Effect of Polyimide-Phosphating Double Coating and Annealing on the Magnetic Properties of Fe-Si-Cr SMCs

Fe-Si-Cr soft magnetic powder cores (SMCs), with high electrical resistivity, magnetic permeability, saturation magnetic induction, and good corrosion resistance, are widely applied to inductors, filters, choke coils, etc. However, with the development of electronic technology with high frequency and high power density, the relative decline in the magnetic properties limits the high-frequency application of SMCs. In this paper, the phosphating process and polyimide (PI) insulation coating is applied to Fe-Si-Cr SMCs to reduce the core loss, including hysteresis loss and eddy current loss. The microstructure and composition of Fe-Si-Cr powders were analyzed by SEM, XRD, and Fourier-transform infrared spectra, respectively. The structural characteristics of the Fe-Si-Cr @ phosphate layer @ PI layer core–shell double coating were studied, and the best process parameters were determined through experiments. For SMCs with 0.4 wt% content of PI, the relative permeability is greater than 68%, and the core loss is the lowest, 7086 mW/cm3; annealed at 500 °C, the relative permeability is greater than 57%, and the core loss is the lowest, 6222 mW/cm3. A 0.4 wt% content of PI, annealed at 500 °C, exhibits the ideal magnetic properties: μe = 47 H/m, P = 6222 mW/cm3.


Introduction
Metal magnetic powder cores, belonging to a kind of soft magnetic composite material, are prepared by mixing ferromagnetic powder with an insulating medium [1]. They are commonly used in transformers, electronic communication, and radar due to the strengths of high saturation induction density, high magnetic permeability, and low total loss [2,3]. In recent years, Fe-Si-Cr SMCs, as new soft magnetic composite materials, have widely been applied to the inductance, filter, choking ring, and similar areas due to their higher electronic resistivity, permeability, and lower core loss in comparison with traditional silicon steel sheets, single-metal-based soft magnetic materials [4]. In high-frequency applications, adding Si can not only reduce the eddy current loss by increasing the resistivity of SMCs but also can form CrSi and CrSi 2 in Fe-Si-Cr SMCs with excellent temperature characteristics [5]. The addition of Cr can improve the mechanical strength, plasticity, and corrosion resistance of SMCs [6]. Compared with other iron-based SMCs, Fe-Si-Cr SMCs offer better broadband response characteristics and lower cost. Unfortunately, the increment in core loss as a result of increased operating frequency limits the large application of Fe-Si-Cr SMCs [7].
To reduce core loss P cv , including hysteresis loss P h and eddy current loss P e , insulating coating and high-pressure forming are usually applied in the manufacturing process [8][9][10][11][12][13][14][15][16][17][18]. Generally, there are two types of coatings used to suppress eddy currents: organic coatings and inorganic coatings [19]. With the advantages of satisfactory adhesion and flexibility, organic substances such as epoxy resin [20] or phenolic resin [21] have been used as the insulating layer of SMCs. Due to high dislocation density and defects, high pressure causes an increase in hysteresis loss P h . In order to eliminate defects such as lattice strain, a high-temperature annealing process is usually used. Some new characterization methods have promoted the study of SMCs [22][23][24]. However, the annealing process above 400 • C easily decomposes the organic resin [25]. Therefore, phosphate [26] and oxide [27,28] are used as the passivation layer of SMCs. However, the phosphate insulating layer will also collapse during the annealing process, resulting in a decrease in resistivity [26]. The organic coating has good adhesion but poor heat resistance. PI has higher heat resistance, insulation resistivity, and mechanical stability than ordinary resins, which is a potential organic coating material for magnetic powders. However, PI is a non-magnetic material; it can increase resistivity but decrease permeability [29]. To optimize the magnetic properties and reduce the core loss, high-temperature annealing is an effective method [30].
The process of preparing SMCs by powder metallurgy has been widely used to lower costs and improve efficiency [31,32]. This method is based on using each fine powder particle to make the insulating coating, which can significantly reduce the core loss of the SMCs. Therefore, the research on high-performance insulating coatings and coating methods for SMCs is currently a popular research subject [33]. Due to the excellent insulation performance of the organic coating but the decomposition temperature being low, it cannot be combined with subsequent high-temperature annealing treatment to eliminate the influence of residual stress during pressing. Therefore, the current research tends to use an inorganic coating to improve the annealing temperature [34]. There are few papers on the research of inorganic + organic double coating, especially research on using PI with high decomposition temperature as an organic coating. Although many inorganic materials also have excellent insulation properties and can significantly reduce eddy current loss, the compact density of inorganically coated SMCs is generally lower than that of those that are organically coated, so there will be defects, such as compact pores, which in turn affect magnetic properties, such as hysteresis loss.
In this paper, to reduce the core loss of SMCs at high frequencies, an inorganic phosphate + organic PI double coating with excellent insulation performance was used to improve powder resistivity and reduce eddy current loss; the organic coating PI with a higher decomposition temperature was used to increase the compact density and increase the annealing temperature to reduce the hysteresis loss. Finally, higher magnetic properties can be obtained by annealing in an argon atmosphere at 500 • C for 1 h.

