (100)-(hex) surface is subjected to the
large tensile stress as compared to the Au (111)-(1 × 1) surface. Besides, it is noticed
that the difference in g (i.e., g = −0.60 J m
−2 ) between the Au (111)3 × 22
and -(1 × 1) surfaces at −0.14 V (SCE) is significantly larger than that (i.e., g =
−0.25 J m
−2 ) between the Au (100)-(hex) and -(1 × 1) surfaces at −0.14 V (SCE),
suggesting that the reconstruction on Au (111) is brought by the large relaxation of
tensile stress toward compressive direction.
3.2.3 Roles of Surface Stress in Surface Reconstruction
The relaxation of surface stress toward compressive direction has been measured
at the reconstruction of the Au (111) and (100) surfaces [8, 9]. The reconstruction
may be driven by the relaxation of surface stress toward compressive direction if
the gain in elastic energy due to the relaxation of surface stress is large enough to
induce the reconstruction. The relaxation of the surface stress (g = −0.60 J m
−2 )
at the reconstruction of the Au (111) surface is larger than that (g = −0.25 J m
−2 )
at the reconstruction of the Au (100) surface. Ibach et al. [8, 9, 20] employed the
continuum model to estimate the relaxation of surface stress from the magnitude
of uniaxial compression in reconstruction of the Au (111) surface. By considering
that the reconstruction induces one-dimensional compression in the surface layer,
the change of bulk stress σ b in the surface layer is given by
σ b =
E (111) ε
1 − ν
2
(111)
(3.1)
where ε is the one-dimensional strain caused by the reconstruction, and E (111) and
ν (111) are Young’s modulus and Poisson’s ratio for the Au (111) electrode, respectively. Assuming that on average, one half of the domain orientations point to a particular direction, the bulk stress averaged over all domain orientations corresponds to
one half of the stress change calculated with Eq. (3.1) [8].
If the reconstructed surface layer is regarded as a free-standing elastic film, the
surface stress relaxation g is formulated by
g =
σ b d (111)
2
=
E (111) εd (111)
2
1 − ν
2
(111)
(3.2)
where d (111) is the thickness of the surface atomic layer. The values of E (111) =
81.3 GPa and ν (111) = 0.57 can be obtained from the values of elastic compliances
(S 11 = 2.34 × 10
−11 Pa
−1 , S 12 = −1.07 × 10
−11 Pa
−1 , and S 44 = 2.38 × 10
−11 Pa
−1 )
for the Au (111) electrode (see Eqs. (4.18) and (4.19) in Sect. 4.3.1 of Chap. 4). The
value of d (111) = 0.235 nm is estimated from the lattice constant a = 0.4786 nm of
77
Au (111)-(1 × 1) surface, and thereby the Au (100)-(hex) surface is subjected to the
large tensile stress as compared to the Au (111)-(1 × 1) surface. Besides, it is noticed
that the difference in g (i.e., g = −0.60 J m
−2 ) between the Au (111)3 × 22
and -(1 × 1) surfaces at −0.14 V (SCE) is significantly larger than that (i.e., g =
−0.25 J m
−2 ) between the Au (100)-(hex) and -(1 × 1) surfaces at −0.14 V (SCE),
suggesting that the reconstruction on Au (111) is brought by the large relaxation of
tensile stress toward compressive direction.
3.2.3 Roles of Surface Stress in Surface Reconstruction
The relaxation of surface stress toward compressive direction has been measured
at the reconstruction of the Au (111) and (100) surfaces [8, 9]. The reconstruction
may be driven by the relaxation of surface stress toward compressive direction if
the gain in elastic energy due to the relaxation of surface stress is large enough to
induce the reconstruction. The relaxation of the surface stress (g = −0.60 J m
−2 )
at the reconstruction of the Au (111) surface is larger than that (g = −0.25 J m
−2 )
at the reconstruction of the Au (100) surface. Ibach et al. [8, 9, 20] employed the
continuum model to estimate the relaxation of surface stress from the magnitude
of uniaxial compression in reconstruction of the Au (111) surface. By considering
that the reconstruction induces one-dimensional compression in the surface layer,
the change of bulk stress σ b in the surface layer is given by
σ b =
E (111) ε
1 − ν
2
(111)
(3.1)
where ε is the one-dimensional strain caused by the reconstruction, and E (111) and
ν (111) are Young’s modulus and Poisson’s ratio for the Au (111) electrode, respectively. Assuming that on average, one half of the domain orientations point to a particular direction, the bulk stress averaged over all domain orientations corresponds to
one half of the stress change calculated with Eq. (3.1) [8].
If the reconstructed surface layer is regarded as a free-standing elastic film, the
surface stress relaxation g is formulated by
g =
σ b d (111)
2
=
E (111) εd (111)
2
1 − ν
2
(111)
(3.2)
where d (111) is the thickness of the surface atomic layer. The values of E (111) =
81.3 GPa and ν (111) = 0.57 can be obtained from the values of elastic compliances
(S 11 = 2.34 × 10
−11 Pa
−1 , S 12 = −1.07 × 10
−11 Pa
−1 , and S 44 = 2.38 × 10
−11 Pa
−1 )
for the Au (111) electrode (see Eqs. (4.18) and (4.19) in Sect. 4.3.1 of Chap. 4). The
value of d (111) = 0.235 nm is estimated from the lattice constant a = 0.4786 nm of