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Article

Microwave Absorbing Properties and Mechanism Analysis of Ni–Doped Fe–Based Metallic Microwires

1
School of Materials Science and Engineering, Inner Mongolia University of Technology, Hohhot 010051, China
2
School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
3
Instrumentation Engineering Faculty, Belarusian National Technical University, 220013 Minsk, Belarus
*
Author to whom correspondence should be addressed.
Metals 2022, 12(12), 2041; https://doi.org/10.3390/met12122041
Submission received: 30 October 2022 / Revised: 18 November 2022 / Accepted: 24 November 2022 / Published: 27 November 2022
(This article belongs to the Special Issue Development and Application of Microscale Metallic Fibers)

Abstract

:
Fe–based metallic microwires possess unique microstructure and size effects, exhibiting favorable mechanical, electrical, and magnetic properties, thus distinguishing them as a possible agents for use as microwave absorbing materials. In this paper, the absorbing properties of Ni–doped Fe–based metallic microwires optimized by orthogonal experiments were investigated, and based on the optimal parameters, the influencing mechanism of the Ni doping amount on the absorbing properties was further analyzed. It was noted that at the frequency f = 8.36 GHz, the maximum reflection loss RL and electromagnetic wave absorption efficiency Aeff can reach −54.89 dB and 99.999%, respectively. Moreover, the Ni doping amount could result in the improved wave-absorbing properties of composites, obtain the corresponding optimal parameters, and even change the position of the maximum absorption peak, which are all of great significance for practical engineering applications.

1. Introduction

Currently, with the rapid development of electronic communication technology, the problem of electromagnetic pollution has become increasingly serious. Electromagnetic radiation may cause many hazards, such as human health risks, damage to electronic equipment, information leakage, etc., and has become one of the common concerns of society. Wave-absorbing materials can effectively prevent and control electromagnetic pollution, and presently, a variety of wave-absorbing materials have been developed and widely used in the military, medical and health, and electronic communications fields [1,2,3]. One example is the aircraft stealth coating, which is not only used for anti-corrosion or aesthetic purposes, improving aerodynamic shape, but is also applied as an anti-radar measure, and the outer covering of the communication cable should protect the internal structure, as well as prevent information leakage. Statistical results show that the electromagnetic radiation encountered in daily life is increasing at an annual ratio of 7% to 14% [4], and the demand for radiation absorbing materials is becoming urgent. Therefore, scientifically designing and manufacturing high-performance, wave-absorbing materials that are “light, thin, wide, and strong” (i.e., with light weight, thin thickness, wide absorption frequency, and strong absorption) [5,6,7,8] has become the key research direction at this stage.
The development integration and of lightweight electronic products have become a major trend; therefore, higher requirements are placed on the performance of materials. It is well known that micron-scale metallic wires can be considered as quasi-one-dimensional materials [9], with unique microstructure and size effects due to their large specific surface area, and they have a notable application in small structural devices and precision instruments [10]. For example, Co–based metallic microfibers are suitable as magnetic sensitive materials due to their unique magnetic domain structure and skin effect [11,12,13]; Gd–based metallic microfibers possess minor magnetic and thermal hysteresis and exhibit excellent magnetocaloric properties around the Curie temperature; thus, they can be used as low-temperature refrigerants [14,15]. Fe–based metallic microfibers exhibit the characteristics of high saturation magnetization, good magnetic permeability, low coercivity, excellent soft magnetic properties, abundant natural resources in production, and low production costs [16,17,18,19,20,21], as well as a high electrical loss tangent angle and magnetic anisotropy, which endow them with potential as a good wave absorbing agent. Yao et al. [22] prepared submicron Fe10Ni90 short fibers by oxalic acid precipitation-pyrolysis, filling them in paraffin, with a mass ratio of 20 wt.%. The reflection loss of the composite reached a maximum of −45.37 dB at 13.90 GHz, with a thickness of 2 mm, and the effective absorption bandwidth was 3.78 GHz. Wang et al. [23] cut glass-coated Fe73.5Si13.5B9Nb3Cu1 amorphous microfibers into short segments with a length of 1 mm, and mixed them with paraffin to test their wave-absorbing properties. It was found that the paraffin-based composite sample showed the best absorbing performance, −39.54 dB, at the thickness of 3.5 mm and the Fe–based metallic microfiber filling ratio of 7 wt.%. In the future, metallic microfibers are expected to show rapid development as wave absorbing agent filling coatings for use in the military, medical, and other fields [24,25]. However, there are still few studies regarding the absorbing performance of these microfibers in the frequency range of 2–18 GHz, and the loss mechanism of micro-scale metallic wires to electromagnetic waves also lacks comprehensive study. Therefore, the absorbing properties and mechanisms of microwires at this frequency range need to be further explored and investigated.
Herein, the microwave absorbing properties of Fe–based metallic microwires were optimized based on orthogonal experiments and transmission line theory, and the influence of Ni doping content on the microwave absorbing properties of metallic microwires composites was analyzed accordingly. Moreover, absorbing materials with high reflection loss and effective absorption bandwidth in the frequency range of 2–18 GHz were obtained, and the absorbing mechanism of Ni–doped Fe–based metallic microwires/paraffin-based composites was further clarified, providing a theoretical basis for the final practical engineering applications.

