The Effects of Si Substitution with C on the Amorphous Forming Ability, Thermal Stability, and Magnetic Properties of an FeSiBPC Amorphous Alloy

: The industrialization of Fe-based amorphous alloys with high a saturation magnetic flux density ( B s ) has been limited so far due to their inadequate amorphous forming ability (AFA). In this study, the effects of substituting Si with C on the AFA, thermal stability, and magnetic properties of Fe 82 Si 6 − x B 9 P 3 C x (x = 0–6) alloys were systematically investigated. The experimental results demonstrate that the AFA, thermal stability, and soft magnetic properties can be significantly enhanced by the addition of C. Specifically, at a copper wheel velocity of 40 m/s, the Fe 82 Si 6 − x B 9 P 3 C x (x = 2, 3, 4, 5 and 6) alloy ribbons exhibit a fully amorphous structure in the as-spun state. The activation energy required for the α -Fe phase crystallization process in Fe 82 Si 6 − x B 9 P 3 C x (x = 0, 2, 4, and 6) alloys is determined to be 326.74, 390.69, 441.06, and 183.87 kJ/mol, respectively. Among all of the compositions studied, the Fe 82 Si 4 B 9 P 3 C 2 alloy exhibits optimized soft magnetic properties, including a low coercivity ( H c ) of 1.7 A/m, a high effective permeability ( µ e ) of 10608 ( f = 1 kHz), and a relatively high Bs of 1.61 T. These improvements may be attributed to a more homogeneous and optimized magnetic domain structure being achieved through proper C addition. This work holds significant implications for the advancement of Fe-based soft magnetic amorphous alloys with high B s .


Introduction
The urgent need to address escalating environmental concerns and the energy crisis necessitates a reduction in the inefficient dissipation of energy.In order to power various applications, there is a growing interest in developing high-efficiency and high-performance devices like transformers and electric motors for electric vehicles.The efficiency of these devices greatly depends on the soft magnetic materials used within them [1][2][3].Soft magnetic materials with desirable characteristics such as a high B s , low H c , and low core loss (P) can significantly enhance their efficiency.Consequently, extensive research has been conducted in recent years on Fe-based amorphous alloys, which exhibit low H c and p values [4][5][6].However, the currently widely used Metglas 2605SA1 (i.e., FeSiB series) has a lower B s of 1.56 T compared to the 1.9-2.0T of a silicon steel alloy, which hinders the miniaturization of soft magnetic devices [7].Therefore, recent studies have primarily focused on enhancing the B s properties of Fe-based amorphous alloys.For Febased amorphous alloys, the B s value is primarily determined by the alloy's composition, indicating the magnetic moment per unit volume.Consequently, a higher percentage of Fe (wt.%) generally corresponds to a higher B s [8].Therefore, in recent years there has been an emphasis on increasing the Fe content (wt.%) in the design of high-B s Fe-based amorphous alloys by considering metalloids with a lower relative atomic mass (B, C, Si and P) as the Metals 2024, 14, 546 2 of 14 primary alloying elements [9,10].However, this conceptual approach results in a decrease in the AFA.When AFA approaches the glass formation limit, there is typically a tendency for partial hierarchical crystallization to occur on the surfaces of the as-cast ribbons during the melt-spinning process, while the majority of the ribbons still maintain an amorphous structure [11].
In 2006, Hitachi Metal successfully developed the FeSiBC series amorphous soft magnetic alloy [12], known as 2605HB1, and filed a patent application.This alloy exhibits a B s greater than 1.6 T and an even lower H c compared to the previously developed 2605SA1.However, due to its high iron content of approximately 80 at.%, the amorphous forming ability of alloy 2605HB1 is compromised.Chang [13] discovered that by combining Fe, B, P, C, and Si in the composition design process, a high B s and AFA can be achieved.The addition of C optimizes the soft magnetic properties resulting in excellent characteristics for the Fe 83 B 10 C 3 Si 3 P 1 amorphous alloy with a high B s value of 1.71 T and a low H c value of 1.5 A/m [14].It has been reported that adding small amounts of C into NANOMET alloys can enhance their AFA without compromising their soft magnetic properties [15,16].The experimental results from Hui indicate that substituting C for Si significantly improves the AFA, B s , and H c of Fe 83.3 Si 4−x B 9 P 3 Cu 0.7 C x amorphous and nanocrystalline alloys [17].However, it remains unclear how the C/Si ratio affects the structure and properties of Fe-based amorphous alloys or whether it can be further adjusted to enhance both their amorphous forming ability and soft magnetic properties.
In our current study, we have developed a novel Fe 82 Si 6−x B 9 P 3 C x (x = 0-6) soft magnetic amorphous alloy system with a high iron content by substituting silicon with carbon.Systematic investigations on the AFA, magnetic properties, and magnetic domain structure were conducted.The underlying mechanism responsible for the enhanced AFA and optimized soft magnetic properties is thoroughly analyzed and discussed.These findings bear significant implications for the advancement of Fe-based soft magnetic amorphous alloys with high saturation magnetization.

Materials and Methods
The master alloy ingots were prepared by induction melting mixtures of high purity Fe (99.95 wt.%), Si (99.999 wt.%), C (99.99 wt.%), pre-alloyed Fe-B (B: 20 wt.%), and Fe-P (P: 18 wt.%) in a high-purity argon atmosphere with nominal compositions of Fe 82 Si 6−x B 9 P 3 C x (x = 0, 1, 2, 3, 4, 5, and 6 in atomic percent).These alloys are denoted as C-0, C-1, C-2, C-3, C-4, C-5, and C-6 hereafter.These ingots were melted for over 5 min to ensure compositional homogeneity after complete melting.Ribbon specimens with a width of approximately 1 mm were prepared using a commonly employed single roller spinning machine under a high-purity argon atmosphere.The amorphous structure and thermal properties of the as-cast ribbons were investigated via X-ray diffraction (XRD) using Cu Kα radiation and differential scanning calorimetry (DSC, NETZSCH 404, Selb, Germany) at a heating rate of 20 • C/min under Ar gas protection.For the isothermal annealing treatment, ribbon specimens were cut to approximately 70 mm in length, wrapped with aluminum foil, and then sealed in quartz tubes under vacuum conditions.Once the annealing furnace reached the desired temperature, the vacuum quartz tubes containing the ribbon specimens were placed into it and held for 10 min, followed by water quenching.The B s were measured using a vibrating sample magnetometer (VSM, Lake Shore 7410, Columbus, OH, USA) under an applied field of 800 kA/m.The H c and µ e at 1 kHz were tested using a DC B-H hysteresis loop tracer (Linkjoin, MATS-2010SD, Loudi, Hunan, China) and an impedance analyzer (Agilent E4990 A, Santa Clara, CA, USA), respectively.The structure of the magnetic domain under different magnetic fields was characterized via magneto-optical Kerr microscopy.

