Online ISSN : 1347-5320
Print ISSN : 1345-9678
ISSN-L : 1345-9678
Equilibrium between Metallic Titanium and Titanium Ions in MgCl2–LiCl Molten Salt
Jinyu WuJianxun SongHongmin ZhuYongchun ShuJilin He
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2019 Volume 60 Issue 3 Pages 374-378


The equilibrium between metallic titanium and titanium ions, 3Ti2+ = 2Ti3+ + Ti, in MgCl2–LiCl molten salt system was revaluated by means of best fitting. The measurement was also carried for the MgCl2–LiCl melt with various composition of LiCl at 1023 K. The results illustrate that the values of Kc correspond well with the composition of the melt which defined as polarizing power.

1. Introduction

The wide application of titanium in the industrial or domestic use has been limited because of its high cost caused by the complicated production process, the Kroll process.1) To explore a promising process with low cost, several methods have been proposed and widely investigated. However, the prediction that the Kroll process would be replaced by an electrochemical route has not been fulfilled;27) attempts involving the electro-deposition of titanium from molten salts have been hampered by the difficulties in eliminating the redox cycling of multivalent titanium ions.2) Thus, for understanding the mechanism, investigation on the equilibrium between titanium ions and metallic titanium is very important.

It has been reported that the electrode reduction from Ti3+ to metallic Ti takes a two-step process, Ti3+ → Ti2+ → Ti, in alkali metal chloride melts except a pure CsCl.8,9) In comparison, Ti3+ was directly reduced to be titanium in a fluoride melts.10) Indeed, the stability of the titanium ions depends on the bath composition. The Ti2+ was more stable in alkali chloride melts, however, in a fluoride melts, the higher oxidation states of Ti4+ and Ti3+ are more stable. It has been reported that equilibrium exists among Ti2+, Ti3+, and metallic titanium in most chloride melts, which can be expressed by eq. (1):   

\begin{equation} \text{3Ti$^{2+}$} = \text{2Ti$^{3+}$} + \text{Ti} \end{equation} (1)
The equilibrium constant, Kc, is defined by eq. (2):   
\begin{equation} K_{c} = \frac{\alpha_{\textit{Ti}^{3+}}^{2}\alpha_{\textit{Ti}}}{\alpha_{\textit{Ti}^{2+}}^{3}} = \frac{x_{\textit{Ti}^{3+}}^{2}\gamma_{\textit{Ti}^{3+}}^{2}}{x_{\textit{Ti}^{2+}}^{3}\gamma_{\textit{Ti}^{2+}}^{3}} \end{equation} (2)
Where αi and i are the activity and the activity coefficient of a species, respectively. And xi is a cationic molar fraction defined by the eq. (3),   
\begin{equation} x_{i} = \frac{n_{i}}{n_{\textit{Mg}^{2+}} + n_{\textit{Li}^{+}} + n_{\textit{Ti}^{2+}} + n_{\textit{Ti}^{3+}}} \end{equation} (3)
In the case of a lower ion concentration, the solutes obey Henry’s law. Here, the concentration quotient, Kc, is defined by the eq. (4),   
\begin{equation} K_{c} = \frac{x_{\textit{Ti}^{3+}}^{2}}{x_{\textit{Ti}^{2+}}^{3}} \end{equation} (4)
Mellgren and Opie investigated that the equilibrium constant (Kc) of the eq. (1) depended on the total titanium concentrations.11) It was also confirmed by Kreye and Kellogg that the Kc value was dispersed in SrCl2–NaCl molten salt.12) Sekimoto et al., in view of some impurities in molten salt and systematic errors, concluded that titanium ions are not only equilibrium with metallic titanium but also with TiOCl(s).1315) Nevertheless, the Kc value was still dispersing especially in a low titanium ion concentration. The relevant work has been done in details and especially for NaCl–KCl and LiCl–KCl systems.1521) The accurate values of Kc were recalculated by best-fitting method under consideration of the TiOCl dissolution.

Though the equilibrium constants of eq. (1) had been investigated by many researchers, the study in the MgCl2–LiCl system has seldom been reported. The previous works in our group show that the divalent species perform more stable in alkali cation series when the ionic radius is smaller. With the smallest cation radius in alkali-metal, the MgCl2–LiCl system is profitable toward the stability of Ti2+, which would attribute to lessen the occurrence of disproportional reaction. Thus, it would be worthy of studying the compositional influence on the equilibrium constant of the reaction, 3 Ti2+ = 2 Ti3+ + Ti, in molten MgCl2–LiCl.

2. Experimental

The major parts of experimental methods are identical to those of our precious reports,1522) in which they were discussed in detail. Thus, here only a brief account of key aspects is given.

Commercially available anhydrous MgCl2 and anhydrous LiCl were used (Sinopharm Chemical Reagent Co., Ltd., analytical grade ≥99.9% and 99.9%, respectively). Before the use as the solvents, both MgCl2 and LiCl were purified by bubbling HCl gas through the melts separately to remove O2− dissolved in the salts, and filtrated through a quartz filter.21) Titanium sub-chloride salts were prepared by the disproportionation of titanium tetrachloride TiCl4 and metallic titanium in the solvent salts.

