156
6 Stresses of Anodic Oxide Films Grown on Metal Electrode
Although most of the metal/metal oxide systems have α PB > 1, the metal/metal oxide
systems such as Li/Li 2 O, Mg/MgO, Ca/CaO, and Ba/BaO have α PB < 1, predicting
the generation of tensile stress due to the oxide film growth. The tensile strength
(96 MPa) of MgO is less than one order of magnitude as much as its compressive
strength (1.4 GPa) [10]. The MgO film on Mg may be non-protective because of
the film fracture or breakdown due to the tensile stress generated during the oxide
film growth. However, in many cases, the real sign of stresses measured during the
oxide film growth is likely opposite to that predicted from α PB . In addition to α PB , the
transport (or transference) number of mobile ion in the oxide film during film growth
is one of main factors that control the sign and magnitude of stresses as explained in
the next section.
6.4 Transport Number of Mobile Ion in Anodic Oxide Film
and Stress Generation
For an anodic oxidation of metal, water molecule is dissociated to 2H
+ and O
2−
at the oxide film/solution interface, while metal atom Me in the metal side at the
metal/oxide film interface is ionized to metal ion Me
z+ by an oxidation reaction (Me
→ Me
z+ + ze
- ). The oxygen ion O
2– generated at the oxide film/solution interface is
transported inward via vacancy site of O
2– ion under a high electric field in the film
to form a new oxide by reacting with Me
z+ ion at the metal/oxide film interface. On
the other hand, Me
z+ ion at the metal/oxide film interface is transported outward via
vacancy or interstitial site in the film to form a new oxide by reacting with O
2– ion
at the oxide film/solution interface. In the case where both O
2– and Me
z+ ions are
mobile for the film growth, the anodic current density i a consists of partial current
densities i o due to the transport of O
2− ion and i m due to the transport of Me
z+ ion:
i a = i o + i m
(6.19)
The transport number of each mobile ion is defined with each partial current density
divided by total current density:
t o =
i o
i a
=
i o
i o + i m
,
(6.20)
t m =
i m
i a
=
i m
i o + i m
,
(6.21)
and
t o + t m = 1,
(6.22)
where t o and t m are the transport numbers of O
2− and Me
z+ ions, respectively.
6 Stresses of Anodic Oxide Films Grown on Metal Electrode
Although most of the metal/metal oxide systems have α PB > 1, the metal/metal oxide
systems such as Li/Li 2 O, Mg/MgO, Ca/CaO, and Ba/BaO have α PB < 1, predicting
the generation of tensile stress due to the oxide film growth. The tensile strength
(96 MPa) of MgO is less than one order of magnitude as much as its compressive
strength (1.4 GPa) [10]. The MgO film on Mg may be non-protective because of
the film fracture or breakdown due to the tensile stress generated during the oxide
film growth. However, in many cases, the real sign of stresses measured during the
oxide film growth is likely opposite to that predicted from α PB . In addition to α PB , the
transport (or transference) number of mobile ion in the oxide film during film growth
is one of main factors that control the sign and magnitude of stresses as explained in
the next section.
6.4 Transport Number of Mobile Ion in Anodic Oxide Film
and Stress Generation
For an anodic oxidation of metal, water molecule is dissociated to 2H
+ and O
2−
at the oxide film/solution interface, while metal atom Me in the metal side at the
metal/oxide film interface is ionized to metal ion Me
z+ by an oxidation reaction (Me
→ Me
z+ + ze
- ). The oxygen ion O
2– generated at the oxide film/solution interface is
transported inward via vacancy site of O
2– ion under a high electric field in the film
to form a new oxide by reacting with Me
z+ ion at the metal/oxide film interface. On
the other hand, Me
z+ ion at the metal/oxide film interface is transported outward via
vacancy or interstitial site in the film to form a new oxide by reacting with O
2– ion
at the oxide film/solution interface. In the case where both O
2– and Me
z+ ions are
mobile for the film growth, the anodic current density i a consists of partial current
densities i o due to the transport of O
2− ion and i m due to the transport of Me
z+ ion:
i a = i o + i m
(6.19)
The transport number of each mobile ion is defined with each partial current density
divided by total current density:
t o =
i o
i a
=
i o
i o + i m
,
(6.20)
t m =
i m
i a
=
i m
i o + i m
,
(6.21)
and
t o + t m = 1,
(6.22)
where t o and t m are the transport numbers of O
2− and Me
z+ ions, respectively.