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Open Access Review Just Accepted
A review of microwave dielectric ceramics: From fundamental mechanisms and property regulation to advanced preparation, applications, and data-driven discovery
Journal of Advanced Ceramics
Available online: 13 May 2026
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Microwave dielectric ceramics (MWDCs) are pivotal to modern wireless communication systems, with their performance governed by three key parameters: relative dielectric constant (εr), Q×f value (product of quality factor Q (reciprocal dielectric loss) and frequency f), and temperature coefficient of resonant frequency (τf). This review systematically summarizes the recent research progress of MWDCs from five interrelated aspects. In terms of performance characterization, standardized resonant methods achieve εr measurement errors below 1% and a tanδ detection limit as low as 10-5. Theoretically, frameworks from complex crystal chemistry to the recently elucidated cation rattling effect enable quantitative interpretation of dielectric behavior. In processing, the cold sintering process achieves ceramic densification below 300 °C, reducing energy consumption by over 97% in comparison with conventional sintering. For applications, these materials have been widely deployed in high-performance substrates, resonators, and filters for 5G/6G communications, with device insertion loss maintained below 1 dB. Additionally, data-driven approaches, particularly machine learning, can accurately predict key dielectric properties with a coefficient of determination (R2) higher than 0.9, accelerating the exploration and development of novel MWDCs. By integrating these perspectives, this review offers a systematic insight into the state-of-the-art progress and future development directions of MWDCs research.

Open Access Research Article Issue
Low-temperature sintering ZTA ceramics with CuO–TiO2–Nb2O5 composite oxide sintering aids for LTCC applications
Journal of Advanced Ceramics 2025, 14(11): 9221185
Published: 24 November 2025
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Zirconia-toughened alumina (ZTA) ceramics have attracted much attention as electronic package substrate materials because of their excellent mechanical properties and chemical stability. The high sintering temperatures of ZTA ceramics restrict their multilayer co-firing with copper electrodes for low-temperature co-fired ceramic (LTCC) applications. To achieve a balance between good properties and low sintering temperatures, this work proposes CuO–TiO2–Nb2O5 (CTN) composite oxide sintering aids for ZTA ceramics to obtain a novel glass-free LTCC material. A low-temperature densification mechanism based on multiphase synergy and interfacial reactions is revealed. The results show that the sintering temperature of ZTA ceramics doped with 5 wt% CTN can be significantly reduced to 1050 °C, resulting in high thermal conductivity (18.7 W/(m·K)), high bending strength (405 MPa), and low dielectric loss (9.97×104@11.97 GHz). The co-firing compatibility with a multilayer copper inner electrode is also demonstrated. This work overcomes the traditional trade-off between low-temperature sintering and high performance in glass-free LTCC materials and provides a new strategy for the design and development of multilayer ceramic substrates with copper inner electrodes.

Research Article Issue
Machine Learning-Based Optimization of Clausius-Mossotti Equation for Dielectric Constant Calculation
Journal of the Chinese Ceramic Society 2025, 53(9): 2643-2650
Published: 12 August 2025
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Introduction

The Clausius-Mossotti (C–M) equation is one of the most fundamental theoretical models to calculate the dielectric constant of materials. As was proposed over a century ago, it has been widely applied in dielectric material research due to its relatively simple mathematical form and clear physical interpretation. The equation, derived based on the Lorentz effective field approximation and the assumption of constant polarization, establishes a relationship among the macroscopic dielectric constant and the microscopic polarizability and unit cell volume. However, with the growing understanding of dielectric materials, it becomes clear that dielectric constant is affected by a range of additional factors, such as bond length, packing density and symmetry. These factors are not captured by the conventional C–M equation, indicating the limitations of the equation. Recently, machine learning (ML) methods show a promise in improving the prediction accuracy of dielectric properties. The ML models can outperform classical equations in terms of accuracy, but they often lack interpretability, which hinders their widespread use in material design and optimization. To address these issues, this study proposed a novel bidirectional embedding approach with domain knowledge and machine learning. The ML-based correction term was integrated into the classical C–M equation, enhancing its predictive accuracy, while retaining physical interpretability. This work could explore a potential of combining physical formulas with ML methods to create more robust and explainable models for material design.

