6.5 Criterion for Stress Generation by Nelson and Oriani
165
layer contains nano-crystals, and the voids filled with oxygen are formed on nanocrystals within the inner layer near the marker position, indicating that the oxygen
evolution occurs on the nano-crystals [32].
The local oxygen evolution requires the transport of the electrolyte to the nanocrystals. Although the mechanism of the electrolyte transport is not clear, it is deduced
that the electrolyte is transported to the nano-crystals through flaws or cracks in the
outer layer of the film. The local oxygen evolution on the nano-crystals in the inner
layer induces the large compressive stress due to local swelling of the inner layer,
which predominates over the tensile stress induced by the volume contraction due to
local crystallization. At the stage (II), therefore, the increase in compressive stress
with time or with cell voltage is ascribed to the local oxygen evolution in the inner
layer [20].
At the stage (III), the slope of the V vs. t curve increases and returns to a value
close to that at the stage (I), indicating that the oxygen evolution ceases to increase
the current efficiency of the film growth. In the response to the increase in current
efficiency, the stress varies from compressive to tensile, passing through a maximum
compressive value of – 60 J m
−2 at about 340 s, corresponding to a cell voltage of
about 13 V. The kinetics of the local oxygen evolution is limited by the delivery rate
of the electrolyte to the nano-crystals, and thus, the oxygen evolution rate reduces
as the film thickness, i.e., the length of the transport path increases. If the length of
the transport path exceeds a critical value, the local oxygen evolution should cease
since the delivery rate of the electrolyte cannot follow the rate of the local oxygen
evolution. This may be the plausible reason for the cease of the local oxygen evolution
[20]. At a cell voltage larger than 13 V, if the tensile stress induced by the volume
contraction due to crystallization of the film prevails over the compressive stress due
to the local oxygen evolution, the tensile stress would develop progressively with
increasing cell voltage.
Other Factors Influencing Film Stress
Nelson–Oriani’s criterion [17] is insufficient to explain the tensile stress of the film at
the stage (III) because of t o > t
c
o . In order to satisfy the condition of the tensile stress
t o < t
c
o , a crystalline titanium oxide with a density larger than that ρ ox = 4.23 g cm
−3
of the most dense oxide phase, i.e., crystalline rutile has to be assumed, which is
obviously unrealistic [24]. Nelson–Oriani’s criterion [17] does not account for the
defective structure of the oxide film. It is known that the anodic oxide films on Ti have
n-type semiconductive properties [26, 33]. Interstitial Ti
3+ ion or oxygen vacancy are
considered to be donors in the anodic oxide film. It has been proposed that the volume
contraction of the oxide film due to annihilation of interstitial ion or generation of
vacancy induces the tensile stress, while the volume expansion due to generation of
interstitial ion or annihilation of vacancy induces the compressive stress [34, 35].
For the anodic oxidation of Al, it has been also pointed out that the changes in sign
and magnitude of stress are associated with the annihilation of cation vacancy or the
generation of oxygen vacancy at the Al/oxide film interface [36].
Fromhold-Jr theoretically derived that stresses are generated by a momentum
exchange due to collision of diffusing defects (interstitial ion or vacancy) with the
165
layer contains nano-crystals, and the voids filled with oxygen are formed on nanocrystals within the inner layer near the marker position, indicating that the oxygen
evolution occurs on the nano-crystals [32].
The local oxygen evolution requires the transport of the electrolyte to the nanocrystals. Although the mechanism of the electrolyte transport is not clear, it is deduced
that the electrolyte is transported to the nano-crystals through flaws or cracks in the
outer layer of the film. The local oxygen evolution on the nano-crystals in the inner
layer induces the large compressive stress due to local swelling of the inner layer,
which predominates over the tensile stress induced by the volume contraction due to
local crystallization. At the stage (II), therefore, the increase in compressive stress
with time or with cell voltage is ascribed to the local oxygen evolution in the inner
layer [20].
At the stage (III), the slope of the V vs. t curve increases and returns to a value
close to that at the stage (I), indicating that the oxygen evolution ceases to increase
the current efficiency of the film growth. In the response to the increase in current
efficiency, the stress varies from compressive to tensile, passing through a maximum
compressive value of – 60 J m
−2 at about 340 s, corresponding to a cell voltage of
about 13 V. The kinetics of the local oxygen evolution is limited by the delivery rate
of the electrolyte to the nano-crystals, and thus, the oxygen evolution rate reduces
as the film thickness, i.e., the length of the transport path increases. If the length of
the transport path exceeds a critical value, the local oxygen evolution should cease
since the delivery rate of the electrolyte cannot follow the rate of the local oxygen
evolution. This may be the plausible reason for the cease of the local oxygen evolution
[20]. At a cell voltage larger than 13 V, if the tensile stress induced by the volume
contraction due to crystallization of the film prevails over the compressive stress due
to the local oxygen evolution, the tensile stress would develop progressively with
increasing cell voltage.
Other Factors Influencing Film Stress
Nelson–Oriani’s criterion [17] is insufficient to explain the tensile stress of the film at
the stage (III) because of t o > t
c
o . In order to satisfy the condition of the tensile stress
t o < t
c
o , a crystalline titanium oxide with a density larger than that ρ ox = 4.23 g cm
−3
of the most dense oxide phase, i.e., crystalline rutile has to be assumed, which is
obviously unrealistic [24]. Nelson–Oriani’s criterion [17] does not account for the
defective structure of the oxide film. It is known that the anodic oxide films on Ti have
n-type semiconductive properties [26, 33]. Interstitial Ti
3+ ion or oxygen vacancy are
considered to be donors in the anodic oxide film. It has been proposed that the volume
contraction of the oxide film due to annihilation of interstitial ion or generation of
vacancy induces the tensile stress, while the volume expansion due to generation of
interstitial ion or annihilation of vacancy induces the compressive stress [34, 35].
For the anodic oxidation of Al, it has been also pointed out that the changes in sign
and magnitude of stress are associated with the annihilation of cation vacancy or the
generation of oxygen vacancy at the Al/oxide film interface [36].
Fromhold-Jr theoretically derived that stresses are generated by a momentum
exchange due to collision of diffusing defects (interstitial ion or vacancy) with the