2. Materials and Methods

Fe–based metallic microwires were prepared as the wave absorber by a rotation dipping process, as reported in our previously study [26,27]. The master alloys were proportioned according to the nominal composition of Fe78–xSi13B9Nix (x = 0, 1, 2, 3, in at.%), and the symbols of FeSiB, FeSiBNi1, FeSiBNi2, and FeSiBNi3 are used to represent the Fe–Si–B–Ni series of metallic microwires. Meanwhile, the wire diameter (35 ± 3 μm) was precisely measured by a helical micrometer, the long wires were cut into short 1 mm segments using scissors, and the segments were then fully mixed with paraffin, according to different mass ratios, to prepare paraffin-based composites with an inner diameter of 3.04 mm, an outer diameter of 7 mm, and a thickness of 1–5 mm. The electromagnetic parameters of the samples in the frequency ranged from 2 GHz to 18 GHz and were measured by a vector network analyzer (VNA, type: N5234B, Keysight Technologies, Santa Rosa, CA, USA). The results for the real part of complex permittivity ε′, the imaginary part of complex permittivity ε″, the real part of complex permeability μ′, the imaginary part of complex permeability μ″ at the corresponding frequency f were obtained and calculated by the self–compiled program software. The reflection loss RL was calculated accordingly by using the transmission line theory. The expression for reflection loss RL is:
R L = 20 lg | μ r ε r tan h ( r d ) 1 μ r ε r tan h ( r d ) + 1 |
where εr is the complex permittivity of the material, μr is the complex permeability of the material, d is the sample thickness, and r is the propagation coefficient of the electromagnetic wave in the material, whose expressions are:
ε r = ε r j ε r
μ r = μ r j μ r
r = i · 2 π   f ( μ r i μ r ) ( ε r i ε r ) c
where c is the speed of light.

