The Effect of Annealing on the Soft Magnetic Properties and Microstructure of Fe₈₂Si₂B₁₃P₁C₃ Amorphous Iron Cores

Abstract

This research paper investigated the impact of normal annealing (NA) and magnetic field annealing (FA) on the soft magnetic properties and microstructure of Fe₈₂Si₂B₁₃P₁C₃ amorphous alloy iron cores. The annealing process involved various methods of magnetic field application: transverse magnetic field annealing (TFA), longitudinal magnetic field annealing (LFA), transverse magnetic field annealing followed by longitudinal magnetic field annealing (TLFA) and longitudinal magnetic field annealing followed by transverse magnetic field annealing (LTFA). The annealed samples were subjected to testing and analysis using techniques such as differential scanning calorimetry (DSC), transmission electron microscopy (TEM), X-ray diffraction (XRD), magnetic performance testing equipment and magneto-optical Kerr microscopy. The obtained results were then compared with those of commercially produced Fe₈₀Si₉B₁₁. Fe₈₂Si₂B₁₃P₁C₃ demonstrated the lowest loss of P_1.4T,2kHz = 8.1 W/kg when annealed in a transverse magnetic field at 370 °C, which was 17% lower than that of Fe₈₀Si₉B₁₁. When influenced by the longitudinal magnetic field, the magnetization curve tended to become more rectangular, and the coercivity (B_3500A/m) of Fe₈₂Si₂B₁₃P₁C₃ reached 1.6 T, which was 0.05 T higher than that of Fe₈₀Si₉B₁₁. During the 370 °C annealing process of the Fe₈₂Si₂B₁₃P₁C₃ amorphous iron core, the internal stress in the strip gradually dissipated, and impurity domains such as fingerprint domains disappeared and aligned with the length direction of the strip. Consequently, wide strip domains with low resistance and easy magnetization were formed, thereby reducing the overall loss of the amorphous iron core.

1. Introduction

Soft magnetic materials and their related devices (inductors, transformers and electrical machines) play a key role in the conversion of energy throughout our world. The conversion of electrical power includes the bidirectional flow of energy between sources, storage and the electrical grid and is accomplished via the use of power electronics. Electrical machines (motors and generators) transform mechanical energy into electrical energy and vice versa. The introduction of wide bandgap (WBG) semiconductors is allowing power conversion electronics and motor controllers to operate at much higher frequencies. This reduces the size requirements for passive components (inductors and capacitors) in power electronics and enables more efficient, high-rotational-speed electrical machines [1]. Fe-based amorphous alloys exhibit superior soft magnetic properties, including relatively high saturated magnetization, high effective permeability, low coercivity and low core loss, especially at middle and high frequencies, compared to other traditional soft magnetic materials, such as ferrite, silicon steel and permalloy. These kinds of alloys with unique structures, excellent magnetic properties and good mechanical properties have attracted much attention in a variety of emerging science and engineering fields [2].

Amorphous alloy ribbons possess desirable properties, such as low losses and high magnetic permeability, making them potential replacements for non-oriented silicon steel in high-frequency motors. This substitution can reduce iron core losses by more than 80% and significantly enhance overall efficiency [3,4,5,6]. However, the saturation magnetic induction strength (B_s) of commercially available amorphous ribbons is only 1.56 T, which is considerably lower than that of non-oriented silicon steel (1.8–2.0 T). This limitation hampers the application of amorphous ribbons in motors. Consequently, there is a pressing need to explore the composition design and applications of high-B_s amorphous alloys, which has become a prominent research and development focus in this field. Although there have been several relevant reports [7,8,9], most of them have been conducted in laboratory settings with a limited number of high-quality samples, which are often narrow in width. These samples are suitable for studying strip characteristics such as saturation magnetic induction and coercivity. However, they are inadequate for producing iron core samples required for the comprehensive testing and analysis of losses and magnetization curves.

