The role of correlations in the determination of the transport properties of LaCl3 in high temperature molten eutectic LiCl–KCl

Adib Samin; Evan Wu; Jinsuo Zhang

doi:10.1515/ract-2016-2721

Article

The role of correlations in the determination of the transport properties of LaCl₃ in high temperature molten eutectic LiCl–KCl

Adib Samin , Evan Wu and Jinsuo Zhang

Published/Copyright: March 13, 2017

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information Explore this Subject

From the journal Radiochimica Acta Volume 105 Issue 8

Abstract

It is important to develop an accurate assessment of fundamental data of lanthanides in high temperature molten salts to enable an efficient application of pyroprocessing. This requires a careful consideration of uncertainties in the reported results. In this study, cyclic voltammetry (CV) tests of LaCl₃ in KCl–LiCl molten salt were conducted at low concentration levels in the molten salt at 723 K and at several scan rates. The CV signals were subsequently analyzed through the conventional CV analysis and using a BET-based model through a nonlinear least-squares fitting procedure. It was determined that the parameters of the model were strongly correlated and the support plane procedure was implemented to assign joint confidence intervals for the diffusivity of lanthanum. Accounting for the correlations led to a significant increase in the uncertainty of the reported diffusivity which led to better agreement with the literature. Accounting for the correlations may be important for higher concentration levels.

Keywords: Cyclic voltammetry; mass transport; kinetics; adsorption; correlations

Acknowlegements

The authors would like to acknowledge the U.S. Department of Energy DOE-NEUP program, project number 14-6489 for supporting this research.

Appendix A

The diffusion equation governs both species’ concentrations in the solution:

(11)∂cO∂t= DO∂2cO∂x2

(12)∂cR∂t= DR∂2cR∂x2

In these equations, c_O and c_R are the concentrations of the oxidized and reduced species, respectively. The domain on which the equations are solved is 0≤x≤L, where we choose L=12DTmax (T_max is the time needed for one full CV cycle). The product is assumed to have a very low diffusivity [D_R~O(10⁻²⁰) cm²/s]. In addition, the adsorption on the electrode is described by the BET isotherm [20]:

(13)ΓR(t)= ΓsK1cR(0, t)(1−KdcR(0, t))(1+K1cR(0, t)−KdcR(0, t))

Here, Γ_s is the maximum surface concentration of the product species, and K₁ and K_d are the adsorption and desorption equilibrium constants. Finally, the boundary conditions for the diffusion equations at the electrode surface describe the kinetics of the reaction. The boundary conditions sufficiently far from the electrode surface are assumed equal to the bulk concentration values:

(14)DO∂cO∂x|x = 0=cO(0, t)kf0e− αnFRT(E − Ef0)− cR(0, t) kb0e(1 − α)nFRT(E − Ef0)

(15)DR∂cR∂x|x = 0=dΓRdt−cO(0, t)kf0e− αnFRT(E − Ef0)+ cR(0, t)kb0e(1 − α)nFRT(E − Ef0)

In the equations, Ef0 is the formal potential, kf0 and kb0 are the reaction rates for the forward and backward directions, respectively evaluated at the formal potential, F is Farad’s constant, R is the universal gas constant, T is the temperature and α is the charge transfer coefficient. In all our simulations we assumed kf0=kb0=k0. The initial conditions and the boundary conditions away from the electrode were selected as follows:

(16)cO(x, t=0)=cO(L, t)=cbulk; cR(x, t=0)=cR(L, t)=0; ΓP(t=0)=0

In the model, the current was defined as:

(17)I=− nFADO∂cO∂x|x = 0

References

1. Henderson, H.: Contemporary World Issues: Nuclear Power: A Reference Handbook (2nd Edition), ABC-CLIO, Santa Barbara, CA, USA, 2014.Search in Google Scholar

2. Hamel, C., Chamelot, P., Laplace, A., Walle, E., Dugne, O., Taxil, P.: Reduction process of uranium(IV) and uranium(III) in molten fluorides. Electrochim. Acta 52, 3995 (2007).10.1016/j.electacta.2006.11.018Search in Google Scholar

3. Laidler, J., Battles, J., Miller, W., Ackerman, J. P., Carls, E. L.: Development of pyroprocessing technology. Prog. Nucl. Energ. 31, 131 (1997).10.1016/0149-1970(96)00007-8Search in Google Scholar

4. Zhang, J.: Kinetic model for electrorefining, part I: model development and validation. Prog. Nucl. Energ. 70, 279 (2014).10.1016/j.pnucene.2013.03.001Search in Google Scholar

5. Kim, S., Paek, S., Kim, T., Park, D.-Y., Ahn, D.-H.: Electrode reactions of Ce³⁺/Ce couple in LiCl–KCl solutions containing CeCl₃ at solid W and liquid Cd electrodes. Electrochim. Acta 85, 332 (2012).10.1016/j.electacta.2012.08.084Search in Google Scholar

6. Tang, H., Pesic, B.: Electrochemical behavior of LaCl₃ and morphology of La deposit on molybdenum substrate in molten LiCl–KCl eutectic salt. Electrochim. Acta 119, 120 (2014).10.1016/j.electacta.2013.11.148Search in Google Scholar

7. Samin, A., Wang, Z., Lahti, E., Simpsonb, M., Zhang, J.: Estimation of key physical properties for LaCl3 in molten eutectic LiCl–KCl by fitting cyclic voltammetry data to a BET-based electrode reaction kinetics model. J. Nucl. Mater. 475, 149 (2016).10.1016/j.jnucmat.2016.04.002Search in Google Scholar

8. Masset, P., Bottomley, B., Konings, R., Malmbeck, R., Rodrigues, A., Serp, J. Glatz, J.: Electrochemistry of uranium in molten LiCl-KCl eutectic. J. Electrochem. Soc. 152, A1109 (2005).10.1149/1.1901083Search in Google Scholar

9. Fukasawa, K., Uehara, A., Nagai, T., Sato, N., Fujii, T., Yamana, H.: Thermodynamic properties of trivalent lanthanide and actinide ions in molten mixtures of LiCl and KCl. J. Nucl. Mater. 424, 17 (2012).10.1016/j.jnucmat.2012.01.009Search in Google Scholar

10. Vandarkuzhali, S., Gogoi, N., Ghosh, S., Prabhakara Reddy, B., Nagarajan, K.: Electrochemical behaviour of LaCl₃ at tungsten and aluminium cathodes in LiCl–KCl eutectic melt. Electrochim. Acta 59, 245 (2012).10.1016/j.electacta.2011.10.062Search in Google Scholar

11. Kim, T., Kim, E., Ahn, D., Kim, K., Paek, S., Jung, Y.: Determination of electrochemical parameters for electrode reaction of La(III)/La(0) redox couple in a high-temperature molten salt solution. Int. J. Electrochem. Sci. 9, 1784 (2014).Search in Google Scholar

12. Gao, F., Wang, C., Liu, L., Guo, J., Chang, S., Chang, L., Li, R., Ouyang, Y.: Electrode process of La(III) in molten LiCl-KCl. J. Rare Earth. 27, 986 (2009).10.1016/S1002-0721(08)60375-0Search in Google Scholar

13. Fabian, C. P., Luca, V., Chamelot, P., Massot, L., Caravaca, C., Lumpkin, G. R.: Experimental and simulation study of the electrode reaction mechanism of La³⁺ in LiCl-KCl eutectic molten salt. J. Electrochem. Soc. 159, F63 (2012).10.1149/2.057204jesSearch in Google Scholar

14. Castrillejo, Y., Bermejo, M. R., Martínez, A. M., Díaz Arocas, P.: Electrochemical behavior of lanthanum and yttrium ions in two molten chlorides with different oxoacidic properties: the eutectic LiCl-KCl and the equimolar mixture CaCl2-NaCl. J. Min. Metal. B 39, 109 (2003).10.2298/JMMB0302109CSearch in Google Scholar

15. Lantelme, F., Berghoute, Y.: Electrochemical studies of LaCl₃ and GdCl3 dissolved in fused LiCl-KCl. J. Electrochem. Soc. 146, 4137 (1999).10.1149/1.1392604Search in Google Scholar

16. Coleman, T. F., Li, Y.: An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optimiz. 6, 418 (1996).10.1137/0806023Search in Google Scholar

17. Lakowicz, J. R.: Topics in Fluorescence Spectroscopy: Vol. 2: Principles, Springer, New York, 1992.Search in Google Scholar

18. Bard, A. J., Faulkner, L. R.: Electrochemical Methods: Fundamentals and Applications, Wiley, New York, 2001.Search in Google Scholar

19. Berzins, T., Delahay, P.: Oscillographic polarographic waves for the reversible deposition of metals on solid electrodes. J. Am. Chem. Soc. 75, 555 (1953).10.1021/ja01099a013Search in Google Scholar

20. Brunauer, S., Emmett, P. H., Teller, E.: Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60, 309 (1938).10.1021/ja01269a023Search in Google Scholar

Received: 2016-10-18

Accepted: 2017-1-27

Published Online: 2017-3-13

Published in Print: 2017-7-26

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/ract-2016-2721

Keywords for this article

Cyclic voltammetry; mass transport; kinetics; adsorption; correlations