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Article

Theoretical Prediction and Experimental Validation of the Glass-Forming Ability and Magnetic Properties of Fe-Si-B Metallic Glasses from Atomic Structures

by
Yuhang Jiang
1,
Shangke Jia
1,
Shunwei Chen
1,
Xuelian Li
2,*,
Li Wang
2 and
Xiujun Han
1,*
1
School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
2
School of Mechanical and Electrical Engineering, Shandong University, Weihai 264209, China
*
Authors to whom correspondence should be addressed.
Materials 2022, 15(9), 3149; https://doi.org/10.3390/ma15093149
Submission received: 21 March 2022 / Revised: 21 April 2022 / Accepted: 25 April 2022 / Published: 27 April 2022
(This article belongs to the Section Materials Simulation and Design)
Browse Figures
Versions Notes

Abstract

:
Developing new soft magnetic amorphous alloys with a low cost and high saturation magnetization (Bs) in a simple alloy system has attracted substantial attention for industrialization and commercialization. Herein, the glass-forming ability (GFA), thermodynamic properties, soft magnetic properties, and atomic structures of Fe80+xSi5−xB15 (x = 0–4) amorphous soft magnetic alloys were investigated by ab initio molecular dynamics (AIMD) simulations and experiments. The pair distribution function (PDF), Voronoi polyhedron (VP), coordination number (CN), and chemical short- range order (CSRO) were analyzed based on the AIMD simulations for elucidating the correlations between the atomic structures with the glass-forming ability and magnetic properties. For the studied compositions, the Fe82Si3B15 amorphous alloy was found to exhibit the strongest solute–solute avoidance effect, the longest Fe-Fe bond, a relatively high partial CN for the Fe-Fe pair, and the most pronounced tendency to form more stable clusters. The simulation results indicated that Fe82Si3B15 was the optimum composition balancing the saturation magnetization and the GFA. This prediction was confirmed by experimental observations. The presented work provides a reference for synthesizing new Fe-Si-B magnetic amorphous alloys.

1. Introduction

Fe-based amorphous alloys have excellent soft magnetic properties, high saturation magnetization (Bs), and low coercivity (Hc) [1,2,3,4,5,6]. In addition, they have good mechanical properties and a low price. Therefore, Fe-based amorphous alloys have important potential applications in the field of energy conversion, especially in the power industry [7,8,9]. To reduce energy consumption and the price, many types of amorphous distribution transformers have been developed and launched into the market. Fe-based amorphous alloys have been applied to replace traditional Si-steel and ferrite in fabricating the core.
However, there are still two important challenges to the industrial application of Fe-based soft magnetic amorphous alloys [10]. Firstly, the glass-forming ability (GFA) of Fe-based alloys is unsatisfying. At present, an amorphous alloy transformer core is made by winding and stacking amorphous ribbons, which leads to eddy currents in the joints. Therefore, the improvement of the GFA is important to fabricate thicker amorphous ribbons in order to improve the energy conversion efficiency by reducing the stacking number of the amorphous strips. Secondly, the Bs value of Fe-based soft magnetic alloys needs to be improved. However, the Bs and GFA are normally in contradiction with each other; that is, increasing the Fe content can increase the Bs, but the GFA will deteriorate at the same time. It is rather difficult to concurrently obtain an alloy with the highest saturation magnetization and the best GFA. Therefore, it is important to find a composition that can balance the Bs and GFA. The optimum composition should have the highest Bs and a relatively good GFA.
In the past several decades, many attempts have been made to improve the Bs and many types of Fe-based amorphous alloys have been developed [11,12,13,14], especially Co- and P-containing Fe-based alloys, whose Bs could reach 1.92 T [14]. However, the existence of Co and P prevents their application because of the expensive cost of the raw materials and/or the processing of the pre-alloy ingots. Therefore, it is important to develop soft magnetic amorphous alloys with a high Bs in simple Fe-based alloy systems without Co and P elements. Until now, the most popular materials in the power industry have been Fe-Si-B series such as Fe78–80Si9–11B11–13 (Metglas2605SA1) [7] and Fe82Si4B13C1 (Metglas2605HB1) [15], which only have a Bs of 1.57 and 1.64 T, respectively. The further improvement of Bs of Fe-Si-B alloys is, therefore, still meaningful and open to investigation.
According to previous studies, the atomic structure has important influences on the GFA and magnetic properties [16,17,18,19,20,21]. The atomic structure is mainly characterized by two types of short-range ordering in the first nearest coordination spheres; namely, the topological short-range order (TSRO) and the chemical short-range order (CSRO). The TSRO indicates a tendency to form a certain coordination of atoms in space whereas the CSRO characterizes the tendency of an atom to surround itself with the same or different atoms. Several studies have shown that the solute–solute avoidance effect—namely, solute atoms not situated around the centered solvent atom—could stabilize the cluster and, therefore, improve the GFA [16,17,18]. The solute–solute avoidance effect is a type of CSRO that also plays an important role in affecting the magnetic properties. Vincze et al. found that, in an Fe-B amorphous alloy, the magnetic moment of the Fe atom correlated with the number of metalloid atoms in the first nearest neighbor shell [19].
The question of whether the optimum composition of an Fe-based amorphous alloy can be reasonably predicted from its atomic local structure, especially the CSRO, is of great interest. To address this question, in this work ab initio molecular dynamics (AIMD) simulations were carried out using the Fe-Si-B ternary system as a model. The correlations between the atomic structure with the GFA and magnetic properties were explored. To verify the validity of the simulation results, Fe80+xSi5−xB15 (x = 0–4) amorphous ribbons were prepared by a single roller melt-spinning method. The GFA, thermal stability, and soft magnetic properties were studied by X-ray powder diffraction (XRD), differential scanning calorimetry (DSC), and vibrating sample magnetometer (VSM), respectively. Based on the simulation and experimental results, the Fe82Si3B15 amorphous alloy was determined to be the optimum composition with a relatively good GFA and thermal stability as well as the best soft magnetic properties amongst our developed samples. The presented results in this work provide a reference for synthesizing new Fe-Si-B amorphous alloys with a superior soft magnetic performance and a good GFA.

