Atomic Structure And Magnetic Properties Of The Fe78B13Si9

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Atomic Structure and Magnetic Properties of the Fe78B13Si9 Amorphous Alloy Surface Xuan Li,† Lei Zuo,† Xin Zhang,‡ and Tao Zhang*,† †

J. Phys. Chem. C Downloaded from pubs.acs.org by YORK UNIV on 12/12/18. For personal use only.

Key Laboratory of Aerospace Materials and Performance (Ministry of Education), School of Materials Science and Engineering, Beihang University, Beijing 100191, China ‡ Beijing Starcraft, Beijing 100080, China ABSTRACT: The Fe78B13Si9 amorphous slab, which consists of surface and interior components, was simulated to study the atomic structure and magnetic properties of the surface by ab initio molecular dynamics simulation. It is found that the atomic structure of the surface component is obviously different from that of the interior component. The surface component has higher rhomboidal symmetry (more 1311 and 1321 bond pairs), higher degree of ordering (higher Q4 and Q6 values), and lower average coordination number. On the other hand, the magnetic properties are described by the magnetic moment and partial local density of states of Fe, which reveal that the surface component has larger average Fe magnetic moment than that of the interior component because of the low coordination number of Fe−Fe in the surface component.

1. INTRODUCTION Fe-based amorphous alloys have attracted considerable attention because of their high mechanical properties, excellent soft magnetic properties, and low cost.1−3 Recently, extensive efforts have been made to further improve saturation magnetization and reduce coercivity by increasing the Fe content and optimization of the annealing process.4,5 To understand the novel properties of Fe amorphous alloys, atomic and electronic structures have been investigated by high-energy transmission synchrotron X-ray diffraction, reverse Monte Carlo simulation, and ab initio molecular dynamics (AIMD) simulation.6−8 For example, the simulation study reveals that the alloying elements with large electronegativity and the potential to expand Fe disordered matrix are beneficial to magnetization enhancement in the Fe 85 Si 2 B 8 P 4 Cu 1 amorphous alloy.6 Although Fe-based amorphous alloys have been widely studied by experimental and computational methods, the study of surface is rarely reported for these alloys.9 As we all know, it is important to study the surface in the amorphous and crystalline alloys because many studies have proved that the structure and properties of the surface component are obviously different from those of the interior component.10−13 For example, the surface component has a lower average coordination number, a lower average bond length and packing density, a higher degree of ordering, and a lower glass-transition temperature in the Cu64Zr36 zerodimensional small-size amorphous particles.11 It is also found that the AuSi amorphous alloys exhibit strong surface segregation of Si.10 Besides, a higher magnetic moment is observed in the surface of crystalline Fe.12,13 © XXXX American Chemical Society

Therefore, the study of surface is meaningful for the Febased amorphous alloys. Fe−B−Si alloys are important basic alloys and widely investigated among the Fe-based amorphous alloys.14−16 Among the Fe−B−Si alloys, the Fe78B13Si9 amorphous alloy is representative because it has been used in industrial production. Therefore, the atomic structure and magnetic properties of the Fe78B13Si9 amorphous alloy surface is investigated by ab initio molecular dynamics simulation in the present study. The atomic-level structure is characterized by the pair correlation function (PCF), bond angle distribution (BAD), bond pair (BP), and bond-orientational order (BOO) parameters. Meanwhile, the magnetic moment and local density of states (DOS) of Fe are calculated to investigate the magnetic properties. It is expected that this study could promote the understanding of surface in the Fe-based amorphous alloys.

2. COMPUTATIONAL DETAILS The AIMD simulation and static structural optimization were carried out using the Vienna ab initio simulation package based on density functional theory.17 In our study, exchange− correlation potentials were calculated by Perdew and Wang’s functional with a generalized gradient approximation.18 The projected augmented wave method was used to describe electron−ion interactions.19 Only Γ point was used to sample the Brillouin zone. The value of plane-wave cutoff energy was set to be 450 eV. Received: July 8, 2018 Revised: November 3, 2018 Published: November 30, 2018 A

DOI: 10.1021/acs.jpcc.8b06516 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. (a) Composition variation of Fe along the Z-axis. (b) Pair correlation functions of the two-dimensional Fe78B13Si9 amorphous slab. (c−e) Partial pair correlation function of surface and interior components in the Fe78B13Si9 amorphous slab.

