Preparation and Electromagnetic Absorption Properties of Fe73.2Si16.2B6.6Nb3Cu1 Nanocrystalline Powder

In order to decrease and control electromagnetic pollution, absorbing materials with better electromagnetic wave absorption properties should be developed. In this paper, a nanocrystalline alloy ribbon with the composition of Fe73.2Si16.2B6.6Nb3Cu1 was designed and prepared. Nanocrystalline alloy powder was obtained by high-energy ball milling treatment. The effects of ball milling time on the soft magnetic properties, microstructure, morphology, and electromagnetic wave absorption properties of alloy powder were investigated. The results showed that, as time increased, α-(Fe, Si) gradually transformed into the amorphous phase, and the maximum saturation magnetization (Ms) reached 135.25 emu/g. The nanocrystalline alloy powder was flakelike, and the minimum average particle size of the powder reached 6.87 μm. The alloy powder obtained by ball milling for 12 h had the best electromagnetic absorption performance, and the minimum reflection loss RLmin at the frequency of 6.52 GHz reached −46.15 dB (matched thickness was 3.5 mm). As time increased, the best matched frequency moved to the high-frequency direction, and the best matched thickness decreased, while the maximum effective absorption bandwidth ΔfRL<−10 dB was 7.22 GHz (10.78–18 GHz).


Introduction
With the development of the power electronics industry, the problem of electromagnetic pollution has become more and more serious. In order to solve the increasingly serious electromagnetic pollution problem, it is necessary to develop excellent absorbing materials. Usually, the absorbing material is composed of an absorber and a matrix material, and the absorber is the key to affecting the absorbing performance of the absorbing material. Absorbing materials can also be used in military stealth technology, which is a cutting-edge technology to avoid military radar detection, identification, and tracking strikes. Therefore, the development of absorbing materials with excellent performance is of great practical significance [1,2].

Experimental Procedures
Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 alloy ingots were melted by vacuum arc smelting, and the amorphous alloy ribbon (22 µm in thickness) was prepared by a single-roll melt-spinning method. The amorphous alloy ribbon was annealed in vacuum to get Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 nanocrystalline alloy ribbon. The specific process was as follows: firstly, the amorphous ribbon was heated to 450 • C in a vacuum environment, and the temperature was held for 100 min. Then, the temperature was continuously heated to 530 • C, and the temperature was held for 100 min. Finally, the ribbon-containing nanocrystalline structure was obtained by cooling in the furnace. Then, nanocrystalline alloy powders were prepared by the dry milling method. The nanocrystalline ribbons were put into a stainless-steel vacuum ball milling tank with a ball-to-material ratio of 10:1. The tank was pumped to 8 × 10 −2 MPa for high-energy mechanical ball milling. The rotating speed was 250 r/min. In this experiment, the ball milling time was set to 6, 8, 10, and 12 h according to the powder yield. Hence, the nanocrystalline alloy powders were obtained after mechanical high-energy ball milling. The saturation magnetization (M s ) and coercivity (H C ) of the powders were measured by a vibrating sample magnetometer (VSM) (Lake Shore 7410) (Lake Shore Company, Westerville, OH, USA). The phase and microstructure of the powders were characterized by X-ray diffraction (XRD-6000, Cu target) (Shimadzu, Japan) and transmission electron microscopy (JEM-2100F) (JEOL, Akishima, Japan). The micromorphology of the powder was observed under a scanning electron microscope (SEM) (JSM-6360LV) (JEOL, Akishima, Japan), and its elements were analyzed by an energy-dispersive spectrometry (EDS). A vector network analyzer (VNA) (8720B) (Keysight, Santa Rosa, CA, USA) was used to measure the absorbing properties of the powder. The mass ratio of the alloy powder to the paraffin wax was 7:3. Figure 1a shows the VSM results of Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 nanocrystalline alloy ribbon and powder after ball milling for 6, 8, 10, and 12 h. As can be seen from the figure, the initial M S of the nanocrystalline alloy ribbon without ball milling treatment was 132.03 emu/g. After 6 h of ball milling treatment, the initial M S increased to 135.25 emu/g, and then decreased gradually with the increase in ball milling time. After 12 h of ball milling, the initial M S decreased to 132.20 emu/g. The H C of the nanocrystalline alloy powder was between 0 and 16 Oe. pan) and transmission electron microscopy (JEM-2100F)(JEOL, Akishima, Japan). The micromorphology of the powder was observed under a scanning electron microscope (SEM) (JSM-6360LV) (JEOL, Akishima, Japan), and its elements were analyzed by an energy-dispersive spectrometry (EDS). A vector network analyzer (VNA) (8720B) (Keysight, Santa Rosa, CA, USA) was used to measure the absorbing properties of the powder. The mass ratio of the alloy powder to the paraffin wax was 7:3. Figure 1a shows the VSM results of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy ribbon and powder after ball milling for 6, 8, 10, and 12 h. As can be seen from the figure, the initial MS of the nanocrystalline alloy ribbon without ball milling treatment was 132.03 emu/g. After 6 h of ball milling treatment, the initial MS increased to 135.25 emu/g, and then decreased gradually with the increase in ball milling time. After 12 h of ball milling, the initial MS decreased to 132.20 emu/g. The HC of the nanocrystalline alloy powder was between 0 and 16 Oe. In order to study the mechanism of the change in soft magnetic properties, the microstructure of the alloy powder was characterized. Figure 2 shows the EDS map of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline ribbon, as well as the XRD and TEM images of the nonannealed Fe73.2Si16.2B6.6Nb3Cu1 amorphous alloy and the annealed nanocrystalline alloy. For EDS, the detection range of the element is the element whose atomic number is after the oxygen element. The content of elements with an atomic number lower than that of oxygen cannot be determined. Therefore, the detection of the B element content here is not accurate. According to Figure 2a, the gap between the nominal composition and the actual composition of the comparative analysis material was within an acceptable range; hence, it can be considered that the actual composition of this material was Fe73.2Si16.2B6.6Nb3Cu1. According to Figure 2b,c, it can be determined that the material was amorphous when not annealed. The XRD image in Figure 2d shows that the diffraction peak of the α-(Fe, Si) phase can be seen in the XRD pattern of the ribbon, indicating that the α-(Fe, Si) phase precipitated on the amorphous matrix after annealing. Furthermore, the diffraction peak of the α-(Fe, Si) phase still existed in the XRD curve of the nanocrystalline alloy powder after 6-12 h ball milling, indicating that the nanocrystalline alloy powder was still a mixed structure of amorphous and nanocrystalline. As time increased, the intensity of the diffraction peak decreased gradually, indicating that the content of α-(Fe, Si) phase decreased. The grain size calculated by the Debye-Scherrer formula is shown in Table 1. As time increased, the diffraction peak gradually became wider, and the size of the nano-grains decreased gradually. Figure 2e shows the TEM images of the nanocrystalline alloy after 12 h ball milling. The crystal structure and amorphous struc- In order to study the mechanism of the change in soft magnetic properties, the microstructure of the alloy powder was characterized. Figure 2 shows the EDS map of Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 nanocrystalline ribbon, as well as the XRD and TEM images of the nonannealed Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 amorphous alloy and the annealed nanocrystalline alloy. For EDS, the detection range of the element is the element whose atomic number is after the oxygen element. The content of elements with an atomic number lower than that of oxygen cannot be determined. Therefore, the detection of the B element content here is not accurate. According to Figure 2a, the gap between the nominal composition and the actual composition of the comparative analysis material was within an acceptable range; hence, it can be considered that the actual composition of this material was Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 . According to Figure 2b,c, it can be determined that the material was amorphous when not annealed. The XRD image in Figure 2d shows that the diffraction peak of the α-(Fe, Si) phase can be seen in the XRD pattern of the ribbon, indicating that the α-(Fe, Si) phase precipitated on the amorphous matrix after annealing. Furthermore, the diffraction peak of the α-(Fe, Si) phase still existed in the XRD curve of the nanocrystalline alloy powder after 6-12 h ball milling, indicating that the nanocrystalline alloy powder was still a mixed structure of amorphous and nanocrystalline. As time increased, the intensity of the diffraction peak decreased gradually, indicating that the content of α-(Fe, Si) phase decreased. The grain size calculated by the Debye-Scherrer formula is shown in Table 1. As time increased, the diffraction peak gradually became wider, and the size of the nano-grains decreased gradually. Figure 2e shows the TEM images of the nanocrystalline alloy after 12 h ball milling. The crystal structure and amorphous structure can be observed in the high-resolution image. The crystal phase was determined to be the α-(Fe, Si) phase by calibration of the diffraction pattern, confirming that the alloy powder was a mixed structure of amorphous and nanocrystalline phase. The size of the crystal phase was about 10 nm, consistent with the XRD results. The changes in microstructure and structure of the nanocrystalline alloy resulted in a change in the soft magnetic properties of the alloy. According to Table 1, after 6 h of ball milling, large atoms Nb and Cu were gradually dissolved in the α-(Fe, Si) phase, and the crystal phase was gradually transformed into the amorphous phase, resulting in a larger lattice constant and a larger shift in the diffraction peak of the crystal phase to a lower angle. According to the Bethe-Slater curve, a larger atomic spacing causes an increase in Ms. Therefore, the