Exploring the Core-shell Structure of BaTiO₃-based Dielectric Ceramics Using Machine Learning Models and Interpretability Analysis

Abstract

A machine learning (ML)-based random forest (RF) classification model algorithm was employed to investigate the main factors affecting the formation of the core-shell structure of BaTiO₃-based ceramics and their interpretability was analyzed by using Shapley additive explanations (SHAP). An F1-score changed from 0.879 5 to 0.931 0, accuracy from 0.845 0 to 0.907 0, precision from 0.871 4 to 0.900 0, recall from 0.892 9 to 0.964 3, and ROC/AUC value of 0.97±0.03 was achieved by the RF classification with the optimal set of features containing only 5 features, demonstrating the high accuracy of our model and its high robustness. During the interpretability analysis of the model, it was found that the electronegativity, melting point, and sintering temperature of the dopant contribute highly to the formation of the core-shell structure, and based on these characteristics, specific ranges were delineated and twelve elements were finally obtained that metall the requirements, namely Si, Sc, Mn, Fe, Co, Ni, Pd, Er, Tm, Lu, Pa, and Cm. In the process of exploring the structure of the core-shell, the doping elements can be effectively localized to be selected by choosing the range of features.

Keywords

machine learning / BaTiO₃ / core-shell structure / random forest classifier

References

[1] Lu Y, Hao H, Zhang S, et al. Microstructure and Dielectric Characteristics of Nb₂O₅ Doped BaTiO₃-Bi(Zn_1/2Ti_1/2)O₃ Ceramics for Capacitor Applications[J]. Journal of the European Ceramic Society, 2017, 37(1): 123-128.

[2] Gong H, Wang X, Zhang S, et al. Grain Size Effect on Electrical and Reliability Characteristics of Modified Fine-Grained BaTiO₃ Ceramics for MLCCs[J]. Journal of the European Ceramic Society, 2014, 34(7): 1 733-1 739.

[3] Li JH, Wang SF, Hsu YF, et al. Effects of Sc₂O₃ and MgO Additions on the Dielectric Properties of BaTiO₃-Based X8R Materials[J]. Journal of Alloys and Compounds, 2018, 768: 122-129.

[4] Lai X, Hao H, Liu Z, et al. Structure and Dielectric Properties of MgO-Coated BaTiO₃ Ceramics[J]. Journal of Materials Science: Materials in Electronics, 2020, 31(11): 8 963-8 970.

[5] Zhang W, Jiang Y, Xiao M, et al. High DC-Bias Stability and Reliability in BaTiO₃-Based Multilayer Ceramic Capacitors: The Role of the Core-Shell Structure and the Electrode[J]. ACS Applied Materials & Interfaces, American Chemical Society, 2023

[6] Feng H, Tang L, Zeng G, et al. Core-Shell Nanomaterials: Applications in Energy Storage and Conversion[J]. Advances in Colloid and Interface Science, 2019, 267: 26-46.

[7] Hao H, Liu H, Zhang S, et al. Fabrication, Structure and Property of BaTiO₃-Based Dielectric Ceramics with a Multilayer Core-Shell Structure[J]. Scripta Materialia, 2012, 67(5): 451-454.

[8] Wu S, Zhu Z, Yao Z, et al. Compositionally Tunable High Temperature Mn-Doped BiFeO₃-BaTiO₃ Lead-Free Piezoceramics[J]. Journal of Materials Science: Materials in Electronics, 2023, 34(1): 36

[9] Wang J E, Baek C, Jung Y H, et al. Surface-to-Core Structure Evolution of Gradient BaTiO₃-Ba₁-xSr_xTiO₃ Core-Shell Nanoparticles[J]. Applied Surface Science, 2019, 487: 278-284.

[10] Xiao M, Zhen Y, Zhu C, et al. Effect of Ho-Dy Co-doping on the Electrical Properties and Reliability of BaTiO₃-Based Nanoceramics for Base Metal Electrode Multilayer Ceramic Capacitor[J]. Journal of the American Ceramic Society, 2023, 106(10): 5 898-5 906.

[11] Hsing IH, Chen TH. Dy-modified Barium Calcium Titanate Sintered in a Reducing Atmosphere: Crystal Structure, Microstructure, and Electrical Characteristics[J]. Ceramics International, 2022, 48(22): 33 315-33 322.

