Mechanistic Analysis of Anodic Dissolution of Zr in Acidic Fluoride Media

Anodic dissolution of Zr in 10 mM HF was investigated using potentiodynamic polarization and electrochemical impedance spectroscopy. The surface state of the electrode was analyzed using X-ray photon spectroscopy, and the surface morphology was characterized using atomic force microscopy. EIS data acquired at multiple dc potentials were subjected to mechanistic analysis. Reaction mechanism analysis approach reveals that at least four intermediates are required to describe the observed results. The intermediatesarelikelytobeZrsub-oxides,oxyﬂuoridesandZrO 2 .Theproposedmechanismsuccessfullypredictsthemajorfeatures observed in polarization and impedance spectra. At low overpotentials, the fractional surface coverage of Zr 3 + species is higher than that of Zr 4 + species, and the electrochemical dissolution rate is higher than the chemical dissolution rate. As the overpotential increases, the surface is covered with Zr 4 + species and chemical dissolution rate becomes comparable to electrochemical dissolution rate. Although the surface is covered with Zr 4 + species at higher overpotentials, signiﬁcant chemical and electrochemical dissolution processes continue to occur and hence Zr is not protected in acidic ﬂuoride media under anodic conditions. EEC results are not presented. Earlier, by analyzing the polarization data in HF solutions, we proposed a four step mechanism with two adsorbed intermediates to describe Zr anodic dissolution.

Zirconium and alloys containing Zr are extensively used in the nuclear power industry as fuel cladding agents, in chemical industries as an alloying component, and in biomedical implants. [1][2][3][4] The wide acceptance of this metal and its alloys is due to their superior mechanical strength, and high resistance toward corrosion, and H 2 embrittlement. [5][6][7][8] These properties are due to the formation of a stable, protective passive film of ZrO 2 . [9][10][11] Although Zr exhibits excellent corrosion resistance in most of the harsh environments, it readily dissolves in acidic fluoride media. 6,7,12,13 Earlier scientific reports on Zr dissolution are mostly based on conventional techniques, such as weight loss measurements, 14 measurement of volume of H 2 gas evolved, 7 and steady-state polarization techniques. 15 Prono et al. 16 have analyzed the polarization of Zr in 0.12 M NaF + 7 M HNO 3 and proposed a seven-step mechanism comprising three competitive paths to describe the dissolution. This analysis was limited to the modeling of polarization data obtained at a single concentration. In our previous work, Zr anodic dissolution mechanism in the acidic fluoride medium was studied using the mechanistic analysis of current potential polarization data in various HF solutions. 17 A mechanism containing two adsorbed intermediates and two dissolution steps, shown in Eq. 1, was proposed. The model successfully predicted the major characteristics of the polarization curves, and the results predicted that the chemical and the electrochemical dissolution steps were affected by the concentration of HF − 2 and HF, respectively. Anodic dissolution of other valve metals such as Ti 18,19 and Nb 20 have been characterized using potentiodynamic polarization and electrochemical impedance spectroscopy (EIS). Compared to the polarization data, which is obtained at the dc limit, electrochemical impedance spectra (EIS) contain more information about the system, as they are acquired in a wide range of frequencies. [21][22][23] Mechanistic models based on multiple impedance spectra, along with potentiodynamic polarization curves, can provide valuable insights into the actual interfacial reactions. This is due * Electrochemical Society Member. z E-mail: srinivar@iitm.ac.in to the fact that even minor reactions can influence the EIS features significantly.
In this work, Zr anodic dissolution in HF solutions was investigated using potentiodynamic polarization and EIS. The Zr surface was also characterized using atomic force microscopy (AFM) and X-ray photoelectron spectroscopy (XPS). A detailed mechanistic description of the reaction is offered to explain the results. Analysis of our data illustrates the versatility of EIS as an in situ characterization tool and the utility of reaction mechanism analysis (RMA) to understand the interfacial reactions.

