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Mechanism of anodic oxidation of molybdenum in nearly-neutral electrolytes studied by electrochemical impedance spectroscopy and X-ray photoelectron spectroscopy
Electrochimica Acta 56 (2011) 7899–7906
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Mechanism of anodic oxidation of molybdenum in nearly-neutral electrolytes studied by electrochemical impedance spectroscopy and X-ray photoelectron spectroscopy Manuela Petrova a , Martin Bojinov a,∗ , Sandrine Zanna b , Philippe Marcus b a b
University of Chemical Technology and Metallurgy, 8 Kl. Ohridski Blvd., 1756 Sofia, Bulgaria Laboratoire de Physico-Chimie des Surfaces, CNRS-ENSCP (UMR7045), 11 Rue Pierre et Marie Curie, 75005 Paris, France
a r t i c l e
i n f o
Article history: Received 12 July 2010 Received in revised form 2 December 2010 Accepted 5 December 2010 Available online 15 December 2010 Keywords: Molybdenum Anodic oxidation Electrochemical impedance spectroscopy X-ray photoelectron spectroscopy Kinetic model
a b s t r a c t Anodic oxidation of molybdenum in weakly acidic, nearly neutral and weakly alkaline electrolytes was studied by voltammetric and electrochemical impedance spectroscopic measurements in a wide potential and pH range. Current vs. potential curves were found to exhibit two pseudo-Tafel regions suggesting two parallel pathways of the dissolution process. Electrochemical impedance spectra indicated the presence of at least two reaction intermediates. X-ray photoelectron spectroscopic (XPS) results pointed to the formation of an oxide containing Mo(IV), Mo(V) and Mo(VI), the exact ratio between different valence states depending on potential and pH of the solution. A physico-chemical model of the processes is proposed and a set of kinetic equations for the steady-state current vs. potential curve and the impedance response are derived. The model is found to reproduce quantitatively the current vs. potential curves and impedance spectra at a range of potentials and pH and to agree qualitatively with the XPS results. Subject to further improvement, the model could serve as a starting point for the optimization of the electrochemical fabrication of functional molybdenum oxide coatings. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Molybdenum and its alloys are employed in a number of industrial fields, including electrical and electronic devices. For example, Mo is employed as a buffer between low-expansion materials used in integrated circuit packages and the copper normally used to supply electrical power to, and remove heat from, such devices [1]. It is also sought to replace silicon substrates used in certain devices. On the other hand, molybdenum oxide can exhibit pronounced electro- and photochromism and thus might act as an excellent photonic material for a number of technical applications [2]. Recently, thermal thin Mo oxides have been thoroughly investigated in relation to the processes of intercalation of Li in such films [3]. The electrochemical preparation of functional oxide coatings is a technology that takes advantage of the long-term experience in the field of both corrosion and deposition of metals [4]. The thickness and morphology of the oxide films can be controlled by the electrochemical parameters and relatively uniform deposits can be obtained on complex shapes. Recently
∗ Corresponding author. Tel.: +359 889 298 679; fax: +359 2 868 20 36. E-mail addresses: [email protected], [email protected] (M. Bojinov). 0013-4686/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2010.12.022
binary oxides of Mo have been obtained via anodic electrodeposition on a parent substrate in weakly alkaline solutions. These materials have been studied as hosts for lanthanide activated lasers [5–7]. In order to optimise the anodic electrodeposition process of such films, more data on its mechanism are needed. The anodic oxidation/dissolution of Mo in acidic solutions has been extensively studied [1,8–14], and quantitative models for the process have been proposed and compared to experimental data [11–13]. In particular, it has been demonstrated that the oxidative dissolution of the passive film follows two parallel pathways with several reaction intermediates with a range of oxidation states of Mo [12]. It has also been shown that thick barrier-like anodic films on Mo can be grown formed in quasi-anhydrous electrolytes such as concentrated phosphoric acid and phosphate esters [15]. On the other hand, experimental data concerning the anodic oxidation process in electrolytes with pH close to neutral are scarce [1,16,17]. Accordingly, the aim of the present work is the experimental characterization and modeling of the anodic oxidation of Mo in weakly acidic, nearly neutral and weakly alkaline electrolytes. Particularly, electrochemical and surface analytical data on the process in the pH range of 4–9 are collected and discussed. A physicochemical model of the process is proposed on the basis of the
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obtained results and its ability to describe the experimental data is evaluated. 2. Experimental 2.1. Electrodes and electrolytes Working electrodes made of pure Mo sheets (99.9%, Goodfellow) with an exposed area 0.4–1.5 cm2 were used. The surface was mechanically abraded with finer grade emery paper, degreased with acetone, rinsed with bidistilled water and dried with hot air. A conventional three-electrode cell was used, featuring a platinum mesh counter electrode located symmetrically around the working electrode, and a 3 M KCl/AgCl/Ag electrode as a reference (E = 0.201 V vs. SHE). All the potentials in the paper are given vs. this kind of reference electrode. The pH of the electrolytes was adjusted by using of suitable buffer solutions – 0.2 M Na3 C6 H5 O7 ·12H2 O and 0.2 M C6 H8 O7 (pH 4.0 ± 0.1), 0.5 M H3 BO3 + 0.025 M Na2 B4 O7 ·10H2 O (pH 7.2 ± 0.1) and 0.05 M H3 BO3 + 0.5 M Na2 B4 O7 ·10H2 O (pH 9.2 ± 0.1). 0.5 M Na2 SO4 was added to all the solutions as an inert electrolyte. The experiments were conducted at room temperature (22 ± 2 ◦ C) in naturally aerated solutions. 2.2. Apparatus and procedure The steady-state current–potential curves and the electrochemical impedance spectra were measured by an Autolab PGSTAT 30/FRA2 apparatus (Eco Chemie, Netherlands). After reaching a stationary value of the current density at a constant potential (current variation ≤ 2%), electrochemical impedance spectra were measured in the frequency range of 20 mHz to 51 kHz at an ac amplitude of 10 mV (rms). The reproducibility of the impedance spectra was ±2% (by impedance magnitude) and ±3◦ (by phase angle). The linearity condition was checked by measuring spectra at ac amplitudes ranging from 5 to 20 mV (rms). The causality of the spectra was verified by a Kramers–Kronig compatibility test embedded in the measurement software. For the fitting and simulation of impedance spectra, Maple and Origin based routines were employed. A Thermo Electron Escalab 250 spectrometer with a monochromated Al K␣ radiation (1486.6 eV) was used for X-ray Photoelectron Spectroscopy. The analyser pass energy was 100 eV for survey spectra and 20 eV for high resolution spectra, and a 500 m2 area was analysed. The photoelectron take-off angle between the surface and the direction in which the photoelectrons were analysed, was 90◦ . Curve fitting of the spectra was performed with the Avantage Thermo Electron software. For the calculation of the surface composition, inelastic mean free paths calculated by Tanuma et al. [18] and the photoemission cross sections determined by Scofield [19] were used. 3. Results 3.1. Electrochemical measurements The steady state current–potential curves of molybdenum in solutions with pH 4, 7 and 9 are presented in Fig. 1. In the region from −0.2 V to 0.2 V, the values of the current density at constant potential were observed to increase with pH from 4 to 9. At pH values higher than or equal to 7, steady state polarization curves exhibit two quasi-Tafel regions, the change of mechanism being observed at the more negative potential, the higher the pH of the solution. The value of the current density was found to be independent on electrolyte stirring in the whole potential interval studied, indicating that transport in the electrolyte is not rate limiting. The
Fig. 1. Current–potential curves in electrolytes with different pH values. Symbols – experimental data; lines – calculated values according to the proposed model.
