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# Determination of Diffusion Coefficients of Mg²⁺ Ions from Molten LiCl-KCl-MgCl₂†

HYO YEOL RYU and SANG MUN JEONG*

Department of Chemical Engineering, Chungbuk National University, Heungduk-gu, Cheongju, Chungbuk 361-763, Republic of Korea

*Corresponding author: Fax: +82 43 2692370; E-mail: smjeong@chungbuk.ac.kr

Published online: 23 June 2014; AJC-15396

The diffusion coefficients of Mg²⁺ ions at molybdenum electrode in molten LiCl-KCl-MgCl₂ at 670 °C were determined using the cyclic voltammetry, chronoamperometry and chronopotentiometry, which were calculated to be 1.47 × 10⁻⁶, 1.23 × 10⁻⁶ and 1.67 × 10⁻⁶ cm²/s, respectively. The activation energy for the diffusion process of Mg²⁺ ions was found to be 106.3 kJ/mol. The underpotential deposition (UPD) of Li⁺ ions on the pre-deposited Mg and the codeposition of Mg²⁺ and Li⁺ ions led a formation of liquid Mg-Li solution at a more positive potential than a potential for Li deposition.

**Keywords:** Magnesium, Diffusion coefficient, Activation energy, LiCl-KCl-MgCl₂.

## INTRODUCTION

Recently, molten salt electrolysis has been considered to be an important method for preparing light metals and alloys due to its simplicity and economic advantages¹,². The basic data such as diffusion coefficient, activation energy, etc. are important in developing this technology more efficiently³. Several studies have reported on the electrode process of Mg²⁺ ions in molten chlorides⁴⁻⁷. However, due to the variations in the experimental conditions such as salt composition and temperature in the molten salt, the basic data reported in previous publications differ considerably⁸⁻¹⁰. Therefore, the diffusion coefficients of Mg²⁺ ions need to be further investigated.

In the present study, electrochemical techniques including cyclic voltammetry (CV), chronoamperometry (CA) and chronopotentiometry (CP) were used to determine the diffusion coefficients of Mg²⁺ ions at an inert molybdenum electrode in a molten LiCl-KCl-MgCl₂ system at 670 °C. Also, the activation energy for the diffusion process of Mg²⁺ ions was calculated by Arrhenius equation.

## EXPERIMENTAL

Anhydrous LiCl (98.2 % purity; Samchun Chemicals, Korea), KCl (99 % purity; Samchun Chemicals, Korea) and MgCl₂ (96 % purity; Samchun Chemicals, Korea) were used as electrolytes in this study. A molybdenum wire (0.5 mm in diameter), graphite rod (13 mm in diameter) and Ag/AgCl electrode were used as the working electrode, counter electrode

and reference electrode, respectively. The reference electrode was fabricated as follows: AgCl (1 wt %) was added in a mixture of LiCl-KCl (60 : 40 in mole percent) and the salt was put in a mullite tube with a closed end. A silver wire (0.5 mm in diameter) was immersed to salt inside the tube. A LiCl-KCl mixture of 300 g that contained various MgCl₂ concentrations was placed in the MgO crucible and then heated and maintained at 670 °C. A potentiostat (PGSTAT302N, Metrohm Autolab, Netherlands) was used to conduct three electrochemical techniques. In the cyclic voltammetry experiments, the diffusion coefficient of Mg²⁺ ions is calculated at various temperatures between 670 and 710 °C. The chronoamperometry measurement was conducted through applying a potential in a range from -2.2 to -3.0 V to the cell. The chronopotentiometry measurement was also conducted through applying a current between 25 and 225 mA to the cell.

## RESULTS AND DISCUSSION

**Cyclic voltammetry:** Fig. 1(a) shows the cyclic voltammograms of a molybdenum wire at various MgCl₂ concentrations in the LiCl-KCl molten salt. In the eutectic LiCl-KCl, the sharp increase in the cathodic/anodic current is caused from a redox couple of Li⁺/Li. After the addition of 5 wt % MgCl₂, a cathodic current peak at -1.7 V (vs. Ag/AgCl) appeared due to the reduction of Mg²⁺ ions to Mg metal (Mg²⁺/Mg). It is clear that the electrode process of Mg²⁺ ions is controlled by the diffusion rate and mass transfer¹¹. The cathodic current at -2.1 V (vs. Ag/AgCl) probably corresponds to the formation of a
liquid Mg-Li solution which is formed by underpotential deposition (UPD) of lithium on the liquid Mg already deposited on the molybdenum electrode¹¹ and codeposition of Mg²⁺ and Li⁺ ions. The corresponding reaction can be understood as follows:

$$Mg + Li^{+} + e^{-} \rightleftharpoons Mg-Li alloy \quad (1)$$

$$Mg^{2+} + Li^{+} + 3e^{-} \rightleftharpoons Mg-Li alloy \quad (2)$$

In the reverse scans, two re-oxidation peaks associated with the dissolution of Li and Mg metals were observed. When the MgCl₂ concentration was increased to 10 wt %, more reduction reactions of Mg²⁺ ions occurred due to the increase in the MgCl₂ concentration. Fig. 1(b) shows the cyclic voltammetric graphs at various scan rates (100-350 mV/s) in LiCl-KCl-MgCl₂ (5 wt %). An increase in the current with an increase in the scan rates was observed, which indicates that a fast electrode reaction occurred at higher scan rates through the thin diffusion layer. Fig. 1(c) shows a plot of the current density against the inverse square root of the scan rate for the cyclic voltammetric graphs at various temperatures (670-710 °C). The plot of i vs. v⁻¹/² exhibited a linear relationship at a given temperature window over the scan rate ranges (100-350 mV/s). The diffusion coefficient was calculated using the Randles-Sevcik equation, as follows:

$$i_p = 0.61 \left( \frac{F^3}{RT} \right)^{1/2} n^{3/2} AD^{1/2} C_o v^{1/2} \quad (3)$$

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<figure><img src="image_4.png" /><figcaption>Fig. 1. (a) CV graphs of a Mo wire at 100 mV/s in LiCl-KCl-MgCl₂ (MgCl₂ = 0, 5, 8 and 10 wt %), (b) CV graphs of a Mo wire at various scan rates (100-350 mV/s), (c) plot of the current density against the inverse square root of time at between 670 and 710 °C and (d) plot of the diffusion coefficient of Mg²⁺ ions and the reciprocal of temperature</figcaption></figure>

where iₚ is the reduction peak current (A), A is the electrode surface area (cm²), C₀ is the Mg²⁺ concentration (mol/cm³), D is the diffusion coefficient (cm²/s), F is Faraday's constant (96,485 C/mol) and t is the scan rate. The diffusion coefficient of Mg²⁺ ions was 1.47 × 10⁻⁶ cm²/s at 670 °C. Table-1 summarized the diffusion coefficients of Mg²⁺ ions at various temperatures between 670 and 710 °C. As the temperature of the molten salt increased, the diffusion coefficient also increased due to the temperature dependence on the diffusion of electro-active species. Fig. 1(d) shows an Arrhenius plot of the diffusion coefficients of Mg²⁺ ions and the reciprocal of temperature. The plot of ln D vs. T⁻¹ exhibited a linear relationship over the range of temperatures. The activation energy for the diffusion processes of Mg²⁺ ions was calculated using the Arrhenius equation. The values of the activation energy and pre-exponential factor were 106.3 kJ/mol and 1.134, respectively.

**Chronoamperometry:** Fig. 2(a) shows the chronoamperograms of a molybdenum wire with different applied potentials from -1.6 to -2.6 V in LiCl-KCl-MgCl₂ (5 wt %) at 760 °C. The current curves exhibited a typical tendency in the chronoamperometry experiments, which indicated that the reduction of Mg²⁺ ions was a diffusion-controlled reaction. At an applied potential of -1.8 V, the current increased sharply due to the reduction of Mg²⁺ ions. When the applied potential changed from -2.0 to -2.1 V, the current increased sharply again, which probably indicated that the reduction of Li⁺ ions was accompanied