M S of the powder increased after 6 h of ball milling and decreased gradually with the increase in ball-milling time from 6 h to 12 h. This is because the content of the α-(Fe, Si) soft magnetic phase in the alloy gradually decreased with the increase in ball milling time. Moreover, the amorphous phase had a lower M S ; hence, the M S of the alloy decreased. As time increased, H C of nanocrystalline alloy powder showed an increasing trend, which was due to the increase in the internal stress of the alloy caused by the ball milling treatment. ture can be observed in the high-resolution image. The crystal phase was determined to be the α-(Fe, Si) phase by calibration of the diffraction pattern, confirming that the alloy powder was a mixed structure of amorphous and nanocrystalline phase. The size of the crystal phase was about 10 nm, consistent with the XRD results. The changes in microstructure and structure of the nanocrystalline alloy resulted in a change in the soft magnetic properties of the alloy. According to Table 1, after 6 h of ball milling, large atoms Nb and Cu were gradually dissolved in the α-(Fe, Si) phase, and the crystal phase was gradually transformed into the amorphous phase, resulting in a larger lattice constant and a larger shift in the diffraction peak of the crystal phase to a lower angle. According to the Bethe-Slater curve, a larger atomic spacing causes an increase in Ms. Therefore, the MS of the powder increased after 6 h of ball milling and decreased gradually with the increase in ball-milling time from 6 h to 12 h. This is because the content of the α-(Fe, Si) soft magnetic phase in the alloy gradually decreased with the increase in ball milling time. Moreover, the amorphous phase had a lower MS; hence, the MS of the alloy decreased. As time increased, HC of nanocrystalline alloy powder showed an increasing trend, which was due to the increase in the internal stress of the alloy caused by the ball milling treatment.    Figure 3a-d show the SEM images of nanocrystalline alloy powders after 6 h, 8 h, 10 h, and 12 h ball milling, respectively. It can be observed from the figure that the nanocrystalline alloy powders were flat sheets. According to the Snoek limit principle [30], the absorbent with flake morphology can more easily obtain better absorbing performance. The particle size of the nanocrystalline powder was statistically analyzed, and the curve of particle size distribution with ball milling time is shown in Figure 4a. It can be seen that the particle size distribution of the nanocrystalline alloy powder ranged from 1 to 45 µm. As time increased, the particle size of the powder gradually decreased to a smaller size. Furthermore, the average particle size of the nanocrystalline alloy powder decreased with the increase in ball milling time, from 7.90 µm after 6 h to 6.87 µm after 12 h, as shown in Figure 4b.  Figure 3a-d show the SEM images of nanocrystalline alloy powders after 6 h, 8 h, 10 h, and 12 h ball milling, respectively. It can be observed from the figure that the nanocrystalline alloy powders were flat sheets. According to the Snoek limit principle [30], the absorbent with flake morphology can more easily obtain better absorbing performance. The particle size of the nanocrystalline powder was statistically analyzed, and the curve of particle size distribution with ball milling time is shown in Figure 4a. It can be seen that the particle size distribution of the nanocrystalline alloy powder ranged from 1 to 45 μm. As time increased, the particle size of the powder gradually decreased to a smaller size. Furthermore, the average particle size of the nanocrystalline alloy powder decreased with the increase in ball milling time, from 7.90 μm after 6 h to 6.87 μm after 12 h, as shown in Figure 4b.  The electromagnetic wave absorption performance is evaluated mainly through the alternating field of the material of the complex dielectric constant (ε r = ε − jε ) and complex permeability (µ r = µ − jµ ). The real part (ε and µ ) and the imaginary part (ε and µ ) reflect the storage capacity and extinguish extent of the electromagnetic energy for certain materials, where a larger value indicates stronger storage or extinguish performance. The complex dielectric constant curve of Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 nanocrystalline alloy powder is shown in Figure 5. The ε value of the nanocrystalline alloy was 7.00-7.88, while ε was −0.24-0.08. It can also be observed from the figure that ε and ε of the nanocrystalline alloy powder fluctuated as frequency increased. With the increase in milling time, ε and ε showed a downward trend, because both the content and the size of α-(Fe, Si) were gradually reduced; thus, the crystal phase changed to an amorphous phase, and the interface between crystalline and amorphous phases was reduced. Accordingly, the interfacial polarization was abated, and the polarization loss was reduced. The electromagnetic wave absorption performance is evaluated mainly through the alternating field of the material of the complex dielectric constant (εr = ε′ − jε″) and complex permeability (μr = μ′ − jμ″). The real part (ε′ and μ′) and the imaginary part (ε″ and μ″) reflect the storage capacity and extinguish extent of the electromagnetic