Molecular dynamics simulations were performed using the LAMMPS29 package with the Fe-C MEAM potential developed by Liyanage et al.30. A 76 × 101 × 68 Å3 of the box consists of approximately 21,000 atoms of bcc-Fe (top side) and around 27,000 atoms of Fe3C (bottom side) with periodic boundary conditions. The Fe3C structure was simulated with orthorhombic unit cells with lattice parameters a = 5.09Å, b = 6.74Å and c = 4.53Å. The Baker-Nutting and the Pitsch of orientation directions between ferrite and cementite were applied. The Baker-Nutting and Pitsch are (001)cementite // (001)ferrite with [110]cementite // [100]ferrite, and (001)cementite // (101)ferrite with cementite // ferrite, respectively. The boxes were minimized by the conjugate gradient method31. After minimization, the two orientation directions were analyzed using the Open Visualization Tool (OVITO)32.
Figure 2 shows the volume fraction of precipitates, which JMatPro software version 12 predicted at 180 °C in all FeSi samples to estimate phases besides the ferritic phase upon aging at 180 °C. The carbon content variations significantly influenced the formation of cementite in the FeSi samples. The 0.41FeSi sample exhibited the highest volume fraction of cementite, followed by the 0.18FeSi sample. In contrast, the volume fraction of cementite in the 0.05FeSi sample could be considered negligible, as it remained below 0.5 vol%. This also accounts for other predicted carbides and precipitates, including MP and MnS. The temperature-dependent distribution of cementite is illustrated in Fig. 3, which shows a gradual increase in the amount of cementite as the aging temperature rises.
Figure 4 shows optical microstructure images and the grain size distribution of all the samples before aging. The phase form in the three samples was ferrite. All samples exhibited equiaxed grains along the TD-LD section. There is no significant difference in microstructure for TD and LD. It indicates that all grains are independent of either LD or TD. Note that no sign of precipitate was found in all three samples.
Figure 5 presents SEM images of all the samples along with their grain size distribution after aging. The aged samples showed no abnormal growth throughout the TD-LD section. The variation in the average grain size among the three samples was minimal (Table 2). Note that the aging temperature was considerably low for the grain growth of the ferrite.
Upon the aging process, precipitates (white dots) were found in the 0.41FeSi and the 0.18FeSi aged samples. However, the 0.05FeSi sample did not show any precipitates. In Fig. 5a, the precipitates in the 0.41FeSi aged sample were distributed almost homogeneously throughout the TD-LD section within the ferrite grain. The density of the precipitate observed in the 0.41FeSi sample was approximately 10/1000 µm, and the composition of the precipitate comprised Fe and C.
On the other hand, the 0.18FeSi aged sample exhibited a significantly lower number of precipitates compared to the 0.41FeSi sample, with a density of approximately 1.5/1000 µm, almost seven times lower than that of the 0.41FeSi sample. The composition of the precipitates was identified as (Fe, Al)C. The Al peak in this sample was significantly higher than that of the 0.41FeSi sample, as the 0.18FeSi sample had a higher Al content compared to the 0.41FeSi sample (Table 1). The SEM images of the three aged samples showed a correlation between the number of precipitates and the carbon content. The data also suggests that an increase in carbon content by two times leads to more than doubling the number of precipitates formed upon aging.
The distributions of crystal orientation derived from the neutron diffraction data for both the initial and the aged samples are presented in Figs. 6 and 7. Although the samples for both conditions are taken from the same component, differences in crystal orientation distribution may arise. The Φ, φ1, φ2 in the orientation distribution function (ODFs) are Euler angles which describe an orientation of a crystal. The ODFs presented in Fig. 6a-c and Fig. 7a-c are the φ2 = 0 and φ2 = 45 sections in which the distribution of cube texture, {110}<100 > Goss texture, {hkl}<100 > or LD//<100> (η-fiber), {100}< uvw > or ND//<100> (θ-fiber), {hkl}<110> (α-fiber) and {111}< uvw> (γ-fiber) among the initial and aged samples can be observed. The η-fiber comprises orientation components in which LD is aligned with < 100>, regardless of the plane orientation. The θ-fiber comprises orientation components in which ND is aligned with < 100>, while the in-plane directions may vary. The same interpretation approach can be applied to the α- and γ-fibers. Their density is then listed in Tables 3 and 4 to examine their trend among the 0.41FeSi, 0.18FeSi and 0.05FeSi samples of each condition, further correlating with their magnetic properties. The favorable orientation component is < 100>, which acts as an easy direction for magnetization in NO-FeSi. This component is advantageous when it lies within the sheet plane and aligns with the rolling direction. Therefore, the {100}<100 > cube is preferred in the NO-FeSi. Other orientations with < 100 > component belong to η-fiber and θ-fiber. The Goss texture is part of the η-fiber, while the cube texture appears in both the η- and θ-fibers.
