6.4 Transport Number of Mobile Ion in Anodic …
157
For practical determination of the transport number of mobile ion during anodic
oxidation of valve metals, a thin surface layer is tagged with a completely immobile atom (served as Kirkendall marker), whose position is then pursued during the
subsequent anodic oxidation. After the anodic oxidation, the transport number of
the mobile ion can be determined from the position of the marker atom in the oxide
film since the part of the oxide film above the marker position is due to the transport
of Me
z+ ion, while the part of the oxide film underneath the marker position is due
to the transport of O
2− ion. Radiotracer techniques of inert gas atom such as Xe
125
and Rn
222 [6, 11] and nuclear micro-analysis of O
18 /O
16 [12–15] have been used to
investigate the transport of the mobile ion in the anodic oxide films on valve metals.
Rutherford backscattering spectroscopy (RBS) [16] was also used to determine the
position of ion-implanted marker atoms (Xe, Ar, Kr, etc.) during anodic oxidation of
Al. If Me
z+ ion does not dissolve into solution through the oxide film during anodic
oxidation, t m can be determined from
t m =
d mr, f
d t,f
,
(6.23)
where d mr, f is the thickness of the oxide film above the marker position, and d t,f is the
total thickness of the oxide film. On the other hand, in the case where some amount
of Me
z+ ion dissolves into solution through the oxide film during anodic oxidation,
t m is modified to
t m =
d mr, f + ξ d t,f
(1 + ξ )d t,f
,
(6.24)
where ξ is the fraction of d t,f corresponding to the dissolved amount of Me
z+ ion.
For the prediction of the sign of film stress from the Pilling–Bedworth ratio in
Eq. (6.18), it is implicitly assumed that O
2– ion generated at the oxide film/solution
interface is solely transported inward to form a new oxide only at the metal/oxide
film interface during film growth, i.e. t o is unity. Since the metal/oxide film interface
is mechanically constrained, a volume change due to the oxide formation at the
metal/oxide film interface induces a stress. As shown schematically in Fig. 6.3a, in
the case of α PB > 1, the volume expands due to the oxide formation at the metal/oxide
film interface, which induces the compressive stress. By contrast, if Me
z+ ion at
the metal/oxide film interface is solely transported outward, the oxide film/solution
interface, i.e. t m is unity, new oxide forms only at the oxide film/solution interface.
As shown schematically in Fig. 6.3b, the vacancy of metal atom in the metal side at
the metal/oxide film interface is created due to the oxidation of Me atom, followed
by the transfer of Me
z+ ion toward the oxide film/solution interface. The vacancy of
metal atom provides a free space in the metal side to induce tensile stress as far as
the metal vacancy does not sink into the metal substrate. The creation of the metal
vacancy in the metal side at the metal/oxide film interface induces tensile stress.
157
For practical determination of the transport number of mobile ion during anodic
oxidation of valve metals, a thin surface layer is tagged with a completely immobile atom (served as Kirkendall marker), whose position is then pursued during the
subsequent anodic oxidation. After the anodic oxidation, the transport number of
the mobile ion can be determined from the position of the marker atom in the oxide
film since the part of the oxide film above the marker position is due to the transport
of Me
z+ ion, while the part of the oxide film underneath the marker position is due
to the transport of O
2− ion. Radiotracer techniques of inert gas atom such as Xe
125
and Rn
222 [6, 11] and nuclear micro-analysis of O
18 /O
16 [12–15] have been used to
investigate the transport of the mobile ion in the anodic oxide films on valve metals.
Rutherford backscattering spectroscopy (RBS) [16] was also used to determine the
position of ion-implanted marker atoms (Xe, Ar, Kr, etc.) during anodic oxidation of
Al. If Me
z+ ion does not dissolve into solution through the oxide film during anodic
oxidation, t m can be determined from
t m =
d mr, f
d t,f
,
(6.23)
where d mr, f is the thickness of the oxide film above the marker position, and d t,f is the
total thickness of the oxide film. On the other hand, in the case where some amount
of Me
z+ ion dissolves into solution through the oxide film during anodic oxidation,
t m is modified to
t m =
d mr, f + ξ d t,f
(1 + ξ )d t,f
,
(6.24)
where ξ is the fraction of d t,f corresponding to the dissolved amount of Me
z+ ion.
For the prediction of the sign of film stress from the Pilling–Bedworth ratio in
Eq. (6.18), it is implicitly assumed that O
2– ion generated at the oxide film/solution
interface is solely transported inward to form a new oxide only at the metal/oxide
film interface during film growth, i.e. t o is unity. Since the metal/oxide film interface
is mechanically constrained, a volume change due to the oxide formation at the
metal/oxide film interface induces a stress. As shown schematically in Fig. 6.3a, in
the case of α PB > 1, the volume expands due to the oxide formation at the metal/oxide
film interface, which induces the compressive stress. By contrast, if Me
z+ ion at
the metal/oxide film interface is solely transported outward, the oxide film/solution
interface, i.e. t m is unity, new oxide forms only at the oxide film/solution interface.
As shown schematically in Fig. 6.3b, the vacancy of metal atom in the metal side at
the metal/oxide film interface is created due to the oxidation of Me atom, followed
by the transfer of Me
z+ ion toward the oxide film/solution interface. The vacancy of
metal atom provides a free space in the metal side to induce tensile stress as far as
the metal vacancy does not sink into the metal substrate. The creation of the metal
vacancy in the metal side at the metal/oxide film interface induces tensile stress.