Effect of Ball Milling on the Absorption Properties of Fe3O4

FeCl3∙6H2O was used as raw material to produce Fe3O4, using the solvothermal method with ethylene glycol as the solvent. Fe3O4, with different particle sizes, was obtained via mechanical ball-milling by controlling the milling time. Effect of the milling time on the structure, morphology, and electromagnetic parameters of Fe3O4 were studied, and the absorption properties and mechanism of Fe3O4, for different milling times were analyzed. The results showed that the integrity of the original small spherical structure decreased as the ball milling time increased. Fe3O4 showed excellent microwave absorptions as the milling time reached 2 h, the reflection loss reached the maximum of −21.19 dB at 4.64 GHz as the thickness was 6.55 mm.


Introduction
Thanks to progress in science and technology, electromagnetic waves are now widely used in people's lives. However, there are more only benefits but also problems like pollution. To reduce the impact of electromagnetic waves on the environment, research and development of absorption materials has become a popular research topic [1][2][3][4][5].
As one of the ferrites with an anti-spinel structure, Fe 3 O 4 is a common magnetic material, which has the characteristics of low cost, simple production, and good magnetic properties [6][7][8]. Since it can generate large magnetic losses in alternating electromagnetic fields, Fe 3 O 4 is one of the most widely used conventional absorption materials. However, due to the Snoek limitation in the high-frequency region, easy oxidation, high density, and narrow absorption frequency, the comprehensive electromagnetic wave attenuation properties of Fe 3 O 4 are also limited. An effective way to improve electromagnetic wave absorption of Fe 3 O 4 , is to prepare materials with hollow, nanometer-sized structures [9][10][11][12]. Hollow structures can increase the attenuation of electromagnetic waves via multiple reflections of the incident electromagnetic waves within the cavity. Due to the high proportion of atoms on the surface of the particles, nanomaterials are prone to interface polarization, which can cause multiple scattering. Moreover, nanomaterials show quantum size effects, which split the electron energy levels of particles, and the splitting interval corresponds to the energy range of electromagnetic waves, which opens a new absorption channel [13][14][15].
Mechanical ball milling is the simplest and most used method to prepare micro/nano particles. It refers to the method of placing a material into a ball mill and grinding the material to produce broken particles and fine particles via reciprocal action between material and grinding balls. This method is characterized by a simple process and high yield, which is usually divided into two types: dry milling Materials 2020, 13, 883 2 of 12 and wet milling. Wet milling can easily grind the product to a fine size and produce more uniform nanoscale particles.
At present, chemical synthesis is the most common method to prepare electromagnetic wave absorbers with different micro/nano sizes. However, the preparation method is difficult, the required time is long and the yield is low. In addition, the size of the prepared materials is uncertain. Therefore, it is expected to obtain particles with different particle diameters using the simplest mechanical ball-milling method, which is based on the chemical synthesis method. In this paper, the Fe 3 O 4 , absorption material was synthesized using the hydrothermal method, and the ball milling method was used to study the changes of phase, morphology, structure, and electromagnetic parameters of Fe 3 O 4 , at different ball-milling times. The effects of structure and size of Fe 3 O 4 absorption material on the electromagnetic-wave attenuation performance were analyzed, and the feasibility of preparing nano-absorption-materials using mechanical ball-milling was discussed.

Preparation of Fe 3 O 4
(1) Preparation of the Fe 3 O 4 absorption material: 45 ml of ethylene glycol was placed in a beaker, then, 4 g of urea and 2 g of polyvinyl pyrrolidine were added, and evenly dispersed ultrasonically. Subsequently, 1-2 g of FeCl 3 ·6H 2 O was weighed, using an electronic balance, and added to the above solution. Then, ultrasonic treatment was preformed until the FeCl 3 ·6H 2 O was uniformly dispersed in the solution. Next, the solution was placed in a 100 ml high-pressure autoclave containing polytetrafluoroethylene, and the reaction was performed at 200 • C for 12 h. After the reaction, the sample was taken out, washed with anhydrous ethanol and distilled water many times, and dried for 24 h in a vacuum drying oven.
