Method Development for Quantitative Analysis of Actinides in Molten Salts

This paper describes how electrochemical techniques have been used to develop a method for high-precision, real-time quantitative measurements of the concentration of actinides, present in in molten salts as actinide chlorides, for pyrochemical process monitoring applications. Possible reasons for discrepancies between reported measurements obtained with electrochemical techniques have been investigated and a combination of methods to improve their precision has been established. The combination of methods consists of selecting a suitable electroanalytical measurement technique, experimentally verifying assumptions used in its theoretical analysis, ensuring reproducible conditions at the electrode/electrolyte interface, and using an improved method to eliminate the need to know the electrode surface area. By following the developed procedures and reﬁning both experimental techniques and data analysis methods, precise and reproducible measurements were obtained for U and Pu in LiCl/KCl eutectic at 773 K. Preliminary results showed that cyclic voltammetry, along with a method of standard area addition, are very promising tools for in situ quantitative measurements with a degree of precision comparable to destructive analysis techniques. work

Electrorefining is the main step in pyrochemical reprocessing. During this process, actinides are separated from the bulk of the fission product elements by electrochemical dissolution and electrotransport onto a solid or liquid cathode. The goal of the process is to maximize the separation and recovery of actinides from chlorinated fission products so that minimal amounts of actinides are lost to the process waste stream. [1][2][3][4][5] In addition to efficient actinide recovery, there is a need to address the safeguarding the recycle system. 5 Highprecision, real-time concentration measurements of actinides, present as actinide chlorides, in molten salts are required for process monitoring and control and could be used to support traditional material control and accountability techniques. Development of these measurements is essential to implement and operate a commercial fuel reprocessing facility. [6][7][8][9][10] Electrochemical techniques are well suited for in situ monitoring because they allow rapid, real-time measurements, are compatible with remote handling operations, and do not require the use of standards. Also, the equipment is not affected by the high radiation field present in a fuel processing operation. 9,10 Unlike offline destructive analysis techniques, in situ methods do not require representative sample collection and preparation, and therefore avoid problems with sample contamination and degradation. In addition, analytical results can be received in a relatively short period (for example, less than 2 minutes).
In an electrochemical cell, the measured potential (E), current (i), or charge (Q) is related to the quantity of the analyte in the solution; therefore, it can serve as an analytical signal for concentration measurements. 11,12 Depending on the applied potential or current waveform and the observed variables, many different methods are available for use, namely cyclic voltammetry (CV), chronoamperometry (CA), chronopotentiometry (CP), square-wave voltammetry (SWV), normal-pulse voltammetry (NPV), and others. Often one set of electrodes and electronics can be used for multiple measurement techniques. The challenge is to identify and demonstrate an electrochemical technique that can be used in molten chloride salts containing several actinides (e.g. U, Pu) for high-precision and accurate concentration determination of the dissolved actinides. A number of things have to be considered when choosing an analytical method for quantitative analysis: accuracy and precision, sensitivity and selectiv-ity, a solid theoretical basis of the method, and the simplicity of data acquisition.
Iizuka et al. 6 investigated the application of SWV and NPV to online monitoring of actinide concentrations in molten chlorides for use in pyrochemical processes. They examined the relationship between peak currents and the concentration of actinides (U, Pu) in the solution but no relation describing the current in terms of concentration was reported or verified, thus making any quantitative calculations impossible based on the data in the paper. SWV was found to be very sensitive and allowed easy separation among the current peaks; however, the concentration dependence of the peak current was found to be nonlinear at concentrations greater than 0.5 wt%. It was concluded that SWV could be used for very low-concentration measurements, but it is not suitable where concentrations are higher than 0.5 wt%, as is typically the case for the normal operation of an electrorefiner. NPV was found to be more promising, because it showed a linear response of the peak current up to a concentration of 1.7 wt% Pu; however, no quantitative results were reported. Iizuka et al. 6 concluded that, compared with SWV, NPV was more promising for process monitoring, although optimization of the method is still required in order for it to be used at higher concentrations.
