On the Anodic Dissolution of Tantalum and Niobium in Hydroﬂuoric Acid

Ta and Nb are group V valve metals which resist corrosion. Anodic dissolution of Ta and Nb in acidic ﬂuoride media of varying HF concentration is investigated using potentiodynamic polarization and electrochemical impedance spectroscopy. Polarization curves showed a clear active and passive region in all the solutions employed in this study. At a given HF concentration, Nb anodic polarization currents are larger compared to those of Ta. EIS of Ta and Nb exhibited a low frequency capacitive loop in active region, and a low frequency negative differential resistance in the passive region. The surface of Ta and Nb was characterized using XPS, and it reveals the presence of both sub oxide and pentoxide. The electrochemical results could be explained by a four step mechanism involving sub-oxide and pentoxide intermediates. The analysis shows that direct dissolution of sub-oxide occurs via an electrochemical pathway and is facilitated by HF − 2 species and HF in undissociated form. On the other hand, chemical dissolution of pentoxide, which occurs in parallel, is facilitated by the HF species in undissociated form.

Tantalum and Niobium are transition metals which are covered with a tenacious oxide that offers protection from attack by most chemical reagents. 1,2 Oxide formation on these group V valve metals is rapid and in almost all environments, with few exceptions. 3,4 Ta oxide (Ta 2 O 5 ) is used as an important material in capacitors and resistive memories, 5 and anodic oxidation of Ta has been studied extensively. 6 Although Ta and Nb are highly resistant to corrosion, fluoride ions in an acidic environment can dissolve their surface oxides. This has been exploited to form porous Ta and Nb oxides by anodic oxidation in a fluoride electrolyte. 1,[7][8][9][10][11][12][13][14] By anodizing Ta in an electrolyte containing concentrated HF and H 2 SO 4 , at a potential of 10-20 V, nano-dimpled Ta 2 O 5 surface could be obtained. 10,11 Addition of buffered phosphate to this solution results in nanowire/bundle formation. 11 Self-organized porous Ta 2 O 5 can be formed by anodizing Ta in anhydrous glycerol in K 2 HPO 4 at 180 • C at an applied potential of 20 V. Ta foil immersed in 1 M H 2 SO 4 and 2 wt% HF and maintained in the potential range of 10-20 V yields a nano-porous surface, with pore diameter in the range 2-10 nm. 8 Sloppy et al. sputter deposited Ta films on Si, and anodized them in 0.1 M H 3 PO 4 in the potential range of 20-100 V. 15 They proposed that the oxide structure consists of two layers, an inner barrier layer and an outer layer that incorporates some solution species. The growth kinetics were analyzed using both the high field model and the point defect model (PDM), with the PDM offering a better description of Ta anodization. By analyzing the impedance response of the anodized Ta, the parameters of PDM can be obtained, and the oxide thickness values and ionic current densities were successfully compared with the experimental results. 6 In an earlier study, Sapra et al. 4 investigated Ta dissolution in 2.5 M HF at anodic conditions using cyclic voltammetry and EIS. By analyzing the high and mid frequency data, the electrode-electrolyte interface was characterized and the charge transfer resistance values were extracted. The low frequency patterns were quite unusual, and were not modelled quantitatively.
Nb electrodissolution in warm alkali was studied using polarization and EIS 16 and the effect of changing the cation on the dissolution was reported. 17 Cattarin et al. studied the effect of pH and fluoride ion concentration and employed surface charge approach to simulate the EIS results and estimate film formation rate. 18 Bojinov et al. 19 studied anodic polarization and impedance of Nb in a solution with * Electrochemical Society Member. z E-mail: srinivar@iitm.ac.in 0.4 M fluoride ion concentration at pH 2, as well as in 5 M NaOH at 60 • C, and the data was analyzed using surface charge approach. The dissolution of Nb in 500 mM HF was studied using potentiodynamic polarization and EIS, and a four-step mechanism involving two adsorbed species based on reaction mechanism analysis was proposed. 20 It was proposed that chemical and electrochemical dissolution occur in two parallel pathways. Although the anodization and formation of porous oxides of Ta and Nb in acidic fluoride media have been widely studied, the detailed mechanism and kinetics of the oxidation and dissolution process of these metals in HF solutions are poorly understood. Electrochemical impedance spectroscopy (EIS) is a powerful technique that is often used to extract kinetic information of electrochemical systems. [21][22][23][24] In this work, we propose a mechanism to describe Ta and Nb anodic dissolution in acidic fluoride media. Potentiodynamic polarization data was acquired in solutions with various HF concentrations and the impedance spectra were obtained at multiple dc potentials in two different HF concentrations. The electrochemical data were analyzed in the frame work of mechanistic analysis to obtain insights into the kinetics and to identify the solution species participating in the dissolution process.

