Microwave All-Dielectric Metamaterial Design of FeSiAl/MWCNT Composite for Low-Frequency Broadband-Absorbing Properties

Abstract

FeSiAl flakes were fabricated by vibrating ball milling the FeSiAl ribbons. And the microwave absorption properties of FeSiAl flakes were improved by doping the multi-wall carbon nanotubes (MWCNTs) with different mass concentrations. The results show that the FeSiAl/MWCNT composites exhibit significantly improved microwave absorption performance with advantages of strong and broadband absorption in the L-band and S-band. In particular, the reflection loss (RL) of the FeSiAl/MWCNT2 composite reaches −7.4 dB at 1.0 GHz, whereupon, through the electromagnetic simulation software CST Microwave Studio, FeSiAl/MWCNT2 all-dielectric metamaterial absorbers (ADMMAs) were macroscopically designed, achieving an ultra-wideband absorption (RL ≤ −10 dB) of 14.4 GHz (3.6~18.0 GHz). It is recognized that the standing wavelength resonance and diffraction effect are responsible for absorbing electromagnetic waves, and the broadband absorption is improved via dielectric dispersion; their synergistic effect makes the ADMMAs exhibit good microwave absorption performance. This work provides a useful method for designing microwave absorption materials with broadband absorption.

1. Introduction

FeSiAl alloy is a soft magnetic material widely used due to the advantages of good saturation magnetization, low coercivity, and high resistivity [1,2]. In particular, the flake-shaped Sendust alloy has a higher magnetic permeability under a low-frequency range, demonstrating an excellent microwave absorption performance in the P-band and L-band. Nonetheless, FeSiAl absorbents exhibit poor broadband absorption performance due to poor magnetic–dielectric impedance matching, which is caused by the rapid decrease in the real part of permeability with frequency. It is difficult to fulfill the requirements of high-performance absorption in the S, C, X, and Ku bands [3,4,5,6,7,8,9]. As a magnetic absorbent, FeSiAl can only produce an absorption peak within a narrow frequency bandwidth depending on magnetic resonance, and its resonant frequency is usually in the low-frequency band (below 500 MHz). Consequently, if the real part of the permittivity of the magnetic absorber has a similar change trend as the permeability, which significantly decreases in the GHz, the impedance matching characteristics of the absorbents should be significantly improved, thereby broadening the absorption bandwidth [10,11,12,13,14,15,16]. For instance, Sun et al. prepared an FeSiAl/graphite composite by using the ball milling method, and the absorption bandwidth with an RL value lower than −10 dB reached up to 2.4 GHz (13.68~16.08 GHz) at 1.5 mm [17]. Nowadays, Li et al. constructed a CNTs/FeSiAl composite through the in suit growth of CNTs on FeSiAl flakes, which achieved less than −10 dB bandwidth from 12 to 15.52 GHz with a thickness of 1.7 mm [18]. The previous study demonstrated that the dielectric response of magnetic absorbers is regulated by doping carbon-based materials, and the absorption bandwidth is broadened effectively. Moreover, multi-wall carbon nanotubes have become a popular material in recent years, due to their abundance of lattice defects, which creates polarization centers in the dielectric response effect [19,20]. Furthermore, their unique lattice structure leads to high electron mobility, enabling significant dielectric modulation with only a small amount of doping [21,22].

Based on the method for improving magnetic absorbents, as mentioned above, we selected an FeSiAl absorbent with good performance obtained through our process exploration. The absorbent could maintain high real and imaginary permeability in the low-frequency band with a low filling concentration (55 wt%). Next, the FeSiAl/MWCNT composites were prepared by doping MWCNTs with different mass concentrations to FeSiAl absorbent (55 wt%). We extensively discussed the synergistic effects and absorption mechanisms of FeSiAl/MWCNT composites, and the results indicated that the absorption capacity of the FeSiAl absorbent could be improved in the low-frequency band. In particular, the RL value of the FeSiAl/MWCNT2 composite reached −7.4 dB at 1.0 GHz. However, the absorption performance of the FeSiAl/MWCNT composites remained insufficient in the X and Ku bands.

