Phase behavior of empirical potentials of titanium dioxide

Abstract

In recent years, several relatively similar empirical models of titanium dioxide have been proposed as reparameterisations of the potential of Matsui and Akaogi, with the Buckingham interaction replaced by a Lennard-Jones interaction. However, because of the steepness of the repulsive region of the Lennard-Jones potential, such reparameterised models result in rather different mechanical and thermodynamic properties compared to the original potential. Here, we use free-energy calculations based on the Einstein crystal method to compute the phase diagram of both the Matsui-Akaogi potential and one of its Lennard-Jones-based reparameterisations. Both potentials are able to support a large number of distinct crystalline polymorphs of titanium dioxide that have been observed in experiment, but the regions of thermodynamic stability of the individual phases are significantly different from one another. Moreover, neither potential results in phase behaviour that is fully consistent with the available experimental evidence. arXiv:1908.03497v1 [cond-mat.stat-mech]

Predicting the phase diagram of titanium dioxide with random search and pattern recognition

“…For RSS and accurate free energy calculations, we focus on the simple MA empirical pair potential for TiO 2 15 because of its low computational cost. 9 We performed RSS at 0 GPa, 20 GPa, 40 GPa and 60 GPa using the AIRSS 16,17 package interfaced with Lammps. 18 For each RSS run, we first chose a reasonable cell shape at random, and added 2, 3, 4, 6, 8, 9 or 12 formula units TiO 2 of into the simulation cell at random positions while keeping the initial density of the cell close to the typical density range of this system.…”

“…Specifically, we computed the chemical potentials of the polymorphs using Frenkel-Ladd integration 8,19 and subsequent TI along isobars and isotherms, as detailed in ref. 9.…”

“…To obtain a more accurate estimate of S, one can use the harmonic approximation, 6 or if resources allow, the TI method. 6,8,9…”

“…Although Gibbs energies can be computed using free-energy methods such as thermodynamic integration (TI), 6,8,9 such calculations are non-trivial and usually require long simulations, making them both expensive and tedious if one wants to use the PES computed from first-principles methods such as density-functional theory (DFT). 10 Moreover, crystal-structure prediction schemes typically result in a multitude of structures.…”

High-pressure phase behaviors of titanium dioxide revealed by a $Δ$-learning potential

“…For problems that demand large system sizes and long simulation times, many studies utilise empirical potentials such as the Matsui-Akaogi (MA) potential 28 , which has been shown to perform poorly compared to DFT, for example the incorrect prediction of the ordering of the stable phases 29 , which contribute to the poor prediction of the TiO 2 pressure-temperature phase diagram compared to DFT or experiments 30 . Recently, some machine learning potentials of titanium dioxide have also been developed 31 .…”