Relaxation upon isothermal annealing below the crystallization transition temperature is applied to release the residual stress in metallic amorphous alloys [10] to enhance their soft magnetic performance [8]. Ordinarily, the soft magnetic properties of amorphous alloys can be further optimized through appropriate annealing characteristics, such as the annealing temperature, heating rate and holding time [11]. As-spun amorphous ribbons are usually subjected to magnetic field annealing to improve their soft magnetic properties (SMPs) [12]. Magnetic field annealing treatment can bring about a process of atomic pair ordering and the decline of the coercive field [13]. Magnetic field annealing has a positive effect on changing the domain-sensitive direction and unifying the easy magnetization direction [14]. Magnetic field annealing causes the formation of strip domains in the sample for optimal SMPs [15]. Magnetic field annealing can promote inner stress release and modulate the domain structure, which directly affects soft magnetic alloys [16]. However, the mechanism of the effect of magnetic field annealing on SMPs is not yet clear.

This paper focuses on the utilization of planar flow continuous casting technology to produce wide amorphous alloy ribbons and high-quality annular amorphous iron core samples based on the previously developed Fe₈₂Si₂B₁₃P₁C₃ alloy, which possesses a high saturation magnetic induction strength. This study systematically investigates the impact of heat treatment processes on the soft magnetic properties of these amorphous iron cores, aiming to uncover the underlying mechanisms of magnetic domain morphology on the magnetic properties. By employing this approach, a heat treatment technique is developed for amorphous iron cores with a high saturation magnetic induction strength and low loss. Furthermore, systematic magnetization curves and loss data are obtained, which are expected to offer valuable insight for the application of Fe₈₂Si₂B₁₃P₁C₃ amorphous ribbons in motors.

2. Methods

Sample source: The GFA and soft magnetic properties of as-spun Fe₈₀Si₉B_(11−x)P_x amorphous alloys were improved due to the incorporation of a minor amount of P element. However, excess P led to a reduction in iron content and the deterioration of saturation magnetization [17]. Wide amorphous alloy ribbons with compositions of Fe₈₀Si₉B₁₁ (1K101) and Fe₈₂Si₂B₁₃P₁C₃ were produced using planar flow continuous casting. The ribbons had a width of 150 ± 0.5 mm and a thickness of 25 ± 1 µm. These wide ribbons were subsequently cut into 10 mm narrow ribbons and wound into circular amorphous samples. The resulting samples had an outer diameter of φ_outer = 35 mm, an inner diameter of φ_inner = 25 mm and a height of h = 10 mm.

• Annealing experiments:

Normal annealing (NA): The amorphous iron core was positioned within the annealing area of the furnace. The furnace door was closed, and the interior was evacuated before being filled with nitrogen gas. The temperature of the furnace was then raised from room temperature to the designated holding temperature (Fe₈₀Si₉B₁₁:370–420 °C and Fe₈₂Si₂B₁₃P₁C₃:340–390 °C) at a heating rate of 6 °C/min. The temperature was maintained at the holding temperature for a duration of 40 min, followed by furnace cooling until reaching room temperature to allow for sample removal.

• Magnetic field annealing (FA):

In the case of transverse magnetic field annealing (TFA), as depicted in Figure 1a, pure iron magnetic poles of equal inner and outer diameters and a length of 150 mm were affixed on both sides of the sample. Subsequently, the furnace door was closed, and the furnace was evacuated and filled with nitrogen. The heating rate was set at 6 °C/min. Upon reaching the desired temperature, a transverse magnetic field was applied with the specified current. After a holding period of 40 min, the sample was cooled to room temperature and removed from the furnace.

During longitudinal magnetic field annealing (LFA), as illustrated in Figure 1b, the sample was threaded to the center of the copper rod. The remaining procedures were identical to those of TFA, with the exception that a longitudinal magnetic field was applied.

