The CMAS corrosion behavior of high-entropy (Y0.2Dy0.2Er0.2Tm0.2Yb0.2)4Hf3O12 hafnate material prepared by ultrafast high-temperature sintering (UHS)

High-temperature molten calcium-magnesium-alumina-silicate (CMAS) corrosion has become a fatal factor for the failure of aero-engine thermal barrier coatings. In this study, a promising entropy-stabilized (Y_0.2Dy_0.2Er_0.2Tm_0.2Yb_0.2)₄Hf₃O₁₂ (5YH) hafnate was prepared by the emerging ultrafast high-temperature sintering (UHS), and its corrosion and wetting behavior of molten CMAS were investigated. For the corrosion mechanism, the precipitation of the high-entropy apatite phase promotes the formation of the HfO₂ phase, and it can improve the density and stability of the slow-growing reaction layer, hindering the further penetration of molten CMAS. At 1300 ℃, a reaction layer with a three-layered morphology is generated, resulting from the decreased viscosity of the molten CMAS. Moreover, computational analysis shows that molten CMAS on the 5YH surface has a larger contact angle (17°) than traditional YSZ (13°), and the spreading area is about 90 % of traditional YSZ, which benefits for its good CMAS corrosion resistance.     

New class of high-entropy defect fluorite oxides RE2(Ce0.2Zr0.2Hf0.2Sn0.2Ti0.2)2O7 (RE = Y,Ho, Er,or Yb) as promising thermal barrier coatings

High-entropy ceramics exhibit great application potential as thermal barrier coating (TBC) materials. Herein, a series of novel high-entropy ceramics with RE₂(Ce_0.2Zr_0.2Hf_0.2Sn_0.2Ti_0.2)₂O₇ (RE₂HE₂O₇, RE = Y, Ho, Er, or Yb) compositions were fabricated via a solid-state reaction. X-ray diffraction (XRD) and energy dispersive spectrometry (EDS) mapping analyses confirmed that RE₂HE₂O₇ formed a single defect fluorite structure with uniform elemental distribution. The thermophysical properties of the RE₂HE₂O₇ ceramics were investigated systematically. The results show that RE₂HE₂O₇ ceramics have excellent high-temperature phase stability, high thermal expansion coefficients (10.3–11.7 × 10^?6 K^-1, 1200 ℃), and low thermal conductivities (1.10-1.37 W m^-1 K^-1, 25 ℃). In addition, RE₂HE₂O₇ ceramics have a high Vickers hardness (13.7–15.0 GPa) and relatively low fracture toughness (1.14-1.27 MPa m^0.5). The outstanding properties of the RE₂HE₂O₇ ceramics indicate that they could be candidates for the next generation of TBC materials.     

Ultrafast high-temperature synthesis and densification of high-entropy carbides

Recently, high-entropy carbides have attracted great attention due to their remarkable component complexity and excellent properties. However, the high melting points and low self-diffusion coefficients of carbides lead to the difficulties in forming solid solution and sintering densification. In this work, six dense multicomponent carbides (containing 5–8 cations) were prepared by a novel ultrafast high-temperature sintering (UHS) technique within a full period of 6 min, and three of them formed a single-phase high-entropy solid solution. The solid solubility of the UHSed multicomponent carbides was highly sensitive to the compositional variation. The presence of Cr₃C₂ liquid had significant contributions to the formation of solid solution and the densification of multicomponent carbides. All UHSed multicomponent carbides exhibited high hardness, which, unexpectedly, did not simply increase with increasing number of the components. The highest nanohardness with a value of 36.6 ± 1.5 GPa was achieved in the (Ti_1/5Cr_1/5Nb_1/5Ta_1/5V_1/5)C_x high-entropy carbide. This work is expected to expedite the development of high-entropy carbides and broaden the application of UHS in the synthesis and densification of advanced ceramics.     