3. Results and Discussion

3.1. Optimization of Microwave Absorbing Properties of Fe–Based Metallic Microwires Based on Orthogonal Experiments

According to the previous study [27], the FeSiBNi2 metallic microwires exhibited the best comprehensive properties; therefore, they were selected as the wave absorber in the orthogonal experiment. Figure 1 shows the electromagnetic parameters of the as–prepared FeSiBNi2 metallic microwires with a mass ratio of 30 wt.%, a sample thickness of 1–5 mm, and a frequency range of 2–18 GHz. The values of the real part ε′ and the imaginary part ε″ of the complex permittivity of samples with different thicknesses vary in the range of 6.28–25.04 and −1.76–11.74, respectively. Except for the ε′ and ε″ curves of the samples with a thickness of 1 mm, which tend to be horizontal, the samples with other thicknesses exhibit an obvious resonance phenomena in the whole frequency range, as shown in Figure 1a,b. The real part of complex permeability μ′ and the imaginary part of complex permeability μ″ of samples with different thicknesses range from 0.66–1.64 and −0.22–0.82, respectively, and the curves show different degrees of fluctuation, as shown in Figure 1c,d.
When the mass ratio of the FeSiBNi2 metal short wires is 30 wt.%, only the samples with thicknesses of 1 mm and 4 mm fail to exhibit effective absorption peaks in the frequency range of 2–18 GHz, while the samples with other thicknesses can effectively absorb electromagnetic waves, and the absorption efficiency Aeff exceeds 90%. The sample with a thickness of 1.5 mm shows the largest effective absorption bandwidth (EAB) (<−10 dB) [28], of 3.42 GHz (14.58–18 GHz); the sample with a thickness of 4.5 mm exhibits the strongest absorption of electromagnetic waves at a frequency of 4.04 GHz, which is −25.18 dB, and the absorption efficiency Aeff reaches 99%, as shown in Figure 2.
Under the same conditions, a quarter–wavelength matching model is usually used to explain the relationship between the sample thickness and the corresponding frequency of the maximum absorption peak, and the formula is as follows [29,30,31]:
t m = n λ 4 = n c 4 f m | ε r μ r | ( n = 1 ,   3 ,   5 )
where tm—the thickness of samples;
fm—the frequency corresponding to the maximum absorption peak;
λ—the wavelength of the electromagnetic wave in the absorber.
The quarter–wavelength matching model is essentially the thickness matching of the material. At a relatively low frequency, the complex permittivity and complex permeability of the material are relatively lower, depending on the frequency, so for thicker materials, the corresponding absorption peaks are shifted to relatively low frequencies. The corresponding relationship between thickness and frequency is directly reflected in Figure 2. As the thickness of the sample increases, the frequency corresponding to the maximum absorption peak tends to be of a lower frequency, which conforms to the quarter–wavelength matching model.
Figure 3 displays the electromagnetic parameters of the as–prepared FeSiBNi2 metallic short microwires with a mass ratio of 40 wt.%, a sample thickness of 1–5 mm, and a frequency range of 2–18 GHz. As shown in Figure 3a,b, the values of ε′ and ε″ for samples with different thicknesses are in the range of 5.98–32.51 and −6.45–15.81, respectively. In the relatively low frequency stage, the curves of ε′ and ε″ are relatively smooth, and as the frequency increases, the curves of ε′ and ε″ both show obvious resonance. Figure 3c,d shows the relationship between μ′ and μ″ with frequency, respectively, where the value of μ′ is in the range of 0.42–3.17, and the value of μ″ is in the range of 0.55–1.66. In the frequency range from 2 GHz to 6 GHz, the changes in μ′ and μ″ are relatively small, while at the frequency greater than 6 GHz, the curves begin to show larger resonance peaks.
Figure 4 reveals the relationship between reflection loss and frequency and sample thickness for samples with different thicknesses in the frequency range of 2–18 GHz, with the mass ratio of the as–prepared FeSiBNi2 metallic microwires being 40 wt.