Test method: The amorphous nature of the alloy strip was assessed using X-ray diffraction (XRD) with Cu Kα (λ = 0.15406 nm) radiation in the range of 30–90° taking 0.2 s for one step of 0.02°. FEI Strata 400S focused ion beam scanning electron microscopy (FIB-SEM) was used to cut the ribbon, and FEI Talos F200s transmission electron microscopy (TEM) was used to observe the cross-section of the ribbon (FEI, Los Angeles, CA, USA). Thermal parameters, including the crystallization temperature (T_x) and crystallization peak (T_p), were analyzed via differential thermal analysis (DSC) at a heating rate of 10 °C/min under the protection of argon gas to establish an appropriate range of annealing temperatures. The loss and hysteresis loop of the amorphous iron core were measured using both direct current (model TD8150) and alternating current (model TK7500) magnetic performance testing instruments. Additionally, a magneto-optical Kerr effect (MOKE, Evico 4-873K/950 MT) microscope was employed to examine the magnetic domain structures (evico magnetics GmbH, Dresden, Germany).

3. Results and Discussion

In this study, the magnetic properties of the novel amorphous strip (Fe₈₂Si₂B₁₃P₁C₃) were systematically investigated under various heat treatment processes. The research aimed to understand the influence of magnetic fields on the morphology and orientation of magnetic domains and elucidate the underlying mechanisms.

3.1. Structure and Performance Analysis of Fe₈₂Si₂B₁₃P₁C₃ Ribbons

The XRD pattern of the as-spun Fe₈₂Si₂B₁₃P₁C₃ strip is presented in Figure 2a. The diffraction curve reveals a distinct diffuse peak near the diffraction angle of 2θ = 45°, and no sharp crystallization peaks are observed. This pattern confirms that the strip possesses an amorphous structure. Figure 2b displays the high-resolution TEM (HRTEM) image and the selected area electron diffraction (SAED) pattern of the as-spun Fe₈₂Si₂B₁₃P₁C₃ strip. The atomic arrangement within the structure exhibits disorder, which is indicative of an amorphous structure. The presence of diffraction halos in the pattern further supports the amorphous nature of the strip.

Figure 2c presents the results of the DSC tests conducted on the Fe₈₂Si₂B₁₃P₁C₃ and Fe₈₀Si₉B₁₁ strip samples. Both samples exhibit two distinct exothermic peaks. The crystallization onset temperature (T_x1) was determined by analyzing the tangent to the initial arc of the first exothermic peak. As indicated in

Table 1. Thermodynamic properties of Fe₈₂Si₂B₁₃P₁C₃ and Fe₈₀Si₉B₁₁ ribbons in as-spun state.

Item	Tx1 (°C)	Tp1 (°C)	Tp2 (°C)	ΔTp = Tp2 − Tp1 (°C)
Fe82Si2B13P1C3	480	509	550	41
Fe80Si9B11	508	524	564	40
Difference (TFe82Si2B13P1C3 − TFe80Si9B11)	−28	−15	−14	1

, the T_x1 of the Fe₈₂Si₂B₁₃P₁C₃ strip was 28 °C lower than that of Fe₈₀Si₉B₁₁. This observation suggests that the addition of P and C elements promotes the early precipitation of the α-Fe phase. The temperature range from the Curie temperature (T_c) to T_x1 is commonly considered an optimal heat treatment interval for amorphous ribbons. Furthermore, the ideal annealing temperature is typically achieved by reducing the temperature by 80–120 °C from T_x1. These criteria serve as essential guidelines for determining the appropriate annealing temperature [18]. Figure 2c shows two crystallization peaks, with the first corresponding to the precipitation of the α-Fe phase and the second corresponding to the formation of the Fe–B phase [19,20]. Table 1 reveals that the crystallization peak temperatures of the Fe₈₂Si₂B₁₃P₁C₃ strip are lower than those of Fe₈₀Si₉B₁₁, and the gaps ΔT_p between the crystallization peaks remain relatively consistent for both ribbons.