Preparation of SMCs
Fe-Si-Cr powders with d50 = 10 µm were prepared by gas atomization, consisting of 3.3 wt% Si, 6.5 wt% Cr, and balance of Fe. The preparation process of Fe-Si-Cr @ phosphate layer @ PI layer core-shell double coating and SMCs is divided into three steps: phosphating, coating, and annealing, as shown in Figure 1. First, Fe-Si-Cr powders were pretreated with phosphate, as shown in Figure 1a. The phosphating procedure was carried out in 50 mL of acetone, mechanical stirring at room temperature for one hour followed by drying at 80 • C for one hour. Secondly, we prepared PI coating, as shown in Figure 1b. The Fe-Si-Cr powders were mixed uniformly with the various PI of 0 wt%, 0.4 wt%, 0.7 wt%, 1.0 wt%, respectively (the PI cannot be dissolved into the water or alcohol solution and can be dissolved with N-Methyl pyrrolidone), and air-dried at 80 • C for 12 h. The dry powders were passed through a screen of −100 mesh. Finally, we prepared and annealed the SMCs; as shown in Figure 1c, the coated Fe-Cr-Si powder was uniformly mixed with zinc stearate lubricant (0.6 wt%). Next, the coated powders were pressed into cores under applied axial stress of 600 MPa with outer diameter of 14 mm, inner diameter of 8 mm, and height of about 3 mm. Lastly, the SMCs were annealed at different temperatures from 300 • C to 500 • C for one hour in argon atmosphere with a pipe furnace. about 3 mm. Lastly, the SMCs were annealed at different temperatures from 300 °C °C for one hour in argon atmosphere with a pipe furnace.

Test Method and Material Characterization
The inductance of the Fe-Si-Cr SMCs was measured by the LCR bridge test we calculated the magnetic permeability by using Equation (1): where μe is the effective permeability, L is the inductance of sample core, and L mean flux density path of the ring sample. N is the number of turns of the coil (N = is the area of cross-section. Figure 2 shows the magnetic powder core to be tested. The SMCs sample to be tested: (a) magnetic powder core size and (b) coil windin magnetic performance test.

Test Method and Material Characterization
The inductance of the Fe-Si-Cr SMCs was measured by the LCR bridge tester, and we calculated the magnetic permeability by using Equation (1): where µ e is the effective permeability, L is the inductance of sample core, and L e is the mean flux density path of the ring sample. N is the number of turns of the coil (N = 25), A e is the area of cross-section. Figure 2 shows the magnetic powder core to be tested.

Test Method and Material Characterization
The inductance of the Fe-Si-Cr SMCs was measured by the LCR bridge tester, an we calculated the magnetic permeability by using Equation (1): where μe is the effective permeability, L is the inductance of sample core, and Le is th mean flux density path of the ring sample. N is the number of turns of the coil (N = 25), A is the area of cross-section. Figure 2 shows the magnetic powder core to be tested.   The microstructure of uncoated and coated Fe-Si-Cr powder was characterized by scanning electron microscopy (SEM, LEO1450, CARL ZEISS, Oberkochen, Germany) equipped with the energy dispersive X-ray spectrometry (EDS, Quanta-200, CARL ZEISS, Oberkochen, Germany). FTIR was used to verify the phosphating effect and the coating effect of PI (Thermo Scientific Nicolet iS5, Thermo Fisher Scientific, Waltham, MA, USA). XRD was used to characterize the structure of the powder and SMCs (Rigaku Ultima IV, Rigaku Corporation, Tokyo, Japan). The kinetics of thermal decomposition of PI was investigated using synchronous thermal analyzer (TG-DSC, Q600, METTLER-TOLEDO, DE, USA). LCR bridge tester (TH2829C, Agitek, Xi'an, China) is used to measure the inductance of SMCs, the core loss was measured by an auto testing system for SMCs (IWATSU SY-943, IWATSU ELECTRIC, Tokyo, Japan) in the frequency range of 100 kHz −1 MHz, and the magnetic flux density was set to 50 mT.

Characteristics of Phosphated and Coated Layer
After the two-step process of phosphating and coating, the oxide layer of the raw powder particles can be removed, and a certain thickness of the phosphate layer and PI insulation layer can be obtained, as shown in Figure 3. On the one hand, phosphating can remove the oxide layer on the surface of the original powder, including iron oxide, chromium oxide, and silicon oxide. On the other hand, a phosphating layer can be formed on the surface of powder in the phosphating process so as to increase the resistivity and reduce the eddy current loss [35]. PI is a non-magnetic material; it can increase resistivity but reduce permeability. To increase the insulation resistance without damaging the magnetic permeability, it is necessary to determine the appropriate content of PI additionthat is, to optimize the thickness of the Fe-Si-Cr @ phosphate layer @ PI layer core-shell double coating. rials 2022, 15, x FOR PEER REVIEW 4 of equipped with the energy dispersive X-ray spectrometry (EDS, Quanta-200, CARL ZEI Oberkochen, Germany). FTIR was used to verify the phosphating effect and the coati effect of PI (Thermo Scientific Nicolet iS5, Thermo Fisher Scientific, Waltham, MA, USA XRD was used to characterize the structure of the powder and SMCs (Rigaku Ultima Rigaku Corporation, Tokyo, Japan). The kinetics of thermal decomposition of PI was vestigated using synchronous thermal analyzer (TG-DSC, Q600, METTLER-TOLED DE, USA). LCR bridge tester (TH2829C, Agitek, Xi`an, China) is used to measure the ductance of SMCs, the core loss was measured by an auto testing system for SM (IWATSU SY-943, IWATSU ELECTRIC, Tokyo, Japan) in the frequency range of 100 kH MHz, and the magnetic flux density was set to 50 mT.

Characteristics of Phosphated and Coated Layer
After the two-step process of phosphating and coating, the oxide layer of the r powder particles can be removed, and a certain thickness of the phosphate layer and insulation layer can be obtained, as shown in Figure 3. On the one hand, phosphating c remove the oxide layer on the surface of the original powder, including iron oxide, ch mium oxide, and silicon oxide. On the other hand, a phosphating layer can be formed the surface of powder in the phosphating process so as to increase the resistivity and duce the eddy current loss [35]. PI is a non-magnetic material; it can increase resistiv but reduce permeability. To increase the insulation resistance without damaging the ma netic permeability, it is necessary to determine the appropriate content of PI addition that is, to optimize the thickness of the Fe-Si-Cr @ phosphate layer @ PI layer core-sh double coating. The SEM images of the Fe-Si-Cr raw powder and the phosphated powder are show in Figure 4. It can be seen from Figure 4a that the distribution of the Fe-Si-Cr raw powd particles is relatively dispersed, and most of the particles are spherical or nearly spheri (spindle shape). This is because the cooling rate of the gas atomization process is slow than that of the water atomization process, and it is easy to obtain a spherical powder. the same time, for the surface oxide layer of powder particles, the gas-atomization proc is much smaller than the water-atomization process. It can be seen from Figure 4b that t surface of the Fe-Si-Cr powder particles after phosphating is smooth, which indicates th the phosphate layer is evenly distributed on the surface of the powder. After the ph phating treatment, the phosphated substance-the reaction product of phosphoric ac

