4.3 Changes in Surface Stress during UPD
113
0.37
0.36
0.35
0.34
0.33
0.32
a
nn / nm
-0.25
-0.20
-0.15
-0.10
-0.05
E / V (SHE)
-8
-6
-4
-2
0
2
4
/ 10
-2
Fig. 4.5 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 elastic strain of
the hcp Pb monolayer ε on the ordinate in the right-hand side of Fig. 4.5 is converted from a nn
by assuming ε = 0 at −0.05 V (SHE). Modified with the permission from [23], Copyright 1995,
American Chemical Society
the bulk deposition of Pb. The value of a nn decreases with decreasing potential from
−0.05 V (SHE), indicating that the hcp Pb-UPD monolayer is subjected to electrocompression. The elastic strain ε of the hcp Pb-UPD monolayer on the ordinate in
the right-hand side of Fig. 4.5 is converted from a nn by assuming ε = 0 at −0.05 V
(SHE). Friesen et al. [11] and Stafford and Bertocci [13] converted the surface stress
versus potential data into the surface stress versus elastic strain data and found the
almost linear relationship between and ε in the electro-compressive region. In
Fig. 4.6, the values of measured as a function of potential in the anodic potential
scan from −0.24 V (SHE) in Fig. 4.3b are plotted versus ε in the same potential range
in Fig. 4.5, indicating the linear relationship between and ε with an average slope
of 16.7 J m
−2 [14]. The average slope of 16.7 J m
−2 coincides with that (16.8 J m
−2 )
obtained by Stafford and Bertocci [13].
If the hcp Pb-UPD monolayer is regarded as a free-standing elastic film, the
relationship between and ε is represented by
= Y (111) εd (111) ,
(4.17)
where Y (111) is the biaxial modulus of the hcp film and d (111) is the film thickness.
The value of Y Pb(111) d (111) = 16.7 J m
−2 for the hcp Pb-UPD monolayer on Au (111)
electrode is obtained from the slope of the linear relationship in Fig. 4.6. On the
other hand, the value of Y Pb(111) d (111) for bulk Pb (111) can be calculated since the
elastic compliances S i j of bulk Pb are known. Young’s modulus E (111) , Poisson’s
ratio ν (111) , and biaxial modulus Y (111) for bulk Pb (111) are derived from the values
of S i j [27] as follows:
113
0.37
0.36
0.35
0.34
0.33
0.32
a
nn / nm
-0.25
-0.20
-0.15
-0.10
-0.05
E / V (SHE)
-8
-6
-4
-2
0
2
4
/ 10
-2
Fig. 4.5 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 elastic strain of
the hcp Pb monolayer ε on the ordinate in the right-hand side of Fig. 4.5 is converted from a nn
by assuming ε = 0 at −0.05 V (SHE). Modified with the permission from [23], Copyright 1995,
American Chemical Society
the bulk deposition of Pb. The value of a nn decreases with decreasing potential from
−0.05 V (SHE), indicating that the hcp Pb-UPD monolayer is subjected to electrocompression. The elastic strain ε of the hcp Pb-UPD monolayer on the ordinate in
the right-hand side of Fig. 4.5 is converted from a nn by assuming ε = 0 at −0.05 V
(SHE). Friesen et al. [11] and Stafford and Bertocci [13] converted the surface stress
versus potential data into the surface stress versus elastic strain data and found the
almost linear relationship between and ε in the electro-compressive region. In
Fig. 4.6, the values of measured as a function of potential in the anodic potential
scan from −0.24 V (SHE) in Fig. 4.3b are plotted versus ε in the same potential range
in Fig. 4.5, indicating the linear relationship between and ε with an average slope
of 16.7 J m
−2 [14]. The average slope of 16.7 J m
−2 coincides with that (16.8 J m
−2 )
obtained by Stafford and Bertocci [13].
If the hcp Pb-UPD monolayer is regarded as a free-standing elastic film, the
relationship between and ε is represented by
= Y (111) εd (111) ,
(4.17)
where Y (111) is the biaxial modulus of the hcp film and d (111) is the film thickness.
The value of Y Pb(111) d (111) = 16.7 J m
−2 for the hcp Pb-UPD monolayer on Au (111)
electrode is obtained from the slope of the linear relationship in Fig. 4.6. On the
other hand, the value of Y Pb(111) d (111) for bulk Pb (111) can be calculated since the
elastic compliances S i j of bulk Pb are known. Young’s modulus E (111) , Poisson’s
ratio ν (111) , and biaxial modulus Y (111) for bulk Pb (111) are derived from the values
of S i j [27] as follows: