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Article

Effects of the Substitution of B and C for P on Magnetic Properties of FePCB Amorphous Alloys

by
Shuwei Lu
1,2,*,
Xuan Chen
1,2 and
Qiqi Zheng
1,2
1
Xinjiang Key Laboratory of Solid State Physics and Devices, Xinjiang University, Urumqi 830046, China
2
School of Physics Science and Technology, Xinjiang University, Urumqi 830046, China
*
Author to whom correspondence should be addressed.
Metals 2024, 14(7), 757; https://doi.org/10.3390/met14070757
Submission received: 16 May 2024 / Revised: 23 June 2024 / Accepted: 24 June 2024 / Published: 26 June 2024
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Abstract

:
In the present study, first-principles molecular dynamics simulations were employed to study the effects of small amounts of B and C substituted for P on the structure and magnetic properties of Fe80P13C7, Fe80P10C7B3, and Fe80P8C9B3 amorphous alloys. A small amount of B and C replacing P atoms increases the icosahedral structure of the amorphous alloys, especially the increase in the regular icosahedral structure. The saturation magnetization of the three kinds of amorphous alloys gradually increases with the addition of B and C atoms, and the results of experimental and simulated calculations show consistent trends. The substitution of P atoms by B and C atoms leads to the aggregation of Fe atoms, which increases the magnetic moment of the iron atoms. In addition, the improvement of local structural symmetry may be one of the reasons for the increase in saturation magnetization of amorphous alloys. The substitution of a small number of B and C atoms plays an important role in improving the saturation magnetization of the amorphous alloy, which has a certain guiding significance for the development of amorphous alloys with excellent soft magnetic properties.