Experimental
Electrochemical experiments were carried out in a conventional three electrode cell using PARSTAT 2263 (AMETEK, USA). Ta (99.9%) and Nb (99.8%) annealed rods were procured from Alfa Aesar and were cut into discs of 4.75 and 5 mm diameter, respectively. The discs were embedded in Teflon holders exposing only one face to the electrolyte. An RDE setup (Pine Instruments MSR) was employed to rotate the working electrode at an angular speed of 900 rpm. A Pt mesh was used as the counter electrode and Ag/AgCl (saturated KCl) was used as reference electrode. Prior to all the experiments, the electrode was polished with fine grit paper and 0.3 μm alumina powder, ultrasonicated in ethanol, followed by rinsing in deionized water and drying with nitrogen gas. In order to minimize the effect of solution resistance, a supporting electrolyte (Na 2 SO 4 ) at 1 M concentration was used. The HF concentration was varied from 250 to 1000 mM.
The experiments were carried out at room temperature (∼26 • C). Potentiodynamic polarization data were acquired by sweeping the potential from open circuit potential (OCP) to 0.9 V above OCP, at a scan rate of 2 mV s −1 . The steady state current values measured during EIS experiments matched well with the potentiodynamic polarization C259 results, confirming that the scan rate of 2 mV s −1 is sufficiently low. The impedance measurements were carried out by superimposing an ac amplitude of 10 mV (rms) on various dc potentials in the anodic region. The frequency range employed for Nb was 100 kHz to 100 mHz and 100 kHz to 10 mHz for Ta, because data at lower frequencies were scattered and not reproducible. EIS data validation was performed with linear Kramer-Kronig transform (KKT) software. 25 Repeat runs were conducted for all the experiments to ensure the reproducibility. XPS on Ta and Nb was acquired using SPECS Surface Nano Analysis GmbH spectrometer with an X-ray source of Al Kα at 1486.7 eV. The data were corrected with reference to C1s peak energy of 284.8 eV. The peaks were deconvoluted using XPS Peak 4.1 software.

Results and Discussion
Potentiodynamic polarization. -Fig. 1 shows the anodic polarization curves of Ta and Nb in 250 mM, 500 mM, 750 mM and 1000 mM HF solutions. Experimental data are shown as continuous lines with markers. The dotted lines represent mechanistic modelling results, discussed later. The open circuit potential (OCP) of Ta in HF was in the range of −0.4 to −0.54 V vs. Ag/AgCl with lower values corresponding to higher concentration. The OCP of Nb in HF was about −0.53 V vs. Ag/AgCl and was more or less independent of HF concentration. For both Ta and Nb, OCP values stabilized within 15 min and the polarization and impedance experiments were conducted after OCP stabilization. The current recorded for both the metals in solution without HF was very low, showing that the contribution of the supporting electrolyte to the dissolution is negligible. Fig. 1 shows that both metals exhibit an initial increase in current followed by a decrease in the current. In the case of Ta dissolution, the reproducibility in the current density was in the range of 7 to 35 μA cm −2 for Ta dissolution, with higher variation corresponding to higher peak current values. In the repeat runs, the maximum deviation was seen near the peak location. For Nb, the corresponding reproducibility was in the range of 0.3 to 1.0 mA cm −2 , with higher values corresponding to higher peak current values. The region of positive current potential slope corresponds to active dissolution, where the dissolution rate is much larger than the film formation rate. The region of negative slope corresponds to the increased rate of passive film formation. This active-passive transition behavior is typical of the valve metals Nb, Ta and Ti in HF solutions. 4,18,20,26 In comparison, another valve metal, Zr, exhibits limited passivation and the current decreases only slightly after the transition. 27 The peak potential and current values for the data shown in Fig. 1 are listed in Table I. The peak current increases with the increase in HF concentration for both the metals. While there is no significant shift in the peak potential for Ta with the change in HF concentration, the peak potential shifts slightly to more positive values at higher HF concentrations for Nb. A comparison of Figs. 1a and 1b shows that, at a given HF concentration, Ta dissolution currents are of more than an order of magnitude lower than Nb dissolution currents. The peak potential values in Table I show that, compared to Nb, Ta begins to passivate at lower over potentials. Clearly Ta is better than Nb in resisting attack by HF.  Effect of HF concentration.