Anodic oxidation of tungsten in sulphuric acid solution—Influence of hydrofluoric acid addition

Materials Chemistry and Physics 112 (2008) 702–710

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Anodic oxidation of tungsten in sulphuric acid solution—Influence of hydrofluoric acid addition Vasil Karastoyanov, Martin Bojinov ∗ Department of Physical Chemistry, University of Chemical Technology and Metallurgy, Kl. Ohridski Bvld. 8, 1756 Sofia, Bulgaria

a r t i c l e

i n f o

Article history: Received 21 June 2007 Received in revised form 12 May 2008 Accepted 15 June 2008 Keywords: Tungsten Sulphate-fluoride electrolyte Anodic films Oxides Point defects Impedance spectroscopy

a b s t r a c t The anodic oxidation of tungsten has been studied in 1 M H2 SO4 solutions containing 0–0.25 M HF. The active-to-passive transition is observed in the potential range 0.4–1.0 V vs. SCE, indicating coupling between film formation and metal dissolution reactions. Steady-state currents measured in the passivation and passivity ranges increase significantly with increasing fluoride concentration, indicating enhanced dissolution of the oxide film. The electrochemical impedance response is dominated by the processes in the barrier sublayer and at its interface with the electrolyte. The presence of a pseudo-inductive loop in the impedance spectra at intermediate frequencies indicates point defect interaction during the film growth and dissolution processes. A kinetic model including the recombination reaction between positively and negatively charged point defects at the film/solution interface as well as an elaborate kinetic scheme for the tungsten dissolution through the film mediated by cation vacancies is proposed. It is found to reproduce satisfactorily the steady-state currents and the impedance spectra as depending on potential in the range 0.4–5 V. Such a model for the conduction mechanism in the barrier sublayer is believed to be an essential part of a modelling approach to the formation of a nanoporous overlayer on tungsten in fluoride-containing solutions. © 2008 Elsevier B.V. All rights reserved.

1. Introduction There have been numerous attempts to further improve the performance of Pt-type electrocatalysts for methanol oxidation using a large range of two- and multicomponent systems. A promising method for enhancing oxidative reactivity is a combination of Ptbased systems with large-surface-area nanocrystalline inorganic oxide matrices that would ensure the metal–support interactions, a homogeneous distribution of catalytic centers, facilitated charge distribution, and overall stability [1,2]. Among applicable inorganic compounds, tungsten oxide seems to promote electrocatalytic oxidation of methanol by interacting with Pt via hydrogen spillover or through the formation of highly conductive tungsten bronzes [3–9]. In addition, tungsten oxide has been receiving considerable attention in recent years for its NOx , CO, and H2 S gas sensing properties [10,11] as well as for use in electrochromic [12–19], photochromic [20,21] and transparent conducting electrode applications [22,23]. Therefore, our interest is in developing a relatively simple route of producing ordered nanoporous tungsten oxide structures based on anodization. Anodization of W to produce compact barrier-type oxides has been reported by numerous authors over the past 30

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (M. Bojinov). 0254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2008.06.029

years [24–47]. It has been found that the film composition is very close or practically identical to WO3 . The lower value of the dielectric constant of the films formed in H3 PO4 when compared to other electrolytes points to a possible incorporation of anions from this electrolyte into the film, although the levels of incorporation are much lower when compared to those in oxides on other valve metals. The anodic film is a wide band-gap amorphous semiconductor (mobility gap, 2.8–3.1 eV), and the photocurrent vs. potential dependence was tentatively described by the low-field limit of the Poole–Frenkel law. The donor concentration as estimated from Mott–Schottky analysis has been found to depend on film thickness either according to a power or an exponential law. Photoelectrochemical impedance and transient measurements point to a major role of the first atomic layer near the film/electrolyte interface in the kinetics of electron-hole recombination via surface states: initially, surface recombination reduces the photocurrent and subsequently, the number of surface states diminishes gradually by photodissolution of the first atomic layer. In addition, in situ thickness vs. time measurements have indicated that dissolution of the oxide plays an important role during film growth and the process of thickness increase is controlled by interfacial processes rather than conduction in the bulk oxide. The formation of ordered nanoporous anodic oxides on W has been reported very recently during oxidation in oxalic acid [48] and sulphate-fluoride electrolytes [49] at comparatively low voltages, whereas a possibility of fast growth of oxide

