Evaluation of overpotentials on graphite and liquid Bi–Mg electrodes by current interruption

Abstract

Our group proposes a new titanium smelting process via Bi–Ti alloy. This process is comprised of reduction of TiCl₄ by Bi–Mg liquid alloy, separation of Ti from Bi by distillation, and Mg electrolysis. In this study, the Mg electrolysis with Bi–Mg liquid alloy cathode was investigated. We firstly measured the IR-corrected polarization curves on graphite and Bi–Mg liquid alloys by the current interruption method. The results indicated that the Bi–Mg alloy cathode can reduce the electricity consumption of the Mg electrolysis. In addition, from the relaxation curves on graphite and Bi–Mg alloys, the concentration overpotential on the Bi–Mg alloy is mainly due to mass transfer of Mg from the electrode/molten salt interface to the liquid alloy bulk. At current densities higher than 300 mA cm⁻², Mg-rich solid phases such as Bi₂Mg₃ and/or pure solid Mg are assumed to be deposited on the Bi–Mg liquid alloy cathode. Finally, we estimated the electricity consumption of the Mg electrolysis in the new smelting process based on the measured overpotentials, assuming that Bi–Mg liquid alloy cathode is stirred sufficiently and a low current density, 275 mA cm⁻², is applied. Under these conditions, the total electricity consumption of the Mg electrolysis in the new process will be lower than that in the Kroll process when the anode–cathode distance is smaller than 8 cm.

Graphic abstract

IR-corrected polarization curves of (a) Mg²⁺ reduction on graphite and Bi–Mg liquid alloys and (b) Cl₂ evolution on graphite in MgCl₂–NaCl–KCl at 550 °C were measured by the current interruption method, and electricity consumption of Mg electrolysis in the new Ti smelting process was estimated from these results.

Appendix 1

1.1 Calculation of the theoretical electricity consumption of Mg electrolysis

Data used for the thermodynamic calculation are given in Table 1. The activities of MgCl₂ in Table 1 are calculated by a subregular solution model, in which the excess molar Gibbs energy of ternary molten salt, G^ex, is represented as Eq. (8).

Table 1 Data used for the calculation of theoretical electricity consumption of the Mg electrolysis in the Kroll process and the new process

$$ G^{\text{ex}} \, = \, \varOmega_{12} x_{1} x_{2} \, + \, \varOmega_{23} x_{2} x_{3} \, + \varOmega_{31} x_{3} x_{1} $$

(8)

In Eq. (8), x₁, x₂, and x₃ are the mole fractions of components 1, 2, and 3 in the ternary molten salts, respectively, and Ω_ij are interaction parameters of binary molten salts composed of i and j. The compositions of the molten salts are shown in Table 1. We defined the components 1 and 2 as MgCl₂ and NaCl, respectively. The component 3 is defined as CaCl₂ or KCl in the Kroll process or new process, respectively. The activity coefficient of MgCl₂, γ₁, can be calculated from the following equation.

$$ RT{ \ln }\gamma_{1} { = }G^{\text{ex}} \, - x_{ 2} \left( {\frac{{\partial G^{\text{ex}} }}{{\partial x_{2} }}} \right)_{{P, T, x_{ 3} }} - x_{ 3} \left( {\frac{{\partial G^{\text{ex}} }}{{\partial x_{3} }}} \right)_{{P, T, x_{ 2} }} $$

(9)

In Eq. (9), R is the gas constant, T is the absolute temperature, P is the pressure. Then, interaction parameters of the binary salts, Ω_ij, are collected as below.

For MgCl₂–NaCl, NaCl–CaCl₂, and KCl–MgCl₂ binary salts, data points of excess molar Gibbs energies for binary salts, $G_{ij}^{\text{ex}}$, are reported in literature [30]. Then, Ω_ij are obtained by Eq. (10) and fitted by Eq. (11) which is a Redlich–Kister polynomial [31].

$$ \varOmega_{ij} { = }\frac{{G_{ij}^{\text{ex}} }}{{y_{i} \, y_{j} }} $$

(10)

$$ \varOmega_{ij} { = }\sum\limits_{{n{ = 0}}}^{m} {L_{n}^{ij} } \left( {y_{i} \, - \, y_{j} } \right)^{n}\ (m \, \le { 3)} $$

(11)

In Eqs. (10) and (11), y_i and y_j are mole fractions of i and j in the binary salts, and $L_{n}^{ij}$ should be function of temperature. However, we assumed that $L_{n}^{ij}$ are independent of temperature and adopted the data above 700 °C. Then, Ω_ij are function of the mole fractions. Figure 13 shows Ω_ij versus y_i − y_j and fitted curves by Eq. (11). The fitting parameters, ${{L}}_{{n}}^{{ij}}$, are shown in Table 2. As for CaCl₂–MgCl₂ [32] and NaCl–KCl [33] molten salts, interaction parameters are reported as Eqs. (12) and (13), respectively.

Fig. 13

Interaction parameters of MgCl₂–NaCl, NaCl–CaCl₂, and KCl–MgCl₂ molten salts calculated from the reported data. Solid lines are fitted curves by Eq. (11)

Table 2 Parameters used for the calculation

$$ {\text{CaCl}}_{2}{-}{\text{MgCl}}_{2}{:}\ \varOmega /{\text{kJ}}\,{\text{mol}}^{{ - 1}} = 9.87 - 15.1{\text{y}}_{{{\text{CaCl}}_{2} }} + 5.44{\text{y}}_{{{\text{CaCl}}_{2} }}^{2} $$

(12)

$$ {\text{NaCl}}{-}{\text{KCl}}\!\!\!:\varOmega /{\text{kJ mol}}^{{{-1}}} = -2.05 - 0.272y_{\text{NaCl}} $$

(13)

Using these data, parameters $L_{n}^{ij}$ are obtained as shown in Table 2.

Finally, each Ω_ij expressed as Eq. (11) is substituted into Eqs. (8) and (9) under the condition that y_i − y_j is equal to x_i − x_j, which is called a Muggianu-type approximation [34].