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Passivity of titanium, part IV: reversible oxygen vacancy generation/annihilation

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Bumwook Roh
Bumwook Roh
Bumwook Roh
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Digby Macdonald at Pennsylvania State University
Digby Macdonald
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Abstract and Figures

A simplified Point Defect Model incorporating reversible oxygen vacancy generation/annihilation at the metal/film interface has been used to investigate the impedance of anodized titanium in 0.5 M H2SO4, the oxygen vacancy profile in the anodic titanium oxide film, and the surface oxygen vacancy concentration. This simplified Point Defect Model (PDM), which considers the oxygen vacancy as the only point defect in the film, successfully accounts for the impedance of anodized titanium over the potential range explored. The results indicate that there is a thin region of the non-uniform oxygen vacancy concentration adjacent to the film/solution interface, which has an exponentially decreasing dopant (VO⋅⋅ {V}_O^{\cdot \cdot } ) concentration. The results of the investigation show that the surface oxygen vacancy concentration normalized to the bulk oxygen vacancy concentration is in the range of 0.05–0.15 and is essentially independent of potential.
A schematic of the physicochemical processes that are envisioned to occur within the oxide (TiOx/2) film formed on titanium, according to the Point Defect Model. The metal/film and the film/solution interfaces are depicted by the solid lines and the reactions are located at the interface where they occur. The film/solution interface is defined as x = 0 and the metal/film interface is defined as x = L, where L is the oxide film thickness. Ti ≡ titanium atom; TiTi ≡ titanium cation in a normal cation lattice site; VO..≡\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {V}_O^{..}\equiv $$\end{document} oxygen vacancy; OO ≡ oxygen ion in a normal anion lattice site; TiΓ+ ≡ titanium cation in the solution phase. The oxidation state of the ions/vacancies are labeled as Γ and χ. Oxygen vacancies are formed at the metal/film interface and consumed at the film/solution.
A schematic of the physicochemical processes that are envisioned to occur within the oxide (TiOx/2) film formed on titanium, according to the Point Defect Model. The metal/film and the film/solution interfaces are depicted by the solid lines and the reactions are located at the interface where they occur. The film/solution interface is defined as x = 0 and the metal/film interface is defined as x = L, where L is the oxide film thickness. Ti ≡ titanium atom; TiTi ≡ titanium cation in a normal cation lattice site; VO..≡\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {V}_O^{..}\equiv $$\end{document} oxygen vacancy; OO ≡ oxygen ion in a normal anion lattice site; TiΓ+ ≡ titanium cation in the solution phase. The oxidation state of the ions/vacancies are labeled as Γ and χ. Oxygen vacancies are formed at the metal/film interface and consumed at the film/solution.
… 
Sensitivity analysis, showing the effect of model parameter values on the calculated impedance spectra comparing the measured spectra of the anodic titanium oxide film formed on 2.24VSHE.
Sensitivity analysis, showing the effect of model parameter values on the calculated impedance spectra comparing the measured spectra of the anodic titanium oxide film formed on 2.24VSHE.
… 
Dependencies of the standard rate constants ( ki00\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {k}_i^{00} $$\end{document} and k¯i00\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{k}}_i^{00} $$\end{document}), the electric field strngth (ε), and the transfer coefficients (αi and α¯2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\alpha}}_2 $$\end{document}) on the applied voltage. Data taken from Table 2.
Dependencies of the standard rate constants ( ki00\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {k}_i^{00} $$\end{document} and k¯i00\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{k}}_i^{00} $$\end{document}), the electric field strngth (ε), and the transfer coefficients (αi and α¯2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\alpha}}_2 $$\end{document}) on the applied voltage. Data taken from Table 2.
… 
Barrier layer thickness in the steady state from the optimization of the PDM on impedance data compared with the experimental thickness. * : measured by Ohtsuka et al. [14].
Barrier layer thickness in the steady state from the optimization of the PDM on impedance data compared with the experimental thickness. * : measured by Ohtsuka et al. [14].
… 
Current density in the steady state as a function of the film formation potential(●: experimental data, ○: simulated data).
+7
Current density in the steady state as a function of the film formation potential(●: experimental data, ○: simulated data).