slope of current–potential curves at higher potentials decreases significantly with increasing pH. Figs. 2–4 present the impedance spectra in the investigated range of potentials (−0.1/0.35 V) for the three studied electrolytes. The magnitude of the impedance at low frequencies (about 0.01 Hz), which can be considered as inversely proportional to the overall reaction rate in the steady state, decreases quasiexponentially with the potential (Figs. 2–4, left) in accordance with the increase of current density with potential (Fig. 1). At constant overpotential, the magnitude of the impedance at very low frequencies decreases with increasing pH, also in accordance with the current vs. potential data. The dependence of the low-frequency impedance magnitude on potential in the region from 0 to 0.3 V is the weaker, the higher the pH of the solution, which can be correlated to the weaker dependence of the current density on potential in the same range. By preliminary deconvolution of the spectra, at least three time constants (situated at ca. 20–100 Hz, around 1 Hz, and below 0.1 Hz) were detected in the curves of the phase angle of the impedance as a function of the frequency (Figs. 2–4, right graphs). This was taken as an indication for the presence of at least two intermediates of the anodic dissolution process. A rough estimation of the capacitance associated with the highest frequency process from the frequency of the corresponding peak in the phase angle vs. frequency curve indicated rather large values (higher than 100 F cm−2 ). This observation indicated that the anodic film formed is most probably very thin and/or conductive. Of course, if the resistance of the formed oxide is of the order of the uncompensated electrolyte resistance, the measured values at the high-frequency end of the spectra would include a contribution of the oxide resistance. This would explain the variation of the high-frequency limit of the impedance magnitude as observed e.g. in Fig. 4. Summarizing, it can be stated that the interfacial processes dominate the impedance response throughout the investigated potential and pH range. This finding is in close analogy to what has been reported earlier for the anodic dissolution of Mo in acidic solutions [11,12]. 3.2. XPS analyses of the anodic films The composition and thickness of the obtained oxides was estimated by angle-resolved X-ray photoelectron spectroscopy. The detailed spectra of Mo 3d measured for oxides formed at 0.1 V in solutions of pH 4, 7 and 9 are shown in Fig. 5, whereas the estimated percentages of different valence states of Mo at the oxide surface are collected in Fig. 6a. The atomic ratio of total oxygen
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Fig. 2. Impedance spectra in pH 4 solution for a range of potentials. Left – impedance magnitude vs. frequency; right – phase angle vs. frequency. Symbols – experimental data; lines – calculated values according to the proposed model.
Fig. 3. Impedance spectra in a pH 7 solution for a range of potentials. Left – impedance magnitude vs. frequency; right – phase angle vs. frequency. Symbols – experimental data; lines – calculated values according to the proposed model.
(determined by taking into account both the oxide and hydroxide form in the respective O 1s spectra) and oxidized Mo is shown in Fig. 6b. Using a simple bilayer model, the thickness of the oxides has been estimated from the Mo 3d spectra, and the obtained
values as depending on pH and applied potential are depicted in Fig. 6c. On the overall, the results indicate the formation of a mixedvalence oxide containing Mo(IV), Mo(V) and Mo(VI), the exact ratio
Fig. 4. Impedance spectra in a pH 9 solution for a range of potentials. Left – impedance magnitude vs. frequency; right – phase angle vs. frequency. Symbols – experimental data; lines – calculated values according to the proposed model.
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Fig. 5. Detailed Mo 3d XP spectra for the film formed at 0.1 V in solutions with pH 4, 7 and 9.
between different valence states depending on potential and pH of the solution. The surface oxides are found to be rather thin (less than 10 nm) with the notable exception of the film formed at 0.2 V in a pH 7 solution, for which no peak of metallic Mo could be detected.
On the basis of the thickness estimates, it can be concluded that mostly soluble products are formed during oxidation of Mo in the investigated electrolytes. The values of the O/Mo ratio, which are between 2 and 2.8 (Fig. 6b), tend also to indicate that the surface
Fig. 6. (a) Distribution of the valence states of Mo as depending on potential and pH. (b) Atomic ratio of total oxygen and oxidized molybdenum as depending on potential and pH. (c) Film thickness estimated from XPS as depending on potential and pH.
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interface are adjusted by the rate of oxidative dissolution, in analogy to what has been proposed for the transpassivity of pure Mo, Cr and Ni [12,13,20,21]. The oxidative dissolution process itself is assumed to follow two parallel paths with the formation of Mo(V) and Mo(VI) intermediate species, as shown in Fig. 7. This scheme is to a certain extent analogous, albeit considerably simpler, than that proposed earlier by some of us for the transpassive dissolution of Mo in acidic solutions (pH <3) [11,12]. The main difference is that the isovalent dissolution of Mo(VI)ad to form Mo(VI)sol (k4 step) is regarded as a chemical reaction (in other words, independent on potential), whereas the k5 reaction is written as k5
Mo(V)ad −→Mo(VI)sol + e− Fig. 7. A scheme of the proposed model for anodic oxidation of molybdenum.