2. Simulation and Experimental Details

AIMD simulations were used to gain an insight into the local atomic structure, employing a generalized gradient approximation (GGA) [22,23] with a Perdew–Burke–Ernzerhof (PBE) formalism based on the density functional theory (DFT) as implemented in the Vienna Ab Initio Simulation Package (VASP 5.4.1) [24,25,26,27]. The simulated configuration of the Fe80+xSi5−xB15(x = 0–4) amorphous alloys contained 100 atoms in a cubic cell with periodic boundary conditions. The simulation was performed in a canonical ensemble with a Nosé thermostat. The equation of motion was solved via a velocity Verlet algorithm with a timestep of 4 fs. Only the Γ point was applied to the sampling in the Brillion zone of the supercell. The systems were firstly melted at T = 2100 K for 4 ps and then quenched to T = 300 K with a cooling rate of 4 × 1013 K/s. The volume of the system was adjusted to correspond with zero total pressure. The last 5000 configurations were collected for the statistics.
To verify the simulation results, alloy ingots with a nominal composition of Fe80+xSi5−xB15 (x = 0–4) were prepared by induction melting into the mixtures of Fe (99.99 wt%), the commercial Fe-B master alloy (19.35 wt% B), and Si (99.99 wt%) in a highly purified argon atmosphere. Before the induction melting, the vacuum chamber was evacuated to 1 × 10−3 Pa and then backfilled with high-purity argon. This evacuation–washing process was repeated three times to ensure the removal of the residual oxygen. To ensure compositional homogeneity, the alloy ingots were melted 4–5 times. The melt-spun ribbons, with a thickness of 20–30 μm and width of 1 mm, were prepared by a single roller melt-spinning method under a high-purity argon atmosphere.
The structures of the melt-spun ribbons were identified by XRD with Cu Kα radiation. The thermal stability parameters of the amorphous alloys, including the onset crystallization temperature (Tx), melting temperature (Tm), and liquidus temperature (Tl), were examined by DSC at a heating rate of 0.67 K/s. The Bs value was measured by VSM under an applied field of 1600 kA/m at room temperature. The Hc was measured under a field of 800 A/m with a DC B-H loop tracer. The density (ρ) was measured by the Archimedean method using pure water as the fluid.

