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6 Stresses of Anodic Oxide Films Grown on Metal Electrode
amorphous oxide film formed during anodic oxidation under a high galvanostatic
current density [22, 23] since the increase in density of anodic oxide film due to
crystallization induces tensile stress because of the volume contraction of the film.
On the other hand, the sign of the film stress observed during anodic oxidation of Zr
and Hf satisfies Nelson–Oriani’s criterion [17]. Particularly, the stress measurement
during anodic oxidation of a sputter-deposited Zr thin film in sulfuric acid solution
[24] confirmed that the stress generated in anodic oxide film on Zr is compressive
and satisfies Nelson–Oriani’s criterion. In the cases of Al and Ti, the assessment for
Nelson–Oriani’s criterion [17] is complicated because the signs of both predicted
and observed film stresses vary depending on the experimental conditions of anodic
oxidation. We explain the stress generation behavior during anodic oxidation of Al
and Ti in the following subsections and discuss the matching with Nelson–Oriani’s
criterion [17].
6.5.1 Stress Generation during Anodic Oxidation of Al
The stress generated during anodic oxidation of Al in ammonium borate and ammonium citrate solutions has been measured as a function of galvanostatic current
density [25]. The stress of the anodic oxide film itself obtained by subtracting the
compressive stress component due to electrostriction is compressive at low current
density and tensile at high current density. The stress transition from compressive
to tensile takes place at about 0.5 mA cm
−2 . The stress transition from compressive
to tensile at 0.6 mA cm
−2 was also observed for the film stress generated during
anodic oxidation of Al in 0.1 M H 2 SO 4 solution [17]. In general, the anodic oxide
film formed on Al at high current density is amorphous, while the film formed
at low current density contains crystalline [23]. The values of α PB = 1.3 − 1.4 and
1.6 – 1.7 have been reported for crystalline Al 2 O 3 on Al and for glassy Al 2 O 3 on Al,
respectively [23]. According to the measurement of the transport number of mobile
ion in anodic oxide films [11], the transport number of O
2− ion t o decreases from
0.67 to 0.28 with increasing current density from 0.1 to 10 mA cm
−2 for anodic
oxidation of Al in ammonium citrate solution.
If the values of t o = 0.4 and α PB = 1.7 are employed for the amorphous film
formed on Al at a current density higher than 0.5 mA cm
−2 , an inequality of t o <
t
c
o = 0.59 holds, predicting the tensile film stress from Nelson–Oriani’s criterion
[17], which is consistent with the sign of the observed film stress. On the other hand,
if the values of t o = 0.67 and α PB = 1.55 are employed for the crystalline-containing
film formed on Al at a current density lower than 0.5 mA cm
−2 , t o is slightly larger
than t
c
o = 0.65, suggesting that the sign of the film stress is minus (compressive),
which is consistent with the sign of the observed film stress. However, it seems
difficult to predict the sign of the film stress because the predicted sign of the film
stress on Al at the low current density is reversed depending on the selected values
of t o and α PB . The recent study of the stress variations during the growth of anodic
oxide film on Al up to 25 V at galvanostatic current densities of 2.0 – 12.5 mA cm
−2
6 Stresses of Anodic Oxide Films Grown on Metal Electrode
amorphous oxide film formed during anodic oxidation under a high galvanostatic
current density [22, 23] since the increase in density of anodic oxide film due to
crystallization induces tensile stress because of the volume contraction of the film.
On the other hand, the sign of the film stress observed during anodic oxidation of Zr
and Hf satisfies Nelson–Oriani’s criterion [17]. Particularly, the stress measurement
during anodic oxidation of a sputter-deposited Zr thin film in sulfuric acid solution
[24] confirmed that the stress generated in anodic oxide film on Zr is compressive
and satisfies Nelson–Oriani’s criterion. In the cases of Al and Ti, the assessment for
Nelson–Oriani’s criterion [17] is complicated because the signs of both predicted
and observed film stresses vary depending on the experimental conditions of anodic
oxidation. We explain the stress generation behavior during anodic oxidation of Al
and Ti in the following subsections and discuss the matching with Nelson–Oriani’s
criterion [17].
6.5.1 Stress Generation during Anodic Oxidation of Al
The stress generated during anodic oxidation of Al in ammonium borate and ammonium citrate solutions has been measured as a function of galvanostatic current
density [25]. The stress of the anodic oxide film itself obtained by subtracting the
compressive stress component due to electrostriction is compressive at low current
density and tensile at high current density. The stress transition from compressive
to tensile takes place at about 0.5 mA cm
−2 . The stress transition from compressive
to tensile at 0.6 mA cm
−2 was also observed for the film stress generated during
anodic oxidation of Al in 0.1 M H 2 SO 4 solution [17]. In general, the anodic oxide
film formed on Al at high current density is amorphous, while the film formed
at low current density contains crystalline [23]. The values of α PB = 1.3 − 1.4 and
1.6 – 1.7 have been reported for crystalline Al 2 O 3 on Al and for glassy Al 2 O 3 on Al,
respectively [23]. According to the measurement of the transport number of mobile
ion in anodic oxide films [11], the transport number of O
2− ion t o decreases from
0.67 to 0.28 with increasing current density from 0.1 to 10 mA cm
−2 for anodic
oxidation of Al in ammonium citrate solution.
If the values of t o = 0.4 and α PB = 1.7 are employed for the amorphous film
formed on Al at a current density higher than 0.5 mA cm
−2 , an inequality of t o <
t
c
o = 0.59 holds, predicting the tensile film stress from Nelson–Oriani’s criterion
[17], which is consistent with the sign of the observed film stress. On the other hand,
if the values of t o = 0.67 and α PB = 1.55 are employed for the crystalline-containing
film formed on Al at a current density lower than 0.5 mA cm
−2 , t o is slightly larger
than t
c
o = 0.65, suggesting that the sign of the film stress is minus (compressive),
which is consistent with the sign of the observed film stress. However, it seems
difficult to predict the sign of the film stress because the predicted sign of the film
stress on Al at the low current density is reversed depending on the selected values
of t o and α PB . The recent study of the stress variations during the growth of anodic
oxide film on Al up to 25 V at galvanostatic current densities of 2.0 – 12.5 mA cm
−2