V. Karastoyanov, M. Bojinov / Materials Chemistry and Physics 112 (2008) 702–710

Nomenclature a bi

VO ••  V6W

half-jump distance (cm) coefficients of the interfacial reactions (i = 2, 31) (V−1 ) capacitance of the barrier layer (F cm−2 ) pseudo-capacitance due to modulation of film thickness (F cm−2 ) diffusion coefficient of cation vacancies (cm2 s−1 ) diffusion coefficient of oxygen vacancies (cm2 s−1 ) applied potential (V) electric field strength (V cm−1 ) Faraday constant (96485 C mol−1 ) current density (A cm−2 ) current density due to cation vacancies (A cm−2 ) current density due to oxygen vacancies (A cm−2 ) imaginary unit flux of cation vacancies (mol cm−2 s−1 ) flux of oxygen vacancies (mol cm−2 s−1 ) rate constant of the film dissolution reaction (cm s−1 ) rate constants of the interfacial reactions (i = 2, 31, 32, 4) (mol cm−2 s−1 ) constant defined in Eq. (17) (A cm−2 ) constant defined in Eq. (18) (A cm−2 ) thickness of the barrier layer (cm) thickness of the cation vacancy accumulation layer at the film/solution interface (cm) tungsten atom in the metal phase capture cross section for a positive defect (cm2 C−1 ) oxygen position in the barrier film negative surface charge due to accumulation of cation vacancies (C cm−2 ) oxygen vacancy in the barrier film tungsten cation vacancy in the barrier film

WV W

W(V) in a W(VI) position in the barrier film

WVI W WVI∗ W

W(VI) in a W(VI) position in the barrier film W(VI) in a W(VI)* position in the outermost cation layer of the film impedance due to cation vacancies ( cm2 ) impedance due to cation vacancies at the film/solution interface ( cm2 ) impedance due to transport of cation vacancies in the film ( cm2 ) impedance due to oxygen vacancies ( cm2 ) impedance due to transport of oxygen vacancies in the film ( cm2 )

Cb CO DM DO E → F I IM IO j JM JO kd ki kM kWO3 L LF/S m S OO qn





ZM ZM,F/S ZM,f ZO ZO,f

Greek letters ˛ polarizability of the film/solution interface ˛2 , ˛31 transfer coefficients ˇ total number of cation positions per unit surface (mol cm−2 ) 5 fraction of W(V) in W(VI) positions in the outermost layer of the film 6 fraction of W(VI) in W(VI) positions in the outermost layer of the film fraction of W(VI) in W(VI)* positions in the outer6∗ most layer of the film ε dielectric constant of the film ε0 dielectric permittivity of vacuum (F cm−1 ) ω angular frequency (rad s−1 )

703

nanotubes promoted by oxide breakdown in chloride or perchlorate electrolytes at higher voltages has been also demonstrated [50]. In the present paper, we report electrochemical measurements of the formation and properties of the anodic oxide on W in 1 M H2 SO4 containing 0–0.25 M HF. Steady-state current vs. potential curves and electrochemical impedance spectroscopic measurements have been employed to characterise the individual steps of the overall oxidation reactions that are detectable by electrochemical means. The impedance spectra as depending on potential and fluoride concentration have been quantitatively interpreted by the surface charge approach proposed earlier [37,38] and several kinetic, transport and structural parameters characterising the conduction mechanism in the oxides have been estimated. The limitations of the proposed approach are discussed, particularly with regard to the description of the processes of subsequent formation of an ordered nanoporous overlayer at higher potentials. 2. Experimental The working electrode material was pure W (99.9%, Goodfellow). Wire or disc shaped cuts of that material were insulated with epoxy resin and inserted in PTFE holders in order to expose an area of 0.00785 cm2 to the electrolyte. The working electrodes were mechanically abraded with emery paper up to grade 2400, rinsed with bidistilled water and dried by hot compressed air. The electrolytes were prepared from reagent grade H2 SO4 and HF using bidistilled water. A conventional electrolytic cell featuring a large area Pt mesh counter electrode and a saturated calomel reference electrode was employed. All the potentials in the present paper are given vs. this electrode. Measurements were performed at room temperature (20 ± 1 ◦ C) in naturally aerated solutions. The electrochemical measurements—steady-state polarisation curves and impedance spectra in the range 0.4–5.0 V vs. SCE have been carried out using an Autolab PGSTAT30 + FRA, GPES and FRA2 software (EcoChemie), After a steady-state current was reached (criterion: variation of the current with time less than ±2% by magnitude), impedance spectra were registered in the frequency range 20 mHz to 51 kHz at an ac amplitude of 15 mV. The reproducibility of the impedance spectra was ±1% by impedance magnitude and ±2◦ by phase angle. The linearity of the impedance spectra has been checked by measuring spectra at ac amplitudes ranging from 5 to 20 mV, whereas the causality by a Kramers–Kronig compatibility test embedded in the measurement software. For the fitting and simulation of impedance spectra Origin 7.5 based routines were employed.

