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Slight distortions can cause dramatic changes in the properties of crystalline perovskite materials and their derivatives. Due to the numerous types of distortions and unclarified distortion-structure relations, a quantitative distortion manipulation for the desired crystalline phase of perovskite materials suitable for various application remains challenging. Here, by establishing parameter sets to systematically describe the types, magnitudes and positional relations involved in distortions, we are able to interpret the structural regulations and manipulation strategies in 7 reported crystal systems. Through the construction of distortion-phase-property functional curves, we further propose a paradigm to quantify the structural distortion manipulation for desired perovskite phases. Using the example of perovskite-like tungsten oxides, we successfully quantify their volume shrinkage and symmetry increase during lithiation. This work verifies that the complicated research and development of perovskite materials can be simplified into a mathematical problem solving process, which will inspire researchers with different backgrounds to participate, especially mathematicians and computer scientists.
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