Ultra-Low Core Loss and High-Frequency Permeability Stability in Hot-Press Sintered FeSi Soft Magnetic Composites by Fe2O3 Nanoparticles Air Gap Filling

Abstract

Soft magnetic materials are crucial in motors, generators, transformers, and many electronic devices. We synthesized the FeSi soft magnetic composites (SMCs) with different doping contents of Fe₂O₃ nanopowders as fillers via the hot-press sintering technique. This work explores the incorporation of high-resistivity magnetic fillers through a novel compaction technique and investigates the influence of Fe₂O₃ nanopowder on the structure and magnetic properties of Fe₂O₃ nanopowder-filled composites. The finding reveals that Fe₂O₃ nanopowders effectively fill the air gaps between FeSi powders, increasing SMC density. Moreover, all samples exhibit excellent effective permeability frequency stability, ranging from 15 kHz to 100 kHz. Notably, the effective permeability µ_e improves from 22.32 to 30.45, a 36.42% increase, when the Fe₂O₃ doping concentration increases from 0 to 2 wt%. Adding Fe₂O₃ nanopowders also enhances electrical resistivity, leading to a 37.21% reduction in eddy current loss in samples for 5 wt% Fe₂O₃ addition, compared to undoped samples. Furthermore, as Fe₂O₃ content increases from 0 to 5 wt%, the power loss P_cv of the Fe₂O₃-doped Fe-6.5Si SMCs decreases from 25.63 kW/m³ to 16.13 kW/m³, a 37% reduction. These results suggest that Fe₂O₃-doped FeSi SMCs, with their superior soft magnetic properties, hold significant potential for use in high-power and high-frequency electronic applications.

1. Introduction

Soft magnetic composites (SMCs) are ferromagnetic materials, synthesized by enclosing them in a thin, resistive insulating layer, forming a core–shell heterogeneous structure [1,2,3,4,5,6]. Because of their distinctive three-dimensional isotropic ferromagnetic behavior, high saturation magnetic flux density, high magnetic permeability, low coercivity, high specific electrical resistivity, and low core loss, SMCs are of great interest to scientists and engineers for use in a variety of electromagnetic devices, including motors, transformers, sensors, and inductors [7,8,9,10]. Among Fe-based SMCs such as Fe-Si, Fe-Si-Al, Fe-Ni, Fe-Ni-Mo, and amorphous SMCs based on their composition [11,12,13,14], the FeSi alloy is preferred for SMCs due to its relatively high resistance and saturation magnetization density [15,16,17]. To meet the growing demands for higher-frequency electronic products, SMCs need high magnetic permeability and low core loss [18,19,20,21,22].

Fe-6.5 wt%Si SMCs have garnered significant attention because of their excellent magnetic properties, including high magnetic permeability, high saturation magnetization, excellent DC bias characteristics, low magnetocrystalline anisotropy, and nearly zero magnetostrictive coefficient [23,24]. However, the brittleness of FeSi results in low compaction density and low permeability [25]. More forming agents and higher compacting pressure are required to achieve desirable properties, although excessive non-magnetic forming agents can reduce the permeability and magnetization of SMCs [15,26]. Excessive pressure during compaction can damage the insulation layer, increasing internal stress and thus reducing permeability and increasing magnetic loss [27]. The advancement of low-loss technologies and the miniaturization of power electronics components depend on optimizing the magnetic properties of SMCs [15]. Therefore, enhancing the high-frequency characteristics of SMCs is essential for specific applications.

To improve the magnetic properties of SMCs, strategies such as particle size matching [28], insulation coating, novel annealing techniques [29], and incorporating tiny, soft metallic magnetic particles [30,31] have been employed. The choice of insulation coating has received significant attention because it has a significant impact on the soft magnetic properties of magnetic powder cores, such as high-frequency loss, frequency stability, and so on. There are two categories of insulation coating: organic and inorganic. Nevertheless, the non-magnetic insulation coating, whether it is organic or inorganic, greatly reduces the saturation magnetization and permeability of magnetic powder cores, which weakens the magnetic properties of magnetic powder cores. Consequently, it is particularly important to use insulation coating with high resistivity and excellent magnetic properties. To address this issue, various ferromagnetic materials such as Mn-Zn ferrites Ni-Zn ferrites, and FexOy have been considered suitable insulators with good soft magnetic properties.

