Grain size modulation to optimize the wave-absorbing properties of FeSiCr alloy micropowder

Abstract

In this paper, the ball-milled flake FeSiCr alloy is subjected to a vacuum annealing temperature between 300 and 500 °C. The results show that the appropriate heat treatment temperature increases the average grain size of the material, eliminates defects and internal stresses, and improves the complex permeability of the material. The optimum wave-absorbing performance of the material is achieved when the heat treatment temperature is 400 °C with the minimum reflectivity RL_min reaching −56.33 dB at a frequency f of 3.97 GHz, corresponding to the thickness of the wave-absorbing coating, d = 4.0 mm. This work provides an important reference value for application of FeSi-based alloy micropowder soft magnetic materials in the field of microwave absorption.

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1. Introduction

In recent years, electronic information technology has flourished with the rapid progress of wireless communication technology.¹ At present, more and more electronic devices are being used in a wide range of areas, and the ensuing increasingly serious problem of electromagnetic radiation pollution has become a focus of attention.^2–5 The wave absorbing materials used for electromagnetic protection are the key to solving the problem of electromagnetic radiation pollution. Currently, wave-absorbing materials are widely used in civil, commercial and military fields, and have become a hotspot for researchers.^6–9

FeSi-based soft magnetic alloys have high Curie temperatures, good thermal stability and high permeability, and have great potential in high-temperature magnetic wave-absorbing materials.^10,11 The flattening of spherical FeSi-based alloys by a ball milling process is an effective means to further improve the electromagnetic properties of the materials, but the defects and internal stresses in the materials after ball milling unfavorably influence the microwave permeability of the materials.¹² Reportedly, the annealing process can improve the soft magnetic properties of mechanically alloyed nanocrystalline materials by increasing the average grain size of the materials and eliminating defects and internal stresses.^12–18 For example, Gong et al.¹¹ carried out vacuum annealing of flaky Fe–Co–Zr alloys prepared by aerosolization and mechanical ball milling at different temperatures, and the results showed that the average grain size increased and the internal strain decreased with the increase in annealing temperature. The saturation flux density of the annealed samples decreased slightly and the coercivity decreased significantly. The annealed samples depicted larger values of μ′ compared to the ball-milled samples, while the maximum value of μ′′ increased with increasing temperature. This study showed that the appropriate annealing temperature helped to improve the microwave absorbing properties of the metal flakes. Ding et al.¹⁷ subjected the flaky nanocrystalline structured Fe–Si powders obtained by mechanical alloying (ball milling) to vacuum heat treatment at 200–700 °C, and the results showed that the annealing process at the appropriate temperature (450 °C) could improve the magnetic properties of mechanically alloyed nanocrystalline materials by eliminating the internal stresses and increasing the average grain size. Li et al.¹⁹ made flake nanocrystalline structured FeSiAl alloys using a high-energy ball milling method and vacuum annealing at 400–800 °C under a N₂ atmosphere, and the results showed that the annealing heat treatment eliminated the internal defects and residual stresses of the flake nanocrystalline structured FeSiAl alloys, and increased the magnetic permeability. However, when annealed at a temperature of 600 °C or higher, N₂ reacts with FeSiAl and nitrides are generated on the surface of the samples, the reaction process becomes more prominent with the increase in temperature, and the nitrides impede the movement of free electrons and lower the dielectric constant. Zhou et al.²⁰ vacuum heat-treated lamellar FeSiAl nano-micropowder obtained from ball milling at 573 K to improve the grain size and magnetic permeability of the material.

This research work comparatively investigates the effects of heat treatment temperature on the surface morphology, grain size, electromagnetic properties and wave-absorbing properties of flaky FeSiCr nanopowders by vacuum annealing of ball-milled flaky FeSiCr soft magnetic alloy micropowder at 300–500 °C. The study of grain growth and the changing law of electromagnetic properties of FeSi-based nanocrystalline wave-absorbing materials at high temperature has an important reference value for the development of wave-absorbing materials.

2. Experimental

The ball-milled FeSiCr micropowder (marked as S₀) (Fe-84.8 wt% Si-5.3 wt% Cr-9.9 wt%) (Hunan HuaLiu New Material Co., Ltd) was placed in a tube furnace and sealed, the vacuum of the tube furnace was then evacuated to 10⁻¹ Pa with a mechanical pump, and then argon was introduced at the same pressure inside and outside the chamber. The argon gas was kept in circulation at a constant flow rate, the heating rate was 5 °C min⁻¹, the heat treatment holding time was 3 h, and the heat treatment temperatures were 300 °C, 400 °C, and 500 °C, marked as S₁, S₂ and S₃, respectively. The phase structure of the samples was analyzed using an X-ray diffractometer Pana lytic Empyrean with Cu K_α radiation (Cu K_α radiation, scanning angle 5–90°, room temperature). The morphological structure of the samples was characterized by scanning electron microscopy (SEM-FEI MLA650F, USA). The electromagnetic parameters were measured by a vector network analyzer (3672B-S, CETC, China) after 50 wt% of the sample was homogeneously mixed with 50 wt% of paraffin wax and formed into a coaxial ring (Φ_outer = 7.0 mm, Φ_inner = 3 mm, thickness = 3 mm).

3. Results and discussion

Fig. 1(a) shows the XRD patterns of samples S₀–S₃. As shown, the characteristic peaks of samples S₀–S₃ at 2θ = 44.7°, 65.2° and 82.5° correspond to the (110), (200), and (211) crystal planes of the Fe₈SiCr phase, respectively (JCPDS card no. 65-5584). Compared with the non-vacuum annealing sample S₀, the diffraction peak intensities of samples S₁–S₃ gradually increase, and the half-peak widths narrow as the vacuum annealing temperature is increased from 300 °C to 500 °C. This is attributed to the annealing effect of the vacuum annealing, which repaired the internal crystal structure of the lamellar FeSiCr while eliminating the internal stresses and defects of the lamellar FeSiCr alloy micropowder.^21,22Fig. 1(b) shows the average grain size plots of the S₀–S₃ samples. In this case, the average grain size of the FeSiCr alloy micropowder was calculated according to Scherrer's formula and Hall–Williamson's formula:^23,24

D = kλ/(β cos θ) (1)

β cos θ = (kλ/D) + 4ε sin θ (2)

where β is the half-peak width, k is the Scherrer's constant of 0.89, λ is the X-ray wavelength taken as 0.154 nm, θ is the diffraction angle, and D is the average grain size. From Fig. 1(b), it can be seen that the grain sizes of samples S₁–S₃ increased after vacuum heat treatment compared to sample S₀. Along with the increase in grain size, the lattice distortion degree of the samples decreases, the orderliness increases, and the internal stress decreases.²³

Fig. 1 (a) XRD pattern and (b) grain size map of the S₀–S₃ samples.

Fig. 2 (a)–(d) show the SEM images of samples S₀–S₃, respectively. Fig. 2(a)–(d) show that the surface morphology of the FeSiCr micropowder has no obvious change with the increase in the vacuum annealing temperature, and it still presents a flaky morphology. This indicates that the vacuum annealing did not have much effect on the micro-morphology of the samples. In order to distinguish whether the phases of other oxides were generated during the vacuum annealing, TEM was used to characterize sample S₂. Fig. 2(e) and (f) show the TEM morphology of sample S₂, which can be seen to be flaky. Fig. 2(g) shows the HRTEM image of the area shown in the orange box in (f). As shown, the measured lattice stripe spacings of 0.144 nm and 0.116 nm correspond to the (200) and (211) crystal planes of the Fe₈SiCr phase, respectively. Fig. 2(i)–(k) show the EDS mapping of sample S₂ in the field of view of Fig. 2(h), which corresponds to the three elements of Fe, Si and Cr, respectively, and the three elements can be seen uniformly distributed on the FeSiCr surface. In general, the original morphology of the samples was maintained during the vacuum annealing and no other oxide phases were produced.

Fig. 2 (a)–(d) SEM images of the S₀–S₃ samples; (e)–(f) TEM, (g) HRTEM, and (h)–(k) EDS element mapping images of the S₃ samples, respectively.

Fig. 3(a)–(d) show the electromagnetic parameters of samples S₀–S₃ in the frequency range of 2–18 GHz, and Fig. 3(e) and (f) show the M–H plot and eddy current loss (C₀) plot of samples S₀–S₃, respectively. From Fig. 3(a) and (b), it can be seen that the real (ε′) and imaginary (ε′′) parts of the dielectric constants of samples S₀–S₃ decrease with the increase in the vacuum annealing temperature. Based on the Debye relaxation theory, the complex dielectric constant ε_r can be expressed by eqn (3)–(5):²⁵

where ω is the angular frequency, τ is the polarization relaxation time, ε_s and ε_∞ denote the static permittivity and the relative permittivity in the high-frequency limit, respectively, τ_D is the temperature-dependent relaxation time, k is the Boltzmann constant, and T is the temperature. The vacuum annealing eliminates the defects and internal stresses inside the FeSiCr soft magnetic alloy micropowder during ball milling, and the inhomogeneity is weakened, which makes the free energy ΔE value increase, and according to eqn (3)–(5), the value of τ_D increases, and thus the intrinsic electric dipole orientation polarization relaxation time τ increases, thus causing the complex permittivity ε_r to decrease.²⁶

Fig. 3 Complex permittivity (a) and (b), complex permeability (c) and (d), M–H curves (e) and C₀ plots (f) for the S₀–S₃ samples.

From Fig. 3(c) and (d), the μ′ and μ′′ of the heat-treated S₁–S₃ samples are improved compared to the sample S₀. This is because the crystallization effect and stress relief brought about by the vacuum heat treatment improves the soft magnetic properties of the FeSiCr micropowder, reduces the magnetic anisotropy of the material, and enhances the overall complex permeability of the magnetic powder.²⁷ It is noteworthy that the composite permeability of the S₃ sample is reduced relative to the composite permeability of the S₂ sample due to the fact that at the higher temperature, the crystallinity of the S₃ sample is the highest, as can be observed from Fig. 1(b). However, excessively high crystallinity leads to an increase in grain size and a decrease in the interaction of magnetic moments, resulting in a decrease in magnetic permeability.²⁸

Fig. 3(e) shows the hysteresis line profiles of the S₀–S₃ samples. The vacuum annealing enhances the saturation magnetization, J_s values, of the S₁–S₃ samples relative to the S₀ sample. Based on the magnetic domain theory, the magnetic permeability can be expressed as:^29,30

μ_r = pJ_s²/μ₀|k| (6)

where J_s is the saturation magnetization, p is a dimensionless perfector with a value close to 1, and k represents the effective anisotropy constant. Therefore, an enhancement in J_s leads to a concomitant enhancement in the complex permeability μ_r.

Eddy current loss (C₀ = μ′′(μ′)⁻²f⁻¹) is a common type of magnetic loss in magnetic materials. The magnetic flux and magnetic induction strength of ferromagnetic metal in an alternating electric field will issue a corresponding change according to the law of electromagnetic induction, and this change will cause the generation of annular induced eddy currents inside the ferromagnetic metal in the direction perpendicular to the magnetic flux. The generation of eddy currents excites a magnetic field to stop the change in magnetic flux caused by the external magnetic field, and therefore, the increase in eddy current losses reduces the permeability of the ferromagnetic metal.²⁹ In general, for the magnetic loss mechanism of wave-absorbing materials in this frequency band, eddy current loss and natural resonance dominate.^31,32 Among them, when the value of C₀ is constant, the magnetic loss mechanism is caused by eddy current loss; when C₀ varies with frequency, natural resonance dominates.²⁹ From Fig. 3(f), it can be seen that the C₀ values of samples S₁–S₃ fluctuate with the frequency change in the frequency range of 2–18 GHz, which indicates that the natural resonance losses dominate the magnetic losses. The reduction of eddy current losses leads to an increase in the permeability of ferromagnetic metals, thus compared to sample S₀, the heat treatment leads to a reduction in internal defects in samples S₁–S₃, which have an inhibitory effect on the formation of eddy currents, leading to an increase in permeability.³³

According to the transmission theory, the reflectivity RL of the incident electromagnetic wave can be calculated by eqn (7) and (8):^27,34

RL (dB) = −20 lg|(Z_in − Z₀)/(Z_in + Z₀)| (8)

where, f, d and c represent frequency, coating thickness and speed of light respectively. The smaller the RL value is, the stronger the wave-absorbing performance of wave-absorbing materials. In general, the frequency range of RL ≤ −10 dB is called the effective absorption bandwidth, and in this range, the absorption efficiency is 90%; when RL ≤ −20 dB, 99.9% of the electromagnetic wave is absorbed.^34,35Fig. 4(a)–(d) show the 3D plots of the reflection losses of samples S₀–S₃ as a function of f and d. From Fig. 4(c) and (d), it is obviously observed that samples S₂ and S₃ have excellent wave-absorbing properties. Sample S₂ has RL_min = −56.33 dB at f = 3.97 GHz, d = 4.0 mm; sample S₃ has RL_min = −44.41 dB at f = 3.75 GHz, d = 4.23 mm. In order to compare the wave absorption performance of samples S₂ and S₃ more obviously, the histograms of effective absorption bandwidth (EAB) (RL ≤ −10 dB and ≤ −20 dB) at different thicknesses are calculated in this paper, as shown in Fig. 4(e) and (f). Samples S₂ and S₃ have wide effective bandwidths in the thickness range of 1.5–2.5 mm with RL ≤ −10 dB and in the thickness range of 2.5–3.5 mm with RL ≤ −20 dB. In summary, samples S₂ and S₃ have superior microwave absorption properties in the majority of the thickness range (1.5–3.5 mm).