1. Introduction

Compared with crystalline alloys, amorphous alloys do not exhibit the translational symmetry of the body structure and do not have grain boundaries. Therefore, it exhibits abnormalities in its mechanical, electrical, and other characteristics, which has aroused great interest in its application. The soft magnetic properties of amorphous alloys have been studied earlier in academic research and industrial applications, and they are widely used in the energy and industrial fields, such as transformers, inductors, magnetic shielding doors, and motors. Compared to the traditional soft magnetic materials, Fe-based amorphous alloys have excellent soft magnetic properties, such as high saturation magnetization (Ms), high magnetic permeability, ultralow coercivity (Hc), and low core loss [1,2,3], e.g., Ms of the Fe–M–(P, C, B, Si) (where M = Ga or Mo) bulk metallic glass alloys are in the range of 1.10–1.53 T, depending on the Fe content and the type of metalloid element. The Hc is less than 3 A/m, and the effective permeability at 1 kHz is between 10,000 and 50,000 [1]. At present, with the continuous development of science and technology, the demand for soft magnetic materials in various fields is also increasing. Therefore, developing Fe-based amorphous alloys with excellent soft magnetic properties has become a popular research topic [4,5,6,7,8,9,10].
With the in-depth exploration of the structure, mechanical, and magnetic properties of amorphous alloys, the full picture of amorphous alloys is gradually being recognized by researchers. Amorphous alloys can usually be divided into three kinds of categories: transition metal-metalloid amorphous alloys, rare earth-transition group amorphous alloys, and transition metal-transition metal amorphous alloys. Among them, amorphous alloys composed of transition metals and metalloids are also the most abundant and widely used today. The Fe-based amorphous alloys are composed of approximately 80% of transition metals and 20% of metalloids. The metalloids mainly include P, B, C, Si, Ge, and other elements. Although the concentration of these metalloids is low, they play an indispensable role in the stability, forming ability, and excellent magnetic properties of the amorphous alloys.
Researchers have enhanced the magnetic properties of Fe-based amorphous alloys by changing the composition and proportion of transition metals and metalloid elements. Some investigators have improved the magnetic properties of Fe-based amorphous alloys by varying the content of transition metals, such as increasing the Fe content of amorphous alloys [11,12,13] or adding Co [14,15,16]. Some researchers have simultaneously changed the ratio of transition metals and metalloids to enhance the magnetic properties of alloys [17,18,19]. There are also researchers who only improve the magnetic properties of amorphous alloys by changing the composition of metalloids [20,21,22,23,24,25,26,27]. Xu et al. [21] investigated the microstructure, magnetic properties, and bending ductility of Fe85Si1.5−xB9Cu0.5P4Cx(x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) alloy ribbons with the high Fe content. The partial substitution of Si by C improved the glass forming ability (GFA) of the alloys and increased the maximum thickness of glassy from 19 μm to 25 μm. The addition of C raises the first crystallization temperature, while the reduction of Si slightly decreases the second crystallization temperature. In the amorphous state, the Ms and Hc decrease slightly with the increase of C, from 1.58 T and 10.0 A/m to 1.57 T and 9.3 A/m, respectively. After the optimal annealing treatment, the highest Ms of Fe85Si1.4B9Cu0.5P4C0.1 nanocrystalline alloy is 1.93 T, and the lowest Hc is 5.8 A/m. Li et al. [23] prepared high-Fe alloys with the nominal composition of Fe85B11-xCxP4 (x = 0, 0.5, 1, 2, 3, 4) by the melt-spun method and investigated the effects of the C content on the glass formation, crystallization behavior and magnetic properties of Fe–B–C–P alloys. The results show that the completely amorphous structure is only formed in Fe85B9C2P4. The α-Fe phase gradually appears with the continuous addition of C. The appropriate annealing temperature and time can significantly increase the Ms and reduce the Hc. Fe85B9C2P4 amorphous alloy annealed at 698 K for 600–1200 s shows excellent soft magnetic properties, typical Ms of about 1.51–1.53 T, Hc of about 5.0–5.1 A/m. The low cost of raw materials and good soft magnetic properties make the alloy have broad application prospects. Moreover, Shi et al. [24] systematically studied the effect of a small amount of C replacing B on the magnetic properties of FeBCSiP amorphous alloys. The results indicate that the addition of C can significantly increase the Ms of FeBCSiP amorphous alloys and the magnetic flux density at 800 A/m. The Ms of the amorphous alloys increased from 1.61 T (Fe83B13Si3P1) to 1.65–1.71 T (Fe83B13-xCxSi3P1, x = 1.5, 2, 3, 4, 5). The Fe83B10C3Si3P1 amorphous alloy has excellent soft magnetic properties with a high Ms of 1.71 T and a low Hc of 1.5 A/m. The research has shown that the addition of C leads to an increase in the alloy density, and the weakening of metal-sp/metal-d binding is the main reason for the increase in Ms. The above research indicates that the addition of metalloids can improve the soft magnetic properties of Fe-based amorphous alloys and provide an effective approach for the development of amorphous alloys with the excellent soft magnetic properties.
The improvement of the soft magnetic properties of amorphous alloys by replacing metalloids has gradually attracted increasing amounts of research attention. Zuo et al. [22] successfully prepared Fe80(P, C, B)20 bulk metallic glass by combining flux treatment and J-quenching technology. The results showed that using B instead of C or P and C instead of P significantly increased the Ms and Curie temperature of the Fe80(P, C, B)20 amorphous alloys. To determine why replacing a small number of metalloid elements can improve soft magnetic properties, they conducted a more in-depth analysis based on the magnetic valence theory. However, they found that the magnetic valence could not well explain the effect of metalloids on the magnetic properties of amorphous alloys. Studies have shown that magnetic valence theory cannot well explain the soft magnetic properties of Fe–M (metalloid) amorphous alloys [28]. Therefore, the mechanism underlying the effect of metalloids on the soft magnetic properties of amorphous alloys needs further study.
With the advent of computer simulation, researchers have used computers to simulate a large number of disordered structures and reached a conclusion consistent with that of experiments [29,30,31,32]. The process of computer simulation starts from the microstructure of atoms, simulates the alloy from high temperature to low temperature, obtains the amorphous structure through a reasonable construction model, and finds the correlation between the structure and physical properties. In 2018, Chen et al. [29] studied the structure, magnetic, and electronic properties of Fe82Si4B10P4 metallic glass by ab initio molecular dynamics methods. The results show that the saturation flux density obtained by simulations is close to the values obtained by the experiments. The Fe atom around P has a large magnetic moment, and P plays an important role in improving Ms. In 2022, Jiang et al. [30] investigated the GFA, thermodynamic properties, soft magnetic properties, and atomic structures of Fe80−xSi5−xB15 (x = 0–4) amorphous alloys via ab initio molecular dynamics simulations and experiments. The simulation results show that interactions between the Fe and metalloid (M = Si, B) atoms are strong and that a proper Si addition enhances the GFA, thermal stability, and magnetic performance of the alloys. Fe82Si3B15 is the best component to balance the Ms and GFA. The prediction is confirmed by the experimental observations. In 2023, Ma et al. [32] used experimental methods and ab initio molecular dynamics to study the effects of the addition of Y and Nb on the thermal stability, GFA, and magnetic softness of Co75B25 metallic glass (MG). The calculation results show that the B-centered prism units are the primary structure-forming units connected by vertex-, edge-, and face-shared atoms, while the Co-centered units tend to be connected to the Co/B-centered units by intercross-shared atoms. The addition of Y and Nb not only plays the role of connecting atoms but also increases the strength of bonds and the fraction of icosahedral-like units. In addition, the improvement of structural stability and homogeneity leads to enhanced magnetic softness. These studies show that computer simulation has gradually become an effective means to study amorphous alloys and provides a useful reference and guidance for the development of amorphous alloys with excellent soft magnetic properties.
Currently, there is relatively less research on the effect of the addition of metalloids on the magnetic properties of amorphous alloys. The effects of small amounts of B and C substituted for P on the magnetic properties of FePCB amorphous alloys were studied systematically by the method of molecular dynamics methods. By studying the geometric and electronic structures of amorphous alloys, the intrinsic correlation mechanism between the structure and magnetic properties is explored.