Macrostructure optimization has been proved to be an effective approach to enhance the absorption performance of absorbers [23,24,25]. In particular, all-dielectric metamaterials completely constructed with dielectric materials, which have the advantages of simple structures, isotropy, and low preparation costs compared to traditional metal-based metamaterials, and many different kinds of ADMMAs have been designed [26,27,28,29,30]. For instance, Zhuang et al. deployed an FeCo soft magnetic composite with a droplet shape as the primary resonant element, obtaining an absorptivity (90%) from 7.8 GHz to 13.8 GHz [31]. Nowadays, a broadband ADMMA designed with carbon black can achieve a bandwidth (RL ≤ −10 dB) from 6.1 GHz to 18.0 GHz under a total thickness of 3.9 mm [32]. Therefore, we used CST electromagnetic simulation software for metamaterial design, which was combined with the dielectric regulation method, and the ADDMA was designed by optimizing the geometric parameters of the periodic units. The results showed a significant improvement in the broadband absorbent, and the FeSiAl/MWCNT2 ADMMA achieved an ultra-broadband absorption from 3.6 GHz to 18.0 GHz. We analyzed the dielectric dispersion effect of MWCNTs contributing to broadband absorption properties of ADMMAs. This work provides valuable insights into material dielectric control at the microscale and the macrostructure optimization design of microwave absorbers.

2. Materials and Methods

Initially, the FeSiAl flakes were prepared using Fe, Si, and Al, each with a purity of over 99.9%, and following the atomic ratio of Sendust alloy (85 wt% Fe; 9.6 wt% Si; 5.4 wt% Al). It was smelted with a vacuum arc Melter (WK series, Physcience Opto-Electronics Co., Ltd., Beijing, China) under Ar atmosphere at 10 × 10⁻³ MPa. Next, the smelted FeSiAl alloy was transferred to a vacuum stripping machine (WK-IIB, Physcience Opto-electronics Co., Ltd., Beijing, China) within an Ar atmosphere (5 × 10⁻³ MPa), and the FeSiAl melt-spun ribbons were fabricated at a frequency of 100 Hz (the line speed of the copper wheel is 70 m/s). Then, the FeSiAl melt-spun ribbons (thickness less than 1 μm) were placed in a high-speed vibrating ball mill (QM-3B, Nanjing Nanda Instrument Co., Ltd., Nanjing, China) with a vibrating frequency of 1200 rpm, and the FeSiAl powders were produced after being milled for 6 h with a ball-to-powder weight ratio of 20:1 in ethanol. Finally, the well-prepared FeSiAl flakes were mixed with molten paraffin at a mass ratio of 55 wt% and labeled as an FeSiAl sample. And then the FeSiAl flakes/multi-wall carbon nanotubes composites were obtained using a simple preparation method by stirring the mixture of FeSiAl flakes (55 wt%), MWCNTs (purchased by Nanjing XFNANO Materials Tech. Co., Ltd., Nanjing, China), and molten paraffin using a hotplate stirrer for 5 min. The diameter of MWCNTs was 1–2 nm, the length was 5–30 μm, the special surface area (SSA) was more than 690 m²/g, and the SEM image of MWCNTs was shown in Figure S1 (Supporting Information). The mass ratios of MWCNTs in the mixture were 1 wt%, 2 wt%, and 3 wt%, and then the prepared FeSiAl/MWCNT composites were labeled FeSiAl/MWCNT1, FeSiAl/MWCNT2, and FeSiAl/MWCNT3, respectively.

The morphologies and microstructures of the FeSiAl powders were examined via X-ray diffraction (XRD, Bruker D8 ADVANCE, Billerica, MA, USA) and scanning electron microscopy (SEM, Hitachi S4800, Tokyo, Japan). The XRD diffraction patterns of the FeSiAl powders were tested from 20° to 80° with a scan step of 0.02°/s and 50 steps per degree using Cu Ka radiation, and analyzed by using Jade 6.0 software. The magnetic properties of the FeSiAl flakes were evaluated using a vibrating sample magnetometer (VSM, Lakeshore, Model 7400 series) at room temperature. The electromagnetic parameters of the FeSiAl and FeSiAl/MWCNT samples were measured using the coaxial-line method with a vector network analyzer (VNA, Agilent PNA N5244A, Santa Clara, CA, USA), covering a frequency range of 0.2~18 GHz. The measured samples were pressed into a toroidal shape (φ_in = 3.04 mm, φ_out = 7.00 mm) with a thickness of 3~4 mm. Based on the transmission line theory, the reflection loss (RL) values can be computed using the following formulas [33,34].