Characteristics of the Phosphated Layer
The SEM images of the Fe-Si-Cr raw powder and the phosphated powder are shown in Figure 4. It can be seen from Figure 4a that the distribution of the Fe-Si-Cr raw powder particles is relatively dispersed, and most of the particles are spherical or nearly spherical (spindle shape). This is because the cooling rate of the gas atomization process is slower than that of the water atomization process, and it is easy to obtain a spherical powder. At the same time, for the surface oxide layer of powder particles, the gas-atomization process is much smaller than the water-atomization process. It can be seen from Figure 4b that the surface of the Fe-Si-Cr powder particles after phosphating is smooth, which indicates that the phosphate layer is evenly distributed on the surface of the powder. After the phosphating treatment, the phosphated substance-the reaction product of phosphoric acid, iron, and chromium-cannot be observed intuitively and is further characterized by other methods in a follow-up. The energy spectrum characteristics of the powder after phosphating are shown Figure 5. It can be clearly observed that the p element is evenly distributed on the surfa of the powder, which indicates that a phosphate layer is formed on the surface of the F Si-Cr powder. The presence of phosphate can improve the resistivity of Fe-Si-Cr powd so as to ensure a relatively low eddy current loss and good processability [36].  Figure 6 is a microscopic image of Fe-Si-Cr powder coated with different content PI. In Figure 6a, the Fe-Si-Cr powder is uncoated after phosphating. The powder is re tively dispersed and has an average particle size of 10 μm. In Figure 6b,c, the Fe-Sipowder coated with PI is a mostly irregular, spherical powder. Meanwhile, there is a union as a result of the bonding effect of PI. The energy spectrum characteristics of the powder after phosphating are shown in Figure 5. It can be clearly observed that the p element is evenly distributed on the surface of the powder, which indicates that a phosphate layer is formed on the surface of the Fe-Si-Cr powder. The presence of phosphate can improve the resistivity of Fe-Si-Cr powder so as to ensure a relatively low eddy current loss and good processability [36]. The energy spectrum characteristics of the powder after phosphating are shown in Figure 5. It can be clearly observed that the p element is evenly distributed on the surface of the powder, which indicates that a phosphate layer is formed on the surface of the Fe-Si-Cr powder. The presence of phosphate can improve the resistivity of Fe-Si-Cr powder so as to ensure a relatively low eddy current loss and good processability [36].  Figure 6 is a microscopic image of Fe-Si-Cr powder coated with different content of PI. In Figure 6a, the Fe-Si-Cr powder is uncoated after phosphating. The powder is relatively dispersed and has an average particle size of 10 μm. In Figure 6b,c, the Fe-Si-Cr powder coated with PI is a mostly irregular, spherical powder. Meanwhile, there is a reunion as a result of the bonding effect of PI. In Figure 6a, the Fe-Si-Cr powder is uncoated after phosphating. The powder is relatively dispersed and has an average particle size of 10 µm. In Figure 6b,c, the Fe-Si-Cr powder coated with PI is a mostly irregular, spherical powder. Meanwhile, there is a reunion as a result of the bonding effect of PI.  Figure 7 shows the Fourier-transform infrared spectrum. It can be seen from the Fe-Si-Cr raw powder that the broad absorption peak at 3438 cm −1 is the -OH stretching vibration of adsorbed water, and the absorption peaks at 2928 cm −1 and 2855 cm −1 are the symmetric and asymmetric stretching vibrations of -CH in the methylene group. The absorption peak at 1626 cm −1 is the -OH bending vibration of water molecules, the absorption peak at 1110 cm −1 is the asymmetric stretching vibration of Si-O-Si or Fe-O-Si, and the absorption peak at 663 cm −1 is caused by the stretching vibration of Cr-O. For the phosphated powder, new absorption peaks appear at 567 cm −1 and 802 cm −1 ; the absorption peak at 567 cm −1 is the bending vibration of O-P-O and the asymmetric stretching vibration of P-O at 802 cm −1 . According to these two absorptions, the presence of the peak can determine that the sample contains PO and the intensity of the absorption peak at 1112 cm −1 becomes lower. It is possible that phosphoric acid interacts with Fe-O-Si, which reduces its content. For the phosphated and coated powder, new absorption peaks appeared at 1725 cm −1 , 1387 cm −1 , 1250 cm −1 , and 724 cm −1 . These absorption peaks are all caused by the characteristic peaks of PI. Among them, 1725 cm −1 is carbonyl C=O stretching vibration, 1387 cm −1 is C-N stretching vibration, 1250 cm −1 is C-O stretching vibration, and 720 cm −1 is C-O bending vibration, indicating that the powder is successfully coated with PI [37][38][39].         [40,41]. The Si and Cr atoms are solid-dissolved in the crystal lattice of α-Fe, and a solid solution of bcc -α-Fe (Si, Cr) is formed. It can be seen from the figure that the characteristic peak intensity after phosphating is significantly lower than the characteristic peak intensity before phosphating. This is due to the reaction of iron and phosphoric acid to form a phosphate layer, which reduces the characteristic peak intensity of α-Fe [42], and FTIR spectroscopy analysis also confirmed the existence of the phosphate layer. As the amount of PI coating increases from 0 to 1.0 wt%, the characteristic peak intensity also shows a downward trend. This is because the thickening of the PI layer weakens the X-ray absorption of the Fe-Si-Cr matrix. However, due to the thinner phosphate layer and PI layer, the XRD failed to detect the phosphide and PI phases.  Figure 8 is the XRD pattern of Fe-Si-Cr powders with different PI coating amounts Three sharp characteristic peaks (110), (200), and (211) are detected, which are consisten with the peaks of the α-Fe and Fe3Si [40,41]. The Si and Cr atoms are solid-dissolved in the crystal lattice of α-Fe, and a solid solution of bcc -α-Fe (Si, Cr) is formed. It can be seen from the figure that the characteristic peak intensity after phosphating is significantly lower than the characteristic peak intensity before phosphating. This is due to the reaction of iron and phosphoric acid to form a phosphate layer, which reduces the characteristic peak intensity of α-Fe [42], and FTIR spectroscopy analysis also confirmed the existence of the phosphate layer. As the amount of PI coating increases from 0 to 1.0 wt%, the char acteristic peak intensity also shows a downward trend. This is because the thickening o the PI layer weakens the X-ray absorption of the Fe-Si-Cr matrix. However, due to the thinner phosphate layer and PI layer, the XRD failed to detect the phosphide and P phases.