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<table><caption>TABLE-1
DIFFUSION COEFFICIENTS OF Mg²⁺ IONS AT VARIOUS TEMPERATURES</caption><thead><tr><th>Melt temperature (°C)</th><th>670</th><th>680</th><th>690</th><th>700</th><th>710</th></tr></thead><tbody><tr><th>Diffusion coefficient of Mg<sup>2+</sup> ions (cm<sup>2</sup>/s)</th><td>1.47 × 10<sup>-6</sup></td><td>1.64 × 10<sup>-6</sup></td><td>1.96 × 10<sup>-6</sup></td><td>2.30 × 10<sup>-6</sup></td><td>2.47 × 10<sup>-6</sup></td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>Fig. 2. (a) Chronoamperograms of a molybdenum wire at various applied potentials (-1.6 to -2.6 V) and (b) plot of the current density against the inverse square root of time</figcaption></figure>

with that of Mg²⁺ ions. Accordingly, the co-deposition of Mg²⁺ and Li⁺ ions occurred at negative values lower than -2.1 V. Fig. 2(b) shows the plot of the current density against the inverse square root of time for the chronoamperometry graphs. The plot of i vs. t¹/² exhibited a linear relationship for a period of time (0.3-2 s) over the range of applied potentials, where the diffusion coefficient can be calculated using the Cottrell equation, as follows:

$$i(t) = \frac{nFAD_{O}^{1/2}C_{O}}{\pi^{1/2}t^{1/2}} \quad (4)$$

where i is the reduction current (A), A is the electrode surface area (cm²), C₀ is the Mg²⁺ concentration (mol/cm³), F is Faraday's constant (96,485 C/mol) and D is the diffusion coefficient (cm²/s). The diffusion coefficient of Mg²⁺ ions at between -1.8 and -2.0 V was 1.23 × 10⁻⁶ cm²/s at 670 °C. At an applied potential between -2.1 and -2.6 V where the co-deposition of Mg²⁺ and Li⁺ ions occurs as shown in cyclic voltammetric experiment.

**Chronopotentiometry:** Fig. 3(a) shows the chronopotentiograms of a Mo wire at various applied currents (25-225 mA) in LiCl-KCl-MgCl₂ (5 wt %) at 760 °C. At a current lower than 100 mA, the current curves exhibited two potential plateaus

<figure><img src="image_8.png" /><figcaption>Fig. 3. (a) Chronopotentiograms of a molybdenum wire at various applied currents (25-225 mA) and (b) plot of the current against the inverse square root of transition time (T)</figcaption></figure>

that are associated with the reduction of Mg²⁺ ions (Plateaus 1) and Li⁺ ions (Plateaus 2). The flux of Mg²⁺ ions to the electrode surface was not sufficiently large and thus the potential is shifted to a more negative value where the co-deposition of Mg²⁺ and Li⁺ ions takes place. This result suggests that the electrode process of Mg²⁺ ions was a diffusion-controlled reaction¹²,¹³. Fig. 3(b) shows the plot of the current against the inverse square root of transition time (τ) from the chronopotentiometry graphs. The plot of i vs. τ¹/² exhibited a linear relationship over the range of applied currents. The diffusion coefficient of Mg²⁺ ions was calculated using the Sand's equation, as follows:

$$i\tau^{1/2} = \frac{nFAC_{O}D^{1/2}\pi^{1/2}}{2} \quad (5)$$

where i is the reduction current (A), F is Faraday's constant (96,485 C/mol), τ is the transition time (s), A is the surface area (cm²), C₀ is the Mg²⁺ concentrations (mol/cm³) and D is the diffusion coefficient (cm²/s). The diffusion coefficient of Mg²⁺ ions on a molybdenum wire was 1.67 × 10⁻⁶ cm²/s at 670 °C. The values of diffusion coefficients exhibit a similar level regardless of the analytical techniques.
**Conclusion**

The cyclic voltammetry, chronoamperometry and chronopotentiometry were conducted to determine the diffusion coefficients of Mg²⁺ ions at a molybdenum electrode in molten LiCl-KCl-MgCl₂ at 670 °C, which was found to be 1.47 × 10⁻⁶, 1.23 × 10⁻⁶ and 1.67 × 10⁻⁶ cm²/s, respectively. The temperature dependence on diffusion coefficients was investigated and the activation energy for the diffusion process of Mg²⁺ ions was calculated to be 106.3 kJ/mol. The electrode process of Mg²⁺ ions was a diffusion-controlled reaction. Also, the underpotential deposition (UPD) of Li⁺ ions on the pre-deposited Mg and the codeposition of Mg²⁺ and Li⁺ ions led a formation of liquid Mg-Li solution at a more positive potential than a potential for Li deposition.

**ACKNOWLEDGEMENTS**

This work was supported by the Technology Innovation Program (2011T00200211) funded by the Ministry of Knowledge Economy (MKE, Korea).

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