To prepare SiBCN/FeSiAl composites, we first fabricated SiBCN ceramics via a polymer precursor method^[23]. Subsequently, SiBCN ceramics with a flake-like graphene structure were obtained through high-energy ball milling. The prepared SiBCN was then incorporated into flake-shaped FeSiAl to tailor the microwave properties. Epoxy resin was selected as a temporary binder to take advantage of its good processability for fabricating complex-shaped green bodies. The preparation procedure is illustrated in Figure 1. Specifically, the SiBCN and flake-shaped FeSiAl were weighed according to a predetermined ratio and placed into a ball milling jar. Ball milling was conducted at a ball-to-powder ratio of 5:1 and a rotational speed of 300 r/min for one hour. The as-obtained composite powder was uniformly blended with epoxy resin. Subsequently, the slurry was poured into a pre-designed mold. After drying and solidification, the material was released from the mold to obtain the green body. After green-body forming, the debinding process was carried out under an argon atmosphere. First, heating to 50 °C at 1 °C/min, then to 300 °C at 0.2 °C/min with a 1 h hold, followed by heating to 500 °C at 0.1 °C/min with a 2 h hold, and finally to 800 °C at 0.5 °C/min with a 2 h hold to ensure complete decomposition and volatilization of the resin. The sample was then sintered at 1,500 °C for 3 h.

The microstructures of flake-shaped FeSiAl powder and the composite powder were characterized using field-emission scanning electron microscopy (FESEM, Nova 400 NanoSEM, USA). Coaxial ring (inner diameter of 3.04 mm, outer diameter of 7.0 mm), waveguide fixture, and torsion metamaterial absorber (dimensions of 180 mm × 180 mm × 15 mm) samples were fabricated via mold casting. The complex permittivity and complex permeability of the microwave absorbing materials were measured over the frequency range of 2 to 18 GHz using a vector network analyzer (VNA, Ceyear 3672c) equipped with a coaxial test fixture. To evaluate the microwave absorption performance of the SiBCN/FeSiAl based metamaterial at elevated temperatures, a custom-designed experimental setup incorporating an antenna-based measurement system combined with a programmable heating stage was employed. This setup allowed for in situ reflectivity testing across a broad temperature interval, spanning from ambient conditions up to 800 °C, all while preserving thermal stability. The measurement procedure followed a three-step sequence. Initially, the specimen was raised to the desired temperature at a ramp rate of 10 °C/min. Subsequently, it was held isothermally for 15 min to achieve thermal equilibration. Finally, reflectivity data were acquired over the 2~18 GHz frequency band using the arch-based technique.

As shown in the X-ray diffraction (XRD) pattern [Figure 2A], the final sample is a fully inorganic ceramic matrix composite, composed of BN, FeSiAl, SiC, CN, FeSi and graphene, together with the residual amorphous SiBCN matrix (corresponding to the broad diffuse hump in the pattern), where the sharp diffraction peaks superimposed on the amorphous hump indicate that the SiBCN matrix underwent partial crystallization at 1,500 °C, which is consistent with the reported high-temperature crystallization behavior of SiBCN ceramics in the literature. Figure 2B-D presents the matrix material with 20% SiBCN. As shown in Figure 2B, FeSiAl exhibits a flake-like structure. FeSiAl alloy possesses a high saturation magnetization (Ms). When applied in the GHz frequency range, this alloy achieves effective dissipation of microwave wave energy primarily through eddy current loss mechanisms and natural resonance effects. The flake-shaped FeSiAl exhibits magnetocrystalline anisotropy, which can overcome the Snoek limit and enhance the magnetic loss capability. According to previous studies, the main constituents of SiBCN ceramics are Si₃N₄, SiC, and graphite. The high-energy collisions and local instantaneous high temperatures generated during high-energy ball milling induce exfoliation, amorphization, and even vaporization-redeposition of graphite, thereby producing flake-like graphene. The dielectric loss generated by its excellent electrical conductivity can combine with the microwave synergy effect formed after compositing with FeSiAl to efficiently absorb and attenuate microwave waves.