Experimental
Electrochemical experiments.-A rotating-disk Zr electrode (RDE) (5 mm diameter, 99% purity; Alfa Aesar) was used as a working electrode in a standard three-electrode cell, with Ag/AgCl (in 3.5 M KCl) as the reference and Pt wire as the counter electrode. Before each experiment, the working electrode was polished mechanically using successive grades of sand paper (400, 800, 1000, and 1200) and ultrasonicated in the ethanol medium. A PARSTAT 2263 (AME-TEK) potentiostat was used to acquire the electrochemical data and the electrode was rotated at 900 rpm (Pine Instruments MSR). The electrode rotation at 900 rpm was found to be sufficient to eliminate the mass transfer limitations. At lower rotational speeds, potentiodynamic polarization current values were found to be lower at most overpotentials. All experiments were conducted at room temperature (∼25 • C), and the solutions were prepared using high purity water (Millipore).
The experiments were conducted by immersing the Zr RDE in 10 mM HF solutions with 100 mM Na 2 SO 4 as the supporting electrolyte. All the measurements were performed after the open circuit potential (OCP) stabilized (∼15 min). In the test solution, the OCP of Zr electrode was −960 mV vs. Ag/AgCl. Potentiodynamic polarization data were obtained by sweeping the potential from −950 to +50 mV vs. Ag/AgCl at a scan rate of 2 mV/s. EIS data were obtained by adding an ac potential perturbation (10 mV rms) to the dc potential, in a frequency range of 100 kHz to 139 mHz. Seven frequency points per decade with logarithmic spacing were employed. EIS data were acquired at three dc potentials in the active region (0.075, 0.1, and 0.15 V vs. OCP) and at two dc potentials in the passive region (0.5 and 0.8 V vs. OCP). These dc potentials were chosen based on the analysis of the polarization curve. EIS data were validated using linear Kramer-Kronig transformation (KKT) software. 24 RMA was performed using a program written in Matlab. Surface characterization tools.-The morphology of the surface held in the active and passive regions was analyzed using AFM (Bruker). The surface state of the electrode held in the active dissolution region was also analyzed using XPS. A SPECS Surface Nano Analysis GmbH spectrometer was used to acquire XPS data and the X-ray source was Al Kα radiation at 1486.7 eV. Zr electrode was held at 0.2 V vs. OCP for 1 hour in 10 mM HF solution. The electrode was then rinsed with water and dried in N 2 stream, and the surface was analyzed using XPS. The binding energy values were corrected using the peak of the adventitious carbon, which is expected to be present at 284.8 eV. 25 The data were analyzed using XPS Peak 4.1 software (R.W.M. Kwok).

Results and Discussion
Potentiodynamic polarization.- Figure 1 shows the potentiodynamic polarization curve of Zr RDE immersed in 10 mM HF solution. An active region of dissolution was observed up to 0.2 V vs. OCP where the current increases rapidly with the overpotential. The current shows a decreasing trend between 0.2-0.5 V vs. OCP, and slight increase near 0.5 V vs. OCP. At potentials above 0.6 V vs. OCP, a slight decrease in the current values corresponding to the passive region of dissolution was observed. The region above 0.2 V vs. OCP can be considered as passive, although strictly speaking the surface is not well protected in this region. The current values are high and a significant dissolution continues to occur. For other valve metals such as Ti, 18,19,26 Nb, 27 and Ta, 28 a rapid decrease in current density is reported at potentials beyond the transition potential. Zr metal shows unusual behavior in the passive region compared to the other valve metals. 5,17,29 However, since the current decreases at least slightly with potential, this region is termed as passive. The data shows significant fluctuations in the current values in the passive region, which was found to be the case in all repeat runs. These fluctuations are likely due to continuous oxide formation and destruction. 17,29 The polarization data along with impedance spectra, were subjected to mechanistic modeling, as described in the later part of this paper.