3. Results 3.1. Current vs. potential curves The current vs. potential curves were measured in the potential range from 0.4 to 5 V in order to characterise the active-to-passive

Fig. 1. Current vs. potential curves of W in 1 M H2 SO4 for various concentrations of added HF. Points: experimental values; solid lines: best-fit calculation according to the proposed model.

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transition and the passive range of W. Fig. 1 shows current vs. potential curves of W measured in 1 M H2 SO4 + (0–0.25 M) HF. The active-to-passive transition is observed in the potential range 0.4–1.0 V and is the more pronounced, the higher is the HF concentration. In other words, the passivation current density is larger at higher HF concentrations and the difference in magnitude between the passivation current density and the current density in the passive state is also larger. This fact indicates that dissolution of W through the oxide is favoured by HF addition to 1 M H2 SO4 . On the other hand, there is no systematic dependence of the passivation potential on HF concentration, which probably means that the nature of the rate limiting steps of the overall reaction is not altered by HF addition to the 1 M H2 SO4 electrolyte. In the passive range (above 1 V), the current density slightly decreases with increasing potential and reaches constant values. On the overall, in this region the current density is only slightly dependent on potential, indicating that the chemical dissolution of the oxide is probably the rate controlling step of the overall oxidation process. The steady-state current in the passive state increases quasi-linearly with HF concentration implying a first order of the film dissolution reaction with respect to HF. 3.2. Impedance spectra The impedance spectra for the W/WO3 /H2 SO4 system with different HF concentrations in the passivation region (0.4–1.0 V) are presented in Figs. 2–5. Compilations of spectra at 5.0 V in all the studied electrolytes are shown in Fig. 6.

The impedance magnitude at low frequencies Zf→0 decreases significantly with increasing HF concentration, in line with the increase in the current density (Fig. 1). On the other hand, at potentials above the active-to-passive transition Zf→0 increases with increasing potential, as observed also by other authors in a range of solutions [36,37,44]. This trend most probably reflects the influence of the film thickness (which increases linearly with potential, as is well known for oxide growth on valve metals) on the impedance magnitude [36,37,44]. The oxide film resistance and capacitance dominate the impedance profile at high-frequencies. The presence of two overlapped time constants in this frequency region seems to suggest a duplex nature of the anodic film, as already suggested by other authors [41]. In the intermediate frequency range, a pseudoinductive response becomes visible at potentials higher than 0.5 V, i.e. in general before the passivation peak, in analogy to earlier results with Nb in sulphate-fluoride electrolytes and Mo in phosphoric acid [38]. The appearance of such response has been earlier ascribed to relaxation phenomena due to the formation and time variation of a negative surface charge at the oxide film/solution interface [36,37]. This part of impedance spectra can be described with a low frequency time constant,  LF = Rsc Lsc . The value of this time constant (or the inverse of the characteristic frequency of the inductive loop) decreases with increasing HF concentration which indicates an accelerating effect of HF addition on the build-up of the surface charge in the transient regime. The pseudo-inductive (or negative capacitance) behaviour can be related to the increase of the rate of transport of dominating point defects (anion vacan-

Fig. 2. Impedance spectra of W in 1 M H2 SO4 . Closed squares: experimental spectra; open circles: calculated spectra according to the proposed model. Parameter is frequency in Hz.

