170
6 Stresses of Anodic Oxide Films Grown on Metal Electrode
residual stress, the relaxation of the residual stress caused by the growth of the anodic
oxide film in addition to the anodic dissolution of the substrate metal has to be taken
into account to evaluate exactly the film stress [20, 46]. Particularly, if the residual
stress of the substrate metal is significantly large, the neglect of the relaxation of the
residual stress leads to the major mistakes for the determination of magnitude or sign
of the film stress.
6.8 Cathodic Polarization of Anodic Oxide Film
It has been reported [47] that a stress variation toward compressive direction is
brought by a cathodic polarization after the formation of anodic oxide film on a
sputter-deposited Ti thin film under a potentiostatic anodic oxidation in pH 8.4 borate
solution. Figure 6.8 shows (a) the cyclic potential steps, starting from 5.7 to 0.5 V
(RHE), then repeating between - 0.5 V and 0.5 V (RHE), and finally returning from
−0.5 to 5.7 V (RHE), (b) the corresponding changes in current density, i, and (c)
the corresponding stress variations (σ f · d f ) for the anodic oxide film formed on the
sputter-deposited Ti thin film for 1 h at 5.7 V (RHE) in pH 8.4 borate solution [47].
After each potential step, the potential is kept for 1 h to observe the steady-state
behavior. The stress varies toward compressive direction during the formation of
anodic oxide film at 5.7 V (RHE), which is consistent with previous results obtained
under the same anodic polarization conditions for the sputter-deposited Ti thin film
[19]. The ellipsometrical thickness of the anodic oxide film formed on Ti for 1 h at
5.7 V (RHE) is about 18 nm, irrespective of kinds of electrolytes used in experiments
[5].
At the first potential step from 5.7 to −0.5 V (RHE), (σ f · d f ) passes through an
instantaneous change toward tensile direction and then changes toward compressive
direction. The instantaneous change may result from the relaxation of the electrostriction stress component. The final changes of (σ f · d f ) toward compressive direction
result from the compositional changes of the anodic oxide film on Ti due to cathodic
polarization at −0.5 V (RHE). The compositional changes of the anodic oxide film
on Ti during cathodic polarization in pH 6.9 phosphate solution have been investigated by ellipsometry [48]. It has been proposed that the following compositional
changes of the anodic oxide film, accompanying hydrogen absorption, take place
during cathodic polarization [48]:
TiO 2 + xH
+
aq + xe
−
= TiO 2−x (OH) x ,
(6.37)
where x varies from 0 to 1 with changing cathodic potential from −0.25 to −0.9 V
(RHE). Simultaneously, the complex refractive index of the oxide film, N f = n − ki
(n: refractive index, k: extinction index) changes from N f = 2.1 − 0.03i to 1.85 −
0.35i [48]. In addition, the valence change of titanium ions has to be taken into
consideration to maintain the charge neutrality during hydrogen ingress. Therefore,
Eq. (6.37) can be rewritten by introducing the valence change of titanium ions [47]:
6 Stresses of Anodic Oxide Films Grown on Metal Electrode
residual stress, the relaxation of the residual stress caused by the growth of the anodic
oxide film in addition to the anodic dissolution of the substrate metal has to be taken
into account to evaluate exactly the film stress [20, 46]. Particularly, if the residual
stress of the substrate metal is significantly large, the neglect of the relaxation of the
residual stress leads to the major mistakes for the determination of magnitude or sign
of the film stress.
6.8 Cathodic Polarization of Anodic Oxide Film
It has been reported [47] that a stress variation toward compressive direction is
brought by a cathodic polarization after the formation of anodic oxide film on a
sputter-deposited Ti thin film under a potentiostatic anodic oxidation in pH 8.4 borate
solution. Figure 6.8 shows (a) the cyclic potential steps, starting from 5.7 to 0.5 V
(RHE), then repeating between - 0.5 V and 0.5 V (RHE), and finally returning from
−0.5 to 5.7 V (RHE), (b) the corresponding changes in current density, i, and (c)
the corresponding stress variations (σ f · d f ) for the anodic oxide film formed on the
sputter-deposited Ti thin film for 1 h at 5.7 V (RHE) in pH 8.4 borate solution [47].
After each potential step, the potential is kept for 1 h to observe the steady-state
behavior. The stress varies toward compressive direction during the formation of
anodic oxide film at 5.7 V (RHE), which is consistent with previous results obtained
under the same anodic polarization conditions for the sputter-deposited Ti thin film
[19]. The ellipsometrical thickness of the anodic oxide film formed on Ti for 1 h at
5.7 V (RHE) is about 18 nm, irrespective of kinds of electrolytes used in experiments
[5].
At the first potential step from 5.7 to −0.5 V (RHE), (σ f · d f ) passes through an
instantaneous change toward tensile direction and then changes toward compressive
direction. The instantaneous change may result from the relaxation of the electrostriction stress component. The final changes of (σ f · d f ) toward compressive direction
result from the compositional changes of the anodic oxide film on Ti due to cathodic
polarization at −0.5 V (RHE). The compositional changes of the anodic oxide film
on Ti during cathodic polarization in pH 6.9 phosphate solution have been investigated by ellipsometry [48]. It has been proposed that the following compositional
changes of the anodic oxide film, accompanying hydrogen absorption, take place
during cathodic polarization [48]:
TiO 2 + xH
+
aq + xe
−
= TiO 2−x (OH) x ,
(6.37)
where x varies from 0 to 1 with changing cathodic potential from −0.25 to −0.9 V
(RHE). Simultaneously, the complex refractive index of the oxide film, N f = n − ki
(n: refractive index, k: extinction index) changes from N f = 2.1 − 0.03i to 1.85 −
0.35i [48]. In addition, the valence change of titanium ions has to be taken into
consideration to maintain the charge neutrality during hydrogen ingress. Therefore,
Eq. (6.37) can be rewritten by introducing the valence change of titanium ions [47]: