Electrochemical behavior of zirconium in molten LiF–KF–ZrF₄ at 600 °C

Abstract

In this paper, a detailed study of the electrochemical behavior of zirconium in the molten LiF–KF–ZrF₄ system on an inert molybdenum electrode was carried out at 600 °C. Several electrochemical techniques were employed such as cyclic voltammetry, chronoamperometry and square wave voltammetry. The reduction of zirconium was found to be a multi-step process that at the potentials of 1.15, 1.50 and 1.62 V versus Pt, the corresponding cathodic reactions of Zr⁴⁺/Zr²⁺, Zr²⁺/Zr⁺ and Zr⁺/Zr occurred. The result was further confirmed by the theoretical calculation of the number of transferred electrons according to the cyclic voltammetry and square wave voltammetry analysis. Moreover, based on the cyclic voltammograms, the diffusion coefficient of Zr⁴⁺ ions in the eutectic LiF–KF containing 1 wt% ZrF₄ at 600 °C was estimated to be about 8.31 × 10⁻⁶ cm² s⁻¹. The present electrochemical study on zirconium in the molten fluoride system will be a theoretical reference for future zirconium electrorefining from Zr alloy or scraps.

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Introduction

Zirconium is an important component of nuclear reactors due to its extremely low neutron-absorption cross-section and excellent corrosion-resistance properties. The thermal or slow neutrons are not absorbed and wasted during nuclear reactions by using zirconium as the fuel cladding material, allowing the nuclear reactor to work at a high efficiency. For annual global zirconium metal production, about 85% is consumed by the nuclear power industry. As more nuclear power plants are being or planning to be constructed worldwide, the demand for high purity zirconium will rise in the future.¹

During the head-end processing, metal scraps including zirconium-based cladding hulls are generated following the disassembly and cutting steps of the fuel rods. The generated Zr alloy scraps contain approximately 98% of Zr with other alloying elements such as Sn, Fe, Cr and Nb.² It will be economically beneficial for nuclear power industry if high purity Zr can be effectively refined from the Zr alloy scraps and recycled to nuclear reactor construction. At present there are four main zirconium refining methods including iodide refining process, zone melting process, electron beam melting process as well as molten salt electrorefining process.³ Among them, the electrolysis method based on molten salt is an effective method for the preparation of high-melting point metals and their alloys, and has been developed as a promising process for refining high purity Zr from Zr alloy scraps.^2,4

In order to enhance the efficiency and reliability of the electrorefining process, precise information about reduction and oxidation potentials of Zr in the molten salt should be clearly known beforehand. The electrochemical behaviors of Zr in various molten salt baths have been investigated during electrodeposition or electrorefining process. Numerous studies have been devoted to all-chloride molten salt systems such as LiCl–KCl–ZrCl₄ ^2,5–9 and NaCl–ZrCl₄,¹⁰ and chloride–fluoride mixtures like KCl–NaCl–ZrF₄ and –K₂ZrF₆,^11,12 and LiCl–KCl–K₂ZrF₆ ¹³ at temperatures between 450 °C and 820 °C. The studies on all-chloride salt systems have reported a multi-step reduction process caused by the formation of metal complexes including two soluble states of Zr(IV) and Zr(II), and two insoluble states, Zr(I) and Zr. However, no consensus on the redox mechanism between these states has been found yet mainly because of different experimental conditions such as operation temperature, electrode material and ZrCl₄ content in the molten salt. In order to improve the salt system to be less hygroscopic and volatile, all-fluoride molten baths are recommended, however, very limited results have been reported in this field. In the articles^14,15 published in the early stage (in 1966 and 1985 respectively), the sensitive electrochemical techniques like CV and SWV were not used to adequately illustrate the Zr redox mechanisms in the molten fluoride melts. Gibilaro et al.¹⁶ published their work in a LiF–CaF₂–ZrF₄ system in 2013 and a one-step reduction process of Zr⁴⁺ was reported, where a different supporting electrolyte of LiF–CaF₂ eutectic was used, which could probably lead to different interactions with Zr ions in the melts. This might result in different Zr redox mechanisms from the findings in our present study. Park et al.⁴ reported their work on Zr electrorefining from Zr alloy scraps in a LiF–KF–ZrF₄ system. In their study the reaction mechanism was based on only one simple CV curve to determine the Zr redox potentials, and no more transient electrochemical techniques were further conducted to reveal and understand the Zr electrochemical behavior such as CV with varied scan rates and potential ranges, and SWV. The present systematic investigations are highly motivated by the very limited Zr electrochemical results reported in this field, and in authors' view, even more effort is required to provide better process understanding serving new technology development.