Methods

The data of single-phase microwave dielectric ceramics were collected from published literatures and the Materials Project database. The dataset included materials whose dielectric constants were measured by the Hakki-Coleman method in a frequencies range from 5 to 18 GHz. A machine learning model identified molecular dielectric polarizability per volume (ppv), average bond length (blm) and unit cell volume (va) as the most significant contributors to the dielectric constant in a previous study. To enhance the accuracy of the C–M equation, correction terms were introduced based on the three key features. Symbolic regression, combined with genetic algorithms, was used to derive mathematical expressions for the correction terms. The symbolic regression technique utilized evolutionary algorithms to generate and evolve potential expressions. The structures and parameters of expressions were optimized to minimize prediction errors. Hyperparameters were optimized by a grid search method to identify the best-performing models. The process was carried out iteratively. A total of 16,000 candidate mathematical expressions were generated and compared. Finally, the Pareto front analysis was used to select the optimal expression that balances accuracy and complexity.

Results and Discussion

The revised C–M equation results in significant improvements in its predictive performance. For the Shannon polarizability dataset, the R2 value of the revised C–M equation is increased by 42.29%, and the RMSE value is decreased by 14.72%. The correction term compensates for the inaccuracies of the original equation, particularly in cases where the molecular dielectric polarizability per volume of Shannon value (ppvs) is either overestimated or underestimated. For low-polarizability materials with ppvs values less than 0.2087, the Shannon database tends to underestimate the dielectric constant, and the correction term compensates for this error. Conversely, for high-polarizability materials, the dielectric constant is often overestimated, and the correction term reduces the overestimation. The analysis of the relationship between the correction term (Δppvs) and features reveals that the correction term is most sensitive to ppvs, followed by blm, with va having the least impact. This finding indicates that the dielectric polarizability plays a dominant role in determining the accuracy of the revised C–M equation. The influence of the features on the correction term is further explored through partial derivatives. The first-order partial derivatives show that the correction term’s contribution from ppvs is much greater than that from blm or va. The second-order partial derivatives reveal a non-linear relationship between the correction term and ppvs and blm, while the relationship with va is linear. The results indicate that the compensatory effect of the correction term gradually diminishes, and the suppression effect becomes more pronounced as ppvs increases. This behavior is consistent with the correction mechanism of “elevating the underrated, reducing the overrated”.

Conclusions

This study introduced a bidirectional embedding approach that could integrate machine learning with domain knowledge to enhance both the accuracy and interpretability of the Clausius-Mossotti equation. The revised equation achieved a higher prediction accuracy with a 42.29% increase in R2 and a 14.72% decrease in RMSE via incorporating the correction term derived from symbolic regression. The revised equation retained the physical meaning of the original one. The research could highlight a potential of bidirectional embedding approach to create models that could balance both accuracy and interpretability, offering a promising perspective on optimizing classical equations and material design.

Open Access Issue
Machine learning assisted τf value prediction of ABO3-type microwave dielectric ceramics
Journal of Materiomics 2026, 12(1)
Published: 08 August 2025
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The temperature coefficient of resonance frequency (τf or TCF) is the key parameter for evaluating temperature stability of microwave dielectric ceramics. In this work, a machine learning framework was proposed to predict the τf values of ABO3-type microwave dielectric ceramics. Leveraging a curated dataset of 104 single-phase ABO3-type compounds, we systematically evaluated models based on five machine learning algorithms using 31 structural descriptors as input features. The eXtreme Gradient Boosting (XGB) algorithm emerged as the optimal predictive model, demonstrating robust performance on the test set (R2 = 0.7799, RMSE = 15.7494 × 10−6−1). Consistent results on the validation set further confirmed its generalization capability. Critical features contributing to the model's performance include molecular dielectric polarizability (pm), tolerance factor (tt), ionic volume (Vi) and relative molecular mass (m). Structure-property relationship studies revealed that the pm plays an important role in modulating the τf value by affecting the permittivity. Quantitative thresholds for these critical descriptors were also derived for identifying materials with near-zero τf. This work provides an effective data-driven approach for accelerating the discovery of microwave dielectric ceramics with good temperature stability.