Among the initial samples, their ODFs reveal variations in the density of the observed textures and fibers. A low density of cube and Goss textures is observed, while the η- and θ-fibers exhibit slightly higher densities compared to the cube and Goss textures, with variations across the three samples (Fig. 6a-c). The γ-fiber is more notable in the 0.41FeSi sample (Fig. 6a) but less significant in both the 0.18FeSi (Fig. 6b) and 0.05FeSi samples (Fig. 6c). For the α-fiber, its density is lower than that of the γ-fiber in the 0.41FeSi sample (Fig. 6a), but the densities of these two fibers are relatively similar in the 0.18FeSi and 0.05FeSi samples (Fig. 6b-c).
In Table 3, the 0.41FeSi sample exhibits the highest density of cube texture among the three samples. It also presents the highest θ-fiber density, while exhibiting the lowest η-fiber density. In contrast, the highest η-fiber density is observed in the 0.18FeSi sample, followed by the 0.05FeSi sample. Compared to the 0.41FeSi sample, the Goss texture in the 0.18FeSi sample is slightly higher, whereas in the 0.05FeSi sample, it is slightly lower. The density of the γ-fiber is lower than the density of the < 100 > components. The γ-fiber has a {111} plane, which presents the hard direction for magnetization. The density of both components in the γ-fiber is highest in the 0.41FeSi sample, significantly lower in the 0.18FeSi sample, and lowest in the 0.05FeSi sample. For the α-fiber, this fiber has a < 110 > direction, which is the medium direction for magnetization. However, one of its orientations, {001}<110>, can contribute to an increase in the easy direction intensity because the {001}<110 > component also belongs to the θ-fiber. The density of the α-fiber is much lower compared to the η- or θ-fiber across all three samples. In the 0.41FeSi sample, the α-fiber density is considerably lower than that of the γ-fiber. Conversely, in the 0.18FeSi and 0.05FeSi samples, the α-fiber density is higher than that of the γ-fiber.
The cumulative density for the initial samples indicates that the 0.41FeSi sample has a relatively high density of < 100 > components, with the θ-fiber ({100}< uvw> ) contributing the most, followed by the η-fiber ({hkl}<100> ). Within the η-fiber in the 0.41FeSi sample, the cube texture ({100}<100> ) is stronger than the Goss texture ({110}<001> ). In contrast, the 0.18FeSi sample exhibits a more pronounced η-fiber, with a lower cube texture but a higher Goss texture relative to the 0.41FeSi sample. The θ-fiber is the second highest density in the 0.18FeSi sample. A similar texture distribution is observed in the 0.05FeSi sample, except that the Goss texture exceeds the cube texture.
Figure 7 presents the density distribution of observed textures and fibers in the aged samples. The ODFs of the three samples reveal the presence of the θ-fiber and cube texture, with variations in their η-fiber and Goss texture (Fig. 7a-c). The γ-fiber is prominent in the 0.41FeSi (Fig. 7a) and 0.05FeSi samples (Fig. 7c), but less pronounced in the 0.18FeSi sample (Fig. 7b). For the α-fiber, all three samples exhibit a weaker α-fiber compared to their γ-fiber.