(2) Ball milling treatment of the prepared Fe 3 O 4 : To prevent the introduction of impurities caused by the abrasion of the grinding balls in the ball-mill tank during dry milling, wet milling was used. Fe 3 O 4 samples were placed into the ball-mill tank, following the ratio of grinding ball:material:alcohol = 7:4:3, and ball milling for 0, 0.5, 1, 1.5, and 2 h, respectively. After filtration, they were placed in a vacuum-drying oven and dried for 6 h to obtain ball-milled Fe 3 O 4 particles. The morphology, structure, surface elements, and the electromagnetic parameters were analyzed using field emission scanning electron microscope (FESEM, JEOLJSM-6500F, Eindhoven, Holland), transmission electron microscopy (TEM, Tecnai-TF20, Oberkochen, German), X-ray diffraction (XRD, D/MAX-2500PC, Rigaku, Tokyo, Japan), X-ray photoelectron spectroscopy (XPS, Thermo Fisher Scientific, Massachusetts, U.S.A) and vector network analyzer (VNA, N5242A, Agilent, USA)SEM, TEM, XRD, XPS, and VNA, respectively. The electromagnetic parameters of the measured samples were prepared by mixing the products (60%) with molten paraffin wax (40%), and placing them into a toroidal mold (Φ in = 3 mm, Φ out = 7 mm) with a thickness of 2.5-3.0mm.

Testing and Characterization
A high-power turning-target polycrystalline SmartLab XRD (D/MAX-2500PC, Rigaku, Tokyo, Japan) was used, and the test condition was set as Cu target, with a scanning rate of 2 • /min and a scanning range of 5-90 • . The surface morphology of the samples was analyzed using FESEM (SU-8010, Hitachi, Tokyo, Japan)HitachiThe microstructure of the samples was analyzed using TEM (JEM 2100, Tokyo, Japan). The electromagnetic parameters of the samples were measured using VNA (N5242A, Agilent, Santa Clara, CA, USA), and the filling amount of the samples in paraffin was 40%.

Phase Analysis of Fe 3 O 4
In order to analyze the effect of ball-milling time on the structure of Fe 3 O 4 , a polycrystalline target-turning X-ray diffraction analysis was performed. Figure 1 shows the XRD spectra of Fe 3 O 4 at different ball-milling times. It was found that the diffraction peaks were sharp and strong, indicating that the prepared nanoparticles had high crystallinity. When the ball-milling time was 0 h, peaks at 30.2 • , 35.6 • , 43.2 • , 53.6 • , 57.1 • , and 62.4 • in the figure corresponded to the crystal planes of (220), (311), (400), (422), (511), and (440), respectively. According to the crystal plane, corresponding to the diffraction peak position, it can be known that the grain was Fe 3 O 4 . As the ball-milling time increased, the intensity of the diffraction peaks of Fe 3 O 4 decreased, while the impurity peaks in the XRD spectra increased. This indicates that the milling energy increased along with the milling time, and the Fe 3 O 4 particles broke up. Therefore, the grain size decreased and the material was further refined. However, it was also more prone to undergo oxidation. In this case, the product was a mixture of In order to analyze the effect of ball-milling time on the structure of Fe3O4, a polycrystalline target-turning X-ray diffraction analysis was performed. Figure 1 shows the XRD spectra of Fe3O4 at different ball-milling times. It was found that the diffraction peaks were sharp and strong, indicating that the prepared nanoparticles had high crystallinity. When the ball-milling time was 0 h, peaks at 30.2°, 35.6°, 43.2°, 53.6°, 57.1°, and 62.4° in the figure corresponded to the crystal planes of (220), (311), (400), (422), (511), and (440), respectively. According to the crystal plane, corresponding to the diffraction peak position, it can be known that the grain was Fe3O4. As the ball-milling time increased, the intensity of the diffraction peaks of Fe3O4 decreased, while the impurity peaks in the XRD spectra increased. This indicates that the milling energy increased along with the milling time, and the Fe3O4 particles broke up. Therefore, the grain size decreased and the material was further refined. However, it was also more prone to undergo oxidation. In this case, the product was a mixture of Fe3O4 and Fe2O3, and the extension of ball-grinding time affected the crystal structure of Fe3O4.  