V. Karastoyanov, M. Bojinov / Materials Chemistry and Physics 112 (2008) 702–710

705

Fig. 3. Impedance spectra of W in 1 M H2 SO4 + 0.05 M HF. Closed squares: experimental spectra; open circles: calculated spectra according to the proposed model. Parameter is frequency in Hz.

cies) across the oxide film due to the presence of surface charge built up from the charge carriers of opposite sign. This approach was earlier confirmed by one of us for barrier film growth on tungsten in H2 SO4 solution at potentials above the passivation peak [37]. At the low-frequency end, a further capacitive response is detected. In the active-to-passive transition region, it is most probably due to the passivation reaction since it tends to turn to a positive dc limit at potentials below ca. 0.7 V and to a negative dc limit at potentials above that value. In the passive region, the capacitive response at low frequencies can be due to the relaxation of film thickness with ac modulation, as proposed by a range of authors [37,38,51,52]. Preliminary attempts to fit the data using the equivalent circuit proposed in Ref. [37] have given satisfactory results in the potential range above 1 V, however, as the use of equivalent

circuits is in many cases misleading, we preferred to quantitatively compare the data directly with a physico-chemical model of the interface, as already done in our previous work on the passivation of Nb [38]. Summarising, the current vs. potential curves and the ac impedance spectra in the passivation and passivity ranges of W in sulphate-fluoride solutions indicate a coupling between the dissolution of tungsten and the formation of a passivating oxide. In order to estimate in a quantitative fashion the kinetic and transport parameters pertinent to these two processes, an appropriate physico-chemical model has to be devised. The next section is devoted to the detailed description of this model, which is based on an earlier approach to the passivation and passivity of Nb in sulphate-fluoride solutions [38].

Fig. 4. Impedance spectra of W in 1 M H2 SO4 + 0.1 M HF. Closed squares: experimental spectra; open circles: calculated spectra according to the proposed model. Parameter is frequency in Hz.

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Fig. 5. Impedance spectra of W in 1 M H2 SO4 + 0.25M HF. Closed squares: experimental spectra; open circles: calculated spectra according to the proposed model. Parameter is frequency in Hz.

4. Discussion



k32

The oxide of tungsten that forms at open circuit in an aqueous solution can be regarded as mixed-valency oxide [53] in which W(V) and W(VI) position coexist the cation sublattice, together with a certain concentration of W(VI) cation vacancies. A significant concentration of oxygen vacancies is assumed to exist in the anion sublattice as W(V) cation vacancies are neglected for simplicity. The growth of the passive film [35,41] proceeds at the metal/film interface with oxidation of the metal: m → WW + 3V O

••

+ 6em

(1)

The oxygen vacancy is transported through the barrier film by high-field assisted migration and reacts with absorbed water at the film/solution interface achieving film growth: k4

3VO •• + 3H2 O−→3OO + 6H+

kd

(3)

in acidic and alkaline electrolytes, respectively. In fluoride containing electrolytes, oxyfluorocomplexes of W(VI) are probably formed, which is expected to increase the solubility of the film and thus the steady-state current density governed by chemical dissolution of the oxide. W(V) at the F/S interface undergoes either oxidative dissolution as or transforms, also via oxidation, into a passivating W(VI)* species W6+ aq that dissolves isovalently: k2



6+ 6  WV W −→Waq + e + VW

0 exp(b E) are the rate conwhere k2 = k20 exp(b2 E) and k31 = k31 31 stants of the charge transfer steps, b2 = (˛2 F/RT), b31 = (˛31 F/RT) the respective exponential factors and ˛2 , ˛31 the transfer coefficients of these steps. On the other hand, k32 is the rate constant of the chemical reaction (5). Cation vacancies, generated by the above processes, are transported through the film via high-field assisted migration or recombine with oxygen vacancies according to the reaction: 

VO •• + V6W → null

(6)

The high-field migration equations for the transport of cation and anion vacancies are JO = −