The Trend of Magnetic Properties with PI Content
The magnetic properties of SMCs can be characterized by relative permeability and DC bias capability. DC bias refers to the superposition of an alternating current when an alternating magnetic field and DC magnetic field are simultaneously applied to the mag netic core. Figure 9a shows the DC bias capacity curve of Fe-Si-Cr SMCs coated with dif ferent contents of PI. It can be seen from the figure that the DC bias capacity of SMCs without PI is the best. When the applied magnetic field strength is 100 Oe, the relative permeability reaches 75%. Compared with the sample without PI, PI reduces the relative permeability of SMCs; however, when the magnetic field strength is 100 Oe and the P content is 0.4 wt%, the relative permeability is >68%, indicating that its DC bias ability is not poor. In the range of 0~1.0 wt%, the relative permeability increases with the increase in PI content. This is because, in the applied DC magnetic field, SMCs are magnetized, the pressing density of SMCs without PI is low, and the air gap hinders the rotation and dis placement of the magnetic domain, which makes it difficult for SMCs to be magnetized to saturation. However, the compaction density of SMCs with PI is relatively high, the air gap is small, and the displacement and rotation of the magnetic domain are relatively small, so it is easier to be magnetized to saturation. However, the addition of non-mag netic PI resin reduces the proportion of magnetic substances in SMCs. At this time, the resin hinders the rotation and displacement of magnetic domains, such as the gap between