Paek et al. 7 also investigated SWV as a potential tool for quantitative concentration measurements of actinides in molten salts by studying systems composed of Gd and La in LiCl-KCl eutectic salt. Similar to the approach used by Iizuka and his coworkers, 6 they examined the relationship between peak currents and concentration of electroactive species but no quantitative calculations or numerical results were reported. A large deviation from linearity of peak current with concentration was observed at concentrations higher than 1 wt%. Therefore, Paek et al. concluded that SWV is not a suitable technique for quantitative measurements when the concentration of electroactive species in the salt is higher than 1 wt%. A possible reason for the deviation was the increased surface area of the working electrode, which is more significant at higher concentrations. However, no information about the method used for area determination was given, and since the peak currents, rather than peak current densities, were reported, it is assumed that a single unknown area of electrode was used, which could significantly contribute to the error.
To date, no other studies have been found regarding the use of electrochemical methods for quantitative concentration measurement of actinides in molten salts. On the contrary, many studies have used electrochemical methods in molten salts to obtain electrochemical and/or thermodynamic information about actinides (U, Pu, Np, Am, Cm) 1,3-4,13-34 and lanthanides 13,15,16,20,24,[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] in molten salts (e.g., Masset et al. 24 2.7 Masset et al. 25 2.3 Kuznestov et al. 19 1.0 Reddy et al. 30 0.20 Gao 17 3.17 diffusion coefficient, formal potentials, energy of activation). Analysis of these studies revealed significant discrepancies between the obtained results, as well as relatively large errors associated with the measurements. As an example, Table I shows values obtained from several studies for the diffusion coefficient of U 3+ in molten LiCl/KCl at 723 K. As can be seen, the inconsistency of the results obtained using electrochemical techniques can be quite significant. It is clearly evident that accuracy of the measurements and reliability of the data must be improved in order to consider electrochemical techniques for high-precision quantitative concentration measurements. Based on the lessons learned from previous studies using electrochemical techniques in molten salts, several improvements have been developed and will be described. The main purpose of these improvements is to achieve electrochemical measurements that are more precise and accurate for quantitative application. The goal of this work is to demonstrate an electrochemical technique that can be used in molten chloride salts to precisely and accurately determine the concentration of actinides present in the molten salt. Experimental design and methods are described with a special emphasis on the improvements and corrections made to increase the accuracy of the measurements. Finally, the electroanalytical results are compared with destructive analysis methods and the potential for high-precision electroanalytical measurements is discussed.

Experimental
All experiments were carried out in a high-purity argon atmosphere glovebox using a three-electrode small electrochemical cell. The electrolytic bath was a eutectic mixture of high-purity lithium choride (LiCl, Aldrich ≥99%) and potassium chloride (KCl, Aldrich ≥99%). The concentration of uranium in the molten salt was adjusted by adding LiCl-KCl-50 wt%UCl 3 , which was prepared before the measurements by reacting uranium metal with cadmium chloride in LiCl-KCl. The LiCl-KCl-PuCl 3 salt was prepared by chlorinating PuO 2 using ZrCl 4 in a LiCl-KCl eutectic melt. 54 The total concentration of uranium and plutonium ions in the melt was determined by inductively coupled plasma atomic emission spectroscopy (ICP-AES). For the electrochemical study, the U 3+ concentration was varied from approximately 0.5 wt% to approximately 1.73 wt%, and the Pu 3+ concentration was approximately 1.3 wt%. A list of concentrations studied for the initial set of experiments is shown in Table II.