Novel (Sm0.2Lu0.2Yb0.2Y0.2Dy0.2)3TaO7 high-entropy ceramic for thermal barrier coatings

A novel (Sm_0.2Lu_0.2Dy_0.2Yb_0.2Y_0.2)₃TaO₇ (SLT-5RE_0.2) oxide with a single-fluorite structure was synthesized via an optimized sol-gel and sintering method, and its crystal structure, mechanical and thermophysical properties were investigated. The results indicate that the calcined nanoscale powder is of high crystallinity, and bulk sample is of a uniform elemental distribution. Compared to YSZ (6–8 wt.% Y₂O₃ partially stabilized by ZrO₂), SLT-5RE_0.2 exhibits lower Young's modulus, less mean acoustic velocity, and higher Vickers microhardness. Owing to the strengthened anharmonic vibration and phonon scattering, SLT-5RE_0.2 exhibits low thermal conductivity (1.107 W K^?1·m^?1, 900 °C). The high thermal expansion coefficient (11.3 × 10^?6 K^?1, 1200 °C) of SLT-5RE_0.2 ceramic can be ascribed to the reduced lattice energy and ionic spacing as well as the cocktail effect of high-entropy ceramics. The excellent mechanical and thermophysical properties, and excellent phase steadiness during the whole testing temperature cope, indicate that SLT-5RE_0.2 high-entropy ceramic can be a candidate material for thermal barrier coatings.     

Marked reduction in the thermal conductivity of (La0.2Gd0.2Y0.2Yb0.2Er0.2)2Zr2O7 high-entropy ceramics by substituting Zr4+ with Ti4+

The (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂(Zr_1-xTi_x)₂O₇ (x = 0–0.5) high-entropy ceramics were successfully prepared by a solid state reaction method and their structures and thermo-physical properties were investigated. It was found that the high-entropy ceramics demonstrate pure pyrochlore phase with the composition of x = 0.1–0.5, while (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂Zr₂O₇ shows the defective fluorite structure. The sintered high-entropy ceramics are dense and the grain boundaries are clean. The grain size of high-entropy ceramics increases with the Ti⁴⁺ content. The average thermal expansion coefficients of the (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂(Zr_1-xTi_x)₂O₇ high-entropy ceramics range from 10.65 × 10^?6 K^?1 to 10.84 × 10^?6 K^?1. Importantly, the substitution of Zr⁴⁺ with Ti⁴⁺ resulted in a remarkable decrease in thermal conductivity of (La_0.2Gd_0.2Y_0.2Yb_0.2Er_0.2)₂(Zr_1-xTi_x)₂O₇ high-entropy ceramics. It reduced from 1.66 W m^?1 K^?1 to 1.20 W m^?1 K^?1, which should be ascribed to the synergistic effects of mass disorder, size disorder, mixed configuration entropy value and rattlers.     

High-entropy rare-earth disilicate (Lu0.2Yb0.2Er0.2Tm0.2Sc0.2)2Si2O7: A potential environmental barrier coating material

A new high-entropy ceramic (Lu_0.2Yb_0.2Er_0.2Tm_0.2Sc_0.2)₂Si₂O₇ ((5RE_0.2)₂Si₂O₇) was proposed as a potential environmental barrier coating (EBC) material for ceramics matrix composites in this work. Experimental results showed that the (5RE_0.2)₂Si₂O₇ synthesized by solid-phase sintering was a monoclinic solid solution and had good phase stability proved by no obvious absorption/exothermic peak in the DSC curve from room temperature to 1400 °C. It performed a lower coefficient of thermal expansion (2.08 ×10^?6-4.03 ×10^?6 °C^?1) and thermal conductivity (1.76–2.99 W?m^?1?°C^?1) compared with the five single principal RE₂Si₂O₇. In water vapor corrosion tests, (5RE_0.2)₂Si₂O₇ also exhibited better water vapor corrosion resistance attributed to the multiple doping effects. The weight loss was only 3.1831 × 10^?5 g?cm^?2 after 200 h corrosion at 1500 °C, which was lower than that of each single principal RE₂Si₂O₇. Therefore, (5RE_0.2)₂Si₂O₇ could be regarded as a remarkable candidate for EBCs.     

Dielectric properties of (Y0.2Eu0.2Er0.2Dy0.2Lu0.2)3(AlxFe1-x)5O12 high-entropy garnet ceramics

A new kind of novel high-entropy rare earth garnet ceramics (HEREGCs, (Y_0.2Eu_0.2Er_0.2Dy_0.2Lu_0.2)₃(Al_xFe_1-x)₅O₁₂ (x = 0.4–0.6)) was designed and successfully synthesized by solid state reaction method. With the increase of Al content, the relative dielectric constant (ε_r′) at 100 Hz decreases from 4 × 104 to 1 × 102, while the dielectric loss (tanδ) increases from 0.93 to 2.65. The activation energy of grain boundary electrical conductivity (E_gb) and grain electrical conductivity (E_g) are fitted according to Arrhenius’ law, which indicate that the increase of difference between E_gb and E_g lead to the enhancement of dielectric properties. Our results provide the underlying insights needed to guide the study of colossal dielectric materials.     