Glass Forming Ability
To investigate the amorphous forming ability of the Fe 82 Si 6−x B 9 P 3 C x (x = 0, 1, 2, 3, 4, 5, and 6) alloy system, alloy ribbons were prepared using single roll spinning technology with copper wheel line velocities of 45 m/s and 40 m/s, respectively.The XRD patterns of the as-spun alloy ribbons are present in Figure 1.It can be observed from Figure 1a that at a velocity of 45 m/s, only a broad diffuse scattering peak around 44.5 • is visible in the patterns, indicating the formation of an amorphous structure in the alloy ribbons.When the copper wheel velocity decreased to 40 m/s, in addition to the broad diffuse scattering peak at 44.5 • , a sharp crystallization peak corresponding to the (200) plane of the α-Fe phase was observed in the region of 2θ~65 • for the C-0 alloy.For the C-1 alloy, there was a noticeable decrease in the intensity of this crystallization peak at 65 • which suggests that partial crystallization occurred for both the C-0 and C-1 alloys in the as-spun state.However, for the C-2, C-3, C-4, C5, and C-6 alloys, only a broad diffuse scattering peak appears in their respective XRD patterns, indicating that complete amorphous structures are achieved successfully within these five alloy ribbons.
patterns, indicating the formation of an amorphous structure in the alloy ribbons.W the copper wheel velocity decreased to 40 m/s, in addition to the broad diffuse scatt peak at 44.5°, a sharp crystallization peak corresponding to the (200) plane of the phase was observed in the region of 2θ~65° for the C-0 alloy.For the C-1 alloy, ther a noticeable decrease in the intensity of this crystallization peak at 65° which suggest partial crystallization occurred for both the C-0 and C-1 alloys in the as-spun state.ever, for the C-2, C-3, C-4, C5, and C-6 alloys, only a broad diffuse scattering peak ap in their respective XRD patterns, indicating that complete amorphous structure achieved successfully within these five alloy ribbons.
Based on the XRD results presented above, it is suggested that the AFA o Fe82Si6−xB9P3Cx alloy can be enhanced efficiently through the substitution of Si with C improved AFA, resulting from the addition of the C element, can be attributed to fa such as atomic packing, thermodynamics principles, and empirical rules [18].From ological perspective, the atomic radii of iron, silicon, and carbon are 1.27 Å, 1.34 Å 0.86 Å, respectively.Substituting Si with C in the FeSiBPC alloy system leads to a creased difference in atomic sizes which becomes larger and more complex.This a with Inoue's rules which state that the difference between constituent elements' a sizes should exceed 12% for the formation of bulk metallic glasses.Additionally, th nificant size difference among multiple components may result in highly packed a configurations within these alloys.Moreover, the presence of large negative mixin thalpies among constituent elements contributes to high AFA levels.The substituti Si with C increases the amount of negative mixing enthalpy due to a higher the Fe-C having a higher value (−50 kJ/mol) compared to Fe-Si pairs (−35 kJ/mol) [19].This enh ment positively impacts the AFA of these alloys.Generally, the partial crystallization of an amorphous alloy primarily occurs o free surface of alloy ribbons [20].To further analyze the partial crystallization behav the C-0 and C-1 alloys under a velocity of 40 m/s, XRD tests were conducted on bot free surfaces and roller surfaces of the as-spun alloy ribbons.The results are presen Figure 2a.The crystallization peak of (200) is exclusively observed on the free surfa the as-spun ribbons, while it is absent on the roller surface, indicating that crystalliz only occurs at the free surface due to its lower cooling rate.To further investigate t fluences of cooling rate on the phase formation in the as-spun Fe82Si6−xB9P3Cx alloy Based on the XRD results presented above, it is suggested that the AFA of the Fe 82 Si 6−x B 9 P 3 C x alloy can be enhanced efficiently through the substitution of Si with C. The improved AFA, resulting from the addition of the C element, can be attributed to factors such as atomic packing, thermodynamics principles, and empirical rules [18].From a topological perspective, the atomic radii of iron, silicon, and carbon are 1.27 Å, 1.34 Å, and 0.86 Å, respectively.Substituting Si with C in the FeSiBPC alloy system leads to an increased difference in atomic sizes which becomes larger and more complex.This aligns with Inoue's rules which state that the difference between constituent elements' atomic sizes should exceed 12% for the formation of bulk metallic glasses.Additionally, the significant size difference among multiple components may result in highly packed atomic configurations within these alloys.Moreover, the presence of large negative mixing enthalpies among constituent elements contributes to high AFA levels.The substitution of Si with C increases the amount of negative mixing enthalpy due to a higher the Fe-C pairs having a higher value (−50 kJ/mol) compared to Fe-Si pairs (−35 kJ/mol) [19].This enhancement positively impacts the AFA of these alloys.
Generally, the partial crystallization of an amorphous alloy primarily occurs on the free surface of alloy ribbons [20].To further analyze the partial crystallization behavior of the C-0 and C-1 alloys under a velocity of 40 m/s, XRD tests were conducted on both the free surfaces and roller surfaces of the as-spun alloy ribbons.The results are presented in Figure 2a.The crystallization peak of (200) is exclusively observed on the free surface of the as-spun ribbons, while it is absent on the roller surface, indicating that crystallization only occurs at the free surface due to its lower cooling rate.To further investigate the influences of cooling rate on the phase formation in the as-spun Fe 82 Si 6−x B 9 P 3 C x alloy, C-0 and C-2 alloy ribbons were prepared with different cooling rates by adjusting the line velocity of the copper wheel.XRD analysis was conducted and the results are presented in Figure 2b,c.At a velocity of 30 m/s, a crystalline peak at 65 • can still be observed on the free side of the C-0 alloy ribbon.For the C-2 alloy, despite a decrease in the velocity of the copper wheel from 40 m/s to 30 m/s, a fully amorphous structure is achieved in the as-spun ribbon, indicating the excellent AFA of the C-2 alloy.At lower speeds such as 20 m/s, 18 m/s, and 15 m/s, distinct differences are observed between the XRD patterns of the C-0 and C-2 alloys.On the free side, all ribbons exhibit prominent crystallization peaks at approximately 65 • corresponding to the (200) plane of the α-Fe phase.On the roller side, a crystallization peak at 65 • is observed for the C-2 alloy ribbons prepared at 15 m/s and 18 m/s, while no significant crystallization peak is observed at 20 m/s.For the C-0 alloy, only a small crystallization peak appears at around 65 • in the XRD pattern of the ribbon prepared at 20 m/s.However, at both speeds of 15 m/s and 18 m/s, the C-0 alloy ribbons show multiple crystallization peaks near 44.5 • , 65 • , and 82.3 • , corresponding to the (110), (200), and (211) planes of the α-Fe phase, respectively.Additionally, weak crystallization peaks related to the Fe(B, P) compound phase are also found at the left and right sides of 44.5 • , indicating that the C-0 alloy ribbons prepared at 15 m/s and 18 m/s were highly crystallized.In summary, the higher the copper wheel velocity, the lower the intensity of the crystallization peak, and the more pronounced the amorphous broad diffuse scattering peak.Compared with the C-0 alloy, the C-2 alloy exhibits a lower degree of crystallization under the same fabrication conditions, which also suggests that the substitution of C for Si can improve the amorphous forming ability of the alloy system.and C-2 alloy ribbons were prepared with different cooling rates by adjusting th velocity of the copper wheel.XRD analysis was conducted and the results are pres in Figure 2b,c.At a velocity of 30 m/s, a crystalline peak at 65° can still be observed o free side of the C-0 alloy ribbon.For the C-2 alloy, despite a decrease in the velocity copper wheel from 40 m/s to 30 m/s, a fully amorphous structure is achieved in th spun ribbon, indicating the excellent AFA of the C-2 alloy.At lower speeds such as 2 18 m/s, and 15 m/s, distinct differences are observed between the XRD patterns of th and C-2 alloys.On the free side, all ribbons exhibit prominent crystallization peaks proximately 65° corresponding to the (200) plane of the α-Fe phase.On the roller s crystallization peak at 65° is observed for the C-2 alloy ribbons prepared at 15 m/s a m/s, while no significant crystallization peak is observed at 20 m/s.For the C-0 alloy a small crystallization peak appears at around 65° in the XRD pattern of the ribbon pared at 20 m/s.However, at both speeds of 15 m/s and 18 m/s, the C-0 alloy ribbons multiple crystallization peaks near 44.5°, 65°, and 82.3°, corresponding to the (110), and (211) planes of the α-Fe phase, respectively.Additionally, weak crystallization related to the Fe(B, P) compound phase are also found at the left and right sides of indicating that the C-0 alloy ribbons prepared at 15 m/s and 18 m/s were highly cr lized.In summary, the higher the copper wheel velocity, the lower the intensity o crystallization peak, and the more pronounced the amorphous broad diffuse scatt peak.Compared with the C-0 alloy, the C-2 alloy exhibits a lower degree of crystalliz under the same fabrication conditions, which also suggests that the substitution of Si can improve the amorphous forming ability of the alloy system.The change in the thicknesses of the C-0 and C-2 alloy ribbons with the velocity of copper wheel is illustrated in Figure 3a.As depicted, an increase in velocity results in a decrease in ribbon thickness.Moreover, there is minimal variation observed between the thicknesses of the C-0 and C-2 alloy ribbons prepared under identical conditions.When considering a constant thermal conductivity for the copper wheel, a thinner alloy ribbon indicates a higher cooling rate, facilitating the formation of a fully amorphous structure.Notably, at a speed of 20 m/s, the thickness of the alloy ribbon is approximately twice that at 40 m/s; this discrepancy also accounts for the significant differences present in the XRD patterns at varying speeds.Additionally, as the alloy ribbon becomes thicker, there is an increased disparity in the cooling rates between the roller surface and the free surface, particularly evident at lower speeds, which further contributes to variations between their respective structures.Figure 3b summarizes the phase formation for both the C-0 and C-2 alloys across different cooling rates while comparing them to the Fe 83.3 Si 4 B 8 P 4 Cu 0.7 and Fe 84.75 Si 2 B 9 P 3 C 0.5 Cu 0.75 alloys.The findings demonstrate that the C-2 alloy exhibits superior amorphous forming ability, which is conducive to its industrial production.
Metals 2024, 14, x FOR PEER REVIEW 5 The change in the thicknesses of the C-0 and C-2 alloy ribbons with the veloc copper wheel is illustrated in Figure 3a.As depicted, an increase in velocity result decrease in ribbon thickness.Moreover, there is minimal variation observed betwee thicknesses of the C-0 and C-2 alloy ribbons prepared under identical conditions.W considering a constant thermal conductivity for the copper wheel, a thinner alloy r indicates a higher cooling rate, facilitating the formation of a fully amorphous stru Notably, at a speed of 20 m/s, the thickness of the alloy ribbon is approximately twic at 40 m/s; this discrepancy also accounts for the significant differences present in the patterns at varying speeds.Additionally, as the alloy ribbon becomes thicker, there increased disparity in the cooling rates between the roller surface and the free su particularly evident at lower speeds, which further contributes to variations between respective structures.Figure 3b summarizes the phase formation for both the C-0 a 2 alloys across different cooling rates while comparing them to the Fe83.3Si4B8P4Cu0Fe84.75Si2B9P3C0.5Cu0.75alloys.The findings demonstrate that the C-2 alloy exhibits sup amorphous forming ability, which is conducive to its industrial production.

Thermal Stability
The thermal stability of the as-spun Fe82Si6−xB9P3Cx amorphous alloy ribbon characterized through DSC analysis.To ensure a uniform comparison, all experim samples were prepared as amorphous ribbons at a copper wheel velocity of 45 m/s DSC results are presented in Figure 4.All DSC curves exhibit two crystallization exo mic peaks, corresponding to the formation of a soft magnetic α-Fe phase and the pr tation of the Fe(B,P) compound phase, respectively.The results indicate that an inc in C content initially leads to an increase and then a decrease in the initial crystalliz temperature (Tx1) of the α-Fe phase.Among these alloys, C-3 exhibits the highest Tx1 (491.4 °C).A higher Tx1 suggests a greater difficulty in crystallization during the he process, indicating an enhanced thermal stability.On the other hand, both the initial tallization temperature (Tx2) and the peak temperature (Tp2) of the Fe(B,P) comp phase decrease with increasing C content; however, when the C content exceeds 2 a becomes difficult to distinguish Tx2 due to the presence of overlapping crystalliz peaks.As shown in Figure 4b, all of the DSC curves display an endothermic peak sponding to Curie temperature transition of amorphous alloys, with its peak represe the Tc point.It is observed that Tc initially increases and then decreases with increas content; among them, the C-3 alloy achieves the highest Tc value (368.3 °C).The TG ysis was conducted on the C-2 alloy ribbons to validate the accuracy of the Tc rea obtained from DSC.

