Interpretable model of dielectric constant for rational design of microwave dielectric materials: a machine learning study

Abstract

Machine learning (ML) has advantages in studying fundamental properties of materials and comprehending structure-property correlations. In this study, we employed sure independence screening and sparsifying operator (SISSO) method (ML technique) to explore the experimental dielectric constant, temperature coefficient of frequency resonator, and quality factor of inorganic oxide microwave dielectric materials. Among the constructed white-box models, the highest accuracy, with a coefficient of determination (R²) of 0.8, was observed in predicting the dielectric constants of the quaternary materials. Additionally, we proposed a straightforward strategy to merge the ternary and quaternary datasets in a single training, aiming to address the issue of data scarcity in ML research. Although this strategy slightly compromises the model accuracy, it has the advantage of creating a more unified trained model for structural-property relationship understanding. Using the unified and interpretable model trained with the merged dataset, we derived a general rule governing the dielectric constant of materials. Our ML findings regarding the dielectric property provide fundamental insights for designing microwave dielectric materials with diverse dielectric constants.

Keywords

Dielectric constant / machine learning / interpretable model / merged dataset

References

[1] Sebastian MT.Dielectric materials for wireless communication. 1st Edition. Elsevier: 2008.

[2] Sebastian MT,Jantunen H.Low-loss dielectric ceramic materials and their properties.Int Mater Rev2015;60:392-412

[3] Reaney IM.Microwave dielectric ceramics for resonators and filters in mobile phone networks.J Am Ceram Soc2006;89:2063-72

[4] Schmidt J,Botti S.Recent advances and applications of machine learning in solid-state materials science.npj Comput Mater2019;5:221

[5] Wang AY,Kauwe SK.Machine learning for materials scientists: an introductory guide toward best practices.Chem Mater2020;32:4954-65

[6] Gomes CP,van Dover RB.Computational sustainability meets materials science.Nat Rev Mater2021;6:645-7

[7] Barr JA,Ashton M,Sinnott SB.High-throughput density functional calculations to optimize properties and interfacial chemistry of piezoelectric materials.Phys Rev Mater2018;2:025002

[8] Schleder GR,Acosta CM,Fazzio A.From DFT to machine learning: recent approaches to materials science - a review.J Phys Mater2019;2:032001

[9] Jain A,Moore CJ.A high-throughput infrastructure for density functional theory calculations.Comput Mater Sci2011;50:2295-310

[10] Petousis I,Ballouz E.High-throughput screening of inorganic compounds for the discovery of novel dielectric and optical materials.Sci Data2017;4:160134 PMCID:PMC5315501

[11] Petousis I,Hautier G.Benchmarking density functional perturbation theory to enable high-throughput screening of materials for dielectric constant and refractive index.Phys Rev B2016;93:115151

[12] Umeda Y,Moriwake H.Prediction of dielectric constants using a combination of first principles calculations and machine learning.Jpn J Appl Phys2019;58:SLLC01

[13] Jain A,Hautier G.Commentary: the materials project: a materials genome approach to accelerating materials innovation.APL Mater2013;1:011002

[14] Takahashi A,Miyamoto J,Oba F.Machine learning models for predicting the dielectric constants of oxides based on high-throughput first-principles calculations.Phys Rev Mater2020;4:103801

[15] Tin Kam Ho. The random subspace method for constructing decision forests.IEEE Trans Pattern Anal Mach Intell1998;20:832-44

[16] Gopakumar A,Wolverton C.Identification of high-dielectric constant compounds from statistical design.npj Comput Mater2022;8:832

[17] Saal JE,Aykol M,Wolverton C.Materials design and discovery with high-throughput density functional theory: the open quantum materials database (OQMD).JOM2013;65:1501-9

[18] Qin J,Ma M.Machine learning approaches for permittivity prediction and rational design of microwave dielectric ceramics.J Materiomics2021;7:1284-93

[19] Ouyang R,Ahmetcik E,Ghiringhelli LM.SISSO: a compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates.Phys Rev Mater2018;2:083802

[20] Neil Alford Home Page. Available online: https://www.imperial.ac.uk/people/n.alford. (accessed on 2024-01-25)

[21] Shannon RD.Dielectric polarizabilities of ions in oxides and fluorides.J Appl Phys1993;73:348-66

[22] Chen XM,Li Y.Microstructures and microwave dielectric characteristics of Ba_6-3x(Sm_1-yLa_y)_8+2xTi₁₈O₅₄ solid solutions (x = 2/3 and 0.75).J Electroceram2002;9:31-5

[23] Okawa T,Ohsato H.Site occupancy of Bi ions and microwave dielectric properties in Bi-doped Ba_6-3xR_8+2xTi₁₈O₅₄ (R = rare earth, x = 2/3) solid solutions.Mater Chem Phys2003;79:199-203

[24] A. A. Baikov Institute of Metallurgy and Materials Science. Available online: https://phases.imet-db.ru/elements (accessed on 2024-01-25).

[25] Choudhary S,Chakraborty T.Atomic polarizability: a periodic descriptor.J Chem Res2020;44:227-34

[26] Shannon RD.Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides.Acta Cryst A1976;32:751-67

[27] Qin J,Ma M.Optimizing and extending ion dielectric polarizability database for microwave frequencies using machine learning methods.npj Comput Mater2023;9:1093

[28] Guo M,Dou G.A new microwave dielectric ceramics for LTCC applications: Li₂Mg₂(WO₄)₃ ceramics.J Mater Sci Mater Electron2014;25:3712-5

[29] Zhang J.Synthesis and microwave dielectric properties of Li₂Mg₂(WO₄)₃ ceramics.Mater Lett2015;158:92-4

[30] Wu J.Effect of crystallization on microwave dielectric properties of stoichiometric cordierite glasses containing B₂O₃ and P₂O₅.J Mater Res2000;15:222-7

[31] Wang F,Zeng Y.Enhanced microwave dielectric properties in Mg₂Al₄Si₅O₁₈ through Cu²⁺ substitution.Eur J Inorg Chem2021;2021:2464-70

[32] Yao GG,Zhang HW.Microwave dielectric properties of Li₂MgTi₃O₈ ceramics produced by reaction-sintering method.J Mater Sci Mater Electron2013;24:1128-31

[33] George S.Microwave dielectric properties of novel temperature stable high Q Li₂Mg_1-xZn_xTi₃O₈ and Li₂A_1-xCa_xTi₃O₈ (A = Mg, Zn) ceramics.J Eur Ceram Soc2010;30:2585-92

[34] Wu S,Jiang C,Ma Q.Synthesis of monoclinic CaSnSiO₅ ceramics and their microwave dielectric properties.Mater Lett2013;91:239-41

[35] Du K,Li J.Optimised phase compositions and improved microwave dielectric properties based on calcium tin silicates.J Eur Ceram Soc2019;39:340-5

[36] Došler U,Suvorov D.The synthesis and microwave dielectric properties of Mg₃B₂O₆ and Mg₂B₂O₅ ceramics.J Eur Ceram Soc2010;30:413-8

[37] Chang S,Tseng C.Microwave dielectric properties of ultra-low temperature fired Li₃BO₃ ceramics.J Alloys Compd2017;698:814-8