4.2. Main equations oxide has a mixed valence, and these results seem to be in a good agreement with the distribution of Mo states as deduced from the Mo 3d spectra (Fig. 6a). Summarizing, the analysis of the electrochemical and surface analytical data points to the anodic formation of a thin, probably conductive mixed-valence oxide layer, through which oxidation of Mo proceeds to yield mainly soluble end products. An attempt to rationalize the experimental facts obtained by a kinetic model is made in the next section. 4. Discussion 4.1. Physical model A schematic representation of the proposed model is presented in Fig. 7. In accordance with the XPS results, it can be assumed that in the investigated range of potentials, Mo is covered by a thin Mo(IV) oxide film (e.g. MoO2 ). This film grows at its interface with the Mo metal via the oxidation reaction kO
Mo + 2H2 O−→MoO2 + 4e− + 4H+ Of course, the growth of the oxide can be split into the following elementary steps k1O
− (metal/film)Mo−→MoMo + 2V•• O + 4e •• (film) transport of VO k2O + (film/solution)2V•• O + 2H2 O−→2OO + 4H
where MoMo and OO are molybdenum and oxygen positions in the oxide network, and V•• O an oxygen vacancy. However, no evidence for the formation of a barrier-like film has been found in the electrochemical measurements, thus it can be assumed that ionic and electronic transport through the MoO2 layer are not rate determining. Thus the applied potential is supposed to be entirely consumed at the film/solution interface. Since the obtained electrochemical and XPS results indicated that the formed oxide is very thin and conductive, the overall reaction rate is most probably limited by the rate of dissolution of Mo through the film, mediated e.g. by Mo cation vacancies, V4Mo
In order to transfer the proposed physical picture into a mathematical model, the following assumptions are made: • The thickness of the MoO2 layer does not increase in the investigated potential region, i.e. all the current is consumed by the reaction of dissolution of Mo through the film. • The MoO2 film is very thin and/or very defective, thus the overall process is limited by the rates of the reactions at the film/solution interface, and accordingly, all the applied potential is consumed at the film/solution interface. • The rates of the steps 2, 3 and 5 follow a Tafel dependence on the applied potential expressed vs., the reference electrode: ki = kio exp(bi E), i = 2, 3 and 5, where kio are the rate constants at E = 0 vs. reference and bi = ˛i F/RT are the exponential coefficients for the individual steps. • The adsorption of the intermediates follows a Langmuir-type isotherm. Based on these assumptions, the balance of charges results in the following expression for the instantaneous Faradaic current density: iF = k2 (1 − 5 − 6 ) + (k3 + k5 )5 F
(1)
where 5 and 6 are the surface coverages of Mo(V) and Mo(VI), respectively. The respective instantaneous coverages of the respective species are determined by the material balances: ˇ
d5 = k2 (1 − 5 − 6 ) − k3 5 − k5 5 , dt
ˇ
d6 = k3 5 − k4 6 dt
(2)
− (metal/film)Mo + V4Mo −→MoIV Mo + 4e 4 (film)transport of VMo k2 ...k5 (film/solution)MoIV −→ Mo(VI)sol + V4Mo + 2e− Mo
Here the parameter ˇ stands for the maximum concentration of cation sites at the film/solution interface that are available for the oxidative dissolution to take place. It is worth mentioning that in the case of processes taking place at oxidized metal electrodes, the physical meanings of both ˇ and i are somewhat relaxed, i.e. it is deemed possible that the overall process extends to a depth larger than a monolayer. The above assumption was also implied in the treatment of Al dissolution [22,23], and in fact, such a generalized concept has been recently used for the passivation of steel in alkaline media [24]. The steady-state solution (d i /dt = 0) leads to the equation of the stationary current–potential curve
In fact, it is assumed that oxidative dissolution of Mo(IV) at the layer/solution interface determines the overall rate of the process in the potential and pH range studied, i.e. the rate of transport of cation vacancies and that of the oxidation reaction at the metal/film
iF = k2 (1 − 5 − 6 ) + (k3 + k5 ) 5 F k2 k4 k2 k3 ¯ 5 = , ¯ 6 = (k2 + k3 + k5 )k4 + k2 k3 (k2 + k3 + k5 )k4 + k2 k3
k1
(3)
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In turn, a small amplitude ac solution around a given applied dc potential value results in the following system of equations
d5 d6 diF = b2 k2 (1 − 5 − 6 ) + (b3 k3 + b5 k5 )5 − k2 + FdE dE dE d5 +(k3 + k5 ) dE d5 d5 d6 jωˇ = b2 k2 (1 − 5 − 6 ) − (b3 k3 + b5 k5 )5 + k2 + dE dE dE d5 −(k3 + k5 ) dE d6 d5 d6 jωˇ = b3 k3 5 − b4 k4 6 + k3 − k4 dE dE dE (4) Solving this system of equations, an expression for the Faradaic admittance diF /dE is obtained as follows: diF A + jB = Rt−1 + F dE D + jG Rt−1 = F[b2 k2 (1 − 5 − 6 ) + (b3 k3 + b5 k5 ) 5 ] A = (k2 − k3 − k5 )x5 − k3 x6 , B = (k2 − k3 − k5 )y5 − k3 y6 D = (k4 k2 + k3 + k5 ) + k2 k3 − ω2 ˇ2 , G = (k2 + k3 + k4 + k5 )ωˇ x5 = b3 (k3 + k4 )k5 ¯ 5 − b2 k2 k4 (1 − ¯ 5 − ¯ 6 ) + b5 k4 k5 ¯ 5 , y5 = ωˇ[b3 k3 ¯ 5 − b2 k2 (1 − ¯ 5 − ¯ 6 ) + b5 k5 ¯ 5 ], x6 = k3 [b2 k2 (1 − ¯ 5 − ¯ 6 ) + b3 k2 ¯ 5 − k5 (b3 − b5 )¯ 5 ] y6 = ωˇb3 k3 ¯ 5
Fig. 8. Dependence of the rate constants at a potential of 0 V on the concentration of hydroxyl ions in solution.
(5)
The overall impedance Z is then calculated by the appropriate addition of the interfacial capacitance (represented by a constant phase element to take into account the geometrical and/or energetical roughness of the film/solution interface) and the uncompensated solution resistance Z = Rel +
1 n
(jω) Yint + diF /dE
(6)
where Yint and n are the usual CPE parameters. 4.3. Estimation of kinetic parameters In order to obtain reliable estimates of the kinetic parameters, a two-step procedure has been adopted. First, the current vs. potential curve for the respective electrolyte solution has been fitted to Eq. (3) to deduce the initial estimates of the rate constants ki , i = 2–5 and the exponential coefficients bi , i = 2, 3 and 5. Second, using these initial estimates, the impedance spectra for at least five potentials in each solution have been simultaneously fitted to Eqs. (2)–(6). The fitting was performed so that kinetic parameters that showed a mutual dependency higher than 0.7 have never have been set free simultaneously. Statistical weighting was used for the experimental data sets and the errors of parameter estimation were multiplied by the square root of the reduced Chi-square value resulting from the fit. As the reduced Chi-square value was found to be always less than 0.05 and the R2 factor greater than 0.97, such a procedure resulted in a sufficient number of degrees of freedom in the system in order to obtain statistically reliable values of the kinetic constants. As a result, optimal values of the kinetic parameters, as well as of the parameter ˇ and the CPE parameters Yint and n, have been calculated. The calculated steady state current vs. potential curves for the studied materials are presented in Fig. 1, whereas the calculated impedance spectra are shown in Figs. 2 and 4 with solid lines. It can be stated that both the steady state and small amplitude ac response are predicted with sufficient accuracy by the employed model. The dependences of the reaction rate constants kio on pH (or equivalently, on the concentration of hydroxyl ions in the solution) are shown in Fig. 8. The dependences of the interfacial capacitance Cint and the CPE exponent n on potential and pH are collected in Fig. 9. Finally, the best-fit values of the exponential coefficients and the parameter ˇ
Fig. 9. Dependence of the interfacial capacitance and the CPE exponent on potential and pH.
are presented in Table 1. The following conclusions can be drawn from the values of the kinetic constants: • It is encouraging that the experimental data are described with a rather homogeneous set of kinetic parameters, in what concerns mainly the transfer coefficients, which exhibit reasonable values for single-electron transfer steps (˛2 = 0.75 ± 0.12, ˛3 = 0.185 ± 0.035, and ˛5 = 0.37). Thus the overall mechanism does not seem to change significantly in the pH range studied. • The orders of the individual kinetic steps with respect to OH− concentration (n2 , n3 and n5 ) are fractional, as observed also by other authors [21] and also by some of us [25,26]. In fact, the order of the k2 step vs. cOH− is rather close to one, implying that it can be represented as a hydroxylation reaction k2
4+ − MoIV Mo + OH −→Mo(OH)ad + e
Table 1 Kinetic parameters of the anodic oxidation reaction as depending on pH. Parameter
pH 4
pH 7
pH 9
˛2 ˛3 ˛5 ˇ/mol cm−2
0.68 0.23 0.37 0.070
0.63 0.22 0.37 0.072
0.87 0.15 0.37 0.16
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Fig. 10. Calculated surface fractions of Mo(IV), Mo(V) and Mo(VI) as depending on potential in pH 7 and pH 9 solutions.