The Trend of Magnetic Properties with PI Content
The magnetic properties of SMCs can be characterized by relative permeability and DC bias capability. DC bias refers to the superposition of an alternating current when an alternating magnetic field and DC magnetic field are simultaneously applied to the magnetic core. Figure 9a shows the DC bias capacity curve of Fe-Si-Cr SMCs coated with different contents of PI. It can be seen from the figure that the DC bias capacity of SMCs without PI is the best. When the applied magnetic field strength is 100 Oe, the relative permeability reaches 75%. Compared with the sample without PI, PI reduces the relative permeability of SMCs; however, when the magnetic field strength is 100 Oe and the PI content is 0.4 wt%, the relative permeability is >68%, indicating that its DC bias ability is not poor. In the range of 0~1.0 wt%, the relative permeability increases with the increase in PI content. This is because, in the applied DC magnetic field, SMCs are magnetized, the pressing density of SMCs without PI is low, and the air gap hinders the rotation and displacement of the magnetic domain, which makes it difficult for SMCs to be magnetized to saturation. However, the compaction density of SMCs with PI is relatively high, the air gap is small, and the displacement and rotation of the magnetic domain are relatively small, so it is easier to be magnetized to saturation. However, the addition of non-magnetic PI resin reduces the proportion of magnetic substances in SMCs. At this time, the resin hinders the rotation and displacement of magnetic domains, such as the gap between particles. Therefore, the relative permeability decreases compared with that without PI resin. rials 2022, 15, x FOR PEER REVIEW 8 of particles. Therefore, the relative permeability decreases compared with that without resin.  Figure 9b is the core loss curve of Fe-Si-Cr SMCs coated with different PI conten The total loss (Pcv) is composed of hysteresis loss (Ph), eddy current loss (Pe), and residu loss (Pc). The residual loss is the micro-eddy current generated by the magnetic doma wall, which is very small compared to the hysteresis loss and eddy current loss. It can ignored. The core loss of all the samples increases with the increase in frequency; at t same frequency, the SMCs have the smallest core loss at the 0.4 wt% PI. When the f quency is 1000 Hz, the core loss is 7086 mW/cm 3 . Due to the application of double-ins lating coatings, the coated cores exhibit lower magnetic loss than uncoated cores; insul ing coated layers effectively hinder the current of intra-particles and inter-particles a thus reduce the eddy current loss. When the PI content is 1.0 wt%, the core loss is t largest. Because the insulating layer is a non-magnetic substance, it acts as a hindrance the magnetization process of the Fe-Si-Cr SMCs, resulting in an increase in hysteresis lo When the insulating layer is thicker, the eddy current loss is reduced, while the hystere loss is increased so that the total core loss is increased.

The Choice of the Annealing Temperature and the Change of the Phase Composi tion
From the point of view of eliminating residual stress, the higher the annealing te perature, the better the effect. However, the selection of the annealing temperature shou consider the influence of the passivation layer and coated layer. Phosphating treatme will form a passivation layer on the surface of the powder, and the phosphating layer w crystallize with iron at 500 °C [43]. In addition, the final annealing temperature should determined in combination with the heat resistance of the PI coating. As shown in Figu 10, according to the DSC curve, PI has an endothermic peak near 607 °C, which is t thermal decomposition temperature of PI. According to the TG curve, the 2% therm weight loss temperature is as high as 500 °C (mainly due to the evaporation of adsorb water in PI powder), and the maximum heat-resistant temperature of PI can reach 600 ° Therefore, the final annealing temperature range is determined as 300~500 °C.  Figure 9b is the core loss curve of Fe-Si-Cr SMCs coated with different PI contents. The total loss (P cv ) is composed of hysteresis loss (P h ), eddy current loss (P e ), and residual loss (P c ). The residual loss is the micro-eddy current generated by the magnetic domain wall, which is very small compared to the hysteresis loss and eddy current loss. It can be ignored. The core loss of all the samples increases with the increase in frequency; at the same frequency, the SMCs have the smallest core loss at the 0.4 wt% PI. When the frequency is 1000 Hz, the core loss is 7086 mW/cm 3 . Due to the application of double-insulating coatings, the coated cores exhibit lower magnetic loss than uncoated cores; insulating coated layers effectively hinder the current of intra-particles and inter-particles and thus reduce the eddy current loss. When the PI content is 1.0 wt%, the core loss is the largest. Because the insulating layer is a non-magnetic substance, it acts as a hindrance in the magnetization process of the Fe-Si-Cr SMCs, resulting in an increase in hysteresis loss. When the insulating layer is thicker, the eddy current loss is reduced, while the hysteresis loss is increased so that the total core loss is increased. From the point of view of eliminating residual stress, the higher the annealing temperature, the better the effect. However, the selection of the annealing temperature should consider the influence of the passivation layer and coated layer. Phosphating treatment will form a passivation layer on the surface of the powder, and the phosphating layer will crystallize with iron at 500 • C [43]. In addition, the final annealing temperature should be determined in combination with the heat resistance of the PI coating. As shown in Figure 10, according to the DSC curve, PI has an endothermic peak near 607 • C, which is the thermal decomposition temperature of PI. According to the TG curve, the 2% thermal weight loss temperature is as high as 500 • C (mainly due to the evaporation of adsorbed water in PI powder), and the maximum heat-resistant temperature of PI can reach 600 • C. Therefore, the final annealing temperature range is determined as 300~500 • C.