Fig. 4 (a)–(d) 3D plots of reflectance relative to f and d. (e) and (f) Histograms of EAB ≤ −10 dB and EAB ≤ −20 dB for different matching thicknesses for the S₀–S₃ samples.

The electromagnetic wave loss mechanism of the material needs to be resolved next. Fig. 5(a)–(d) show the plots of dielectric loss coefficient (tan δ_E), Cole–Cole curve, magnetic loss coefficient (tan δ_M), and attenuation constant of samples S₀–S₃, respectively. From Fig. 5(a), the tan δ_E (tan δ_E = ε′′/ε′) values of the S₁–S₃ samples after vacuum annealing decrease relative to the S₀ samples, which is attributed to the fact that the reduction of the complex dielectric constant of the material makes the dielectric loss weakened as well. According to the Debye relaxation theory, a Cole–Cole semicircle represents a Debye relaxation loss process with the following expression:^36–38

where ω (ω = 2πf) is the angular frequency, τ is the polarization relaxation time, and ε_s and ε_∞ denote the static permittivity and the relative permittivity in the high frequency limit, respectively. From Fig. 5(b), it can be observed that the Cole–Cole curves of each sample appear as multiple segments in the shape of semicircles, indicating that multiple polarization relaxation processes occur under the alternating electric field. Compared to the S₀ sample, the number of Debye relaxation semicircles of the S₁–S₃ samples after vacuum annealing is reduced, which indicates the weakening of the dielectric loss of the S₁–S₃ samples.

Fig. 5 Plots of dielectric loss (a), Cole–Cole curve (b), magnetic loss (c) and decay constant (d) for the S₀–S₃ samples.

In Fig. 5(c), the tan δ_M (tan δ_M = μ′′/μ′) values of the S₁–S₃ samples are significantly enhanced relative to those of the S₀ samples. This is because the vacuum annealing has eliminated the internal stresses and defects generated by the mechanical ball milling, improved the soft magnetic properties, reduced the magnetic anisotropy, and increased the complex permeability of the materials, which has led to an enhancement of the material's magnetic loss.

The magnitude of the attenuation constant (α) value is usually used to indicate the strength of the material's loss capability for electromagnetic waves, with the following expression:³⁹

From Fig. 5(d), the α value of the S₁–S₃ samples decreases with the increase in vacuum annealing temperature, which indicates that the higher the vacuum annealing temperature, the weaker the electromagnetic wave loss ability of the FeSiCr micropowder. Sample S₁ has the largest α value but relatively low wave-absorbing performance; sample S₂ has the best wave-absorbing performance, but the α value is not the largest, so it is necessary to consider the effect of impedance matching on the wave-absorbing performance of the material.

To further analyze sample S₂, which has the best electromagnetic wave absorption performance, the COMSOL finite element method is applied to establish the FeSiCr model,⁴⁰ and simulate and analyze the surface current density (SCD) and volume loss density (VLD). From Fig. 4, the S₂ sample has the best electromagnetic wave absorption performance at f = 3.97 GHz; moreover, as known from Fig. 5(d), the S₂ sample has the best attenuation constant at f = 18 GHz. Therefore, we simulate the SCD and VLD of sample S₂ at f = 3.97 GHz and f = 18 GHz. As shown in Fig. 6, by comparing the left and right SCD distributions and VLD values at f equal to 3.97 GHz and 18 GHz, respectively, we found that the surface current density of sample S₂ is the smallest at f = 3.97 GHz, indicating the optimal impedance matching performance.⁴¹ In addition, we also analyzed the VLD maps at f = 3.97 GHz and 18 GHz. As shown in Fig. 6(c) and (d), the bulk loss density of sample S₂ at f = 18 GHz is much higher than that at f = 3.97 GHz, which is the same as the variation in the attenuation constant in Fig. 5(d). Impedance matching is the key to determining the wave-absorbing performance of materials. However, the excellent wave-absorbing performance is not only related to the impedance matching but also to the attenuation constant, and both are indispensable.

Fig. 6 (a) SCD of S₂ at f = 3.97 GHz, (b) SCD of S₂ at f = 18 GHz, (c) VLD of S₂ at f = 3.97 GHz, and (d) VLD of S₂ at f = 18 GHz.

