Microwave dielectric properties prediction and validation for multi-phase synergistic barium niobate based LTCC

In this study, H 3 BO 3 -doped Barium-Niobate based LTCC ceramics were prepared via mixed oxide method, achieving a reduction in sintering temperature from 1350 °C to 900 °C through liquid-phase sintering. The addition of H 3 BO 3 induced a controlled multi-phase microstructure comprising Ba 5 Nb 4 O 15 , BaB 2 O 6 and BaNb 2 O 6 , with phase volume fractions quantified by Rietveld refinement. These three phases regulate the relative permittivity (εᵣ), quality factor (Q × f), and temperature coefficient of resonant frequency (τ f ) of the material. The optimal microwave properties (εᵣ = 37.5, Q × f = 45,025 GHz, τ f  = 23.78 ppm/°C) was obtained by sintering at 900 °C for 4 h and adding 2 wt% H 3 BO 3 . Beyond material optimization, this work establishes and validates a predictive modeling framework for composite permittivity by integrating intrinsic phase permittivities derived from ionic polarizability with quantitative phase analysis and three effective medium theories: Lichtenecker logarithmic rule (LLR), Maxwell-Garnett (MG), and Bruggeman (BG). Comparison of the three models against experimental data demonstrates that the LLR model, assuming random phase distribution, provides the best agreement with measured εᵣ values. The MG and BG models yield similar predictions but both consistently overestimate permittivity, failing to fully capture the dielectric response of the actual microstructure observed by SEM. The LLR model was further refined by introducing a phase interaction term (β), which physically accounts for depolarizing fields at interfaces and reduces the average prediction deviation from 10% to 2%. Q × f cannot be reliably predicted by simple mixing rules due to its sensitivity to extrinsic factors, whereas τ f approximately follows a linear compound addition rule enabling rational phase composition control. This integrated approach provides a generalizable framework for the predictive design of multi-phase dielectric composites.