3. Results and Discussion

3.1. AIMD Simulations

AIMD simulations have been widely used to study the atomic structure of metallic glasses [28,29]. The TSRO and CSRO of the Fe80+xSi5−xB15 (x = 0–4) metallic glasses were investigated by AIMD simulations and the correlations between their GFA and magnetic properties were explored.
The total and partial pair distribution functions (PDFs) of the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys at 300 K are plotted in Figure 1, in which all characteristic broad peaks can be observed, demonstrating the appearance of an amorphous structure. The positions of the first peaks of gtotal(r) for the different compositions showed mere changes at 2.4 Å. The first peaks of gFe-M(r) were intense, indicating the strong interactions between the Fe and metalloid (M = Si, B) atoms. Noticeably, there existed a shoulder peak at around 2.1 Å in the first peak of gtotal(r) for all the compositions. Interestingly, the first peak of gFe-B(r) was also located at the same position, indicating that the shoulder peak resulted from a relatively large amount of Fe-B neighboring pairs with a considerably shorter distance than the Fe-Fe and Fe-Si pairs. These observations were consistent with the results in the literature for Fe78Si9B13 [30], Fe82Si4B10P4 [24], and Fe85Si2B9P4 [31]. For all the compositions, the first peak of gFe-B(r) for the Fe82Si3B15 amorphous alloy was the highest, indicating that the Fe–B interaction was the strongest in Fe82Si3B15 due to the strong chemical bond. The gSi-Si(r), gSi-B(r), and gB-B(r) curves possessed negligible first peaks, suggesting the presence of solute–solute avoidance [16,32,33]. The full solute–solute avoidance stabilized the alloy system in both the melted and amorphous states by forming relatively stable atomic clusters, which decreased the constituent segregation and increased the GFA [18]. As shown in Figure 1, there were almost no first peaks in the gSi-Si(r), gSi-B(r), and gB-B(r) curves for the Fe82Si3B15 alloy, indicating its better solute–solute avoidance compared with the other compositions; this indicated that it had a good thermal stability and GFA.
The partial Fe-Fe PDFs for the five compositions at 300 K are shown in Figure 2 and the positions of the first peaks for gFe-Fe(r) and rFe-Fe are listed in Table 1. Fe82Si3B15 and Fe80Si5B15 had an equivalent rFe-Fe, the largest in all compositions, indicating that the Fe-Fe bond for these two compositions was the longest. The longer Fe-Fe bond favored the larger size of the Fe-centered cluster, in which more Fe and metalloid atoms could be contained. Considering that clusters with a larger size are unfavorable for the diffusion of atoms, we predicted that the GFA of Fe82Si3B15 should be high. In addition, the long bond between Fe atoms is beneficial to the magnetic properties [20,34]; therefore, we speculated that the Fe80Si5B15 and Fe82Si3B15 alloys might also have higher magnetic properties than the other three compositions.
To further study the topological short-range order of the structure, a Voronoi polyhedron (VP) analysis was carried out [35,36]. The position of the first minimum (at ~3.1 Å) after the first peak in the gtotal(r) curve was taken as the cut-off range for the atomic neighboring. The VP index was defined as (n3, n4, n5, and n6), in which ni denoted the number of i-sided faces of the VP.
The major types of VP indices with Fe- and M-centered clusters and the corresponding distribution of coordination numbers (CNs) of the Fe80+xSi5−xB15 (x = 0–4) alloys are shown in Figure 3. As shown in Figure 3a, the (0, 1, 10, 2), (0, 2, 8, 4), and (0, 3, 6, 4) polyhedrons had the maximum proportion. Derived polyhedrons such as (0,1,10, 3) and (0, 1, 10, 4), which occupied similar rates, were also found around the Fe atoms. The Si-centered (0, 1, 10, 2) and (0, 3, 6, 4) clusters accounted for a large proportion, similar to the cluster types of the Fe-centered ones, as shown in Figure 3b. In the amorphous Fe84Si1B15 alloy, amongst the Si-centered VP, the (0, 0, 12, 0) type had the maximum ratio of 47.6%, probably due to the single Si atom, resulting in the non-uniformity of its structure in the Fe84Si1B15 alloy. In Figure 3c, amongst the B-centered VP, the (0, 3, 6, 0), (0, 2, 8, 0), and (0, 3, 6, 1) polyhedrons played a major role. Most of these conformed with the behavior of Fe78Si9B13 [32] and Fe82Si4B10P4 [24] metallic glasses.
The CN was calculated based on the basic theory of a VP partition. The number of facets on the VP surface (practically n3 + n4 + n5 + n6) was equal to the number of the neighboring atoms—i.e., the CN—because each facet represented the boundary of a neighboring atom. The distributions of CNs in the Fe-, Si-, and B-centered clusters of the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys are illustrated in Figure 3. The Fe-centered clusters showed dominant CNs of 14 and 15, mainly attributed to the (0, 2, 8, 4), (0, 2, 8, 5), (0, 3, 6, 5), and (0, 3, 6, 6) polyhedrons. As can be seen in Figure 3e, the Si-centered cluster had a major CN of 13, which was mainly due to the (0, 1, 10, 2) polyhedron. The CN of the B-centered ones was 10 because of the (0, 2, 8, 0) polyhedron. According to the spatial connectivities between the clusters, the large clusters such as (0, 2, 8, 4) and (0, 1, 10, 2) had a strong tendency to connect to the small clusters (e.g., (0, 2, 8, 0), (0, 3, 6, 0), and (0, 4, 4, 0)), leading to dense cluster packing [37]. It could be concluded that there was a strong connection tendency between the larger clusters (Fe-centered) and the smaller ones (Si- and B-centered).
To further analyze the influence of the local structure on the GFA and atomic magnetic moment, the total and partial CNs for the Fe80+xSi5−xB15 (x = 0–4) alloys were counted; the results are presented in Table 2, Table 3 and Table 4. Evidently, in the five compositions, the partial CNs of Si-Si, Si-B, B-Si, and B-B were the least in the Fe82Si3B15 alloy. This indicated that Fe82Si3B15 had the strongest solute–solute avoidance and thus had the best GFA, which was consistent with the findings from the PDFs. In addition, according to Heisenberg [38,39], the atomic magnetic moment depends on the number of Fe atoms in the nearest neighbor (NN) shell; that is, more nearest neighbor Fe atoms correspond with higher atomic magnetic moments. As shown in Table 2, the partial CN of the Fe-Fe pair in Fe84Si1B15 and Fe82Si3B15 were large (12.8 and 12.5) and that of Fe80Si5B15 was the smallest (12.1). From this point of view, the Fe84Si1B15 and Fe82Si3B15 alloys should have had higher atomic magnetic moments than the other compositions. Considering the above-mentioned length of the Fe-Fe bond, the Fe82Si3B15 alloy was speculated to have the highest Bs.
The fraction of atom-centered CSROs, confined to the NN shell, is shown in Figure 4 and Table 5. The index <n1, n2, n3, n4> along the lateral axis defined the CSRO type, in which ni indicated the total number of Fe, Si, or B atoms in the chemical component. For instance, index <13, 0, 2> in Figure 4a denotes that this type of Fe-centered CSRO in the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys contained 13 Fe atoms, 0 Si atom, and 2 B atoms. In the M-centered CSROs, when the same M atom existed in the NN shell, the CSRO was defined as the S-type. If the atoms in the NN shell were all Fe atoms, then this CSRO was called a P-type CSRO [18].
From Figure 4 and Table 5, it could be seen that, although the same M atoms were found in the NN shell of M, most of the surrounding atoms were Fe, indicating the formation of M-centered clusters in the Fe80+xSi5−xB15 (x = 0–4) alloys. In addition, by decreasing the Si content to 3 at.%, the fractions of the S-type reached a minimum of 0.0 and 0.6% for the Si-centered and B-centered CSROs, respectively. This indicated that the same atoms were rarely found around the Si or B atoms, resulting in an increased possibility of surrounding by the Fe atoms, which implied that the Si and B atoms had a dispersed distribution and that the solute–solute avoidance effect for the Fe82Si3B15 amorphous alloy was the strongest. On the other hand, Fe-centered clusters that were only surrounded by Fe atoms (P-type) were rarely found, which showed the presence of few pure Fe clusters. Thus, the Fe atoms were mainly located in the NN atoms of all elements, making the distribution of Fe atoms more uniform. With the increase in Fe content (80 at.% → 84 at.%), the proportion of Fe-centered P-type CSROs increased from 2.5 to 8.9%, which indicated that the content of pure Fe clusters increased with the Fe content.
In connection with the above-mentioned results of the PDF, VP, CN, and CSRO, we concluded that, in the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys, the Fe82Si3B15 alloy was the optimum composition, combining a good thermal stability with the GFA and magnetic properties. To further verify the simulation results, the Fe-based amorphous alloys were prepared by specific experiments, and XRD, DSC, and VSM analyses were used for the determination of the structure, thermophysical properties, and magnetism, respectively.