Thermal Stability
The thermal stability of the as-spun Fe 82 Si 6−x B 9 P 3 C x amorphous alloy ribbons was characterized through DSC analysis.To ensure a uniform comparison, all experimental samples were prepared as amorphous ribbons at a copper wheel velocity of 45 m/s.The DSC results are presented in Figure 4.All DSC curves exhibit two crystallization exothermic peaks, corresponding to the formation of a soft magnetic α-Fe phase and the precipitation of the Fe(B,P) compound phase, respectively.The results indicate that an increase in C content initially leads to an increase and then a decrease in the initial crystallization temperature (T x1 ) of the α-Fe phase.Among these alloys, C-3 exhibits the highest T x1 value (491.4 • C).A higher T x1 suggests a greater difficulty in crystallization during the heating process, indicating an enhanced thermal stability.On the other hand, both the initial crystallization temperature (T x2 ) and the peak temperature (T p2 ) of the Fe(B,P) compound phase decrease with increasing C content; however, when the C content exceeds 2 at.% it becomes difficult to distinguish T x2 due to the presence of overlapping crystallization peaks.As shown in Figure 4b, all of the DSC curves display an endothermic peak corresponding to Curie temperature transition of amorphous alloys, with its peak representing the T c point.It is observed that T c initially increases and then decreases with increasing C content; among them, the C-3 alloy achieves the highest T c value (368.3 • C).The TG analysis was conducted on the C-2 alloy ribbons to validate the accuracy of the T c readings obtained from DSC.The excellent soft magnetic properties of most Fe-based amorphous alloys w Cu are attributed to the uniformity of their structure, and it is not anticipated that cl or crystallization will occur during stress relief annealing [21].Tx1-Tc is commonl ployed as a quantitative measure for characterizing the ability of amorphous allo achieve favorable soft magnetic properties.A higher value indicates that the alloy c tuate stress-pinned magnetic domains more easily without undergoing crystalli during conventional annealing [22].As shown in Figure 4c  The excellent soft magnetic properties of most Fe-based amorphous alloys without Cu are attributed to the uniformity of their structure, and it is not anticipated that clusters or crystallization will occur during stress relief annealing [21].T x1 -T c is commonly employed as a quantitative measure for characterizing the ability of amorphous alloys to achieve favorable soft magnetic properties.A higher value indicates that the alloy can actuate stress-pinned magnetic domains more easily without undergoing crystallization during conventional annealing [22].As shown in Figure 4c 5.It is evident that as the heating rate increases from 10 • C/min to 40 • C/min, the crystallization peaks shift towards higher temperatures, indicating pronounced kinetic characteristics.This phenomenon can be attributed to the fact that at lower heating rates, atoms within the amorphous structure have sufficient time to absorb energy for motion and diffusion rearrangement leading to crystallization at lower temperatures.Conversely, higher heating rates result in shorter atomic diffusion and rearrangement times within the amorphous phase, thereby pushing the crystallization process towards higher temperatures [23,24].
Metals 2024, 14, x FOR PEER REVIEW 7 have an increased propensity for impeding atomic diffusion motion.Consequently, a city of Si atoms and an elevated level of order in the amorphous structure result to a nounced decrease in its thermal stability.Specifically, Tx1 is significantly reduced 482.7 °C to 445.8 °C, while Tc also experiences a reduction albeit within a narrower than Tx1 (from 123.0 °C to 107.4 °C).Therefore, Tx1-Tc is also reduced.
The thermal stability and non-isothermal crystallization behavior of Fe82Si6−xB amorphous alloy ribbons were further investigated by conducting DSC tests at diff heating rates (10, 20, 30, and 40 K/min) for C-0, C-2, C-4, and C-6 alloys.The resulting curves are presented in Figure 5.It is evident that as the heating rate increases fro °C/min to 40 °C/min, the crystallization peaks shift towards higher temperatures, in ing pronounced kinetic characteristics.This phenomenon can be attributed to the fac at lower heating rates, atoms within the amorphous structure have sufficient time sorb energy for motion and diffusion rearrangement leading to crystallization at temperatures.Conversely, higher heating rates result in shorter atomic diffusion an arrangement times within the amorphous phase, thereby pushing the crystallization cess towards higher temperatures [23,24].In the process of crystallization, the amorphous structure must absorb sufficie ergy to overcome a specific energy barrier known as the activation energy (Ea).A h Ea indicates greater stability of the amorphous structure.Based on the characteristic perature values obtained from DSC curves, the activation energies for α-Fe phase cr lization process in Fe82Si6−xB9P3Cx amorphous alloys were determined using the Kiss equation, as shown in Figure 6.The activation energies derived for the α-Fe phase tallization process are presented in Table 1.It is observed that as the C content incr In the process of crystallization, the amorphous structure must absorb sufficient energy to overcome a specific energy barrier known as the activation energy (E a ).A higher E a indicates greater stability of the amorphous structure.Based on the characteristic temperature values obtained from DSC curves, the activation energies for α-Fe phase crystallization process in Fe 82 Si 6−x B 9 P 3 C x amorphous alloys were determined using the Kissinger equation, as shown in Figure 6.The activation energies derived for the α-Fe phase crystallization process are presented in Table 1.It is observed that as the C content increases, E p1 and E p1 initially increase before decreasing again in the Fe 82 Si 6−x B 9 P 3 C x alloy system.Among all four of the alloys, the C-4 alloy exhibits the highest E x1 of 441.06 kJ/mol and E p1 of 465.09 kJ/mol, indicating that an appropriate substitution of C for Si element enhances thermal stability of the Fe 82 Si 6−x B 9 P 3 C x amorphous alloys.However, when the carbon content continues to rise in the C-6 alloy, Ex1 and Ep1 decreases significantly.Notably, the E p1 values are slightly higher than the E p1 values for the C-0, C-2, C-4, and C-6 alloys, suggesting that grain growth in the α-Fe(Si) phase is more difficult than nucleation in this alloy system [25].
Metals 2024, 14, x FOR PEER REVIEW 8 Ep1 and Ep1 initially increase before decreasing again in the Fe82Si6−xB9P3Cx alloy sy Among all four of the alloys, the C-4 alloy exhibits the highest Ex1 of 441.06 kJ/mol an of 465.09 kJ/mol, indicating that an appropriate substitution of C for Si element enh thermal stability of the Fe82Si6−xB9P3Cx amorphous alloys.However, when the carbon tent continues to rise in the C-6 alloy, Ex1 and Ep1 decreases significantly.Notabl Ep1 values are slightly higher than the Ep1 values for the C-0, C-2, C-4, and C-6 alloys gesting that grain growth in the α-Fe(Si) phase is more difficult than nucleation i alloy system [25].