Surface characterization.-The surface morphology of the Zr electrode dissolving in the 10 mM HF solution in the active and passive region was studied using AFM. The active region topography was obtained by keeping the electrode at 0.2 V vs. OCP for 1 hour. The result is shown in Fig. 2a. The surface exhibits a highly rough topography due to the active dissolution of the metal. AFM image in the passive region was obtained by holding the electrode at 0.8 V vs. OCP (Fig. 2b) and the surface shows a relatively less roughness compared to that held in the active region. This is probably due to the formation of an oxide or oxyfluoride layer on top of the metal in the passive region. The XPS spectra of Zr 3d, F 1 s and O 1 s are presented in Fig. 3. The experimental data are shown as filled circles, whereas the model results are presented as a continuous line. The de-convoluted peaks are shown as dashed lines. In Figs. 3a, three peaks at 177.93, 182.12, and 182.66 eV corresponding to Zr 3d 5/2 levels were resolved. These were attributed to Zr-metallic (3d 5/2 ), Zr 4+ (3d 5/2 ), and Zr 3+ (3d 5/2 ) respectively. Three peaks at 180.33, 184.52, and 185.06 eV corresponding to Zr-metallic (3d 3/2 ), Zr 4+ (3d 3/2 ), and Zr 3+ (3d 3/2 ) respectively, were also resolved. The energy difference of the doublet peaks of Zr 3d 5/2 and Zr 3d 3/2 was 2.4 eV, which matches well with the literature reports. 30,31 The charged species of Zr can be an oxide or oxyfluoride or fluoride. In earlier publications, the binding energy of Zr-oxide (Zr 2 O 3 -3d 5/2 ) was reported to be present at 182.6 eV, 32 and that of zirconium oxyfluoride (Zr 0.332 O 0.639 F 0.021 -3d 5/2 ) was reported at 182.5 eV. 33 These values are close to the binding energy values (182.66 eV) obtained for Zr 3+ (3d 5/2 ) in this study. Hence the observed peaks for Zr 3+ in these samples can arise from Zr sub-oxide and Zr-oxy fluoride. Literature indicates that the peaks corresponding to Zr 4+ (3d 5/2 ) in the oxide form (ZrO 2 ) would be present at about 182.0 eV, 17,30 and this is close to the value observed (182.12 eV) in this work. The other possible forms of Zr 4+ in this case are fluorides and oxyfluorides. ZrF 4 and ZrOF 2 are reported to show 3d 5/2 peaks at 185.4 34,35 and 186.8 eV, 32 respectively. Analysis of the XPS data reported here does not show any evidence for the presence of ZrF 4 or ZrOF 2 on the sample surface. Figures 3b and 3c show the F 1 s and O 1 s spectra of the sample surface respectively. The F 1 s spectra shows two peaks at 684.44 and 685.29 eV. The peak at 684.44 eV would correspond to zirconium oxy fluoride 33 and the peak at 685.29 eV can be attributed to the F 1 s of NaF. 36 Since Na 2 SO 4 was used as the supporting electrolyte, traces of NaF could be present on the surface. The O 1 s spectra show two peaks at 529.86 and 532.04 eV. The peak near 529.86 eV is attributed to metal oxides, 35,37,38 and that near 532.04 eV corresponds to the adsorbed oxygen. 31 The XPS data can be used to identify the species present on Electrochemical impedance spectroscopy.-Markers A, B, and C in Fig. 1 correspond to three dc potentials in the active region of dissolution, which are 0.075, 0.1, and 0.15 V vs. OCP, respectively. Markers D and E correspond to 0.5 and 0.8 V vs. OCP in the passive region of dissolution. EIS data were measured at these five dc potentials. Figure 4 shows the complex plane plots of the EIS data of Zr in 10 mM HF solution in both active and passive regions. The experimental EIS data were tested using linear KKT, 24 and the validation results are shown as lines in Fig. 4. Since the EIS data in the passive region show negative resistance, KKT transformation was performed in the admittance mode. It is seen that the spectra are KKT compliant, and the residual errors were found to be less than 2%. Figure 4a shows that the impedance spectra in the active region exhibit two capacitive loops in the high and mid frequency ranges and a pseudo-inductive loop in the low frequency range. The high frequency loop can be attributed to the double layer and the charge transfer resistance (which is the high frequency limit of the faradaic impedance). The mid and low frequency loops can be attributed to the response of the faradaic process, which are described in the following section, to potential perturbations at these frequencies, since the contribution of double layer current to the total current will be very small at these frequencies. Figure 4b shows that the EIS spectra in the passive region exhibit a pseudo-inductive loop in the mid frequency region and an apparent negative resistance and capacitance at low   Fig. 4b shows that, post inductive loop at slightly lower frequencies, a capacitive arc is exhibited, i.e. as frequency decreases, the data points in the complex plane plot move toward larger Z Re values, as indicated by the arrow in the inset of Fig. 4b. At even lower frequencies, a negative resistance is exhibited. This low frequency negative resistance is also seen in EIS spectra acquired in the passive region for other valve metals like Ti, Nb and Ta dissolution in HF. 18,20,27,28 Earlier, Cattarin et al. 27 studied the anodic dissolution of Nb in HF and the data acquired in the passive region exhibited a pseudo inductive loop at mid frequencies and a negative differential resistance at low frequencies. The spectra in the transpassive region exhibited a pseudo inductive loop at mid frequencies and a capacitive behavior at low frequencies. The impedance spectra in the transpassive dissolution region were modeled using an equivalent electrical circuit which accounts for the film present on the surface.

