基于机器学习的BiFeO3-PbTiO3-BaTiO3固溶体居里温度预测
Curie Temperature Prediction of BiFeO3-PbTiO3-BaTiO3 Solid Solution Based on Machine Learning
图 & 表
图 1. ABO3钙钛矿结构示意图
Fig. 1. Schematic diagram of ABO3 perovskite structure
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图 2. Tc与μ和μ*A/B的关系
Fig. 2. Relationship between Tc and μ or μ*A/B
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图 3. Tc与候选描述符的相关性
Fig. 3. Correlations between the Tc and the candidate descriptors
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图 4. 不同运算方式下μ和μ*A/B随维度变化的RMSE和MaxAE
Fig. 4. RMSE and MaxAE of μ and μ*A/B varied with dimension under different operation modes
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图 5. 采用两个描述符(a)和三个描述符(b)拟合结果的RMSE和MaxAE随维度的变化
Fig. 5. RMSE and MaxAE of two descriptors (a) and three descriptors (b) as a function of dimension
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图 6. 描述符的变化和模型维度对拟合结果RMSE和MaxAE的影响
Fig. 6. Effects of the changes of descriptor and model dimension on the RMSE and MaxAE
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图 7. 训练集(黑色方块)和测试集(红色圆形)的实验Tc与预测Tc
Fig. 7. Experimental Tc and prediction Tc for training set (black square) and test set (red circle)
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表 1基础描述符及其物理意义
Table1. Basic descriptor and related physical meaning
| Feature | Name | Physical attributes |
|---|
| μ | Reduced mass | Reduced mass of atoms | | A/B | Ionic radius | Shannon ion radius | | A/B_C | Covalent radius | The covalent bond radius of an atom | | A/B_E | Electronegativity | Electronegativity of atoms | | A/B_NV | NValence | The number of electrons of unfilled orbitals | | A/B_NU | NUfilled | The number of electrons of unfilled orbitals | | A/B_S | Space group numbering | The serial number of the element's space group in the space group table | | Ti,Fe,Ba,Pb,Bi | Element content | Element content ratio of metal ions |
|
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表 2调整描述符参数后的测试集
Table2. The test sets after adjusting descriptor parameters
| Sample | Tc/℃ (y)
| μʹ (x1)
| A/Bʹ (x2)
| A/B_NU (x3)
| Ba (x4)
| Pb (x5)
| Bi (x6)
|
|---|
| Bi0.62Pb0.23Ba0.15Fe0.62Ti0.38O3 | 547 | 0.2821 | 0.3882 | 0.5036 | 0.0750 | 0.1150 | 0.3100 | | Bi0.6Pb0.25Ba0.15Fe0.6Ti0.4O3 | 540 | 0.2690 | 0.4606 | 0.5000 | 0.0750 | 0.1250 | 0.3000 | | Bi0.54Pb0.31Ba0.15Fe0.54Ti0.46O3 | 502 | 0.2295 | 0.6789 | 0.4897 | 0.0750 | 0.1550 | 0.2700 |
|
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表 3外部验证集结果
Table3. Results of external verification set
| Sample | Experim-ental Tc/℃
| Predi-ction Tc/℃
| Abso-lute error/℃
| Rela-tive-error/%
|
|---|
| Bi0.62Pb0.23Ba0.15Fe0.62Ti0.38O3 | 547 | 544.91 | 2.09 | 0.38 | | Bi0.6Pb0.25Ba0.15Fe0.6Ti0.4O3 | 540 | 536.12 | 3.88 | 0.72 | | Bi0.54Pb0.31Ba0.15Fe0.54Ti0.46O3 | 502 | 492.52 | 9.48 | 1.89 |
|
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焦志翔, 贾帆豪, 王永晨, 陈建国, 任伟, 程晋荣. 基于机器学习的BiFeO3-PbTiO3-BaTiO3固溶体居里温度预测[J]. 无机材料学报, 2022, 37(12): 1321. Zhixiang JIAO, Fanhao JIA, Yongchen WANG, Jianguo CHEN, Wei REN, Jinrong CHENG. Curie Temperature Prediction of BiFeO3-PbTiO3-BaTiO3 Solid Solution Based on Machine Learning[J]. Journal of Inorganic Materials, 2022, 37(12): 1321.
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