About 50 g of LiCl-KCl eutectic was put in a 55-mL Inconel (nickel-chromium-iron alloy 601) crucible and heated with an elec-  tric furnace to 773 ± 1 K. The working electrode consisted of either 0.075-cm or 0.1016-cm diameter tungsten (W) wire. The surface area of the working electrode was determined using the standard area addition method, which is described in more detail in Ensuring repeatability of the measurements section. A vertical translator attached directly to the working electrode with an alligator clip was used for varying electrode immersion depths. Another W wire with a 0.2032-cm diameter was used as a counter electrode for tests with salt containing PuCl 3 -LiCl-KCl. For tests on salt containing U 3+ ions, a layer of U metal pre-deposited on the walls of the crucible served as the counter electrode to ensure that the counter reaction did not interfere with the reaction occurring at the working electrode. A schematic diagram and photo of the electrolytic cell with vertical translator are shown in Figure 1 and Figure 2a, 2b, respectively. Initially a silver-silver ion (Ag/Ag + ) electrode (1 wt% Ag-LiCl-KCl) contained within a thinned closed-end, vycor glass tube was used as the reference electrode for the measurements. 55,56 However, the durability of the vycor glass at elevated temperature is very poor and its lifetime is very short. Replacing the closed-end vycor tube with a closed-end mullite tube improved the durability of the electrode but introduced additional redox peaks in the voltammograms, presumably due to formation of salt-soluble species arising from a reaction between mullite and trivalent actinide ions in molten salt. To avoid any contamination from the products of reaction with mullite as well as to improve durability of the reference electrode, a W or Pt wire was used as a quasi-reference electrode. 57 Although the half-potential of this a b  reference is undefined, its potential was stable on the time-scale of the voltammetric measurements. Because the method selected for electrochemical analysis depends on the value of the current rather than the potential, the need for a reference electrode with a well-defined potential is eliminated. For consistency of data representation, all potentials were shifted to the values corresponding to the U 3+ /U 0 or Pu 3+ /Pu 0 reaction.
Electroanalytical measurements were performed with a Solatron Modulab system Model HV100 fitted with the standard potentiostat/galvanostat module and controlled with the ModuLab software package.

Results and Discussion
Development of the method.-Overview of possible reasons of inaccuracies.-Inaccurate active electrode area determination is one of the most common explanations for the discrepancies found in the reported electrochemical studies. In most of the studies, measurements have been made simply by visual determination of the immersion depth, 4,14,17,[22][23][24][25][26][27][28]32,33,39,42,[49][50][51][52][53]58 which has an error associated with capillary effects and wetting between the electrode and the salt at different temperatures. Several studies used wires encased in alumina or other insulating material tubes with a known apparent surface area. 3,16,29,31,34,59 This method, however, has been shown to be ineffective in practice because the encasing material when covered in the salt becomes conductive and contributes to an error in the measurements. It is impractical to use an insulator material in the systems because undesired chemical reactions between metals and insulator material could interfere with the measurements. 44 Another possible reason for the observed discrepancies is uncertainty in the graphical determination of transition time, which is unavoidable when using CP in the analysis. This vagueness is one of the main disadvantages of this technique, which makes it rather unattractive for quantitative analysis, 12,57,60 though very frequently it is used for both D i and E o evaluation. 4,14,17,19,20,[24][25][26][27][28]30,[32][33][34][35][36][37][38][39][40][42][43][44]49,53,61 Similarly, the semi-integration technique frequently employed to analyze CV data 4,24-26,33,39,50,53 could be a contributing factor to the discrepancy, because the evaluation of the limiting value of the current can be very vague.
A different possible reason for the observed discrepancies is inconsistency in the interpretation and verification of the equations used in calculations. Depending on experimental design, testing conditions, and type of measured and controlled parameters, many possible relations govern the behavior of current and/or potential. Choosing the right relation and verifying its accuracy is one of the key requirements for obtaining accurate electrochemical information. It was found, however, that some studies used an incorrect or incomplete theoretical approach for deriving the data; this could have significant impacts on the accuracy of the obtained results. For example, in a few studies 20,34,50 equations describing soluble-soluble couples have been inappropriately used to describe reactions involving the formation of an insoluble product. Kuznetsov and coworkers 19,21 used a relation describing irreversible behavior to calculate the diffusion coefficient of U 3+ from a cyclic voltammogram generated at 1 V/s. At such fast scan rates, the reproducibility and accuracy of calculations is questionable. In addition, none of these studies have considered verifying the semi-infinite linear diffusion approximation assumption used in the majority of the equations in the calculations. This assumption is valid when the size of the electrode is large enough and/or the time of measurement is sufficiently fast, 57,60,62 but these conditions should have been investigated before performing calculations.