Figure 3A-D presents the complex permittivity (ε_r = ε’ - iε”) and relative complex permeability (μ_r = μ’ - iμ”) of SiBCN/FeSiAl composites with varying SiBCN proportions after heat treatment. The measurements were conducted using the coaxial transmission line method with a VNA, over the frequency range of 2 to 18 GHz at room temperature. The hysteresis effect between dielectric polarization and the alternating microwave wave gives rise to frequency dispersion characteristics in ε’. As shown in Figure 3A, the ε’ values of the composites with different SiBCN proportions vary within the ranges of 38.26~26.96, 40.19~26.41, and 32.48~23.06, respectively. Among them, the sample containing 20% SiBCN exhibits the largest ε’. Furthermore, this sample demonstrates the highest ε” and μ” values compared to the other samples, indicating stronger microwave attenuation capability. In addition, the tanδ_e value of the 20% SiBCN sample is also the highest. Therefore, the 20% SiBCN sample exhibits the optimal microwave attenuation performance.

Impedance matching characteristics represent one of the key factors determining whether microwaves can enter the absorbing material in large quantities to be dissipated. Figure 3E shows the impedance matching curves of the composite ceramics with different SiBCN contents with a thickness of 5 mm. It can be observed from the figure that as the SiBCN content increases, the impedance matching value of the composite gradually improves. This indicates that the addition of SiBCN enables more microwaves to enter the ceramic and be dissipated. The dielectric loss tangent (tanδ_ε) and magnetic loss tangent (tanδ_m) of the composite ceramics with different SiBCN contents are shown in Figure 3F.

According to transmission line theory, for a single-layer electromagnetic medium, the microwave absorption performance can be characterized by the RL values. Therefore, the RL values of the SiBCN/FeSiAl composites with different proportions can be calculated based on the complex permittivity and complex permeability as follows^[24]:

(1) $$ Z_{i n}=Z_{0} \sqrt{\frac{\mu_{r}}{\varepsilon_{r}}} \tanh \frac{j 2 \pi f d \sqrt{\mu_{r} \varepsilon_{r}}}{c} $$

(2) $$ R L=20 \lg \left|\frac{Z_{i n}-Z_{0}}{Z_{i n}+Z_{0}}\right| $$

where Z_in is the input impedance at the interface between the material and free space, Z₀ is the characteristic impedance of free space (377 Ω), f is the frequency, d is the thickness, and c is the speed of light in vacuum. The RL of the composites with different proportions was calculated, and the results are shown in Figure 3G-I.

It can be observed from the figures that when the SiBCN content is 20%, the microwave attenuation capability of the composite ceramic is relatively weak. The RL_min is only -8.3 dB at 15.44 GHz, and the bandwidth with RL below -5 dB is 9.44 GHz. When the SiBCN content is increased to 30%, as shown in Figure 3H, the RL_min and the bandwidth for RL < -5 dB are -9.34 dB and 10.72 GHz, respectively. For the sample with 40% SiBCN content, as shown in Figure 3I, the RL_min and the bandwidth for RL < -5 dB reach -12.72 dB and 16 GHz, respectively. The reason why the RL performance of the composite gradually enhances with increasing SiBCN content can be explained by Figure 3C. Although the 20% SiBCN sample exhibits the highest ε” and tanδ_e, its relatively high complex permittivity leads to poor impedance matching with free space, causing most of the incident microwaves to be reflected at the surface rather than entering the absorber. In contrast, the 40% SiBCN sample, despite showing a slightly lower dielectric loss, provides a complex permittivity-to-permeability ratio that is closer to the ideal matching condition (Z_in/Z₀ → 1), allowing more microwaves to penetrate into the material and be effectively dissipated, which ultimately yields the lowest RL_min and the broadest effective absorption bandwidth.

The Nautiloidea represents an elegant gradient spiral architecture. Through the impedance-gradient design of this spiral composite structure, microwaves can gradually dissipate energy when penetrating the material rather than being directly reflected. The constant angle of the spiral ensures directional wave transmission, while the gradient dimensional variation corresponds to the isometric increase of the nautilus shell chambers, which is expected to achieve smooth wave energy attenuation. Therefore, leveraging the spatial hierarchy of the spiral structure, this study designed a torsion gradient cavity metamaterial absorber using the composite ceramic with SiBCN/FeSiAl. The structure is illustrated in Figure 4. The torsion gradient cavity metamaterial absorber consists of periodically arranged unit cells. Here, h₁ represents the height of the gradient structure, h₂ represents the height of the matrix layer, α₁ and β₁ are the twist angle and tilt angle of the gradient structure, respectively, while α₂ and β₂ are the twist angle and tilt angle of the inner chamber structure. Additionally, r₁ and r₂ represent the radii of the upper and lower bases of the unit cell, respectively.