%. As shown, the absorption efficiency of all thickness samples exceeds 90% in this frequency range. With the increase in the thickness, the frequency corresponding to the maximum absorption peak of the sample shifts to the low frequency, and this result conforms to the quarter–wavelength matching model as a whole. However, there is one exception: the maximum absorption peak of the sample with a thickness of 1 mm is between the maximum absorption peaks of the samples with a thickness of 1.5 mm and 2 mm. The reason for this is that, as the frequency increases, both the complex permittivity and the complex permeability change significantly, causing the relationship between the thickness of the sample and the frequency corresponding to the maximum absorption peak to be relatively sensitive to these changes [29], which leads to the unusual “thickness–frequency” relationship. As shown in Figure 4, the sample with a thickness of 2 mm possesses the best electromagnetic wave absorption capability at a frequency of 8.36 GHz, with a maximum reflection loss of −54.89 dB and an absorption efficiency Aeff of 99.999%. It is worth noting that the sample with a thickness of 2 mm shows a second absorption peak in the frequency range of 15.01–15.45 GHz, whose maximum reflection loss is −13.11 dB, and whose corresponding frequency is consistent with the three–quarter wavelength. Further, it can be expressed in Formula (4–1) as: the n of the first absorption peak is 1, and 3 is the n value of the second absorption peak. The remaining thickness samples also have the ability to effectively absorb electromagnetic waves in the frequency range of 2–18 GHz, and the effective absorption bandwidth EAB (<−10 dB) of the sample with a thickness of 1.5 mm is the largest at 4.28 GHz (13.72–18 GHz). In short, the sample with a thickness of 2 mm has two absorption peaks in this frequency range, which effectively broadens the absorption range; the totally effective absorption bandwidth EAB (<−10 dB) is 1.81 GHz (both 7.49–8.86 GHz and 15.01–15.45 GHz), and the absorption efficiency is as high as 99.999%; thus, the absorption performance is the most significant.
Figure 5 present the electromagnetic parameters of the as–prepared FeSiBNi2 short metallic microwires with a mass ratio of 50 wt.%, a thickness of 1–5 mm, and a frequency range of 2–18 GHz. The value distribution of ε′ is in the range of 10.44–39.92, in which there are a large number of resonance peaks, and with the rise in frequency, the ε′ curve shows a trend of first increasing and then decreasing, as shown in Figure 5a. Figure 5b shows the relationship between ε′ and f. The distribution range of ε″ is between 0.3 and 31.5, and the curve is relatively stable in the frequency range of 2–4 GHz, while a large number of resonance peaks appear at the frequency of greater than 4 GHz. Figure 5c,d are the graphs of the relationship between μ′ and μ″ as a function of frequency, and whose distribution ranges are between 0.68–2.04 and −0.25–1.49, respectively, with different degrees of resonance.
Figure 6 shows the relationship between reflection loss and frequency and sample thickness for samples with different thicknesses in the frequency range of 2–18 GHz, with the mass ratio of as–prepared FeSiBNi2 metallic microwires being 50 wt.%. It can be seen that samples with all thicknesses exhibit effective absorption in this frequency range, and the absorption efficiency Aeff reaches 90%. Among these, the reflection loss of the sample with a thickness of 4.5 mm reaches the maximum at the frequency of 2.74 GHz, which is −18.98 dB, and the electromagnetic wave absorption ability is stronger than that of the samples with other thicknesses. The sample with a thickness of 1.5 mm has a maximum effective absorption bandwidth EAB (<−10 dB) of 1.87 GHz (9.47–11.34 GHz). With the increase in sample thickness, the frequency corresponding to the maximum reflection loss of each sample tends to be of low frequency, which conforms to the quarter–wavelength matching model.
In summary, as the mass fraction of the metallic microwires increases, the real part of the complex permittivity ε′ and the imaginary part ε″ of the sample both increase. This is because when the electromagnetic wave enters the interior of the sample, as the number of metallic microwires increases, more interfaces will be formed between the microwires and the paraffin wax—as well as between the microwires—resulting in increased interface polarization. Meanwhile, with the increase in the microwires, the number of defective parts in the microwires will also increase, and more electric dipoles will be formed, thereby increasing the polarization of the dipoles, making the induced electric field stronger and endowing ε′ and ε″ with a wider range. However, with the increase in the doping amount of the metallic microwires, the real part of the complex permeability μ′ and the imaginary part μ″ exhibit no significant change, indicating that the magnetic loss has little effect on the wave-absorbing performance of the sample. When the wire content is constant, the change in the thickness of the sample will lead to the change in the electromagnetic parameters, which will affect the impedance of the composite material, thus affecting the wave absorbing performance of the composite material.

