Fig. 2: Predicted metastable phases and their potential energy surface.
a Structures of β-Ti3O5, ββλ-stacking metastable phase, βλλ-stacking metastable phase and λ-Ti3O5, respectively. The light yellow and purple colors represent the β-like and λ-like structural motifs, respectively. The blue and red balls represent Ti and O atoms, respectively. b Free-energy surface (in electron volt per formula unit, i.e., eV/f.u.) computed from metadynamics simulations at 600 K and 0 GPa. For definition of collective variables di (i = 1, 2 and 3), we refer to “Methods" and Supplementary Fig. 6a. Note that ββλ, λββ, and βλβ are symmetry-equivalent structures, and similarly, βλλ, λβλ, and λλβ are symmetry-equivalent structures. c, Energy-volume curves predicted by DFT (circles and triangles) and machine-learning potential (solid lines) at 0 K and 0 GPa. d Potential energy surface (PES) obtained at 600 K and 0 GPa as a function of employed collective variable. The black dashed line denotes the PES for a concerted β−λ phase transition, whereas the green solid lines denotes the PES for the transition pathway through intermediate metastable phases (corresponding to arrows in b). Source data are provided as a Source Data file. The structure models used are provided in Supplementary Data 1.
