Abstract
Multi-cation oxides have been extensively studied over the past decade for various solid-state applications. The source of their functionality lies in a wide compositional search space derived from countless cation combinations and diverse crystal structures formed in metal oxides. However, due to the vast space and complexity of structure control, material exploration has been limited to dispersed compositions under different synthesis conditions, hindering their systematic understanding and rational design. Here, a crystalline-phase map of multi-cation rare-earth titanates is reported, where three types of crystals, i.e., cubic and hexagonal, and orthorhombic phases, emerge depending on the composition and temperature and exhibit systematic changes. The crystal structures of each phase are thoroughly characterized with X-ray diffraction, electron microscopy, and first-principles calculations. The configurational entropies calculated from the crystallographic information support the phase-boundary shift between hexagonal and orthorhombic phases observed in the phase map. Further, a machine learning procedure is proposed for constructing the map from sparse experimental data, allowing predictive exploration for stable crystalline phases across a large compositional space. These findings may facilitate the design of multi-cation oxides with a desired structure dispersed in a large search space.