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

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.