The salts containing titanium dichloride and excess metallic titanium were held at a designed temperature to reach equilibrium. High-purity argon gas was used to stir the molten salt for making the reaction of titanium ions and titanium metal fast. A quartz sampler consists of an injector and a quartz tube. The injector at the top of the quartz tube (6 mm diameter) is sealed by a rubber plug. By fixing the sampling point at the same location four parallel samples were taken out from molten salts by the quartz sampler for analysis in each experiment, and the average value of the concentrations of titanium ions was considered as the result.

The quantitative analysis of different oxidation states of titanium ions consists of three main steps. The concentrations of Ti2+ and Ti3+ in each sample were determined by H2 volumetric analysis and titration, respectively. Finally, that the concentration of Ti4+ after titration was equal to the concentration of Ti2+ plus Ti3+ was determined by diantipyryl methane spectrophotometry.

In order to investigate the influence of composition on the equilibrium constant of titanium ions, various molar percent of LiCl was added in molten MgCl2–LiCl which were used as studying electrolyte.

3. Results and Discussions

3.1 Equilibrium constant of titanium ions in molten MgCl2–LiCl

Figure 1(a) shows the relationship of the molar fraction (mole percent) between divalent titanium (xTi2+) and trivalent titanium (xTi3+) in MgCl2–LiCl (28 mol%, 72 mol%) melt at 973 K, 1023 K and 1073 K, respectively. Taking the salt composition of MgCl2–LiCl (28 mol%, 72 mol%) is based on the consideration of that at this ratio the system has the lowest liquid transition point.

Fig. 1

xTi3+ and Kc against xTi2+, (a) and (b), in MgCl2–LiCl eutectic melt (xLiCl = 72 mol%) at 973 K, 1023 K and 1073 K, respectively, under metallic titanium existence.

The equilibrium constant curves, 0.1, 0.5, 1.0 and 1.5, which were calculated from $x_{\textit{Ti}^{2 + }}$, were also listed in Fig. 1(a). At all temperatures, the concentration of divalent titanium, xTi2+, was slightly higher than that of trivalent titanium, xTi3+. Moreover, Kc values decreased from 1.5 to 0.5 with the concentration increasing of Ti2+ (xTi2+). The relationship between Kc and xTi2+ under different temperature shows in Fig. 1(b), in which Kc was obtained by calculating original experimental data of xTi2+ and xTi3+. The relationship between Kc and xTi2+ were also plotted in Fig. 1(b) under certain values of xTi3+. It can be found that the equilibrium constant increased in Fig. 1, and the tendencies of the curves in general accord with related literatures.1118) The experimental result indicates that Kc depends on xTi2+, although the Kc value should be a constant because the solutes (TiCl2, TiCl3) obey Henry’s law when the total titanium ion concentration is low. The previous papers often attributed this to the formation of an insoluble deposition, TiOCl(s), on account of the initial oxide ions O2−, Ti3+ in the molten salt.

The best-fitting method was applied to revalue Kc, and the equation can be expressed as follows:1518)   

\begin{equation} x_{\textit{Ti}^{2+}}^{\textit{anal.}} = \left\{\frac{[(x_{\textit{Ti}^{3+}}^{\textit{anal.}} - x_{O^{2-}}^{\textit{init.}})+\sqrt{(x_{\textit{Ti}^{3+}}^{\textit{anal.}} - x_{O^{2-}}^{\textit{init.}})^{2} + 4K_{\text{sp}}}]^{2}}{4K_{\text{c}}}\right\}^{\frac{1}{3}} \end{equation} (5)
where $x_{\textit{Ti}^{2 + }}^{\textit{anal.}}$, $x_{\textit{Ti}^{3 + }}^{\textit{anal.}}$ are the cationic molar fraction of Ti2+ and Ti3+, respectively, getting by H2 volumetric and titration analysis; $x_{\textit{O}^{2 - }}^{\textit{init.}}$ is the initial concentration of oxide ions in molten salt; Kc and Ksp are equilibrium constant and solubility product constant of TiOCl(s), respectively.

In the best-fitting treatment, Kc, Ksp, and initial $x_{\textit{O}^{2 - }}$ were set as the parameters, eq. (5) was employed to fit the experimental data $x_{\textit{Ti}^{2 + }}^{\textit{anal.}}$ and $x_{\textit{Ti}^{3 + }}^{\textit{anal.}}$, in view that they are constants at a fixed temperature. The details of this process have been described in our previous papers.1518)

Figure 2(a), (b) and (c) show best-fitting curves of titanium ions at different temperatures, which correspond well with the experimental data. In addition, for the aim of comparing the equilibrium constant, Kc values were plotted in Fig. 2 which are dash lines and calculated by experimental data (xTi2+ and xTi3+).

Fig. 2

The relationship between the best-fitting curves and the experiment plots (a) at 1073 K, (b) at 1023 K and (c) at 973 K.

