The design of microstructures is essential for tailoring the microwave dielectric properties of ceramics, yet the structure–property relationships in tetragonal scheelite-structured ceramics remain insufficiently understood. In this study, first-principles calculations combined with experiments were used to systematically investigate the interrelations among the sintering behavior, crystal structure, electrical characteristics, bond characteristics, and dielectric performance of NaSrLnMo₃O₁₂ (Ln = Ce, Pr, Eu, Y, and Yb) ceramics. All the compositions crystallized into a tetragonal scheelite structure (space group I4₁/a) and exhibited favorable dielectric properties with optimal sintering temperatures of 775–925 °C, ε_r = 9.8–10.34, Q×f = 30,487–69,445 GHz, and τ_f = −20.55–(−44.24) ppm/°C. The increase in ε_r originated mainly from the increased ionicity of the Na/Sr/Ln–O bonds, whereas the increase in Q×f was attributed to the increased lattice energy of the Mo–O bonds, increased bond valence, and reduced ionic/electricity disorder. The negative shift in τ_f was primarily linked to the increased linear thermal expansion coefficient α_L of the Na/Sr/Ln–O bonds. Furthermore, the electrical characteristics and relaxation mechanisms were examined, and the dielectric response in the terahertz range was confirmed. Finally, NaSrCeMo₃O₁₂ was employed to design and fabricate two antenna devices, verifying its potential for high-frequency communication. This work provides a systematic understanding of the role of Ln in optimizing the dielectric properties of tetragonal scheelite ceramics and clarifies the microscopic mechanisms underlying their performance.

With the rapid advancement of communication technology, microwave dielectric ceramics have emerged as essential materials, and their performance parameters play a critical role in determining application prospects. Practical applications of microwave dielectric ceramics require appropriate dielectric constants to accommodate diverse scenarios, low dielectric loss to enhance signal transmission efficiency, and nearly zero resonant frequency temperature coefficients to enhance stability across varying environments. Understanding dielectric properties across different frequency ranges is crucial for characterizing dielectric materials for various practical applications. Accurate measurements of dielectric properties are essential for predicting device performance and fostering the development of new systems. Both domestic and international scholars have proposed numerous test methods for measuring the performance parameters of microwave dielectric ceramics; however, these techniques are subject to certain limitations. Therefore, a comprehensive understanding of the testing principles, as well as the scope of application and precautions associated with various testing techniques, is essential for accurately assessing performance parameters. Furthermore, categorizing microwave dielectric ceramics based on their dielectric constants for different application scenarios is essential. A comprehensive understanding of the current state of research is essential for steering the development of high-performance microwave dielectric ceramics. This paper initiates the discussion by examining the main performance parameters of microwave dielectric ceramics, followed by a systematic exposition of common testing technologies for these materials. Lastly, a concise overview of existing research systems is provided as a reference point for studying high-performance microwave dielectric ceramics.

The development of dielectric materials with low permittivity and low loss is a great challenge in wireless communication. In this study, LiLn(PO₃)₄ (Ln = La, Sm, Eu) ceramic systems were successfully prepared using the traditional solid-state method. X-ray diffraction analysis indicated that the LiLn(PO₃)₄ ceramics crystallized in a monoclinic structure when sintered at 850–940 ℃. The characteristic peak shifted to higher angles with variations in the Ln element, which was ascribed to a reduction in the cell volume. Further analysis by structure refinement revealed that the reduction in the cell volume resulted from the decrease in chemical bond lengths and the compression of [LiO₄] and [PO₄] tetrahedra. Remarkably, the LiLn(PO₃)₄ ceramic system displayed exceptional performance at low sintering temperatures (910–925 ℃), including a high quality factor (Q·f) of 41,607–75,968 GHz, low temperature coefficient of resonant frequency (τ_f) ranging from −19.64 to −47.49 ppm/℃, low permittivity (ε_r) between 5.04 and 5.26, and low density (3.04–3.26 g/cm³). The application of Phillips–van Vechten–Levine (P–V–L) theory revealed that the increased Q·f value of the LiLn(PO₃)₄ systems can be attributed to the enhanced packing fraction, bond covalency, and lattice energy, and the stability of τ_f was associated with the increase in the bond energy. Furthermore, a prototype microstrip patch antenna using LiEu(PO₃)₄ ceramics was fabricated. The measurement results demonstrated excellent antenna performance with a bandwidth of 360 MHz and a peak gain of 5.11 dB at a central frequency of 5.08 GHz. Therefore, low-ε_r LiLn(PO₃)₄ ceramic systems are promising candidates for microwave/millimeter-wave communication.