… 
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ORIGINAL PAPER
Passivity of titanium, part IV: reversible oxygen
vacancy generation/annihilation
Bumwook Roh
1
&Digby D. Macdonald
2
Received: 20 April 2019 /Revised: 2 July 2019 /Accepted: 5 August 2019
#Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract
A simplified Point Defect Model incorporating reversible oxygen vacancy generation/annihilation at the metal/film interface has been
used to investigate the impedance of anodized titanium in 0.5 M H
2
SO
4
, the oxygen vacancy profile in the anodic titanium oxide film,
and the surface oxygen vacancy concentration. This simplified Point Defect Model (PDM), which considers the oxygen vacancy as the
only point defect in the film, successfully accounts for the impedance of anodized titanium over the potential range explored. The results
indicate that there is a thin region of the non-uniform oxygen vacancy concentration adjacent to the film/solution interface, which has an
exponentially decreasing dopant (V⋅⋅
O) concentration. The results of the investigation show that the surface oxygen vacancy concen-
tration normalized to the bulk oxygen vacancy concentration is in the range of 0.05–0.15 and is essentially independent of potential.
Keywords Titanium .Anodic oxide film .Oxygen vacancy
Introduction
As discussed in Part II of this series [1], the dominant point defect
in the anodic oxide film on titanium is the oxygen vacancy, and
the possibility of the involvement of the oxygen vacancy (V::
O)in
the oxygen electrode reaction (OER) was proposed in Ref. [2].
Still, it is not completely clear how one can differentiate the
possibility of the involvement of the surface oxygen vacancy in
the oxygen electrode reaction (i.e., an electro-catalytic effect)
from the enhancement of charge transfer across the film that
accompanies an increase in the concentration of defects as de-
scribed by Mallouk [3,4]. One approach to resolving this issue is
to ascertain the exact profile of the oxygen vacancy through the
oxide film as a function of potential. Then, with knowledge of
the oxygen vacancy concentration at the surface and within the
bulk of the barrier layer, we may correlate these concentrations
with the kinetics of the oxygen electrode reaction. Such a com-
parison would provide for identifying which effect is the major
cause for changing the kinetics of the OER on the passive sur-
face. Sikora et al.[5,6] developed a method for determining the
profile of the oxygen vacancies through the oxide film.
The present work reports an electrochemical impedance
spectroscopic (EIS) study of the passive film formed by anod-
izing titanium in 0.5 M H
2
SO
4
at ambient temperature (22 °C)
with the objective of determining the oxygen vacancy concen-
tration at the film/solution interface and exploring the defect
distribution profile within the anodic oxide barrier layer. The
EIS data are interpreted in terms of the Point Defect Model
[7–10] through optimization, in order to determine values for
all model parameters. Once known, these parameters are used
to predict the oxygen vacancy distribution through the barrier
layer and to estimate the concentration at the f/s interface where
the OER takes place. Work described in Part II [1]demonstrates
the concentration of oxygen vacancies in the barrier layer is
almost three orders of magnitude greater than the concentration
of titanium interstitials. This affords significant simplification of
the PDM by ignoring the reactions involving the interstitials,
thereby reducing the number of reactions from five to three and
significantly reducing the number of parameters that must be
evaluated by optimization of the PDM on the EIS data. The
adopted PDM is presented in Fig. 1.
"Passivity of titanium, part I: film growth model diagnostics" was
published in (2014) J Solid State Electrochem 18(5):1485-1493
"Passivity of titanium: part II, the defect structure of the anodic oxide
film" was published in (2019) J Solid state Electrochem 23(7):1967-1979
"The passivity of titanium-part III: characterization of the anodic oxide
film" was published in (2019) J Solid State Electrochem 23(7):2001-2008
*Digby D. Macdonald
macdonald@berkeley.edu
1
Hyundai Motor Company, Mabuk-Ri, Gyeonggi-Do, Republic of
Korea
2
Departments of Nuclear Engineering, University of California at
Berkeley, Berkeley, CA 94720, USA
https://doi.org/10.1007/s10008-019-04363-w
Journal of Solid State Electrochemistry (2019) 23:2863–2879
/Published online: 10 September 2019
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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A Point Defect Model for Anodic Passive Films
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The impedance spectrum for a passivated electrode has been computed using the point defect model that was proposed earlier (6, 7). This model predicts that at high frequencies the film/solution interfacial reaction is predominant and thus a variety of semicircles can be observed in the complex impedance plane. At low frequencies, the transport of point defects in the passive film is rate controlling, and a Warburg‐type impedance spectrum is predicted. These predictions are in good agreement with experimental data for passive Ni and Type 304 SS in aqueous buffer systems.
View