density (ρ equals N/V, where N is the total number of atoms and V is the volume of the bulk materials). However, it is inappropriate for the surface of the bulk materials and twodimensional slabs in the simulation. Therefore, the developed PCF is adopted herein,11 which is defined by the following equation

First, the amorphous structure of Fe78B13Si9 was constructed. A cubic supercell with 200 atoms was simulated in a canonical ensemble (NVT) with periodic boundary condition. The original size was determined by the experimentally measured density of the amorphous alloy at room temperature (7.18 g/ cm3). The time step was set to be 2 fs. The system was melted and well equilibrated for 5000 AIMD steps at 1500 K and sequentially quenched to 300 K with a cooling rate of 1 K/ step. At 300 K, the system was relaxed for 3000 AIMD steps. Second, the initial slab was prepared by inserting a 10 Å thick vacuum layer into the obtained amorphous Fe78B13Si9. Finally, a series of AIMD annealing simulations were performed to examine the composition variation of the surface component in the Fe78B13Si9 slab. The initial Fe78B13Si9 slab was equilibrated for 2 ps at 750 K and relaxed for 3 ps at 300 K. The temperature increased from 300 to 750 K and decreased from 750 to 300 K at the rate of 1 K/step. The annealing procedure was repeated for seven cycles until no obvious composition variation was observed. A similar method has also been used in previous studies.10,20 As a comparison, an additional supercell with a different seed for the random generation of the initial configuration was also simulated by the same method. The mentioned results in this article were obtained from the first supercell, which are consistent with the results of the additional supercell.

dn(r ) with S(r )′ρ dr l o fy ij 2 o o jjjr + d ≤ zzzz o o 4πr o 2 o k { o o o o o o f f f yz i y i j z j S(r )′ = o m o 2πr jjjr + 2 − d zzz jjj 2 < r + d and r − d ≤ 2 zzz o o k { k { o o o o o o o jijr − d > f zyz o 2πrf o jj z o o 2 z{ k n

g (r )′ =

(2)

where ρ denotes the number density of the bulk materials, f is the thickness of the slabs, and d denotes the distance between the central atom and the perpendicular bisector plane of the slabs. It should be noted that a part of a spherical shell can be located outside the slabs, and it is not counted in the developed PCF. As we all know, the slabs are composed of surface and interior components. For the surface or interior components, the definition of PCF is the same as that of the slabs, except that ρ is the number density of the surface or the interior component, f is the thickness of the surface or interior component, d denotes the distance between the central atom and the perpendicular bisector plane of the surface or the interior component, and dn(r) denotes the number of atoms in the spherical shell in the surface or the interior component. There are two ways to estimate the thickness of the surface component for the low-dimensional amorphous systems: one is based on the composition variation along the thickness direction for the two-dimensional amorphous films, and the

3. RESULTS AND DISCUSSION 3.1. Partial Pair Correlation Functions. The pair correlation function is one of the most useful methods to describe the atomic structure. The traditional PCF g(r) for the bulk materials can be expressed as21 g (r ) =

dn(r ) withS(r ) = 4πr 2 S(r )ρ d r

(1)

where dn(r) denotes the number of atoms in the spherical shell, S(r) is the surface area of the shell, and ρ is the number B


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Figure 2. Total and partial bond angle distributions of surface and interior components in the Fe78B13Si9 amorphous slab.

neighbor atom is confirmed by the first valley of the corresponding partial PCF curve. Figure 2 shows the bond angle distributions of surface and interior components. As shown in Figure 2a, the total BADs of both surface and interior components show a prominent first peak, a broad second peak, and a rather flat third peak. However, a higher first peak and a lower third peak are observed in the total BAD of the surface component. This indicates that the number of the small bond angles increases and the number of large bond angles decreases from the interior component to the surface component. As shown in Figure 2b−d, the first peaks are roughly at 57, 61, and 71° and the second peaks are at ∼105, 117, and 131° for Fe-, Si-, and B-centered BADs in the interior component, respectively. Besides, the atomic radii of Fe, Si, and B are 1.24, 1.17, and 0.9 Å, respectively.24 Apparently, the peak positions of partial BADs increase with the decrease of the corresponding atomic radii. However, the first two peak positions of Fe-centered BAD are close to those of Si-centered BAD in the surface component. Compared to those of the partial BADs in the interior component, the peaks of Fecentered BAD shift to larger angles and the peaks of Sicentered BAD shift to smaller angles in the surface component. This phenomenon may be qualitatively explained by taking the bond length into account. The average bond length of Fe and its nearest-neighbor atoms decreases (from 2.52 to 2.48 Å) and that of Si and its nearest-neighbor atoms increases (from 2.46 to 2.49 Å) from the interior component to the surface component, which results in the increase or decrease of the corresponding bond angle.25 3.3. Bond Pair Analysis. The bond pair analysis proposed by Honeycutt and Andersen is an effective method to describe the local atomic structure.26 The bond pair between the central atom and the nearest-neighbor atom is defined by the first valley of the corresponding partial PCF curve. Four indexes i, j,

other one is defined by the first valley in the PCF for the zerodimensional amorphous particles.11 The composition can be calculated by subdividing the slab into smaller slabs and counting the number of atoms within each subdivision. The composition variation is not enough to exactly determine the thickness of the surface component of the Fe78B13Si9 slab because the composition variation is dramatic, resulting from only 200 atoms in the Fe78B13Si9 slab. Therefore, as a reference, the first valley in the PCF is also adopted. Using the first valley is not an unreasonable value from the atomic packing short-range order point of view.11,22 The composition variation of Fe along the Z-axis (thickness direction) is shown in Figure 1a. It can be seen that the Fe content obviously deviates from the nominal composition in the surface with a length of about 3 Å. Figure 1b shows that the position of valley is also located at about 3 Å in the total PCF of the twodimensional Fe78B13Si9 amorphous slab. Therefore, 3 Å is adopted to be the thickness of the surface component in the Fe78B13Si9 amorphous slab. Figure 1c−e shows the partial pair correlation functions of surface and interior components. They exhibit typical characters of an amorphous structure with a split in the second peak. Meanwhile, more pronounced splits are observed in the surface partial PCF of Fe−Fe and Fe−Si pairs compared to those in the interior partial PCF, implying a more ordered atomic arrangement in the surface component. Compared to that for the interior partial PCF, the first peak of Fe−Fe is higher in intensity and shifts to a smaller interatomic distance, which indicates a lower average Fe−Fe bond length on the surface. 3.2. Bond Angle Distribution. Bond angle distribution is adopted to represent the spatial relations of the central atom and its two nearest-neighbor atoms.23 The upper limit of the bond length between the central atom and the nearestC


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The Journal of Physical Chemistry C l, and m are used to distinguish the bond pair. If atoms A and B form a bond, i = 1; otherwise i = 2. j denotes the number of near neighbors that form bond with atom A and atom B. l is the number of bonds formed by the shared neighbors. m is added to classify the bond arrangement when the first three indexes are not sufficient to distinguish the bond pair. For example, the 1541 and 1431 bond pairs represent distorted icosahedral ordering and the 1551 bond pair represents perfect icosahedral ordering. The 1421 and 1422 bond pairs are characteristic of the face-centered cubic (fcc) and hexagonal closest packed (hcp) structures, respectively. The fractions of both 1421 and 1422 bond pairs are around 50% in the hcp crystal, whereas the 1421 bond pair is dominant in the fcc crystal. The bcc structure is characterized by 1441 and 1661 bond pairs. The 1311 and 1321 bond pairs reflect a rhomboidal symmetry. The bond pair distributions of surface and interior components are shown in Figure 3. It can be seen that the

N (i)

qlm(i) =

b 1 ∑ Ylm(rij) Nb(i) j = 1

(4)

where Nb(i) denotes the number of the nearest neighbors of the central atom i, Ylm is the spherical harmonics, l is the free integer parameter, m is an integer that runs from −l to l, and rij is the vector from the central atom i to the nearest neighbor j. Then, the coarse-grained version of the BOO parameter is developed by Lechner and Dellago28 as ij 4π Q l(i) = jjjj j 2l + 1 k Here

l

∑ m =−l

y |qlm(i)| zz z { 2z zz

1/2

(5)