frequencies. A careful inspection of
In this work, Zr anodic dissolution in active and passive regions are analyzed and a single mechanism is proposed to explain the observed results.
Reaction mechanism analysis (RMA).-Visual inspection of the complex plane plots of the passive region in Fig. 4b shows two capacitive loops and a pseudo-inductive loop in the passive region in addition to the double layer capacitance at high frequencies. This suggests that at least three time constants are required to model the faradaic processes. Although it is possible to model the impedance spectra using equivalent electrical circuits (EEC), better insights of the anodic dissolution can be obtained using mechanistic analysis and hence EEC results are not presented. Earlier, by analyzing the polarization data in HF solutions, we proposed a four step mechanism with two adsorbed intermediates to describe Zr anodic dissolution. 17 Analyzing the potentiodynamic polarization data along with the EIS data acquired at multiple dc potentials is challenging, but offers more information about the system investigated.
Initially, the mechanism described in Eq. 1 was evaluated to model the experimentally observed features in the impedance spectra of anodic dissolution of Zr in HF based solutions. 40 In the active region, the model could predict two capacitive loops in the high and mid frequency regions, but the pseudo-inductive loop at low frequencies was not predicted by the model. 40 It is to be noted that if an impedance spectrum at one dc potential were modeled, then all the features, including the low frequency inductive loop can be predicted by the mechanism given in Eq. 1. However when all the spectra and the polarization data were modeled together, the mechanism shown in Eq. 1 could not predict all the major features. In the passive region, the model captures the high frequency capacitive loop, mid-frequency pseudo-inductive loop and low frequency negative resistance but failed to predict the positive capacitive arc observed in the intermediate frequencies.
Earlier, it was assumed that all Zr(III) species, whether they are oxides or oxyfluorides or fluorides, can be represented by a single species viz. Zr 3+ ads , and likewise, all Zr(IV) species can be represented by Zr 4+ ads regardless of the associated anions. It appears that a new mechanism, which distinguishes between sub-oxides and oxyfluorides with the same state of charge of the cation, is necessary to satisfactorily explain the EIS results. Therefore, a more detailed reaction mechanism (Fig. 5), which is a superset of the mechanism proposed in the earlier work, was evaluated. The impedance was calculated using the circuit given in Fig. 6, where the faradaic impedance (Z F ) is estimated using the mechanism given in Fig. 5.
In the mechanism described in Fig. 5, the number of intermediate species is four and the overall mechanism is similar to the one proposed in Eq. 1. It must be noted that multi-electron transfer, such as the first step in Fig. 5, is unlikely to occur in an elementary step. Thus, the first step can be regarded as an overall representation of three elementary steps, viz. Zr Zr 3+ ads +e − . Earlier publications have also employed such multi electron steps in mechanistic analysis. [41][42][43] The kinetics of the multi electron steps is given by an equation analogous to the Butler-Volmer equation. 44 The fractional surface coverage values of Figure 6. Equivalent circuit used to model the active and passive EIS spectra of Zr dissolving in 10 mM HF. Z F is calculated using the mechanism shown in Fig. 5.
In this mechanism, the rate constants k 5 and k 6 are independent of the potential as they do not involve any electron transfer. All other rate constants are assumed to vary with potential in an exponential manner as k i = k i0 e b i E , where k i0 is the pre-exponent, and E is the potential measured with respect to OCP. Here, denotes the total number of sites per unit area and 't' denotes the time. The methodology followed for the derivation of the current and impedance expressions is given in the literature in detail. [44][45][46] Langmuir adsorption isotherm model is employed. The mass balance equations corresponding to the adsorbed species are given in Eq. 2.
