Easy-to-use model to reveal the nature of octahedral rotation transformations in perovskites

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Octahedral rotation in perovskites and their transformations have a profound influence on their properties. In this work, an easy-to-use model is proposed to reveal the nature of the oxygen octahedral rotation (OOR) changing behaviors at interfacial regions. Different from first principle simulations and symmetry analysis, we establish a general elastic model with a six angle symbol system based on the intrinsic geometry characteristics of the oxygen octahedra network. In the light of the elastic energy generated by octahedral tilting mismatches at interfaces, the systematic analysis is conducted on the changing behavior and mechanism of octahedral rotation with different OOR patterns. Consequently, it is found that there are two forms of basic component angle changing across the interface, i.e. abrupt change and gradual change, depending on the relationship between the directions of the rotational axis of basic component angles and the interface. Furthermore, the coexistence of two forms at the same interface and a special case for gradual change are investigated, which could hardly be identified or predicted by other models and analysis established previously. Generally, the model can be applied to interpret and predict the octahedral rotation changing behavior in perovskites, involving film/substrate heterostructure in epitaxial synthesized thin films, domain boundaries, etc., which agree with the practical examples. Although the model has its limitations due to the complex chemical configuration in 3D oxygen octahedra network, it is expected to be universal for perovskites. Taking the advantage of mathematical simplicity, this model can be a powerful tool for interfacial engineering in perovskites.