This paper presents a comprehensive electrochemical study on zirconium ions behavior in a LiF–KF eutectic melt on a molybdenum electrode at a constant temperature of 600 °C with several electrochemical techniques. A series of CV measurements were conducted with diverse scan ranges at a constant scan rate to identify typical zirconium redox peaks and at various scan rates within a constant scan range to investigate the electrochemical behaviors of the identified redox peaks. Moreover, cyclic voltammetry, chronoamperometry and square wave voltammetry were employed to determine the reversibility of the redox reactions, rate-controlling step as well as diffusion coefficient of zirconium ions. This study aims to provide a profound understanding of zirconium redox mechanisms in molten fluoride system in particular in a LiF–KF eutectic melt for the optimization of Zr electrorefining process from Zr alloy and scraps.

Experimental

The experimental apparatus used in the present work is represented in Fig. 1. The three-electrode electrochemical cell was assembled in a high purity nickel crucible, which was placed in the constant temperature zone of a cylindrical vessel made of corundum with the support of a corundum tube. The vessel was heated with an electric furnace and the two ends were cooled with circular water. For all the experiments, the operation temperature was measured by a K-type thermocouple with an accuracy of ±1 °C and kept constant at 600 °C with a proportional-integral-derivative (PID) thermal controller. Argon gas of 99.999% purity was continuously applied from the bottom of the furnace with the flow rate of 1 L h⁻¹ to maintain the atmosphere to be inert, which was dehydrated with P₂O₅ and silica gel, and deoxygenated with hot titanium sponge at 850 °C beforehand.

Fig. 1 Schematic diagram of the experimental set-up.

For all the electrochemical measurements, the potentials were referred to a platinum wire (0.5 mm diameter, 99.99% purity) immersed in the molten electrolyte, playing a role of a quasi-reference electrode¹⁷ Pt/PtO_x/O²⁻. An inert molybdenum rod (2 mm diameter, 99.95% purity) was served as the working electrode (WE) and a vitreous carbon rod (3 mm diameter) was used as the counter electrode (CE). The three electrodes were polished by SiC paper to remove impurities on the surface and subsequently washed by distilled water and ethanol with ultrasound, and then dried at 300 °C for 48 h under argon atmosphere.

All the chemicals used in this study were stored in a glove box under an inert argon atmosphere with both O₂ and H₂O levels below 1 ppm before using. The LiF (99.5% purity)–KF (99.9% purity) eutectic with a molar ratio of 51 : 49 was used as the electrolyte. The salt mixture was initially dried at 300 °C for 48 h to remove residual moisture and then melted at the operation temperature in the set-up shown in Fig. 1. Zirconium ions to be investigated were introduced into the melt in the form of ZrF₄ powders (99.99% purity) and the three electrodes were then inserted into the melt with an immersion area of 0.6594 cm² for the working electrode. The reference electrode was positioned near to the working electrode but not to disturb the current distribution between the working and counter electrodes. The electrochemical measurements were carried out 2 h later after inserting the electrodes into the melt for the equilibrium between the molten salt and electrodes. The sublimation of ZrF₄ can be neglected because once it is dissolved into the LiF–KF system, the formed complex compounds such as K₂ZrF₆, K₃ZrF₇, Li₂ZrF₆ and LiKZrF₆ can be much less volatile.⁴ The electrodes and molten salt system were replaced by new ones after each test to eliminate any disturbances from the previous experiment.