2. Computational Methods

First-principles molecular dynamics studies were conducted on Fe80P13C7, Fe80P10C7B3, and Fe80P8C9B3 (subsequently simplified as P13, P10, P8) amorphous alloys by using density functional theory (DFT) and the plane wave pseudopotential method [33,34]. The simulation was realized in the Vienna ab initio simulation package (VASP) code (VASP.5.4.4, University of Vienna, Wien, Austria). The NVT (constant number, volume, temperature) was implemented by controlling the temperature with the Nose thermostat [35]. The velocity Verlet algorithm was used to solve Newton’s equation of motion with a time step of 3 fs. Vanderbilt-type ultrasoft pseudopotential and generalized gradient approximation (GGA) [36] with the PW91 exchange-correlation functional were used in the DFT calculations. The value of plane-wave cutoff energy was set to 450 eV. Only the Γ point was used to sample the Brillion zone in the simulation of the amorphous structure because of the short-range disordered structure of the amorphous material.
Our simulated supercell contains 200 atoms, including 160 Fe atoms and 40 metalloid atoms (P, B, and C). The side length of the initial cell with the periodic boundary condition was estimated by the experimentally measured density of the FePCB amorphous alloy at room temperature [22]. Initially, these Fe, P, C, and B atoms were randomly placed in a cubic box. The system was then melted for 3 ps at a high temperature of 1600 K, and the average external pressure of the system was reduced to zero by fine-tuning the size of the box. Compared with previous literature [31,32], a cooling rate (1.67 × 1014 K/s) of the same order of magnitude was chosen to carry out the research. The final temperature was 300 K. The equilibrium state was calculated at 300 K to obtain the final amorphous structure, and the averaged structural quantities were collected using 1000 configurations of the final molecular dynamics run, such as partial pair distribution functions (PPDFs), total pair distribution functions (TPDFs), Voronoi polyhedra (VPs), coordination number (CN) distribution, and local chemical environment.
The magnetic properties of amorphous alloys were studied through the analysis of electron structure and charge distribution. Electron spins were taken into account throughout the simulation. The calculation of the density of states (DOS) gives the spin-up and spin-down electron distributions of the amorphous alloy elements. The charge gain and loss of each amorphous alloy atom are given by the Bader charge [37]. Several groups of structures are generated using the same simulation method. The results are all consistent. Finally, one of the simulated calculations is randomly selected for analysis.

3. Results and Discussion

Figure 1 shows the Ms obtained from simulated calculations and experiments [22]. The experimental results show that with a small amount of B atoms replacing P, the Ms increases from 1.48 T to 1.50 T. Then, by replacing P with a small amount of C atoms, the Ms of P8 amorphous alloys is 1.52 T. The Ms of the three kinds of amorphous alloys gradually increases as a substitute for small amounts of B and C atoms for P. The Ms obtained from the simulated calculations changes from 1.48 T to 1.58 T, and the trend with the two changes is in good agreement, which indicates the validity of the simulations. Moreover, why does this phenomenon occur? We will conduct a preliminary analysis of the basic properties of the constituent amorphous alloy elements.
Table 1 shows the molar mass, atomic radius, electronegativity, and outer electron distribution of four elements (Fe, P, C, and B). The molar mass of Fe is the highest, while the molar mass of metalloid atoms (P, C, B) is relatively small and gradually decreases, and the B atom has the lowest molar mass. From the perspective of the atomic radius, Fe atoms have the largest radius, and C atoms have the smallest radius. The radius ratios of P, C, and B atoms to Fe atoms are 0.88, 0.62, and 0.73, respectively. The values indicate that the radii of the P atoms are relatively close to that of the Fe atoms, while the radii of the B or C atoms are smaller than those of the Fe atoms. Among the four elements, C has the highest electronegativity, while Fe has the lowest electronegativity. The electronic arrangement shows that the Fe atom has the highest number of valence electrons, with a quantity of 8. In addition, the B atom has the lowest number of valence electrons. Based on the above, the properties of the basic elements constituting amorphous alloys are understood. The properties of these elements affect the structure and magnetic properties of amorphous alloys. The following is a specific analysis and discussion from three aspects to explore why the Ms gradually increases with the addition of a small amount of B and C atoms and to determine the intrinsic connection between the structure and the magnetic properties.

3.1. The Effect of Atomic Size

3.1.1. Partial Pair Distribution Functions

To investigate the effect of different atom sizes on the atomic arrangement of amorphous alloys. PPDFs are analyzed, which is the probability of other atoms appearing within a certain distance from the center atom. It can represent the arrangement of neighboring atoms within a certain range. Figure 2a–c show the PPDFs of three kinds of amorphous alloys at 300 K. Although small amounts of B and C atoms are used to replace P, the positions of the first peaks gFe-Fe(r), gFe-P(r), gFe-C(r), and gFe-B(r) are nearly unchanged, and their position size relationships are rFe-Fe(r) > rFe-P(r) > rFe-B(r) > rFe-C(r). The main reason is that the Fe content accounts for 80%, and the radii of the Fe atoms are the largest, followed by the radii of the P atoms, while the radii of the B or C atoms are relatively small. A small amount of substitution did not affect the position of the first peak between Fe and other atoms. From the graph, it can also be observed that the changes in gP-P(r) of the three kinds of amorphous alloys are complex and irregular after a small amount of P atoms are replaced. However, the position range of the first peak of gP-P(r) in the three kinds of amorphous alloys is approximately 3.5–4.0 Å. The probability of interaction between P and P atoms is relatively small. After a small amount of P is replaced, the positions of the first peak of gC-C(r) in the three kinds of amorphous alloys become 2.8 Å, 3.4 Å, and 3.7 Å. This result indicates that the possibility of interactions between C atoms is relatively low, which is also a manifestation of solute-to-solute avoidance. For the P10 and P8 amorphous alloys, the first peak position of gB-B(r) gradually decreases (5.4 Å, 2.75 Å), indicating an increasing possibility of interaction between B and B atoms, forming B–B diatoms.

3.1.2. Chemical Element Preference

The chemical preference of the three kinds of amorphous alloys was investigated analytically, that is, the possibility of other atoms preferring to appear around the other atoms. Figure 3 shows the probability of four elements (Fe, P, C, and B) appearing in other atoms at 300 K. The first peak of the TPDFs is considered the atomic bonding distance. The percentages of Fe atoms near the Fe atoms in the three kinds of amorphous alloys are 81.4%, 81.6%, and 81.9%, respectively. This indicates the aggregation of Fe atoms, which is beneficial for the formation of amorphous alloys. With the replacement of B and C atoms, the degree of aggregation of Fe atoms slightly increases. The probability of Fe atoms appearing around other atoms (P, C, and B atoms) is greater than that of Fe atoms appearing around Fe atoms. The probability of Fe atoms appearing near P is the highest (93.1–94.3%), indicating that Fe atoms are inclined to appear around P atoms. The possible reason is that the radii of the P atom are larger than that of the B or C atoms but closer to that of the Fe atom. Therefore, the interaction between the Fe and P atoms requires a certain distance, which will accommodate more Fe atoms around P in this region. As the number of P atoms gradually decreases, the probability of P atoms appearing around Fe atoms gradually decreases, while the probability of C atoms appearing around Fe atoms gradually increases, and the probability of B atoms appearing around Fe atoms remains unchanged. The probability of P, C, and B atoms appearing around P, C, and B atoms is relatively low, which is consistent with the analysis of the PPDFs. This result indicates mutual avoidance between solute atoms.

3.1.3. Voronoi Polyhedral and Coordination Number Distribution

The Voronoi polyhedron is analyzed here, which is the smallest closed convex polyhedron enclosed by a vertical bisector of the line connected to the central atom and its neighboring atoms [40]. These indices are mainly represented by four indices <n3 n4 n5 n6>, where ni is the number of i-faces of a polyhedron. Figure 4 shows the main VP distributions centered on atoms (Fe, P, C, or B) in the P13, P10, and P8 amorphous alloys. From Figure 4a, it can be concluded that the Voronoi polyhedron centered on Fe is mainly composed of a distorted icosahedron, with Fe located at the center of the distorted icosahedron and other atoms distributed around it, forming a distorted icosahedron structure. Among them, <0 1 10 2> accounts for the largest proportion, while other distorted icosahedral structures are <0 1 10 3>, <0 2 8 2>, and <0 2 8 4>. Similarly, icosahedral structures have also been reported in previous literature [41]. There is also a regular icosahedral structure <0 0 12 0>. Other polyhedral distributions include <0 3 6 4>, <0 3 6 5>, <0 3 8 2>, <0 3 8 3>, and <0 1 9 3>. Here, as a small number of B and C atoms replace P atoms, the numbers of icosahedra (distorted and regular icosahedra) in the amorphous alloy gradually increase. The regular icosahedra structure has high symmetry, which indicates that replacing larger radius P atoms with B and C atoms increases the local structural symmetry of the amorphous alloys. This may be due to the smaller radii of B or C atoms, which tend to appear in the gap positions. This causes the larger-radius P atoms to be replaced, and the B and C atoms occupy those positions, which increases the distribution of the central atomic polyhedron. Figure 4b shows the distribution of VPs centered on P atoms, with distorted icosahedral structures (<0 2 8 0>, <0 2 8 1>, <0 2 8 2>) and triangular prismatic structures (<0 3 6 1>, <0 3 6 3>) being the main distributions. The distorted icosahedral structure distribution indicates that the P atom also has a local environment similar to that of the Fe atom or is in a substitutional position for the Fe atom. The Voronoi polyhedron centered on the C atom is mainly distributed in <0 4 4 0> Archimedean antiprisms and <0 3 6 0> tri-capped trigonal prisms (TTPs), as shown in Figure 4c. Due to the small number of B atoms, the polyhedral distribution of B atoms is mainly composed of <0 3 6 0> TTPs and <0 2 8 0> distorted icosahedra, as well as other distributions such as <0.4 4 0>, <0 2 7 0>, and <0 3 5 0> polyhedra.
The CN distributions of four atoms in the three kinds of amorphous alloys were calculated by using the VP distribution. The distributions of CN centered on an atom in the three kinds of amorphous alloys are shown in Figure 5. The CN of the Fe atom in the three kinds of amorphous alloys is mainly distributed between 13 and 14, as shown in Figure 5a. This is consistent with the VP analysis of Fe atoms. The icosahedral structure centered on Fe atoms also has a distribution of atoms between approximately 13 and 14. As B and C atoms replace P atoms, the number of Fe atoms with a CN of 14 in the P8 amorphous alloy increases significantly. This is mainly because the atomic radii of B and C are smaller, and an increase in the number of atoms appears in the gap positions. Therefore, the number of atoms with a CN of 14 around Fe atoms increases. The CN centered on P is mainly distributed between 10 and 11 (Figure 5b). As P atoms gradually decrease, the number of P atoms with coordination numbers of 11 or 12 gradually increases, which indicates an increase in the number of atoms appearing around the P atoms. The number of coordination atoms centered on C is mainly 8–9 (Figure 5c), and it is also found that with the substitution of B and C atoms, the distribution of CN (8) centered on C is the largest in the P8 amorphous alloy. The CN centered on B is mainly 9–10 (Figure 5d), and the distribution range is increased. The main reason is that the radii of the B or C atoms are smaller than those of the P atoms. The CN of the corresponding small atom slightly increases after replacing the P atoms.
Through the above analysis, the effect of the atomic radius on the atomic arrangement of amorphous alloys is understood. As atoms with a smaller radius (B or C atoms) replace atoms with a larger radius (P atoms), it can be concluded that the replacement of a smaller atomic radius results in the presence of more Fe atoms around iron, increasing the symmetry of the local structure and the distribution of coordination numbers around some atoms. The distribution of these atoms inevitably affects the magnetic properties of amorphous alloys.