-HF is a weak acid and does not dissociate completely. In addition, the fluoride ions can react with undissociated HF to form other species. The species present in aqueous HF solutions are H + , F − , HF − 2 , H 2 F − 3 and an equilibrium concentration of HF. 28 The dissociation and polymerization of HF involves multiple reactions, as given in Eqs. 1-3. The corresponding equilibrium constants are K EQ1 = 6.84 × 10 −4 , K EQ2 = 5 and K EQ3 = 0.58, respectively. 28 The concentrations of HF dissociation products, in the solutions employed in this study, were determined using the equilibrium constants, and are listed in Table II. Table II shows that, except for the concentration of F − , the concentration of all other species increases with an increase in the nominal HF concentration. However, the concentration of F − species increases up to 750 mM, and then decreases slightly at 1000 mM nominal HF concentration. Initially, a correlation between the transition current and species concentration was sought, and it was found that they correlate well for most species.
Because the predictors (i.e. concentration of various species in HF solutions) are correlated, the actual species involved in the dissolution cannot be unambiguously identified. Therefore, KF (which mainly increases the F − concentration) and H 2 SO 4 (which mainly increases the H + concentration) were added separately to HF solutions, and also studied. The corresponding concentrations of the dissociated species in those solutions are presented in Table II. It is seen from Table II that, with addition of 250 mM KF to 500 mM HF solution, the F − concentration increases about 10 times, while H + concentration actually decreases. The concentrations of HF − 2 and H 2 F − 3 increase by 7 and 5 times respectively. The equilibrium concentration of HF decreases slightly. On the other hand, with the addition of 250 mM H 2 SO 4 to 500 mM HF solution, the concentration of H + increases almost an order of magnitude while the equilibrium HF concentration increases only slightly. Thus, the addition of KF and H 2 SO 4 to HF solutions help break the predictor correlation. Fig. 2 shows the effect of addition of KF and H 2 SO 4 on the anodic polarization behavior of Ta and Nb in HF solution. In case of Ta, the peak current increases only slightly upon addition of H 2 SO 4 , but it increases by ∼ 100% upon addition of KF to the HF solution (Fig. 2a). In case of Nb, the peak current decreases slightly upon addition of H 2 SO 4 , but it increases by ∼ 50% upon addition of KF to the HF solution (Figs. 2b).

Impedance measurements.-Figs.
3a-3f shows complex plane plots of the impedance spectra of Ta dissolving in 500 mM HF. The spectra were acquired in the active and passive regions. The filled markers represent the experimental data and the open triangles represent mechanistic model results, described later. For Ta dissolving in 500 mM HF, the spectra acquired in the active region (50 mV vs. OCP) exhibit two capacitive loops. The high frequency capacitive loop arises from the double layer at the electrode-electrolyte interface and the charge transfer resistance. The loops at mid and low frequencies arise due to the faradaic processes. Fig. 3b shows that, in the passive region (200 mV vs. OCP), a high frequency capacitive loop and a low frequency capacitive loop with negative differential resistance are observed. A negative differential resistance is observed in the passive region when the i-V curve (Fig. 1) has a negative slope, as described in detail in the literature. 20 At a more anodic potential in the passive region (300 mV vs. OCP), in addition to the high frequency capacitive loop and low frequency capacitive loop with negative differential resistance, a mid-frequency pseudo-inductive loop is also seen (Fig. 3c). The mid-frequency data is shown in the inset with expanded scale. The impedance data for Ta in 1000 mM HF exhibited similar results and are shown as complex plane plots in Figs. 3d-3f. A comparison of Figs. 3a-3c with 3d-3f respectively shows that, while the patterns remain the same, the magnitude of impedance is lower at higher HF concentration. In the passive region, the high frequency limit of faradaic impedance, i.e. charge transfer resistance (R t ),   increases with overpotential. An earlier study 4 of Ta anodic dissolution in 2.5 M HF reported two capacitive loops in the active dissolution region and a negative differential resistance at low frequencies in the passive region. Moreover, a pseudo inductive loop was observed at mid-frequencies. The features observed in the impedance spectra shown in Fig. 3 match well with the results reported in the previous study.