All the electrochemical measurements were carried out with a Parstat 4000 potentiostat from Princeton Applied Research, and the data acquisition was performed with the VersaStudio 6.0 software. The transient electrochemical techniques such as cyclic voltammetry, chronoamperometry and square wave voltammetry were used to investigate the redox mechanisms of Zr in the molten melt.

Results and discussion

Cyclic voltammetries in LiF–KF and LiF–KF–ZrF₄ systems

Before main experiments, CV measurement in the blank LiF–KF eutectic was carried out at 600 °C and 100 mV s⁻¹ to obtain background data as shown in Fig. 2 inset (a). The cathodic peak R₀ at about −1.9 V vs. Pt and its corresponding anodic peak O₀ were clearly observed which are due to the deposition and dissolution of metal K respectively.¹⁸ This observation is different from the case in chloride systems that the reduction of Li⁺ is found to be prior to that of K⁺. It can be also seen that the residual current is less than 10 mA, and no redox peaks were found within the potential range between −0.3 and −1.8 V vs. Pt, indicating that the effects of background disturbances from the blank LiF–KF eutectic are negligible for CVs in the LiF–KF–ZrF₄ system.

Fig. 2 Cyclic voltammogram of the LiF–KF–1.0 wt% ZrF₄ system at 600 °C with the scan rate of 100 mV s⁻¹. Inset (a) CV of the blank LiF–KF eutectic melt, (b) the high-resolution CV curve of cathodic peak R₁. Working electrode: Mo (S = 0.6594 cm²), counter electrode: vitreous carbon, reference electrode: Pt.

CV measurement on molybdenum electrode in the molten LiF–KF with the addition of 1 wt% ZrF₄ was conducted at 600 °C with a scan rate of 100 mV s⁻¹ as represented in Fig. 2. In this curve, three cathodic peaks R₁, R₂ and R₃ are observed at about −1.15, −1.50 and −1.62 V vs. Pt respectively, which are attributed to the multi-step reduction of Zr(IV) in molten LiF–KF, and four corresponding anodic peaks of O₁, O₂, O₃ and O₄ are found at around −1.45, −1.35, −1.05 and −0.68 V vs. Pt respectively. Among them, all the redox peaks are relatively sharp and easy to be identified except peak R₁, which is difficult to determine the peak potential unless looking at it closely at high resolution, as can be seen in Fig. 2 inset (b). The identification of each peak will be discussed in detail in the following paragraphs of this paper.

Effect of scan range on peak behaviors

As mentioned in the Introduction, it was concluded that the reduction/oxidation of Zr in all-fluoride salt systems is a one-step process by the previous works.^4,16 However, in the present study the redox behavior of Zr in a molten LiF–KF–ZrF₄ met has been found to follow a multi-step mechanism, which is highly similar to the observations in all-chloride salt systems.^2,5–10 In order to further identify the redox reaction for each peak, CV measurements were conducted at various potential ranges at a fixed scan rate of 100 mV s⁻¹, as represented in Fig. 3. In addition to CV analysis, previous electrolysis results are combined to estimate the Zr redox reactions.^2,5,7 The comparison with the others works is represented in Table 1.

Fig. 3 Cyclic voltammograms of the LiF–KF–1.0 wt% ZrF₄ system at 600 °C with the scan rate of 100 mV s⁻¹ at varied scan ranges. Working electrode: Mo (S = 0.6594 cm²), counter electrode: vitreous carbon, reference electrode: Pt.