3.2. The Effect of Atomic Electronegativity

Crystals have periodic structural characteristics, and their potential field is a periodic function. However, the amorphous materials do not exhibit periodic structural characteristics, because they are short-range ordered. Thus, the potential field in the amorphous materials is also nonperiodic. The probability of electrons appearing around the amorphous atoms is unequal. The distribution of electrons from atom to atom is also uneven. The charge distributions of the three kinds of amorphous alloys were calculated through Bader charge analysis, which is the division of electrons owned by each atom based on a surface with a charge density gradient of zero. Table 2 shows the charge distributions of the four atoms in the P13, P10, and P8 amorphous alloys. The average charge distribution of the Fe atom in the three kinds of amorphous alloys is approximately 7.8 e. The number of electrons lost is approximately 0.2 e, indicating that Fe atoms lose electrons with positive charges, while P atoms obtain electrons with negative charges and obtain electrons with approximately 0.63 e on average. The C or B atoms also have negative electrons on average, which is consistent with the electronegativity of the four atoms analyzed in Table 1. In addition, for the three kinds of amorphous alloys, the average number of electrons gained and lost from the Fe, P, C, and B atoms slightly changed, which means that replacing P atoms with a small number of C and B atoms does not change the average number of electrons gained and lost from each element. However, it still has a certain impact on its distribution range. From the distribution range, for the three kinds of amorphous alloys, there are the Fe atoms with gained and lost electrons, as well as some neutral Fe atoms. The range of electron gain and loss for Fe atoms is the largest (0.52–0.63), followed by P atoms, and C and B atoms are smaller. The above analysis shows that for the three kinds of amorphous alloys, Fe easily loses electrons with positive charges, while metalloid atoms P, C, and B easily obtain electrons with negative charges. According to the previous charge transfer model [42], the sp electrons of metalloid atoms transfer to the band of the transition metal, resulting in a decrease in the Ms. When a small amount of B or C replaces P, the charge transferred to the band of transition metal decreases, and thus, the Ms increases. However, the results of the simulation show that due to the disorder of the amorphous structure, there is charge transfer between atoms, but the amount of charge transfer is small. There are positively charged, negatively charged, and electrically neutral Fe atoms, while metalloid atoms P, C, and B obtain electrons and are negatively charged. On average, it hardly changes the gain or loss of electrons from Fe atoms when a small amount of B or C replaces P. In the local range, the substitution of metalloids affects the charge transfer to a certain extent and inevitably affects the Ms of the amorphous alloy. However, this is not a significant influencing factor. In addition, the simulated calculations show that transition metals lose electrons while metalloids gain electrons. Therefore, the charge transfer model does not support the results of this study.

3.3. The Effect of Electron Configuration

3.3.1. Density of States

The spin polarization and electron arrangement determine the magnetic moment of the system, especially the filling of the transition metal d-band near the Fermi energy. The distributions of the DOS and PDOS are analyzed for the three kinds of amorphous alloys, as shown in Figure 6. Figure 6a shows the DOS of the P13 amorphous alloy. The number of spin-up band-filled electrons is greater than that of spin-down electron-filled electrons, indicating that the system has weak ferromagnetic properties, while the P10 and P8 amorphous alloys also have weak ferromagnetism. Figure 6b shows the contributions of the four elements Fe, P, C, and B in the P10 amorphous alloy to the magnetic properties of the system. The enlarged image in the figure shows the contributions of P, C, and B to magnetism near the Fermi energy. Fe contributes the most to the magnetic properties of the system, while metalloids contribute less. The PDOS of Fe in the P8 amorphous alloy is shown in Figure 6c. The bands near the Fermi level (EF) are mainly attributed to Fe-3d states with a small contribution from the p and s states of Fe. From Figure 6e,f, as small amounts of B and C replace P, the contribution of the p-state of P to the magnetic properties of amorphous alloys gradually decreases. The contribution of C to the magnetic properties of the system slightly increases, as shown in Figure 6g–i, while the contribution of B to the magnetic properties of the system remains almost unchanged. Moreover, there is strong p-d hybridization between the Fe 3d states and 2p states of P, B, and C at −8–−4 eV, which is consistent with the results from the PPDFs.