The EIS complex plane plots of Nb dissolving in 250 mM HF in both active and passive regions are shown in Figs. 4a-4f. The spectrum in Fig. 4a, acquired in the active region (100 mV vs. OCP), shows two well-resolved capacitive loops, one at high frequencies and another at low frequencies. In the passive region (500 mV vs. OCP), apart from the capacitive loop at high frequencies, the spectrum exhibits a pseudo-inductive loop at mid frequencies (Fig. 4b). Moreover, Fig. 4b   also shows that, at low frequencies, a capacitive loop with negative differential resistance is seen. At 600 mV vs. OCP, the spectrum retains these patterns, but shows a higher charge transfer resistance (Fig.  4c). The data corresponding to Nb dissolving in 750 mM HF in active and passive regions are shown in Figs. 4d-4f and the patterns are similar to those observed in Figs. 4a-4c, with higher HF concentra-tion resulting in lower impedance magnitude. The previously reported impedance patterns of Nb anodic dissolution in fluoride media at low pH [18][19][20] show patterns similar to those presented here. For both Ta and Nb dissolution, EIS data reproducibility was within 3% (magnitude) and 3 • (phase), except a few points at low frequency end where the scatter was more. The similarities in the impedance spectra of Ta and Nb may be attributed to the fact that both are group V metals and have similar chemical properties. 29 In the case for which the surface is completely covered with a 3D oxide film, PDM or its variant, the surface charge approach (SCA) can be used to describe the potentiodynamic polarization and impedance data. Earlier reports indicate that when PDM is the appropriate model to describe the system, the low frequency impedance magnitudes are high, and of the order of 10 4 to 10 6 -cm 2 . 30,31 On the other hand, when SCA is used to model transpassive dissolution, an inductive loop is expected to be present in the mid frequencies of impedance spectra. 18 The data in Fig. 3 show that inductive loops are not present in the impedance spectra of Ta dissolving in 500 mM or 1000 mM HF, at 50 mV and 200 mV vs. OCP. The low frequency impedance magnitudes are of the order of 10 3 -cm 2 . On the other hand, Nb dissolving in HF shows mid frequency inductive loop and the low frequency impedance magnitudes are of the order of 10 2 -cm 2 . In addition, as per the SCA model, the low frequency limit of -Z Im will tend toward infinity whereas the experimental results in Figs. 3 and 4 clearly show that the low frequency limiting values of -Z Im tend toward zero. Therefore, the impedance spectra were analyzed using a mechanistic model, as described in later sections. XPS analysis.-The surfaces of Ta electrodes held in active and passive conditions were subjected to XPS analysis, and the results are shown in Fig. 5. The electrode was exposed to 500 mM HF solution for 1h. In the figures, experimental data are shown as markers, the model fit is shown as continuous line and the individual contributions are shown as dashed lines. Fig. 5a shows three peaks at 21.7 eV, 23.1 eV and 26.8 eV corresponding to Ta 4f 7/2 levels and three more peaks at 23.6 eV, 25 eV and 28.7 eV corresponding to Ta 4f 5/2 levels. The spin orbital splitting is 1.9 eV, in accordance with published literature. 32 The peaks at 21.7 eV and 23.6 eV binding energy levels are assigned to metallic Ta, while the peaks at 23.1 eV and 25 eV binding energy levels are assigned to Ta 2+ . 32 On the other hand, the peaks at 26.8 eV and 28.7 eV can be assigned to Ta 5+ . 33 Likewise, Fig. 5b shows three peaks of Ta 4f 5/2 levels at 21.7 eV, 23.1 eV and 27.0 eV and three more peaks of Ta 4f 5/2 levels at 23.6 eV, 25 eV and 28.9 eV, which can be assigned to metallic Ta, Ta 2+ and Ta 5+ respectively. Fig. 6a shows the XPS data of Nb held at 100 mV vs. OCP in 250 mM HF for 1h. Three doublets, with a spin orbital splitting of 2.8 eV are resolved. Based on literature reports, 34 the Nb 3d 5/2 peak at 201.6 eV is assigned to metallic Nb, the one at 203.9 eV is assigned to Nb 2+ and the one at 206.9 eV is assigned to Nb 5+ . On the other hand, XPS of Nb held in the passive region, shown in Fig. 6b 500 and 1000 mM HF (Fig. 3).