Table 1 Comparison of reaction identifications for redox peaks in CV measurements in this work with literature

Data source	This study	Park et al.^5	Lee et al.^2	Sakamura et al.^7
Molten salt	LiF–KF–(1 wt%)ZrF4	LiCl–KCl–(1 wt%)ZrCl4	LiCl–KCl–(4 wt%)ZrCl4	LiCl–KCl–(0.001 mol%)ZrCl4
Temperature (°C)	600	500	500	500
R1	Zr^4+ + 2e → Zr^2+	Zr^4+ + 2e → Zr^2+	Zr^4+ + 2e → Zr^2+	Zr^4+ + 2e → Zr^2+
R2	Zr^2+ + e → Zr^+ (main reaction)	Zr^4+ + 3e → Zr^+ (main reaction)	Zr^2+ + 2e → Zr	Zr^4+ + 4e → Zr
			Zr^4+ + 3e → Zr^+	Zr^4+ + 3e → Zr^+
	Zr^4+ + 3e → Zr^+	Zr^2+ + e → Zr^+
R3	Zr^+ + e → Zr (main reaction)	Zr^+ + e → Zr (main reaction)	Zr^+ + e → Zr	Zr^+ + e → Zr
			Zr^4+ + 4e → Zr
	Zr^2+ + 2e → Zr	Zr^2+ + 2e → Zr
	Zr^4+ + 4e → Zr	Zr^4+ + 4e → Zr
O1	Zr → Zr^+ + e (main reaction)	Zr^+ → Zr^4+ + 3e (main reaction)	Zr^+ → Zr^4+ + 3e	Zr^+ → Zr^4+ + 3e
			Zr → Zr^2+ + 2e
	Zr → Zr^2+ + 2e	Zr^+ → Zr^2+ + e
O2	Zr^+ → Zr^2+ + e	Zr → Zr^4+ + 4e (main reaction)	Zr → Zr^4+ + 4e	Zr → Zr^4+ + 4e
		Zr → Zr^2+ + 2e
O3	Zr^2+ → Zr^4+ + 2e	Zr^2+ → Zr^4+ + 2e	Zr^2+ → Zr^4+ + 2e	Not observed
O4	Zr^+ → Zr^4+ + 3e	Zr^2+ → Zr^4+ + 2e	Not observed	Not observed
		Zr^+ → Zr^4+ + 3e

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For the potential range from −0.5 to −1.4 V vs. Pt, the reduction peak R₁ is unnoticeable. Its existence can be projected by the slope change of the cyclic voltammograms. When the potential sweeping back to positive direction, an oxidation peak O₃ at −1.05 V vs. Pt is evident which should be corresponded to the reduction process R₁. The reduction peak R₁ and oxidation peak O₃ are relatively well known as the soluble–soluble redox reactions between the Zr ions at the oxidation state of +2 and +4 derived as the following partial reactions as shown in eqn (1) and (2).^2,5,7

Peak R₁:

Zr⁴⁺ + 2e → Zr²⁺ (1)

Peak O₃:

Zr²⁺ → Zr⁴⁺ + 2e (2)

As the peak currents of the two redox peaks are very small, it is expected that the redox reactions between Zr⁴⁺ and Zr²⁺ proceed very slowly. The low reaction rate can be attributed to the small exchange current density in Butler–Volmer kinetics.⁵

When the scan range is over −1.5 V vs. Pt, the reduction peak R₂ and oxidation peaks O₂ and O₄ begin to appear. The cathodic process associated with R₂ is believed to be involved with the formation of zirconium products with lower valencies than +2. Lee et al.² estimated that the peak R₂ is associated with the reduction of Zr²⁺ into Zr, and Sakamura et al.⁷ identified peak R₂ as the deposition of metallic Zr from Zr⁴⁺. In this study, it has been proved that there is no Zr deposited on the working electrode at the peak potential of R₂ by chronoamperometry analysis, which will be discussed in detail in the following section. Therefore, the reduction reactions for peak R₂ should be the formation of Zr⁺ from Zr²⁺ and Zr⁴⁺, as described in eqn (3) and (4). This view has been confirmed by Park et al.⁵ The anodic peaks O₂ and O₄ should be corresponded to the reduction reactions at peak R₂, which are attributed to the oxidation reactions of Zr⁺ into Zr²⁺ and Zr⁴⁺ respectively, as shown in eqn (5) and (6).