The Trend of Magnetic Properties with Annealing Temperature
The pressing process will reduce the air gap and produce residual stress in th before the annealing process. Due to the reduction in non-magnetic materials and crease in effective permeability, the DC bias ability becomes worse. The trend of D capacity with heat treatment is shown in Figure 12a; the relative permeability of th annealed at 300 °C is the highest, reaching 69% at 100 Oe. The relative permeab cores reduced gradually with the decrease in the annealing temperature from 30 500 °C. This is because the higher the annealing temperature, the lower the doma resistance, and the corresponding magnetic core is easily magnetized to saturation ever, under a 100 Oe magnetic field intensity, the magnetic permeability of the SM nealed at 500 °C reaches 57%, which also does not show a poor DC bias.

The Trend of Magnetic Properties with Annealing Temperature
The pressing process will reduce the air gap and produce residual stress in th before the annealing process. Due to the reduction in non-magnetic materials and crease in effective permeability, the DC bias ability becomes worse. The trend of capacity with heat treatment is shown in Figure 12a; the relative permeability of th annealed at 300 °C is the highest, reaching 69% at 100 Oe. The relative permea cores reduced gradually with the decrease in the annealing temperature from 30 500 °C. This is because the higher the annealing temperature, the lower the doma resistance, and the corresponding magnetic core is easily magnetized to saturation ever, under a 100 Oe magnetic field intensity, the magnetic permeability of the SM nealed at 500 °C reaches 57%, which also does not show a poor DC bias.

The Trend of Magnetic Properties with Annealing Temperature
The pressing process will reduce the air gap and produce residual stress in the SMCs before the annealing process. Due to the reduction in non-magnetic materials and the increase in effective permeability, the DC bias ability becomes worse. The trend of DC bias capacity with heat treatment is shown in Figure 12a; the relative permeability of the SMCs annealed at 300 • C is the highest, reaching 69% at 100 Oe. The relative permeability of cores reduced gradually with the decrease in the annealing temperature from 300 • C to 500 • C. This is because the higher the annealing temperature, the lower the domain wall resistance, and the corresponding magnetic core is easily magnetized to saturation. However, under a 100 Oe magnetic field intensity, the magnetic permeability of the SMCs annealed at 500 • C reaches 57%, which also does not show a poor DC bias. Annealing can eliminate the residual internal stress and dislocation generated after magnetic particle pressing, compact the structure, reduce air and other defects, reduce the hysteresis loss coefficient, and finally, reduce the hysteresis loss. The higher the annealing temperature, the more thorough the removal of internal stress, air and dislocation, and other defects between magnetic particles, and the more obvious the effect of loss reduction [44,45]. Figure 12b shows the core loss of Fe-Si-Cr SMCs annealed at different temperatures. It can be seen from the figure that the iron loss decreases gradually with the increase in annealing temperature. The core annealed at 500 °C has the lowest loss, which is only 6222 mW/cm 3 at 1000 Hz. Figure 13 shows the effective permeability of Fe-Si-Cr SMCs at different PI contents and different annealing temperatures. It can be seen that all the samples show the same trend; with the increase in PI content, the effective permeability increases first and then decreases at the same temperature. The phenomenon can be ascribed that the increase in PI leads to the high compaction density of the powder, and thereby the air gap decreases and the effective permeability increases, which can be confirmed in Table 1. The density of core coated at 0.4 wt% PI and annealed at 500 °C reached 6.213 g/cm 3 . However, PI is a non-magnetic substance, and the increase in PI causes a decrease in magnetic material and a decrease in effective permeability. The best response was obtained for the sample coated with 0.4 wt% PI. During annealing, the atomic disorder state was changed to an ordered state, the microstructure of Fe-Si-Cr SMCs was optimized well, the air gap was reduced, and the annealed cores were denser, and it can be seen in Table 1 that the density of cores increased with the increase in annealing temperature. Thus, improving the effective permeability of Fe-Si-Cr SMCs, the SMCs show an ideal effect at an annealing temperature of 500 °C. The Fe-Si-Cr SMCs, with 0.4 wt% content of PI and heat treatment temperature at 500 °C, exhibited the best magnetic properties: μe = 47 H/m, p = 6222 mW/cm 3 .  Annealing can eliminate the residual internal stress and dislocation generated after magnetic particle pressing, compact the structure, reduce air and other defects, reduce the hysteresis loss coefficient, and finally, reduce the hysteresis loss. The higher the annealing temperature, the more thorough the removal of internal stress, air and dislocation, and other defects between magnetic particles, and the more obvious the effect of loss reduction [44,45]. Figure 12b shows the core loss of Fe-Si-Cr SMCs annealed at different temperatures. It can be seen from the figure that the iron loss decreases gradually with the increase in annealing temperature. The core annealed at 500 • C has the lowest loss, which is only 6222 mW/cm 3 at 1000 Hz. Figure 13 shows the effective permeability of Fe-Si-Cr SMCs at different PI contents and different annealing temperatures. It can be seen that all the samples show the same trend; with the increase in PI content, the effective permeability increases first and then decreases at the same temperature. The phenomenon can be ascribed that the increase in PI leads to the high compaction density of the powder, and thereby the air gap decreases and the effective permeability increases, which can be confirmed in Table 1. The density of core coated at 0.4 wt% PI and annealed at 500 • C reached 6.213 g/cm 3 . However, PI is a non-magnetic substance, and the increase in PI causes a decrease in magnetic material and a decrease in effective permeability. The best response was obtained for the sample coated with 0.4 wt% PI. During annealing, the atomic disorder state was changed to an ordered state, the microstructure of Fe-Si-Cr SMCs was optimized well, the air gap was reduced, and the annealed cores were denser, and it can be seen in Table 1 that the density of cores increased with the increase in annealing temperature. Thus, improving the effective permeability of Fe-Si-Cr SMCs, the SMCs show an ideal effect at an annealing temperature of 500 • C. The Fe-Si-Cr SMCs, with 0.4 wt% content of PI and heat treatment temperature at 500 • C, exhibited the best magnetic properties: µ e = 47 H/m, p = 6222 mW/cm 3 .  Figure 13. Trend of PI content and annealing temperature on effective permeability of SMCs.

