Distortion manipulation emerges as an efficient approach to obtain desired perovskite phases for various applications. In part Ⅰ of this study, we propose a paradigm to quantify the structural distortion manipulation, which enables us to obtain desired perovskite phases by translating relevant materials research into a single mathematical question. As part Ⅱ of this continuous study, we construct normalized structures by introducing all possible couplings of dominant distortions into a cubic supercell and then compare them with variously shaped primitive/conventional cells known in the database. The structure comparison demonstrates that distortions are the only cause for phase and property variations. This confirms that our proposed distortion parameters can be directly used to construct phases, providing theoretical support for the paradigm in Part Ⅰ. Given the limited number of distortion types, we identify that the positional relations involved in distortion arrangements and couplings are the keys to describe numerous phases. Furtherly, a three-step workflow is proposed with core contents related to the positional relation, distortion hierarchy, and distortion-component-generation ordering in spatial dimension, respectively. The definition basis and value changes of distortion/model parameters in this workflow illustration provide guidelines about how to reveal the logic behind the perovskite phase evolution.

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.

Fe-X-Ni (X = Cr, W and V) combinatorial thin-film (~100 nm thick) materials chips covering the full composition range of ternary systems were fabricated. The crystal structure distribution was mapped by micro-beam X-ray diffractometers (XRD) and the magnetic hysteresis loops over the chip were characterized by a high-throughput magneto-optical Kerr effect (HT-MOKE) system to establish the composition-phase-magnetic properties relationships. The results showed that saturation magnetization for all systems has a strong dependency on alloying composition, and decreases with increasing dopped elements content as a general trend. Although the trend of saturation magnetization in bulk is in good agreement with that from thin films, all bulk samples show almost no coercivity, attributable to the much smaller grain size, and stronger texture in thin-film samples. Comparing the Fe-X-Ni systems under a similar condition, in the out-of-plane, Cr alloying obtained the largest coercivity (~400 mT) followed by W alloying (~300 mT) and then V alloying (~200 mT). We suggest that alloying with different elements leads to the diverse orientation and crystallinity of the fcc phase resulting in different magnetic properties. Meanwhile, the effect of heat treatment on magnetic properties indicates that saturation magnetization is more closely related to the duration of heat treatment.