Peak R₂:

Zr²⁺ + e → Zr⁺ (main reaction) (3)

Zr⁴⁺ + 3e → Zr⁺ (4)

Peak O₂:

Zr⁺ → Zr²⁺ + e (5)

Peak O₄:

Zr⁺ → Zr⁴⁺ + 3e (6)

Extending the potential range to −1.6 V vs. Pt, the reduction peak R₃ and its corresponding oxidation peak O₁ start to be identified, and the both peaks become more and more identified as the expansion of scan range to −1.8 V vs. Pt. Moreover, peak O₂ becomes less conspicuous as enlarging the scan range mainly due to the increasing residual current of peak O₁. The reduction peak R₃ should be attributed to the formation of metallic Zr on the Mo working electrode. Sakamura et al.⁷ suggested that the Zr deposit comes only from the reduction of Zr⁺, and Lee et al.² reported two reduction reactions of Zr⁴⁺/Zr and Zr⁺/Zr at peak R₃. However, in the author's view, all the Zr ions existed in the molten melt, Zr⁺, Zr²⁺ and Zr⁴⁺, contribute to the Zr formation during the cathodic process at R₃, as represented in eqn (7)–(9). This view is also supported by the Park's work.⁵ The anodic peak O₁ corresponded to peak R₃ should be associated with the oxidation process of metallic Zr, probably generating Zr ions at low valence states, Zr⁺ and Zr²⁺, as illustrated in eqn (10) and (11).

Peak R₃:

Zr⁺ + e → Zr (main reaction) (7)

Zr²⁺ + 2e → Zr (8)

Zr⁴⁺ + 4e → Zr (9)

Peak O₁:

Zr → Zr⁺ + e (main reaction) (10)

Zr → Zr²⁺ + 2e (11)

Chronoamperometry

Typical chronoamperograms for Zr deposition on the Mo working electrode was investigated at constant potentials of −1.15, −1.50 and −1.62 V vs. Pt respectively, where the cathodic peaks appeared on the cyclic voltammograms, as shown in Fig. 4. It can be seen that the initial portions of the chronoamperograms increased rapidly which is probably due to the double-layer charging.² The current transients at the reduction potentials of −1.15 and −1.50 V vs. Pt showed almost no current change over time which is attributed to the soluble–soluble reactions during the cathodic processes at R₁ and R₂, associating with no area expansion of the working electrode. This observation demonstrates that the reduction processes of R₁ and R₂ involve no metallic Zr deposition on the electrode. On the other hand, the electrochemical reduction at −1.62 V vs. Pt exhibited a gradual increase in the current over time, which implies an increase in surface area of the electrode, ascribing to the continuous formation of Zr deposits. The chronoamperograms confirms well the assumptions in the previous section that the deposition of metallic Zr happens only during the reduction process of R₃.

Fig. 4 Current transients for Zr deposition in the LiF–KF–1.0 wt% ZrF₄ system at the reduction potentials of −1.15, −1.50 and −1.62 V vs. Pt at 600 °C. Working electrode: Mo (S = 0.6594 cm²); counter electrode: vitreous carbon; reference electrode: Pt.

Effect of scan rate on peak behaviors

Fig. 5 shows the CVs in the LiF–KF–1.0 wt% ZrF₄ system at 600 °C in a constant potential range between −0.5 and −1.8 V vs. Pt while changing the scan rate from 100 to 1500 mV s⁻¹ with the step size of 200 mV s⁻¹. Within this scan range, the four anodic peaks O₁, O₂, O₃ and O₄, and the cathodic peaks R₂ and R₃ are well identified whereas peak R₁ is much less prominent, and the heights of all the redox peaks generally raised with the increase of scan rate. Peak O₁ is the dominant anodic peak with the varied scan rates and it moved 13 mV toward a positive direction as the scan rate increased from 100 to 1500 mV s⁻¹. The potentials of peaks O₂ and O₃ shifted about 11 and 17 mV respectively also to the positive side while the scan rate changing from 100 to 1500 mV s⁻¹. Peak O₂ tended to be less conspicuous with increasing the scan rate mainly due to the height of peak O₁ intensified. Similarly, the change of O₄ was also very small, as to be around 12 mV during the increase in scan rate. For the reduction process, the cathodic peaks R₂ and R₃ shifted to negative values and their potential changes were approximately 68 and 96 mV respectively when the scan rate raised from 100 to 1500 mV s⁻¹.