DO cO (L) exp 2a



2FaE 0 RT



,

JM = cM (0)

DM exp 2a



FaE 0 RT



(7) (2)

In order the film thickness to be invariant with time in the steady state, the film dissolution reaction must be included with a reaction rate constant kd: WO3−x + 2(3 − x)H+ −→W6+ + (3 − x)H2 O

(5)



6+ 6 WVI∗ W −→Waq + VW

4.1. Growth of the passive film and dissolution of tungsten



k31

VI∗  WV W −→WW + e

(4)

The total defect transport current density is I = −2FJO + 6FJM . Here DO and DM are the diffusion coefficients of oxygen and cation vacancies, cO (L) is the concentration of oxygen vacancies at the metal/film interface, cM (0) the respective concentration of cation vacancies at the film/solution interface and a is the half-jump distance for hopping transport. For a detailed list of all the symbols used in the paper, the reader is referred to the Nomenclature section. The electric field strength in the metal/oxide/electrolyte system E 0 is given by the sum of all the potential drops in the system divided by the oxide film thickness [37]: E 0 =

 + M/F + EL F/S L

(8)

 where M/F = (1 − ˛)E − EL, F/S = qn LF/S /εε0 , ˛ is the polarisability of the film/solution interface, qn is the negative surface charge due to accumulation of cation vacancies at the film/solution interface, E is the field strength in the film bulk and LF/S is the width of the cation vacancy accumulation zone [37]. Further, according to

V. Karastoyanov, M. Bojinov / Materials Chemistry and Physics 112 (2008) 702–710

707

Fig. 6. Impedance spectra of W at 5.0 V in 1 M H2 SO4 (above, left), 1 M H2 SO4 + 0.05 M HF (above, right), 1 M H2 SO4 + 0.1 M HF (below, left) and 1 M H2 SO4 + 0.25 M HF (below, right). Parameter is frequency in Hz.

the mixed-conduction model for oxide films [54], the potential drop at the metal/film interface does not depend on the applied potential. In other words, the reactions at this interface are not considered to be rate limiting, rather, their rate is adjusted by the transport processes of point defects in the passive film. The expressions of the instantaneous partial currents due to the transport of oxygen and cation vacancies acquire the form:





qn LF/S 2Fa (1 − ˛)E + , RTL εε0    qn LF/S 6Fa 6FDO cM (0) exp = (1 − ˛)E + 2a RTL εε0

IO = IM



FDO cO (L) exp a

(9)

At the film/solution interface, cation vacancies are (i) generated with a current density IM,F/S , (ii) transported via high-field migration with a current density IM and (iii) react with the oxygen vacancies according to the recombination reaction at a rate of IO Sqn ,

where S is the cross-section of recombination. Then, dqn = IM,F/S − IM − IO Sqn = IO S dt



IM,F/S − IM IO S

 − qn

(10)

According to the dissolution scheme described by reactions (4) and (5), the current density due to cation vacancies at the film/solution interface is given by IM 5 = JM = k2 5 + k32 6∗ 6F

(11)

 5 and 6∗ being the fractions of the F/S interface occupied by W(V) and W(VI)* , referred to the cation sublattice only. It is assumed that the surface concentration of W(V) cation vacancies is considered as negligible with respect to  5 and 6∗ . The material balances in the

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outermost cation layer are correspondingly: ˇ d5 IM = − k2 5 − k31 5 6F dt ˇ d6∗ dt

= k31 5 − k32 6∗

(12)

(13)

In the steady state, Eqs. (12) and (13) become

6F

− k2  5 − k31  5 = 0

I¯O = (14)

∗

k32  5 − k31  6 = 0

(15)

and obviously ¯ 5 + ¯ 6∗ + ¯ 6 = 1

(16)

¯ 6 being the surface fraction occupied by WO3 , i.e. regular W(VI) sites, at which the isovalent dissolution of the oxide (reaction (3)) proceeds. Eqs. (11), (15) and (16) can be used to calculate I¯M,F/S : I¯M,F/S =

6Fk32 (k¯ 2 + k¯ 31 ) (1 − ¯ 6 ) = k¯ M (1 − ¯ 6 ) k¯ 31 + k¯ 32

(17)