In this context, Liu et al. [1] studied the influence of Fe nanoparticles on the soft magnetic properties of Fe-6.5 wt% Si SMCs. Fe addition enhanced magnetic permeability by up to 24% and maintained comparatively low core loss in Fe-6.5 wt% Si SMCs. Zhao et al. [32] reported FeSi/FeNi SMCs with improved soft magnetic properties for a 22.1% core loss reduction and a 43.8% increase in effective permeability. Wang et al. [33] investigated that Co-doping Fe-6.5Si powder significantly increases electrical resistance and saturation magnetization, with decreased core loss and increased effective permeability. Similarly, Luo et al. [34] studied the effect of Fe₂O₃ coating on the structure and magnetic performances of FeSiAl soft magnetic composites prepared via the arc-melting method. The saturation magnetization eventually increased, and coercivity decreased with the increase in Fe₂O₃. In addition, the frequency stability for effective permeability was greatly improved. Though most of the research has been done on FeSi using different strategies, core loss in SMCs is still a major concern due to the low electrical resistivity of metallic magnetic nanoparticles and low compaction techniques. Adding high-resistivity magnetic filler (Fe₂O₃) is crucial to reducing core loss, particularly eddy current loss, without reducing the magnetic contents of SMC. Additionally, novel compaction techniques like hot-press sintering can further enhance the magnetic properties of SMCs by improving densification, preventing grain growth, and applying axial pressure at high temperatures. This work focuses on the incorporation of high-resistivity magnetic fillers using novel compaction techniques.

Here, we employed oxide magnetic nanoparticles (Fe₂O₃) as fillers in FeSi SMCs prepared via the hot-pressing technique and investigated the soft magnetic properties. The appropriate filling of air gaps by Fe₂O₃ nanopowders enhances the surface morphology, density, magnetic permeability, and core loss of the SMCs, resulting in ultra-low core loss, which shows promising applicability in various electronic applications.

2. Materials and Methods

Commercial gas-atomized FeSi powder (Si content 6.5 wt%, purity surpassing 99.9 wt%) with an average particle size of 30 µm was acquired from Hunan Hualiu New Materials Co., Ltd., Changsha, China. Iron oxide nanoparticles (α-Fe₂O₃, 98% purity) with an average particle size of 100 nm were supplied by Sigma Aldrich (St. Louis, MO, USA). Polyvinylpyrrolidone (PVP), Zinc stearate, and ethanol were provided by Sigma Aldrich (Shanghai, China).

The Fe₂O₃ doped Fe-6.5 wt%Si SMCs were made by combining FeSi powders with varying concentrations of Fe₂O₃ nanoparticles (0 wt%, 1 wt%, 2 wt%, 3 wt%, 4 wt%, and 5 wt%); 3.0 wt% PVP and 0.5 wt% Zinc stearate were used as binder and lubricant, respectively. The detailed process is given in the schematic diagram shown in Figure 1. Firstly, through magnetic stirring, Zinc stearate and PVP were dissolved completely in ethanol. After adding the FeSi powder and Fe₂O₃ nanoparticles, the mixture was mechanically stirred until all the ethanol had been removed. It was then dried for an hour at 70 °C in a vacuum environment. The powdered Fe-6.5 wt%Si-Fe₂O₃ composites were then compressed into a toroidal mold with an outside diameter of 20 mm and an inner diameter of 10 mm using a hot-pressing technique under an applied pressure of 70 MPa, after which they were sintered for an hour at 750 °C. Eventually, a systematic characterization of the fabricated Fe₂O₃-doped FeSi SMCs was conducted.

The structural properties of the powders were measured using X-ray diffraction (XRD, D8 Advance Bruker, Billerica, MA, USA) with Cu-Kα radiation at a range of 2θ = 10~90°. The surface morphologies and chemical compositions of composites were analyzed using scanning electron microscopy (HR FE-SEM, Gemini360, Carl Zeiss, Zurich, Switzerland) coupled with an energy-dispersive X-ray spectrometer (EDS). The saturation magnetization of the samples was measured by a Physical Property Measurement System (PPMS DynaCool, Quantum Design, San Diego, CA, USA) with an applied maximum field ranging from 0 to 20,000 Oe. To lower the error fraction, the density of the composites was calculated by averaging the sample mass and dimensions. The electrical resistivity was measured using a four-probe system equipped with a Keithly 2400 source meter (Cleveland, OH, USA). For the frequency-dependent effective permeability μ_e spectra of the cores, a Precision LCR meter (Key Sight E4980A, Keysight Technologies, Santa Rosa, CA, USA) was used. The μ_e of the FeSi-Fe₂O₃ SMCs was determined from the inductance of the core using the following Equation (1) [35]:

