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近年来,软晶格被认为是钙钛矿材料实现缺陷容忍性的主要物理来源,体模量则作为晶格"软硬度"的关键衡量指标。本文针对立方钙钛矿体系,基于SISSO与VS-SISSO方法,构建了两类低维、物理可解释性强的体模量预测模型。首先,基于共价半径、熔点和体积等结构和热力学特征构建的热-结构耦合描述符模型,在测试集上实现了RMSE=7.41 GPa,R2=97.8%的良好预测性能;进一步引入电负性、原子价态与未配对电子数等电子层级特征后,构建了电子-热-结构三重耦合描述符模型,预测精度显著提升,在测试集上RMSE降至5.34 GPa,R2提升至98.35%。基于该模型,我们对超过10,000个卤族和硫族立方钙钛矿进行了高通量预测,筛选出约170种体模量位于10-20 GPa区间、与Pb-I钙钛矿相近的候选体系。研究结果为软晶格机制在无铅体系中的适用性提供了初步支持,并为高通量筛选具缺陷容忍潜力的稳定无铅钙钛矿材料提供了理论依据与数据支撑。本文数据集可在(科学数据银行)数据库https://www.scidb.cn/s/A3IBBn中访问获取。In recent years, soft lattices have been considered a primary physical origin of defect tolerance in lead-halide perovskite materials, with bulk modulus serving as a key indicator of lattice "softness." In this work, we focus on cubic perovskites and construct a dataset of bulk moduli for 213 compounds based on DFT calculations. A total of 138 features were compiled, including 132 statistical features extracted using the Matminer toolkit and 6 manually selected elemental descriptors. Four conventional machine learning regression models (RF, SVR, KRR, and EXR) were employed for prediction, among which the SVR model showed the best performance, achieving a test-set RMSE of 7.35 GPa and R2 of 97.86%. Feature importance analysis revealed that thermodynamic-structural features such as melting point, covalent radius, and atomic volume play dominant roles in determining bulk modulus. Based on the 12 most important features, a thermodynamic-structural coupling descriptor was constructed using the SISSO method, yielding a test-set RMSE of 7.41 GPa and R2 of 97.80%. The resulting descriptor indicates that bulk modulus is proportional to melting point and inversely proportional to atomic volume. Furthermore, the VS-SISSO method was applied by incorporating a random subset selection and iterative variable screening strategy, enabling the selection of electronic-level features such as electronegativity, valence state, and number of unpaired electrons. The resulting electronic-thermodynamic-structural coupling descriptor further improved prediction accuracy, reaching an RMSE of 5.34 GPa and R2 of 98.35% on the test set. Notably, this model effectively distinguishes chalcogen-based (divalent) from halogen-based (monovalent) perovskites in terms of their bulk moduli due to differences in valence states. Based on this model, high-throughput screening was performed on over 10,000 cubic chalcogenide and halide perovskites, identifying approximately 170 lead-free candidates with bulk moduli in the range of 10-20 GPa, comparable to Pb-I perovskites. These results provide preliminary evidence supporting the applicability of the soft-lattice mechanism in lead-free systems and offer theoretical guidance and data support for the high-throughput discovery of stable, defect-tolerant, lead-free perovskite materials.The dataset for this paper is available in the (Scientific Data Bank) database https://www.scidb.cn/s/A3IBBn.
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Keywords:
- Bulk modulus /
- Defect tolerance /
- Soft lattice /
- SISSO /
- VS-SISSO /
- Perovskite /
- Interpretable machine learning
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