The density distribution of the < 100 > component in Table 4 shows that the θ-fiber has the highest density in all three samples. Among the cube and Goss textures, all three samples exhibit a lower Goss texture. The 0.18FeSi sample is characterized by a strong θ-fiber, followed by the η-fiber, with weak cube and Goss textures. The 0.41FeSi and 0.05FeSi samples show a similar sequence to the 0.18FeSi sample; however, the 0.05FeSi sample has a stronger θ-fiber but a weaker η-fiber compared to the 0.41FeSi sample. The Goss texture in the 0.05FeSi sample is the strongest among the three samples, while its cube texture is the second highest after that of the 0.18FeSi sample. The density of the γ-fiber in all three samples is significantly lower than that of the < 100 > component (Table 4). The strongest γ-fiber is observed in the 0.05 FeSi sample, particularly in the {111}<110 > component, which also contributes to the α-fiber. However, in the 0.41 FeSi and 0.18 FeSi samples, the {111}<112 > component exhibits a higher density than the {111}<110 > component. Among these, the 0.41 FeSi sample shows a higher overall γ-fiber density compared to the 0.18 FeSi sample. For the α-fiber (Table 4) the 0.05FeSi sample exhibits the highest density, primarily due to the high density of the {111}<110 > component, which is also observed in the γ-fiber. This sample also has the highest density of the {001}<110 > component, which contributes to the θ-fiber. A similar sequence is observed in the 0.41FeSi sample, which has the second highest α-fiber density. In contrast, the 0.18FeSi sample has the lowest α-fiber density, with the {001}<110 > component being the most prominent within this fiber.
For both the initial and aged samples, the 0.018FeSi sample exhibited the highest cumulative density of {hkl}<100 > and {100}< uvw > components, with contributions primarily from the η-fiber and θ-fiber in the initial and aged samples, respectively. In the initial sample, it is followed by the 0.05FeSi sample, which shows ~ 4% higher cumulative density of < 100 > components than the 0.41FeSi sample. On the other hand, in the aged sample, the 0.41FeSi sample exhibits the second highest cumulative density of < 100 > components after the 0.018FeSi sample, with a value ~ 3% higher than that of the 0.05FeSi sample.
The magnetic properties of the initial and aged samples are presented in Figs. 8 and 9, respectively. The plot of magnetization (M) against magnetic field (H) was presented in three different directions, LD, TD and ND, of each sample. The samples revealed a typical characteristic of a soft magnetic alloy such as a FeSi alloy, that is a narrow width of curves. Among the initial samples (Fig. 8a-c), the hysteresis curves do not show a significant difference in steepness. However, their technical saturation magnetization (Ms) varies in these three directions, especially between the 0.41FeSi and 0.18FeSi, with the 0.05FeSi becoming the lowest in each direction. The highest Ms values for the 0.41FeSi, 0.18FeSi, and 0.05FeSi samples are 1.89 T (in ND), 1.86 T (in TD), and 1.47 T (in ND), respectively. The variation in the direction of the highest Ms indicates the anisotropy of sample direction, suggesting that each sample has a specific direction in which magnetic saturation is less readily achieved.
Saturation magnetization is regarded as an intrinsic property that is largely insensitive to microstructural variations and is primarily dependent on the chemical composition of the alloy. The Ms between the 0.41FeSi and the 0.18FeSi samples is very minor. For the 0.05FeSi sample, it was reported that in Fe-based amorphous alloys, such as FeBSiCP, increasing C content enhances the saturation flux density (Bs), particularly when Si content exceeds 1 at%. Bs and Ms are proportionally related, with the relationship influenced by the permeability of the alloy. A similar effect has been observed in Fe-based high entropy alloys, such as FeSiBAlNi, where C addition contributes to an increase in Ms. Other alloying elements like Al in FeSiAl and AlCoNi HEA are reported to lower Ms. This may explain the lower Ms observed in the 0.05FeSi sample compared to the other two samples, since it has lower C and high Al relative to the other two samples.
The magnetization curves of the aged samples measured along three different directions are presented in Fig. 9. No significant differences in steepness are observed among the aged samples. The highest Ms values are 1.81 T (LD), 1.76 T (ND), and 1.52 T (LD) for the 0.41FeSi, 0.18FeSi, and 0.05FeSi samples, respectively. Between the 0.41FeSi and 0.18FeSi samples, the Ms values in LD and TD exhibit variation, with the 0.41FeSi sample displaying the highest Ms in the LD direction, while the 0.18FeSi sample exhibits the highest Ms in the TD direction. The 0.05FeSi sample consistently exhibits the lowest Ms across all three directions.
The increase in Ms observed in the aged samples, particularly in LD and in all directions of the 0.05FeSi sample, may be associated with rearranging internal atomic defects. In nanocrystalline FeSiCuNbB alloys, it has been reported that aging at 240 °C for up to 240 h can slightly enhance Bs as a result of internal stress relaxation and reduced domain wall pinning, without altering the grain structure. This improvement is attributed to the rearrangement of atomic-scale defects and enhanced mobility of magnetic domains. A similar mechanism may also occur in fully annealed FeSi alloys, where low-temperature aging could contribute to the redistribution of point defects and subtle modifications to domain structures, thereby subtly enhancing magnetic response.