Multi-component strategy for remarkable suppression of thermal conductivity in strontium diyttrium oxide: The case of high-entropy Sr(Y0.2Sm0.2Gd0.2Dy0.2Yb0.2)2O4 ceramic

Anti-spinel oxide SrY₂O₄ has attracted extensive attention as a promising host lattice due to its outstanding high-temperature structural stability and large thermal expansion coefficient (TEC). However, the overhigh thermal conductivity limits its application in the field of thermal barrier coatings. To address this issue, a novel high-entropy Sr(Y_0.2Sm_0.2Gd_0.2Dy_0.2Yb_0.2)₂O₄ ceramic was designed and synthesized for the first time via the solid-state method. It is found that the thermal conductivity of Sr(Y_0.2Sm_0.2Gd_0.2Dy_0.2Yb_0.2)₂O₄ is reduced to 1.61 W·m⁻¹·K⁻¹, 53 % lower than that of SrY₂O₄ (3.44 W·m⁻¹·K⁻¹) at 1500 °C. Furthermore, reasonable TEC (11.53 ×10⁻⁶ K⁻¹, 25 °C ∼ 1500 °C), excellent phase stability, and improved fracture toughness (1.92 ± 0.04 MPa·m^1/2) remained for the high-entropy Sr(Y_0.2Sm_0.2Gd_0.2Dy_0.2Yb_0.2)₂O₄ ceramic, making it a promising material for next-generation thermal barrier coatings.     

Electronic structure and transport properties of sol-gel-derived high-entropy Ba(Zr0.2Sn0.2Ti0.2Hf0.2Nb0.2)O3 thin films

High-entropy perovskite thin films, as the prototypical representative of the high-entropy oxides with novel electrical and magnetic features, have recently attracted great attention. Here, we reported the electronic structure and charge transport properties of sol-gel-derived high-entropy Ba(Zr_0.2Sn_0.2Ti_0.2Hf_0.2Nb_0.2)O₃ thin films annealed at various temperatures. By means of X-ray photoelectron spectroscopy and absorption spectrum, it is found that the conduction-band-minimum shifts downward and the valence-band-maximum shifts upward with the increase of annealing temperature, leading to the narrowed band gap. Electrical resistance measurements confirmed a semiconductor-like behavior for all the thin films. Two charge transport mechanisms, i.e., the thermally-activated transport mechanism at high temperatures and the activation-less transport mechanism at low temperatures, are identified by a self-consistent analysis method. These findings provide a critical insight into the electronic band structure and charge transport behavior of Ba(Zr_0.2Sn_0.2Ti_0.2Hf_0.2Nb_0.2)O₃, validating it as a compelling high-entropy oxide material for future electronic/energy-related technologies.     

Pressureless sintering and properties of (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramics: The effect of pyrolytic carbon

A novel (Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)C high-entropy ceramic was successfully prepared by pressureless sintering at 2200 °C. With increasing content of resin-derived-carbon, the density, and mechanical and thermal properties increased up to a maximum content of 2～4 wt% resin addition, after which further addition was detrimental. All specimens showed high strength (≥347±36 MPa), with the highest value achieving 450±64 MPa, and fracture toughness significantly higher (>20 %) than those of the corresponding monocarbides and Ta_0.5Hf_0.5C, (Ta_1/3Zr_1/3Nb_1/3)C. The thermal conductivity was approximately equivalent to the lowest value of the corresponding mono-carbides, which was assumed to be due to the lattice distortion effect.     

