114
4 Changes in Surface Stress Associated with Underpotential …
Fig. 4.6 Relationship between and ε in the potential region between −0.24 and −0.05 V (SHE)
for the hcp Pb monolayer on Au (111) electrode [14]. The value of is measured as a function
of potential in the anodic potential scan from −0.24 V (SHE) in Fig. 4.3b, while the value of ε is
taken from Fig. 4.5. Reproduced from [14] with permission from The Electrochemical Society
E (111) =
4
(2S 11 + 2S 12 + S 44 )
,
(4.18)
ν (111) = −E (111) ×
(2S 11 + 10S 12 − S 44 )
12
,
(4.19)
and
Y (111) =
E (111)
1 − ν (111)
,
(4.20)
where S 11 = 9.37 × 10
−11 Pa
−1 , S 12 = −4.3 × 10
−11 Pa
−1 , and S 44 = 6.8 ×
10
−11 Pa
−1 are known for bulk Pb [28]. As a result, E Pb(111) = 23.6 GPa, ν (111) =
0.61, and Y Pb(111) = 60.5 GPa are calculated for bulk Pb. The value of d (111) =
0.2858 nm is used for bulk Pb since the lattice constant of Pb is 0.495 nm. The value
of Y Pb(111) d (111) = 17.3 J m
−2 is eventually obtained for bulk Pb, and it is close to
that (16.7 J m
−2 ) for the hcp Pb-UPD monolayer on Au (111) electrode, which is
also in good agreement with the results obtained by Stafford and Bertocci [13].
The value of Y Au(111) d (111) = 44.4 J m
−2 for the Au (1 × 1) monolayer is calculated
as well by using S 11 = 2.34 × 10
−11 Pa
−1 , S 12 = −1.07 × 10
−11 Pa
−1 , S 44 =
2.38 × 10
−11 Pa
−1 , and d (111) = 0.235 nm for bulk Au (111), which is about 2.6
times as much as that (16.7 J m
−2 ) for the hcp Pb-UPD monolayer on the Au (111)
electrode. It is surprising that the value of Y Pb(111) d (111) for the hcp Pb-UPD monolayer
on the Au (111) electrode is nearly equal to that for the same layer in the bulk Pb,
although the reason is not clear. Nevertheless, it has been reported that the elastic
constants of even ultra-thin films with lattice mismatch grown on substrates are
4 Changes in Surface Stress Associated with Underpotential …
Fig. 4.6 Relationship between and ε in the potential region between −0.24 and −0.05 V (SHE)
for the hcp Pb monolayer on Au (111) electrode [14]. The value of is measured as a function
of potential in the anodic potential scan from −0.24 V (SHE) in Fig. 4.3b, while the value of ε is
taken from Fig. 4.5. Reproduced from [14] with permission from The Electrochemical Society
E (111) =
4
(2S 11 + 2S 12 + S 44 )
,
(4.18)
ν (111) = −E (111) ×
(2S 11 + 10S 12 − S 44 )
12
,
(4.19)
and
Y (111) =
E (111)
1 − ν (111)
,
(4.20)
where S 11 = 9.37 × 10
−11 Pa
−1 , S 12 = −4.3 × 10
−11 Pa
−1 , and S 44 = 6.8 ×
10
−11 Pa
−1 are known for bulk Pb [28]. As a result, E Pb(111) = 23.6 GPa, ν (111) =
0.61, and Y Pb(111) = 60.5 GPa are calculated for bulk Pb. The value of d (111) =
0.2858 nm is used for bulk Pb since the lattice constant of Pb is 0.495 nm. The value
of Y Pb(111) d (111) = 17.3 J m
−2 is eventually obtained for bulk Pb, and it is close to
that (16.7 J m
−2 ) for the hcp Pb-UPD monolayer on Au (111) electrode, which is
also in good agreement with the results obtained by Stafford and Bertocci [13].
The value of Y Au(111) d (111) = 44.4 J m
−2 for the Au (1 × 1) monolayer is calculated
as well by using S 11 = 2.34 × 10
−11 Pa
−1 , S 12 = −1.07 × 10
−11 Pa
−1 , S 44 =
2.38 × 10
−11 Pa
−1 , and d (111) = 0.235 nm for bulk Au (111), which is about 2.6
times as much as that (16.7 J m
−2 ) for the hcp Pb-UPD monolayer on the Au (111)
electrode. It is surprising that the value of Y Pb(111) d (111) for the hcp Pb-UPD monolayer
on the Au (111) electrode is nearly equal to that for the same layer in the bulk Pb,
although the reason is not clear. Nevertheless, it has been reported that the elastic
constants of even ultra-thin films with lattice mismatch grown on substrates are