energy for certain materials, where a larger value indicates stronger storage or extinguish performance. The complex dielectric constant curve of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder is shown in Figure 5. The ε′ value of the nanocrystalline alloy was 7.00-7.88, while ε″ was −0.24-0.08. It can also be observed from the figure that ε′ and ε″ of the nanocrystalline alloy powder fluctuated as frequency increased. With the increase in milling time, ε′ and ε″ showed a downward trend, because both the content and the size of α-(Fe, Si) were gradually reduced; thus, the crystal phase changed to an amorphous phase, and the interface between crystalline and amorphous phases was reduced. Accordingly, the interfacial polarization was abated, and the polarization loss was reduced.  Figure 6 shows the complex permeability curve of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder. It can be observed from the figure that μ′ of the nanocrystalline alloy powder ranged from 0.67 to 2.45, while μ″ ranged from 0.21 to 1.15. The nanocrystalline alloy powders had a natural resonance peak near 1.5-2 GHz, and the resonance frequency was less than 10 GHz; therefore, this can be considered as a natural resonance peak. Nanocrystalline alloy powder also showed a strong frequency dependence. With the increase in frequency, the eddy current loss and skin effect increased, resulting in a low powder absorbing performance. With the increase in milling time, the powder particle size decreased, inhibiting the eddy current loss of powder particles. Therefore, with the increase in ball milling time, the powder particle size decreased, while μ″ increased at high frequency, indicating that ball-milling treatment could effectively improve the  The electromagnetic wave absorption performance is evaluated mainly through the alternating field of the material of the complex dielectric constant (εr = ε′ − jε″) and complex permeability (μr = μ′ − jμ″). The real part (ε′ and μ′) and the imaginary part (ε″ and μ″) reflect the storage capacity and extinguish extent of the electromagnetic energy for certain materials, where a larger value indicates stronger storage or extinguish performance. The complex dielectric constant curve of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder is shown in Figure 5. The ε′ value of the nanocrystalline alloy was 7.00-7.88, while ε″ was −0.24-0.08. It can also be observed from the figure that ε′ and ε″ of the nanocrystalline alloy powder fluctuated as frequency increased. With the increase in milling time, ε′ and ε″ showed a downward trend, because both the content and the size of α-(Fe, Si) were gradually reduced; thus, the crystal phase changed to an amorphous phase, and the interface between crystalline and amorphous phases was reduced. Accordingly, the interfacial polarization was abated, and the polarization loss was reduced.  Figure 6 shows the complex permeability curve of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder. It can be observed from the figure that μ′ of the nanocrystalline alloy powder ranged from 0.67 to 2.45, while μ″ ranged from 0.21 to 1.15. The nanocrystalline alloy powders had a natural resonance peak near 1.5-2 GHz, and the resonance frequency was less than 10 GHz; therefore, this can be considered as a natural resonance peak. Nanocrystalline alloy powder also showed a strong frequency dependence. With the increase in frequency, the eddy current loss and skin effect increased, resulting in a low powder absorbing performance. With the increase in milling time, the powder particle size decreased, inhibiting the eddy current loss of powder particles. Therefore, with the increase in ball milling time, the powder particle size decreased, while μ″ increased at high frequency, indicating that ball-milling treatment could effectively improve the  Figure 6 shows the complex permeability curve of Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 nanocrystalline alloy powder. It can be observed from the figure that µ of the nanocrystalline alloy powder ranged from 0.67 to 2.45, while µ ranged from 0.21 to 1.15. The nanocrystalline alloy powders had a natural resonance peak near 1.5-2 GHz, and the resonance frequency was less than 10 GHz; therefore, this can be considered as a natural resonance peak. Nanocrystalline alloy powder also showed a strong frequency dependence. With the increase in frequency, the eddy current loss and skin effect increased, resulting in a low powder absorbing performance. With the increase in milling time, the powder particle size decreased, inhibiting the eddy current loss of powder particles. Therefore, with the increase in ball milling time, the powder particle size decreased, while µ increased at high frequency, indicating that ball-milling treatment could effectively improve the highfrequency wave absorption performance of the nanocrystalline alloy powder. Moreover, with the increase in milling time, the particle size of the alloy decreased gradually, and the magnetic exchange coupling between the nanocrystalline alloy powders increased, leading to higher µ . However, the maximum value of µ decreased gradually because the complex permeability of the alloy is positively correlated to the square value of M S , as shown in Equation (1).