3.2. Effect of Doping Content on Absorbing Properties of Fe–Based Metallic Wire/Paraffin–Based Composites

In order further to explore the effect of Ni doping on the absorbing properties of Fe–based metallic microwires, the FeSiB, FeSiBNi1, FeSiBNi2, and FeSiBNi3 metallic microwires, respesctively, were filled in paraffin with a mass ratio of 40 wt.% to prepare a paraffin-based composite material with a thickness of 2 mm to further test their absorbing properties, and the results were obtained, as shown in Figure 7. Figure 7a,b shows the relationship between the ε′ and f of Ni–doped Fe–based metallic wire/paraffin-based composites. In the figure, the ε′ and ε″ of Fe–based metallic microwires exhibit different degrees of resonance in the whole frequency range, indicating that the electrical loss acts in the whole frequency range. Figure 7c,d shows the relationship between the real part of complex permeability μ′ and the imaginary part μ″ of as–prepared Ni–doped Fe–based metallic microwires as a function of frequency. It can be seen that when the frequency is less than 12 GHz, all the curves of μ′ and μ″ are distributed in a relatively narrow interval, and there is a small–amplitude resonance. However, at frequencies greater than 12 GHz, all the curves show a large resonance, among which, the formant peak of FeSiBNi2 is the largest. In general, the tanδe and the tanδm represent the contributions of electrical and magnetic losses to electromagnetic wave absorption, respectively. At different frequency ranges, since the complex permittivity and complex permeability of Fe–based metallic wires/paraffin-based composites with different Ni doping amounts change continuously with frequency, the electrical loss tangent angle tanδe and the magnetic loss tangent angle tanδm are also constantly changing, and the electrical and magnetic loss curves are intertwined, as shown in Figure 7e,f.
Figure 8 shows the reflection loss curves of the as–prepared Ni–doped Fe–based metallic microwires, in which the reflection loss of the FeSiB metallic microwires reaches the maximum, −11.77 dB, at the frequency of 10.12 GHz, and the effective absorption bandwidth EAB (<−10 dB) is 1.79 GHz (8.90–10.69 GHz). With the addition of Ni, the maximum absorption peak is shifted to low frequency, and the maximum absorption peak of FeSiBNi1 is at 7.82 GHz, the corresponding reflection loss is −13.27 dB, and the effective absorption bandwidth EAB (<−10 dB) is 1.04 GHz (7.28–8.32 GHz). However, the maximum reflection loss of FeSiBNi2 is −54.89 dB, the corresponding frequency is 8.36 GHz, and the total effective absorption bandwidth EAB (<−10 dB) is 1.81 GHz (both 7.49–8.86 GHz and 15.01–15.45 GHz); the maximum reflection loss of FeSiBNi3 is −13.06 dB, the corresponding frequency is 8.14 GHz, and the effective absorption bandwidth EAB (<−10 dB) is 1.76 GHz (7.64–9.40 GHz). In conclusion, with the addition of Ni, the effective absorption bandwidth EAB first decreased and then increased, and the Ni doping significantly changed the absorbing performance of the material, among which the FeSiBNi2 showed the best absorbing performance.