Figure 2 shows the microstructure of Fe3O4 after different ball-milling times. It can be seen from Figure 2a, the Fe3O4, prepared using the hydrothermal method, shows a complete and regular spherical shape, with a spherical diameter 300-400 nm. With the increase in milling time, it was found, from Figure 2b-e, that the morphology of the Fe3O4 particles changed significantly. The original complete Fe3O4 pellets were constantly destroyed, and the particle size significantly reduced. After grinding for 1 h, the dispersion of Fe3O4 became worse, and agglomeration was observed. When the ball-milling time reached 2 h, it was observed that most of the Fe3O4 was ground into broken particles, and only a few intact pellets remained. The size of the broken Fe3O4 particles was 40-80 nm.    Figure 3a, it was found that the Fe3O4, prepared using the hydrothermal method, showed a complete spherical shape, with a deep edge contrast and shallow center contrast, and the Fe3O4 pellets showed a clearly hollow shape. As can be seen from Figure 3b-d, as the ball-milling time increased, the small Fe3O4 pellets were continuously broken, the integrity of the spherical particles continued to decline, and the particles became gradually fragmentated. Local agglomeration also occurred, while the size of the broken particles decreased. In general, the hollow structure of the Fe3O4 absorption material was continuously destroyed with grinding time, but the particle size of the material was continuously reduced. This is consistent with the results observed using SEM.   Figure 3a, it was found that the Fe 3 O 4 , prepared using the hydrothermal method, showed a complete spherical shape, with a deep edge contrast and shallow center contrast, and the Fe 3 O 4 pellets showed a clearly hollow shape. As can be seen from Figure 3b-d, as the ball-milling time increased, the small Fe 3 O 4 pellets were continuously broken, the integrity of the spherical particles continued to decline, and the particles became gradually fragmentated. Local agglomeration also occurred, while the size of the broken particles decreased. In general, the hollow structure of the Fe 3 O 4 absorption material was continuously destroyed with grinding time, but the particle size of the material was continuously reduced. This is consistent with the results observed using SEM.  Figure 4 shows the curves of the complex permittivity and complex permeability of the Fe3O4 absorption material for different grinding times, changing with frequency. Figure 4a shows the curve of the real part of the complex permittivity of the absorption material as a function of frequency. As can be seen from the figure, the real part of the complex permittivity decreased before it increased with increasing ball-grinding time. When the ball-milling time was 1.5 h, the real part was the smallest, and when the milling time reached 2 h, the real part started to increase. Figure 4b displays the curve of the imaginary part of the complex permittivity of the Fe3O4 absorption material, as a function of frequency. It was found that the imaginary part of the complex permittivity decreased first with increasing ball-milling time and then remained basically unchanged. The value that varied with frequency was basically the same. Moreover, wave peaks appeared around 4 GHz, 9 GHz, and 15 GHz, indicating that the products had a strong dielectric loss capability at these three frequencies. The imaginary part of the complex permittivity of the Fe3O4 absorption material decreased as the ball milling time increased. This is because the originally spherical Fe3O4 particles were destroyed after ball milling. For the same mass of powder, the hollow Fe3O4 pellets (with low density) added more materials than the high dense Fe3O4 fragments, and its distribution in paraffin is also greater. Due to the increased contact area, a large number of hollow Fe3O4 spheres formed a macroscopic conductive chain or local conductive network in the material, under the action of the  Figure 4 shows the curves of the complex permittivity and complex permeability of the Fe 3 O 4 absorption material for different grinding times, changing with frequency. Figure 4a shows the curve of the real part of the complex permittivity of the absorption material as a function of frequency. As can be seen from the figure, the real part of the complex permittivity decreased before it increased with increasing ball-grinding time. When the ball-milling time was 1.5 h, the real part was the smallest, and when the milling time reached 2 h, the real part started to increase. Figure 4b displays the curve of the imaginary part of the complex permittivity of the Fe 3 O 4 absorption material, as a function of frequency. It was found that the imaginary part of the complex permittivity decreased first with increasing ball-milling time and then remained basically unchanged. The value that varied with frequency was basically the same. Moreover, wave