The magnetization curve of the as-spun Fe₈₂Si₂B₁₃P₁C₃ strip is depicted in Figure 2d. Under an excitation of 3500 A/m, the values of magnetic induction (B_m) for Fe₈₂Si₂B₁₃P₁C₃ and Fe₈₀Si₉B₁₁ were measured to be 1.34 T and 1.31 T, respectively. The higher Fe content in Fe₈₂Si₂B₁₃P₁C₃ accounts for its elevated B_m value.

3.2. Effects of NA Processes on Magnetic Properties of Amorphous Iron Cores

Based on the DSC test results, Fe₈₀Si₉B₁₁ underwent annealing within the temperature range of 380–420 °C, and Fe₈₂Si₂B₁₃P₁C₃ was annealed at temperatures between 350 and 390 °C. The XRD spectra of the amorphous iron cores are displayed in Figure 3a,b. From the figures, it can be observed that, when Fe₈₀Si₉B₁₁ was annealed at ≤400 °C and Fe₈₂Si₂B₁₃P₁C₃ was annealed at ≤370 °C, a diffuse diffraction peak appeared near 2θ = 45° for both alloys, indicating the retention of their amorphous state. However, when Fe₈₀Si₉B₁₁ was annealed at ≥410 °C and Fe₈₂Si₂B₁₃P₁C₃ was annealed at ≥380 °C, the diffuse peak became sharper, suggesting the precipitation of trace crystalline phases. These crystalline phases can be identified as α-Fe(Si) with a body-centered cubic (bcc) structure. Furthermore, the XRD spectra revealed that, with the increasing annealing temperature, the intensity of the diffraction peak corresponding to the α-Fe(Si) phase gradually strengthened, indicating an augmentation in the crystallization fraction of the α-Fe(Si) phase as the annealing temperature rose.

Figure 4a,b illustrate the loss curves of Fe₈₀Si₉B₁₁ annealed at 370–410 °C and Fe₈₂Si₂B₁₃P₁C₃ annealed at 340–380 °C at different frequencies. The curves display an initial decrease followed by an increase as the heat treatment temperature rises. According to

Table 2. NA losses and B_m values of Fe₈₂Si₂B₁₃P₁C₃ and Fe₈₀Si₉B₁₁ iron cores.

Item	P1.4T,2kHz (W/kg)	P1.4T,2kHz (W/kg)	ΔP1.4T,2kHz (W/kg)	B3500A/m (T)
Fe82Si2B13P1C3	29 (370 °C)	47 (380 °C)	18	1.59 (380 °C)
Fe80Si9B11	36 (400 °C)	58 (410 °C)	22	1.55 (410 °C)
Difference (Fe82Si2B13P1C3 − Fe80Si9B11)	−7	−11	−4	0.04

, the minimum loss for Fe₈₀Si₉B₁₁ was achieved at 400 °C, with a value of P_1.4T,2kHz = 36 W/kg. Similarly, Fe₈₂Si₂B₁₃P₁C₃ reached its minimum loss at 370 °C, with a value of P_1.4T,2kHz = 29 W/kg. Additionally, as the excitation frequency increased, the losses also increased, with the loss at 2 kHz being nearly 100 times higher compared to that at 50 Hz. The losses for Fe₈₀Si₉B₁₁ annealed at 410 °C and Fe₈₂Si₂B₁₃P₁C₃ annealed at 380 °C were P_1.4T,2kHz = 58 W/kg and P_1.4T,2kHz = 47 W/kg, respectively. The XRD curves in Figure 3a,b exhibited crystallization peaks for Fe₈₀Si₉B₁₁ ≥ 410 °C and Fe₈₂Si₂B₁₃P₁C₃ ≥ 380 °C, providing further evidence of increased loss after the crystallization of the amorphous iron cores.

Figure 4c depicts the frequency-dependent loss curves of Fe₈₀Si₉B₁₁ annealed at 400 °C and Fe₈₂Si₂B₁₃P₁C₃ annealed at 370 °C under an excitation of 1.4 T. It is evident that, within the frequency range of 50 Hz to 2 kHz, Fe₈₂Si₂B₁₃P₁C₃ exhibits lower losses compared to those of Fe₈₀Si₉B₁₁ at 1.4 T.