3.3. Mechanism Analysis of Wave–Absorbing Properties of Ni–Doped Fe Based Wire/Paraffin Matrix Composites

Figure 9 reveals the electrical and magnetic loss mechanisms of Ni–doped Fe–based metallic wires/paraffin-based composites in the frequency range of 2–18 GHz. From Figure 9a, many semicircles with different curvature radii can be noted in the four curves, and each semicircle represents a Debye relaxation process, indicating the occurrence of dielectric relaxation loss, which mainly includes interface polarization and dipole polarization. Based on Debye’s theory, ε′ and ε″ can be expressed as [32,33]:
ε = ε + ε s ε 1 + ω 2 τ 2
ε = ( ε s ε ) ω τ ε s + ε ω 2 τ 2  
where ω—angular frequency;
εs—static permittivity;
ε—limit value of permittivity change;
τ—relaxation period.
Based on Formulas (6) and (7), the Cole–Cole Equation (8) can be obtained and expressed as:
[ ε 1 2 ( ε s + ε ) ] 2 + ( ε ) 2 = 1 4 ( ε s + ε ) 2
It can be seen from Figure 9b that all the curves show a trend of first increasing and then decreasing, indicating that with the increase in frequency, the conductance loss first increases and then decreases. In a certain frequency range, Ni doping increases the carrier concentration, which contributes to the improvement in electrical conductivity.
As an important parameter for evaluating conductivity loss, the conductivity can be expressed as [30]:
σ = ω ε 0 ε  
where ε0 is the dielectric constant of free space, which is 8.845 × 10−12 F/m.
By calculating the eddy current loss of the material to determine the type of magnetic loss, and the eddy current loss Co can be expressed by the following formula [30]:
C 0 = μ ( μ ) 2 f 1
As shown in Figure 9c, with the increase in frequency, all the curves first decrease and then increase, without an obvious horizontal straight line, indicating that no composite materials consisting of different compositions show any eddy current loss over the entire frequency range, and that natural resonance is the type of magnetic loss in the frequency range of 2–10 GHz, and exchange resonance is the type of magnetic loss noted in the frequency range of 10–18 GHz.
The results shown above, combined with the relevant electromagnetic parameters, show that the electrical losses of the as–prepared Ni–doped Fe–based metallic wires/paraffin-based composites include resonance loss, conductance loss, interface polarization, and dipole polarization, while the magnetic losses include natural resonance and exchange resonance. The test processes regarding FeSiB, FeSiBNi1, and FeSiBNi3 metallic microwires all adopt the “mass ratio–thickness” scheme optimized by FeSiBNi2 based on the orthogonal test. Due to the change in alloy composition, the test could not be carried out under the respective optimal “mass ratio–thickness” scheme; therefore, it is only used as a reference. However, by comparing the reflection loss of the FeSiB, FeSiBNi1, and FeSiBNi3 metallic microwires, it is found that Ni doping has a great influence on the absorbing performance. The fundamental reason for this is that the addition of Ni changes the composition and structure of the microwires, and the interaction between atoms changes the magnetic anisotropy [34,35,36]; thus, the absorbing performance of the materials varies.
Figure 10 depicts a typical schematic of the mechanism of the different types of electromagnetic loss. The interface polarization loss of Fe–based metallic microwires is mainly the polarization phenomenon at the interface between wires and wires, and wires and paraffin; the dipole polarization is mainly due to the existence of atomic vacancies in the microwires and the heteroatoms in the local area, which produce the macroscopic polarization intensity. With the continuous change in the electromagnetic wave frequency, the moving carriers inside the material also cause the actual conductivity to change, and the induced current causes the loss of internal conductivity. The ferromagnetic resonance occurs because the magnetic moment, caused by electromagnetic waves, strongly absorbs energy in the alternating magnetic field [37].
In summary, the mass ratio of the Fe–based metallic microwires, sample thickness, and the Ni doping amount have a great influence on the microwave absorbing properties of the composites. In this paper, the influencing mechanism of different factors on the microwave absorbing properties of different composites is revealed from the perspectives of electrical loss and magnetic loss. The types of electrical loss mainly include resonance loss, dipole polarization, interface polarization, and conductivity loss, while the types of magnetic loss are natural resonance and exchange resonance, respectively; various different types of losses exert an important impact on the microwave absorption characteristics of Fe–based metallic wire/paraffin-based composites.

4. Conclusions

In summary, by comparatively studying the effect and mechanism of Ni doping on the absorbing properties of Fe–based metallic microwires, the following conclusions are drawn:
(1)
The mass ratio of Fe–based metallic microwires and the thickness of the sample both have a certain impact on the electromagnetic parameters and impedance matching characteristics of the composite material. Based on the analysis results of the orthogonal experiment, the composite material exhibits a better absorption performance with the mass of the FeSiBNi2 metallic microwires of 40 wt.% and the sample thickness of 2 mm; the maximum reflection loss RL and electromagnetic wave absorption efficiency Aeff reach −54.89 dB and 99.999%, respectively, at the frequency f = 8.36 GHz. Simultaneously, there are two effective absorption peaks, corresponding to the frequency ranges of 7.49–8.86 GHz and 15.01–15.45 GHz, respectively; that is, the totally effective absorption bandwidth EAB (<−10 dB) is 1.81 GHz (both 7.49–8.86 GHz and 15.01–15.45 GHz).
(2)
Ni doping changes the chemical composition and structure of Fe–based metallic microwires; the interaction between atoms is enhanced, and the change in magnetic anisotropy leads to the change in magnetic loss, which in turn, has a great influence on the wave-absorbing properties of the composite materials. Among these, when the sample thickness is 2 mm and the microwires mass ratio is 40 wt.%, the FeSiBNi2 metallic wire/paraffin-based composite exhibits better absorbing performance. In the meantime, Ni doping can effectively control the position of the maximum absorption peak, and with the increase in the Ni doping amount, the position of the absorption peak shifts to a lower frequency.
(3)
The types of electrical loss in the Fe–based metallic microwires mainly include resonance loss, dipole polarization, interface polarization, and conductance loss, while the types of magnetic loss include natural resonance and exchange resonance, respectively. Under the combined action of electrical loss and magnetic loss, Fe–based metallic microwires show strong attenuation to electromagnetic waves, exhibiting their potential as excellent wave absorbing agents.