Numerical simulations of the torsion gradient cavity metamaterial’s microwave absorption were performed using the frequency-domain solver of Computer Simulation Technology (CST) Microwave Studio. The analysis focused on the 2~18 GHz band, which covers key operational bands for Wireless Local Area Network (WLAN), satellite links, and military radar. The incident wave was generated via a Floquet port, defined with its electric field in the +X direction and magnetic field in the +Y direction. As in the reflectivity measurements, a perfect electric conductor boundary was introduced behind the test sample, acting as an equivalent to the metal reflector plate employed in the actual RL testing.

Figure 5 illustrates the significant variation in the RL of the torsion gradient cavity metamaterial, designed with the 20% SiBCN ceramic matrix as an example, as a function of structural parameters. The influence of parameter h₁ on the RL of the torsion gradient cavity metamaterial is presented in Figure 5A and E. As h₁ increases, the microwave transmission path is prolonged, which enhances energy dissipation and thereby improves the RL performance. Concurrently, the resonance wavelength undergoes a redshift, with the reflection band shifting toward the lower-frequency regime. A reduced RL value corresponds to superior absorption capability. Specifically, an RL below -10 dB signifies that over 90% of the incident microwave energy is absorbed. At h₁ =10 mm, the EAB extends across the entire 2-18 GHz range, with a strong-absorption bandwidth (RL < -20 dB, absorptivity > 99%) of 6.2 GHz. Moreover, when h₁ is increased to 11 mm, a minimum RL of -50.1 dB is achieved at 12.73 GHz, demonstrating outstanding absorption performance under this condition. Further increments in h₁, however, lead to a saturation trend in the absorption bandwidth. As shown in Figure 5B and F, as r₁ increases from 3.5 mm to 6.5 mm, the bandwidth of the strong microwave absorption region first decreases from 9.4 GHz to 3.5 GHz, then gradually broadens to 6.1 GHz, and subsequently decreases to 2.4 GHz. The size of r₁ directly determines the unit cell dimension of the metamaterial, thereby affecting the resonance frequency, electromagnetic localization effect, and impedance matching performance of the metamaterial. A smaller unit cell size leads to a higher resonance frequency, as smaller structures can support microwave resonance at higher frequencies. An appropriate unit cell size can enhance the local microwave field, thereby improving absorption efficiency. Moreover, a smaller unit cell size typically increases the surface current path, enhancing absorption.

As observed in Figure 5C and G, with fixed parameters h₁ = 13 mm, h₂ = 2 mm, r₁ = 5.5 mm, r₂ = 3.0 mm, α₂ = 10°, β₁ = -10°, β₂ = -15°, both the microwave loss performance and the loss bandwidth gradually increase with increasing α₁. The EAB consistently covers 2~18 GHz. Within the strong absorption region, the bandwidth expands from 5.7 GHz to 6.6 GHz, while the reflection peak value slightly intensifies from -25.2 dB to -25.4 dB. This behavior can be attributed to variations in the helical angle α_1, which alter the conical configuration of the helical segment and its impedance matching characteristics with free space. Additionally, the gradient structural design induces complex multiple reflections and inter-unit interactions, significantly enhancing interference losses arising from path differences. As shown in Figure 5D and H, with an increase in β₁, the strong absorption bandwidth of the torsion gradient cavity metamaterial first broadens and then narrows. Superior microwave absorption performance is observed in the high-frequency region (X-Ku band). Based on a multi-objective synergistic optimization strategy that prioritizes maximizing the EAB as the primary goal, achieving the lowest possible RL_min as the secondary goal, while also taking into account structural thickness and fabrication feasibility. In terms of the optimization algorithm, we employed a Trust Region Optimization Algorithm, with the optimization objective set as RL < -10 dB over the full 2~18 GHz frequency range, and with predefined upper and lower bounds for each parameter. This algorithm constructs a linear model based on a “trust region” around the starting point of the primary optimization data, first performing a global coarse-grid scan to identify high-performance regions, followed by a localized refined search within these regions until convergence is achieved. The optimal design parameters are determined as follows: h₁ = 13 mm, h₂ = 2 mm, r₁ = 5.5 mm, r₂ = 3.0 mm, α₁ = 30°, α₂ = 10°, β₁ = -10°, β₂ = -15°.