Nominal HF concentration (mM)
Potential ( The peak corresponding to Nb 2+ is absent in this case. Because the electrode is transferred from solution to the vacuum chamber for XPS analysis, oxidation of the sample surface cannot be ruled out and XPS results may be used to only identify the species that are likely to be present on the surface during anodic dissolution. In summary, Ta or Nb surface exposed to HF solutions can be in an oxidation state of 0, +2 or +5 and hence, in the mechanistic analysis of the electrochemical data, intermediate species with these oxidation states were chosen, as described in the latter part of this paper. Mechanistic model.-To validate the impedance spectra, the EIS data was analyzed using linear Kronig-Kramers Transform (KKT) software. 25 Linear KKT involves fitting a circuit of many Voigt elements with a constraint on the time constants. The KK transformed data closely match the experimental data (results not shown). The impedance spectra were also fitted to equivalent electrical circuits where the faradaic processes were modeled using resistors and capacitors (results not shown) and it was found that up to two pairs of resistors and capacitors were needed to model the data. However, it is difficult to obtain a picture of the physico-chemical processes from the circuit parameters. Therefore, the polarization data and EIS data were modelled using reaction mechanism analysis (RMA).
The impedance offered by the solution was modelled using a simple resistance (R sol ). The electrode electrolyte interface was modelled by a double layer capacitor in parallel with a faradaic process. The high frequency loops in all the spectra were modelled using a constant phase element (CPE) instead of an ideal capacitor, because they exhibited frequency dispersion of capacitance, and the exponents are in the range of 0.89 to 0.91 for Ta (Table III) and 0.92 to 0.97 for Nb (Table IV). When the electrode is immersed in HF, it continuously undergoes dissolution and re-passivation, resulting in a rough surface with non-uniform activity. Atomic level heterogeneity is one possible cause of the observed CPE behavior, while variation in film properties, diffusion limitations and porous nature of the electrode are a few other possible causes. [35][36][37][38][39][40] While the exact cause of CPE behavior is still debated in the literature, [41][42][43][44] the fact that it is often seen at many electrode-electrolyte interfaces is agreed upon. The effective capacitance can be calculated using Brug's law. 35 For Ta, the effective capacitance was a few tens of μF/cm 2 , whereas for Nb in active dissolution region, it was a few hundred μF/cm 2 . The large value may be due to the relatively large dissolution rate of Nb and correspondingly high surface roughness.
RMA can be used to identify a reaction mechanism that can best explain the observed results. Ta can exist in oxidation states of 0, +2, +4 and +5, 33,45-47 among which +2 and +5 are the most commonly recognized forms of the oxides. Nb exhibits similar stable oxidation states and a dissolution mechanism of Nb in 500 mM HF involving two adsorbed intermediate species, N b 2+ ads and N b 5+ ads was proposed earlier. 20 It was shown that the dissolution occurs through two pathways, direct chemical dissolution of N b 5+ ads and electrochemical dissolution of N b 2+ ads giving up 3 electrons (Eqs. 4-7). Similar works based on reaction mechanism analysis of polarization and impedance data of Ti 26 and Zr 27,48 were reported in the literature, but with oxidation states of 3 and 4 for the intermediate species. In this work, M is used to represent both Ta and Nb.
The assumptions invoked are that mass transfer limitations are negligible, that intermediate species adsorption follows the Langmuir isotherm model, and that rate constants of steps involving electron transfer show an exponential dependence on potential. The model assumes that the bare metal and adsorbed intermediate species are present up to a monolayer. The first two steps are assumed to be reversible and k 1 , k −1 , k 2 and k −2 are the corresponding rate constants. The third (Eq. 6) and fourth (Eq. 7) steps are the dissolution steps and are assumed to be irreversible because the RDE setup and operation ensures that the dissolved species are quickly removed from the electrode-electrolyte interface to the bulk solution. The third step is a chemical step because it does not involve electron transfer, so the corresponding rate constant k 3 is independent of potential. The fourth step is an electrochemical step and k 4 is the corresponding rate constant. Only these two rate constants, viz. k 3 and k 4 , are assumed to be dependent on the solution species concentrations, because they relate to the movement of adsorbed species into the solution. Earlier, a simpler mechanism, as well as variants of the mechanism given in Eqs. (4-7), were evaluated, but the match between predicted polarization and impedance spectra were poor and hence were rejected. In all the mechanisms evaluated, the kinetic parameter values were varied until a match between the simulated and experimental data was obtained. The impedance spectra in the active region can be modeled  250 and 750 mM HF (Fig. 4).