Diffusion bonding of (Hf0.2Zr0.2Ti0.2Ta0.2Nb0.2)C high-entropy ceramic with metallic Ni foil

To prepare large-sized and complex-shaped components, the feasibility of direct diffusion bonding of (Hf_0.2Zr_0.2Ti_0.2Ta_0.2Nb_0.2)C high-entropy ceramic (HEC) and its diffusion bonding with a metallic Ni foil was investigated, and the interfacial microstructure and mechanical properties of HEC/HEC and HEC/Ni/HEC joints were analyzed. For the direct diffusion bonding, reliable joints with a shear strength of 146 MPa could be achieved when the bonding temperature reached 1500 °C under a pressure of 30 MPa. By introducing a metallic Ni foil as the interlayer, the HEC was successfully bonded at the diffusion temperatures from 1150 °C to 1250 °C under 10 MPa through the formation of Ti₂Ni compound phase. Meanwhile, the HEC(Ni) phase formed by the diffusion of Ni into HEC and Ni(s, s) bulks precipitated in the bonding transition zone. The maximum joint shear strength of 151 MPa was obtained by optimizing the Ni-foil thickness, bonding temperature, and holding time.     

Ultrafast densification of high-entropy oxide (La0.2Nd0.2Sm0.2Eu0.2Gd0.2)2Zr2O7 by reactive flash sintering

Pyrochlore-type high-entropy oxides (HEOs) are usually sintered at high temperatures for a long time to achieve full density. Herein, we synthesized pyrochlore-structured (La_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)₂Zr₂O₇ HEOs with densities up to 99 % at a furnace temperature of 1200 °C in seconds via reactive flash sintering (RFS). The resultant HEOs achieved compositional uniformity at the atomic level and exhibited superior modulus, hardness and fracture toughness compared to the counterparts prepared by conventional solid-state sintering (at 1600 °C for 6 h). The underlying mechanisms for the ultrafast densification of the RFSed-HEOs were addressed in view of the roles of electric field, rapid heating, external pressure and internal reactions.     

Directionally solidified Al2O3/(Y0.2Er0.2Yb0.2Ho0.2Lu0.2)3Al5O12 eutectic high-entropy oxide ceramics with well-oriented structure,high hardness,and low thermal conductivity

Directionally solidified Al₂O₃/(Y_0.2Er_0.2Yb_0.2Ho_0.2Lu_0.2)₃Al₅O₁₂ eutectic high-entropy oxide ceramics (HEOCs) were successfully prepared with an optical floating zone furnace. The Al₂O₃/(Y_0.2Er_0.2Yb_0.2Ho_0.2Lu_0.2)₃Al₅O₁₂ eutectic HEOCs were pure phases with uniform distribution of rare-earth elements. The preferred growth orientation relationships were <10−10 > {0001}Al₂O₃ // <110 > {211}(Y_0.2Er_0.2Yb_0.2Ho_0.2Lu_0.2)₃Al₅O₁₂. The indentation fracture toughness and Vickers hardness were 6.8 ± 0.9 MPa·m^1/2 and 16.1 ± 0.3 GPa, which were higher than that of Al₂O₃/Y₃Al₅O₁₂ eutectic ceramics. The room temperature bending strength was 333 ± 42 MPa. Crack bridging, deflection and bifurcation were the main toughening mechanism. Hardness and reduced modulus mapping results illustrated that the hardness of (Y_0.2Er_0.2Yb_0.2Ho_0.2Lu_0.2)₃Al₅O₁₂ was close to that of Al₂O₃. Thermal expansion coefficient of Al₂O₃/(Y_0.2Er_0.2Yb_0.2Ho_0.2Lu_0.2)₃Al₅O₁₂ eutectic HEOCs was very similar to that of Al₂O₃/Y₃Al₅O₁₂ but thermal conductivity was as low as 4.9 Wm⁻¹ K⁻¹ due to strong lattice distortion. These results suggest that high-entropy Al₂O₃/(Y_0.2Er_0.2Yb_0.2Ho_0.2Lu_0.2)₃Al₅O₁₂ eutectic ceramics are promising candidates for structural components application in gas turbine engines.     