It is known that the easiness of each sample to be magnetized, also known as permeability (µ), can be related to the magnetic field strength (H) and the magnetization (M) obtained from the samples' hysteresis curves. This correlation can be expressed through Eq. (1) as follows:
Hence, permeability is proportional to the slope of the linear part of the curve. The calculated slope of all samples is presented in Fig. 10. In Fig. 10a, LD exhibits the steepest slope compared to the other two directions for all initial samples. Among the three samples, the 0.18FeSi sample shows the highest value, followed by the 0.41FeSi and 0.05FeSi samples. These results suggest that the 0.41FeSi and 0.05FeSi samples are harder to magnetize than the 0.18FeSi sample. A similar trend is observed in the aged samples, with the exception that the 0.05FeSi sample exhibits a steeper slope than the 0.41FeSi sample, as shown in Fig. 10b. LD continues to exhibit the steepest slope among the three directions in the aged samples. This observation is relevant to practical applications, as LD corresponds to the teeth region, where easier magnetization in this direction is particularly desirable. Figure 10c presents the average calculated slope for both the initial and aged samples, derived from the three directions for each sample. The average values show that the 0.18FeSi sample exhibits the steepest slope in both the initial and aged samples. The 0.05FeSi sample shows an increase in its average slope compared to the initial, while the 0.18FeSi sample exhibits only a slight decrease, remaining close to its initial value. The 0.41FeSi sample, however, shows a more pronounced reduction in average slope after aging, resulting in a flatter curve that suggests increased difficulty in magnetization.
For soft magnetic alloys, having a lower coercivity (Hc) is preferable as it leads to lower losses during the demagnetization process. Soft magnetic materials typically exhibit coercivity values lower than 1000 A/m. This is consistent with the Hc values of all samples presented in Fig. 11. The Hc values vary across the three directions, however, in LD, both in the initial (Fig. 11a) and aged (Fig. 11b) samples, the 0.41FeSi sample consistently exhibits the highest coercivity, whereas, the 0.18FeSi and 0.05FeSi samples show lower Hc, with no significant difference observed between the two. The average coercivity (Hc) derived from the three directions for both the initial and aged samples is presented in Fig. 11c. In the initial condition, Hc exhibits an inverse relationship with the calculated slope shown in Fig. 10c. However, in the aged condition, the 0.41FeSi sample shows the highest Hc, followed by the 0.18FeSi sample, while the 0.05FeSi sample exhibits the lowest Hc, in which case the value is lower than in the initial sample. The Hc trend in the aged samples differs from that of the initial samples, particularly for the 0.18FeSi sample. This deviation may be attributed to the presence of precipitates. The formation of precipitates increases Hc due to domain wall pinning, which enhances losses associated with the demagnetization process. In the 0.18FeSi sample, the precipitate density appears to influence coercivity (Fig. 11c) but has an insignificant effect on permeability (Fig. 10c). This is not the case for the 0.41FeSi sample, where the higher precipitate number density impacts coercivity and permeability. These observations suggest that the density of precipitates primarily affects coercivity and has minimal impact on permeability unless it exceeds a certain threshold.
Considering that the magnetization process comprises wall movement and domain rotation, the formation of particles and the presence of a preferred orientation owing to the aging process will likely affect the magnetic properties of the samples. For an FeSi sheet, the dominant domain during the movement process is the 180° stripe. The driving force (F) for the 180° stripe domain to move correlates to the angle between the crystal direction, < 100 > direction, and the external magnetic field (H) direction. The cosines of this angle are called practical orientation factors (m). As previously calculated for polycrystals, the average orientation factor () considers 936 subspaces, and the orientation density () is the weight coefficient. The value of can be obtained from the ODF data. The correlation among F, m, and can be expressed as in Eqs. (2) and (3):
where is the vacuum permeability, and M is the domain magnetization vector. This suggests that a sample with a high density in the easy magnetization direction < 100 > is likely to high driving force for domain wall motion when an external field is applied.