Fig. 5 Cyclic voltammograms of the LiF–KF–1.0 wt% ZrF₄ system at 600 °C with the scan range from −0.5 to −1.8 V vs. Pt at varied scan rate from 100 to 1500 mV s⁻¹. Working electrode: Mo (S = 0.6594 cm²); counter electrode: vitreous carbon; reference electrode: Pt.

The relationship between peak potential and scan rate was plotted based on the results obtained from Fig. 5 to check the reversibility of the redox reaction at each peak, as seen in Fig. 6. Peak R₁ was not analyzed due to the ambiguous peak shape. It is clear that the oxidation peaks O₁, O₂, O₃ and O₄ showed very small potential changes as generally to be below 20 mV, indicating the reversibility of these processes. The cathodic reactions R₂ and R₃ are also determined to be close to reversible (quasi-reversible) processes although they showed more significant peak potential changes than the oxidation reactions during the scan rate increase from 100 to 1500 mV s⁻¹. Moreover, the peak currents of oxidation peaks O₁, O₂, O₃ and O₄ and reduction peaks R₂ and R₃ are plotted versus the square root of scan rates in Fig. 7. A linear relationship is clearly observed indicating that all these redox processes associated with zirconium ions involve diffusion-controlled mass transfer.

Fig. 6 Dependence of peak potential on natural logarithm of scan rate from cyclic voltammograms.

Fig. 7 Dependence of peak current on square root of scan rate from cyclic voltammograms.

For a reversible process, the number of transferred electrons during the reduction reactions can be evaluated by the following equation.¹⁹

where E_p is the peak potential, E_p/2 is the half-peak potential, R is a molar gas constant (8.314 J mol⁻¹ K⁻¹), T is the temperature (873 K), n is the number of electrons, and F is a Faraday constant (96 485 C mol⁻¹).

The number of transferred electrons associated with the cathodic peaks R₂ and R₃ were calculated according to eqn (12) at various scan rates and the results are shown in Table 2. The slightly downward trend of the calculated electron transfer values for both R₂ and R₃ indicates the quasi-reversible nature of the reduction reactions.²⁰ The average value of n for the cathodic process at R₂ is given as 1.39, which is consistent with the previous assumption described in eqn (3) and (4) suggesting that it might involve two reduction processes of Zr²⁺/Zr⁺ (major) and Zr⁴⁺/Zr⁺. For the reduction reactions at R₃, the calculated result shows a mean value of 1.24 for n, further confirming that the cathodic process is combined by the reduction reactions of Zr⁺/Zr (major), Zr²⁺/Zr and Zr⁴⁺/Zr, as previously illustrated in eqn (7)–(9).

Table 2 Theoretical calculations of number of transferred electrons at various scan rates

Peak	Scan rate/mV s^−1								Average n
	100	300	500	700	900	1100	1300	1500
R2	1.74	1.62	1.47	1.39	1.29	1.27	1.24	1.17	1.39
R3	1.64	1.51	1.36	1.31	1.09	1.07	1.02	0.96	1.24

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For a diffusion-controlled reversible electrochemical reaction system, the cathodic peak current is given by the Randles–Shevchik equation as follows.²⁰

i_p = 0.4463(nF)^3/2(RT)^−1/2AD^1/2Cν^1/2 (13)

where A is the surface area of the working electrode (0.6594 cm²), n is the number of transferred electrons, D is the diffusion coefficient (cm² s⁻¹), C is the bulk molar concentration of Zr ions (1.28 × 10⁻⁴ mol cm⁻³), and ν is the scan rate (V s⁻¹).

The theoretically calculated diffusion coefficients for the reduction processes of Zr ions at R₂ and R₃ at the temperature of 600 °C are shown in Fig. 8. As it is difficult to determine the exact number of transferred electrons involving the cathodic processes at R₂ and R₃ due to the combination of various reduction reactions, the diffusion coefficients were calculated with the number of electrons varying from 1 to 4. A deviation is given in this figure which is depending on the varied scan rates.