Figure 4d displays the magnetization curves of Fe₈₀Si₉B₁₁ annealed at 400 °C and Fe₈₂Si₂B₁₃P₁C₃ annealed at 370 °C. Prior to the intersection point of the two curves (indicated by the dashed line) at an excitation of 130 A/m, the working magnetic flux density B_m of Fe₈₀Si₉B₁₁ exceeded that of Fe₈₂Si₂B₁₃P₁C₃. However, beyond the excitation of 130 A/m, the B_m of Fe₈₂Si₂B₁₃P₁C₃ surpassed that of Fe₈₀Si₉B₁₁. At an excitation of 3500 A/m, Fe₈₂Si₂B₁₃P₁C₃ exhibited a B_m of 1.59 T, which was higher than that of Fe₈₀Si₉B₁₁ (B_m = 1.55 T). The higher Fe content in Fe₈₂Si₂B₁₃P₁C₃, as indicated in Table 2, contributed to its elevated B_m value beyond an excitation of 130 A/m.

In short, the Fe₈₂Si₂B₁₃P₁C₃ amorphous iron core demonstrated a lower loss than that of Fe₈₀Si₉B₁₁. The Fe₈₂Si₂B₁₃P₁C₃ amorphous iron core in the motor has the advantage of high efficiency, high power density and high torque density. The Fe₈₂Si₂B₁₃P₁C₃ amorphous iron core exhibited a higher B_m than that of Fe₈₀Si₉B₁₁. Compared with Fe₈₀Si₉B₁₁, the amorphous iron core possess a relatively lower B_m, which hampers the miniature of the devices.

Figure 5a,b depict the magnetic domain morphologies of the as-spun Fe₈₀Si₉B₁₁ and Fe₈₂Si₂B₁₃P₁C₃ amorphous ribbons, respectively. Magnetic domains exhibit various types, such as sheet domains, closed domains, checkerboard domains, ripple domains, magnetic bubble domains and their derivatives [21]. Because the amorphous alloys lack grains, the influence of magnetic crystal anisotropy can be disregarded. Thus, the magnetic domain structure is primarily determined according to the residual stress generated during the preparation of the amorphous ribbons [22]. The high stress levels during the extremely cold process of quenching result in magnetic domains with irregular shapes, varying widths, disordered orientations and the presence of fine fingerprint domains. Residual stress has a detrimental effect on magnetic properties, and annealing has been proven to be effective in relieving internal stress and enhancing the magnetic properties of the ribbons [23]. Annealing induces structural relaxation and the release of internal stress in the amorphous strip, causing the magnetic domains within the strip to align along the direction of the easily magnetized axis, which is parallel to the strip’s length. This minimizes magnetic anisotropy within the strip [24]. The magnetic domain morphologies of Fe₈₀Si₉B₁₁ annealed at 370 °C and Fe₈₂Si₂B₁₃P₁C₃ annealed at 340 °C are illustrated in Figure 5c,d, respectively. The chosen annealing temperatures alleviate some stress, resulting in magnetic domains with converging orientations along the length direction of the ribbons. However, the shapes of the domains remain irregular and exhibit varying sizes. The results for Fe₈₀Si₉B₁₁ annealed at 400 °C and Fe₈₂Si₂B₁₃P₁C₃ annealed at 370 °C are presented in Figure 5e,f, respectively. Clearly, as the annealing temperature increases, wide and uniform magnetic domains form with consistent orientations within the ribbons. Moreover, Figure 5g,h demonstrate that, when Fe₈₀Si₉B₁₁ was annealed at 410 °C and Fe₈₂Si₂B₁₃P₁C₃ was annealed at 380 °C, the previously wide magnetic domains started to crack, becoming irregular and narrower. These observations indicate that the annealed amorphous ribbons began to crystallize at these temperatures.

