基于机器学习的BiFeO_(3)-PbTiO_(3)-BaTiO_(3)固溶体居里温度预测

Curie Temperature Prediction of BiFeO_(3)-PbTiO_(3)-BaTiO_(3) Solid Solution Based on Machine Learning

钙钛矿(ABO_(3))型压电陶瓷的发展已有几十年历史,现存有大量数据,从这些数据中寻找出材料结构与性能之间的关系很有意义。本工作收集了BiFeO_(3)-PbTiO_(3)-BaTiO_(3)钙钛矿型压电陶瓷居里温度(Tc)实验数据,通过机器学习,构建钙钛矿型压电陶瓷Tc的预测模型。热力学角度,Tc与约合质量符合二次多项式关系,但偏差较大。选择元素信息、物理量、空间群编号等基础描述符,利用基于压缩感知原理的SISSO(Sure Independence Screening and Sparsifying Operator)方法进行机器学习,找出了Tc与成分之间的相关性。比较不同描述符在不同维度上的均方根误差RMSE(Root Mean Square Error),发现描述符越多、越基础,维数越大、RMSE越小。同时比较相同个数描述符在同一维度下的RMSE,用约合质量、A位和B位的离子半径比、A位和B位的未填充电子数比和Ba、Pb、Bi的元素含量等六个描述符构建出最优的四维模型,其RMSE为0.59℃,最大绝对误差(MaxAE)为1.38,℃外部测试的平均相对误差MRE(Mean Relative Error)为1.00%。结果表明,利用SISSO可以进行有限样本钙钛矿型压电陶瓷Tc的机器学习预测。

Perovskite(ABO_(3))piezoceramics have been developed for several decades,and there are a lot of data available.It is of great significance to find relationships between structure and properties of materials from these data.In this work,experimental data of Curie temperature(Tc)of BiFeO_(3)-PbTiO_(3)-BaTiO_(3) solid solution of perovskite piezoelectric ceramics was collected to build the model to predict the Tc.From the perspective of thermodynamics,the quadratic polynomial relationship between Tc and reduced mass was introduced but the deviation was relatively large.More descriptors(including element information,physical quantities,space groups number)and SISSO(Sure Independence Screening and Sparsifying Operator)were used for machine learning to find the correlation between Tc and components.Comparing the root mean square error(RMSE)of different descriptors and dimensions,it's found that more descriptors,more fundamental the descriptors are,and larger dimension will result in smaller RMSE to be used.Meanwhile,RMSE of the same number of descriptors in the same dimension are compared.The optimal four-dimensional model is build using six descriptors:reduced mass,the ratio of A-and B-site ion radii,the ratio of A-and B-site unfilled electrons and element contents of Ba,Pb and Bi.RMSE and maximum absolute error(MaxAE)of our model are 0.59℃and 1.38℃,respectively.The average relative error(MRE)of external test is 1.00%.Our results indicate that SISSO machine learning based on limited samples is suitable for the predication of Tc of perovskite piezoelectric ceramics.