$$RL \left(\mathrm{dB}\right)=20\log \left|\frac{z_{in}-1}{z_{in}+1}\right|$$

(1)

$$z_{in}=\sqrt{\frac{{\mu }_r}{{\epsilon }_r}}\tan h\left[j\frac{2\pi fd}{c}\sqrt{{\epsilon }_r{\mu }_r}\right]$$

(2)

where Z_in is the normalized input impedance, f is the frequency, and d is the layer thickness. Furthermore, the absorption properties of the FeSiAl/MWCNT2 ADMMA under normal incidence were studied through simulation using the electromagnetic simulation software CST Microwave Studio (CST Studio Suite 2020, Dassault systemes Co., Ltd., Paris, France).

3. Results and Discussion

The SEM measurement was utilized to evaluate the morphology of FeSiAl flakes. As shown in Figure 1a, most of the FeSiAl powders appeared with flake shapes with well-defined particles, and their radial sizes mostly fell within the range of 10~15 μm, while the thickness of the particles was about 0.4 μm. Obviously, the FeSiAl particles had a high aspect ratio (about 25~37.5), which could significantly enhance the low-frequency magnetic permeability [7].

The X-ray diffraction patterns of FeSiAl flakes are illustrated in Figure 1b; there are two diffraction peaks in the range of 10~80°, which appear at 44.6° and 65.0°. These can be determined as the (110) and (200) crystal planes of the α-Fe (PDF#06-0696). The crystal system of FeSiAl flakes is a body-centered cubic (BCC) lattice structure, and the phase structure consists solely of α-Fe phase, as the diffraction peaks of Si and Al atoms are not found in this spectrum, indicating that significant amounts of Si and Al have dissolved into the crystal lattice of α-Fe completely after milling for 6 h [35,36].

It is well known that static magnetic property plays an important role in investigating the permeability of magnetic materials. The magnetic hysteresis loop of FeSiAl flakes is presented in Figure 1c: the saturation magnetization (Ms) value of FeSiAl flakes was 138.6 A·m²·kg⁻¹ (138.6 emu·g⁻¹, CGS), and the coercivity (Hc) was 10,748 A·m⁻¹ (0.0135 T, CGS). Specifically, the FeSiAl sample had a high Ms value and exhibits typical ferromagnetic hysteresis behavior. The high Ms value contributes to the high initial permeability, which can provide a good impedance matching characteristic and broadband microwave absorption for the FeSiAl flakes [37].

The complex permittivity and permeability against frequency for FeSiAl sample, FeSiAl/MWCNT1, FeSiAl/MWCNT2, and FeSiAl/MWCNT3 composites are presented in Figure 2a,b,d,e, respectively. It can be observed that the FeSiAl sample had high ε′ and μ′ values. The high ε′ value can be attributed to the large radial scale, which leads to a long conductive length, facilitating the formation of a conductive network. The ε′ value increases with the MWCNTs doping concentration, and when the doping concentration reaches 2 wt%, the real part of the permittivity exhibits significant dielectric dispersion characteristics. This contributes to the impedance matching characteristics and enhances the broadband microwave absorption [38]. However, at a doping concentration of 3 wt%, the imaginary part of the permittivity rises to about 40, indicating a considerable influence of the conductance loss on the dielectric loss property. Regarding the effect of MWCNT doping on the real and imaginary parts of the permeability, this was observed to be minimal. The high μ′ value at a low frequency can be attributed to the resonance frequency of FeSiAl, which typically occurs in the low-frequency band [5]. Additionally, the real part of the permeability decreases rapidly with frequency, which is related to its low Ms value.