Author Contributions

Conceptualization, J.L.; methodology, J.L., Y.W. and G.Q; investigation, Y.W., R.L., Y.Z. and C.W.; resources, J.L., R.L. and C.W.; formal analysis, J.L. and G.Q.; writing–original draft preparation, J.L., Y.W., R.L. and Y.Z.; writing—review and editing, supervision, R.L., C.W., Y.W. and Y.Z.; project administration, J.L.; funding acquisition, J.L. All authors have read and agreed to the published version of the manuscript.

Funding

This work was financially supported by the National Natural Science Foundation of China (NSFC) under grant nos. 51871124, 52061035, 51561026, and 51401111, the Ministry of Education Fok Ying–tung Foundation for Young Teachers (no. 161043), the “Grassland Talents” Project of the Inner Mongolia Autonomous Region (no. CYYC9025), the Inner Mongolia Natural Science Cultivating Fund for Distinguished Young Scholars (no. 2020JQ05), the Science and Technology Planning Project of the Inner Mongolia Autonomous Region (no. 2020GG0267), the Program for Innovative Research Teams in the Universities of the Inner Mongolia Autonomous Region (no. NMGIRT2211), and the Inner Mongolia University of Technology Key Discipline Team Project of Materials Science (no. ZD202012).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author, Jingshun Liu, upon reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Frequency dependence of electromagnetic parameters of as–prepared FeSiBNi2 metallic microwires mass ratio of 30 wt.%, with different thickness of the composite at 2–18 GHz: (a) ε′; (b) ε″; (c) μ′; (d) μ″.
Figure 1. Frequency dependence of electromagnetic parameters of as–prepared FeSiBNi2 metallic microwires mass ratio of 30 wt.%, with different thickness of the composite at 2–18 GHz: (a) ε′; (b) ε″; (c) μ′; (d) μ″.
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Figure 2. Frequency dependence of reflection loss and sample thickness of as–prepared FeSiBNi2 metallic microwires when the mass ratio is 30 wt.% with the thickness of the composite ranging from 2–18 GHz: (a) frequency dependence of RL curves; (b) 2D contour plots of thickness and reflection loss; (c) 3D variation diagram of reflection loss after fitting.
Figure 2. Frequency dependence of reflection loss and sample thickness of as–prepared FeSiBNi2 metallic microwires when the mass ratio is 30 wt.% with the thickness of the composite ranging from 2–18 GHz: (a) frequency dependence of RL curves; (b) 2D contour plots of thickness and reflection loss; (c) 3D variation diagram of reflection loss after fitting.
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Figure 3. Frequency dependence of electromagnetic parameters of as–prepared FeSiBNi2 metallic microwires with a mass ratio of 40 wt.% with different thicknesses of composite ranging from 2–18 GHz: (a) ε′; (b) ε″; (c) μ′; (d) μ″.
Figure 3. Frequency dependence of electromagnetic parameters of as–prepared FeSiBNi2 metallic microwires with a mass ratio of 40 wt.% with different thicknesses of composite ranging from 2–18 GHz: (a) ε′; (b) ε″; (c) μ′; (d) μ″.
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Figure 4. Frequency dependence of reflection loss and sample thickness of as–prepared FeSiBNi2 metallic microwires with a mass ratio of 40 wt.% with different thicknesses of composite at 2–18 GHz: (a) frequency dependence of RL curves; (b) 2D contour plots of thickness and reflection loss; (c) 3D variation diagram of reflection loss after fitting.
Figure 4. Frequency dependence of reflection loss and sample thickness of as–prepared FeSiBNi2 metallic microwires with a mass ratio of 40 wt.% with different thicknesses of composite at 2–18 GHz: (a) frequency dependence of RL curves; (b) 2D contour plots of thickness and reflection loss; (c) 3D variation diagram of reflection loss after fitting.