The Effect of PI Content and Annealing Temperature on Effective Permeability
In the field of electromagnetism, the total core loss (Pcv) consists of hysteresis lo eddy current loss (Pe), and residual loss (Pc); the residual loss is the micro-eddy generated by the domain wall, which is very small compared with the hysteresis l eddy current loss and can be ignored. Additionally, the total core loss Pcv can be exp as Equation (2) [14,17].
where Kh is the hysteresis loss coefficient, Ke is the eddy current loss coefficient, the frequency. At low frequencies, the increase in total loss is mainly the increase teresis loss, while at medium and high frequencies, the increase in total loss is eddy current loss. The comparison of magnetic properties between this study and erature is shown in Table 2. In this study, the effects of inorganic + organic double and heat treatment on the total core loss of SMCs are preliminarily explored; ho more accurate quantitative research on hysteresis loss and eddy current loss has n completed. In further research, the quantitative results of the influence on each nent of core loss Pcv will be emphatically considered, and the effects of different steps, including powder coating preparation, pressing, and annealing on hystere Ph and eddy current loss Pe will be evaluated so as to provide guidance for industr duction. In addition, the use of organic PI coating can significantly improve the co In the field of electromagnetism, the total core loss (P cv ) consists of hysteresis loss (P h ), eddy current loss (P e ), and residual loss (P c ); the residual loss is the micro-eddy current generated by the domain wall, which is very small compared with the hysteresis loss and eddy current loss and can be ignored. Additionally, the total core loss P cv can be expressed as Equation (2) [14,17].
where K h is the hysteresis loss coefficient, K e is the eddy current loss coefficient, and f is the frequency. At low frequencies, the increase in total loss is mainly the increase in hysteresis loss, while at medium and high frequencies, the increase in total loss is mainly eddy current loss. The comparison of magnetic properties between this study and the literature is shown in Table 2. In this study, the effects of inorganic + organic double coating and heat treatment on the total core loss of SMCs are preliminarily explored; however, more accurate quantitative research on hysteresis loss and eddy current loss has not been completed. In further research, the quantitative results of the influence on each component of core loss P cv will be emphatically considered, and the effects of different process steps, including powder coating preparation, pressing, and annealing on hysteresis loss P h and eddy current loss P e will be evaluated so as to provide guidance for industrial production. In addition, the use of organic PI coating can significantly improve the corrosion resistance of SMCs, which is also worthy of further research.