(1)${\mu }_e={\displaystyle \frac{L{l}_e}{{\mu }_o{N}^2{A}_e}}$

where L denotes the inductance of the core, l_e is the effective magnetic circuit length of the toroidal SMCs, μ_o is the vacuum permeability, N is the number of turns of insulated copper wire twists on the core, and A_e is the SMCs effective cross-section area. To explore the effect of nanopowders on the losses, the frequency-dependent core loss measurement was carried out via an AC loop tracer (IWATSU B-H ANALYZER, SY-8219, Iwatsu Corporation, Tokyo, Japan).

3. Results

Figure 2a, b, and c–h display the SEM images for raw FeSi, Fe₂O₃ nanopowders, and SMCs, with an inset graph showing particle size distribution for FeSi, respectively. The SEM image in Figure 2a shows that FeSi particles are spherical, and the surface is quite smooth. The average particle size is about 10~30 μm. The Fe₂O₃ nanopowders are aggregated, in addition to a uniformly smooth spherical shape, as shown in Figure 2b. The SEM images for all prepared SMCs with different Fe₂O₃ content are illustrated in Figure 2c–h, which shows that adding NP from 0 to 2 wt% filled the pores, indicating increased compact density. However, the excessive addition of NP gives rise to more pores due to aggregation, resulting in a reduced density. The SMC of Fe₂O₃ content 2 wt% becomes a compact distribution and a well-connected network between grains.

Figure 3a,b and c–f depict the SEM images and the corresponding EDS elemental distribution maps for the FeSi-Fe₂O₃ SMCs, respectively. The result demonstrates that there is a uniform distribution of Fe both inside and between the particle regions. This behavior validates the dispersion of the Fe nanoparticles in the pores between the micron-sized FeSi particles. On the other hand, the Si is observed in the particle region only; however, O and C elements are primarily found in the space between the particles.

The XRD patterns of FeSi-Fe₂O₃ SMCs with varying concentrations of Fe₂O₃ NP are presented in Figure 4. In all samples, three distinct characteristic peaks are observed at 44.7°, 65.1°, and 82.5° that correspond to the (110), (200), and (211) bcc crystal structure of the α-Fe (Si) phase. Furthermore, there is no obvious change in the intensity or peak shift when adding Fe₂O₃ nanopowders.

The density and electrical resistivity of FeSi-Fe₂O₃ SMCs are presented in Figure 5a,b, respectively. The density of FeSi-Fe₂O₃ SMCs first increased, reaching a maximum value (7.12 g/cm³) for a sample with 2 wt% of Fe₂O₃, which is 8.2% higher than 6.58 g/cm³ for the sample with the pristine one (0 wt% of Fe₂O₃), and then decreased with a further increase in Fe₂O₃ nanoparticle contents. This increase supports the assumption that the nanoparticles effectively fill interparticle voids between FeSi particles, leading to improved compaction and reduced porosity. With a further increase in Fe₂O₃ nanoparticles, additional pores are created due to agglomeration, which lowers the density of SMCs. Conversely, the electrical resistivity (shown in Figure 5b) gradually increased from 29.55 to 50.70 mΩ-cm with increasing contents of Fe₂O₃ NP from 0–5 wt%, respectively. Interestingly, the sample with the high doping concentration of Fe₂O₃ (5 wt%) has the highest value (50.70 mΩ-cm), which is 71.57% higher than the pristine sample 0 wt% of Fe₂O₃ (29.55 mΩ-cm). These results are reasonable because doping with an insulating material can cause high electrical resistivity. Notably, the electrical resistivity values for our FeSi-Fe₂O₃ SMCs are much higher than those reported [32].