Magnetic Properties
For soft magnetic alloys, the values of Hc and μe are influenced by the structure, ing the annealing treatment crucial in modulating these parameters.The Hc and μe of ples annealed at different temperatures are presented in Figure 7.As the annealing perature increases, the Hc of all alloy ribbons initially decreases and then increases.Figure 7a, it can be observed that the Hc of the alloy system decreases and reaches its imum value when the annealing temperature rises to approximately 360-380 °C.S quently, as the temperature further increases towards Tx1, Hc starts to rise again.W increase in C content, the Hc (i.e., lowest point on the curve) at the optimum anne

Magnetic Properties
For soft magnetic alloys, the values of H c and µ e are influenced by the structure, making the annealing treatment crucial in modulating these parameters.The H c and µ e of samples annealed at different temperatures are presented in Figure 7.As the annealing temperature increases, the H c of all alloy ribbons initially decreases and then increases.
From Figure 7a, it can be observed that the H c of the alloy system decreases and reaches its minimum value when the annealing temperature rises to approximately 360-380 • C. Subsequently, as the temperature further increases towards T x1 , H c starts to rise again.With an increase in C content, the H c (i.e., lowest point on the curve) at the optimum annealing temperature first decreases and then increases.For the C-0, C-1, and C-6 alloys, the lowest point of H c occurs at 360 • C, with corresponding values of 4.1, 3.8, and 4.8 A/m, respectively.On the other hand, for the C-2, C-3, C-4, and C-5 alloys, the lowest point of H c occurs at 380 • C.Among these alloys, the C-2 alloy exhibits the lowest H c (1.7 A/m), the while C-3, C-4, and C-5 alloys have similar lowest H c values (2.3, 2.2, and 2.8 A/m, respectively).The change in H c with annealing temperature for these alloy ribbons can be understood based on the structural evolution that occurs during annealing.Currently, Fe-based amorphous ribbons are primarily produced using single roll melt spinning technology, which results in a high cooling rate and consequently generates significant internal stress within the as-spun ribbon [26].Annealing prior to T x1 allows for the release of this internal stress induced by single roll melt spinning technology, leading to alterations in the microscopic stress field of atoms [27].In this context, we propose that the decrease in H c at 360-380 • C can be attributed to relaxation of the amorphous structure.Furthermore, as T a approaches T x1 , the increase in H c is associated with magnetoelastic anisotropy [28] coupled with magneto-crystalline anisotropy caused by the precipitation of α-Fe grains within the amorphous matrix.As shown in Figure 7b, µ e shows an inverse relationship with annealing temperature compared to H c .For the C-0, C-1, and C-6 alloys, the highest point of µ e appears at 360 • C with corresponding values of 7800, 8134, and 7163, respectively.The C-2 alloy exhibits the highest µ e value of 10,608, followed by 10,108 for C-3, 10,333 for C-4, and 7984 for the C-5 alloy.The magnetic susceptibility is determined at a low applied magnetic field by measuring the displacement of the domain walls, which can vary in width depending on the magnetic anisotropy.The enhancement of µ e that occurred When the ribbons were annealed at the optimal temperature can be attributed to the decrease in magnetoelastic anisotropy caused by the release of internal stress.In summary, for Fe 82 Si 6−x B 9 P 3 C x amorphous alloy ribbons, the substitution of Si elements with an appropriate C element can optimize the soft magnetic performance; however, the excessive replacement of the Si element with the C element may deteriorate the soft magnetic performance.
temperature first decreases and then increases.For the C-0, C-1, and C-6 alloys, the l point of Hc occurs at 360 °C, with corresponding values of 4.1, 3.8, and 4.8 A/m, re tively.On the other hand, for the C-2, C-3, C-4, and C-5 alloys, the lowest point occurs at 380 °C.Among these alloys, the C-2 alloy exhibits the lowest Hc (1.7 A/m while C-3, C-4, and C-5 alloys have similar lowest Hc values (2.3, 2.2, and 2.8 A/m, re tively).The change in Hc with annealing temperature for these alloy ribbons can b derstood based on the structural evolution that occurs during annealing.Currentl based amorphous ribbons are primarily produced using single roll melt spinning tec ogy, which results in a high cooling rate and consequently generates significant in stress within the as-spun ribbon [26].Annealing prior to Tx1 allows for the release o internal stress induced by single roll melt spinning technology, leading to alteratio the microscopic stress field of atoms [27].In this context, we propose that the decre Hc at 360-380 °C can be attributed to relaxation of the amorphous structure.Further as Ta approaches Tx1, the increase in Hc is associated with magnetoelastic anisotrop coupled with magneto-crystalline anisotropy caused by the precipitation of α-Fe g within the amorphous matrix.As shown in Figure 7b, μe shows an inverse relatio with annealing temperature compared to Hc.For the C-0, C-1, and C-6 alloys, the hi point of μe appears at 360 °C with corresponding values of 7800, 8134, and 7163, re tively.The C-2 alloy exhibits the highest μe value of 10,608, followed by 10108 fo 10,333 for C-4, and 7984 for the C-5 alloy.The magnetic susceptibility is determine low applied magnetic field by measuring the displacement of the domain walls, w can vary in width depending on the magnetic anisotropy.The enhancement of μ occurred When the ribbons were annealed at the optimal temperature can be attribu the decrease in magnetoelastic anisotropy caused by the release of internal stress.In mary, for Fe82Si6−xB9P3Cx amorphous alloy ribbons, the substitution of Si elements w appropriate C element can optimize the soft magnetic performance; however, the e sive replacement of the Si element with the C element may deteriorate the soft mag performance.The variation in μe with frequency under different applied magnetic fields for C 2, C-4, and C-6 alloy ribbons annealed at the optimum temperature is shown in Fig respectively .It can be observed that when the amplitude of the applied magnetic remains constant, the μe of all alloy ribbons decreases as the frequency increases, wh a characteristic inherent to soft magnetic materials.As the frequency increases, the m ment and rotation of magnetic moments within the domain walls and domains res to the applied magnetic field.However, when they reach a certain frequency limit, mobility becomes restricted and their contribution to magnetization rotation dimin significantly, resulting in a sharp decline in μe [29].Furthermore, it can be observed The variation in µ e with frequency under different applied magnetic fields for C-0, C-2, C-4, and C-6 alloy ribbons annealed at the optimum temperature is shown in Figure 8, respectively.It can be observed that when the amplitude of the applied magnetic field remains constant, the µ e of all alloy ribbons decreases as the frequency increases, which is a characteristic inherent to soft magnetic materials.As the frequency increases, the movement and rotation of magnetic moments within the domain walls and domains respond to the applied magnetic field.However, when they reach a certain frequency limit, their mobility becomes restricted and their contribution to magnetization rotation diminishes significantly, resulting in a sharp decline in µ e [29].Furthermore, it can be observed that, for frequencies below 20 kHz, µ e gradually increases with increasing AC field amplitudes (H m ) for the C-0, C-2, C-4, and C-6 alloys until it reaches a specific value where further increase in H m leads to a decrease in µ e .The AC field amplitude required for achieving maximum permeability can be considered as a pinning field (H p ) for these ribbons [30].Figure 8 shows that the H p values were determined as follows: 25 A/m for the C-0 alloy; 15 A/m for the C-2 alloy; 20 A/m for the C-4 alloy; and 30A/m for the C-6 alloy, respectively.A lower H p indicates fewer pinned sites, fewer defects, and better magnetic softness.