3.3.2. Local Magnetic Moment

Although the contents of metalloids P, B, and C are relatively low, they have a certain impact on the charge distribution and electron arrangement of amorphous alloys. In amorphous alloys, Fe atoms contain a certain proportion of metalloid elements around them. As metalloid elements easily obtain electrons, the transition metal Fe is inclined to lose electrons, and the number of electrons gained or lost will affect the changes in the local magnetic moment of the amorphous alloys. The contents of metalloids change with the substitution of small amounts of B and C for P, which also causes a change in the contribution of metalloids to magnetism. Although the Fe content remains unchanged throughout the entire process, the position of the Fe atoms in space changes with the variation in the different metalloid contents, thereby affecting the interaction between the Fe atoms and the magnetic properties of the amorphous alloys. The magnetic moment distribution of the Fe atoms in the P13, P10, and P8 amorphous alloys was analyzed, as shown in Figure 7a. For the P13 amorphous alloy, the magnetic moment distribution of the Fe atoms is relatively dispersed, with a distribution range of 2.10 μB, where the minimum magnetic moment is 0.57 μB and the maximum magnetic moment is 2.67 μB. When P is substituted by B atoms with a smaller radius, the magnetic moment distribution of the Fe atoms in the P10 amorphous alloy becomes more concentrated, mainly between 0.86 and 2.68 μB. After replacing P atoms with C, the distribution of Fe atoms with larger magnetic moments becomes more concentrated, especially between 2.0 and 2.2 μB, which has the highest distribution in this range, indicating that the magnetic moment distribution of larger Fe atoms increases as P atoms are replaced. The average magnetic moment of the central Fe atom with the same number of neighboring Fe atoms is illustrated in Figure 7b. As the number of neighboring Fe atoms increases, the magnetic moment of the Fe atoms increases, and it is found that the magnetic moment change trend of the three kinds of amorphous alloys is the same. It is obvious that Fe, with more Fe atoms gathering around it, possesses a larger magnetic moment. The main reason for this phenomenon is that the magnetic moment is sensitive to the Fe–Fe atomic distance. According to the magnetic exchange model, Fe atom pairs with larger distances are supposed to have a stronger ferromagnetic exchange, resulting in a greater magnetic moment. For the P13, P10, and P8 amorphous alloys, a small number of B and C atoms replace P atoms, leading to more Fe atoms appearing around the iron atoms in the amorphous alloy. However, due to the interaction and interaction distance between Fe atoms, more Fe atoms gather within a certain range, requiring more space to accommodate more Fe atoms. Consequently, the distance between Fe atoms increases, resulting in an increase in the magnetic moment.
Moreover, through the analysis of VPs, it is found that with the replacement of B and C atoms, the number of icosahedra increases, especially for regular icosahedra. This indicates an increase in the local structural symmetry of amorphous alloys. Studies have shown that the greater the symmetry of the structure is, the greater the magnetic moment of the atom [43,44], which may be one of the reasons for the increase in the magnetic moment of the FePCB amorphous alloys.

4. Conclusions

To sum up, first-principles molecular dynamics simulations were used to study the effects of the substitution of B and C atoms for P on the magnetic properties of the Fe80P13C7, Fe80P10C7B3, and Fe80P8C9B3 amorphous alloys. The replacement of P atoms increases the icosahedral structure of the amorphous alloys, especially the regular icosahedral structure. Moreover, the diversity of the coordination number distribution of each atom increases. The saturation magnetization of the three kinds of amorphous alloys gradually increases with the addition of B and C atoms, and the experimental results and simulated calculation results show consistent trends. Fe atoms tend to lose electrons with a positive charge, while P, C, and B atoms are inclined to gain electrons with a negative charge. The P, C, and B atoms make a small contribution to magnetism, mainly from the 3d band of Fe. The substitution of P atoms by smaller radius atoms (B or C) results in more Fe atoms appearing around the iron atoms, and the aggregation of iron atoms increases their magnetic moment. The increase in local structural symmetry may be one of the reasons for the increase in saturation magnetization of the amorphous alloys.

Author Contributions

S.L.: Conceptualization, Methodology, Software, Validation, Investigation, Data curation, Resources, Supervision, Writing—original draft, Writing—review and editing. Project administration. X.C.: Software, Investigation. Q.Z.: Methodology, Software. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region (Grant No. 2023D01C07) and the Doctoral Research Foundation Project of Xinjiang University (Grant No. 202302120002).

