Microwave dielectric ceramics are widely used in microwave frequency (i.e., 300 MHz-300 GHz) circuits as communication electronic components such as resonators, filters, and antennas. The dielectric permittivity (ε_r), quality factor (Q×f) and the temperature coefficient of resonant frequency (τ_f) are the main performance index to measure the quality of microwave dielectric ceramics. However, there is a constraint relationship between the performance parameters. In general, the giant ε_r may cause a large dielectric loss and a low Q×f, and the volatility of ε_r originates an enormous τ_f value. Therefore, materials with superior intrinsic microwave dielectric properties are rare. The existing methods of controlling microwave dielectric properties mainly include ion substitution, composite control, laminated control and non-stoichiometric ratio control. These methods often require sacrificing one parameter to satisfy other parameters. High-entropy strategy is a novel regulation method used in inorganic materials. High-entropy ceramics refer to a ceramic system with a configuration entropy (S_c) of 1.5R. The high-entropy effect, sluggish diffusion effect, lattice distortion effect and synergy in components (i.e., cocktail effect) are four special effects of high-entropy ceramics. The high-entropy strategy shows a great potential in dielectric ceramics due to these unique effects. In this paper, high-entropy strategy was used to design rare-earth vanadate ceramics. The impact of high-entropy structure on the microwave dielectric properties was investigated.

High-entropy ceramics of ReVO₄ were synthesized by a solid-phase method with high-purity rare earth oxides (Re₂O₃ with a purity of > 99.9%) and V₂O₅. The ceramics with different chemical formulas (La_0.2Ce_0.2Nd_0.2Sm_0.2Eu_0.2)VO₄, (La_0.2Ce_0.2Nd_0.2Sm_0.2 Gd_0.2)VO₄, and (La_0.2Ce_0.2Nd_0.2Sm_0.2Y_0.2)VO₄, were denoted as Eu-5RVO, Gd-5RVO, and Y-5RVO, respectively. The raw materials were weighed according to a stoichiometric ratio and mixed in a ball mill at a rotational speed of 300 r/min for 6 h. The slurry after milling was dried in an oven at 120 ℃ for 24 h. After grinding, the powders were pre-fired in a Muffle furnace at 800 ℃ for 6 h. Then the prepared powders were further ground for 6 h, dried, and added with a polyvinyl alcohol solution (PVA, 5%) as a binder. The granulated powders were sieved by a 80/120 mesh screen and then pressed into cylindrical bulks with a thickness of 5.5-6.5 mm and diameter of 10 mm at 10 MPa. The samples were heated at 550 ℃ for 6 h to eliminate the binder and sintered at 1 400-1 500 ℃ for 6 h with an increment of 20 ℃ to obtain the dense ceramics.

The crystal structure of the ceramics was analyzed by X-ray diffraction (XRD, PANalytical Co., the Netherlands). The apparent density was determined by Archimedes' drainage method. The microstructure was evaluated by a model S-4800 scanning electron microscope (SEM, Hitachi High-Technologies Co., Japan). The dielectric properties at different microwave frequencies (i.e., 1-20 GHz) were measured by a model Keysight E5071C vector network analyzer (Keysight Technologies Co., USA) in TE₀₁₁ mode based on the Hakki-Coleman method. The temperature coefficient of resonant frequency (τ_f) was calculated via recording the frequency drifting at 25-85 ℃ (i.e., f₂₅ and f₈₅).

The high-entropy ceramics Eu-5RVO, Gd-5RVO, and Y-5RVO exhibit a tetragonal zircon structure with a space group I4₁/amd. The SEM images of the fractured cross-section of high-entropy ceramics ReVO₄ show uniform grains and clear grain boundaries, along with the spatial distribution of elements based on EDS analysis. The ceramics all exhibit a dense microstructure, as well as a promising microwave dielectric performance. The dielectric permittivity is analyzed via the Clausius-Mossotti formula, which is positively correlated to ion polarization. The quality factor is primarily determined by the packing fraction. The bond valence theory is used to reflect the degree of lattice distortion, having a strong relationship with the temperature coefficient of resonance frequency. The results show that the high-entropy strategy can effectively regulate the microwave dielectric properties.

A series of high-entropy ceramics of ReVO₄ were prepared by a solid-state reaction method. All the ceramics were a tetragonal zircon structure with a space group I4₁/amd. The phase structure, microscopic morphology, and vibration characteristics of high-entropy ceramics ReVO₄ were analyzed, and the microwave dielectric properties were analyzed by the Clausius-Mossotti formula, packing fraction, and bond valence theory. The results showed that ceramic Y-5RVO exhibited an optimal microwave dielectric properties (i.e., ε_r of 10.69, Q×f of 11 704 GHz, and τ_f of -21.70×10^-6/℃). It was indicated that the high-entropy ceramics of ReVO₄ could be used as competitive microwave dielectric materials.