• It is important to note that the reaction orders of the k3 and k5 vs. cOH− are approximately the opposite of each other (0.27 and −0.26), which could explain the competition of these reactions during the anodic oxidation of molybdenum. • The interfacial capacitance has been estimated from the CPE parameters Yint and n, as well as the uncompensated resistance of the electrolyte Rel , using the formula proposed some time ago
above), and also the fact that the XPS probe of the surface composition is in fact a probe of a thin 3D layer (or in other words, the in-depth resolution of the XPS could be greater than a monolayer). In that respect, it is worthwhile to mention that no significant differences between the composition as measured at angles of 40◦ and 90◦ have been observed.
−1 + Rt−1 ) ] . The values of the by Brug et al. [27]: Cint = [Yint (Rel interfacial capacitance (Fig. 9) in general increase with potential and do not depend on pH. The values of this capacitance are in fact rather high (of the order of mF cm−2 ) which can at least partly be explained by taking into account the geometrical and energetical roughness of an oxide/electrolyte interface when compared to that of a smooth inert metal electrode. Another way to explain such high capacitance is to interpret it as a Faradaic pseudocapacitance of some intermediate species. Thus on the basis of these results it can be assumed that there are more individual steps of the overall reaction than those detectable by electrochemical means, which is the usual conclusion reached by a range of previous authors [21,22]. One way to verify this is to compare the predictions of the model with the product Rt iF , where Rt could be calculated by fitting the high-frequency part of the data with a simple equivalent circuit. However, the overlap of the time constants in the experimental spectra precluded the use of such a method with any reasonable degree of accuracy. • The value of the parameter ˇ is of the order of 0.1 mol cm−2 , i.e. about an order of magnitude larger than that expected for full monolayer coverage at a smooth inert electrode [22]. Such a value is, however, conceivable because of the supposed defectiveness of the thin layer oxide or hydroxide, which makes the interfacial electrochemical Mo dissolution to behave effectively as a quasi-three-dimensional reaction. Thus the formal surface concentration fractions, i , can be considered here to be equivalent to “thicknesses” of species in the film on the surface and used in the kinetic equations in a way analogous to coverage terms usually involved in kinetic equations [22–24].
5. Conclusions
n−1 1/n
In order to compare the predictions of the model with the surface composition of the film as estimated by XPS, the steady-state values of the surface coverages of the different valence species of Mo have been calculated as depending on pH. Such dependences for the solutions of pH 7 and 9 are shown in Fig. 10. The calculated values are in reasonable qualitative agreement with the experimental XPS estimates, namely, in the potential range of −0.1 to 0.2 V the surface is divided between Mo(IV), Mo(V) and Mo(VI) species (cf. also Fig. 6a). This lends further support to the proposed modeling approach. Full quantitative agreement was not reached, however, which can be due to a number of reasons, including the possibility of the reaction behaving as a quasi-three-dimensional one (see
In the present work, the anodic oxidation of Mo in aqueous electrolytes with pH from 4 to 9 has been studied by electrochemical and surface analytical techniques to get an insight in the mechanism of the process in view of the prospective applications of the obtained molybdenum oxide films. The following main conclusions can be drawn from the experimental results and modeling calculations: (1) Current vs. potential curves of molybdenum in solutions with pH 4, 7 and 9 exhibit two pseudo-Tafel regions suggesting two parallel pathways of the dissolution process via the formation of at least two reaction intermediates with different valence states. The magnitude of the impedance in the range of potentials (−0.1/0.35 V) for the three studied electrolytes at low frequencies (about 0.01 Hz) is inversely proportional to the overall reaction rate in the steady state and decreases quasiexponentially with the potential in accordance with the current vs. potential curves. (2) A closer look at the frequency distribution of the impedance revealed the presence of at least three time constants, indicating that at least two intermediate species are involved in the reaction mechanism. Estimation of the capacitance associated with the highest frequency process suggests that the anodic film formed is most probably very thin and/or conductive, and thus only interfacial processes dominate the impedance response throughout the investigated potential and pH range. (3) The surface analytical results indicate the formation of a mixedvalence oxide containing Mo(IV), Mo(V) and Mo(VI), the exact ratio between different valence states depending on potential and pH of the solution. The presence of residual peaks of Mo(0) indicates that the oxides are rather thin (less than 10 nm); therefore, mostly soluble products are formed during oxidation of Mo in the investigated electrolytes. (4) The obtained results made it possible to elaborate a kinetic model of the processes and to estimate the values of the kinetic parameters associated with the individual reaction steps distinguishable by electrochemical means. The model is found to reproduce quantitatively the current vs. potential curves and impedance spectra at a range of potentials and pH. Full quantitative agreement with the XPS results was not reached which can be due to a number of reasons, including the possibility
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of the reaction behaving as a quasi-three-dimensional process, and also probably because the in-depth resolution of the XPS could be greater than a monolayer. Further work is in progress with the aim to determine the nature of the soluble products formed during the anodic oxidation and thus refine the proposed model. Acknowledgements The Bulgarian part of the research team is grateful for the funding of this work by the National Science Fund, Bulgarian Ministry of Education and Science, under contract ВУХ-307/2007. The funding provided by Université de Pierre et Marie Curie for one of the authors (M.B.) in the form of a visiting professor grant is also gratefully acknowledged. References [1] L. De Rosa, C.R. Tomachuk, J. Springer, D.B. Mitton, S. Saiello, F. Bellucci, Mater. Corros. 55 (2004) 602. [2] T. He, J. Yao, J. Photochem. Photobiol. C 4 (2003) 125. [3] J. Swiatowska-Mrowiecka, S. de Diesbach, V. Maurice, S. Zanna, L. Klein, E. Briand, I. Vickridge, P. Marcus, J. Phys. Chem. C 112 (2008) 11050. [4] J.A. Switzer, J. Am. Ceram. Soc. Bull. 66 (1987) 1521.