The room temperature magnetic hysteresis loop measurement (MH loops) for all samples with different doping concentrations of Fe₂O₃ are shown in Figure 6a. Notably, all the coated samples exhibited good soft magnetic performance with high M_s and very low H_c, as presented in Table 1. Inset of Figure 6a is the expanded plot near the low field range (|H| < 40 Oe) to see the H_c more clearly. To further evaluate the dependence of M_s and H_c on doping concentration, the extracted parameters from MH loops are plotted against Fe₂O₃ contents, as illustrated in Figure 6b. Interestingly, the value of saturation magnetization increases first from 187.96 to 191.31 emu/g as the amount of Fe₂O₃ increases from 0% to 2%, then decreases to 189.90 emu/g with the further increase in Fe₂O₃ content from 2 to 4 wt%, and then increases again in the last sample with 5 wt% of Fe₂O₃ nanopowders. This small enhancement in M_s can be attributed to the low saturation magnetization of Fe₂O₃ (0.726 emu/g). Introducing Fe₂O₃ NP raises the ferromagnetic filling factor by filling the pores in the SMCs and increasing the saturation magnetization. However, doping an excess amount of Fe₂O₃ induces new pores due to agglomeration, which in turn decreases the volume fraction of the ferromagnetic phase, resulting in a decrease in M_s [36]. However, it increased again in the last sample with 5 wt% content of Fe₂O₃. In contrast, the value of Hc followed an opposite trend to M_s. The H_c value drops first from 12.27 to 11.55 Oe with increased Fe₂O₃ contents from 0 to 2 wt% and then follows an increasing trend up to 12.75 Oe with a further increase in Fe₂O₃ nanopowders. Moreover, the lowest value for a sample with 5 wt% doping content of Fe₂O₃ is observed around 10.78 Oe. The results are well understood because it is well-known that the coercive field strongly depends on the crystal structure and defects such as porosity, secondary phases, and interface [37]. Interestingly, the values of H_c for all our samples are much lower in comparison to the reported results [1].

Figure 7 illustrates the frequency-dependent effective permeability μ_e of SMCs with varying content of Fe₂O₃ in the range of 15 kHz to 100 kHz. Due to the growing demand for high-frequency applications of electronic devices, the effective permeability of SMCs must generally remain constant up to high frequencies. Interestingly, all our compact samples showed excellent frequency stability of effective permeability ranging from 10 kHz to 100 kHz. Furthermore, as the Fe₂O₃ content increased from 0 to 2 wt%, the effective permeability μe increased from 22.32 to 30.45. However, as the Fe₂O₃ quantities increased further, the value of μe decreased to 19.32. The maximum value observed for the 2 wt% of NP content is 36.42 %, which is higher than the sample without doping Fe₂O₃. For SMC, the effective permeability can be expressed as [38]:

(2)${\mu }_e={\displaystyle \frac{3+\left({\mu }^{\prime }-1\right)\left(3-3g\right)}{3+g\left({\mu }^{\prime }-1\right)}}$

where μ′ indicates the permeability of the magnetic powders and g is the volume fraction of non-magnetic substances. The effective permeability is correlated with the density and saturation magnetization of the SMCs, as per the equation above. The effective permeability of the magnetic powders is proportional to the density and the square of the M_s [39,40,41]. The incorporation of Fe₂O₃ nanopowders from 0 to 2 wt% enhances the density, saturation magnetization (M_s), and relative permeability. Adding Fe₂O₃ nanopowders beyond 2 wt% decreases both M_s and density, thereby reducing the effective permeability.

To assess the impact of magnetic nanopowders on the AC magnetic property of SMCs, the total core loss (P_cv) versus frequency (f) plots for all Fe₂O₃-doped Fe-6.5wt%Si SMCs measured at an applied magnetic field of 10 mT in the frequency range of 15 to 100 kHz are shown in Figure 8a. The P_cv of Fe₂O₃-doped Fe-6.5wt%Si SMC progressively drops from 25.63 kW/m³ to 16.13 kW/m³ as Fe₂O₃ contents rise from 0 wt% to 5 wt%, as presented in Table 2. Interestingly, for the sample with maximum Fe₂O₃ content (5 wt%), the P_cv is reduced by 35% compared to undoped FeSi (0 wt% of Fe₂O₃) (P_cv = 16.13 kW/m³, f =100 kHz, and B_m = 10 mT). Moreover, the P_cv for our compacted samples is much lower than those of previous results on FeSi SMCs [42,43,44]. This is mostly because of the high resistivity of Fe₂O₃, which blocks the interaction between magnetic particles and lowers the total loss.