I¯M is proposed to be proportional to the surface (1 − ¯ 6 ) not occupied by regular W(VI), whereas I¯O is assumed to flow only on the fraction ¯ 6 : n I¯O = 2Fkd cH ¯ 6 = 2Fkd ¯ 6 = kWO3 ¯ 6 +

kWO3 k¯ M + kWO3

I¯O =

(19)

(20)

k¯ M + kWO3 3

(21)

k¯ M + kWO3

1 1 + ZO ZM

−1 (22)

where Rel is the electrolyte resistance and C is the film capacitance: C −1 =

1−˛ E¯ εε0 E

(1 − ˛)E˜ + q˜ n

L

−1 = ZO,f

LF/S εε0



,

B=

2Fa RT

 2I¯O B IO IO S˛ = (1 − ˛) + E jω + IO S L¯

(25)

(26)

In order to account for the capacitive behaviour observed in the impedance spectra at low frequencies, the ac modulation of the film thickness has to be taken into account. The expression for the ac current density due to that phenomenon has the form: ˜I =

1 − ˛ Vm jωE˜

E 6F

(27)

which corresponds to a pseudo-capacitance in series with the impedance due to transport of oxygen vacancies, = I¯O /(I¯O + I¯M ) being the current efficiency for film formation: CO = (I¯O + I¯M )

1 − ˛ Vm I¯O E 6F

ZO = ZO,f +

(28)

1 jωCO

(29)

4.3.2. Impedance due to generation and transport of cation vacancies The faradaic impedance due to the generation of cation vacancies at the F/S interface is derived from Eqs. (11)–(13).

jωˇ˜ 6∗ ˜ 6∗ =

−1 ZM,F/S

− k˜ 2 ˜ 5 − k˜ 2 ¯ 5 − k˜ 31 ¯ 5 − k¯ 31 ˜ 5 6F = k˜ 31 ¯ 5 − k¯ 31 ˜ 5 − k32 ˜ 6∗

jωˇ˜ 5 =

k¯ 31 ˜ 5 + k˜ 31 ¯ 5 ˇjω + k32 −1 ZM,F/S

6F(ˇjω + k¯ 2 + k¯ 31 )

⎡

From the assumption that currents transported by oxygen and cation vacancies are additive, and taking into account the electronic properties of the oxide, the impedance of the system can be defined as the parallel combination of the impedance due to generation and transport of cation vacancies (ZM ), the impedance due to transport and consumption of oxygen vacancies (ZO ) and the impedance due to the electronic properties of the oxide film (Ze ):





Solving (24) and (25) simultaneously, we obtain for the impedance of transport of oxygen vacancies:

¯ 5 =

4.3. Small amplitude ac solution

Z = Rel + jωC +

2I¯O B

−1 ZM,F/S = 6F[k¯ 2 ¯ 5 + k¯ 2 ˜ 5 + k32 ˜ 6∗ ]

2 k¯ M

2 k¯ WO

(24)

jω + IO S

The total impedance due to oxygen vacancies is then expressed as

then I¯M =

˜ I¯O S˛E(εε 0 /LF/S )

(18)

where n is the reaction order of the chemical dissolution reaction, Eq. (3) with respect to H+ .If we define ¯ 6 as a function of the reaction rates for the formation of W(V) and W(VI) centers: ¯ 6 =

q˜ n =

where x˜ indicates the complex amplitude of a variable x. The migration current of oxygen vacancies in such conditions is given by

4.2. Steady-state solution and total current density

I M,F/S

4.3.1. Impedance due to transport and consumption of oxygen vacancies For a small amplitude sinewave perturbation around a steadystate Eq. (10) transforms into:

(23)

⎢ ⎣

ZM,F/S = 6Fb2 k¯ 2 ¯ 5 ⎢1 +

(30)

(31)

(32)

−

 5 (k˜ 2 + k˜ 31 ) ˇjω + k¯ 2 + k¯ 31

(33)