[5] W.S. Cho, M. Yashima, M. Kakihana, A. Kudo, T. Sakata, M. Yoshimura, J. Am. Ceram. Soc. 80 (1997) 765. [6] W.S. Cho, M. Yoshimura, Solid State Ionics 100 (1997) 143. [7] C.-T. Xia, V.M.J. Fuenzalida, Eur. Ceram. Soc. 23 (2003) 519. [8] M.N. Hull, J. Electroanal. Chem. 38 (1972) 143. [9] M. Uergen, U. Stolz, R. Kirchheim, Corros. Sci. 30 (1990) 377. [10] V. Batrakov, I. Gorichev, N. Simonova, Prot. Met. 29 (1993) 554. [11] M. Bojinov, I. Betova, R. Raicheff, J. Electroanal. Chem. 381 (1995) 123. [12] M. Bojinov, I. Betova, R. Raicheff, Electrochim. Acta 41 (1996) 1173. [13] M. Itagaki, T. Suzuki, K. Watanabe, Electrochim. Acta 42 (1997) 1081. [14] Z. Misirlioglu, A. Aksüt, Corrosion 58 (2002) 899. [15] M. Bojinov, I. Betova, R. Raicheff, J. Electroanal. Chem. 411 (1996) 37. [16] R.D. Armstrong, M.F. Bell, A.A. Metcalfe, J. Electroanal. Chem. 84 (1977) 61. [17] M. Itagaki, T. Suzuki, K. Watanabe, Electrochemistry 64 (1996) 311. [18] S. Tanuma, C.J. Powell, D.R. Penn, Surf. Interface Anal. (1994) 165. [19] J.H. Scofield, J. Electron Spectrosc. Relat. Phenom. 8 (1976) 129. [20] M. Bojinov, G. Fabricius, T. Laitinen, T. Saario, J. Electrochem. Soc. 145 (1998) 2043. [21] M. Keddam, H. Takenouti, N. Yu, J. Electrochem. Soc. 132 (1985) 2561. [22] L. Bai, B. Conway, J. Electrochem. Soc. 137 (1990) 3737. [23] D.D. Macdonald, S. Real, S.I. Smedley, M. Urquidi-Macdonald, J. Electrochem. Soc. 135 (1988) 2410. ˜ F. Vicente, C. Alonso, Elec[24] M. Sanchez-Moreno, H. Takenouti, J.J. Garcia-Jareno, trochim. Acta 54 (2009) 7222. [25] M. Bojinov, I. Betova, R. Raicheff, Electrochim. Acta 44 (1998) 721. [26] I. Betova, M. Bojinov, V. Karastoyanov, P. Kinnunen, T. Saario, Electrochim. Acta 55 (2010) 6163. [27] G.J. Brug, A.L.G. Van den Eeden, M. Sluyters-Rehbach, J.H. Sluyters, J. Electroanal. Chem. 176 (1984) 275.
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Electrochimica Acta journal homepage: www.elsevier.com/locate/electacta
Mechanism of anodic oxidation of molybdenum in nearly-neutral electrolytes studied by electrochemical impedance spectroscopy and X-ray photoelectron spectroscopy Manuela Petrova a , Martin Bojinov a,∗ , Sandrine Zanna b , Philippe Marcus b a b
University of Chemical Technology and Metallurgy, 8 Kl. Ohridski Blvd., 1756 Sofia, Bulgaria Laboratoire de Physico-Chimie des Surfaces, CNRS-ENSCP (UMR7045), 11 Rue Pierre et Marie Curie, 75005 Paris, France
a r t i c l e
i n f o
Article history: Received 12 July 2010 Received in revised form 2 December 2010 Accepted 5 December 2010 Available online 15 December 2010 Keywords: Molybdenum Anodic oxidation Electrochemical impedance spectroscopy X-ray photoelectron spectroscopy Kinetic model
a b s t r a c t Anodic oxidation of molybdenum in weakly acidic, nearly neutral and weakly alkaline electrolytes was studied by voltammetric and electrochemical impedance spectroscopic measurements in a wide potential and pH range. Current vs. potential curves were found to exhibit two pseudo-Tafel regions suggesting two parallel pathways of the dissolution process. Electrochemical impedance spectra indicated the presence of at least two reaction intermediates. X-ray photoelectron spectroscopic (XPS) results pointed to the formation of an oxide containing Mo(IV), Mo(V) and Mo(VI), the exact ratio between different valence states depending on potential and pH of the solution. A physico-chemical model of the processes is proposed and a set of kinetic equations for the steady-state current vs. potential curve and the impedance response are derived. The model is found to reproduce quantitatively the current vs. potential curves and impedance spectra at a range of potentials and pH and to agree qualitatively with the XPS results. Subject to further improvement, the model could serve as a starting point for the optimization of the electrochemical fabrication of functional molybdenum oxide coatings. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction Molybdenum and its alloys are employed in a number of industrial fields, including electrical and electronic devices. For example, Mo is employed as a buffer between low-expansion materials used in integrated circuit packages and the copper normally used to supply electrical power to, and remove heat from, such devices [1]. It is also sought to replace silicon substrates used in certain devices. On the other hand, molybdenum oxide can exhibit pronounced electro- and photochromism and thus might act as an excellent photonic material for a number of technical applications [2]. Recently, thermal thin Mo oxides have been thoroughly investigated in relation to the processes of intercalation of Li in such films [3]. The electrochemical preparation of functional oxide coatings is a technology that takes advantage of the long-term experience in the field of both corrosion and deposition of metals [4]. The thickness and morphology of the oxide films can be controlled by the electrochemical parameters and relatively uniform deposits can be obtained on complex shapes. Recently
∗ Corresponding author. Tel.: +359 889 298 679; fax: +359 2 868 20 36. E-mail addresses: [email protected], [email protected] (M. Bojinov). 0013-4686/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2010.12.022
binary oxides of Mo have been obtained via anodic electrodeposition on a parent substrate in weakly alkaline solutions. These materials have been studied as hosts for lanthanide activated lasers [5–7]. In order to optimise the anodic electrodeposition process of such films, more data on its mechanism are needed. The anodic oxidation/dissolution of Mo in acidic solutions has been extensively studied [1,8–14], and quantitative models for the process have been proposed and compared to experimental data [11–13]. In particular, it has been demonstrated that the oxidative dissolution of the passive film follows two parallel pathways with several reaction intermediates with a range of oxidation states of Mo [12]. It has also been shown that thick barrier-like anodic films on Mo can be grown formed in quasi-anhydrous electrolytes such as concentrated phosphoric acid and phosphate esters [15]. On the other hand, experimental data concerning the anodic oxidation process in electrolytes with pH close to neutral are scarce [1,16,17]. Accordingly, the aim of the present work is the experimental characterization and modeling of the anodic oxidation of Mo in weakly acidic, nearly neutral and weakly alkaline electrolytes. Particularly, electrochemical and surface analytical data on the process in the pH range of 4–9 are collected and discussed. A physicochemical model of the process is proposed on the basis of the
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obtained results and its ability to describe the experimental data is evaluated. 2. Experimental 2.1. Electrodes and electrolytes Working electrodes made of pure Mo sheets (99.9%, Goodfellow) with an exposed area 0.4–1.5 cm2 were used. The surface was mechanically abraded with finer grade emery paper, degreased with acetone, rinsed with bidistilled water and dried with hot air. A conventional three-electrode cell was used, featuring a platinum mesh counter electrode located symmetrically around the working electrode, and a 3 M KCl/AgCl/Ag electrode as a reference (E = 0.201 V vs. SHE). All the potentials in the paper are given vs. this kind of reference electrode. The pH of the electrolytes was adjusted by using of suitable buffer solutions – 0.2 M Na3 C6 H5 O7 ·12H2 O and 0.2 M C6 H8 O7 (pH 4.0 ± 0.1), 0.5 M H3 BO3 + 0.025 M Na2 B4 O7 ·10H2 O (pH 7.2 ± 0.1) and 0.05 M H3 BO3 + 0.5 M Na2 B4 O7 ·10H2 O (pH 9.2 ± 0.1). 0.5 M Na2 SO4 was added to all the solutions as an inert electrolyte. The experiments were conducted at room temperature (22 ± 2 ◦ C) in naturally aerated solutions. 2.2. Apparatus and procedure The steady-state current–potential curves and the electrochemical impedance spectra were measured by an Autolab PGSTAT 30/FRA2 apparatus (Eco Chemie, Netherlands). After reaching a stationary value of the current density at a constant potential (current variation ≤ 2%), electrochemical impedance spectra were measured in the frequency range of 20 mHz to 51 kHz at an ac amplitude of 10 mV (rms). The reproducibility of the impedance spectra was ±2% (by impedance magnitude) and ±3◦ (by phase angle). The linearity condition was checked by measuring spectra at ac amplitudes ranging from 5 to 20 mV (rms). The causality of the spectra was verified by a Kramers–Kronig compatibility test embedded in the measurement software. For the fitting and simulation of impedance spectra, Maple and Origin based routines were employed. A Thermo Electron Escalab 250 spectrometer with a monochromated Al K␣ radiation (1486.6 eV) was used for X-ray Photoelectron Spectroscopy. The analyser pass energy was 100 eV for survey spectra and 20 eV for high resolution spectra, and a 500 m2 area was analysed. The photoelectron take-off angle between the surface and the direction in which the photoelectrons were analysed, was 90◦ . Curve fitting of the spectra was performed with the Avantage Thermo Electron software. For the calculation of the surface composition, inelastic mean free paths calculated by Tanuma et al. [18] and the photoemission cross sections determined by Scofield [19] were used. 3. Results 3.1. Electrochemical measurements The steady state current–potential curves of molybdenum in solutions with pH 4, 7 and 9 are presented in Fig. 1. In the region from −0.2 V to 0.2 V, the values of the current density at constant potential were observed to increase with pH from 4 to 9. At pH values higher than or equal to 7, steady state polarization curves exhibit two quasi-Tafel regions, the change of mechanism being observed at the more negative potential, the higher the pH of the solution. The value of the current density was found to be independent on electrolyte stirring in the whole potential interval studied, indicating that transport in the electrolyte is not rate limiting. The
Fig. 1. Current–potential curves in electrolytes with different pH values. Symbols – experimental data; lines – calculated values according to the proposed model.
