Pressure-Induced Stabilization of 3D Hyperhoneycomb Li₂(Sn_1-xRu_x)O₃

Metal-ordered rock-salt oxides (e.g., AMO₂, A₂MO₃, A₃MO₄) exhibit diverse functionalities arising from cation ordering, yet their structural evolution is difficult to predict due to the lack of systematic design principles. For A₂MO₃ compounds, although two-dimensional (2D) honeycomb structures have been widely explored, the three-dimensional (3D) hyperhoneycomb phase is still rare, despite its appeal as a battery cathode and as a Kitaev spin-liquid candidate. Here, we report pressure-induced phase transitions of Li₂SnO₃, from the ambient-pressure honeycomb phase to a hyperhoneycomb phase at 3 GPa, and subsequently to a Li₂PbO₃-type phase at 8 GPa. By integrating analyses of octahedral connectivity and Madelung energy, together with machine-learning-assisted molecular dynamics simulations, we established the thermodynamic landscape governing these transitions. Specifically, the hyperhoneycomb structure becomes competitive with the honeycomb structure under pressure and is stabilized by elevated temperatures, whereas the Li₂PbO₃-type structure stabilizes only at high pressures. This framework rationalizes the entire sequence of observed pressure-induced phase transitions. Furthermore, the hyperhoneycomb phase is accessible across the entire solid solution of Li₂(Sn_1-xRu_x)O₃, although Ru-rich compositions require higher pressure. Remarkably, the phase-pure hyperhoneycomb x = 0.75 exhibits complete electrochemical lithium deintercalation. Given the prevalence of 2D oxides under ambient conditions, designing hyperhoneycomb phases via pressure highlights a hidden yet attractive chemical space of 3D polymorphs, offering new chemical landscapes and exotic functionalities.