172
6 Stresses of Anodic Oxide Films Grown on Metal Electrode
The reversible current transient and changes of (σ f ·d f ) in response to the cyclic potential steps between −0.5 and 0.5 V (RHE) are originated from the reversible reaction
of Eq. (6.37) or Eq. (6.38) accompanying the volume expansion and contraction of
the oxide film due to the hydrogen absorption and desorption. The steady-state level
of (σ f ·d f ) after the potential step from −0.5 to 0.5 V (RHE) does not deviate significantly from that after the final potential step from −0.5 to 5.7 V (RHE), indicating
that the hydrogen absorbed in the oxide film at −0.5 V (RHE) is completely desorbed
from the film at 0.5 V (RHE).
The difference σ f = 0.32 GPa in film stress between TiOOH and TiO 2 was
calculated by assuming the film thickness of 18 nm and the molar volume (20.8 cm
3
mol
−1 ) [10] for the anatase type of TiO 2 from the linear relation between (σ f ·d f )
and anodic charge Q a (for hydrogen desorption) obtained during potential steps
from various cathodic potentials (−0.7 ~ −0.2 V) to 0.5 V (RHE) after the formation
of the TiO 2 film for 1 h at 5.7 V (RHE) [47]. It has been also reported [50] that
downward and upward potential steps after the formation of the passive film on Ni
induce the alternative changes of (σ f ·d f ) toward compressive and tensile direction,
which was ascribed to the volume expansion and contraction of the film due to
hydrogen absorption and desorption, accompanying the valence changes between
Ni
2+ and Ni
3+ in NiO 1+x film with cation vacancies. Moreover, the stress variations
toward compressive direction have been observed during cathodic reduction of the
passive film (γ-Fe 2 O 3 or γ-FeOOH) on Fe in pH 8.4 borate solution [46], which was
ascribed to the volume expansion due to Fe(OH) 2 formed as an intermediate step of
the cathodic reduction.
6.9 Plastic Flow of Porous Anodic Oxide Film
It is known that porous alumina films are formed by anodic oxidation of Al in
acid solutions [51]. The porous films consist of a thin barrier layer next to the metal
substrate and of an outer porous layer with pores of approximately cylindrical section
as schematically illustrated in Fig. 6.9 [52]. Figure 6.10 shows the scanning electron
microscopic (SEM) images of (a) the substrate surface after removal of the porous
alumina film and of (b) the cross section of the porous alumina film formed on
Al at a cell voltage of 240 V for 1 h in 2 M citric acid [53]. The SEM images
indicate that the porous alumina film has self-organized hexagonal pore arrays. The
growth mechanism of the porous alumina film in phosphoric acid [52, 54] has been
investigated by monitoring the motion of tungsten tracer layer (3–5 nm thick) in a
sputter-deposited Al thin film on substrate Al. Tungsten is an ideal tracer since the
W
6+ ion moves outward in the anodic alumina film much slower than Al
3+ ion [55].
The upper part of Fig. 6.11 shows the transmission electron microscopic (TEM)
images for the cross sections of the sputter-deposited aluminum with an incorporated
tungsten tracer layer, followed by anodic oxidation for (a) 180 s, (b) 240 s, and (d)
350 s at 5 mA cm
−2 in 0.4 M phosphoric acid solution [52, 54]. The lower part of
Fig. 6.11 shows schematically the relative distribution of the tungsten tracer layer in
alumina films corresponding to the TEM cross sections [54]. The TEM cross section
6 Stresses of Anodic Oxide Films Grown on Metal Electrode
The reversible current transient and changes of (σ f ·d f ) in response to the cyclic potential steps between −0.5 and 0.5 V (RHE) are originated from the reversible reaction
of Eq. (6.37) or Eq. (6.38) accompanying the volume expansion and contraction of
the oxide film due to the hydrogen absorption and desorption. The steady-state level
of (σ f ·d f ) after the potential step from −0.5 to 0.5 V (RHE) does not deviate significantly from that after the final potential step from −0.5 to 5.7 V (RHE), indicating
that the hydrogen absorbed in the oxide film at −0.5 V (RHE) is completely desorbed
from the film at 0.5 V (RHE).
The difference σ f = 0.32 GPa in film stress between TiOOH and TiO 2 was
calculated by assuming the film thickness of 18 nm and the molar volume (20.8 cm
3
mol
−1 ) [10] for the anatase type of TiO 2 from the linear relation between (σ f ·d f )
and anodic charge Q a (for hydrogen desorption) obtained during potential steps
from various cathodic potentials (−0.7 ~ −0.2 V) to 0.5 V (RHE) after the formation
of the TiO 2 film for 1 h at 5.7 V (RHE) [47]. It has been also reported [50] that
downward and upward potential steps after the formation of the passive film on Ni
induce the alternative changes of (σ f ·d f ) toward compressive and tensile direction,
which was ascribed to the volume expansion and contraction of the film due to
hydrogen absorption and desorption, accompanying the valence changes between
Ni
2+ and Ni
3+ in NiO 1+x film with cation vacancies. Moreover, the stress variations
toward compressive direction have been observed during cathodic reduction of the
passive film (γ-Fe 2 O 3 or γ-FeOOH) on Fe in pH 8.4 borate solution [46], which was
ascribed to the volume expansion due to Fe(OH) 2 formed as an intermediate step of
the cathodic reduction.
6.9 Plastic Flow of Porous Anodic Oxide Film
It is known that porous alumina films are formed by anodic oxidation of Al in
acid solutions [51]. The porous films consist of a thin barrier layer next to the metal
substrate and of an outer porous layer with pores of approximately cylindrical section
as schematically illustrated in Fig. 6.9 [52]. Figure 6.10 shows the scanning electron
microscopic (SEM) images of (a) the substrate surface after removal of the porous
alumina film and of (b) the cross section of the porous alumina film formed on
Al at a cell voltage of 240 V for 1 h in 2 M citric acid [53]. The SEM images
indicate that the porous alumina film has self-organized hexagonal pore arrays. The
growth mechanism of the porous alumina film in phosphoric acid [52, 54] has been
investigated by monitoring the motion of tungsten tracer layer (3–5 nm thick) in a
sputter-deposited Al thin film on substrate Al. Tungsten is an ideal tracer since the
W
6+ ion moves outward in the anodic alumina film much slower than Al
3+ ion [55].
The upper part of Fig. 6.11 shows the transmission electron microscopic (TEM)
images for the cross sections of the sputter-deposited aluminum with an incorporated
tungsten tracer layer, followed by anodic oxidation for (a) 180 s, (b) 240 s, and (d)
350 s at 5 mA cm
−2 in 0.4 M phosphoric acid solution [52, 54]. The lower part of
Fig. 6.11 shows schematically the relative distribution of the tungsten tracer layer in
alumina films corresponding to the TEM cross sections [54]. The TEM cross section