To investigate the intrinsic microwave dissipation mechanism for the microwave absorption of the four samples, Figure 2c,f demonstrate the loss tangents calculated according to the complex permittivity and permeability of the FeSiAl flakes sample, FeSiAl/MWCNT1, FeSiAl/MWCNT2, and FeSiAl/MWCNT3 composites. It is evident that the magnetic loss angles ($\tan {\delta }_{\mu }=\mu ″/\mu ’$) vary little with frequency, which is consistent with the results shown in Figure 2d,e. On the other hand, the dielectric loss angles ($\tan {\delta }_{\epsilon }=\epsilon ″/\epsilon ’$) noticeably increase with the filling concentration, indicating that the interfacial polarization, defect polarization, and electric conductivity are significantly enhanced in the composite by doping MWCNTs. According to free electron theory, the electric conductivity (σ) is proportional to the imaginary part of the permeability (${\epsilon }^{″}$); it can be expressed by Equation (3), as below [39,40]:

$$\sigma =2\pi {\epsilon }^{″}{\epsilon }_{0}f$$

(3)

where σ is the electric conductivity, ${\epsilon }_0$ represents the vacuum permittivity, and f is frequency, respectively.

Cole–Cole circles are usually used to describe dielectric response mechanisms, where the semicircle in the Cole–Cole curve indicates the polarization relaxation process and the linear part corresponds to the occurrence of conductivity loss. As shown in Figure 3, the variation trends for the curves of the three samples were basically the same, indicating that the main dielectric response mechanisms within the composite material were not significantly different with the varying doping concentrations, and the differing concentrations led to variations in the strength of the response. Typically, within a composite material, there exist multiple dielectric relaxation mechanisms that can be described using a modified Cole–Cole model [41]:

$${\chi }^{\ast }\left(\omega \right)={\chi }^{\prime }-i{\chi }^{″}=\frac{{\chi }_s}{1+{\left(i\omega \tau \right)}^n}=\frac{{\chi }_{s\alpha }}{1+{\left(i\omega {\tau }_{\alpha }\right)}^{n_{\alpha }}}+\frac{{\chi }_{s\beta }}{1+{\left(i\omega {\tau }_{\beta }\right)}^{n_{\beta }}}$$

(4)

The above equation mainly encompasses two relaxation mechanisms, where τ_α and τ_β represent the relaxation time constants of the two relaxation processes, n_α and n_β denote the shape parameters of the two relaxation processes with 0 ≤ n ≤ 1, and χ_sα and χ_sβ correspond to the static polarizabilities. From Figure 3, it is evident that the relaxation center frequency in the high-frequency range exhibits minimal variation with increasing quantities of MWCNTs addition, remaining around 10 GHz, and the response frequency changes subtly with the increase in MWCNT doping concentration; this relaxation in the high-frequency band is caused by the defect polarization of the MWCNTs, and the response frequency is relatively less affected by concentration changes. In contrast, the center frequency of responses in the low-frequency range undergoes significant fluctuations as the concentration varies. For instance, at an addition of 3 wt%, the response frequency was 2.1 GHz, while at 1 wt% addition, the frequency increased to 5.7 GHz. The response frequency moves significantly towards a low-frequency band with the doping concentration, and this behavior aligns with the response characteristics of interface polarization stemming from spatial charge accumulation, and can be analyzed using circuit models [42]. The interface effects within the composite material can be likened to a capacitive circuit, where the increasing concentration of carbon nanotubes enlarges the interface area with the composite material. This enlargement is analogous to the augmentation of the area of capacitor plates, resulting in an increase in capacitance. The resonant frequency formula of a capacitive circuit is f = 1/(2πRC), thus explaining the rapid decrease in the relaxation frequency of interface polarization as the concentration increases.

Furthermore, the tails of the three Cole–Cole curves approximate linearly; this portion corresponds to conductivity loss, including the contributions of both alternating current conductivity and the real part of the hopping conductivity. However, as shown in Figure 3, it can be observed that the frequency of the nearly linear curves vary significantly at different concentrations, and the starting frequency decreases as the concentration increases. The main reason is that the increase in MWCNT concentration leads to a broad distribution range of interface relaxation time constants. The broadening frequency linewidth of the loss covers a large region, which conceals the contribution of the conductivity loss, due to the conductivity loss shifting to low-frequency ranges. Additionally, it is worth mentioning that, according to the theory proposed by Joncher et al. [43], as the conductivity of the composite increases, the dispersion effect of the real part of the dielectric becomes more significant. This can be verified by the dielectric measurement curve of the composite with 3 wt% MWCNT doping concentration. However, the increased conductivity of the composite enhances its metallic properties, which is unfavorable for electromagnetic wave penetration into the material’s interior. Therefore, achieving a balance is necessary when using carbon-based materials to modulate the dielectric response of magnetic absorbers for broadening the absorption bandwidth [44,45,46]. This involves determining the optimal additive amount to simultaneously enhance absorption intensity and absorption bandwidth.