In addition, with respect to accuracy of the measurements, sparse information is provided concerning the reproducibility of the measurements in the reported studies. Kuznestov et al. 19 commented on the continuous change in the CVs with time when studying a UCl 3 -LiCl-KCl system and continuous degradation of the current. Store et al. 61 reported two consecutive voltammograms of PbCl 2 -LiCl-KCl that differ significantly from each other, but none of these studies commented on the reason for the variances. In addition, Poa et al., 29 who studied systems with high concentrations of U and Pu in molten salts, reported a discrepancy between results using the same experimental setup. In the majority of the studies, however, no information about the reproducibility of the measurements has been found.
Selecting a suitable method.-Several criteria are important when choosing an electroanalytical method for making accurate quantitative measurements. The most important one is availability of a welldeveloped theory describing either potential, current, or charge in terms of concentration. Well-established theories are available for the majority of electrochemical techniques involving soluble-soluble reactions. 57,60,63 Because redox reactions of interest for actinide ions in molten salts usually involve the formation of an insoluble product, a well-developed theory pointing to the appropriate redox chemistry is required. Compared with open-circuit potentiometry, voltammetry has the advantages of higher sensitivity and the ability to simultaneously examine multiple analytes. In addition, using the current instead of potential in concentration calculations eliminates the error associated with potential measurements and the logarithmic relationship between E and concentration. Therefore, selecting a technique that does not require the value of potential to be used in the calculations is desirable. This approach is also very useful in making measurements in non-aqueous media, for which finding a stable reference electrode can be quite challenging.
Another criterion in selecting a suitable method for high-precision measurements is the shape of the resulting response signal. In general, techniques generating peak-shaped voltammograms are preferable over plateau-shaped curves because of the much smaller error associated with graphical evaluation. Most problematic is the uncertainty in graphical determination of the transient time in CP data. Problems with inaccurate CP curves and the difficulties with correcting for background currents discourage the use of controlled-current techniques as opposed to voltammetric methods. 57 Similar issues exist with the semi-integration (SI) method that involves the evaluation of semi-integrated limiting current, which very rarely reaches a constant well-defined value but instead keeps increasing with time. Therefore, to achieve consistent data and avoid errors associated with graphical evaluation, techniques generating peak-shaped voltammograms were used. Both CV and SWV were investigated as possible candidates for high-precision quantitative measurements of actinides in molten salts.
Equations describing the peak current as a function of concentration for reversible reactions involving formation of an insoluble product for CV and SWV are shown in Equations 1 and 2, respectively: 60,62,64,65 In the equations, A is the area of the working electrode (cm 2 ), v is the scan rate (V/s), T is the temperature of the melt in K, D i is the diffusion coefficient of the electroactive species (cm 2 /s), f is the applied frequency (Hz), and E is the magnitude of the square wave potential (V).
Ensuring repeatability of the measurements.-One of the important components of the precision of a measurement is repeatability, which is usually reported as standard deviation. 66 It measures how close the agreement is between successive measurements that were carried out under the same conditions. Repeatability is a very important aspect in data analysis, but almost no information about it or standard deviation of the obtained measurements appears in the reported studies. Testing for repeatability of measurements is especially important for reactions involving formation of an insoluble product because the deposited material continuously alters the structure and size of the electrode surface.
