Curie Temperature Prediction of BiFeO3-PbTiO3-BaTiO3 Solid Solution Based on Machine Learning

doi:10.15541/jim20220080

Abstract

Abstract:

Perovskite (ABO₃) 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 (T_c) of BiFeO₃-PbTiO₃-BaTiO₃ solid solution of perovskite piezoelectric ceramics was collected to build the model to predict the T_c. From the perspective of thermodynamics, the quadratic polynomial relationship between T_c 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 T_c 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 T_c of perovskite piezoelectric ceramics.

Key words: perovskite piezoelectric ceramics, machine learning, Curie temperature, SISSO

CLC Number:

TQ174

JIAO Zhixiang, JIA Fanhao, WANG Yongchen, CHEN Jianguo, REN Wei, CHENG Jinrong. Curie Temperature Prediction of BiFeO₃-PbTiO₃-BaTiO₃ Solid Solution Based on Machine Learning[J]. Journal of Inorganic Materials, 2022, 37(12): 1321-1328.

Figures/Tables 10

Fig. 1 Schematic diagram of ABO3 perovskite structure

Table 1 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

Fig. 2 Relationship between Tc and μ or μ*A/B

Fig. 3 Correlations between the Tc and the candidate descriptors

Fig. 4 RMSE and MaxAE of μ and μ*A/B varied with dimension under different operation modes (a, c) use operation mode 1; (b, d) use operation mode 2; (a, b) use the descriptor μ; (c, d) use the descriptor μ*A/B

Fig. 5 RMSE and MaxAE of two descriptors (a) and three descriptors (b) as a function of dimension

Fig. 6 Effects of the changes of descriptor and model dimension on the RMSE and MaxAE (a) μ and A/B are the first two descriptors, and the third descriptor changes; (b) μ, A/B, Ba, Pb, and Bi are the first five descriptors, and the sixth descriptor changes; (c) μ and A/B are the first two descriptors and the third to seventh descriptors are introduced one by one. (d) Effect of the change of the dimension of the model fitted by six finally selected descriptors (μ, A/B, A/B_NU, Ba, Pb, and Bi) on RMSE and MaxAE

Table 2 The test sets after adjusting descriptor parameters

Sample	T_c/℃ (y)	μʹ (x₁)	A/Bʹ (x₂)	A/B_NU (x₃)	Ba (x₄)	Pb (x₅)	Bi (x₆)
Bi_0.62Pb_0.23Ba_0.15Fe_0.62Ti_0.38O₃	547	0.2821	0.3882	0.5036	0.0750	0.1150	0.3100
Bi_0.6Pb_0.25Ba_0.15Fe_0.6Ti_0.4O₃	540	0.2690	0.4606	0.5000	0.0750	0.1250	0.3000
Bi_0.54Pb_0.31Ba_0.15Fe_0.54Ti_0.46O₃	502	0.2295	0.6789	0.4897	0.0750	0.1550	0.2700

Table 3 Results of external verification set

Sample	Experim- ental T_c/℃	Predi- ction T_c/℃	Abso- lute error/℃	Rela- tive- error/%
Bi_0.62Pb_0.23Ba_0.15Fe_0.62Ti_0.38O₃	547	544.91	2.09	0.38
Bi_0.6Pb_0.25Ba_0.15Fe_0.6Ti_0.4O₃	540	536.12	3.88	0.72
Bi_0.54Pb_0.31Ba_0.15Fe_0.54Ti_0.46O₃	502	492.52	9.48	1.89

Fig 7 Experimental Tc and prediction Tc for training set (black square) and test set (red circle)

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Curie Temperature Prediction of BiFeO₃-PbTiO₃-BaTiO₃ Solid Solution Based on Machine Learning

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