For the purpose of the microwave absorption characteristics, reflection loss curves at various thickness were simulated using Equations (1) and (2). It can be seen from Figure 4a–d that the minimum RL value of the FeSiAl/MWCNT1 composite reached −10.2 dB at 1.6 GHz with a thickness of 5.0 mm, and the RL values of the other samples could not achieve −10 dB within a thickness of 1.0–5.0 mm. The FeSiAl/MWCNT2 exhibits excellent low-frequency microwave absorption properties, which satisfy the requirements of engineering applications. Its matching absorption peak even reached 1.0 GHz with a thickness of 5.0 mm, and the minimum RL value was −7.5 dB. All the samples exhibited a similar trend, the absorption peak shifting towards a lower frequency range with the increase in sample thickness, and the amplitudes of RL value increased first and then decreased afterwards. As the doping concentration of MWCNT increased, the absorption peak shifted further towards lower frequencies, and the peak value decreased. This phenomenon can be attributed to the increase in the ε value of the FeSiAl/MWCNT composite with higher doping concentration, which leads to a poorer impedance matching effect.

A quarter-wavelength resonance theory can explain this behavior, where the ideal matching thickness (t_m) of the absorbing coating (Dallenbach layer) should be an odd multiple of a quarter wavelength. When the phase difference is an odd multiple of a quarter wavelength, interference cancellation occurs, resulting in a significant weakening of the reflected electromagnetic wave. The calculation formula for this is as follows [47]:

$$t_m=\frac{nc}{4f_m\sqrt{\left|{\mu }_r{\epsilon }_r\right|}} \left(n=1,3,5\dots \right)$$

(5)

where c is the light velocity in vacuum and $f_m$ is the peak frequency of absorbing materials. The reflection loss curves on the frequency and thickness of the four samples are illustrated in Figure 4e–h, and the t_m with nλ/4 (n = 1, 3) position curves calculated by Equation (5) are also shown in these figures. It is obvious that absorption regions are concentrate on the 1/4 and 3/4 wavelength regions, and the absorption mechanism of the single-layer absorbing coating can be explained by the 1/4 wavelength resonance model.

As mentioned above, it is evident that the real and imaginary parts of permittivity increase with MWCNT doping, and the dielectric dispersion becomes more pronounced. However, we observed that the impedance matching became worse with the increase in the overall conductivity and complex permittivity. Though these characteristics are unsuitable for continuous coating or plating, they are needed in ADMMA design. Thus, we used the FeSiAl/MWCNT2 composite to construct ADMMA, the periodic unit structures of which are depicted in Figure 5a,b. The absorption properties were optimized using the geometric parameter optimization method, with h = 4.5 mm, h₁ = 1.3 mm, r = 1.6 mm, and p = 4.1 mm. For comparison, we also simulated the absorption properties of an ADMMA based on an FeSiAl composite with the same geometric dimensions. The RL curves of both absorbers are presented in Figure 5c. It can be observed that both the ADMMAs display two absorption peaks, and the FeSiAl/MWCNT2 ADMMA exhibits superior absorption performance, achieving a broadband absorption from 3.6 GHz to 18 GHz. Meanwhile, the FeSiAl/MWCNT2 ADMMA maintains good absorption property at low frequency, with an RL value of −6 dB at 2 GHz.

