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

TL;DR

This study develops a machine learning potential for TiO$_2$ that accurately models high-pressure phases and phase transitions, enabling efficient simulations of thermodynamic behaviors and dynamic transformations at finite temperatures.

Contribution

We introduce a $ riangle$-learning potential combining empirical and DFT data to accurately predict TiO$_2$ phase behaviors under high pressure and temperature.

Findings

Accurate phase diagram of TiO$_2$ from 0 to 70 GPa and 100 to 1500 K.

Observation of anatase-to-baddeleyite transformation at 20 GPa.

Identification of cotunnite formation at 45-55 GPa at high temperature.

Abstract

Titanium dioxide has been extensively studied in the rutile or anatase phases, 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 TiO$_2$ phases at 0~K, 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 stablities of the various polymorphs. To model the thermodynamic behaviors of ambient and high-pressure phases of TiO$_2$, 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 $\Delta$-learning potential contains long-range electrostatic interactions, and predicts the 0~K enthalpies of stable TiO$_2$ phases that are in good agreement with DFT. We construct a pressure-temperature phase diagram of TiO$_2$ 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 300~K, we observe predominantly anatase-to-baddeleyite transformation at about 20~GPa, via a martensitic two-step mechanism with highly ordered and collective atomic motion. 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. The pressures computed for these transitions show good agreement with experiments. Our results shed light on how to synthesize and stabilize high-pressure TiO$_2$ phases, and our method is generally applicable to other functional materials with multiple polymorphs.