Novel Yb_xCe_1−xO_2−0.5x (x = 0–0.8) ceramics, designed by replacing Ce⁴⁺ with Yb³⁺ ions were prepared by conventional oxide reaction, and the structural stability of the cubic fluorite structure was assessed using lattice energy and ionic properties of Ce/Yb–O bonds. The oxygen vacancy caused by unequal substitution, which played a decisive role in bond ionicity and lattice energy, was analyzed experimentally by XPS and also theoretically by first principles. The Yb_xCe_1−xO_2−0.5x ceramics maintain a stable cubic fluorite structure when x ≤ 0.47, corresponding to the minimum lattice energy of 4142 kJ/mol with the lowest ionicity as ƒ_i = 87.57%. For microwave dielectric properties, when the Yb_xCe_1−xO_2−0.5x (x = 0–0.4) ceramics are pure phase, the porosity-corrected permittivity is dependent on the bond ionicity. The Q׃ values are related to the lattice energy and grain distribution. The temperature coefficient of resonance frequency has been analyzed using bond valence. When the Yb_xCe_1−xO_2−0.5x (x = 0.5–0.8) ceramics are multiple phases, the microwave dielectric properties are associated with the phase composition and grain growth.

Microwave dielectric ceramics (MWDCs) with low dielectric constant and low dielectric loss are desired in contemporary society, where the communication frequency is developing to high frequency (sub-6G). Herein, Nd₂(Zr_1−xTi_x)₃(MoO₄)₉ (NZ_1−xT_xM, x = 0.02–0.10) ceramics were prepared through a solid-phase process. According to X-ray diffraction (XRD) patterns, the ceramics could form a pure crystal structure with the R $\overline{3}$c (167) space group. The internal parameters affecting the properties of the ceramics were calculated and analyzed by employing Clausius–Mossotti relationship, Shannon’s rule, and Phillips–van Vechten–Levine (P–V–L) theory. Furthermore, theoretical dielectric loss of the ceramics was measured and analyzed by a Fourier transform infrared (IR) radiation spectrometer. Notably, when x = 0.08 and sintered at 700 ℃, optimal microwave dielectric properties of the ceramics were obtained, including a dielectric constant (ε_r) = 10.94, Q·f = 82,525 GHz (at 9.62 GHz), and near-zero resonant frequency temperature coefficient (τ_f) = −12.99 ppm/℃. This study not only obtained an MWDC with excellent properties but also deeply analyzed the effects of Ti⁴⁺ on the microwave dielectric properties and chemical bond characteristics of Nd₂Zr₃(MoO₄)₉ (NZM), which laid a solid foundation for the development of rare-earth molybdate MWDC system.

In this study, a sequence of Ce₂[Zr_1-x(Co_1/2W_1/2)_x]₃(MoO₄)₉ (CZ_1-x(CW)_xM) (x = 0.02–0.10) ceramics with excellent microwave dielectric properties were obtained by the traditional solid-phase method. The crystal structure, dielectric properties, and chemical bond characters of the ceramics were characterized and analyzed. X-ray diffraction and Rietveld refinement analysis show that CZ_1-x(CW)_xM could form a single-phase of the triangular crystal system in the entire doping range. The microstructure of the ceramic samples was obtained by scanning electron microscopy. The sintering temperature was reduced and the gain of the sample was refined as the increase of doping ion content. Furthermore, the intrinsic factors affecting the properties of CZ_1-x(CW)_xM were analyzed by employing P-V-L theory and through in-depth infrared analysis. When x was 0.04 and the sintering temperature was 750 ℃, the best dielectric properties of the samples were achieved, including ε_r = 9.95, Q·f = 80, 803 GHz (at 9.99 GHz), and τ_f = − 9.10 ppm/℃.

Dense microwave dielectric ceramics of Ce₂[Zr_1-x(Al_1/2Ta_1/2)_x]₃(MoO₄)₉ (CZMAT) (x = 0.02-0.10) were prepared by the conventional solid-state route. The effects of (Al_1/2Ta_1/2)⁴⁺ on their microstructures, sintering behaviors, and microwave dielectric properties were systematically investigated. On the basis of the X-ray diffraction (XRD) results, all the samples were matched well with Pr₂Zr₃(MoO₄)₉ structures, which belonged to the space group $R\overline{3}c.$ The lattice parameters were obtained using the Rietveld refinement method. The correlations between the chemical bond parameters and microwave dielectric properties were calculated and analyzed by using the Phillips-Van Vechten-Levine (P-V-L) theory. Excellent dielectric properties of Ce₂[Zr_0.94(Al_1/2Ta_1/2)_0.06]₃(MoO₄)₉ with a relative permittivity (ɛ_r) of 10.46, quality factor (Q × f ) of 83,796 GHz, and temperature coefficient of resonant frequency (τ_f) of -11.50 ppm/℃ were achieved at 850 ℃.