slope of current–potential curves at higher potentials decreases significantly with increasing pH. Figs. 2–4 present the impedance spectra in the investigated range of potentials (−0.1/0.35 V) for the three studied electrolytes. The magnitude of the impedance at low frequencies (about 0.01 Hz), which can be considered as inversely proportional to the overall reaction rate in the steady state, decreases quasiexponentially with the potential (Figs. 2–4, left) in accordance with the increase of current density with potential (Fig. 1). At constant overpotential, the magnitude of the impedance at very low frequencies decreases with increasing pH, also in accordance with the current vs. potential data. The dependence of the low-frequency impedance magnitude on potential in the region from 0 to 0.3 V is the weaker, the higher the pH of the solution, which can be correlated to the weaker dependence of the current density on potential in the same range. By preliminary deconvolution of the spectra, at least three time constants (situated at ca. 20–100 Hz, around 1 Hz, and below 0.1 Hz) were detected in the curves of the phase angle of the impedance as a function of the frequency (Figs. 2–4, right graphs). This was taken as an indication for the presence of at least two intermediates of the anodic dissolution process. A rough estimation of the capacitance associated with the highest frequency process from the frequency of the corresponding peak in the phase angle vs. frequency curve indicated rather large values (higher than 100 F cm−2 ). This observation indicated that the anodic film formed is most probably very thin and/or conductive. Of course, if the resistance of the formed oxide is of the order of the uncompensated electrolyte resistance, the measured values at the high-frequency end of the spectra would include a contribution of the oxide resistance. This would explain the variation of the high-frequency limit of the impedance magnitude as observed e.g. in Fig. 4. Summarizing, it can be stated that the interfacial processes dominate the impedance response throughout the investigated potential and pH range. This finding is in close analogy to what has been reported earlier for the anodic dissolution of Mo in acidic solutions [11,12]. 3.2. XPS analyses of the anodic films The composition and thickness of the obtained oxides was estimated by angle-resolved X-ray photoelectron spectroscopy. The detailed spectra of Mo 3d measured for oxides formed at 0.1 V in solutions of pH 4, 7 and 9 are shown in Fig. 5, whereas the estimated percentages of different valence states of Mo at the oxide surface are collected in Fig. 6a. The atomic ratio of total oxygen
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Fig. 2. Impedance spectra in pH 4 solution for a range of potentials. Left – impedance magnitude vs. frequency; right – phase angle vs. frequency. Symbols – experimental data; lines – calculated values according to the proposed model.
Fig. 3. Impedance spectra in a pH 7 solution for a range of potentials. Left – impedance magnitude vs. frequency; right – phase angle vs. frequency. Symbols – experimental data; lines – calculated values according to the proposed model.
(determined by taking into account both the oxide and hydroxide form in the respective O 1s spectra) and oxidized Mo is shown in Fig. 6b. Using a simple bilayer model, the thickness of the oxides has been estimated from the Mo 3d spectra, and the obtained
values as depending on pH and applied potential are depicted in Fig. 6c. On the overall, the results indicate the formation of a mixedvalence oxide containing Mo(IV), Mo(V) and Mo(VI), the exact ratio
Fig. 4. Impedance spectra in a pH 9 solution for a range of potentials. Left – impedance magnitude vs. frequency; right – phase angle vs. frequency. Symbols – experimental data; lines – calculated values according to the proposed model.
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Fig. 5. Detailed Mo 3d XP spectra for the film formed at 0.1 V in solutions with pH 4, 7 and 9.
between different valence states depending on potential and pH of the solution. The surface oxides are found to be rather thin (less than 10 nm) with the notable exception of the film formed at 0.2 V in a pH 7 solution, for which no peak of metallic Mo could be detected.
On the basis of the thickness estimates, it can be concluded that mostly soluble products are formed during oxidation of Mo in the investigated electrolytes. The values of the O/Mo ratio, which are between 2 and 2.8 (Fig. 6b), tend also to indicate that the surface
Fig. 6. (a) Distribution of the valence states of Mo as depending on potential and pH. (b) Atomic ratio of total oxygen and oxidized molybdenum as depending on potential and pH. (c) Film thickness estimated from XPS as depending on potential and pH.
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interface are adjusted by the rate of oxidative dissolution, in analogy to what has been proposed for the transpassivity of pure Mo, Cr and Ni [12,13,20,21]. The oxidative dissolution process itself is assumed to follow two parallel paths with the formation of Mo(V) and Mo(VI) intermediate species, as shown in Fig. 7. This scheme is to a certain extent analogous, albeit considerably simpler, than that proposed earlier by some of us for the transpassive dissolution of Mo in acidic solutions (pH <3) [11,12]. The main difference is that the isovalent dissolution of Mo(VI)ad to form Mo(VI)sol (k4 step) is regarded as a chemical reaction (in other words, independent on potential), whereas the k5 reaction is written as k5
Mo(V)ad −→Mo(VI)sol + e− Fig. 7. A scheme of the proposed model for anodic oxidation of molybdenum.
