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中国物理学会期刊

铅基钙钛矿铁电晶体高临界转变温度的机器学习研究

CSTR: 32037.14.aps.68.20190942

High critical transition temperature of lead-based perovskite ferroelectric crystals: A machine learning study

CSTR: 32037.14.aps.68.20190942
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  • 铁电材料由铁电相转化为顺电相的临界温度被称为居里温度, 是铁电材料的一个关键指标. 本文使用固溶体组成元素的基本物理性质等特征对不同组分和配比的铅基钙钛矿铁电固溶体进行了统一的描述, 采用岭回归、支持向量回归、极端随机森林回归等机器学习方法对铅基钙钛矿铁电固溶体的居里温度进行了学习. 使用交叉验证的方法对学习效果进行验证, 得到上述机器学习方法对材料居里温度的预测值与实验值之间的平均误差分别为14.4, 14.7, 16.1 K, 集成三种回归方法优化的模型在交叉验证中测得的平均误差为13.9 K. 在此基础上对超过20万种铅基钙钛矿的居里温度进行了预测, 给出了两种可能具有高居里温度的铁电材料.

     

    Ferroelectrics undergoes a reversible structural phase from the ferroelectric phase to the paraelectric phase when its temperature exceeds the critical temperature namely Curie temperature Tc. As ferro-paraelectric phase transition is always accompanied by heat-flow, dielectric and pyroelectric anomaly, the value of Tc is extremely important for ferroelectrics. In this paper, the Curie temperature of lead-based perovskite ferroelectric solid solution is studied by machine learning methods including kernel ridge regression (KRR), support vector regression (SVR) and extremely randomized trees regression (ETR). We collect the Tc values of 205 different lead-based perovskites from published experimental papers, both simple perovskites with only one type of B site ion and complex perovskites with up to 5 kinds of ions in B position such as PMN-PFN-PZT are gathered. The diversity of our dataset is guaranteed for the good generalization of our model in perovskite solid solution of different complexity. The features are constructed from the physical and chemical properties of the B site elements in corresponding materials. The weighted-average and variance of the elemental properties are calculated and fed to machine learning models. We use the 5 runs of ten fold cross-validation method to evaluate the machine learning models. The hyperparameters are also chosen carefully with the cross-validation to avoid over fitting. The radial basis function kernel is used in both KRR and SVR. The insensitive error in the SVR is set to be 4 which is comparable to the random error in experiment. From our cross-validation, we find that the mean average errors (MAEs) between the predicted and experimental values of the machine learning methods are 14.4 K, 14.7 K, and 16.1 K, respectively. And the root-mean-square errors (RMSEs) are 22.5 K, 23.4 K, 23.8 K, respectively. After the optimization and the evaluation, our three machine learning models are stacked together by averaging the output of each regression model and thus building an ensemble model. The MAE of the ensemble model is 13.9 K. The RMSE of the ensemble model is 21.4 K. The predicted values keep a correlation coefficient of 0.97 with the experimental values. From the variance reduction in ETR, we derive the importance of our features when determining the Curie temperatures. The five most important factors in our ETR model are " weighted-average thermal conductivity”, " weighted-average conductivity”, " variance of specific heat capacity”, " weighted-average element number”, and " weighted-average relative atomic displacement”. We predict the Curie temperatures higher than those of 200000 types of lead-based perovskites after being trained. Now, we provide two ferroelectric materials that may have high Curie temperatures: 0.02PbMn1/2Nb1/2O3-0.98PbTiO3 (0.02PMN-0.98PT) and 0.02PbGa1/2Nb1/2-0.02PbMn1/2Nb1/2O3-0.96PbTiO3 (0.02PGN-0.02PMN-0.96PT). The predicted Curie temperatures of them are 481 ℃ and 466 ℃, respectively.

     

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