Metals 2024, 14, x FOR PEER REVIEW 10 for frequencies below 20 kHz, μe gradually increases with increasing AC field ampli (Hm) for the C-0, C-2, C-4, and C-6 alloys until it reaches a specific value where fu increase in Hm leads to a decrease in μe.The AC field amplitude required for achi maximum permeability can be considered as a pinning field (Hp) for these ribbons Figure 8 shows that the Hp values were determined as follows: 25 A/m for the C-0 15 A/m for the C-2 alloy; 20A/m for the C-4 alloy; and 30A/m for the C-6 alloy, respect A lower Hp indicates fewer pinned sites, fewer defects, and better magnetic softness The Bs parameter of the alloy is a crucial magnetic property, and VSM tests conducted on the ribbons annealed at the optimal annealing temperature.The resu Hysteresis loops are presented in 9. To further investigate the influence of C tion on the soft magnetic properties of Fe82Si6−xB9P3Cx, the relationship between Hc, μ Bs with varying C content is summarized in Table 2.As depicted in Figure 9, all o amorphous alloy samples exhibit rapid saturation magnetization under a small ap magnetic field, indicating the presence of typical soft magnetic characteristics withi alloy system.With the inclusion of C, it becomes evident from Table 2 that the valu Bs significantly increase from 1.59 T for the C-0 alloy to 1.63 T for the C-6 alloy.Th hancement in Bs can be explained from two perspectives: Firstly, since C has a sm relative atomic mass than Si, replacing Si with C in Fe82Si6−xB9P3Cx promotes an incre the Fe element mass fraction from 92.94 wt.% for the C-0 alloy to 94.58 wt.% for th alloy, thereby elevating Bs.Secondly, the local environment plays a significant role termining the ferromagnetic behavior within metallic glasses.Previous studies hav ported that metalloid-sp/metal-d bonding leads to moment reduction in 3d-based a phous alloys around 0 K, consequently causing a decrease in Bs.In terms of topology siderations, metalloids with smaller atomic radii possess lower theoretical coordin numbers [31], which diminishes metalloid-sp/metal-d bonding and subsequent creases the Bs value within amorphous alloys.Therefore, substituting Si with sm The B s parameter of the alloy is a crucial magnetic property, and VSM tests were conducted on the ribbons annealed at the optimal annealing temperature.The resulting Hysteresis loops are presented in Figure 9.To further investigate the influence of C addition on the soft magnetic properties of Fe 82 Si 6−x B 9 P 3 C x , the relationship between H c , µ e , and B s with varying C content is summarized in Table 2.As depicted in Figure 9, all of the amorphous alloy samples exhibit rapid saturation magnetization under a small applied magnetic field, indicating the presence of typical soft magnetic characteristics within this alloy system.With the inclusion of C, it becomes evident from Table 2 that the values of B s significantly increase from 1.59 T for the C-0 alloy to 1.63 T for the C-6 alloy.The enhancement in B s can be explained from two perspectives: Firstly, since C has a smaller relative atomic mass than Si, replacing Si with C in Fe 82 Si 6−x B 9 P 3 C x promotes an increase in the Fe element mass fraction from 92.94 wt.% for the C-0 alloy to 94.58 wt.% for the C-6 alloy, thereby elevating B s .Secondly, the local environment plays a significant role in determining the ferromagnetic behavior within metallic glasses.Previous studies have reported that metalloid-sp/metal-d bonding leads to moment reduction in 3d-based amorphous alloys around 0 K, consequently causing a decrease in B s .In terms of topology considerations, metalloids with smaller atomic radii possess lower theoretical coordination numbers [31], which diminishes metalloid-sp/metal-d bonding and subsequently increases the B s value within amorphous alloys.Therefore, substituting Si with smaller atomic radius counterpart such as C tends to enhance the B s value within an Fe 82 Si 6−x B 9 P 3 C x alloy system.Combined with the observed variations in H c and µ e upon C addition, as depicted in Table 2, it can be inferred that the soft magnetic properties can be effectively optimized through carbon incorporation.Notably, the C-2 alloy demonstrates exceptional comprehensive soft magnetic properties, characterized by a high B s of 1.61 T, a low H c of 1.7 A/m, and a significantly elevated µ e reaching 10,608.
Metals 2024, 14, x FOR PEER REVIEW 11 of 14 atomic radius counterpart such as C tends to enhance the Bs value within an Fe82Si6−xB9P3Cx alloy system.Combined with the observed variations in Hc and μe upon C addition, as depicted in Table 2, it can be inferred that the soft magnetic properties can be effectively optimized through carbon incorporation.Notably, the C-2 alloy demonstrates exceptional comprehensive soft magnetic properties, characterized by a high Bs of 1.61 T, a low Hc of 1.7 A/m, and a significantly elevated μe reaching 10,608.To further investigate the reasons behind the changes in soft magnetic properties between C-0 and C-2 alloy ribbons in both as-spun and optimally annealed states, their magnetic domain patterns under zero field can be examined using a magneto-optical Kerr microscope, as depicted in Figure 10.It is evident from the figure that the magnetic structure of both alloys in the as-spun state exhibits irregularity, characterized by wide magnetic domains and numerous narrow domains.The rapid quenching process during fabrication induces significant internal stress in the as-spun ribbons, resulting in vertical magnetic anisotropy and a chaotic and irregular magnetic domain structure [32,33].Internal stress, if present, can interact with the positive magnetostriction in the amorphous ribbons to induce a magnetic anisotropy perpendicular or parallel to the stress direction, depending on whether it is tensile or compressive in nature [34].According to Tejedor et al.'s research [35], both surfaces of the as-spun amorphous ribbon experience compressive stress that gradually transitions into tensile stress at its center.Tsukahara et al. [36] observed that the magnitude of the anisotropy perpendicular to the stress determines the domain structure and width.Conversely, after annealing treatment, there is a transition in the easy  To further investigate the reasons behind the changes in soft magnetic properties between C-0 and C-2 alloy ribbons in both as-spun and optimally annealed states, their magnetic domain patterns under zero field can be examined using a magneto-optical Kerr microscope, as depicted in Figure 10.It is evident from the figure that the magnetic structure of both alloys in the as-spun state exhibits irregularity, characterized by wide magnetic domains and numerous narrow domains.The rapid quenching process during fabrication induces significant internal stress in the as-spun ribbons, resulting in vertical magnetic anisotropy and a chaotic and irregular magnetic domain structure [32,33].Internal stress, if present, can interact with the positive magnetostriction in the amorphous ribbons to induce a magnetic anisotropy perpendicular or parallel to the stress direction, depending on whether it is tensile or compressive in nature [34].According to Tejedor et al.'s research [35], both surfaces of the as-spun amorphous ribbon experience compressive stress that gradually transitions into tensile stress at its center.Tsukahara et al. [36] observed that the magnitude of the anisotropy perpendicular to the stress determines the domain structure and width.Conversely, after annealing treatment, there is a transition in the easy magnetization direction accompanied by an increase in the domain width due to stress release [34,35].As shown in Figure 10b,d, both C-0 and C-2 alloys exhibit wider magnetic domain structures with relatively flat walls compared to their as-spun state counterparts.This uniformity facilitates the movement of the magnetic domains and the rotation of the magnetic moments during alloy magnetization process.Blázquez et al. [37] propose that, in Fe-based amorphous ribbons, there exists an inverse relationship between the coercivity and the width of magnetic domains, indicating that wider magnetic domains result in lower H c values.Moreover, in comparison to the C-2 alloy, the C-0 alloy exhibits a certain degree of bifurcation in its magnetic domains with increased irregularity.This observation may be attributed to the fact that the C-2 alloy undergoes annealing at a temperature that is 20 • C higher than that of C-0 alloy; higher annealing temperatures are known to facilitate the unpinning process of magnetic domains.The analysis of domain patterns provides valuable insights into understanding the variations in H c values for both C-0 and C-2 alloys under different conditions.
Metals 2024, 14, x FOR PEER REVIEW 12 magnetization direction accompanied by an increase in the domain width due to s release [34,35].As shown in Figure 10b,d, both C-0 and C-2 alloys exhibit wider mag domain structures with relatively flat walls compared to their as-spun state counterp This uniformity facilitates the movement of the magnetic domains and the rotation o magnetic moments during alloy magnetization process.Blázquez et al. [37] propose in Fe-based amorphous ribbons, there exists an inverse relationship between the coe ity and the width of magnetic domains, indicating that wider magnetic domains resu lower Hc values.Moreover, in comparison to the C-2 alloy, the C-0 alloy exhibits a ce degree of bifurcation in its magnetic domains with increased irregularity.This observ may be attributed to the fact that the C-2 alloy undergoes annealing at a temperature is 20 °C higher than that of C-0 alloy; higher annealing temperatures are known to f tate the unpinning process of magnetic domains.The analysis of domain patterns vides valuable insights into understanding the variations in Hc values for both C-0 an 2 alloys under different conditions.