3.2. Experimental Determination

The melt-spun ribbons of the Fe80+xSi5−xB15 (x = 0–4) alloys were prepared by single roller melt-spinning with a linear velocity of 30 or 35 m/s under a highly purified argon atmosphere. XRD was used to analyze the phase structure of these ribbons (Figure 5). Before polishing, an amorphous structure was formed in the ribbons with an Fe content below 82 at.%, but further increasing the Fe content induced the formation of the α-Fe phase, as shown in Figure 5a,b. After polishing, the α-Fe phase could still be found in the ribbons with a high Fe content that were prepared at the linear velocity of 30 m/s, but only one amorphous broad peak could be found in all ribbons prepared at the linear velocity of 35 m/s, as illustrated in Figure 5c,d. The existence of the α-Fe phase was due to the crystallization layer on the free surface of the melt-spun ribbons, which was an indication of a decreased GFA. It should be noted that, when further increasing the Fe content, the GFA of the alloys was worse, as reported in the literature [40,41]. Thus, according to the XRD results, we concluded that the formation of the amorphous phase was affected by the Fe content and that the GFA decreased noticeably if the Fe content exceeded 82 at.%. For Fe80Si5B15, Fe81Si4B15, and Fe82Si3B15, their GFA could not be distinguished based on the XRD results. However, it was reasonable to suppose that Fe82Si3B15 had a relatively good GFA in the five compositions covered in this work.
To quantitatively characterize the thermodynamic properties of the ribbons, the polished Fe80+xSi5−xB15 (x = 0–4) amorphous ribbons prepared with a linear velocity of 35 m/s were investigated by DSC. Figure 6 shows the DSC curves of the ribbons at a heating rate of 0.67 K/s under a highly purified argon atmosphere. Two exothermic peaks existed in each DSC curve except for the Fe84Si1B15 amorphous alloy. The exothermic peak of the Fe84Si1B15 amorphous alloy was asymmetric, which could indicate that there was no single crystallization process. We speculated that the precipitation phases of the Si-added alloys were more complicated. In the DSC curves, no obvious glass transition temperature could be detected for all alloys. The crystallization temperatures (Tx) are summarized in Table 6. It could be seen that in the Fe80+xSi5−xB15 (x = 0–4) alloys, the Tx values decreased as x increased.
The DSC curves of the melting processes for the Fe80+xSi5−xB15 (x = 0–4) alloys are presented in Figure 7. The onset and end temperatures of the melting endothermic events denoted by Tm and Tl are summarized in Table 6. Many parameters can be used to estimate the GFA such as the reduced glass transition temperature, Trg = Tg/Tl [42], and γ = [Tx/(Tl + Tg)] [43,44]. For amorphous alloys without an obvious glass transition temperature in the DSC determination, Trg is often replaced by Trx = Tx/Tl for characterizing the GFA [8], and Hc is also an alternative because its decrease is usually accompanied by an increase in the GFA [45]. The changes of Trx and Hc with the value of x for the Fe80+xSi5−xB15 (x = 0–4) alloys are illustrated in Figure 8 and the two parameters are added to Table 6. For Hc, the values for x = 0–2 were close and much lower than the values for x = 3 and 4. For Trx, amongst the five components, x = 2 at.% also showed a relatively high value although it was not the highest one. From these two parameters, we could conclude that the Fe82Si3B15 alloy had a relatively good thermal stability and GFA.
The magnetic properties of these glassy alloys were further investigated. The hysteresis loops of the as-quenched ribbons are presented in Figure 9a. Three individual amorphous alloy ribbons of each composition, which were prepared at a linear velocity of 35 m/s and polished, were selected for the VSM test to improve the reliability of the data. All samples exhibited the typical loops of soft magnetic amorphous alloys. The Bs values were derived from the density ρ (measured by the Archimedean method), the permeability of the vacuum (μ0 = 4π × 10−7 N/A2), and the saturated mass magnetization σs according to the expression Bs = μ0·σs·ρ. The results are illustrated in Figure 9b and also tabulated in Table 6. It could be seen that, with an increase of x, the Bs values of the amorphous ribbons first increased and then decreased. The maximum Bs value of 1.69 T was reached at x = 2 at.%. For the Bs of 1.69 T, the content of Si was 3 at.%, the σs value was 182.5 Am2/kg, and ρ was 7.36 × 103 kg/m3. We noted that for the same sample (3 at.% Si) in the previous literature [46,47], σs was reported to be 177 Am2/kg, with ρ being 7.41 × 103 kg/m3 and, accordingly, the Bs value was calculated to be 1.65 T, which was slightly lower than our result (1.69 T). Considering the possible difference in the experiments, including the ribbon quality and the testing equipment, such a slight variation was considered to be reasonable. Overall, our results indicated that when the Fe content was less than 82 at.% in the Fe-Si-B amorphous alloys, the Bs value increased with the increase in Fe content and this trend was reversed with a higher Fe content. This observation was in agreement with a previous report [8].
Combining the results of the XRD, DSC, and VSM analyses, a conclusion could be made that, amongst the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys, the Fe82Si3B15 amorphous alloy had the highest saturation magnetization and a relatively good GFA. Considering the balance between the soft magnetic properties and the GFA, Fe82Si3B15 was determined to be the optimum composition. Such an experimental observation confirmed our prediction based on the simulation results.