Calcium-Magnesium-Aluminosilicate (CMAS) corrosion resistance of high entropy rare-earth phosphate (Lu0.2Yb0.2Er0.2Y0.2Gd0.2)PO4: A novel environmental barrier coating candidate

Single phase (Lu_0.2Yb_0.2Er_0.2Y_0.2Gd_0.2)PO₄ was synthesized, and its thermal properties and CMAS resistance were investigated to explore its potential as an environmental barrier coating (EBC) candidate. The high entropy phosphate (Lu_0.2Yb_0.2Er_0.2Y_0.2Gd_0.2)PO₄ displays a lower thermal conductivity (2.86 W m⁻¹ K⁻¹ at 1250 K) than all the single component xenotime phase rare-earth phosphates. Interaction of (Lu_0.2Yb_0.2Er_0.2Y_0.2Gd_0.2)PO₄ pellets with CMAS at 1300 °C led to the formation of a dense and uniformed Ca₈MgRE(PO₄)₇ reaction layer, which halted the CMAS penetration into the bulk pellet. At 1400 and 1500 °C the (Lu_0.2Yb_0.2Er_0.2Y_0.2Gd_0.2)PO₄-CMAS corrosion showed CMAS penetrating beyond the reaction layer into the bulk pellet via the grain boundaries, and SiO₂ precipitates remaining at the pellet surface. The effects of duration, temperature, and compositions on the resistance against CMAS corrosion are discussed within the context of optimizing materials design and performance of high entropy rare-earth phosphates as candidates for advanced EBC applications.     

High-entropy transparent (Y0.2La0.2Gd0.2Yb0.2Dy0.2)2Zr2O7 ceramics as novel phosphor materials with multi-wavelength excitation and emission properties

High-entropy ceramics have been extensively studied because of their novel intrinsic properties and have significant potential for application in various fields. In this study, a novel high-entropy transparent ceramic phosphor (Y_0.2La_0.2Gd_0.2Yb_0.2Dy_0.2)₂Zr₂O₇ was successfully prepared via a solid-state reaction and vacuum sintering. X-ray diffraction and scanning electron microscopy analyses were performed to analyze the phases and microstructures of the as-prepared powders and sintered ceramics. The highest in-line transmittance of the developed ceramic was 74 % in both visible and infrared regions. To reveal its luminescent properties as a potential WLED material, the photoluminescence of ceramic samples was analyzed using multi-excitation and emission spectra. Strong emissions originating from Dy³⁺ and Gd³⁺ were observed, and the emission color was effectively regulated under multi-wavelength excitation. Combining excellent optical transmittance with unique photoluminescence performance, the (Y_0.2La_0.2Gd_0.2Yb_0.2Dy_0.2)₂Zr₂O₇ high-entropy transparent ceramics can find potential applications as a novel WLED material with multi-wavelength excitation and tunable emission.     

Orthorhombic to tetragonal polymorphic transformation of YTa3O9 and its inhibition through the design of high-entropy (Y0.2La0.2Ce0.2Nd0.2Gd0.2)Ta3O9

To explore the mechanism of phase transformation, YTa₃O₉ was prepared by an integrated one-step synthesis and sintering method at 1500 °C using Y₂O₃ and Ta₂O₅ powders as starting materials. High-temperature XRD patterns and Raman spectra showed that a phase transformation from orthorhombic to tetragonal took place in YTa₃O₉ through the bond length and angle changes at 300–400 °C, which caused a thermal conductivity rise. To inhibit the phase transformation, a high-entropy (Y_0.2La_0.2Ce_0.2Nd_0.2Gd_0.2)Ta₃O₉ (HE RETa₃O₉) was designed and synthesized at 1550 °C using the integrated solid-state synthesis and sintering method. In tetragonal structured HE RETa₃O₉, phase transformation was inhibited by the high-entropy effect. Furthermore, HE RETa₃O₉ exhibited low thermal conductivity, and its tendency to increase with temperature was alleviated (1.69 W/m·K, 1073 K). Good phase stability, low thermal conductivity and comparable fracture toughness to YSZ make HE RETa₃O₉ promising as a new thermal barrier coating material.     