peaks appeared around 4 GHz, 9 GHz, and 15 GHz, indicating that the products had a strong dielectric loss capability at these three frequencies. The imaginary part of the complex permittivity of the Fe 3 O 4 absorption material decreased as the ball milling time increased. This is because the originally spherical Fe 3 O 4 particles were destroyed after ball milling. For the same mass of powder, the hollow Fe 3 O 4 pellets (with low density) added more materials than the high dense Fe 3 O 4 fragments, and its distribution in paraffin is also greater. Due to the increased contact area, a large number of hollow Fe 3 O 4 spheres formed a macroscopic conductive chain or local conductive network in the material, under the action of the electromagnetic field. Therefore, in the absence of ball grinding, the absorption material with a large amount of Fe 3 O 4 hollow pellets, had both a higher electrical conductivity and dielectric constant. As the ball-milling time increased, the small spherical structures of Fe 3 O 4 were destroyed, which resulted in a decrease in electrical conductivity and permittivity of the material. The Fe 3 O 4 pellets were ground when the ball-milling time reached 2 h. However, due to sufficient ball-grinding time, the size of the broken particles was smaller and it was easier to form a conductive network. The conductivity of the material showed a rising trend, and the permittivity increased significantly, especially at high frequencies. Figure 4c,d shows the curves of the real and imaginary parts of the complex permeability of the Fe 3 O 4 absorption material, as a function of frequency. As shown in the figures, with increasing frequency, both real and imaginary parts of the complex magnetic permeability of Fe 3 O 4 , at different ball-milling times, decreased continuously and remained unchanged afterwards. It gradually decreased with the increase of ball-milling time. This is because, when the hollow balls were ground, the material lost the advantage of the hollow structure and reduced the reflection loss of incident electromagnetic waves in the cavity. This, thus, reduced the magnetic loss capacity of the absorption material. However, the imaginary part of the magnetic permeability changed slightly with the ball-milling time, which indicates that the destruction of the hollow small sphere structure of Fe 3 O 4 had no significant effect on the magnetic loss of the material.  The electromagnetic wave loss factor is usually used to characterize the absorption attenuation capacity of a material, and it can be described as [16] tanδ = tanδ E + tan δ M (1) The electromagnetic wave loss factor is usually used to characterize the absorption attenuation capacity of a material, and it can be described as [16] tan δ = tan δ E + tan δ M

Electromagnetic Parameter Analysis of Fe 3 O 4 at Different Ball-Milling Times
In the formula: tan δ E is the tangent of electrical loss, tan δ E = ε /ε ; tan δ M is the tangent of magnetic loss, tan δ M = µ /µ . Among them, ε" and ε are the imaginary and real parts of the complex permittivity, and µ" and µ are the imaginary and real parts of the complex permeability, respectively. It can be seen that materials with better electromagnetic-wave attenuation can be obtained by increasing the imaginary part and lowering the real part of the absorption material. Figure 5 shows the dielectric loss tangent and magnetic loss tangent of Fe 3 O 4 absorption material at different ball milling times. From Figure 5a,b, it can be seen that, with increasing ball-milling time, the electrical loss tangent of Fe 3 O 4 absorption material gradually decreased in the low frequency band. However, in the high frequency band, it first decreased before it increased. This is explained as follows: During the ball milling process, the fragmentation degree of small spherical Fe 3 O 4 absorption material improved continuously. This reduced the micro-interface of the absorption material on the whole, weakened the multiple reflection of the incident electromagnetic wave inside the material structure, and further degraded the interface polarization and dielectric loss of the Fe 3 O 4 absorption material. On the other hand, as the milling time reached 2 h, even though the small spherical Fe 3 O 4 was basically broken, due to the sufficient ball-milling time, the broken particles were ground into finer and more uniform nano-sized particles. Compared with other short-time grinding, the conductivity and dielectric loss of the Fe 3 O 4 absorption materials were improved, especially in the high-frequency band.