4. Conclusions

In this work, the atomic structure, GFA, thermal stability, and soft magnetic properties of Fe80+xSi5−xB15 (x = 0–4) amorphous alloys were studied by a combination of AIMD simulations and experiments. The AIMD simulation results of the PDF, VP, CN, and CSRO showed that the interactions between the Fe and metalloid (M = Si, B) atoms were strong and a proper Si addition enhanced the GFA, thermal stability, and magnetic performance of the alloys. Compared with the other alloys, the Fe82Si3B15 amorphous alloy had relatively stable atomic clusters and featured a strong solute–solute avoidance effect, thus featuring a good thermal stability, an enhanced GFA, and good magnetic properties. To confirm the simulation results, the Fe80+xSi5−xB15 (x = 0–4) amorphous ribbons were prepared by a single roller melt-spinning method. The Fe82Si3B15 amorphous alloy showed a relatively good thermal stability and GFA. More importantly, it exhibited a saturated magnetization as high as 1.69 T and a low coercivity of 6.5 A/m. The investigations in this work on Fe-Si-B amorphous alloys provide a theoretical reference for further industrialization and commercialization.

Author Contributions

Conceptualization, Y.J.; methodology, X.L. and L.W.; software, X.H.; validation, S.J.; formal analysis, X.H. and X.L.; investigation, S.C. and L.W.; resources, X.H.; data curation, Y.J.; writing—original draft preparation, Y.J.; writing—review and editing, X.H. and S.C.; visualization, S.J.; supervision, X.H. and X.L.; project administration, X.H.; funding acquisition, X.H. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Colleges and Universities Twenty Terms Foundation of Jinan City (2019GXRC034), the National Natural Science Foundation of China (51671134), the Shandong Provincial Key Research and Development Program (Major Scientific and Technological Innovation Project) (2019JZZY010337), and the Natural Science Foundation of Shandong Province (ZR2019MEM040 and ZR2020ME008).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Acknowledgments

We acknowledge financial support from the Colleges and Universities Twenty Terms Foundation of Jinan City (2019GXRC034), the National Natural Science Foundation of China (51671134), the Shandong Provincial Key Research and Development Program (Major Scientific and Technological Innovation Project) (2019JZZY010337), and the Natural Science Foundation of Shandong Province (ZR2019MEM040 and ZR2020ME008).