[12] Gong H, Wang X, Zhang S, et al. Influence of Sintering Temperature on Core-Shell Structure Evolution and Reliability in Dy Modified BaTiO₃ Dielectric Ceramics: Influence of Sintering Temperature on Core-Shell Structure[J]. Physica Status Solidi (a), 2014, 211(5): 1 213-1 218.

[13] Wang Y, Cui B, Liu Y, et al. Fabrication of Submicron La₂O₃-Coated BaTiO₃ Particles and Fine-Grained Ceramics with Temperature-Stable Dielectric Properties[J]. Scripta Materialia, 2014, 90–91: 49-52.

[14] Puli V S, Li P, Adireddy S, et al. Crystal Structure, Dielectric, Ferroelectric and Energy Storage Properties of La-Doped BaTiO₃ Semiconducting Ceramics[J]. Journal of Advanced Dielectrics, 2015, 05(03): 1 550 027

[15] Gong H, Wang X, Zhang S, et al. Synergistic Effect of Rare-Earth Elements on the Dielectric Properties and Reliability of BaTiO₃-Based Ceramics for Multilayer Ceramic Capacitors[J]. Materials Research Bulletin, 2016, 73: 233-239.

[16] Park KJ, Kim CH, Yoon YJ, et al. Doping Behaviors of Dysprosium, Yttrium and Holmium in BaTiO₃ Ceramics[J]. Journal of the European Ceramic Society, 2009, 29(9): 1 735-1 741.

[17] Zhang Y, Wang X, Kim J, et al. Effect of Rare Earth Oxide Content on Nanograined Base Metal Electrode Multilayer Ceramic Capacitor Powder Prepared by Aqueous Chemical Coating Method[J]. Japanese Journal of Applied Physics, 2013, 52(2R): 021 501

[18] Kishi H, Okino Y, Honda M, et al. The Effect of MgO and Rare-Earth Oxide on Formation Behavior of Core-Shell Structure in BaTiO₃[J]. Japanese Journal of Applied Physics, 1997, 36(9S): 5 954

[19] Kirianov A, Hagiwara T, Kishi H, et al. Effect of Ho/Mg Ratio on Formation of Core-Shell Structure in BaTiO₃ and on Dielectric Properties of BaTiO₃ Ceramics[J]. Japanese Journal of Applied Physics, 2002, 41(Part111B): 6 934-6 937.

[20] Huang X, Liu H, Hao H, et al. Microstructure Effect on Dielectric Properties of MgO-Doped BaTiO₃-BiYO₃ Ceramics[J]. Ceramics International, 2015, 41(6): 7 489-7 495.

[21] Chang CY, Wang WN, Huang CY. Effect of MgO and Y₂O₃ Doping on the Formation of Core-Shell Structure in BaTiO₃ Ceramics[J]. Journal of the American Ceramic Society, 2013, 96(8): 2 570-2 576.

[22] Jain T A, Chen C C, Fung K Z. Effects of Bi₄Ti₃O₁₂ Addition on the Microstructure and Dielectric Properties of Mn-Doped BaTiO₃-Based X8R Ceramics[J]. Journal of Alloys and Compounds, 2009, 476(1–2): 414-419.

[23] Jose R, Ramakrishna S. Materials 4.0: Materials Big Data Enabled Materials Discovery[J]. Applied Materials Today, 2018, 10: 127-132.

[24] Agrawal A, Choudhary A. Perspective: Materials Informatics and Big Data: Realization of the “Fourth Paradigm” of Science in Materials Science[J]. APL Materials, 2016, 4(5): 053 208

[25] Himanen L, Geurts A, Foster A S, et al. Data-Driven Materials Science: Status, Challenges, and Perspectives[J]. Advanced Science, 2019, 6(21): 1 900 808

[26] Kirklin S, Saal J E, Meredig B, et al. The Open Quantum Materials Database (OQMD): Assessing the Accuracy of DFT Formation Energies[J]. npj Computational Materials, 2015, 1(1): 15 010

[27] Spadaccini N, Hall S R. Extensions to the STAR File Syntax[J]. Journal of Chemical Information and Modeling, 2012, 52(8): 1 901-1 906.

[28] Baliyan A, Imai H. Machine Learning Based Analytical Framework for Automatic Hyperspectral Raman Analysis of Lithium-Ion Battery Electrodes[J]. Scientific Reports, 2019, 9(1): 18 241

[29] Jain A, Ong SP, Hautier G, et al. Commentary: The Materials Project: A Materials Genome Approach to Accelerating Materials Innovation[J]. APL Materials, 2013, 1(1): 011 002

[30] Liu Y, Niu C, Wang Z, et al. Machine Learning in Materials Genome Initiative: A Review[J]. Journal of Materials Science & Technology, 2020, 57: 113-122.