At steady-state conditions, Eq. 2 can be set to zero to calculate the corresponding fractional surface coverage values of the intermediates (appendix A). The expression for faradaic current is given by and the steady-state current is given by Here, F is the Faraday constant. The expressions of rate constant and surface coverage terms can be expanded using the Taylor series, and linearized by neglecting the higher order terms.
After linearization of Eqs. 2 and 3, the faradaic impedance can be written as 44,[47][48][49] where R −1 ct is ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 207.241.231.81 Downloaded on 2018-07-20 to IP Table I Fig. 4 were modeled using the circuit given in Fig. 6 The total impedance, Z T can be written as

. Solution resistance (R sol ) and double layer CPE parameters used in model fits. The data shown in
where Z CPE is the impedance of the constant phase element, given by The  Table I. The values of solution resistance are close to 10 -cm 2 at all dc potentials. The values of constant phase exponent vary between 0.89 and 0.96, which indicates that the surface is heterogeneous in nature. [50][51][52] This is also evident from the AFM images (Fig. 2). The best fit kinetic parameters, estimated using an optimization program written in Matlab, are shown in Table II.
The rate constant values at two dc potentials each in the active and passive regions are listed in Table III. In the passive region, the forward rate constants k 1-dc , k 2-dc , k 3-dc and k 4-dc are significantly larger than the respective reverse rate constants k -1-dc , k -2-dc , k -3-dc and k -4-dc , indicating that the reaction can be considered irreversible in the passive region. However, in the active region, the reverse reactions cannot be neglected. A comparison of the chemical dissolution steps by the two pathways show that k 6 is significantly larger than k 5 and that the chemical dissolution rate via Zr 4+ ads (2) intermediate species will be more than the corresponding dissolution rate via Zr 4+ ads (1) species. On the other hand, k 8-dc is almost two orders of magnitude less than k 7-dc and hence electrochemical dissolution Zr 3+ ads (2) intermediate species will be much less than the electrochemical dissolution via Zr 3+ ads(1) species.  -Table II. Optimized parameters used to simulate the model fit in Figs. 7 and 8 using the mechanism shown in Fig. 5.

Parameter
Value k 10 (mol cm −2 s −1 ) 1 . 8 6 × 10 −6 k 20 5.99 × 10 −7 k 30 1.56 × 10 −7 k 40 1.32 × 10 −9 k 50 2.08 × 10 −9 k 60 9.31 × 10 −9 k 70 2.75 × 10 −8 k 80 1.64 × 10 −11 k -10 8.81 × 10 −7 k -20 1.49 × 10 −8 k - 30 6.76 × 10 −7 k - 40 1.05 crease in the current in the active region and the continuous decrease in current in the passive region. 40 The present detailed model also captures the slight increase in current increase near 0.5 V vs. OCP in the passive region. The model predictions for the EIS data in both active  and passive regions are shown as complex plane plots in Figs. 8a-8e and the match is semi-quantitative. In the active region, the model predicts two capacitive loops in the high and mid-frequency regions and the pseudo-inductive loop in the low frequencies. In the passive region, apart from high frequency capacitive loop and the mid-frequency pseudo-inductive loop, the model captures the capacitive arc shown by the arrow in the inset of Fig. 4b, and the negative resistance at lower frequencies. It is worth noting that the earlier simpler model, with two adsorbed intermediates, could not capture the low frequency pseudo inductive loops in the active region or the capacitive arc in the passive region described above. 40 The analysis shows that, to successfully model the complete data set, species with the same charge but different chemical composition have to be treated as separate entities.