Based on the optimized structural parameters, the electromagnetic parameters of SiBCN/FeSiAl composite materials were simulated at different ratios. The results are shown in Figure 6A. The EAB of the metamaterial structure calculated based on different electromagnetic parameter materials all cover 2~18 GHz, proving that the absorption performance of the absorbing metamaterial is concentrated on its structural geometric parameters rather than the intrinsic electromagnetic parameters of the material. To evaluate the high-temperature electromagnetic wave (EMW) absorption performance of the torsion gradient cavity metamaterial, the metamaterial array was processed into a 180 mm × 180 mm sample, and the reflection loss was tested as shown in Figure 6B-D. The test results show that the simulated EAB covers 2-18 GHz with an RL_min of -24.4 dB at 10.86 GHz. At room temperature, the measured EAB is 2.4~18 GHz with an RL_min of -36 dB at 13 GHz. At 400 °C, the EAB is 3.6-18 GHz with an RL_min of -21.5 dB at 13.1 GHz. At 600 °C, the EAB is 3.6-18 GHz with an RL_min of -23 dB at 12.8 GHz. At 800 °C, the EAB is 3.0-18 GHz with an RL_min of -25.7 dB at 13 GHz. The experimental results are in good overall agreement with the simulations, with all measured RL_min values below -20 dB and EAB values exceeding 14.4 GHz across the entire temperature range. After one thermal cycle, the EAB at 800 °C is 3.7-17.9 GHz, with a RL_min of -21.7 dB at 12.6 GHz. Furthermore, the RL_min variation remains within 16%, and the peak frequency shift is less than 0.4 GHz after thermal cycling, fully demonstrating that this composite exhibits excellent and stable microwave absorption performance across the broad temperature range of 25-800 °C. Figure 6E shows the thermogravimetry (TG) curve of the matrix material with 20% SiBCN. It can be seen from the figure that there is almost no obvious weight change for the material. The TG analysis results demonstrate the structural reliability and oxidation resistance of this composite material under high-temperature service conditions, providing strong support for its practical engineering applications.

The absorption peak frequency shifts from 10.86 GHz in simulation to 13.0 GHz in experiment, with a deviation of +2.14 GHz (approximately 19.7%). The RL_min changes from -24.4 dB to -36 dB, with a deviation of 11.6 dB. The EAB changes from 16 GHz (2~18 GHz) to 15.6 GHz (2.4~18 GHz), with a deviation of 0.4 GHz (approximately 2.5%). These deviations primarily originate from the following factors. First, fabrication tolerance is the main cause of the high-frequency shift of the absorption peak, as feature sizes in the metamaterial structure are subject to machining errors of approximately ±0.1 mm, and according to the inverse relationship between resonant frequency and structural dimensions, dimensional shrinkage directly leads to a shift of the resonant frequency toward higher frequencies. Second, measurement errors in electromagnetic parameters introduce approximately ±5% uncertainty in the complex permittivity and permeability used as simulation inputs, which in turn affects the accuracy of RL peak depth calculations. Third, surface roughness and finite-size effects also influence the measured results, because the simulation assumes an ideally smooth surface and infinite periodic boundary conditions, whereas the measured sample has a finite size (180 mm × 180 mm), and edge diffraction effects can introduce certain frequency drifts and loss variations. Fourth, measurement uncertainties in the arch-reflector test system can introduce approximately ±0.2 GHz frequency deviation and approximately ±1.5 dB amplitude error. Based on the above analysis, the deviations between simulation and experiment fall within a reasonable range, and the two are in strong agreement in terms of the number of absorption peaks and overall trend, which fully verifies the reliability of the simulation model and design methodology.

The equivalent dielectric constant (ε_eff) and equivalent magnetic permeability (μ_eff) of the structure were calculated using the equivalent medium theory^[25,26]. As shown in Figure 6F and G, the real part of the effective complex dielectric constant of the structure is distributed between -3.2 and 88. The real part of the effective complex magnetic permeability is distributed between -53.7 and 34.0, and the imaginary part of the permeability increases from 0 of the dielectric material to 1.8~92.2, indicating that the design of the torsion gradient cavity metamaterial significantly improves the microwave loss performance of the material. As a representative technology in the field of electronics, the Smith Chart provides a fast, low-computation, and graphical method to evaluate impedance-matching performance. The Smith impedance spectrum of the torsion gradient cavity metamaterial is shown in Figure 6H. The metamaterial has four intersections with the horizontal real axis, indicating that the metamaterial structure has four resonances, and the projection of the real axis of the impedance curve is between 0.5 and 2, indicating that the impedance of the structure is nearly ideal and meets the requirement of RL < -10 dB. This is something that a single material cannot achieve. Figure 6I shows the power at different frequencies of the metamaterial absorber.