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Figure 5. Frequency dependence of electromagnetic parameters of as–prepared FeSiBNi2 metallic microwires when the mass ratio is 50 wt.% with different thicknesses of the composite at 2–18 GHz: (a) ε′; (b) ε″; (c) μ′; (d) μ″.
Figure 5. Frequency dependence of electromagnetic parameters of as–prepared FeSiBNi2 metallic microwires when the mass ratio is 50 wt.% with different thicknesses of the composite at 2–18 GHz: (a) ε′; (b) ε″; (c) μ′; (d) μ″.
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Figure 6. Frequency dependence of reflection loss and sample thickness of as–prepared FeSiBNi2 metallic microwires with a mass ratio of 50 wt.% with different thicknesses of composite at 2–18 GHz: (a) frequency dependence of RL curves; (b) 2D contour plots of thickness and reflection loss; (c) 3D variation diagram of reflection loss after fitting.
Figure 6. Frequency dependence of reflection loss and sample thickness of as–prepared FeSiBNi2 metallic microwires with a mass ratio of 50 wt.% with different thicknesses of composite at 2–18 GHz: (a) frequency dependence of RL curves; (b) 2D contour plots of thickness and reflection loss; (c) 3D variation diagram of reflection loss after fitting.
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Figure 7. Frequency dependence of electromagnetic parameters of as–prepared Ni–doped Fe–based metallic microwires/paraffin matrix composites at 2–18 GHz: (a) ε′; (b) ε″; (c) μ′; (d) μ″; (e) tanδe; (f) tanδm.
Figure 7. Frequency dependence of electromagnetic parameters of as–prepared Ni–doped Fe–based metallic microwires/paraffin matrix composites at 2–18 GHz: (a) ε′; (b) ε″; (c) μ′; (d) μ″; (e) tanδe; (f) tanδm.
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Figure 8. Frequency dependence of reflection loss of as–prepared Ni–doped Fe–based metallic microwires/paraffin matrix composites at 2–18 GHz.
Figure 8. Frequency dependence of reflection loss of as–prepared Ni–doped Fe–based metallic microwires/paraffin matrix composites at 2–18 GHz.
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Figure 9. Loss mechanism of as–prepared Ni–doped Fe–based metallic microwires/paraffin matrix composites at 2–18 GHz: (a) Cole–Cole curves; (b) frequency dependence of dielectric conductivity; (c) frequency dependence of eddy current loss.
Figure 9. Loss mechanism of as–prepared Ni–doped Fe–based metallic microwires/paraffin matrix composites at 2–18 GHz: (a) Cole–Cole curves; (b) frequency dependence of dielectric conductivity; (c) frequency dependence of eddy current loss.
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Figure 10. Schematic diagram of the electromagnetic loss mechanisms of Fe–based metallic microwires.
Figure 10. Schematic diagram of the electromagnetic loss mechanisms of Fe–based metallic microwires.
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Liu, J.; Wang, Y.; Qu, G.; Liu, R.; Zhang, Y.; Wang, C. Microwave Absorbing Properties and Mechanism Analysis of Ni–Doped Fe–Based Metallic Microwires. Metals 2022, 12, 2041. https://doi.org/10.3390/met12122041

AMA Style

Liu J, Wang Y, Qu G, Liu R, Zhang Y, Wang C. Microwave Absorbing Properties and Mechanism Analysis of Ni–Doped Fe–Based Metallic Microwires. Metals. 2022; 12(12):2041. https://doi.org/10.3390/met12122041

Chicago/Turabian Style

Liu, Jingshun, Yamei Wang, Guanda Qu, Rui Liu, Yun Zhang, and Congliang Wang. 2022. "Microwave Absorbing Properties and Mechanism Analysis of Ni–Doped Fe–Based Metallic Microwires" Metals 12, no. 12: 2041. https://doi.org/10.3390/met12122041

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