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Suryanarayana, C.; Inoue, A. Iron-based bulk metallic glasses. Int. Mater. Rev. 2013, 58, 131–166. [Google Scholar] [CrossRef]
  2. Jiles, D. Recent advances and future directions in magnetic materials. Acta Mater. 2003, 51, 5907–5939. [Google Scholar] [CrossRef]
  3. Li, J.F.; Liu, X.; Zhao, S.F.; Ding, H.Y.; Yao, K.F. Fe-based bulk amorphous alloys with iron contents as high as 82 at%. J. Magn. Magn. Mater. 2015, 386, 107–110. [Google Scholar] [CrossRef]
  4. Wang, A.; Zhao, C.; Men, H.; He, A.; Chang, C.; Wang, X.; Li, R.W. Fe-based amorphous alloys for wide ribbon production with high Bs and outstanding amorphous forming ability. J. Alloys Compd. 2015, 630, 209–213. [Google Scholar] [CrossRef]
  5. Wang, A.; Zhao, C.; He, A.; Men, H.; Chang, C.; Wang, X. Composition design of high Bs Fe-based amorphous alloys with good amorphous-forming ability. J. Alloys Compd. 2016, 656, 729–734. [Google Scholar] [CrossRef]
  6. Li, X.; Sun, B.; Qu, C.; Ji, H.; Wang, L. The formation mechanism of novel Fe–P–B metallic glasses: A perspective from nearly free electron model. J. Alloys Compd. 2015, 620, 358–360. [Google Scholar] [CrossRef]
  7. Mouhamad, M.; Elleau, C.; Mazaleyrat, F.; Guillaume, C.; Jarry, B. Physicochemical and accelerated aging tests of Metglas 2605SA1 and Metglas 2605HB1 amorphous ribbons for power applications. IEEE. Trans. Magn. 2011, 47, 3192–3195. [Google Scholar] [CrossRef] [Green Version]
  8. Yue, S.; Zhang, H.; Cheng, R.; Wang, A.; Dong, Y.; He, A.; Ni, H.; Liu, C.-T. Magnetic and thermal stabilities of FeSiB eutectic amorphous alloys: Compositional effects. J. Alloys Compd. 2019, 776, 833–838. [Google Scholar] [CrossRef]
  9. Li, X.; Liu, J.; Qu, C.; Song, K.; Wang, L. Effects of Nb on the precipitation of α-Fe, glass forming ability and magnetic properties of Fe85B10P5 alloys. J. Alloys Compd. 2017, 694, 643–646. [Google Scholar] [CrossRef]
  10. Zhang, J.; Chang, C.; Wang, A.; Shen, B. Development of quaternary Fe-based bulk metallic glasses with high saturation magnetization above 1.6 T. J. Non-Cryst. Solids 2012, 358, 1443–1446. [Google Scholar] [CrossRef]
  11. Kong, F.; Chang, C.; Inoue, A.; Shalaan, E.; Al-Marzouki, F. Fe-based amorphous soft magnetic alloys with high saturation magnetization and good bending ductility. J. Alloys Compd. 2014, 615, 163–166. [Google Scholar] [CrossRef]
  12. Han, Y.; Kong, F.; Chang, C.; Zhu, S.; Inoue, A.; Shalaan, E.-S.; Al-Marzouki, F. Syntheses and corrosion behaviors of Fe-based amorphous soft magnetic alloys with high-saturation magnetization near 1.7 T. J. Mater. Res. 2015, 30, 547–555. [Google Scholar] [CrossRef]
  13. Pang, L.L.; Inoue, A.; Zanaeva, E.N.; Wang, F.; Bazlov, A.I.; Han, Y.; Shull, R.B. Nanocrystallization, good soft magnetic properties and ultrahigh mechanical strength for Fe82–85B13–16Si1Cu1 amorphous alloys. J. Alloys Compd. 2019, 785, 25–37. [Google Scholar] [CrossRef]
  14. Wang, F.; Inoue, A.; Han, Y.; Zhu, S.; Kong, F.; Zanaeva, E.; Liu, G.; Shalaan, E.; Al-Marzouki, F.; Obaid, A. Soft magnetic Fe-Co-based amorphous alloys with extremely high saturation magnetization exceeding 1.9 T and low coercivity of 2 A/m. J. Alloys Compd. 2017, 723, 376–384. [Google Scholar] [CrossRef]
  15. Ogawa, Y.; Naoe, M.; Yoshizawa, Y.; Hasegawa, R. Magnetic properties of high Bs Fe-based amorphous material. J. Magn. Magn. Mater. 2006, 304, e675–e677. [Google Scholar] [CrossRef]
  16. Sheng, H.; Luo, W.; Alamgir, F.; Bai, J.; Ma, E. Atomic packing and short-to-medium-range order in metallic glasses. Nature 2006, 439, 419–425. [Google Scholar] [CrossRef]
  17. Yu, Q.; Wang, X.; Lou, H.; Cao, Q.; Jiang, J. Atomic packing in Fe-based metallic glasses. Acta Mater. 2016, 102, 116–124. [Google Scholar] [CrossRef]
  18. Dong, B.; Zhou, S.; Li, D.; Qin, J.; Pan, S.; Wang, Y.; Li, Z. Effects of solute–solute avoidance on metallic glass formation. J. Non-Cryst. Solids 2012, 358, 2749–2752. [Google Scholar] [CrossRef]
  19. Vincze, I.; Boudreaux, D.; Tegze, M. Short-range order in Fe-B metallic glass alloys. Phys. Rev. B 1979, 19, 4896. [Google Scholar] [CrossRef]
  20. Zhang, W.; Li, Q.; Duan, H. Study of the effects of metalloid elements (P, C, B) on Fe-based amorphous alloys by ab initio molecular dynamics simulations. J. Appl. Phys. 2015, 117, 104901. [Google Scholar] [CrossRef]
  21. Kaban, I.; Jovari, P.; Waske, A.; Stoica, M.; Bednarčik, J.; Beuneu, B.; Mattern, N.; Eckert, J. Atomic structure and magnetic properties of Fe–Nb–B metallic glasses. J. Alloys Compd. 2014, 586, S189–S193. [Google Scholar] [CrossRef] [Green Version]
  22. Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  23. Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  24. Chen, H.; Dong, B.; Zhou, S.; Li, X.; Qin, J. Structural, magnetic, and electronic properties of Fe82Si4B10P4 metallic glass. Sci. Rep. 2018, 8, 1–8. [Google Scholar] [CrossRef] [PubMed] [Green Version]
  25. Kresse, G.; Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 1993, 47, 558. [Google Scholar] [CrossRef] [PubMed]
  26. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169. [Google Scholar] [CrossRef] [PubMed]
  27. Chen, H.; Li, Y.; Huang, L.; Li, J. Influential electronic and magnetic properties of the gallium sulfide monolayer by substitutional doping. J. Phys. Chem. C 2015, 119, 29148–29156. [Google Scholar] [CrossRef]