Eqn (13)–(15) are the |Δ| function equations, and the impedance matching can be evaluated by the |Δ| value; a smaller |Δ| value indicates the better impedance matching, and the region of |Δ| ≤ 0.4 is usually regarded as the effective impedance matching.^42,43 The variation in the |Δ| function for the S₀–S₃ samples is obtained by calculation as shown in Fig. 7(a)–(d).

where f is the frequency, d is the thickness of the wave-absorbing coating, c is the speed of light, is the real part of the permittivity, is the real part of the magnetic permeability, δ_e is the tangent of the dielectric loss, and δ_m is the tangent of the magnetic loss. Fig. 7(e) shows pie charts of the percentage area of the region with |Δ| ≤ 0.4 obtained from the calculation. Sample S₁ has the highest α value and the strongest attenuation ability, but its |Δ| ≤ 0.4 area is the smallest, and its impedance matching is poor, while sample S₃ has the largest area of |Δ| ≤ 0.4 but has the smallest α value, and sample S₂ has the optimal reflective loss among all the samples and relatively high α, which is also a good attenuation of the electromagnetic wave. Meanwhile, the impedance matching of sample S₂ is not the best among all the samples, however, the moderate impedance matching makes the three of them reach a balance within the material, which leads to the optimized wave-absorbing performance of sample S₂. This suggests that a balance between the electromagnetic wave attenuation ability and impedance matching is needed when the electromagnetic parameters of the material are regulated to improve the wave-absorbing performance.

Fig. 7 Impedance matching plots for samples S₀–S₃ (a)–(d) and pie charts of the percentage area of the region with |Δ| ≤ 0.4 (e).

Fig. 8 shows the flow chart of heat treatment of FeSiCr and the microwave absorption mechanism. After vacuum annealing, the internal stresses of the material are eliminated, defects are reduced, and magnetic losses are increased. At a simultaneous time, a suitable impedance matching of FeSiCr was ensured, enabling the effective absorption and loss of the incident electromagnetic waves. In addition, due to the enhanced soft magnetic properties of the materials, the magnetic loss mechanism is increased, and it can be seen in Fig. 3(f) that natural resonance dominates in the magnetic loss mechanism. In summary, the synergistic effect of interfacial polarization, magnetic loss and natural resonance increases the microwave absorption performance of the FeSiCr soft magnetic alloy.

Fig. 8 The thermal treatment flow chart of FeSiCr and the EMW absorption mechanism.

4. Conclusions

Vacuum annealing at 300 °C, 400 °C and 500 °C was carried out on the flaky FeSiCr micropowder, respectively. The results show that the FeSiCr magnetic powders eliminated the residual internal stresses and defects of the materials after vacuum annealing (300–500 °C), so that the crystallinity of the S₁–S₃ samples gradually became better. With the increase in heat treatment temperature, the average grain size of the FeSiCr magnetic powder wave-absorbing materials increases, the macroscopic morphology remains stable, and the magnetic permeability is enhanced. The material exhibits the optimized wave-absorbing performance when the heat treatment temperature is 400 °C; RL_min = −56.33 dB at f = 3.97 GHz, which corresponds to the thickness of wave-absorbing coating, d = 4.0 mm. Vacuum annealing at the appropriate temperature can increase the permeability, balance the electromagnetic wave attenuation ability and impedance matching of the material, and thus achieve the enhancement of wave-absorbing performance. This research work provides a certain reference value for the application of FeSi-based soft magnetic alloy micropowder in the field of wave-absorbing materials.

Author contributions

Weiwei Dong and Wenmiao Zhang: conceptualization, methodology, investigation, writing – original draft preparation, funding acquisition. Lei Wang: writing – review & editing, funding acquisition, supervision. Sajjad Ur Rehman: experiments. Yifeng Hu, Tongxiang Liang, Changcai Chen, Jianping Zou: experiments, data acquisition. Haiping Zou: supervision, writing – review & editing, Funding acquisition.

Data availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of interest

All the authors listed declare that the paper (“Grain size modulation to optimize the wave-absorbing properties of FeSiCr alloy micropowder”) is original research that has not been submitted for publication to other journals, and all the authors listed have read the paper and agree with its submission to Physical Chemistry Chemical Physics.

Acknowledgements

Weiwei Dong and Wenmiao Zhang contributed equally to this article. This work was supported by the Program for Qingjiang Excellent Young Talents, JXUST (No. JXUSTQJYX2020001), the National Natural Science Foundation of China (No. 52001147), the Jiangxi Provincial Natural Science Foundation (No. 20212BAB204021), and the Jiangxi Province Key Laboratory of Magnetic Metallic Materials and Devices (2024SSY05061).

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