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Emerging wurtzite ferroelectric materials have aroused significant interest due to their high spontaneous polarization magnitude (Ps). However, there is a limited understanding of the key factors that influence Ps. Herein, a machine-learning regression model is developed to predict the Ps using a dataset consisting of 40 binary and 89 simple ternary wurtzite materials. Features are extracted based on elemental properties, crystal parameters and electronic properties. Feature selection is carried out using the Boruta algorithm and distance correlation analysis, resulting in a comprehensive machine learning model. Furthermore, SHapley Additive exPlanations analysis identifies the average cation-ion potential (IPi_Aave) and the lattice parameter (a) as significant determinants of Ps, with IPi_Aave having the most prominent effect. A lower IPi_Aave corresponds to a lower Ps in the material. Additionally, a exhibits an approximately negative correlation with Ps. This multifactorial analysis fills the existing gap in understanding the determinants of Ps, and makes a foundational contribution to the evaluating emerging wurtzite materials and expediting the discovery of high-performance ferroelectric materials. The dataset in this work can be accessed in the Scientific Data Bank https://www.doi.org/10.57760/sciencedb.j00213.00073 .-
Keywords:
- wurtzite ferroelectric materials /
- spontaneous polarization magnitude /
- machine learning /
- first principles methods
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图 1 (a)初始筛选元素在元素周期表内的体现, 其中蓝色代表阳离子, 橙色代表阴离子; (b)元素筛选的条件和具体流程; (c) 二元纤锌矿材料合理的元素组成
Figure 1. (a) The representation of initial screening elements in the periodic table, where blue represents cations and orange represents anions; (b) the conditions and specific process for screening; (c) reasonable composition elements of binary wurtzite materials obtained through screening.
图 2 (a) AB, (b) A1A2B, (c) AB1B2体系的Ps数值; (d)单价、二价、三价阳离子和整个数据集的箱线图
Figure 2. Ps of (a) AB, (b) A1A2B, and (c) AB1B2 systems; (d) box plots of Ps for monovalent, divalent, and trivalent cations as well as all systems.
图 3 四面体结构参数示意图
Figure 3. Schematic diagram of tetrahedral structure parameters.
图 4 曲线路径示意图
Figure 4. Schematic diagram of curve path.
图 5 (a) 元素基本属性特征; (b) 晶体结构特征; (c) DC特征; (d) COHP, BC, ELF特征; (e) DOS特征的组内距离自相关系数热图; (f) 保留特征的组间距离自相关系数热图
Figure 5. Heatmap of distance correlation coefficients for (a) element properties; (b) crystal parameters; (c) DC properties; (d) COHP, BC, ELF properties; (e) DOS properties; (f) feature preserving inter group distance autocorrelation coefficient heat map.
图 6 6种含105特征机器学习模型的(a) R2, (b) RMSE, (c) XGBR模型的预测散点图; 6种含10特征机器学习模型的(d) R2, (e)RMSE, (f) XGBR模型的预测散点图
Figure 6. (a) R2 and (b) RMSE values of six machine-learning models and (c) scatter plot of the XGBR model with 105 features; (d) R2 and (e) RMSE values of six machine-learning models and (f) scatter plot of the XGBR model with 10 features.
图 7 含10个特征XGBR模型的 (a) SHAP散点图和(b) SHAP特征重要性, (c) IPi_Aave, (d) a, (e) IPi_Bave特征的部分依赖图
Figure 7. (a) SHAP summary plot, (b) SHAP feature importance of XGBR model with 10 features; partial dependence plots for the top three important features of (c) IPi_Aave, (d)a, (e) IPi_Bave.
表 1 用于描述纤锌矿材料的特征类型——元素基本属性
Table 1. Parameters describing the characteristic types of wurtzite materials—Basic element attributes.
特征 定义 特征 定义 aN 原子序数 aM 相对原子质量 ICV ICSD数据库内晶体体积 aD 原子密度 X 电负性 VE 价电子 Rc 共价半径 Ri 离子半径 Ra 原子半径 IPi 离子势(VE/Ri) FIP 第一电离势 SIP 第二电离势 TIP 第三电离势 CP 化学势 FAE 自由原子能量 Men 门捷列夫数 
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表 3 用于描述纤锌矿材料的特征类型——四面体结构参数
Table 3. Parameters describing the characteristic types of wurtzite materials——Tetrahedral structure parameters.
特征 定义 特征 定义 COHP分析 ICa, ICe 轴向键与平向键键强 ICa-ICe 轴向键与平向键键强的差值 ICa/ICe 轴向键与平向键键强的比值 IC 四面体内平均键强 BC分析 AtV 原子体积 Bad 巴德电荷 DOS分析 Bc_tot 总能带中心 Bc_out 外层轨道的能带中心 Bw_tot 总能带宽度 Bw_out 外层轨道的能带宽度 Bs_tot 总能带偏度 Bs_out 外层轨道的能带偏度 Bk_tot 总能带峰度 Bk_out 外层轨道的能带峰度 ELF分析 ELF _Cat 阳离子位置的ELF值 ELF_Ani 阴离子位置的ELF值 ELF_dCA 阴阳离子位置ELF值的差值 ELF_Max ELF曲线峰值 ELF_MP ELF曲线峰值的位置 ELF_F ELF曲线半峰全宽 DC分析 DC_Cat 阳离子位置的DC值 DC_Ani 阴离子位置的DC值 DC_dCA 阴阳离子位置DC值的差值 DC_Max DC曲线峰值 DC_MP DC曲线峰值的位置 DC_F DC曲线半峰全宽
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表 2 用于描述纤锌矿材料的特征类型——晶体结构参数
Table 2. Parameters describing the characteristic types of wurtzite materials——Crystal structure parameters.
特征 定义 特征 定义 c, a 晶胞参数 c/a 晶胞参数比值 V 晶胞体积 S 晶胞底面积 H_tetra 四面体高度 V_tetra 四面体体积 d 阳离子到四面体底部的距离 μ 四面体内部曲折度(d/H_tetra) La, Le 轴向键与平向键键长 La-Le 轴向键与平向键键长的差值 La/Le 轴向键与平向键键长的比值 L 四面体内平均键长 Aa, Ae 轴向键与平向键键角 Aa-Ae 轴向键与平向键键角的差值 Aa/Ae 轴向键与平向键键角的比值 A 四面体内平均键角
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