Figure 3(a), (b) and (c) are outcomes of the equilibrium constant Kc after best-fitting. Also, the original Kc data are given as a comparison. It can be seen that all experiment data Kc are revalued back to a constant value and they were equal to the best-fitting values. As can be seen from Fig. 3, the equilibrium constant increased when the temperature increased from 973 K to 1023 K under a certain concentration of titanium ions. The other two parameters, $x_{\textit{O}^{2 - }}$ and Ksp, were calculated as the best-fitting parameters by fitting the experimental data. The calculated results of Kc, Ksp and $x_{\textit{O}^{2 - }}$ at 973 K, 1023 K and 1073 K are shown in Table 1. The Kc values at 973 K, 1023 K and 1073 K were recalculated as 0.016, 0.062, and 0.191, respectively. It can be also concluded that the real values of equilibrium constant are much lower than the calculated values (0.1, 0.5, 1.0…) according the concentrations of xTi2+ and xTi3+.

Fig. 3

The relationship between the Kc of the experiment data, and best-fitting parameters (a) at 973 K, (b) 1023 K and (c) 1073 K for titanium ions in MgCl2–LiCl eutectic melt (xLiCl = 72 mol%).

Table 1 Best-fitting parameters of Kc, Ksp, and initial $x_{\textit{O}^{2 - }}$ at different temperatures in MgCl2–LiCl eutectic melt.

3.2 Composition influence of the melt on equilibrium constant

It was reported that Kc value related to the composition of the molten salt at fixed temperature.17) In order to illustrate the influence of the composition of the melt on the Kc value, melts content with different ratios of LiCl were used. The results are shown in Fig. 4. It can be seen that Kc increased with the increase of mole fraction of LiCl in melt, which suggests that the thermodynamic stability of Ti3+ complex increased.

Fig. 4

The relationship between molar fraction of LiCl in molten MgCl2–LiCl and equilibrium constant at 1023 K.

As far as we know, the molten salts are fully made up of cations and anions. And here ions can be classified into the free ions and complex ions. It can not avoid the illustration of interaction of cations and anions when taking about the stabilization of them. Hence, the polarization power (P) of component cations in the molten salt was employed to interpret the result. The ri and P values are shown in Table 2.

Table 2 Ionic radius and polarizing power of cations.

The relationship between Kc and P is shown in Fig. 5.

Fig. 5

The relationship between polarizing power of electrolyte and equilibrium constant at 1023 K.

It shows that the Kc values are decreased by the increasing of polarizing power of MgCl2–LiCl–TiClx molten salt, owing to the LiCl ratio decrease or the MgCl2 ratio increase, which means that the addition of LiCl ratio in the MgCl2–LiCl–TiClx in a high level makes the polarizing powers smaller, resulting in relative stabilization of Ti3+ complex. In alkali cation series, the ionic radius is in the order of Li+ < Na+ < K+ < Rb+ < Cs+, and the polarizing ability is in the inverse order. There is a similar trend of polarizing power in the alkaline earth cation series. Mg2+ attracts with Cl strongly. Hence, there could be strong interaction among Mg2+ and chloride ions surrounding the solute Ti3+. Besides, as the major components in the melt of MgCl2–LiCl–TiClx, Mg2+ and Li+ exhibit strong polarizing power in the alkali metal ion order and alkali earth metal ion order, respectively. To titanium ions, as the minority components, it is concluded that the Ti3+ complex is less stable in binary alkali and alkaline earth chloride mixtures with larger polarizing power, however, the case of Ti2+ in the salts is much stable. It was concluded by Song et al. that a stronger polarizing power of electrolyte brings out a less stability of $\text{TiCl}_{6}^{3 - }$ and smaller Kc value.17) The comparison of Kc values with previous studies was done in this work. The Kc values in molten LiCl–KCl, LiCl–CsCl are also shown in Fig. 5. It is clearly that Kc was proportional to P and a constant value of polarizing power corresponds with a constant Kc either in CsCl–LiCl, KCl–LiCl or MgCl2–LiCl at 1023 K. More importantly, the results obtained in this paper could be even extrapolated from previous works, because the Kc should be a constant value when polarizing power is constant.

4. Conclusions

The equilibrium among metallic titanium and titanium ions, 3Ti2+ = 2Ti3+ + Ti, in molten MgCl2–LiCl was evaluated by the best-fitting method. Results also show that the equilibrium constant, Kc, increased with the increase of temperature. The polarizing power was used to illustrate the influence of composition of the molten salt on the Kc value, and it shows that the Kc value is small while the polarizing power is strong regardless in CsCl–LiCl, KCl–LiCl or MgCl2–LiCl.


The authors thank supports from Collaborative Innovation Center of Henan Resources and Materials Industry, Zhengzhou University and Startup Research Fund of Zhengzhou University (No. 32210804). The authors are grateful to the National Natural Science Foundation of China (No. 51322402).

© 2019 The Japan Institute of Metals and Materials