  28. Shan, G.; Zhang, J.L.; Li, J.; Zhang, S.; Jiang, Z.; Huang, Y.; Shek, C.-H. Atomic-level structures and physical properties of magnetic CoSiB metallic glasses. J. Magn. Magn. Mater. 2014, 352, 49–55. [Google Scholar] [CrossRef]
  29. Lizárraga, R. Structural and magnetic properties of the Gd-based bulk metallic glasses GdFe2, GdCo2, and GdNi2 from first principles. Phys. Rev. B 2016, 94, 174201. [Google Scholar] [CrossRef]
  30. Li, X.; Wang, J.; Qin, J.; Dong, B. The relationship between atomic structure and magnetic property of amorphous Fe78Si9B13 alloy at different pressures. J. Magn. Magn. Mater. 2017, 443, 216–221. [Google Scholar] [CrossRef]
  31. Wang, Y.; Takeuchi, A.; Makino, A.; Liang, Y.; Kawazoe, Y. Atomic packing and diffusion in Fe85Si2B9P4 amorphous alloy analyzed by ab initio molecular dynamics simulation. J. Appl. Phys. 2015, 117, 17B705. [Google Scholar] [CrossRef]
  32. Miracle, D.B.; Egami, T.; Flores, K.M.; Kelton, K.F. Structural aspects of metallic glasses. MRS Bull. 2007, 32, 629–634. [Google Scholar] [CrossRef]
  33. Luo, W.; Sheng, H.; Ma, E. Pair correlation functions and structural building schemes in amorphous alloys. Appl. Phys. Lett. 2006, 89, 131927. [Google Scholar] [CrossRef]
  34. Moroni, E.; Kresse, G.; Hafner, J.; Furthmüller. Ultrasoft pseudopotentials applied to magnetic Fe, Co, and Ni: From atoms to solids. Phys. Rev. B 1997, 56, 15629. [Google Scholar] [CrossRef]
  35. Sheng, H.; Cheng, Y.; Lee, P.; Shastri, S.; Ma, E. Atomic packing in multicomponent aluminum-based metallic glasses. Acta Mater. 2008, 56, 6264–6272. [Google Scholar] [CrossRef]
  36. Sha, Z.; Feng, Y.; Li, Y. Statistical composition-structure-property correlation and glass-forming ability based on the full icosahedra in Cu–Zr metallic glasses. Appl. Phys. Lett. 2010, 96, 061903. [Google Scholar] [CrossRef]
  37. Li, H.; Lu, Z.; Wang, S.; Wu, Y.; Lu, Z. Fe-based bulk metallic glasses: Glass formation, fabrication, properties and applications. Prog. Mater. Sci. 2019, 103, 235–318. [Google Scholar] [CrossRef]
  38. Jiao, Z.; Li, H.; Gao, J.; Wu, Y.; Lu, Z. Effects of alloying elements on glass formation, mechanical and soft-magnetic properties of Fe-based metallic glasses. Intermetallics 2011, 19, 1502–1508. [Google Scholar] [CrossRef]
  39. Heisenberg, W. Zur Theorie des Ferromagnetismus. Z. Phys. 1928, 49, 619. [Google Scholar] [CrossRef]
  40. Dong, C.; Inoue, A.; Wang, X.; Kong, F.; Zanaeva, E.; Wang, F.; Bazlov, A.; Zhu, S.; Li, Q. Soft magnetic properties of Fe82–83B14–15Si2C0.5–1 amorphous alloys with high saturation magnetization above 1.7 T. J. Non-Cryst. Solids 2018, 500, 173–180. [Google Scholar] [CrossRef]
  41. Jin, Y.; Fan, X.; Men, H.; Liu, X.; Shen, B. FePCCu nanocrystalline alloys with excellent soft magnetic properties. Sci. China Technol. Sci. 2012, 55, 3419–3424. [Google Scholar] [CrossRef]
  42. Turnbull, D. Under what conditions can a glass be formed? Contemp. Phys 1969, 10, 473–488. [Google Scholar] [CrossRef]
  43. Lu, Z.; Liu, C. Glass formation criterion for various glass-forming systems. Phys. Rev. Lett. 2003, 91, 115505. [Google Scholar] [CrossRef] [PubMed]
  44. Masood, A.; Biswas, A.; Ström, V.; Belova, L.; Ågren, J.; Rao, K. The effect of Ni-substitution on physical properties of Fe72−xB24Nb4Nix bulk metallic glassy alloys. MRS Online Proc. Libr. (OPL) 2011, 1300, 607. [Google Scholar] [CrossRef] [Green Version]
  45. Li, X.; Song, K.; Wu, Y.; Ji, H.; Wang, L. The mismatch entropy for bulk metallic glasses: A thermodynamic approach. Mater. Lett. 2013, 107, 17–19. [Google Scholar] [CrossRef]
  46. Luborsky, F.; Becker, J.; Walter, J.; Liebermann, H. Formation and magnetic properties of Fe-B-Si amorphous alloys. IEEE. Trans. Magn. 1979, 15, 1146–1149. [Google Scholar] [CrossRef]
  47. Carow-Watamura, U.; Louzguine, D.; Takeuchi, A. B-Fe-Si (144). Landolt Börnstein 2011, 37, 200. [Google Scholar] [CrossRef]
Materials 15 03149 g001 550
Figure 1. Total and partial PDFs of the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys at 300 K. (a) Fe80Si5B15, (b) Fe81Si4B15, (c) Fe82Si3B15, (d) Fe83Si2B15 and (e) Fe84Si1B15.
Figure 1. Total and partial PDFs of the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys at 300 K. (a) Fe80Si5B15, (b) Fe81Si4B15, (c) Fe82Si3B15, (d) Fe83Si2B15 and (e) Fe84Si1B15.
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Materials 15 03149 g002 550
Figure 2. Partial PDFs for Fe-Fe pairs in the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys at 300 K. The insert is the enlarged part of the first peaks.
Figure 2. Partial PDFs for Fe-Fe pairs in the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys at 300 K. The insert is the enlarged part of the first peaks.
Materials 15 03149 g002
Materials 15 03149 g003 550
Figure 3. Distributions of typical VP indices for (a) Fe-, (b) Si-, and (c) B-centered clusters and the corresponding distributions of the CNs for (d) Fe-, (e) Si-, and (f) B-centered in the Fe80+xSi5−xB15 (x = 0–4) alloys at 300 K. The VP is defined as the polyhedron with minimum volume constituted by the vertical bisected surfaces between neighboring atoms.
Figure 3. Distributions of typical VP indices for (a) Fe-, (b) Si-, and (c) B-centered clusters and the corresponding distributions of the CNs for (d) Fe-, (e) Si-, and (f) B-centered in the Fe80+xSi5−xB15 (x = 0–4) alloys at 300 K. The VP is defined as the polyhedron with minimum volume constituted by the vertical bisected surfaces between neighboring atoms.
