Fig. 2: PolymorphGen unveils dynamic phase transitions across crystal systems.

a Snapshots of MgSiO₃ configurations²⁷ from multithermal multibaric simulations, including perovskite, defective perovskite, liquid-crystal interface, and liquid structures, are visualized based on energy states, with dark hues indicating low-energy crystalline phases and light hues indicating high-energy disordered states. Inset atomic structures are coloured by element: orange‑yellow for Mg, blue for Si, and red for O. b Snapshots of the solid-solid phase transition in Ti₃O₅²⁸, encompassing β, λ, and α crystalline phases, are visualized based on energy states, with dark hues indicating low-energy crystalline phases and light hues indicating high-energy disordered states, while ellipses highlight the regions of transition states TS¹ and TS², as well as configurations sampled by metadynamics. Ellipses are for visual guidance only, highlighting regions identified with additional energy information and do not represent automatic clustering from the entropy-symmetry landscape. Inset atomic structures are coloured by element: blue for Ti and red for O. c PolymorphGen generated and experimental³² structure factor S(Q) of paracrystalline diamond. Inset: The crystal and entropy view of the paracrystalline diamond model generated by PolymorphGen. HD, hexagonal diamond; CD, cubic diamond. d Comparison of the relative frequency distribution of the number of atoms in paracrystalline diamond structures generated by PolymorphGen and MD. e Snapshots of graphite-to-diamond configurations generated by PolymorphGen, visualized based on energy states. The distribution reveals distinct regions corresponding to the graphite (Gr) phase, other phase, CD phase, Gr-other transition phase, and Gr-CD transition phase. Inset atomic structures are coloured by structural type: purple for graphene, dark grey for other, blue for cubic diamond, and cyan for cubic diamond (1st neighbour). f Energy profile of graphite-to-diamond transformation pathways from PolymorphGen compared to the nudged elastic band (NEB) method. Inset: Typical structures of Path I and Path II. Source data are provided as a Source Data file.