The hysteresis curve for the initial samples, shown in Fig. 8, along with the calculated slope plots in Fig. 10a and c, indicates that the 0.18FeSi sample has the steepest curve. The orientation density distribution in Table 3 further reveals that the 0.18FeSi sample has the highest cumulative density of {hkl}<100 > and {100}< uvw > components, followed by the 0.05FeSi and 0.41FeSi samples. Between the 0.41FeSi and 0.05FeSi samples, there is only a minor difference in the cumulative density of the < 100 > components. The 0.05FeSi sample has a slightly higher value, exceeding that of the 0.41FeSi sample by 0.97. However, a slight decrease in the calculated slope is observed for the 0.05FeSi sample compared to the 0.41FeSi sample, with reductions of 0.83 in LD, 0.88 in TD, and 0.60 in ND. This may be attributed to the highest density of cube texture in the 0.41FeSi sample. The cube texture ({100}<100> ) is considered the most favorable orientation for achieving good magnetization, as the < 100 > easy magnetization direction lies both in the sheet plane and along the component teeth direction (LD).
In the hysteresis curve, domain rotation becomes dominant beyond the linear region with steep slope, where a large magnetic field (H) is required to produce only a slight increase in magnetization (M) as it approaches saturation. The magnetization process continues until the direction of M in each domain parallels the applied field. The anisotropy energy (E) of a cubic crystal is required to rotate a domain in a particular [uvw] direction is described in Eq. (4):
where K, K, and K are the constants for certain materials at a given temperature. α, α, and α are the cosines of angles a, b, and c between the M and crystal axes, respectively. The values of a, b, c, α, α, and α for [100], [110], and [111] are listed in Table 5.
For iron, K is positive. Therefore, E[100] < E[110] < E[111] when K is zero. This indicates that the < 100 > direction requires the lowest energy for M to rotate. Therefore, for the sample with a higher density in the < 100 > direction, less H is required to overcome the energy of anisotropy, leading to a higher saturation magnetization compared with the sample with a lower < 100 > density. Among the initial samples, the 0.18FeSi sample, which exhibited the highest cumulative density of < 100 > components, showed a high Ms (2.31 T). Interestingly, the 0.41FeSi sample, with a slightly lower cumulative density of < 100 > components than the 0.05FeSi sample (by ~ 3%), achieved the highest Ms (2.32 T) among the three. This may be attributed to its stronger cube texture ({100}<100> ), which offers optimal alignment for domain rotation. These results suggest that, in addition to the quantity of < 100 > components, the specific crystallographic alignment associated with the cube texture plays a crucial role in enhancing magnetic saturation.
In the aged samples, the steeper slope compared to the initial condition, as shown in Fig. 10c, is influenced by the crystallographic texture listed in Table 4. Among the three samples, the 0.41FeSi sample exhibits the highest cumulative density of the < 100 > components, followed by the 0.18FeSi sample, with a slightly lower value observed in the 0.05FeSi sample. However, the trend in the calculated slope differs from that of the initial samples, likely due to the presence of precipitates in samples with higher carbon content, which interfere with the magnetization process. The slope in the 0.41FeSi sample is the lowest among the aged samples and is even lower than that of its initial state. In contrast, the 0.18FeSi sample still exhibits the highest slope, showing minimal change from its initial value, likely due to an approximately 30% increase in the cumulative density of the < 100 > component. Unlike coercivity, the slope in the 0.18FeSi sample appears less influenced by the presence of precipitates, possibly because the precipitate density remains relatively low.
The observed changes, both in slope and coercivity for the 0.41FeSi sample, and in coercivity alone for the 0.18FeSi sample, indicate deterioration in the magnetic properties of the aged samples. These variations are strongly influenced by the carbon content, which affects the number of precipitates formed during the aging process. The number of precipitates formed after aging in this sample was the largest, with an average size of approximately 2 μm (Fig. 5a). The 0.18FeSi sample exhibited precipitates with an average size of 1.6 μm after the aging process (Fig. 5b). However, no precipitates were observed in the 0.05FeSi sample, as shown in Fig. 5c. This sample exhibits a steeper slope than the 0.41FeSi sample but remains flatter than that of the 0.18FeSi sample. Although it has a similar < 100 > component density to the 0.41FeSi sample, its higher γ-fiber density, associated with hard magnetization directions, likely impedes magnetization. Nevertheless, a higher cumulative density of the < 100 > component relative to the initial sample contributes to the steeper slope.