Results and Discussion
where µ i is the initial permeability, µ 0 is the free-space permeability, K 1 is the magnetocrystalline anisotropy coefficient, λ S is the magnetostriction coefficient, σ is the internal stress density, β is the volume fraction of impurities, δ is the domain wall thickness, and d is the particle size of impurities. Thus, µ obeys the same law as M S . ders increased, leading to higher μ′. However, the maximum value of μ″ decreased gradually because the complex permeability of the alloy is positively correlated to the square value of MS, as shown in Equation (1).
where μi is the initial permeability, μ0 is the free-space permeability, K1 is the magnetocrystalline anisotropy coefficient, λS is the magnetostriction coefficient, σ is the internal stress density, β is the volume fraction of impurities, δ is the domain wall thickness, and d is the particle size of impurities. Thus, μ″ obeys the same law as MS.  Figure 7 shows the variation curve of the dielectric loss tangent angle tgδε and magnetic loss tangent angle tgδμ with frequency of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder milling (6-12 h). It can be seen that the tgδε of nanocrystalline alloy powder ranged from −0.03 to 0.01, while tgδμ ranged from 0.32 to 0.76. tgδμ was much larger than tgδε, indicating a strong magnetic loss property; hence, this is a magnetic loss absorbing material. tgδμ first increased and then decreased with the increase in frequency. The peak value of tgδμ was between 5.5 GHz and 7.8 GHz. With the increase in ball milling time, tgδμ in the high-frequency band increased gradually. The peak of tgδμ gradually moved in the high-frequency direction, indicating that the high-frequency absorption performance was improved.   Figure 7 shows the variation curve of the dielectric loss tangent angle tgδ ε and magnetic loss tangent angle tgδ µ with frequency of Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 nanocrystalline alloy powder milling (6-12 h). It can be seen that the tgδε of nanocrystalline alloy powder ranged from −0.03 to 0.01, while tgδ µ ranged from 0.32 to 0.76. tgδ µ was much larger than tgδε, indicating a strong magnetic loss property; hence, this is a magnetic loss absorbing material. tgδ µ first increased and then decreased with the increase in frequency. The peak value of tgδ µ was between 5.5 GHz and 7.8 GHz. With the increase in ball milling time, tgδ µ in the high-frequency band increased gradually. The peak of tgδ µ gradually moved in the high-frequency direction, indicating that the high-frequency absorption performance was improved. ders increased, leading to higher μ′. However, the maximum value of μ″ decreased gradually because the complex permeability of the alloy is positively correlated to the square value of MS, as shown in Equation (1).