Fig. 8 Plots of calculated diffusion coefficient versus varied number of transferred electrons.

The diffusion coefficient of Zr⁴⁺ in molten LiF–KF–ZrF₄ at 600 °C was estimated to be within the range of 1.32 × 10⁻⁶ to 1.53 × 10⁻⁵ cm² s⁻¹ and the average value appears to be 8.31 × 10⁻⁶ cm² s⁻¹. The diffusion coefficient obtained in this study was compared with some previous results as seen in Table 3. Since the data for fluoride salt systems can be hardly found from open literature, our result was compared to that in chloride salt systems.

Table 3 Comparison of diffusion coefficient of Zr⁴⁺ obtained in this work with literature

Data source	Molten salt	Temperature (°C)	Average D (cm^2 s^−1)
This study	LiF–KF–ZrF4	600	8.31 × 10^−6
Chen et al.^13	LiCl–KCl–K2ZrF6	500	3.06 × 10^−6
Lee et al.^2	LiCl–KCl–ZrCl4	500	7.77 × 10^−6
Park et al.^5	LiCl–KCl–ZrCl4	500	1.63 × 10^−5
Fabian et al.^21	LiCl–KCl–ZrCl4	500	1.50 × 10^−5
Yamada et al.^22	LiCl–KCl–ZrCl4	500	1.13 × 10^−5

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Based on the empirical formulations by Chen et al.,¹³ the diffusion coefficient of Zr⁴⁺ in a LiCl–KCl–K₂ZrF₆ system at 500 °C was determined to be about 3.06 × 10⁻⁶ cm² s⁻¹. Lee et al.² estimated the diffusion coefficient of Zr ion at the oxidation state of +4 in a molten LiCl–KCl–ZrCl₄ melt at 500 °C as to be 7.77 × 10⁻⁶ from cyclic voltammograms. Their results agree well with the diffusion coefficient obtained in this study. Moreover, in the molten LiCl–KCl–ZrCl₄ bath at 500 °C, Park et al.⁵ and Fabian et al.²¹ obtained Zr⁴⁺ diffusion coefficients of 1.63 × 10⁻⁵ cm² s⁻¹ and 1.50 × 10⁻⁵ cm² s⁻¹ respectively based on cyclic voltammetry analysis, and the result reported by Yamada et al.²² was 1.13 × 10⁻⁵ determined via a capillary method. The diffusion coefficient determined in the present work is slightly smaller mainly due to the fact that in their works the operation temperature of 500 °C is about 150 °C over the melting point of the salt mixture whereas the present work has a lower temperature difference of approximately 100 °C, which could probably lead to the relative high viscosity and poor mobility of the molten salt mixture, further resulting in difficult diffusions of the Zr ions in the melt. Moreover, the diffusion coefficient obtained by Lee et al.² is about two times smaller than that reported by the literature,^5,21,22 although they used the same electrolyte and operation temperature. Some other experimental conditions such as zirconium ion concentration, and electrode material may also influence the diffusion coefficient evaluation.

Square wave voltammetry

As reported in the previous works,^23,24 square wave voltammetry is a more sensitive transient method than cyclic voltammetry. Since the reduction peak R₁ was not clearly distinguished in the CV measurements discussed above, square wave voltammetry (SWV) was conducted to further investigate the reduction progress of Zr⁴⁺ particularly to get a better understanding on the cathodic process at peak R₁. Fig. 9 exhibits the SWVs obtained in the LiF–KF eutectic containing ZrF₄ (1 wt%) with the signal frequencies of 20, 30 and 40 Hz respectively at 600 °C, scanning from −0.8 to −1.8 V vs. Pt. The three cathodic peaks of R₂, R₃ and in particular R₁ are clearly seen in the SWVs. The observation of multiple cathodic peaks further confirms the multi-step reduction mechanism of zirconium. The identified reduction peaks are consistent with those collected from the previous CV measurements. Moreover, the relationship between the peak currents and the square root of frequency is plotted in Fig. 10. A good linear relationship was obtained further confirming that the multi-step reduction of zirconium is close to a reversible process.