The effect of different ball-milling times on the magnetic loss tangent of Fe 3 O 4 absorption material was not obvious, which indicates that with the extension of the ball-milling time, although the Fe 3 O 4 absorption material was gradually broken from the original small spherical shape into fine particles and the structure of the material changed significantly, it had no effect on its magnetic loss. Therefore, changing the microstructure of Fe 3 O 4 absorption material via ball milling mainly affected the dielectric properties of the material.

Effect of Ball-Milling Time on the Absorption Mechanism
Through the analysis of electromagnetic parameters and loss factor, it was implied that the microstructure of the Fe3O4 absorption material was changed by ball milling, and its dielectric loss was greatly affected by the refining material size. To learn more about the dielectric loss, Cole-Cole diagrams were used to study the dielectric properties of Fe3O4 absorption material at different ball-milling times.
The formula for the permittivity with different frequencies [17] was proposed by K. S. Cole and R. H. Cole

Effect of Ball-Milling Time on the Absorption Mechanism
Through the analysis of electromagnetic parameters and loss factor, it was implied that the microstructure of the Fe 3 O 4 absorption material was changed by ball milling, and its dielectric loss was greatly affected by the refining material size. To learn more about the dielectric loss, Cole-Cole diagrams were used to study the dielectric properties of Fe 3 O 4 absorption material at different ball-milling times.
The formula for the permittivity with different frequencies [17] was proposed by K. S. Cole and Materials 2020, 13, 883 8 of 12 Here, τ 0 , α, ε ∞ , and ε S represent the relaxation time, parameter variable, optical frequency permittivity and static dielectric constant, respectively. The complex permittivity ε can be expressed by as [18] ε = ε − jε (3) The real part ε and imaginary part ε of the permittivity are The Cole-Cole circular equation for the real and imaginary parts of the complex permittivity can be obtained by combining Equations (3) and (4).
It can be seen that the center coordinates were ( ε S +ε ∞ 2 , σε r +σ R ωτ ), and the radius was ε S −ε ∞ 2 . Thus, Cole-Cole diagrams of the Fe 3 O 4 absorption material, at different ball milling times, can be obtained-see Figure 6.
Here, 0 , α, ∞ , and ε represent the relaxation time, parameter variable, optical frequency permittivity and static dielectric constant, respectively. The complex permittivity ε can be expressed by as [18] The real part ε ′ and imaginary part ε ′′ of the permittivity are The Cole-Cole circular equation for the real and imaginary parts of the complex permittivity can be obtained by combining Equations (3) and (4).
It can be seen that the center coordinates were ( ε +ε ∞ 2 , ε + ), and the radius was Cole-Cole diagrams of the Fe3O4 absorption material, at different ball milling times, can be obtained -see Figure 6. According to the center coordinates and radii in Figure 6, the optical frequency permittivity ∞ , the static permittivity , and the conductivity  = r+R can be calculated. It can be seen that the semi-circle radius and vertical coordinate of the material, after ball grinding, decreased before it increased. This indicates that the optical frequency permittivity ∞ and static permittivity decreased, after ball milling, and the electric conductivity first decreased and then increased, which is consistent with the results of the dielectric-loss analysis. Therefore, although the dielectric loss of the Fe3O4 absorption material can be improved using a sufficiently long ball-milling time, the overall dielectric-loss decreases more than that for the hollow small spherical Fe3O4 without ball grinding. Its absorption mechanism was the same as the polarization relaxation before ball milling, and both involve interfacial polarization and dipole polarization relaxation loss. According to the center coordinates and radii in Figure 6, the optical frequency permittivity ε ∞ , the static permittivity ε s , and the conductivity σ = σr + σR can be calculated. It can be seen that the semi-circle radius and vertical coordinate of the material, after ball grinding, decreased before it increased. This indicates that the optical frequency permittivity ε ∞ and static permittivity ε s decreased, after ball milling, and the electric conductivity first decreased and then increased, which is consistent with the results of the dielectric-loss analysis. Therefore, although the dielectric loss of the Fe 3 O 4 absorption material can be improved using a sufficiently long ball-milling time, the overall dielectric-loss decreases more than that for the hollow small spherical Fe 3 O 4 without ball grinding. Its absorption mechanism was the same as the polarization relaxation before ball milling, and both involve interfacial polarization and dipole polarization relaxation loss.