To obtain accurate measurements and repeatable results, the electrode and its diffusion layer must be renewed before each measurement so the same electrode/electrolyte interface conditions are obtained at the beginning of each test. If the diffusion layer is not effectively renewed, progressive depletion of the electroactive species can occur and products can build up, either in the diffusion layer or on the surface of the electrode. 57 These effects usually cause degradation of the response and irreproducible waveforms. Testing for repeatability of measurements is especially important for reactions that result in the formation of an insoluble product, since they involve continuous alterations of the structure and size of the electrode surface. Repeatability of voltammetric measurements in molten LiCl-KCl-UCl 3 was investigated by obtaining multiple consecutive cyclic voltammograms without applying any renewal procedures, and simply scanning at 50 mV/s from −0.3 to +0.3 V versus U 3+ /U 0 . After running 10 consecutive tests, initial and final voltammograms were compared and the results are shown in Figure 3. As can be seen, successive voltammograms obtained without any renewal procedure are definitely not the same and a continuous degradation of the current response caused by the depletion of the diffusion layer is clearly manifested. The values of cathodic peak currents in Figure 3 differ by almost 50%; as a result, depending on which voltammogram is used in the analysis, the inaccuracy of the results can be quite significant. To obtain accurate measurements and reliable data, the repeatability of voltammograms clearly must be improved.
There are four different methods to renew the concentration profile at the working electrode and to ensure representative conditions. 57 A brief description of each method is provided in Table III. These techniques have been extensively tested by applying each step individually as well as in different combinations, and an effective method to renew the working electrode surface to obtain repeatable and reliable measurements was developed. This conditioning process consists of different combinations of steps 1, 2, and/or 3 from Table III. The order and extent to which each of the steps is implemented depends on experimental conditions (e.g., concentration of the electroactive species in the salt, type of electrochemical technique used, duration of the measurement).
The duration of each step depends on the concentration of the electroactive species present in the salt and the rate at which the  Step No. Description

1.
Clean electrode by applying an oxidative potential to the working electrode for a controlled time in order to remove contaminants.

2.
Hold the working electrode at some potential where no redox reactions occur until initial conditions are restored.

3.
Wait for a period of time long enough without applying any voltage (open circuit) for the diffusion to replace the consumed electroreactants.

4.
Stir the solution at the base potential where no redox reactions occur after each measurement.
voltammogram is generated. The higher the concentration of the electroactive species and/or slower the scan rate (or lower the frequency), the longer the duration of each step and more extensive procedures to renew the working electrode surface, and obtain repeatable and reliable measurements. A value of oxidizing potential needed to recondition the electrode surface was found to depend on the nature of the electrochemical system being studied. For a system containing UCl 3 in LiCl/KCl, this value was found to be about 1 volt positive of the cathodic peak corresponding to the U 3+ /U 0 reduction peak. An exact value of the required oxidizing potential is selected based on the peak's position in the voltammogram. An example of CVs obtained for salt concentration 2 from Table II is shown in Figure 4 (CV II). The peaks corresponding to the reduction of U 3+ /U 0 and oxidation of solid U 0 to U 3+ are clearly defined. Two additional peaks are present in the voltammogram (Red and Ox in Figure 4) and their existence has been reported in other studies. 4,24,25,32,34,51,59 These studies proposed that the peaks are a result of the formation of a monolayer at the surface of the electrode due to interactions between metal and the surface of the W electrode. The large separation between the peaks is extremely unusual and the suggested origin of the pair of peaks remains speculative. It was observed that the reduction peak (Red in Figure 4) disappeared when the switching potential was positive of the oxidation peak Ox (CV I in Figure 4), which is consistent with what others reported. 4,32 With regard to repeatability of the measurements, without applying a potential more positive than oxidation peak Ox, the consecutive voltammograms did not produce the same results for U 3+ /U 0 peak measurement (CVI and CVII in Figure 4). Although the difference does not appear to be large initially, it continuously increases and the number of measurements causes significant inaccuracies in the data. Therefore, the cleaning potential needs to be more positive than the oxidation potential of the oxidation peak Ox (∼0.9 V positive of U 3+ /U 0 ), but at the same time not so positive as to cause oxidation of U 3+ to U 4+ (∼1 V positive of U 3+ /U 0 ) which   would alter the concentration of the amount of U 3+ ions present at the electrode/electrolyte interface and result in imprecise measurements. A detailed description of the procedures required to achieve repeatable voltammograms in this study appears in Table IV. When these steps were applied between each measurement, voltammograms and peak currents were highly repeatable and very consistent. Figure 5 shows CVs obtained for the same salt and test conditions as in Figure 3 but with the cleaning/renewing steps applied between each measurement. The improvement in reproducibility is quite remarkable. A relative standard deviation obtained from 20 consecutive peak current measurements was less than 0.5%.