Conclusions
The effects of carbon addition on the amorphous FeSiBPC alloy systems were tematically investigated in this study, focusing on the AFA, thermal stability, and netic properties.The underlying mechanism responsible for the enhanced AFA and mized soft magnetic properties was thoroughly analyzed and discussed.For as-Fe82Si6−xB9P3Cx (x = 0, 1, 2, 3, 4, 5, and 6) alloy ribbons prepared at a copper wheel vel of 40 m/s, it was observed that alloys containing more than 1 atomic percent of ca exhibited a fully amorphous structure.This suggests that incorporating an approp amount of carbon element can effectively enhance the AFA in this specific alloy sy The introduction of carbon to the C-2 and C-4 alloys resulted in higher Ex1 and Ep1 v compared to those observed in the C-0 alloy.This indicates that the proper incorpor of carbon enhances the thermal stability of these amorphous ribbons.Furthermore soft magnetic properties can be effectively optimized through the addition of C. By ad

Conclusions
The effects of carbon addition on the amorphous FeSiBPC alloy systems were systematically investigated in this study, focusing on the AFA, thermal stability, and magnetic properties.The underlying mechanism responsible for the enhanced AFA and optimized soft magnetic properties was thoroughly analyzed and discussed.For as-spun Fe 82 Si 6−x B 9 P 3 C x (x = 0, 1, 2, 3, 4, 5, and 6) alloy ribbons prepared at a copper wheel velocity of 40 m/s, it was observed that alloys containing more than 1 atomic percent of carbon exhibited a fully amorphous structure.This suggests that incorporating an appropriate amount of carbon element can effectively enhance the AFA in this specific alloy system.The introduction of carbon to the C-2 and C-4 alloys resulted in higher E x1 and E p1 values compared to those observed in the C-0 alloy.This indicates that the proper incorporation of carbon enhances the thermal stability of these amorphous ribbons.Furthermore, the soft magnetic properties can be effectively optimized through the addition of C. By adding precisely 2 at.% C, the Fe 82 Si 4 B 9 P 3 C 2 alloy demonstrated optimized soft magnetic properties including a low H c of 1.7 A/m, a high µ e of 10608 (f = 1 kHz), and a relatively high B s of 1.61 T. These improvements may be attributed to achieving a more homogeneous and optimized

Figure 1 .
Figure 1.XRD patterns of the as-spun Fe 82 Si 6−x B 9 P 3 C x alloy ribbons at different copper wheel line velocities: (a) 45 m/s; (b) 40 m/s.