where μi is the initial permeability, μ0 is the free-space permeability, K1 is the magnetocrystalline anisotropy coefficient, λS is the magnetostriction coefficient, σ is the internal stress density, β is the volume fraction of impurities, δ is the domain wall thickness, and d is the particle size of impurities. Thus, μ″ obeys the same law as MS.  Figure 7 shows the variation curve of the dielectric loss tangent angle tgδε and magnetic loss tangent angle tgδμ with frequency of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder milling (6-12 h). It can be seen that the tgδε of nanocrystalline alloy powder ranged from −0.03 to 0.01, while tgδμ ranged from 0.32 to 0.76. tgδμ was much larger than tgδε, indicating a strong magnetic loss property; hence, this is a magnetic loss absorbing material. tgδμ first increased and then decreased with the increase in frequency. The peak value of tgδμ was between 5.5 GHz and 7.8 GHz. With the increase in ball milling time, tgδμ in the high-frequency band increased gradually. The peak of tgδμ gradually moved in the high-frequency direction, indicating that the high-frequency absorption performance was improved.  The magnetic loss of materials is mainly caused by hysteresis loss, domain wall resonance, natural resonance, and eddy current loss. The hysteresis loss in the weak electromagnetic field can be ignored, while the domain wall resonance only appears at low frequency (<2 GHz); thus, the magnetic loss in the range of gigabits mainly includes two forms: natural resonance and eddy current loss. Eddy current losses can be expressed as shown in Equation (2), where f, σ, and d represent the frequency, conductivity, and absorber thickness, respectively. If the magnetic loss of the material is only caused by eddy current loss, then the value of C 0 should remain constant over all frequency bands. The C 0 value of Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 nanocrystalline alloy powder is shown in Figure 8. It can be seen that the C 0 value of the nanocrystalline alloy powder decreased with the increase in frequency, indicating that the magnetic loss of the nanocrystalline alloy included eddy current loss and natural resonance. Among them, the formant of natural resonance appeared near 1.5-2 GHz.
two forms: natural resonance and eddy current loss. Eddy current losses can be expressed as shown in Equation (2), where f, σ, and d represent the frequency, conductivity, and absorber thickness, respectively. If the magnetic loss of the material is only caused by eddy current loss, then the value of C0 should remain constant over all frequency bands. The C0 value of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder is shown in Figure 8. It can be seen that the C0 value of the nanocrystalline alloy powder decreased with the increase in frequency, indicating that the magnetic loss of the nanocrystalline alloy included eddy current loss and natural resonance. Among them, the formant of natural resonance appeared near 1.5-2 GHz. The reflection loss RL of the alloy can be calculated according to the transmission line principle, as shown in Equations (3) and (4), where Z0 is the wave impedance in free space, Zin is the dielectric wave impedance, f is the frequency of the incident electromagnetic wave, c is the speed of light (3 × 10 8 m/s), and d is the thickness of the absorbent (mm). Figure 9 shows the wave absorption curve of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder. It can be seen that the reflection loss of the fixed thickness of the nanocrystalline alloy powder decreased first and then increased with the increase in frequency. It featured an absorption peak, and the minimum reflection loss Rlmin could be obtained for the alloy powder at a specific thickness. Absorbers that are too thin or too thick will absorb electromagnetic waves differently due to the effect of impedance matching. The minimum reflection loss of nanocrystalline alloy powder after 6-12 h ball milling was about −40 dB. As shown in Figure 10, the minimum reflection loss Rlmin of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder and the corresponding frequency and thickness of Rlmin (i.e., the best matched frequency fRlmin and the best matched thickness dRlmin) changed with ball milling time. Rlmin increased first and then decreased with the increase in ball milling time, reaching the minimum value of −46.15 dB after 12 h of ball milling. The fRlmin of the alloy powder moved in the high-frequency direction with the increase in milling time, from 3.64 GHz for 6 h to 6.52 GHz for 12 h. Because the particle size of the alloy powder decreased, the skin effect was weakened, and the negative effect of eddy current loss on the high-frequency wave absorption performance was weakened. The dRlmin of the alloy powder decreased with the increase in milling time, which was conducive to the lightweight design of the absorber. The minimum matching thickness reached 3.5 mm after 12 h of ball milling. The reflection loss RL of the alloy can be calculated according to the transmission line principle, as shown in Equations (3) and (4), where Z 0 is the wave impedance in free space, Z in is the dielectric wave impedance, f is the frequency of the incident electromagnetic wave, c is the speed of light (3 × 10 8 m/s), and d is the thickness of the absorbent (mm). Figure 9 shows the wave absorption curve of Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 nanocrystalline alloy powder. It can be seen that the reflection loss of the fixed thickness of the nanocrystalline alloy powder decreased first and then increased with the increase in frequency. It featured an absorption peak, and the minimum reflection loss Rl min could be obtained for the alloy powder at a specific thickness. Absorbers that are too thin or too thick will absorb electromagnetic waves differently due to the effect of impedance matching. The minimum reflection loss of nanocrystalline alloy powder after 6-12 h ball milling was about −40 dB. As shown in Figure 10, the minimum reflection loss Rl min of Fe 73.2 Si 16.2 B 6.6 Nb 3 Cu 1 nanocrystalline alloy powder and the corresponding frequency and thickness of Rl min (i.e., the best matched frequency f Rlmin and the best matched thickness d Rlmin ) changed with ball milling time. Rl min increased first and then decreased with the increase in ball milling time, reaching the minimum value of −46.15 dB after 12 h of ball milling. The f Rlmin of the alloy powder moved in the high-frequency direction with the increase in milling time, from 3.64 GHz for 6 h to 6.52 GHz for 12 h. Because the particle size of the alloy powder decreased, the skin effect was weakened, and the negative effect of eddy current loss on the high-frequency wave absorption performance was weakened. The d Rlmin of the alloy powder decreased with the increase in milling time, which was conducive to the lightweight design of the absorber. The minimum matching thickness reached 3.5 mm after 12 h of ball milling.