The loss mechanisms of magnetic loss materials mainly include hysteresis loss, eddy current loss, domain-wall resonance, natural resonance, exchange resonance, and others. In general, hysteresis loss is small in weak external magnetic fields, and domain-wall resonance occurs for the range of 1-100 MHz. Using Aharroni's theory, when one dimension of a nanomaterial is reduced to the nanometer level, it may generate a resonance mode with higher resonance than the natural resonance. The exchange resonance has been confirmed in many studies. The particle size of the Fe 3 O 4 absorption material, prepared via ball milling, was within the nanometer range. Hence, there was some exchange resonance loss. To study the loss of magnetic absorption materials, the following formula is generally used [19] Here, σ is the conductivity of the material, and µ 0 is the vacuum permeability. In other words, if there is only eddy-current loss, the right side of the formula should be constant. Based on the calculation of electromagnetic parameters, the µ (µ ) −2 f −1 vs. frequency curve of the Fe 3 O 4 absorption material at different milling time was obtained-see Figure 7. It can be seen that as the ball-milling time increased, and the µ (µ ) −2 f −1 C0 value of the sample increased for the frequency range of 2-8 GHz. This indicates that the sample's natural resonance-loss capacity at 4-6 GHz increased after ball milling. This was attributed to the enhanced anisotropy of the magnetic crystals after ball milling, which leads to the enhanced anisotropic field, the internal equivalent field enhancement of the ferromagnet, and the increased energy consumption generated by the damping effect. At 8-18 GHz, µ (µ ) −2 f −1 remained basically unchanged, and the eddy-current loss was the main absorption mechanism at this time.
Materials 2020, 13, 883 9 of 13 The loss mechanisms of magnetic loss materials mainly include hysteresis loss, eddy current loss, domain-wall resonance, natural resonance, exchange resonance, and others. In general, hysteresis loss is small in weak external magnetic fields, and domain-wall resonance occurs for the range of 1-100 MHz. Using Aharroni's theory, when one dimension of a nanomaterial is reduced to the nanometer level, it may generate a resonance mode with higher resonance than the natural resonance. The exchange resonance has been confirmed in many studies. The particle size of the Fe3O4 absorption material, prepared via ball milling, was within the nanometer range. Hence, there was some exchange resonance loss. To study the loss of magnetic absorption materials, the following formula is generally used [19] Here, σ is the conductivity of the material, and μ 0 is the vacuum permeability. In other words, if there is only eddy-current loss, the right side of the formula should be constant. Based on the calculation of electromagnetic parameters, the μ ′′ (μ ′ ) −2 f −1 vs. frequency curve of the Fe3O4 absorption material at different milling time was obtained -see Figure 7. It can be seen that as the ball-milling time increased, and the μ ′′ (μ ′ ) −2 f −1 C0 value of the sample increased for the frequency range of 2-8 GHz. This indicates that the sample's natural resonance-loss capacity at 4-6 GHz increased after ball milling. This was attributed to the enhanced anisotropy of the magnetic crystals after ball milling, which leads to the enhanced anisotropic field, the internal equivalent field enhancement of the ferromagnet, and the increased energy consumption generated by the damping effect. At 8-18 GHz, μ ′′ (μ ′ ) −2 f −1 remained basically unchanged, and the eddy-current loss was the main absorption mechanism at this time.

Effects of Ball-Milling Time on Absorption
To study the absorption of materials, reflectivity was simulated using MATLAB software, based on the electromagnetic parameters measured by a vector network analyzer. The electromagnetic wave absorption capacity was expressed by the reflection loss RL (dB) as [20] RL(dB) = 20 log | − 1 + 1 | (9)

Effects of Ball-Milling Time on Absorption
To study the absorption of materials, reflectivity was simulated using MATLAB software, based on the electromagnetic parameters measured by a vector network analyzer. The electromagnetic wave absorption capacity was expressed by the reflection loss RL (dB) as [20] Here, h is the Planck constant, c is the speed of electromagnetic waves in vacuum, f is the frequency, d is the thickness of the material, Zin is the input impedance, µ 0 and ε 0 are the permeability and permittivity of free space, ε r and µ r are the permittivity and magnetic permeability of the material.