⎤

b31 k¯ 31 (k¯ 2 − k¯ 31 ) 2 ))) 1 + j(ωˇk¯ 2 b2 /(b2 k32 k¯ 2 + b31 k¯ 31 2 ¯ ¯ ¯ ¯ × (b2 k2 k32 + b31 k31 + k31 k2 (b2 − b31 )

⎥ ⎥ ⎦

(34) The impedance of the transport of cation vacancies is written in complete analogy to Eq. (26) as −1 ZM,f =

 IM IO S˛ 6I¯M B (1 − ˛) + = E jω + IO S L¯

(35)

The total impedance due to generation and transport of cation vacancies, ZM , is then given by ZM = ZM,f + ZM,F/S

(36)

V. Karastoyanov, M. Bojinov / Materials Chemistry and Physics 112 (2008) 702–710

709

Table 1 Kinetic and transport parameters as depending on HF concentration Parameter −1

b2 (V ) b31 (V−1 ) ˇ (nmol cm−2 ) a (nm) E (MV cm−1 ) ˛ S (mC−1 cm2 )

1 M H2 SO4

1 M H2 SO4 + 0.05 M HF

1 M H2 SO4 + 0.1 M HF

1 M H2 SO4 + 0.25 M HF

12.7 13.0 0.10 0.37 3.1 0.39 15.7

11.7 13.5 0.15 0.39 3.7 0.39 10.4

12.5 13.1 0.44 0.39 3.7 0.39 6.8

13.3 13.8 0.62 0.45 3.7 0.39 9.1

The total impedance is then calculated using Eqs. (22), (23), (29) and (36). 4.4. Comparison with the experimental results In order to obtain quantitative estimates of the kinetic and transport parameters of the model, the following two-step calculation procedure was adopted. First, the total current density vs. potential curves have been fitted to the sum of Eqs. (20) and (21) with 0 , b , k  k20 , b2 , k31 31 32 and kd as adjustable parameters. Second, keeping these values constant, the impedance spectra at potentials from 0.4 to 5 V have been fitted to the sum of Eqs. (22), (23), (29) and  ˛, a, S, and ˇ as adjustable parameters, assum(36), using E, ing a dielectric constant of 54 [29] and using the molar volume of WO3 (31 cm3 mol−1 ) for the oxide phase of the passive film. The current vs. potential curves calculated by this best-fit procedure are shown in Fig. 1 with solid lines, whereas the calculated spectra for each solution at a range of potentials are presented with open symbols in Figs. 2–6. The estimated values of the rate con0 , k  stants k20 , k31 32 and kd as depending on the HF concentration are shown in Fig. 7, whereas the remaining parameters are collected in Table 1. A satisfactory agreement for both the magnitude and the frequency distribution of the impedance is obtained in the whole potential range, indicating the validity of the proposed approach. The main discrepancies lie around the fact that at certain potentials the exact diameters of the two high-frequency loops are not matched with sufficient accuracy. While a better match could be gained by allowing some of the above parameters to vary with potential during the fit, this was not considered worthy due to the already large number of parameters involved in the calculation. It is encouraging that the whole set of data in a large potential range and in four solutions are reproduced with a rather homogeneous set of parameters (Table 1 and Fig. 7). The part of the

Fig. 7. Dependences of the standard rate constants at the film/electrolyte interface on HF concentration.