In order to analyze the absorption mechanisms, we used the effective medium approximation theory and treated the upper layer, consisting of periodic block arrays, as an effective medium. Consequently, we derived the electromagnetic parameters of the effective medium for both the FeSiAl and FeSiAl/MWCNT2 ADMMAs, with their complex permittivity and complex permeability shown in Figure 6a,c, respectively. Next, we replaced the upper layer with plate layers of the same thickness and electromagnetic parameters. The effective RL curves were displayed alongside the actual RL curves in Figure 6b,d, respectively. From the results of effective RL and actual RL curves, it can be observed that both actual curves had two absorption peaks, while both effective curves had only one peak, appearing near the first peak of corresponding actual curves. Meanwhile, since the ε′ value of the FeSiAl/MWCNT2 composite presented much more obvious frequency dispersion characteristics, and the FeSiAl/MWCNT2 ADMMA exhibited superior broadband performance through the macrostructure design. Hence, the FeSiAl/MWCNT2 ADMMA was selected for further analysis.

As shown in Figure 6d, it can be observed that both curves matched well in the low-frequency range, and the absorption peak of the effective curve near 6 GHz corresponded to the first absorption peak of the actual curve. However, as the frequency increased, the differences between the two became more significant, especially after 10.7 GHz; the effective RL value could not reach −10 dB, with the second absorption peak disappearing. That is because as the unit size becomes smaller relative to the wavelength, the electromagnetic parameters of the effective medium can more accurately reflect the overall response to electromagnetic waves. As the frequency increases, the wavelength becomes smaller and the influence of specific details in the structure becomes more significant and cannot be ignored. The obvious discrepancy between the effective and actual RL curves in the high-frequency range indicates that the standing wave resonance is not the main mechanism of the traditional two-layer absorbers. In practice, other mechanisms caused by the structure also contribute to the overall absorption, which cannot be ignored.

From Figure 7c, it can be seen that the RL curve of the FeSiAl/MWCNT2 ADDMA exhibits two absorption peaks, at 4.8 GHz and 14.5 GHz, respectively. The first absorption peak is attributed to the standing wave resonance of the traditional two-layer absorbing material. We simulated the distribution of magnetic field density, electric field density, and energy loss density at 4.8 GHz (y-z plane), as shown in Figure 7a–c. It can be observed that the energy loss mainly occurred near the junction between the bottom edge of the block and the lower plate, which is also the region where the internal electromagnetic field is strong, especially the magnetic field. This is because the magnetic resonance frequency of FeSiAl is very low, resulting in a high imaginary part of permeability (μ″) in the low-frequency range. Additionally, the real parts of both permittivity and permeability revealed strong frequency dispersion characteristics in the low-frequency range, broadening the absorption peak. Hence, the FeSiAl/MWCNT2 ADDMA maintained an RL value of −6 dB at 2 GHz.

The distribution of magnetic field density, electric field density, and energy loss density on the top surface (x-y plane) of the block at 14.5 GHz were simulated, as shown in Figure 7d–f and Figure S2 (Supporting Information). It can be observed that the energy loss mainly occurred near the top corners of the block, which is also where the internal electromagnetic field is strong. This is because as the frequency increases, the unit size approaches the wavelength, and diffraction effects become more apparent. The significant edge diffraction resulted in localized field enhancement at the edges and corners. Additionally, the μ″ value at high frequency was lower than the μ″ value at low frequency, while the imaginary part of permittivity (ε″) remained high. Thus, both the dielectric loss and magnetic loss play an important role.

4. Conclusions

In conclusion, we fabricated FeSiAl flakes and FeSiAl/multi-wall carbon nanotube (MWCNT) composites. The result shows that the doping of MWCNT enhances the dielectric loss of the composite by increasing the interfacial polarization, conduction, and defect polarization loss. Compared with the FeSiAl flakes, the FeSiAl/MWCNT composites exhibited a greatly improved microwave absorption performance, with advantages of strong and broadband absorption in the low-frequency band, and with a thickness of 5.0 mm. The RL value of the FeSiAl/MWCNT2 composite reached −7.4 dB at 1.0 GHz. Moreover, by combining FeSiAl/MWCNT2 absorbing materials with all-dielectric metamaterial design, we achieved a remarkable absorption bandwidth (below −10 dB) of 14.4 GHz (3.6~18.0 GHz) with two absorption peaks. The first peak is attributable to standing wavelength resonance, while the other can be ascribed to diffraction effects. The improvement in broadband characteristics brought about by dielectric dispersion also makes an important contribution. This work provides inspiration and insight for the design of all-dielectric metamaterial absorbers, which have great potential for practical applications in future.