Magnetic domain observations not only provide insight into the spatial distribution of domains within ferromagnetic materials but also serve as a foundation for investigating the magnetic properties of amorphous iron cores. During the magnetization process of these cores, the magnetic domain walls undergo bending, which can be impeded by impurities or internal stress within the material. To overcome these obstacles, partial excitation is employed to induce the bending of magnetic domain walls, resulting in their conversion into heat and subsequent energy losses. This motion of the domain walls generates eddy current losses. As the heat treatment temperature increases, the internal stress within the amorphous iron cores gradually diminishes, and impurities such as fingerprint domains gradually disappear. Consequently, the magnetic domains become more uniform, as illustrated in Figure 5e,f. In this scenario, wide strip domains characterized by low resistance and uniform changes are formed, leading to a reduction in the overall losses of the amorphous iron cores, as demonstrated by the red curves in Figure 4a,b.

3.3. Effects of FA on Magnetic Properties of Amorphous Iron Cores

Figure 6a illustrates the effect of the annealing temperature on the loss under a transverse magnetic field of 10.6 kA/m. The results indicate that the loss first decreases and then increases with the increasing annealing temperature. Specifically, the minimum loss for Fe₈₀Si₉B₁₁, recorded at P_1.4T,2kHz = 12.3 W/kg, is achieved at an annealing temperature of 400 °C. Similarly, the lowest loss for Fe₈₂Si₂B₁₃P₁C₃, measured at P_1.4T,2kHz = 11.3 W/kg, occurs at an annealing temperature of 370 °C. As the annealing temperature is further increased, the losses begin to rise, reaching P_1.4T,2kHz = 20.2 W/kg for Fe₈₀Si₉B₁₁ annealed at 410 °C and P_1.4T,2kHz = 12.8 W/kg for Fe₈₂Si₂B₁₃P₁C₃ annealed at 380 °C. Notably, the loss of Fe₈₂Si₂B₁₃P₁C₃ in the case of TFA is significantly lower than that of Fe₈₀Si₉B₁₁ (As shown by the dashed line). To further investigate the impact of changing the transverse magnetic field on the magnetic properties, different magnetic field intensities were applied to the Fe₈₂Si₂B₁₃P₁C₃ amorphous iron core at an annealing temperature of 370 °C. Figure 6b displays the variations in the loss. With an increased magnetic field intensity of 31.8 kA/m, the loss further decreased to P_1.4T,2kHz = 8.1 W/kg, which is notably superior to the loss of the NA sample at 370 °C (P_1.4T,2kHz = 29 W/kg), as shown in Figure 4d.

This study also examined the impact of different annealing processes, including NA, TFA, LFA, TLFA and LTFA, on the magnetic properties of Fe₈₂Si₂B₁₃P₁C₃ when annealed at 370 °C. Figure 6c demonstrates that the sample treated with TFA exhibited the lowest loss, measured at P_1.4T,2kHz = 8.1 W/kg, which was significantly superior to the losses observed in the other annealing processes. Conversely, LFA showed a poor loss performance. LTFA resulted in a loss of P_1.4T,2kHz = 11.9 W/kg, which was better than that of TLFA (P_1.4T,2kHz = 30.7 W/kg), as outlined in

Table 3. NA losses for Fe₈₂Si₂B₁₃P₁C₃ and Fe₈₀Si₉B₁₁ iron cores.

Item	P1.4T,2kHz (W/kg) 10.6 kA/m	P1.4T,2kHz (W/kg) 10.6 kA/m	P1.4T,2kHz (W/kg) 31.8 kA/m	P1.4T,2kHz (W/kg) LTFA	P1.4T,2kHz (W/kg) TLFA
Fe82Si2B13P1C3	11.3 (370 °C)	12.8 (380 °C)	8.1 (370 °C)	11.9 (370 °C)	30.7 (370 °C)
Fe80Si9B11	12.3 (400 °C)	20.2 (410 °C)	9.8 (400 °C)	12.5 (400 °C)	32.1 (400 °C)
Difference (P Fe82Si2B13P1C3 − P Fe80Si9B11)	−1	−7.4	−1.7	−0.6	−1.4

.