According to Bertotti’s classical theory of loss separation, P_cv primarily falls into three categories: hysteresis losses (Ph), eddy current losses (Pe), and residual losses (Pr), as follows [45]:

(3)$P_{cv}=P_e+P_h+P_r$

where P_cv represents the total core loss, P_h is the hysteresis loss, P_e is the eddy current loss, and P_r is the residual or excessive loss. In power applications, P_r often has a very low value in comparison to P_h and P_e [46]. Consequently, in our situation, it may be disregarded, and the simplified equation is as follows:

(4)$P_{cv}=P_e+P_h$

Hysteresis loss signifies the energy lost per unit volume during a single magnetization cycle, and it can be written as follows:

(5)$P_h=f\varnothing HdB=k_h{B}_m^{3}f$

where B_m represents the applied magnetic flux density, f is the magnetic field frequency, and k_h is the hysteresis loss coefficient.

The eddy current loss that results from the application of Faraday’s law to ferromagnetic materials magnetized in an alternating magnetic field can be described by the following equation [2,47]:

(6)$P_e={\displaystyle \frac{k_e{B}_m^2{d}_{eff}^2}{\rho }}{f}^2$

where k_e is the eddy current loss coefficient, d_eff is the effective diameter of the particles, B_m is the applied magnetic flux density, and ρ is the electrical resistivity of SMCs. Combining Equations (3) and (4), the above Equation (2) can be rewritten as:

(7)$P_{cv}=k_h\times f+k_e\times f^2$

Hysteresis loss and eddy current loss are known to be proportional to frequency (f) and the square of frequency (f²), respectively. Kollar’s loss separation model states that the total energy loss W_t (J/m³) is determined by dividing Equation (5) by the frequency as given below:

(8)$W_t={\displaystyle \frac{P_{cv}}{f}}=k_h+k_e\times f$

The P_cv/f versus f fitted curves with linear Equation (5) for all the SMCs with different Fe₂O₃ contents are shown in Figure 8b. Our experimental results (solid dots) agreed well with the corresponding fits (dashed lines). The k_h and k_e are derived from the intercept and slope of the fits, respectively [37]. Using the fitting formula, the hysteresis losses Ph and eddy current loss Pe are extracted and plotted against f, as seen in Figure 8c and Figure 8d, respectively.

The value of P_h at f = 100 kHz first dropped from 19.022 kW/m³ to 14.43 as the Fe₂O₃ contents changed from 0 to 3wt%, as shown in Figure 8c. It subsequently increased to 33.19 kW/m³ for the sample with 4 wt% Fe₂O₃ contents and then dropped again to 11.97 kW/m³ for the sample with 5 wt% Fe₂O₃. It is commonly known that hysteresis loss and coercivity are directly related [1]. Therefore, the changing trend of H_c, which coincides with the altering trend of P_h, may be one possible explanation. In our case, the lowest P_h value recorded for a sample containing 5 wt% of Fe₂O₃ is approximately 11.97 kW/m³.

In contrast, the P_e versus f plot shown in Figure 8d followed a gradually decreasing trend with the increase in Fe₂O₃ contents, except for the sample with 2 wt% and 4 wt% of Fe₂O₃ contents. The value of P_e at f = 100 kHz declined from 6.61 to 4.15 kW/cm³ as the Fe₂O₃ contents changed from 0 to 5 wt%. Since Pe is inversely proportional to electrical resistivity according to Equation (6), the increased electrical resistivity of SMCs might be the possible reason for the decrease in P_e, as indicated in Table 2. Consequently, the SMC particles’ surface can be coated with a high electrical resistive insulating layer to efficiently inhibit eddy currents between them, thereby lowering the P_e. For the samples with 2 wt% and 4 wt% of Fe₂O₃, P_e is around 25.33 kW/m³ and 16.07 kW/m³, respectively. This can be ascribed to higher density because when magnetic particles (e.g., FeSi) are closely packed or poorly insulated, electrical paths can form between them, allowing eddy currents to circulate more easily under alternating magnetic fields. This, in turn, increases Pe. Interestingly, the P_e is greatly decreased by 37.21% when 5 wt% Fe₂O₃ NP is added. Figure 9 displays the comparison of the high-frequency magnetic performance of FeSi/Fe₂O₃(NP) SMCs in this work with previously reported different Fe-based SMCs. The remarkable soft magnetic properties of FeSi-Fe₂O₃ SMCs in this work will find widespread use in high-power and high-frequency electronic applications. Further lowering eddy current losses in the high-frequency range and methodically examining the composites’ mechanical and thermal properties over extended operating conditions are the goals of our upcoming studies.

