Abstract
Titanium dioxide has been extensively studied in the rutile or anatase phase, while its high-pressure phases are less well-understood, despite that many are thought to have interesting optical, mechanical, and electrochemical properties. First-principles methods, such as density functional theory (DFT), are often used to compute the enthalpies of TiO2 phases at 0K, but they are expensive and, thus, impractical for long time scale and large system-size simulations at finite temperatures. On the other hand, cheap empirical potentials fail to capture the relative stabilities of various polymorphs. To model the thermodynamic behaviors of ambient and high-pressure phases of TiO2, we design an empirical model as a baseline and then train a machine learning potential based on the difference between the DFT data and the empirical model. This so-called Δ-learning potential contains long-range electrostatic interactions and predicts the 0K enthalpies of stable TiO2 phases that are in good agreement with DFT. We construct a pressure-temperature phase diagram of TiO2 in the range 0 < P < 70 GPa and 100 < T < 1500 K. We then simulate dynamic phase transition processes by compressing anatase at different temperatures. At 300K, we predominantly observe an anatase-to-baddeleyite transformation at about 20GPa via a martensitic two-step mechanism with a highly ordered and collective atomic motion. At 2000K, anatase can transform into cotunnite around 45-55GPa in a thermally activated and probabilistic manner, accompanied by diffusive movement of oxygen atoms. The pressures computed for these transitions show good agreement with experiments. Our results shed light on how to synthesize and stabilize high-pressure TiO2 phases, and our method is generally applicable to other functional materials with multiple polymorphs.
Highlights
Titanium dioxide is widely used in a range of industries as a white pigment and in biomedical applications, such as drug delivery.[1]
At 2000 K, anatase can transform into cotunnite around 45–55 GPa in a thermally activated and probabilistic manner, accompanied by diffusive movement of oxygen atoms
For problems that demand large system sizes and long simulation times, many studies utilize empirical potentials, such as the Matsui–Akaogi (MA) potential,[32] which has been shown to perform poorly compared to density functional theory (DFT), for example, the incorrect prediction of the ordering of the stable phases,[33] which contribute to the poor prediction of the TiO2 pressure–temperature phase diagram compared to DFT or experiments.[34]
Summary
Titanium dioxide is widely used in a range of industries as a white pigment and in biomedical applications, such as drug delivery.[1]. For problems that demand large system sizes and long simulation times, many studies utilize empirical potentials, such as the Matsui–Akaogi (MA) potential,[32] which has been shown to perform poorly compared to DFT, for example, the incorrect prediction of the ordering of the stable phases,[33] which contribute to the poor prediction of the TiO2 pressure–temperature phase diagram compared to DFT or experiments.[34]. We aim at understanding the highpressure phase behaviors of titanium dioxide, including the pressure–temperature phase diagram and the mechanism of solid–solid transitions. To this end, we trained a machine learning potential (MLP) to accurately model all known and unknown phases of titanium dioxide for pressures up to 70 GPa and temperatures up to 2000 K based on DFT but at orders of magnitude smaller computational cost. The Δ-learning potential is used to determine the relative metastability of the phases and investigate some of the phase transitions between anatase, baddeleyite, and cotunnite
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