Fig. 9 SWVs of the LiF–KF–1.0 wt% ZrF₄ system at 600 °C with the scan range from −0.8 to −1.8 V vs. Pt at varied frequencies from 20 to 40 Hz with a step potential of 1 mV. Inset: High-resolution SWV curve of cathodic peak R₁ at the frequency of 40 Hz. Working electrode: Mo (S = 0.6594 cm²); counter electrode: vitreous carbon; reference electrode: Pt.

Fig. 10 Dependence of peak current on square root of frequency from SWVs.

For a Gaussian shaped peak in square wave voltammetry, a mathematical analysis of the peak yields an equation which can associate the half-width of the peak (W_1/2) and the number of transferred electrons (n),²⁵ as represented in eqn (14).

It can be seen from Fig. 9 that the peak shape is not symmetrical in nature. Similar observations were reported in the studies of U³⁺ and Nd³⁺,^26,27 which had been ascribed to the nucleation effects. In the current reaction system, it is likely to be attributed to the close positions of the multiple reduction peaks that the peak shapes could be affected by each other. All the reduction peaks should be fitted to keep Gaussian shape to determine the width of the half peak. For instance, in the fitted curve of Fig. 9, the dotted curve indicates the fitted one of peak R₁. With eqn (14), the number of exchanged electrons during the cathodic reactions at R₁, R₂ and R₃ were estimated at the frequencies of 20, 30 and 40 Hz respectively, and the results are listed in Table 4. The calculated number of exchanged electrons for R₁ shows a mean value of 1.83, suggesting a two electron-transfer reduction of Zr⁴⁺/Zr²⁺ which agrees well with the prediction illustrated in eqn (1). Moreover, the n calculations for R₂ and R₃ are also in fair agreement with the estimations from cyclic voltammograms discussed above.

Table 4 Theoretical calculations of number of transferred electrons at various frequencies

Frequency (Hz)	W1/2(R1) (V)	W1/2(R2) (V)	W1/2(R3) (V)	nR1	nR2	nR3
20	0.135	0.201	0.215	1.96	1.32	1.23
30	0.142	0.213	0.239	1.87	1.24	1.11
40	0.160	0.236	0.245	1.66	1.12	1.08
Average	—	—	—	1.83	1.23	1.11

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Conclusions

The electrochemical behavior of zirconium was investigated in molten eutectic LiF–KF containing 1 wt% ZrF₄ at 600 °C on an inert molybdenum electrode with several electrochemical techniques such as cyclic voltammetry, chronoamperometry and square wave voltammetry. The reduction of zirconium was found to be a diffusion-controlled process which follows a multi-step reduction mechanism of Zr⁴⁺/Zr²⁺, Zr²⁺/Zr⁺ and Zr⁺/Zr at 1.15, 1.50 and 1.62 V versus Pt respectively. This was further confirmed by the theoretical calculation of number of exchanged electrons with both cyclic voltammetry and square wave voltammetry results. The diffusion coefficient of Zr⁴⁺ at 600 °C in the eutectic LiF–KF melt was evaluated with Randles–Shevchik equation as to be approximately 8.31 × 10⁻⁶ cm² s⁻¹ according to the cyclic voltammetry analysis. The electrochemical investigations on zirconium in the present study will supply a theoretical support for the zirconium electrorefining from Zr alloys and scraps in molten fluoride salts in the future.

Acknowledgements

The authors acknowledge the financial support of the National Natural Science Foundation of China (NSFC) Grant No. 51274005 and 51174055. The first author's stay at Delft University of Technology (TU Delft) for the present research in the Netherlands is financially supported by the Chinese Scholarship Council (CSC). The authors thank Prof. Jilt Sietsma and Dr Zhi Sun from TU Delft, Dr Huijun Liu at Chinese Academy of Sciences (CAS) and Dr Yanqing Cai at Northeastern University (NEU) for their constructive discussions during this work.

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