The changes in the surface coverage of various intermediate species with changes in the overpotential are calculated using Eqs. A1-A4. Figure 9 shows the variation in surface coverage of each adsorbed species with respect to the potential. The fractional surface coverage of the bare metal is very small as compared to the coverage of other entities and it decreases further with an increase in the overpotential. The fractional surface coverage of Zr 3+ ads (1) initially increases up to a potential of about 0.15 V vs. OCP and then it decreases with an increase in overpotential. There is a significant amount Zr 3+ ads (2) in the active region, and its fractional surface coverage continuously decreases with overpotential. Figure 9 also shows that the surface coverage of Zr 4+ ads (1) and Zr 4+ ads (2) increases slowly in the initial phase, but at higher overpotentials, it increases rapidly. These findings are comparable to the surface coverage plots obtained for 10 mM HF solution using the mechanism shown in Eq. 1, 17 which did not distinguish between the various forms of Zr oxides and oxy fluorides.
The intermediate species Zr 3+ ads (1) , Zr 3+ ads (2) , Zr 4+ ads (1) and Zr 4+ ads (2) are likely to be Zr oxyfluorides or fluorides. However, their identities could not be established unambiguously. It is to be noted that the electrode surface may change while the electrode is transferred from the cell to the ultra-high vacuum in the XPS chamber. XPS analysis could not be performed in situ, and hence the nature of the species, when Zr was immersed in HF solution, could not be determined unambiguously. If the solution HF concentration changes, the reaction rates, and consequently the fractional surface coverage values of the intermediates, are also expected to change. The variation in the electrochemical and chemical dissolution rates with respect to the overpotential is shown in Fig. 10. The rate of chemical dissolution increases continuously with overpotential and nearly saturates at 0.8 V vs. OCP, whereas the electrochemical dissolution shows an increase up to 0.18 V vs. OCP, and decreases slowly at higher potentials. The chemical dissolution pathway depends on the rate constants k 5 and k 6 and the surface coverage values of Zr 4+ ads (1) and Zr 4+ ads (2) . Since these rate constants are independent of potential, the chemical dissolution rate follows the increasing trend of the surface coverage of Zr 4+ ads(1) Figure 9. Variation of steady state surface coverage of the adsorbed species and the bare metal with respect to the overpotential, based on the proposed mechanism.
) unless CC License in place (see abstract  and Zr 4+ ads (2) . The electrochemical dissolution is a function of the rate constants k 7 , and k 8 as well as the surface coverage of Zr 3+ ads(1) and Zr 3+ ads (2) . The rate constant k 8 is three orders of magnitude smaller than k 7 and the total electrochemical dissolution rate is determined by the dissolution step involving k 7 and Zr 3+ ads (1) . This electrochemical dissolution rate increases with overpotential due to the increase in k 7 and Zr 3+ ads (1) , until about 0.18 V vs. OCP. Further increase in the overpotential reduces the electrochemical dissolution, since the decrease in Zr 3+ ads(1) surface coverage is more than the increase in rate constant k 7 . The initial increase and the further decrease in electrochemical dissolution rate is the combined effect of the change in these two variables with overpotential. In the passive region, both dissolution rates are significant and contribute toward Zr dissolution, which explains the poor passivation of the Zr metal in acidic fluoride media.

Conclusions
The detailed mechanism of Zr anodic dissolution in acidic fluoride media was identified using mechanistic analysis of potentiodynamic polarization and EIS data acquired at multiple dc potentials in both active and passive regions. XPS results provide evidence for the presence of Zr(III) and Zr(IV) species, as well as oxides, and oxyfluorides on the electrode surface. The proposed mechanism contains four adsorbed intermediates, which are likely to be oxides, sub-oxides and oxyfluorides of Zr. The changes in the fractional surface coverage of the intermediates with respect to potential was estimated. The model predicts that, at large overpotentials, although the surface is covered with Zr(IV) species, both chemical and electrochemical dissolution rates are significant, leading to insufficient passivation of Zr. k 1dc (1 + β) , ε = β × γ , and φ = β × δ The mass balance equations can be linearized and arranged as where A 1 = k 1dc + k −1dc + k 3dc + k 7dc + jω B 1 = k 1dc C 1 = k 1dc − k −3dc D 1 = k 1dc E 1 = (b 1 k 1dc (1 − θ 1ss − θ 2ss − θ 3ss − θ 4ss ) − b −1 k −1dc θ 1ss − b 3 k 3dc θ 1ss +b −3 k −3dc θ 3ss − b 7 k 7dc θ 1ss ) These equations can be solved simultaneously to determine the variation of fractional surface coverage values with potential.