Processing-dependent stabilization of a dissimilar rare-earth boride in high-entropy (Ti0.2Zr0.2Hf0.2Ta0.2Er0.2)B2 with enhanced hardness and grain boundary segregation

This study demonstrates that 20% of a rare-earth (RE) diboride (ErB₂) can be stabilized in a high-entropy transition metal (TM) diboride, despite the dissimilar chemical properties of RE and TM elements and large differences in lattice parameters of ErB₂ and typical TMB₂. However, the phase formation depends on the fabrication route, which is a noteworthy observation. Specifically, single-phase (Ti_0.2Zr_0.2Hf_0.2Ta_0.2Er_0.2)B₂ is synthesized via reactive spark plasma sintering (SPS) using elemental boron and metal elements. In contract, a specimen made by borocarbothermal reduction of binary oxides and SPS possess significant amounts of two Er-rich secondary phases. Notably, the RE addition in high-entropy TM diboride leads to improved hardness. Aberration-corrected scanning transmission electron microscopy (AC STEM) and energy-dispersive X-ray spectroscopy (EDS) elemental analyses further reveal significant Er segregation at grain boundaries. This work suggests that high-entropy ceramics can have significant solubilities of dissimilar components that may enable new, tunable, and improved properties.     

Microstructure and water corrosion behavior of (Lu0.2Yb0.2Er0.2Tm0.2Sc0.2)2Si2O7 high-entropy rare-earth disilicate coating for SiC coated C/C composites

In order to make carbon/carbon composites suitable for application in gas turbine engine, it is necessary to develop environmental barrier coatings (EBCs) to protect them from reacting with water vapor. In our previous work, a novel high-entropy rare-earth disilicate (Lu_0.2Yb_0.2Er_0.2Tm_0.2Sc_0.2)₂Si₂O₇ ((5RE_0.2)₂Si₂O₇) has been developed and verified as a promising candidate for EBCs. In this work, the (5RE_0.2)₂Si₂O₇ coating was synthesized on the surface of SiC coated C/C composites by supersonic atmospheric plasma spraying method. The protective performance and mechanism of this coating under high temperature water vapor environment was explored in detail. Results showed that the weight change of the sample coated with (5RE_0.2)₂Si₂O₇ was only 0.2% after corrosion for 100 h at 1500 ºC, which proved that (5RE_0.2)₂Si₂O₇ coating could significantly improve the resistance of C/C composites against water vapor corrosion. This work may provide theoretical basis for the design and application of high-entropy rare-earth silicates as EBCs.     

Synthesis,microstructure and mechanical properties of high-entropy (VNbTaMoW)C5 ceramics

High-entropy ceramics (HEC) with a fixed composition of (VNbTaMoW)C₅ were prepared by spark plasma sintering (SPS) from 1500 °C to 2200 °C. XRD, TEM, HRTEM, SAED and EDX were used to investigate effects of the sintering temperatures on compositional homogeneity, constituent phases and microstructure of the HECs. The results showed that single-phase HEC formed at a temperature as low as 1600 °C while ultimate elemental distribution homogeneity could be obtained at 2200 °C. Elemental distribution homogenization was accompanied by microstructural coarsening and oxide impurities aggregating at grain boundaries as temperature increased. SPS at 1900 °C for 12 min could yield uniform HECs (VNbTaMoW)C₅ with Vickers hardness, nanohardness, fracture toughness and Young’s modulus reaching 19.6 GPa, 29.7 GPa, 5.4 MPa m^1/2 and 551 GPa, respectively. The resultant HECs showed excellent wear resistance when coupled with WC at room temperature.     

Crystal structure and microwave dielectric properties of (Mg0.2Ni0.2Zn0.2Co0.2Mn0.2)2SiO4 - A novel high-entropy ceramic

Novel (Mg_0.2Ni_0.2Zn_0.2Co_0.2Mn_0.2)₂SiO₄ (A5SO) high-entropy microwave dielectric ceramics with olivine structure were prepared in the sintering temperature range of 1100 °C–1300 °C via the solid-phase reaction route. The crystal structure was confirmed by XRD, Raman, and Rietveld refinement. Optimal microwave dielectric properties (ε_r = 8.02, tanδ = 0.00051 at 14.5 GHz, and τ_f = ?38.2 ppm/°C) were obtained at the sintering temperature of 1250 °C, where a relative density of 95.1% was detected. The complex chemical bonding theory manifests that the ε_r value of A5SO is mainly affected by the ionicity of A-O (A = Mg, Ni, Zn, Co, Mn) bond, while the dielectric loss is affected by both A-O and Si–O lattice energy. The τ_f value is mainly influenced by the [A(2)O₆] oxygen octahedral distortion (1.8 × 10^?3). The experimental results of this study provide both theoretical and practical guidance for high-entropy microwave dielectric ceramic applications.