Nominal HF concentration (mM)
Potential ( using one adsorbed intermediate, but because the XPS data shows that Ta and Nb are present in oxidations states of 0, +2 and +5, a mechanism with these two intermediates is proposed.
A mechanism normally consists only of elementary steps, viz. the number of electrons transferred in a step is at most one, 49 and the order of the reaction is at most two. However, multi electron transfer step has often been condensed in the literature into a pseudo-elementary step, 50,51 if it is assumed that one of them is rate limiting. 52 In the Eqs. 4-7 the more liberal interpretation of the term mechanism is used. In the following equations, θ 2+ ,θ 5+ and θ V represent the fractional surface coverage values of M 2+ ads , M 5+ ads and bare metal respectively, with the constraint that the sum of all the fractional coverage values is unity. The mass balance equations corresponding to mechanism presented in Eqs. 4-7 are and the faradaic current density is given by the Eq. 10 [10] When small amplitude perturbations are employed, the faradaic impedance can be written as Here, R t is the charge transfer resistance and is given by Eqs. 8 and 9 can be expanded in Taylor series, and linearized to yield the following linear equations Solving Eqs. 13 and 14, we get Substituting the results of Eqs. 12, 15 and 16 in Eq. 11, the faradaic impedance can be calculated. Total impedance is given by The subscript "dc" refers to the value of the rate constant at a given dc potential, while the superscript "SS" refers to value of the fractional surface coverage evaluated at the steady state. R sol is the solution resistance and Q and α are the constant phase element (CPE) parameters employed to model the double layer. The angular frequency of the sinusoidal perturbation is given by ω. The derivatives of fractional surface coverage with potential can be obtained by expanding the Eqs. 8-9 in Taylor series and neglecting the second and higher order terms. [53][54][55] The pre-exponents of the rate constants k 3 and k 4 are written as where, X, Y and Z can take all the possible HF dissociation species combinations. X, Y and Z can be the same species or can be different.
In an earlier work, 56 polarization data of Nb in multiple concentrations of HF was analyzed. The standard rate constants k 30 and k 40 were related to the species as k 30 = k 30 [X ] β and k 40 = k 40 [Y ] γ . Although a good match with the polarization data was obtained with X = HF − 2 and Y = HF, when the impedance data at various dc potentials were included in the analysis, matches were very poor (results not shown) and the model could not predict many of the features of the impedance spectra. For both Ta and Nb, acceptable results were obtained when the expressions for k 30 and k 40 from the Eqs. 18 and 19 were used with X = HF, Y = HF − 2 and Z = HF. Thus, the electrochemical dissolution is certainly not an elementary step, and is only an approximation to several successive steps. A pictorial representation of the proposed mechanism, along with the solution species affecting various steps, is given in Fig. 7.