It can be seen from Figure 8 that the small spherical Fe 3 O 4 , without ball grinding, had a good absorption performance. When the matching thickness was 5.94 mm, it had the largest reflection loss capability at 3.84 GHz, and the reflection-loss reached −20.17 dB. When the matching thickness was 5.24 mm, it had the maximum reflection-loss capability at 15.28 GHz, reaching −41.25 dB. When the matching thickness was 5.98 mm, it showed the maximum reflection loss capability at 13.12 GHz, and the maximum reflection loss was 38.39 dB. This indicates that it had good absorption at both low and high frequencies. It can be seen from Figure 8 that the small spherical Fe3O4, without ball grinding, had a good absorption performance. When the matching thickness was 5.94 mm, it had the largest reflection loss capability at 3.84 GHz, and the reflection-loss reached -20.17 dB. When the matching thickness was 5.24 mm, it had the maximum reflection-loss capability at 15.28 GHz, reaching -41.25 dB. When the matching thickness was 5.98 mm, it showed the maximum reflection loss capability at 13.12 GHz, and the maximum reflection loss was 38.39 dB. This indicates that it had good absorption at both low and high frequencies.
However, as the ball-milling time increased, the absorption of Fe3O4 first decreased before it increased. This was because, when the hollow spherical Fe3O4 was ball milled, the hollow structure of the surface was destroyed, and the multiple reflection ability was reduced. Although the obtained Fe3O4 fragment particles were much finer, the overall electromagnetic wave attenuation performance still showed a significant decline. After ball milling for 0.5 h, the absorption performance of Fe3O4 decreased significantly, which suggest that the hollow spherical microstructure had a significant effect on the absorption of Fe3O4. With the extension of the ball-milling time, when the ball-milling times were 1 h and 1.5 h, a large number of Fe3O4 pellets were broken, the hollow structure severely damaged, and the dielectric loss continued to decrease. Thus, its maximum reflection loss at high frequencies was lower than -10 dB. However, as the ball-milling time continued to increase to 2 h, the spherical structure was almost ball-milled into finer nanoparticles. Because its nanoparticles were smaller in size and had a large specific surface area, it was beneficial to improve the absorption performance of Fe3O4. Therefore, compared with other ball grinding times, the absorption of Fe3O4 was significantly improved. When the matching thickness was 6.55 mm, there was a large reflection loss at 4.64 GHz, and the maximum reflection loss was -21.19 dB.

Conclusions
Effect of ball milling time on microstructure and absorption properties of Fe3O4 were investigated systematically. According to the above results, conclusions can be summarized at these following aspects.  However, as the ball-milling time increased, the absorption of Fe 3 O 4 first decreased before it increased. This was because, when the hollow spherical Fe 3 O 4 was ball milled, the hollow structure of the surface was destroyed, and the multiple reflection ability was reduced. Although the obtained Fe 3 O 4 fragment particles were much finer, the overall electromagnetic wave attenuation performance still showed a significant decline. After ball milling for 0.5 h, the absorption performance of Fe 3 O 4 decreased significantly, which suggest that the hollow spherical microstructure had a significant effect on the absorption of Fe 3 O 4 . With the extension of the ball-milling time, when the ball-milling times were 1 h and 1.5 h, a large number of Fe 3 O 4 pellets were broken, the hollow structure severely damaged, and the dielectric loss continued to decrease. Thus, its maximum reflection loss at high frequencies was lower than −10 dB. However, as the ball-milling time continued to increase to 2 h, the spherical structure was almost ball-milled into finer nanoparticles. Because its nanoparticles were smaller in size and had a large specific surface area, it was beneficial to improve the absorption performance of Fe 3 O 4 . Therefore, compared with other ball grinding times, the absorption of Fe 3 O 4 was significantly improved. When the matching thickness was 6.55 mm, there was a large reflection loss at 4.64 GHz, and the maximum reflection loss was −21.19 dB.

Conclusions
Effect of ball milling time on microstructure and absorption properties of Fe 3 O 4 were investigated systematically. According to the above results, conclusions can be summarized at these following aspects.