Determination of electrode surface area.-One of the methods that has been be used to determine surface area of the WE using electrochemical methods in molten salts is the standard area addition method used together with CP technique. [35][36][37][38]44,48 The surface area of the working electrode was defined by changing the immersion depth of the working electrode by small controlled increments and measuring the transition time while keeping everything else constant (e.g., temperature, value of applied current). Plotting the square root of a transition time as a function of surface area of working electrode generates a linear plot from which the initial area of the electrode can be calculated. Determination of the surface area using this method was shown to be highly accurate and precise. A similar approach can be applied to any electrochemical technique for which the relation between area and a measured parameter (e.g., potential, current, charge) is known. Equations 1 and 2 show that for both cases the peak current is directly proportional to the surface area of the electrode. Therefore, plotting the peak current as a function of controlled immersion depth generates a linear plot described by Equations 4 and 5 for CV and SWV, respectively:  Table II before (CV I) and after multiple measurements (CV II) with application of the developed conditioning procedure, v = 50 mV/s.  Table II with various surface areas of the working electrode (v = 50 mV/s, reference electrode: W wire, T = 773 K).
With this approach, the area of the electrode ( A) is eliminated from Equations 1 and 2 and replaced with a well-known diameter of the electrode (d). An example voltammogram is shown in Figure 6 for salt concentration 2 (Table II) with different immersion depths of the working electrode. As expected, the peak height (i p ) becomes larger as the surface area of the working electrode increases. The plot of peak current as a function of immersion height of the working electrode is shown in Figure 7. Very good linearity and repeatability of measurements were obtained when the proper conditioning procedure (described in Evaluation of the method section) was applied. Using the slope described by Equations 4 and 5 rather than a sole peak current for quantitative concentration calculations improves the statistics for the concentration and significantly decreases the error associated with the measurements, as it has an accuracy inherent to any standard addition method. To eliminate the possible error associated with the wetting of the electrode by the salt while increasing or decreasing the immersion depth of the electrode, multiple measurements were obtained by changing the immersion depth in both directions and comparing the results for hysteresis. It should be pointed out that Equations 4 and 5 describe only the faradaic current flowing in the electrochemical cell without any effect of double-layer capacitance or uncompensated resistance (i R drop). Since at solid electrodes the faradaic processes are rarely dominated by the charging current 57 and as shown in Figure 6, the background currents are orders of magnitude lower than the measured peak currents, the contribution of the capacitive current was assumed to be negligible. To compensate for any possible distortions caused by the i R drop in the cell, the method of current interrupt available in the potentiostat experiment Relationship between cathodic peak current and height of working electrode corresponding to voltammograms shown in Figure 6. The complete data set obtained for salt concentration 2 is shown in Figure 11.
) unless CC License in place (see abstract

No.
Description Comments

No mass transport by migration
Verification not required in molten salts 2.
No mass transport by forced and/or thermal convection Verification not required for a stationary cell with no rotating electrodes; very slow scan rates must be avoided 3.
Reaction is reversible (limited by mass transfer to the electrode) Reversibility verification required (section Comparison of CV and SWV and section further verifications of CV) 4.
Linear diffusion approximation Verification of applicability of Equation 6 required (section Further verifications of CV) 5.
Unity activity of the deposit Approximate verification required (section Further verifications of CV) setup was used but it did not seem to have any impact on the shape of the voltammograms. Since the resistance of the molten salt and the measured currents are very small, the effect of uncompensated resistance was assumed to be negligible as well.