The simulated polarization data for Ta are shown as dotted lines in Fig. 1a and the kinetic parameters are listed in Table V. Note that only one set of parameters, given in Table V, is used throughout the potential range and all solutions. In earlier reports [53][54][55]57,58 which employ mechanistic analysis of electrochemical reactions in multiple solutions, an independent set of kinetic parameters was proposed for each solution. It is difficult to extract the relationship between the kinetic parameters and solution species concentration from those results. In this work, a physically meaningful relationship is employed to describe the dependence of rate constants on the potential as well as solution species concentration. Although modelling the entire data set of Ta (or Nb) using one set of parameters is very challenging, valuable insights can be obtained by this method. The model predicted the active-passive regions clearly for all the concentrations studied. The active-passive transition potential is close to the actual experimental transition potential. The simulated polarization results for Nb is shown in Fig. 1b and

Parameters
Units Values also predicts the polarization data well for both Ta and Nb when the KF or H 2 SO 4 are added (dotted lines in Fig. 2). The model correctly predicts an increase in peak current density with the addition of KF to 500 mM HF for both metals. It also predicts the slight decrease in current density for Nb with the addition of H 2 SO 4 , and an increase in current density for Ta with the addition of H 2 SO 4 . Fig. 3 shows the complex plane plots of simulated spectra along with the experimental results for Ta in 500 mM and 1000 mM HF. At the active potential (50 mV vs. OCP) in both the concentrations (Figs. 3a and 3d), the model not only captures two capacitive loops that were seen in experimental data but also predicts an additional capacitive loop at low frequencies. If a reaction mechanism involves two adsorbed intermediates, the resulting spectra will contain up to three loops in the complex plane representation of EIS. However, if the relaxation times of the adsorbed species are too close or if the data were not acquired in a wide frequency range, fewer loops may be observed. Figs. 3b and 3e show that, in the passive potential at 200 mV vs. OCP in both 500 mM and 1000 mM, the simulated results show a qualitative match with measured spectra predicting the high frequency capacitive loop as well as the low frequency capacitive loop with negative differential resistance. In the passive region (300 mV vs. OCP), in both 500 mM and 1000 mM HF, Figs. 3c and 3f show that the model successfully predicts the high frequency capacitive loop and the low frequency capacitive loop with negative differential

Parameters
Units Values resistance, but fails to capture the mid-frequency pseudo-inductive loop.
The complex plane plots of impedance spectra predicted by the model for anodic dissolution of Nb in 250 mM and 750 mM HF are given in Fig. 4 and the kinetic parameters employed are given in Table VI. Figs. 4a and 4d show, that in the active region (100 mV vs. OCP) at both the concentrations, the proposed mechanism closely matches the two capacitive loops observed. An examination of Figs. 4b and 4e show that in the passive region (500 mV vs. OCP), the high frequency loop and mid frequency features are captured well, and the model successfully predicts the mid frequency inductive loop. However, the prediction in the low frequency is only qualitative. At 600 mV vs. OCP in the passive region, the model predictions closely match the observed spectra, as shown in Figs. 4c and 4f. The model spectra shows the high frequency capacitive loop, mid frequency inductive loop and the low frequency capacitive loop with negative differential resistance. The dissolution mechanism analyzed for both Ta and Nb are identical, and the model predictions are equally good for the both metals. This is not surprising, because both metals have similar chemical properties and also qualitatively identical features in the impedance spectra in both the active and passive regions.
The variation of fractional surface coverage of Ta bare metal (θ SS V ) and the adsorbed species (θ SS 2+ and θ SS 5+ ) with potential in a concentration of 500 mM HF, as predicted by the mechanism, is shown in Fig. 8a. At OCP, more than half of the surface consists of bare Ta, with low coverage of T a 2+ ads and T a 5+ ads . In the active region, an increase in potential causes the fractional surface coverage of both intermediate species to increase. Correspondingly, the surface coverage of bare metal decreases with potential. Near the transition potential, the fractional surface coverage of T a 2+ ads species reaches a maximum, and decreases with potential. On the other hand, the fractional surface coverage of T a 5+ ads increases with potential in both active and passive regions. Beyond a potential of 300 mV vs. OCP, the model predicts that the surface is mostly covered with T a 5+ ads film, but a small fraction of the surface is still covered with T a 2+ ads species. At higher potentials, when the passivation is complete, a 3D film likely to form accompanied by passive dissolution. 19 A similar trend is predicted for the variation of fractional surface coverage of N b 2+ ads and N b 5+ ads with potential (Fig. 8b) in 250 mM HF. Here, the fractional surface coverage of N b 5+ ads increases until a potential of 400 mV vs. OCP and is almost close to unity, but a small fraction of the surface is still covered with N b 2+ ads species. When a 3D film is present on the surface, the SCA model predicts that the product R t × i will be linearly related to the potential. Calculations show that in the case of Ta dissolution in HF, the product R t × i was linearly related to the potential, but the relationship was clearly nonlinear for Nb (results not shown). On the other hand, the absence of a mid-frequency pseudo inductive loop in the EIS data of Ta dissolving in HF at 50 and 200 mV vs. OCP suggests that the SCA model may not be applicable here.
