6.5 Criterion for Stress Generation by Nelson and Oriani
161
in 0.4 M H 3 PO 4 solution, followed by dissolution of the oxide film in open-circuit in
the same solution [18] indicated that the stress of the oxide film itself after removal of
the compressive stress component due to the electrostriction is compressive, while
the stress varies to tensile by dissolution of the oxide film. This means that the
tensile stress near the metal/oxide interface is masked with the compressive stress
in the oxide film. The stress in the oxide film near the oxide/solution interface is not
accounted for Nelson–Oriani’s criterion [17] since the oxide film/solution interface
is regarded as mechanically unconstrained. Consequently, Nelson–Oriani’s criterion
[17] is not sufficient to explain all the results of the stress generation during anodic
oxidation of Al under various experimental conditions.
6.5.2 Stress Generation during Anodic Oxidation of Ti
The stress generation behavior during anodic oxidation of Ti is much complicated
as compared to that during anodic oxidation of Al. According to the stress measurement during anodic oxidation of a sputter-deposited Ti thin film (with a thickness of
250 nm) on a glass plate by a potential step up to 10.7 V (RHE) in pH 8.4 borate
solution [19] as shown in Fig. 6.4b, the value of (σ f · d f ) at 1 h-anodic oxidation
is compressive and decreases toward compressive direction with increasing applied
potential E, i.e. with increasing thickness of the anodic oxide film d f (see Fig. 6.4c).
The anodic current density i a (see Fig. 6.4a) increases with increasing E, but it does
not exceed 60 μA cm
−2 at 10.7 V (RHE). The thickness of the anodic oxide film
d f in Fig. 6.4c was converted from the thickness of the anodic oxide film measured
by ellipsometry at 1 h-potentiostatic oxidation of Ti in pH 6.9 phosphate solution
[5]. Here, it is reminded that a potential (RHE) in the abscissa of Fig. 6.4 is referred
to a reversible hydrogen electrode (pH = 0) and can be converted to a potential
(SHE), referred to a standard reversible hydrogen electrode (pH = 0) by using the
relationship of E(RHE) = E(SHE) + 0.059pH. The use of E (RHE) is convenient
to compare the thickness of anodic oxide films formed on metals as a function of
applied potential in solutions with different pH values.
The average compressive stress of σ f ≈ −500 MPa for the anodic oxide films
formed on Ti in the potential region between 1.7 V and 10.7 V (RHE) is obtained from
the linear relation between (σ f · d f ) and d f . The electrostriction component of about
−20 MPa was estimated from the stress relaxation during a cathodic potential scan of
1 mV s
−1 from the film formation potential to a flat band potential of 0.0 V (RHE) [26]
for the anodic oxide film after 1 h-anodic oxidation. As listed in Table 6.2, for anodic
oxidation of Ti, t o = 0.61 − 0.65 is close to t
c
o = 0.42 − 0.59. According to laser
Raman spectroscopic study [27], an anatase type of TiO 2 film grows during anodic
oxidation of Ti at potentials higher than 4 V (RHE) in pH 6.9 phosphate solution. If an
anatase type of the film is formed, the value of α PB = 1.96 is obtained by substituting
V ox = 20.8 cm
3 mol
−1 [10] and V Ti = 10.6 cm
3 mol
−1 into Eq. (6.18). Therefore,
t o > t
c
o = 0.51 holds for the growth of anatase type of TiO 2 film, implying that the
161
in 0.4 M H 3 PO 4 solution, followed by dissolution of the oxide film in open-circuit in
the same solution [18] indicated that the stress of the oxide film itself after removal of
the compressive stress component due to the electrostriction is compressive, while
the stress varies to tensile by dissolution of the oxide film. This means that the
tensile stress near the metal/oxide interface is masked with the compressive stress
in the oxide film. The stress in the oxide film near the oxide/solution interface is not
accounted for Nelson–Oriani’s criterion [17] since the oxide film/solution interface
is regarded as mechanically unconstrained. Consequently, Nelson–Oriani’s criterion
[17] is not sufficient to explain all the results of the stress generation during anodic
oxidation of Al under various experimental conditions.
6.5.2 Stress Generation during Anodic Oxidation of Ti
The stress generation behavior during anodic oxidation of Ti is much complicated
as compared to that during anodic oxidation of Al. According to the stress measurement during anodic oxidation of a sputter-deposited Ti thin film (with a thickness of
250 nm) on a glass plate by a potential step up to 10.7 V (RHE) in pH 8.4 borate
solution [19] as shown in Fig. 6.4b, the value of (σ f · d f ) at 1 h-anodic oxidation
is compressive and decreases toward compressive direction with increasing applied
potential E, i.e. with increasing thickness of the anodic oxide film d f (see Fig. 6.4c).
The anodic current density i a (see Fig. 6.4a) increases with increasing E, but it does
not exceed 60 μA cm
−2 at 10.7 V (RHE). The thickness of the anodic oxide film
d f in Fig. 6.4c was converted from the thickness of the anodic oxide film measured
by ellipsometry at 1 h-potentiostatic oxidation of Ti in pH 6.9 phosphate solution
[5]. Here, it is reminded that a potential (RHE) in the abscissa of Fig. 6.4 is referred
to a reversible hydrogen electrode (pH = 0) and can be converted to a potential
(SHE), referred to a standard reversible hydrogen electrode (pH = 0) by using the
relationship of E(RHE) = E(SHE) + 0.059pH. The use of E (RHE) is convenient
to compare the thickness of anodic oxide films formed on metals as a function of
applied potential in solutions with different pH values.
The average compressive stress of σ f ≈ −500 MPa for the anodic oxide films
formed on Ti in the potential region between 1.7 V and 10.7 V (RHE) is obtained from
the linear relation between (σ f · d f ) and d f . The electrostriction component of about
−20 MPa was estimated from the stress relaxation during a cathodic potential scan of
1 mV s
−1 from the film formation potential to a flat band potential of 0.0 V (RHE) [26]
for the anodic oxide film after 1 h-anodic oxidation. As listed in Table 6.2, for anodic
oxidation of Ti, t o = 0.61 − 0.65 is close to t
c
o = 0.42 − 0.59. According to laser
Raman spectroscopic study [27], an anatase type of TiO 2 film grows during anodic
oxidation of Ti at potentials higher than 4 V (RHE) in pH 6.9 phosphate solution. If an
anatase type of the film is formed, the value of α PB = 1.96 is obtained by substituting
V ox = 20.8 cm
3 mol
−1 [10] and V Ti = 10.6 cm
3 mol
−1 into Eq. (6.18). Therefore,
t o > t
c
o = 0.51 holds for the growth of anatase type of TiO 2 film, implying that the