4. Conclusions

In summary, the soft magnetic characteristics of Fe-6.5wt%Si-Fe₂O₃ SMCs prepared via the hot-press technique with different doping concentrations of Fe₂O₃ (0–5 wt%) were systematically studied. The incorporation of high-resistivity Fe₂O₃ effectively filled interparticle gaps, increased density, and enhanced resistivity. As a result, the effective permeability significantly improved from 22.32 to 30.45 (a 36.4% increase), while eddy current loss decreased by 37.2% at 5 wt% Fe₂O₃. Furthermore, increasing Fe₂O₃ content also decreased the total core loss from 25.63 to 16.13 kW/m³. These results show that FeSi/FeO₃ SMCs have a great deal of potential for high-frequency power applications.

Author Contributions

Conceptualization, M.A. and J.R.; methodology, validation, & investigation, M.A., D.H., W.S., S.C., C.P., Y.K., S.K. and B.L.; formal analysis, M.A., Y.K. and J.R.; resources, Y.K., J.R.; data curation, M.A.; writing—original draft preparation, M.A.; writing—review and editing, J.R.; visualization, M.A.; supervision, J.R.; project administration, J.R.; funding acquisition, Y.K. and J.R. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

Authors Changsun Pak and Youngkwang Kim were employed by the company R-Materials Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

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Figures and Tables

Figure 1 Schematic diagram for FeSi/Fe₂O₃ SMCs preparation.

Figure 2 SEM images of (a) Raw FeSi powder, (b) Fe₂O₃ nanopowders, Fe-6.5 wt%Si-Fe₂O₃ SMCs with (c) 0 wt%, (d) 1 wt%, (e) 2 wt%, (f) 3 wt%, (g) 4 wt%, and (h) 5 wt% of Fe₂O₃ nanoparticles. The inset shows the particle size distribution for FeSi SMCs.

Figure 3 (a,b) SEM image of polished surface (c–f) EDS maps of corresponding FeSi-Fe₂O₃ (2 wt%) SMCs.

Figure 4 XRD of FeSi-Fe₂O₃ (0, 1, 2, 3, 4, and 5 wt%) SMCs.

Figure 5 (a) Density and (b) electrical resistivity of FeSi-Fe₂O₃ SMC samples, respectively.

Figure 6 (a) MH hysteresis loops of FeSi-Fe₂O₃ SMCs, with an Inset graph to see the H_c (b) M_s (left axis) and H_c (right axis) with Fe₂O₃ contents.

Figure 7 Frequency-dependent effective permeability spectra for all FeSi-Fe₂O₃ samples.

Figure 8 (a) Total core loss P_cv, (b) P_cv/f, (c) hysteresis loss P_h, and (d) eddy current loss P_e as a function of frequency for FeSi-Fe₂O₃ SMC samples.

Figure 9 Performance comparison of FeSi-Fe₂O₃ SMCs with the previously reported Fe-based SMCs [40,41,42,46,47,48,49,50].

Table 1

M_s and H_c of FeSi-Fe₂O₃ SMCs with different Fe₂O₃ nanoparticle contents.

Contents wt%	0 wt%	1 wt%	2 wt%	3 wt%	4 wt%	5 wt%
Ms	187.6	191.21	191.31	189.36	188.98	189.9
Hc	12.27	11.83	11.55	12.27	12.75	10.78

Table 2

Variations in permeability, the core loss, coercivity, density, and electrical resistivity of SMCs versus Fe₂O₃ nanoparticle contents.

Contents wt%	Pcv(kW/m3) f = 100 kHz, Bm = 10 mT	Ph(kW/m3) f = 100 kHz, Bm = 10 mT	Pe(kW/m3) f = 100 kHz, Bm = 10 mT	μe	ρ (g/cm3)	ρ (mΩ-cm)
0	25.63	19.02	6.61	21.57	6.56	29.55
1	26.68	21.61	5.07	25.89	6.88	30.23
2	43.45	18.11	25.33	30.05	7.12	34.18
3	18.05	14.43	4.38	22.51	6.94	36.34
4	49.26	33.19	16.07	21.29	6.79	40.96
5	16.13	11.97	4.153	18.67	6.71	50.70

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