Figure 2 .
Figure 2. XRD patterns of as-spun C-0 and C-2 alloy ribbons prepared in different conditions C-0 and C-1 alloy ribbons prepared at 40 m/s; (b) XRD patterns of the free side of C-0 and C-2 ribbons and (c) XRD patterns of the wheel side of C-0 and C-2 alloy ribbons

Figure 2 .
Figure 2. XRD patterns of as-spun C-0 and C-2 alloy ribbons prepared in different conditions.(a) C-0 and C-1 alloy ribbons prepared at 40 m/s; (b) XRD patterns of the free side of C-0 and C-2 alloy ribbons and (c) XRD patterns of the wheel side of C-0 and C-2 alloy ribbons.

Figure 3 .
Figure 3. (a) The relationship between the thicknesses of C-0 and C-2 alloy ribbons and th velocity of the copper wheel.(b) Schematic comparison of phase formation of different alloys laboratory conditions and the RD patterns of as-spun C-0 and C-2 alloy ribbons prepared in di conditions.

Figure 3 .
Figure 3. (a) The relationship between the thicknesses of C-0 and C-2 alloy ribbons and the line velocity of the copper wheel.(b) Schematic comparison of phase formation of different alloys under laboratory conditions and the RD patterns of as-spun C-0 and C-2 alloy ribbons prepared in different conditions.

Figure 4 .
Figure 4. (a) DSC curves of as-spun Fe82Si6−xB9P3Cx amorphous alloys (x = 0-6) at a heating rat °C/min; (b) enlarged image of the A area in (a); (c) the changes in Tx1, Tx2 and Tx1-Tc with C c and (d) TG curve of C-2 alloy ribbons.
, the appropriate substi of Si with C not only enhances the Tx1 and Tc values of the alloy ribbon but also inc Tx1-Tc.The C-2, C-3, C-4, and C-5 alloys exhibit higher Tx1-Tc values, exceeding 12 while the C-0, C-1, and C-6 alloys demonstrate lower Tx1-Tc values.When Si is rep with C, both Tx1 and Tc initially increase before decreasing.This phenomenon can plained from two aspects: Firstly, taking into consideration the example of the C-0 and C-2 alloy; after replacing Si with an appropriate amount of carbon (C) in a four ponent Fe-Si-B-P-C system, it transforms into a five-component Fe-Si-B-P-C system may have a microalloying effect resulting in a more complex configuration of the phous structure.Additionally, this atomic size difference enhances the thermal sta within the amorphous structure, resulting in a significant increase in Tx1 from 475.3 485.5 °C, while Tc shows only marginal improvement due to short-range order e within amorphous alloys (from 360.3 °C to 362.2 °C).Consequently, there is an o increase in the value of Tx1-Tc.Secondly, taking into account examples such as the C C-6 alloys and following the excessive substitution of Si with C, the system trans from a five-component Fe-Si-B-P-C system back to a four-component Fe-C-B-P s where any microalloying effects disappear potentially improving order degree w amorphous structures.Moreover, due to their larger size compared to C atoms, Si

Figure 4 .
Figure 4. (a) DSC curves of as-spun Fe 82 Si 6−x B 9 P 3 C x amorphous alloys (x = 0-6) at a heating rate of 20 • C/min; (b) enlarged image of the A area in (a); (c) the changes in T x1 , T x2 and T x1 -T c with C content; and (d) TG curve of C-2 alloy ribbons.
, the appropriate substitution of Si with C not only enhances the T x1 and T c values of the alloy ribbon but also increases T x1 -T c .The C-2, C-3, C-4, and C-5 alloys exhibit higher T x1 -T c values, exceeding 120 • C, while the C-0, C-1, and C-6 alloys demonstrate lower T x1 -T c values.When Si is replaced with C, both T x1 and T c initially increase before decreasing.This phenomenon can be explained from two aspects: Firstly, taking into consideration the example of the C-0 alloy and C-2 alloy; after replacing Si with an appropriate amount of carbon (C) in a four-component Fe-Si-B-P-C system, it transforms into a five-component Fe-Si-B-P-C system which may have a microalloying effect resulting in a more complex configuration of the amorphous structure.Additionally, this atomic size difference enhances the thermal stability within the amorphous structure, resulting in a significant increase in T x1 from 475.3 • C to 485.5 • C, while T c shows only marginal improvement due to short-range order effects within amorphous alloys (from 360.3 • C to 362.2 • C).Consequently, there is an overall increase in the value of T x1 -T c .Secondly, taking into account examples such as the C-4 and C-6 alloys and following the excessive substitution of Si with C, the system transitions from a five-component Fe-Si-B-P-C system back to a four-component Fe-C-B-P system where any microalloying effects disappear potentially improving order degree within amorphous structures.Moreover, due to their larger size compared to C atoms, Si atoms have an increased propensity for impeding atomic diffusion motion.Consequently, a scarcity of Si atoms and an elevated level of order in the amorphous structure result to a pronounced decrease in its thermal stability.Specifically, T x1 is significantly reduced from 482.7 • C to 445.8 • C, while T c also experiences a reduction albeit within a narrower range than T x1 (from 123.0 • C to 107.4 • C).Therefore, T x1 -T c is also reduced.The thermal stability and non-isothermal crystallization behavior of Fe 82 Si 6−x B 9 P 3 C x amorphous alloy ribbons were further investigated by conducting DSC tests at different heating rates (10, 20, 30, and 40 K/min) for C-0, C-2, C-4, and C-6 alloys.The resulting DSC curves are presented in Figure

Figure 7 .
Figure 7. Annealing temperature (T a ) dependence of (a) H c and (b) µ e for Fe 82 Si 6−x B 9 P 3 C x amorphous ribbons annealed for 10 min.

Figure 9 .
Figure 9. Hysteresis loops of the Fe82Si6−xB9P3Cx amorphous alloys ribbons after annealing at suitable conditions.

Figure 9 .
Figure 9. Hysteresis loops of the Fe 82 Si 6−x B 9 P 3 C x amorphous alloys ribbons after annealing at conditions.

Table 1 .
The activation energies for the α-Fe phase crystallization process derived from the Kis curves.

Table 1 .
The activation energies for the α-Fe phase crystallization process derived from the Kissinger curves.

Table 2 .
The relationship between Bs, Hc, and μe with varying C content.

Table 2 .
The relationship between B s , H c , and µ e with varying C content.Composition B s (T) H c (A/m) µ e (@1 kHz)