Data Availability Statement

Data is contained within the article.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Figure 1. Comparison of the experimental and calculated Ms in the P13, P10, and P8 amorphous alloys.
Figure 1. Comparison of the experimental and calculated Ms in the P13, P10, and P8 amorphous alloys.
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Figure 2. PPDFs of (a) P13, (b) P10, and (c) P8 amorphous alloys at 300 K.
Figure 2. PPDFs of (a) P13, (b) P10, and (c) P8 amorphous alloys at 300 K.
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Figure 3. Chemical element preferences of the P13, P10, and P8 amorphous alloys at 300 K. The black dotted lines represent the proportions of Fe (80%), P (13%), and C (7%). The bar graph of each color represents the percentage of Fe, P, C, or B in the amorphous alloy around a certain element (Fe, P C, or B). The abscissa represents the four elements Fe, P, C, and B.
Figure 3. Chemical element preferences of the P13, P10, and P8 amorphous alloys at 300 K. The black dotted lines represent the proportions of Fe (80%), P (13%), and C (7%). The bar graph of each color represents the percentage of Fe, P, C, or B in the amorphous alloy around a certain element (Fe, P C, or B). The abscissa represents the four elements Fe, P, C, and B.
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Figure 4. Numbers of VPs with central (a) Fe, (b) P, (c) C, and (d) B atoms for the P13, P10, and P8 amorphous alloys at 300 K.
Figure 4. Numbers of VPs with central (a) Fe, (b) P, (c) C, and (d) B atoms for the P13, P10, and P8 amorphous alloys at 300 K.
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Figure 5. Coordination number distributions of (a) Fe, (b) P, (c) C, and (d) B atoms in the P13, P10, and P8 amorphous alloys at 300 K.
Figure 5. Coordination number distributions of (a) Fe, (b) P, (c) C, and (d) B atoms in the P13, P10, and P8 amorphous alloys at 300 K.
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Figure 6. DOS and PDOS of the P13, P10, and P8 amorphous alloys. (a) DOS of P13 amorphous alloy, (d,g) PDOS of P and C in P13 amorphous alloy; (b) PDOS of Fe, P, C and B in P10 amorphous alloy, the insert is an enlarged view of the PDOS in the energy range from −7.5 eV to 2.5 eV, (e,h) PDOS of P, C and B in P10 amorphous alloy; (c) PDOS of Fe in P8 amorphous alloy, (f,i) PDOS of P, C and B in P8 amorphous alloy.
Figure 6. DOS and PDOS of the P13, P10, and P8 amorphous alloys. (a) DOS of P13 amorphous alloy, (d,g) PDOS of P and C in P13 amorphous alloy; (b) PDOS of Fe, P, C and B in P10 amorphous alloy, the insert is an enlarged view of the PDOS in the energy range from −7.5 eV to 2.5 eV, (e,h) PDOS of P, C and B in P10 amorphous alloy; (c) PDOS of Fe in P8 amorphous alloy, (f,i) PDOS of P, C and B in P8 amorphous alloy.
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Figure 7. (a) Magnetic moment distribution of Fe atoms, and (b) relationship between the number of nearest-neighbor Fe atoms and the magnetic moment of Fe atoms in the P13, P10, and P8 amorphous alloys.
Figure 7. (a) Magnetic moment distribution of Fe atoms, and (b) relationship between the number of nearest-neighbor Fe atoms and the magnetic moment of Fe atoms in the P13, P10, and P8 amorphous alloys.
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Table 1. Molar mass, atomic radius, electronegativity, and valence electron distribution of the four elements.
Table 1. Molar mass, atomic radius, electronegativity, and valence electron distribution of the four elements.
FePCB
Molar mass/(g/mol)55.8530.9712.0110.81
Atomic radius/(nm) [38]0.1240.1090.0770.090
Electronegativity [39]1.832.192.552.04
Valence electron distribution3d84s2 (8)3s23p3 (5)2s22p2 (4)2s22p1 (3)
Table 2. Charge distributions of the P13, P10, and P8 amorphous alloys.
Table 2. Charge distributions of the P13, P10, and P8 amorphous alloys.
FePCB
P13Average7.815.635.03
Aver. Diff.−0.190.631.03
Distribution7.52–8.045.50–5.734.94–5.09
Range0.520.230.15
P10Average7.815.625.043.54
Aver. Diff.−0.190.621.040.54
Distribution7.51–8.145.45–5.735–5.113.50–3.58
Range0.630.280.110.08
P8Average7.805.635.043.50
Aver. Diff.−0.200.631.040.50
Distribution7.53–8.065.56–5.735–5.113.41–3.58
Range0.530.170.110.17
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Lu, S.; Chen, X.; Zheng, Q. Effects of the Substitution of B and C for P on Magnetic Properties of FePCB Amorphous Alloys. Metals 2024, 14, 757. https://doi.org/10.3390/met14070757

AMA Style

Lu S, Chen X, Zheng Q. Effects of the Substitution of B and C for P on Magnetic Properties of FePCB Amorphous Alloys. Metals. 2024; 14(7):757. https://doi.org/10.3390/met14070757

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Lu, Shuwei, Xuan Chen, and Qiqi Zheng. 2024. "Effects of the Substitution of B and C for P on Magnetic Properties of FePCB Amorphous Alloys" Metals 14, no. 7: 757. https://doi.org/10.3390/met14070757

APA Style

Lu, S., Chen, X., & Zheng, Q. (2024). Effects of the Substitution of B and C for P on Magnetic Properties of FePCB Amorphous Alloys. Metals, 14(7), 757. https://doi.org/10.3390/met14070757

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