The microwave loss mechanism of the torsion gradient cavity metamaterial is visually demonstrated by analyzing the electric field distribution, magnetic field distribution, and power loss density distribution at the start frequency (2.00 GHz), the RL_min frequency point (10.86 GHz), and the ending frequency point (18.00 GHz), as shown in Figure 7. The figure that extensive electric field concentration appears on the sample surface. This strong electric field concentration is attributed to the improved impedance matching and the high equivalent permittivity resulting from the torsion gradient cavity metamaterial. Within the torsion gradient cavity metamaterial structure, the magnetic field distribution exhibits a clear frequency-dependent spatial shift. While it remains largely confined to the lower layer at low frequencies, it progressively migrates to the upper layer with increasing frequency. This behavior suggests that the bottom layer plays a dominant role in absorbing low-frequency microwaves. The power loss density distribution at 2.00 GHz is mainly concentrated in the lower layer, which is consistent with the magnetic field distribution. This indicates that at 2.00 GHz, magnetic loss plays a dominant role in the lower layer. As the frequency increases, significant changes occur in the electric and magnetic fields on the surface of the material, which indicates the structural effect of the metamaterial. As frequency increases, both the electric and magnetic fields on the material surface change significantly, reflecting the structural effect of the metamaterial. The strong electric and magnetic fields near and inside the cavity of the metamaterial indicate the presence of edge diffraction or secondary scattering in these regions. The metastructure achieves broadband absorption through a combination of material loss and structural effects. At 10.86 GHz, the combined effect of electric loss on the surface and magnetic loss inside the material results in the maximum electromagnetic loss. The microwave loss at 18.00 GHz also results from the combined action of electric loss and magnetic loss. By extracting the electric and magnetic field distributions at each frequency point using CST field monitors, we obtained the quantitative loss contributions at each frequency: the total power loss is 0.487 W at 2 GHz, 0.498 W at 10.86 GHz, and 0.498 W at 18 GHz. Combined with the effective electromagnetic parameters of the material at each frequency for loss contribution separation, where ε” = -9.23 and μ” = 1.85 at 2 GHz, ε” = 3.79 and μ” = 4.49 at 10.86 GHz, and ε” = 3.90 and μ” = 2.63 at 18 GHz. The quantitative results reveal that at the low-frequency band of 2 GHz, magnetic loss dominates due to the negative ε” value reflecting low-frequency dispersive behavior. At the intermediate frequency of 10.86 GHz, electric and magnetic losses reach a synergistic balance, jointly contributing to the formation of the strong absorption peak. At the high frequency of 18 GHz, ε” further increases to 3.90 with significantly enhanced electric loss contribution, while μ” decreases to 2.63 with relatively weakened magnetic loss, yet the total loss level remains high. These quantitative results are in strong agreement with the qualitative trends observed in the field distribution and power loss density contour maps at different frequencies. Therefore, a rational structural design enables the absorber to exhibit not only a nearly ideal electromagnetic response but also multiple loss mechanisms simultaneously, thereby enhancing its electromagnetic wave absorption capability.

A comparison between the torsion gradient cavity metamaterial designed in this work and the high-temperature-resistant metamaterial structures previously reported in the literature is presented in Figure 7B. The figure shows that the operating temperature range of previously reported metamaterials for microwave absorption spans from 400 °C to 1,100 °C. Due to thermal attenuation of the complex permeability and complex permittivity at elevated temperatures, impedance mismatch is aggravated, while the increased electrical conductivity enhances surface reflection. Consequently, the microwave absorption bandwidth at high temperatures is often limited, typically below 8 GHz. In contrast, the metamaterial designed in this work achieves a microwave absorption bandwidth of 15 GHz while maintaining a low RL_min value. Therefore, the SiBCN/FeSiAl torsion gradient cavity metamaterial not only demonstrates excellent electromagnetic wave absorption capability but also offers high-temperature resistance, a wide frequency band, strong absorption, and multi-functional integration compared to other composite materials. This work further demonstrates its distinctive strengths in high-temperature suitability and structural integrability.