The stability of three phases of TiCl 3 : a molecular dynamics approach

. Titanium is produced commercially by the Kroll process, which involves the magnesiothermic reduction of titanium tetrachloride (TiCl 4 ). However, this is not suitable for developing a continuous reduction process. Recently, there have been attempts to develop a new continuous titanium production process by magnesiothermic reduction of other subchlorides such as titanium trichloride. In this study, the DL_POLY code was employed to investigate the influence of temperature on TiCl 3 (α, β, γ). We found that the γ-phase is ordered, and all phases are spontaneous at 50 – 2000 K. The order of stability is β> α> γ, in agreement with other reported work. These findings suggest that TiCl 3 might be used as a potential medium in the titanium production process.


Introduction
Titanium has excellent properties such as good conductivity, non-magnetic property, nontoxicity, biocompatibility and excellent corrosion resistance [1]. This metal is significant in various industries, such as the medical and aerospace industries [2,3]. The metal and powder form of titanium can be produced through the Kroll process, which involves the reduction of TiCl4 with Mg or titanium scraps [4,5]. This results in the formation of titanium subchlorides, either titanium trichloride (TiCl3) or titanium dichloride (TiCl2) [5].
However, this process occurs extremely fast, with the formed titanium deposits firmly adhering to the reactor [6]. Some experimental studies have reported on the magnesiothermic reduction of TiCl2 or TiCl3 [4,5]. Despite the efforts made through experimental studies, some challenges are encountered that are not limited to the blockage of the supply pathway for magnesium and the method results in an incomplete reduction process [4]. The Kroll process is similar to the Hunter process, which involves the reduction of TiCl4 with Na and results in the formation of the TiCl2 titanium subchloride [7].
In addition, the TiCl2 and TiCl3 titanium subchlorides have catalytic applications such as in the production of polymers from α-olefins [8]. Furthermore, titanium subchlorides as a feed material are advantageous since the heat produced by titanium subchloride reduction is reported to be significantly less than that produced by the reduction of TiCl4; thus, a (semi-) continuous process can be designed [4].
In this paper, we employ a molecular dynamics approach to understand the titanium formation process. We report on the diffusion coefficient, entropy and Gibbs free energy for the α, β and γ phases. The paper is organised in the following manner: Section 2 provides the methodology; the diffusion coefficient, entropy and Gibbs free energy are presented and discussed in Section 3; and lastly, the conclusion is provided in section 4.

Methodology
The TiCl3 structures were validated using the general utility lattice program (GULP) code [9]. This code supports molecular dynamics and geometry optimisation of clusters and molecules using a wide range of potential models. The equilibrium lattice parameters were calculated as a=b=6.11Å, c= 4.15 Å for P-31m, a=b=5.03 Å, c=5.95 Å for P63/mcm and a=b=5.28 Å, c= 12.78 Å for P3112. Molecular dynamics simulations were performed using DL_POLY code [10,11] with an NVT ensemble employing the Nosé-Hoover thermostat and barostat. The code may be used to understand materials' stability, reactivity, and structure. All temperature dependence calculations were performed on the (3x3) supercell with 5832 atoms for P-31m and P63/mcm structures, and 5176 atoms for P3112 structure. A radial cutoff of 9.95 Å was used, and the time step was set at 1e -6 ns employing a simulation time of 200 ps.

Results and discussion
The diffusion coefficient, entropy and Gibbs free energy were investigated for the P-31m (αphase), P63/mcm (β-phase) and P3112 (γ-phase) space groups of TiCl3. Firstly, we discuss the diffusion coefficient (DC) for the structures. This was done to understand the motion of Ti and Cl in the structures and trace the trajectories of these ions. Secondly, the entropy results will be discussed. This property is used to understand the effect of temperature on the atoms in the structures, i.e., atom disorder and randomness. Finally, the Gibbs free energy is estimated to determine the stability and equilibrium conditions of the structures. Figure 1 shows the diffusion coefficient plot for P-31m, P63/mcm and P3112 structures. This was done to compare the DC rate of the three structures as a function of temperature. The P-31m and P63/mcm curves show an exponential increase in the DC rate as temperature increases. However, the P3112 system depicts no atomic activity as a function of temperature, i.e., the diffusivity/diffusion rate reverts to zero for all temperatures. It is observed that the Ti-Cl DC curves for the structures are similar and coincide at 50 K -1100 K, however, at different DC rates. At 1100 -2000 K, the P-31m structure diffuses faster than the P63/mcm and P3112 structures. These observations reveal the diffusion rate order as; DCP-31m>DCP63/mcm>DCP3112. This could result from the molecular weight of the structures, which suggests that P-31m has a lower molecular weight than the other two structures. Figure 2 depicts the entropy of the P-31m, P63/mcm and P3112 structures at the temperature range of 50 -2000 K. It is to be noted that negative entropy indicates a decrease in the disorder of atoms whilst a positive entropy indicates an increase in disorder [12]. The P-31m structure shows an increase in the disorder of atoms at 800 K. At 50 -700 K and 900 -2000 K, the atoms are ordered. This is indicated by the zero entropy values. The P63/mcm structure (β-phase) shows a decrease in the disorder of atoms at 100 K and an increase at 600 -700 K. Atoms are ordered in the temperature range of 200 -500 K and 800 -2000 K. For the P3112 structure, the atoms are ordered at 200 -800 K and 1000 -2000 K. There is a decrease in the disorder of atoms at 50 -100 K and 900 K. The observed positive entropy suggests a phase transition as atoms are free to move. This suggests possible melting at 800 K for α-phase and at 600 -700 K for β-phase.

Gibbs free energy
The Gibbs free energy was used to characterise the structures, as shown in figure 3. We observe a linear increase in the Gibbs free energy with increased temperature. The Gibbs free energy values are negative for all the structures at 50 -2000 K. This suggests that reactions in the structures are spontaneous (exothermic). The Gibbs free energy is also used to estimate the stability of the phases. We note the order of stability of the phases as β(P63/mcm)>α(P-31m)>γ(P3112) which makes the P3112 structure thermodynamically unfavourable. This is in agreement with other reported work [13].

Conclusion
We employed molecular dynamics to investigate the temperature dependence of three phases of TiCl3 at different temperatures. The results revealed that diffusion rate of P-31m structure is higher than that of P63/mcm and P3112 systems. Results from the entropy calculations showed that there is a degree of ordering in the atoms at higher temperatures (1000 -2000 K). The Gibbs free energy display an exothermic behaviour, and spontaneity decreases with an increase in temperature. Furthermore, the findings suggest that TiCl3 can be used as a potential medium in titanium production processes.