Evaluation of the Method.-Comparison of CV and SWV.-As described in Development of the method section, CV and SWV are the most suitable for high-precision quantitative actinide concentration measurements in molten salts, and both of these techniques were examined in this study. Equations describing peak current either for the CV or SWV technique (Equations 1 and 2) were derived based on several assumptions; therefore, attaining and verifying these assumptions are essential in order to obtain correct results. Table V lists these assumptions together with the information on whether or not an additional verification is required. Assumptions 1 and 2 do not require verification, given that the experiment is done in molten salts, without any stirring or vibrations in the electrochemical cell. Also, to eliminate any thermal convection effects, very slow scan rates or low frequencies should be avoided. To verify the third assumption, the relationship between peak current and peak potential with polarization rate has to be investigated for both techniques. A system can be considered reversible as long as the peak current increases linearly with the square root of scan rate and the peak potential remains constant with the logarithm of the scan rate.
CV and SWV experiments were completed for each salt composition listed in Table II. Figure 8 shows plots of CV peak heights as a function of the square root of scan rate for concentrations 1, 2, and 3. As can be seen, the plots are highly linear for all three compositions for scan rates up to 0.6 V/s. Figure 9 shows the plot of SWV peak heights as a function of the square root of frequency for the same salt compositions. It is clearly evident from the graph that the plots are only linear for very low frequencies and the range of the linear portion varies with concentration. In addition, SWV has an additional variable parameter, step size ( E), and its dependence on peak height should be examined as well. Comparing the results in Figure 8 with those of Figure 9, SWV is more difficult to interpret and apply than CV.  Table II.  Table II. Therefore, CV is a preferred method for quantitative concentration measurements for actinides in molten salts.
Further verifications of CV.-Linearity of peak current with the square root of scan rate is not the only requirement that needs to be verified to ensure reversibility of the reaction. Another important prerequisite, very often overlooked in other studies, is the stability of peak potential with polarization rate. Peak potentials were plotted as a logarithm of the scan rate for salt compositions 1, 2, and 3, and the results are shown in Figure 10. Based on plots from Figure 8 and Figure 10, the upper limit at which the system can be considered reversible (i.e., purely diffusion controlled with fast electron transfer kinetics) is about 200 mV/s. At higher scan rates, peak potentials start shifting toward negative potentials, which indicates that the reaction becomes quasi-reversible (i.e., electron kinetics start playing a role in the experiment).  Table II Figure 11. Linear relationship obtained for salt concentration 1, 2, 3, and 4 listed in Table II at different electrode immersion depths.
Two additional assumptions that have to be verified for Equation 4 to apply are the unit activity of the deposit and the linear diffusion approximation. The activity of the metal can be assumed to be unity only when at least one monolayer of deposit is present at the electrode. 57,67 In CV involving the formation of an insoluble product, at the beginning of the measurement there is effectively no deposited metal at the surface of the inert electrode, and at the very initial segments of a reduction wave, the activity of the deposit can be much smaller than unity. Once enough current flows through the cell, a monolayer is formed, and the activity of the deposit can be assumed to be unity. To estimate the number of atoms sufficient to cover the entire surface of the electrode with at least one monolayer, a simple calculation can be made and the approximate amount of charge required to form this monolayer can be obtained. 62 From this value and observations of the cathodic wave, a conclusion can be made as to whether or not the unit activity is a valid assumption. Using the value corresponding to the largest possible surface area of the electrode used in this study (0.5 cm 2 ), it was calculated that the deposition of a complete monolayer of uranium or plutonium requires only 0.42 mC of charge. Using a CV obtained at the largest possible immersion depth and smallest concentration of the electroactive species (No. 1 from Table II), this amount of electricity is supplied to the cell in the bottom segment of the wave, where the pre-peak (Red in Figure 4) is observed. Therefore, a monolayer of uranium should have been formed at potentials far more positive than U 3+ /U 0 deposition. Thus, the assumption of unit activity for the deposit in our test is a valid assumption, provided that deposit had been uniformly distributed. It is also worthwhile to note that the results are consistent with the comments made by others about the pre-peak being a result of the monolayer formation at the surface of the electrode. 4,24,25,34,51,59 The linear diffusion approximation can be used for cylindrical or spherical electrodes under conditions described by the relation shown in Equation 6, where t is the time elapsed since the beginning of the electrolysis in seconds, D i is the diffusion coefficient in cm 2 /s and r is the radius of the electrode (cm). 62 Therefore, either by increasing the scan rate of the experiment or using an electrode with larger diameter, applicability of the linear diffusion approximation can be satisfied. On the other hand, the scan rate can be increased only up to a point where the reaction remains limited by mass transport and fulfills the reversibility requirements. Using this approach, the linear diffusion approximation was confirmed for each measurement obtained in this study. For salt compositions 1, 2, 3, and 4, the linear diffusion approximation was confirmed for each measurement using a scan rate of 50 mV/s.