Figure 7a,b present the magnetic domain morphologies of Fe₈₂Si₂B₁₃P₁C₃ annealed at 370 °C under transverse and longitudinal magnetic fields, respectively. In the case of TFA, the magnetic domain morphology appeared finer and exhibited a greater consistency in direction, as depicted in Figure 7c,d. When the longitudinal magnetic field was applied first or later, an increase in Z-shaped bending within the magnetic domains was observed, with the magnetic domain morphology of LTFA appearing finer compared to that of TLFA.

In conclusion, the morphology and orientation of magnetic domains were found to be closely related to the magnetic properties of the material. Furthermore, the results suggest that the presence and alteration of elements have an impact on the morphology of magnetic domains, consequently influencing the magnetic properties of the material.

Figure 8 illustrates the magnetization curves of Fe₈₂Si₂B₁₃P₁C₃ amorphous iron cores subjected to various treatments: NA, TFA, LFA, TLFA and LTFA at 370 °C. In Figure 8a, under an applied excitation of 3500 A/m, the B_m values of the treatment processes were arranged in ascending order as TFA < LTFA < NA < LFA < TLFA. Particularly, the B_m values of LFA and TLFA closely overlapped, both reaching 1.6 T. Figure 8b presents enlarged images at the inflection points. The ordering of B_m values under an excitation of 200 A/m was consistent with that under 3500 A/m. Notably, the LFA magnetization curve exhibited a distinct rectangular shape, enhancing the maximum permeability and residual magnetic induction strength while also increasing the loss. Conversely, TFA resulted in a flattened magnetization curve, promoting a more stable magnetic permeability, lower residual magnetic induction strength and reduced loss. The low-loss amorphous alloy iron core proves to be an exceptional material for pulse transformers. Magnetic field heat treatment can introduce uniaxial magnetic anisotropy to the amorphous iron core, enabling precise control of its size, direction and modulation of the magnetization curve to fulfill specific application requirements.

4. Conclusions

This study conducted a comprehensive investigation into the impact of NA and FA on the magnetic properties of an Fe₈₂Si₂B₁₃P₁C₃ amorphous iron core and compared it with an Fe₈₀Si₉B₁₁ amorphous iron core. The findings can be summarized as follows.

(1)

The Fe₈₂Si₂B₁₃P₁C₃ amorphous iron core, subjected to TFA, demonstrated a lower loss of P_1.4T,2kHz = 8.1 W/kg, which was 17% less than that of Fe₈₀Si₉B₁₁ with a loss of P_1.4T,2kHz = 9.8 W/kg. Furthermore, the Fe₈₂Si₂B₁₃P₁C₃ amorphous iron core exhibited a higher B_3500A/m value of 1.6 T under LFA, which was 0.05 T greater than the B_3500A/m value of Fe₈₀Si₉B₁₁ (B_3500A/m = 1.55 T). The optimal heat treatment temperature for Fe₈₂Si₂B₁₃P₁C₃ was 30 °C lower than that of Fe₈₀Si₉B₁₁, contributing to improved toughness of the amorphous ribbons.

(2)

As the heat treatment temperature of Fe₈₂Si₂B₁₃P₁C₃ increased to 370 °C, the internal stress gradually dissipated, resulting in the disappearance of impurity domains, such as fingerprint domains. Moreover, the magnetic domains within the strip underwent a transformation, aligning themselves with the length direction of the strip. This led to the formation of wide strip domains with low resistance, facilitating easy magnetization and ultimately reducing the overall loss of the amorphous iron core.

(3)

For Fe₈₂Si₂B₁₃P₁C₃ amorphous iron cores under an applied excitation of 3500 A/m, the B_m values of the treatment processes were arranged in ascending order as TFA < LTFA < NA < LFA < TLFA. Particularly, the B_m values of LFA and TLFA closely overlapped, with both reaching 1.6 T.