potential consumed at the film/solution interface ˛, the exponential coefficients b2 and b31 are independent on potential within the calculational error (Table 1), preserving values typical for film covered electrodes (the corresponding transfer coefficients ˛2 and ˛31 are ca. 0.3–0.35). The values of the field strength are also well within the limits of the very high-field approximation used in the present treatment. The main effect of HF addition is on two groups of 0 , k , k and parameters—on one hand, the rate constants k20 , k31 32 d the maximum surface concentration of W(VI)* sites ˇ (characterising the processes of oxidation at the film/solution interface and generation of cation vacancies, as well as the chemical dissolution of the film) and on the other, the half-jump distance a and the capture cross-section of recombination of cation and anion vacancies at the film/solution interface, S. The reaction orders of the steps 0 , k , k with respect to HF concentration are given in the k20 , k31 32 d inserts of Fig. 7 and range between 0.7 and 1.5. Thus tentatively 0 = these reaction rate constants can be written as k20 = k200 cHF , k31 1.5 0.7 00 00 0  k31 cHF , k32 = k32 cHF , kd = kd cHF . The maximum surface concentration of W(VI)* sites ˇ increases with HF concentration indicating an increased defectiveness of the outermost layer of oxide in the presence of HF. The same could be noticed for the maximum surface concentration of cation vacancies since the capture cross section of recombination can be related to such a parameter by the equation S = (6FˇM )−1 . The values of ˇM calculated from the S values collected in Table 1 are of the order of 0.11–0.25 nmol cm−2 , i.e. are rather close to the value of ˇ. This can be taken as a further proof that the cation vacancies are generated by the reaction sequence (4) and (5) involving W(V) and W(VI)* sites. 5. Conclusions The following conclusions can be drawn from the results obtained in the present work: • The active-to-passive transition of W in 1 M H2 SO4 is the more prominent, the higher the addition of HF to the electrolyte. This fact can be tentatively related to the increased production of cation vacancies by an increasingly non-stoichiometric outermost layer of the oxide film. The reaction steps of W(V) oxidation to W(VI)* and its subsequent isovalent dissolution have orders with respect to HF that are close to unity indicating a strong accelerating effect of HF on these two steps. • In all studied electrolytes, the current density for W in the passive state is only slightly dependent on potential, indicating that the chemical dissolution of the oxide is probably the rate controlling step of the overall oxidation process in this region. The steady-state current increases quasi-linearly with HF concentration implying a first order of the film dissolution reaction with respect to HF, which has been predicted also by the calculations on the basis of the proposed model. • The qualitative shape of impedance spectra is not affected by fluoride addition. The impedance magnitude at low frequencies decreases with increasing fluoride concentration in accordance

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to the concentration dependence of the steady-state current density. The increase of the impedance magnitude at low frequencies with potential can be explained by the effect of increasing film thickness. • A quantitative kinetic model involving processes at the film/solution interface and in the film bulk and also dissolution of tungsten through the oxide and oxide growth/dissolution as parallel reaction paths has been found to reproduce quantitatively the steady-state current vs. potential curves and the impedance spectra in a wide range of potentials and solution compositions. The pseudo-inductive feature at intermediate frequencies is explained by the interaction between two current carriers of opposite sign which accelerates the transport of the major current carrier in the transient regime. • The main kinetic parameters of the model have been estimated and on the basis of their values hypotheses on the effect of HF addition on the respective rates of the processes of oxide film growth and tungsten dissolution through the forming oxide have been proposed. The main effect of electrolyte composition is on the cross-section of recombination of current carriers at the film/solution interface, which can be tentatively ascribed to the influence of adsorbed fluoride ions on the defect structure of the outermost layer of the anodic film. • In order to describe the transformation of the barrier film into a duplex oxide featuring a barrier sublayer and an ordered nanoporous overlayer (or equivalently, a system of oxide nanotubes), a more refined approach to the processes taking place at the film/solution interface at high potentials (several tens of volts) is needed. To propose such an approach, a microstructural investigation of the different stages of nanoporous overlayer formation has to be performed. Such an investigation is in progress and the results will be communicated in the near future. Moreover, further work is in progress to clarify the effect of pH at constant fluoride concentration on the passivation and passivity of tungsten in sulphate solutions. Acknowledgement The funding of this work by the National Science Fund, Bulgarian Ministry of Education and Science, under contract BYX-307/2007 is gratefully acknowledged. References [1] A. Hamnett, Interfacial Electrochemistry—Theory, Experiment and Applications, Dekker, New York, 1999, pp. 871–873 (Chapter 47). [2] P.J. Barczuk, H. Tsuchiya, J.M. Macak, P. Schmuki, D. Szymanska, O. Makowski, K. Miecznikowski, P.J. Kulesza, Electrochem. Solid State Lett. 9 (2006) E13. [3] P.J. Kulesza, L.R. Faulkner, J. Electroanal. Chem. Interf. Electrochem. 259 (1989) 81. [4] P.K. Shen, A.C.C. Tseung, J. Electrochem. Soc. 141 (1994) 3082.

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