Results of concentration measurements.-Using the developed and described methods, CVs at different working electrode immersion depths were obtained for salt concentrations 1, 2, 3, and 4 (Table II)  using a scan rate of 50 mV/s and a 0.075-cm-diameter tungsten electrode. Each test was repeated several times by gradually increasing the height of the electrode from a low immersion depth and then working in the opposite direction to ensure reproducibility of the measurements and to obtain the relative error of the collected measurements. Results from the tests are shown in Figure 11 and Table VI. As can be seen, the precision of the slopes is very good with a very small relative error that averages 1% with a 99.9% CI.
To calculate the concentration of the actinide species using the slope data, the value of the diffusion coefficient is required. Several studies have measured the diffusion coefficient of U 3+ and Pu 3+4,24 in the LiCl/KCl eutectic at different temperatures. 4,17,19,21,24,25,30,42 At the temperature used in this study (773 K), there have been several reported values of diffusion coefficient (D i ) for U 3+ and Pu 3+ in LiCl/KCl and a summary of the data is shown in Tables VII and VIII for U and Pu, respectively. For results obtained for U 3+ diffusion coefficient, there is significant disagreement between obtained values; therefore using an average value of D i does not seem to be a good approach. Diffusion coefficient data determined by Kuznestov et al. 19,21 appear to have the smallest error associated with the measurements; these researchers also used one of the most reliable approaches for determining data, so their value was used for calculations. For the Pu 3+ diffusion coefficient at 773 K only one study has been found, but its value was determined using several different techniques and relatively good consistency was obtained. 4 Therefore, an average value of 1.6 × 10 −5 cm 2 /s was used in the calculations. Using these values of diffusion coefficients, the concentration of U 3+ and Pu 3+ were calculated and the results are summarized in Table IX. Very good agreement is observed between electrochemical concentration measurements and sample analysis by ICP-AES.

Conclusions
The applicability of electrochemical methods for quantitative concentration measurements of actinides in molten salts was investigated for use in the pyrochemical process. Possible reasons for discrepancies between reported values obtained using electrochemical techniques have been investigated and methods to improve these measurements have been established. The methods to improve the accuracy and precision of the electroanalytical measurements consist of selecting a suitable technique, constantly renewing the electrode/electrolyte interface, optimizing experimental parameters to ensure the validity of the assumptions used in the analysis (e.g., linear diffusion approximation, reversibility of the reaction), and using an improved method of surface area determination. It was demonstrated that by following the developed procedures and a refined data analysis method very precise and reproducible measurements are achievable. Both CV and SWV were examined, and CV has been shown to give the most reliable data over a wide range of experimental conditions. The concentrations of U and Pu were calculated from slopes of peak currents at different electrode immersion depths. The measurements obtained using CV are in excellent agreement with ICP-AES concentration measurements with extremely small relative error. These initial results demonstrate that CV is a very promising tool for quantitative measurements of actinides concentrations in molten salts. However, a more detailed examination of this technique is needed to investigate its suitability at various possible experimental conditions expected in the normal operation of the electrorefiner in pyrochemical reprocessing (e.g., higher than several weight percent concentration for the actinide trichlorides, analysis of multiple components in the salt). Both the application of CV at high concentrations of actinides in the salt and analysis of CV containing multiple components have been studied and will be presented in another article.