The anodic dissolution rates of Ta and Nb in various HF solutions are also predicted by the model and the results are presented in Fig. 9. The variation of chemical and electrochemical dissolution rates of Ta with potential is presented in Fig. 9a. The chemical dissolution rate of Ta in 500 mM HF is more than one order of magnitude lower than the electrochemical dissolution rate. The chemical dissolution rate is also about two orders of magnitude lower than that of another valve metal, Ti, in 100 mM HF. 26 The chemical dissolution rate is proportional to rate constant k 3 and the fractional surface coverage of T a 5+ ads . While the rate constant k 3 is independent of potential, the fractional surface coverage of T a 5+ ads increases with potential and eventually saturates, hence the chemical dissolution rate follows this trend. As a result, the saturation of chemical dissolution occurs at the same potential where the surface coverage of T a 5+ ads saturates. On the other hand, electrochemical dissolution depends on both k 4 and fractional surface coverage of T a 2+ ads . The electrochemical dissolution follows a similar trend of variation in fractional surface coverage of T a 2+ ads with potential, i.e. it increases initially, and after reaching a peak value, decreases at higher potentials. But the maximum dissolution and maximum fractional surface coverage of T a 2+ ads occurs at different potentials. This is because of the fact that both k 4 and fractional surface coverage of T a 2+ ads vary with potential. The consolidated effect of variation of k 4 and fractional surface coverage of T a 2+ ads with potential on dissolution rates yield the results shown in Fig. 9a. A similar trend is predicted for Nb, as shown in Fig. 9b. A comparison of Figs. 9a and 9b show that, although Ta and Nb trends are qualitatively similar, the predicted dissolution rates are an order of magnitude higher for Nb.
The changes in chemical and electrochemical dissolution of Ta with addition of KF and H 2 SO 4 are shown in Fig. 10a. The addition of KF results in slight decrease in concentration of equilibrium concentration of HF and a substantial increase in concentration of HF − 2 . The decrease in equilibrium concentration of HF with the addition of KF decreases the rate constant k 3 as given by Eq. 18, hence the chemical dissolution decreases. On the other hand, the rate of electrochemical dissolution is associated with the concentration of both HF 2 − and equilibrium concentration of HF by exponential powers γ and δ respectively (Eq. 19). The decrease in equilibrium concentration of HF tends to decrease the electrochemical dissolution whereas the substantial increase in concentration of H F − 2 tends to increase the electrochemical dissolution. Even though γ is slightly less than δ (Table V), the substantial increase in concentration of HF − 2 overcomes the effect of decrease in equilibrium concentration of HF and results in an increase in the electrochemical dissolution. Addition of H 2 SO 4 slightly increases the equilibrium concentration of HF and decreases the concentration of HF − 2 . The increase in equilibrium concentration of HF causes the increase in chemical dissolution. Because δ is slightly higher than γ, the slight increase in equilibrium concentration of HF more than compensates the effect of HF − 2 and results in an increase in the electrochemical dissolution. The chemical and electrochemical dissolution rates of Nb in HF with and without additives are shown in the Fig. 10b. Both the chemical and electrochemical dissolution rates follow trends similar to that of Ta. However, Nb dissolution rates are one order higher than those of Ta. The significant decrease in concentration of HF − 2 with addition of H 2 SO 4 overcomes the effect of slight increase in equilibrium concentration of HF, hence decreases the electrochemical dissolution of Nb. The aggressive nature of HF, coupled with the almost instantaneous passivation of valve metals in most of the environments, limits the number of techniques that can be employed to characterize valve metal dissolution in acidic fluoride media. The present work illustrates the power of reaction mechanistic analysis of electrochemical data to characterize the kinetics of such complex systems.

Conclusions
Anodic dissolution of Ta and Nb in solutions with varying HF concentrations was studied using polarization and electrochemical impedance spectroscopy. Impedance data in the passive region for both the metals showed negative differential resistance at low frequencies and in some cases, pseudo-inductive loops at mid-frequencies. XPS analysis shows that Nb and Ta can exist in an oxidation state of 0 or 2 or 5 on the surface. A mechanism with two adsorbed intermediates and two dissolution steps adequately captures the salient features of the polarization and impedance spectra in the active and passive regions. The variation of fractional surface coverage values of the intermediate species and the dissolution rates by two different pathways, were estimated. It is proposed that the chemical dissolution of both the metals is influenced by the equilibrium concentration of HF and the electrochemical dissolution is influenced by both equilibrium concentration of HF and HF − 2 . The chemical and electrochemical dissolution rates are an order of magnitude higher for Nb compared to Ta, which explains the higher resistance offered by Ta to HF attack.