The relationship between precipitates and texture development in FeSi steels is quite complex. Precipitates play a significant role in controlling grain size and considered beneficial throughout the manufacturing process. The coarsening process does not occur uniformly, rather, it proceeds incrementally from regions where precipitates are located at high-energy grain boundaries. Therefore, if grains with certain crystallographic orientation are surrounded by high-energy grain boundaries, they will coarsen first, while other grains remain pinned. This behavior likely strengthens certain orientations, thereby influencing texture development in the sample, resulting in a more pronounced final texture.
The formation of precipitates requires crystallographic coherency between the precipitate and the matrix to minimize mismatch and overcome the nucleation barrier upon aging. In FeSi steel, the orientation relationships (OR) for cementite and the ferrite matrix may conform to either the Baker-Nutting (BN) or Pitsch (P) models. The specific relationship is influenced by factors such as chemical composition and processing parameters, including aging temperature and cooling rate. Using a molecular dynamics simulation, Fig. 12 shows the BN-OR (Fig. 12a-c) and P-OR (Fig. 12d-f) between cementite and bcc-Fe. Note that iron and carbon atoms are shown in orange and grey, respectively. The BN-OR is defined by the alignment of (001) // (001) with [110] // [100]. Figure 12a shows ferrite (top side) and cementite (bottom side) from the X direction, which is parallel to the [100] direction of ferrite, while Fig. 12b and c show ferrite and cementite, respectively, along Z direction, which is parallel to [001] of ferrite and cementite. On the other hand, the P-OR is characterized by the alignment of (001) // (101) and // . Figure 12d shows ferrite and cementite from [direction of ferrite (X direction). Moreover, Fig. 12e and f show ferrite and cementite, respectively, along the Z direction, which is parallel to the [101] direction of ferrite and [001] of cementite. These orientation relationships are consistent with previous studies on anisotropic magnetic aging, which indicate a preference for cementite to precipitate on the {100} ferrite plane. Additionally, another potential preferred site for precipitation is along the {110} planes of the matrix.
Since in rotating magnetic field applications the preferred texture corresponds to planes with a ⟨100⟩ direction, it is important to suppress orientation relationships that disrupt this alignment. Although the BN-OR is frequently observed, it is energetically less favorable due to its higher interfacial distortion, and it promotes cementite precipitation along the {100} ferrite planes, which may interfere with magnetic anisotropy. On the other hand, P-ORs, e.g. Pitsch-Schrader and Pitsch-Petch, are more energetically favorable and tend to form under rapid cooling or deformation. However, these relationships often lead to the formation of {110}⟨111⟩ texture components, which are less favorable for magnetic performance. The relatively higher density of several components within LD//⟨110⟩ and ND//⟨111⟩ observed in the 0.41FeSi aged sample, compared to the 0.18FeSi aged sample, may suggest an increased tendency for cementite to align with Pitsch-type orientation relationships. Given that P-OR is typically associated with {101} or {110} habit planes and growth along ⟨111⟩ directions, the observed texture could reflect a microstructural environment favorable to such alignment. Furthermore, grain boundary character may also influence this behavior, in which, high-angle grain boundaries (HAGBs) can act as favorable sites for incoherent or misaligned precipitates (e.g., BN-OR), while low-angle boundaries (LAGBs) may support the formation of P-OR by offering aligned, lower-energy interfaces. Therefore, careful adjustment of processing parameters is essential to limit the formation of both BN-OR and P-OR, thereby enhancing the development of magnetically favorable ⟨100⟩ textures.
Coarsening of precipitates to reduce domain wall hindrance appears to be effective primarily for sulfides and oxides. Furthermore, precipitate coarsening within the grain seems to have a more pronounced influence on magnetic properties than those located at grain boundaries. A noticeable decrease in the slope of the linear region of the hysteresis curve in the aged 0.41FeSi sample corresponds to the formation of larger precipitates, which increased in size from 1.6 to 2 μm as the carbon content increased. Lower precipitate density results in a less pronounced flattening of the curve, leading to a smaller decrease in slope. In this region, the magnetization mechanism is dominated by domain wall motion. The 0.41FeSi sample becomes more difficult to magnetize after aging due to its higher precipitate number density compared to the other samples. In contrast, although the 0.18FeSi sample also contains precipitates, they are smaller in size and lower in number density. Its high < 100 > component density contributes to the observed behavior in its hysteresis curve after aging, which shows that the sample is easier to magnetize but more difficult to demagnetize compared to the initial sample. This suggests that favorable crystal orientation can enhance magnetization, but its beneficial effect is limited when the precipitate density exceeds a certain threshold.