[31] Shen Z, Liu H, Shen Y, et al. Machine Learning in Energy Storage Materials[J]. Interdisciplinary Materials, 2022, 1(2): 175-195.

[32] Lv C, Zhou X, Zhong L, et al. Machine Learning: An Advanced Platform for Materials Development and State Prediction in Lithium-Ion Batteries[J]. Advanced Materials, 2022, 34(25): 2 101 474

[33] Yuan R, Xue D, Li J, et al. Disentangling the Effect of Doping Chemistry on the Energy Storage Properties of Barium Titanate Ferroelectrics Using Data Science Tools[J]. Journal of Materials Chemistry C, Royal Society of Chemistry, 2022, 10(10): 3 804-3 811.

[34] Lin X, Li C, Hao H, et al. Accelerated Search for ABO₃-Type the Electronic Contribution of Polycrystalline Dielectric Constants by Machine Learning[J]. Computational Materials Science, 2021, 193: 110 404.

[35] He Y, Yan W, Liu Y, et al. Searching High Dielectric Permittivity in Barium Titanate Based Material by Machine Learning Prediction[C]. 2018 12th International Conference on the Properties and Applications of Dielectric Materials (ICPADM), 2018: 983–986

[36] Priya P, Aluru N R. Accelerated Design and Discovery of Perovskites with High Conductivity for Energy Applications through Machine Learning[J]. npj Computational Materials, 2021, 7(1): 90

[37] Li C, Hao H, Xu B, et al. Improved Physics-Based Structural Descriptors of Perovskite Materials Enable Higher Accuracy of Machine Learning[J]. Computational Materials Science, 2021, 198: 110 714.

[38] Hao Y. Analogical Discovery of Disordered Perovskite Oxides by Crystal Structure Information Hidden in Unsupervised Material Fingerprints[J]. npj Computational Materials, 2021, 7(1): 75

[39] Janiesch C, Zschech P, Heinrich K. Machine Learning and Deep Learning[J]. Electronic Markets, 2021, 31(3): 685-695.

[40] Xu P, Ji X, Li M, et al. Small Data Machine Learning in Materials Science[J]. npj Computational Materials, 2023, 9(1): 42

[41] Khaire U M, Dhanalakshmi R. Stability of Feature Selection Algorithm: A Review[J]. Journal of King Saud University - Computer and Information Sciences, 2022, 34(4): 1 060-1 073.

[42] Choudhary K, Decost B, Chen C, et al. Recent Advances and Applications of Deep Learning Methods in Materials Science[J]. npj Computational Materials, 2022, 8(1): 59

[43] Li C, Hao H, Xu B, et al. A Progressive Learning Method for Predicting the Band Gap of ABO₃ Perovskites Using an Instrumental Variable[J]. Journal of Materials Chemistry C, Royal Society of Chemistry, 2020, 8(9): 3 127-3 136.

[44] Key Signatures of Prominence Materials and Category of Cold Materials Identified by Random Forest Classifier—IOPscience[OL]. https://iopscience.iop.org/article/10.3847/1538-4365/ace447, 2023-12-22

[45] Bentéjac C, Csörgő A, Martinez-Munoz G. A Comparative Analysis of Gradient Boosting Algorithms[J]. Artificial Intelligence Review, 2021, 54(3): 1 937-1 967.

[46] Ong S P, Richards W D, Jain A, et al. Python Materials Genomics (Pymatgen): A Robust, Open-Source Python Library for Materials Analysis[J]. Computational Materials Science, 2013, 68: 314-319.

[47] Balachandran PV, Kowalski B, Sehirlioglu A, et al. Experimental Search for High-Temperature Ferroelectric Perovskites Guided by Two-Step Machine Learning[J]. Nature Communications, 2018, 9(1): 1 668

[48] Baptista ML, Goebel K, Henriques EMP. Relation between Prognostics Predictor Evaluation Metrics and Local Interpretability SHAP Values[J]. Artificial Intelligence, 2022, 306: 103 667.

[49] Zhong X, Gallagher B, Liu S, et al. Explainable Machine Learning in Materials Science[J]. npj Computational Materials, 2022, 8(1): 204