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Materials 15 03149 g004 550
Figure 4. Fractions of the Fe- and M-centered CSROs in the Fe80+xSi5−xB15 (x = 0–4) alloys at 300 K: (a) Fe-centered; (b) Si-centered; and (c) B-centered.
Figure 4. Fractions of the Fe- and M-centered CSROs in the Fe80+xSi5−xB15 (x = 0–4) alloys at 300 K: (a) Fe-centered; (b) Si-centered; and (c) B-centered.
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Materials 15 03149 g005 550
Figure 5. XRD patterns for the free surface of the Fe80+xSi5−xB15 (x = 0–4) melt-spun ribbons (a,b) before and (c,d) after polishing the surface layer. The alloys are prepared with a linear velocity of 30 or 35 m/s.
Figure 5. XRD patterns for the free surface of the Fe80+xSi5−xB15 (x = 0–4) melt-spun ribbons (a,b) before and (c,d) after polishing the surface layer. The alloys are prepared with a linear velocity of 30 or 35 m/s.
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Materials 15 03149 g006 550
Figure 6. DSC curves of the Fe80+xSi5−xB15 (x = 0–4) amorphous ribbons.
Figure 6. DSC curves of the Fe80+xSi5−xB15 (x = 0–4) amorphous ribbons.
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Materials 15 03149 g007 550
Figure 7. DSC curves of the melting processes for the Fe80+xSi5−xB15 (x = 0–4) alloys.
Figure 7. DSC curves of the melting processes for the Fe80+xSi5−xB15 (x = 0–4) alloys.
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Materials 15 03149 g008 550
Figure 8. Changes in Trx and Hc of the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys.
Figure 8. Changes in Trx and Hc of the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys.
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Materials 15 03149 g009 550
Figure 9. (a) Hysteresis loops of the Fe80+xSi5−xB15 (x = 0–4) amorphous ribbons. The insert shows the enlarged partial hysteresis curves of the samples. (b) The ρ, σs, and Bs values as functions of Fe content.
Figure 9. (a) Hysteresis loops of the Fe80+xSi5−xB15 (x = 0–4) amorphous ribbons. The insert shows the enlarged partial hysteresis curves of the samples. (b) The ρ, σs, and Bs values as functions of Fe content.
Materials 15 03149 g009
Table
Table 1. Positions of the first peaks for gFe-Fe(r) at 300 K.
Table 1. Positions of the first peaks for gFe-Fe(r) at 300 K.
AlloysFe80Si5B15Fe81Si4B15Fe82Si3B15Fe83Si2B15Fe84Si1B15
rFe-Fe2.452.432.452.422.43
Table
Table 2. Fe-centered total and partial CNs in the Fe80+xSi5−xB15 (x = 0–4) alloys.
Table 2. Fe-centered total and partial CNs in the Fe80+xSi5−xB15 (x = 0–4) alloys.
AlloysFe-FeFe-SiFe-BTotal CN
Fe80Si5B1512.100.811.6814.59
Fe81Si4B1512.320.651.7014.67
Fe82Si3B1512.450.451.8014.70
Fe83Si2B1512.400.321.8214.55
Fe84Si1B1512.800.141.7014.64
Table
Table 3. Si-centered total and partial CNs in the Fe80+xSi5−xB15 (x = 0–4) alloys.
Table 3. Si-centered total and partial CNs in the Fe80+xSi5−xB15 (x = 0–4) alloys.
AlloysSi-FeSi-SiSi-BTotal CN
Fe80Si5B1512.9300.7613.69
Fe81Si4B1513.090.040.2713.40
Fe82Si3B1512.2600.1812.44
Fe83Si2B1513.4600.2913.75
Fe84Si1B1512.0200.4712.49
Table
Table 4. B-centered total and partial CNs in the Fe80+xSi5−xB15 (x = 0–4) alloys.
Table 4. B-centered total and partial CNs in the Fe80+xSi5−xB15 (x = 0–4) alloys.
AlloysB-FeB-SiB-BTotal CN
Fe80Si5B158.970.250.449.66
Fe81Si4B159.170.070.409.64
Fe82Si3B159.740.0309.77
Fe83Si2B1510.080.040.3710.49
Fe84Si1B159.500.030.279.80
Table
Table 5. Type and fraction of atom-centered CSROs in the Fe80+xSi5−xB15 (x = 0–4) alloys.
Table 5. Type and fraction of atom-centered CSROs in the Fe80+xSi5−xB15 (x = 0–4) alloys.
AlloysCSRO TypeFeSiB
Fe80Si5B15P-type2.5%34.6%39.2%
S-type100.0%0.0%35.5%
Fe81Si4B15P-type5.8%72.3%59.8%
S-type100.0%4.4%40.0%
Fe82Si3B15P-type4.9%82.4%95.6%
S-type100.0%0.0%0.6%
Fe83Si2B15P-type5.3%71.2%60.5%
S-type100.0%0.0%35.6%
Fe84Si1B15P-type8.6%52.7%70.1%
S-type100.0%0.0%26.7%
Table
Table 6. Thermal properties (Tx, Tm, and Tl) and magnetic properties (Bs and Hc) of the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys.
Table 6. Thermal properties (Tx, Tm, and Tl) and magnetic properties (Bs and Hc) of the Fe80+xSi5−xB15 (x = 0–4) amorphous alloys.
CompositionsThermal PropertiesMagnetic Properties
Tx (K)Tm (K)Tl (K)TrxBs (T)Hc (A/m)
Fe80Si5B15793144114730.5381.625.9
Fe81Si4B15781144915140.5161.656.4
Fe82Si3B15765144415000.5101.696.5
Fe83Si2B15735144315170.4851.668.6
Fe84Si1B15728144515050.4841.679.5
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Jiang, Y.; Jia, S.; Chen, S.; Li, X.; Wang, L.; Han, X. Theoretical Prediction and Experimental Validation of the Glass-Forming Ability and Magnetic Properties of Fe-Si-B Metallic Glasses from Atomic Structures. Materials 2022, 15, 3149. https://doi.org/10.3390/ma15093149

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Jiang Y, Jia S, Chen S, Li X, Wang L, Han X. Theoretical Prediction and Experimental Validation of the Glass-Forming Ability and Magnetic Properties of Fe-Si-B Metallic Glasses from Atomic Structures. Materials. 2022; 15(9):3149. https://doi.org/10.3390/ma15093149

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Jiang, Yuhang, Shangke Jia, Shunwei Chen, Xuelian Li, Li Wang, and Xiujun Han. 2022. "Theoretical Prediction and Experimental Validation of the Glass-Forming Ability and Magnetic Properties of Fe-Si-B Metallic Glasses from Atomic Structures" Materials 15, no. 9: 3149. https://doi.org/10.3390/ma15093149

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