4.2. Main equations oxide has a mixed valence, and these results seem to be in a good agreement with the distribution of Mo states as deduced from the Mo 3d spectra (Fig. 6a). Summarizing, the analysis of the electrochemical and surface analytical data points to the anodic formation of a thin, probably conductive mixed-valence oxide layer, through which oxidation of Mo proceeds to yield mainly soluble end products. An attempt to rationalize the experimental facts obtained by a kinetic model is made in the next section. 4. Discussion 4.1. Physical model A schematic representation of the proposed model is presented in Fig. 7. In accordance with the XPS results, it can be assumed that in the investigated range of potentials, Mo is covered by a thin Mo(IV) oxide film (e.g. MoO2 ). This film grows at its interface with the Mo metal via the oxidation reaction kO
Mo + 2H2 O−→MoO2 + 4e− + 4H+ Of course, the growth of the oxide can be split into the following elementary steps k1O
− (metal/film)Mo−→MoMo + 2V•• O + 4e •• (film) transport of VO k2O + (film/solution)2V•• O + 2H2 O−→2OO + 4H
where MoMo and OO are molybdenum and oxygen positions in the oxide network, and V•• O an oxygen vacancy. However, no evidence for the formation of a barrier-like film has been found in the electrochemical measurements, thus it can be assumed that ionic and electronic transport through the MoO2 layer are not rate determining. Thus the applied potential is supposed to be entirely consumed at the film/solution interface. Since the obtained electrochemical and XPS results indicated that the formed oxide is very thin and conductive, the overall reaction rate is most probably limited by the rate of dissolution of Mo through the film, mediated e.g. by Mo cation vacancies, V4Mo
In order to transfer the proposed physical picture into a mathematical model, the following assumptions are made: • The thickness of the MoO2 layer does not increase in the investigated potential region, i.e. all the current is consumed by the reaction of dissolution of Mo through the film. • The MoO2 film is very thin and/or very defective, thus the overall process is limited by the rates of the reactions at the film/solution interface, and accordingly, all the applied potential is consumed at the film/solution interface. • The rates of the steps 2, 3 and 5 follow a Tafel dependence on the applied potential expressed vs., the reference electrode: ki = kio exp(bi E), i = 2, 3 and 5, where kio are the rate constants at E = 0 vs. reference and bi = ˛i F/RT are the exponential coefficients for the individual steps. • The adsorption of the intermediates follows a Langmuir-type isotherm. Based on these assumptions, the balance of charges results in the following expression for the instantaneous Faradaic current density: iF = k2 (1 − 5 − 6 ) + (k3 + k5 )5 F
(1)
where 5 and 6 are the surface coverages of Mo(V) and Mo(VI), respectively. The respective instantaneous coverages of the respective species are determined by the material balances: ˇ
d5 = k2 (1 − 5 − 6 ) − k3 5 − k5 5 , dt
ˇ
d6 = k3 5 − k4 6 dt
(2)
− (metal/film)Mo + V4Mo −→MoIV Mo + 4e 4 (film)transport of VMo k2 ...k5 (film/solution)MoIV −→ Mo(VI)sol + V4Mo + 2e− Mo
Here the parameter ˇ stands for the maximum concentration of cation sites at the film/solution interface that are available for the oxidative dissolution to take place. It is worth mentioning that in the case of processes taking place at oxidized metal electrodes, the physical meanings of both ˇ and i are somewhat relaxed, i.e. it is deemed possible that the overall process extends to a depth larger than a monolayer. The above assumption was also implied in the treatment of Al dissolution [22,23], and in fact, such a generalized concept has been recently used for the passivation of steel in alkaline media [24]. The steady-state solution (d i /dt = 0) leads to the equation of the stationary current–potential curve
In fact, it is assumed that oxidative dissolution of Mo(IV) at the layer/solution interface determines the overall rate of the process in the potential and pH range studied, i.e. the rate of transport of cation vacancies and that of the oxidation reaction at the metal/film
iF = k2 (1 − 5 − 6 ) + (k3 + k5 ) 5 F k2 k4 k2 k3 ¯ 5 = , ¯ 6 = (k2 + k3 + k5 )k4 + k2 k3 (k2 + k3 + k5 )k4 + k2 k3
k1
(3)
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In turn, a small amplitude ac solution around a given applied dc potential value results in the following system of equations
d5 d6 diF = b2 k2 (1 − 5 − 6 ) + (b3 k3 + b5 k5 )5 − k2 + FdE dE dE d5 +(k3 + k5 ) dE d5 d5 d6 jωˇ = b2 k2 (1 − 5 − 6 ) − (b3 k3 + b5 k5 )5 + k2 + dE dE dE d5 −(k3 + k5 ) dE d6 d5 d6 jωˇ = b3 k3 5 − b4 k4 6 + k3 − k4 dE dE dE (4) Solving this system of equations, an expression for the Faradaic admittance diF /dE is obtained as follows: diF A + jB = Rt−1 + F dE D + jG Rt−1 = F[b2 k2 (1 − 5 − 6 ) + (b3 k3 + b5 k5 ) 5 ] A = (k2 − k3 − k5 )x5 − k3 x6 , B = (k2 − k3 − k5 )y5 − k3 y6 D = (k4 k2 + k3 + k5 ) + k2 k3 − ω2 ˇ2 , G = (k2 + k3 + k4 + k5 )ωˇ x5 = b3 (k3 + k4 )k5 ¯ 5 − b2 k2 k4 (1 − ¯ 5 − ¯ 6 ) + b5 k4 k5 ¯ 5 , y5 = ωˇ[b3 k3 ¯ 5 − b2 k2 (1 − ¯ 5 − ¯ 6 ) + b5 k5 ¯ 5 ], x6 = k3 [b2 k2 (1 − ¯ 5 − ¯ 6 ) + b3 k2 ¯ 5 − k5 (b3 − b5 )¯ 5 ] y6 = ωˇb3 k3 ¯ 5
Fig. 8. Dependence of the rate constants at a potential of 0 V on the concentration of hydroxyl ions in solution.
(5)
The overall impedance Z is then calculated by the appropriate addition of the interfacial capacitance (represented by a constant phase element to take into account the geometrical and/or energetical roughness of the film/solution interface) and the uncompensated solution resistance Z = Rel +
1 n
(jω) Yint + diF /dE
(6)
where Yint and n are the usual CPE parameters. 4.3. Estimation of kinetic parameters In order to obtain reliable estimates of the kinetic parameters, a two-step procedure has been adopted. First, the current vs. potential curve for the respective electrolyte solution has been fitted to Eq. (3) to deduce the initial estimates of the rate constants ki , i = 2–5 and the exponential coefficients bi , i = 2, 3 and 5. Second, using these initial estimates, the impedance spectra for at least five potentials in each solution have been simultaneously fitted to Eqs. (2)–(6). The fitting was performed so that kinetic parameters that showed a mutual dependency higher than 0.7 have never have been set free simultaneously. Statistical weighting was used for the experimental data sets and the errors of parameter estimation were multiplied by the square root of the reduced Chi-square value resulting from the fit. As the reduced Chi-square value was found to be always less than 0.05 and the R2 factor greater than 0.97, such a procedure resulted in a sufficient number of degrees of freedom in the system in order to obtain statistically reliable values of the kinetic constants. As a result, optimal values of the kinetic parameters, as well as of the parameter ˇ and the CPE parameters Yint and n, have been calculated. The calculated steady state current vs. potential curves for the studied materials are presented in Fig. 1, whereas the calculated impedance spectra are shown in Figs. 2 and 4 with solid lines. It can be stated that both the steady state and small amplitude ac response are predicted with sufficient accuracy by the employed model. The dependences of the reaction rate constants kio on pH (or equivalently, on the concentration of hydroxyl ions in the solution) are shown in Fig. 8. The dependences of the interfacial capacitance Cint and the CPE exponent n on potential and pH are collected in Fig. 9. Finally, the best-fit values of the exponential coefficients and the parameter ˇ
Fig. 9. Dependence of the interfacial capacitance and the CPE exponent on potential and pH.