(4)      The contour lines in the figure represent 90% effective absorption below −10 dB and 99% absorption below −20 dB, respectively. It can be seen that the nanocrystalline alloy powder of ball milling for 12 h had the best bandwidth performance, and the effective absorption bandwidth was higher below −10 dB when the thickness of the absorbent was 2 mm, while ∆f RL<−10 dB was up to 7.22 GHz (10.78-18 GHz), covering nearly half of the X-band and all of the Ku band. Figure 11a-d show the contour plot of reflection loss of Fe73.2Si16.2B6.6Nb3Cu1 nanocrystalline alloy powder after ball milling for 6-12 h as a function of thickness and frequency. The contour lines in the figure represent 90% effective absorption below −10 dB and 99% absorption below −20 dB, respectively. It can be seen that the nanocrystalline alloy powder of ball milling for 12 h had the best bandwidth performance, and the effective absorption bandwidth was higher below −10 dB when the thickness of the absorbent was 2 mm, while ΔfRL<−10 dB was up to 7.22 GHz (10.78-18 GHz), covering nearly half of the X-band and all of the Ku band.

Conclusions
(1) After ball milling, the nanocrystalline alloy remained an amorphousnanocrystalline mixed structure. With the increase in ball milling time, α-(Fe, Si) gradually transformed into the amorphous phase, and the maximum Ms reached 135.25 emu/g.
(2) The nanocrystalline alloy powder after ball milling was flakelike. The minimum average particle size of the powder reached 6.87 μm. The decrease in particle size weakened the skin effect caused by eddy current loss and enhanced the absorption performance of high-frequency electromagnetic waves.
(3) Nanocrystalline alloy powders had excellent electromagnetic absorption properties. The real part μ′ of the complex permeability ranged from 0.60 to 1.97, and the imaginary part μ″ and tgδμ reached the maxima of 1.15 and 0.76, respectively. The alloy powder obtained from ball milling for 12 h had the best electromagnetic absorption performance, and the minimum reflection loss RLmin at the frequency of 6.52 GHz reached −46.15 dB (matched thickness = 3.5 mm).
(4) With the increase in ball milling time, the best matched frequency moved to a higher frequency, and the best matched thickness decreased. When the thickness of the absorbent was 2 mm, the maximum effective absorption bandwidth Δ fRL<−10 dB was 7.22 GHz (10.78-18 GHz).

Conclusions
(1) After ball milling, the nanocrystalline alloy remained an amorphous-nanocrystalline mixed structure. With the increase in ball milling time, α-(Fe, Si) gradually transformed into the amorphous phase, and the maximum M s reached 135.25 emu/g.
(2) The nanocrystalline alloy powder after ball milling was flakelike. The minimum average particle size of the powder reached 6.87 µm. The decrease in particle size weakened the skin effect caused by eddy current loss and enhanced the absorption performance of high-frequency electromagnetic waves.
(3) Nanocrystalline alloy powders had excellent electromagnetic absorption properties. The real part µ of the complex permeability ranged from 0.60 to 1.97, and the imaginary part µ and tgδ µ reached the maxima of 1.15 and 0.76, respectively. The alloy powder obtained from ball milling for 12 h had the best electromagnetic absorption performance, and the minimum reflection loss RL min at the frequency of 6.52 GHz reached −46.15 dB (matched thickness = 3.5 mm).
(4) With the increase in ball milling time, the best matched frequency moved to a higher frequency, and the best matched thickness decreased. When the thickness of the absorbent was 2 mm, the maximum effective absorption bandwidth ∆ f RL<−10 dB was 7.22 GHz (10.78-18 GHz).

Data Availability Statement:
The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.