Open Access Research paper Issue
Machine learning assisted Q×f value prediction of ABO4-type microwave dielectric ceramics
Journal of Materiomics 2025, 11(4)
Published: 10 August 2024
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Microwave dielectric ceramics (MWDCs) with a high Q×f value can improve the performance of radio frequency components like resonators, filters, antennas and so on. However, the quantitative structure-property relationship (QSPR) for the Q×f value is complicated and unclear. In this study, machine learning methods were used to explore the QSPR and build up Q×f value prediction model based on a dataset of 164 ABO4-type MWDCs. We employed five commonly-used algorithms for modeling, and 35 structural features having correlations with Q×f value were used as input. In order to describe structure from both global and local perspectives, three different feature construction methods were compared. The optimal model based on support vector regression with radial basis function kernel shows good performances and generalization capability. The features contained in the optimal model are primitive cell volume, molecular dielectric polarizability and electronegativity with A- and B-site mean method. The relationships between property and structure were discussed. The model used for the Q×f value prediction of tetragonal scheelite shows excellent performances (R2 = 0.8115 and RMSE = 8362.73 GHz), but it needs auxiliary features of average bond length, theoretical density and polarizability per unit volume for monoclinic wolframite ceramics to improve model prediction ability.

Open Access Research paper Issue
A lead-free KNN-based, co-fired multilayered piezoceramic energy harvester with a high output current and power
Journal of Materiomics 2025, 11(2): 100876
Published: 19 May 2024
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To date, most of the reported piezoelectric energy harvesters (PEHs) use lead-based Pb(Zr,Ti)O3 (PZT) piezoceramic family, which is obviously harmful to the environment. In recent years, the PEHs constructed with lead-free piezoceramics have been developed rapidly. However, their force-to-electric (FE) output performances are still unsatisfactory. To address this issue, here we present a PEH assembled with lead-free potassium sodium niobate (KNN) based co-fired multilayered piezoceramics (MLPCs), which show a high output current and power. First, high-quality KNN-based MLPCs are prepared by tape-casting process. Each MLPC contains 11 piezoceramic layers, and the cross-section SEM image of the MLPC indicates that the ceramic layers are well connected with the Ag/Pd inner electrode layers. The d33 of a single MLPC reaches up to 4675 pC/N. The FE output performance of KNN-MLPC based PEH is then tested. The inherent advantages of multilayered ceramics enable the PEH to achieve a peak-to-peak output current of up to 1.48 mA and a peak-to-peak output power of 2.19 mW under a harmonic force load of 6 kN at 14 Hz. Finally, the PEH is tested to validate its practical application in real road environments, demonstrating its promising for the use of self-powered monitoring sensors for collecting traffic data.

Open Access Research Article Issue
Unusual local electric field concentration in multilayer ceramic capacitors
Journal of Materiomics 2023, 9(2): 403-409
Published: 12 October 2022
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Local electric-field around multitype pores (dielectric pore, interface pore, electrode pore) in multilayer ceramic capacitors (MLCCs) was investigated using Kelvin probe force microscopy combined with the finite element simulation to understand the effect of pores on the electric reliability of MLCCs. Electric-field is found to be concentrated significantly in the vicinity of these pores and the strength of the local electric-field is 1.5–5.0 times of the nominal strength. Unexpectedly, the concentration degree of the pores in the inner electrode is much higher than that in the dielectrics and dielectric-electrode interfaces. Meanwhile, geometry orientations are found to have a remarkable influence on the local electric field strength. The pores act as an insulation degradation precursor via local electric, thermal center, and oxygen vacancies accumulation center. Such unusual local electric field concentration of multitype pores can provide new insights into the understanding of insulation degradation evolution, processing tailoring and design optimization for MLCCs.

Open Access Research Article Issue
Machine learning approaches for permittivity prediction and rational design of microwave dielectric ceramics
Journal of Materiomics 2021, 7(6): 1284-1293
Published: 04 March 2021
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Low permittivity microwave dielectric ceramics (MWDCs) are attracting great interest because of their promising applications in the new era of 5G and IoT. Although theoretical rules and computational methods are of practical use for permittivity prediction, unsatisfactory predictability and universality impede rational design of new high-performance materials. In this work, based on a dataset of 254 single-phase microwave dielectric ceramics (MWDCs), machine learning (ML) methods established a high accuracy model for permittivity prediction and gave insights of quantitative chemistry/structure-property relationships. We employed five commonly-used algorithms, and introduced 32 intrinsic chemical, structural and thermodynamic features which have correlations with permittivity for modeling. Machine learning results help identify the permittivity decisive factors, including polarizability per unit volume, average bond length, and average cell volume per atom. The feature-property relationships were discussed. The optimal model constructed by support vector regression with radial basis function kernel was validated its superior predictability and generalization by verification dataset. Low permittivity material systems were screened from a dataset of ~3300 materials without reported microwave permittivity by high-throughput prediction using optimal model. Several predicted low permittivity ceramics were synthesized, and the experimental results agree well with ML prediction, which confirmed the reliability of the prediction model.

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