are presented in Table 1. The following conclusions can be drawn from the values of the kinetic constants: • It is encouraging that the experimental data are described with a rather homogeneous set of kinetic parameters, in what concerns mainly the transfer coefficients, which exhibit reasonable values for single-electron transfer steps (˛2 = 0.75 ± 0.12, ˛3 = 0.185 ± 0.035, and ˛5 = 0.37). Thus the overall mechanism does not seem to change significantly in the pH range studied. • The orders of the individual kinetic steps with respect to OH− concentration (n2 , n3 and n5 ) are fractional, as observed also by other authors [21] and also by some of us [25,26]. In fact, the order of the k2 step vs. cOH− is rather close to one, implying that it can be represented as a hydroxylation reaction k2
4+ − MoIV Mo + OH −→Mo(OH)ad + e
Table 1 Kinetic parameters of the anodic oxidation reaction as depending on pH. Parameter
pH 4
pH 7
pH 9
˛2 ˛3 ˛5 ˇ/mol cm−2
0.68 0.23 0.37 0.070
0.63 0.22 0.37 0.072
0.87 0.15 0.37 0.16
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Fig. 10. Calculated surface fractions of Mo(IV), Mo(V) and Mo(VI) as depending on potential in pH 7 and pH 9 solutions.
• It is important to note that the reaction orders of the k3 and k5 vs. cOH− are approximately the opposite of each other (0.27 and −0.26), which could explain the competition of these reactions during the anodic oxidation of molybdenum. • The interfacial capacitance has been estimated from the CPE parameters Yint and n, as well as the uncompensated resistance of the electrolyte Rel , using the formula proposed some time ago
above), and also the fact that the XPS probe of the surface composition is in fact a probe of a thin 3D layer (or in other words, the in-depth resolution of the XPS could be greater than a monolayer). In that respect, it is worthwhile to mention that no significant differences between the composition as measured at angles of 40◦ and 90◦ have been observed.
−1 + Rt−1 ) ] . The values of the by Brug et al. [27]: Cint = [Yint (Rel interfacial capacitance (Fig. 9) in general increase with potential and do not depend on pH. The values of this capacitance are in fact rather high (of the order of mF cm−2 ) which can at least partly be explained by taking into account the geometrical and energetical roughness of an oxide/electrolyte interface when compared to that of a smooth inert metal electrode. Another way to explain such high capacitance is to interpret it as a Faradaic pseudocapacitance of some intermediate species. Thus on the basis of these results it can be assumed that there are more individual steps of the overall reaction than those detectable by electrochemical means, which is the usual conclusion reached by a range of previous authors [21,22]. One way to verify this is to compare the predictions of the model with the product Rt iF , where Rt could be calculated by fitting the high-frequency part of the data with a simple equivalent circuit. However, the overlap of the time constants in the experimental spectra precluded the use of such a method with any reasonable degree of accuracy. • The value of the parameter ˇ is of the order of 0.1 mol cm−2 , i.e. about an order of magnitude larger than that expected for full monolayer coverage at a smooth inert electrode [22]. Such a value is, however, conceivable because of the supposed defectiveness of the thin layer oxide or hydroxide, which makes the interfacial electrochemical Mo dissolution to behave effectively as a quasi-three-dimensional reaction. Thus the formal surface concentration fractions, i , can be considered here to be equivalent to “thicknesses” of species in the film on the surface and used in the kinetic equations in a way analogous to coverage terms usually involved in kinetic equations [22–24].
5. Conclusions
n−1 1/n
In order to compare the predictions of the model with the surface composition of the film as estimated by XPS, the steady-state values of the surface coverages of the different valence species of Mo have been calculated as depending on pH. Such dependences for the solutions of pH 7 and 9 are shown in Fig. 10. The calculated values are in reasonable qualitative agreement with the experimental XPS estimates, namely, in the potential range of −0.1 to 0.2 V the surface is divided between Mo(IV), Mo(V) and Mo(VI) species (cf. also Fig. 6a). This lends further support to the proposed modeling approach. Full quantitative agreement was not reached, however, which can be due to a number of reasons, including the possibility of the reaction behaving as a quasi-three-dimensional one (see
In the present work, the anodic oxidation of Mo in aqueous electrolytes with pH from 4 to 9 has been studied by electrochemical and surface analytical techniques to get an insight in the mechanism of the process in view of the prospective applications of the obtained molybdenum oxide films. The following main conclusions can be drawn from the experimental results and modeling calculations: (1) Current vs. potential curves of molybdenum in solutions with pH 4, 7 and 9 exhibit two pseudo-Tafel regions suggesting two parallel pathways of the dissolution process via the formation of at least two reaction intermediates with different valence states. The magnitude of the impedance in the range of potentials (−0.1/0.35 V) for the three studied electrolytes at low frequencies (about 0.01 Hz) is inversely proportional to the overall reaction rate in the steady state and decreases quasiexponentially with the potential in accordance with the current vs. potential curves. (2) A closer look at the frequency distribution of the impedance revealed the presence of at least three time constants, indicating that at least two intermediate species are involved in the reaction mechanism. Estimation of the capacitance associated with the highest frequency process suggests that the anodic film formed is most probably very thin and/or conductive, and thus only interfacial processes dominate the impedance response throughout the investigated potential and pH range. (3) The surface analytical results indicate the formation of a mixedvalence oxide containing Mo(IV), Mo(V) and Mo(VI), the exact ratio between different valence states depending on potential and pH of the solution. The presence of residual peaks of Mo(0) indicates that the oxides are rather thin (less than 10 nm); therefore, mostly soluble products are formed during oxidation of Mo in the investigated electrolytes. (4) The obtained results made it possible to elaborate a kinetic model of the processes and to estimate the values of the kinetic parameters associated with the individual reaction steps distinguishable by electrochemical means. The model is found to reproduce quantitatively the current vs. potential curves and impedance spectra at a range of potentials and pH. Full quantitative agreement with the XPS results was not reached which can be due to a number of reasons, including the possibility
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of the reaction behaving as a quasi-three-dimensional process, and also probably because the in-depth resolution of the XPS could be greater than a monolayer. Further work is in progress with the aim to determine the nature of the soluble products formed during the anodic oxidation and thus refine the proposed model. Acknowledgements The Bulgarian part of the research team is grateful for the funding of this work by the National Science Fund, Bulgarian Ministry of Education and Science, under contract ВУХ-307/2007. The funding provided by Université de Pierre et Marie Curie for one of the authors (M.B.) in the form of a visiting professor grant is also gratefully acknowledged. References [1] L. De Rosa, C.R. Tomachuk, J. Springer, D.B. Mitton, S. Saiello, F. Bellucci, Mater. Corros. 55 (2004) 602. [2] T. He, J. Yao, J. Photochem. Photobiol. C 4 (2003) 125. [3] J. Swiatowska-Mrowiecka, S. de Diesbach, V. Maurice, S. Zanna, L. Klein, E. Briand, I. Vickridge, P. Marcus, J. Phys. Chem. C 112 (2008) 11050. [4] J.A. Switzer, J. Am. Ceram. Soc. Bull. 66 (1987) 1521.
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