Ñ (i)

qlm ̅ (i ) =

b 1 q (k ) ∑ Ñ b(i) k = 0 lm

(6)

where the sum of k from 0 to Ñ b(i) runs over all of the nearest neighbors of the central atom i and atom i itself. It is clear that the information of the second neighbor shell is taken into account in the coarse-grained version. Two flows of the local bond order parameters are pointed out by Mickel et al.29 Therefore, the coarse-grained version is adopted to describe the bond-orientational order of the slab. Among the Ql parameters, Q4 and Q6 are the most prominent order parameters to determine the crystal structures.28 Higher average Q4 and Q6 represent a higher degree of the crystallike symmetries in the simulated system.11,28 Figure 4 displays

Figure 3. Distribution of bond pairs of surface and interior components in the Fe78B13Si9 amorphous slab.

icosahedral BPs, with indexes of 1551, 1541, and 1431, are preponderant and their fractions are about 61 and 74% for surface and interior components, respectively. This indicates that the icosahedral ordering with 5-fold symmetry is dominant in both surface and interior components. It is found that the fractions of crystalline BPs, with indexes of 1421, 1422, 1441, and 1661, in the surface component are obviously less than those in the interior component. As shown in Figure 3, a small number of 1311 and 1321 BPs is detected in the interior component. However, the proportion of 1311 and 1321 BPs is as large as 24% in the surface component. One reason may be that the atoms in the surface component have fewer near neighbors, which results in fewer bonds formed by the shared neighbors. 3.4. Bond-Orientational Order. The bond-orientational order parameter is used to characterize the atomic cluster symmetry in the slab. Steinhardt et al. introduced the local bond order parameters27 ij 4π ql(i) = jjjj j 2l + 1 k

l

∑ m =−l

y |qlm(i)| zz z {

Figure 4. Variation of Q4 and Q6 along the Z-axis in the Fe78B13Si9 amorphous slab.

the variation of Q4 and Q6 along the Z-axis. In the interior component, a nearly constant Q4 and slowly varying Q6 are observed. Meanwhile, Q4 and Q6 exhibit a steep increase in the surface component. The average Q4 values are 0.070 and 0.043 and the average Q6 values are 0.20 and 0.15 for surface and interior components, respectively. The higher Q4 and Q6 values represent a higher degree of ordering in the surface component. It cannot be speculated that more crystal-like clusters exist in the surface component because the average Q4 and Q6 values are obviously less than those for body-centered cubic (bcc), fcc, and hcp crystals.28 3.5. Magnetic Moment and Local Density of States (DOS) of Fe. The atomic structure is distinctly different between the surface and interior components in the slab, which has an important effect on the magnetic property. Figure 5

2z zz

1/2

(3)

Here D


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interior component. However, the Fe d spin-down states do not reveal this trend. This is because of a concomitant transfer of electrons from the spin-down states to the spin-up states as the coordination number decreases from the interior to the surface component.12 Besides, the Fe d states split into two main peaks and the peaks of spin-down states shift to a higher energy, which is consistent with some Fe-based metallic glass.30,31

4. CONCLUSIONS Ab initio molecular dynamics simulation was adopted to study the atomic structure and magnetic properties of the surface in the Fe78B13Si9 amorphous slab. The atomic structure of the surface component is remarkably different from that of the interior component in the following aspects: (1) the first peak shifts to a smaller interatomic distance, and the second peak has more pronounced splits in the surface partial PCF of Fe− Fe pair compared to those in the interior partial PCF; (2) the first two peak positions of Fe-centered BAD are close to those of Si-centered BAD in the surface component because of the decrease of the average bond length of Fe-centered atoms and increase of the average bond length of Si-centered atoms; (3) there are more icosahedral and crystalline BPs in the interior component and more 1311 and 1321 BPs in the surface component; and (4) higher Q4 and Q6 values are observed in the surface component. Besides, it is found that the magnetic moment increases with the decrease of the number of magnetic atoms around the central atoms in the first shell and the surface component has a larger average magnetic moment (2.23 μB) than that of the interior component (2.01 μB) in the Fe78B13Si9 amorphous slab.

Figure 5. Distribution of Fe magnetic moment along the Z-axis in the Fe78B13Si9 amorphous slab.

shows the distribution of Fe magnetic moment along the Zaxis. The average coordination number of Fe−Fe along the Zaxis is also presented for comparison. It can be seen that the Fe magnetic moment is almost invariable in the interior component. In the surface component, the Fe magnetic moment drastically increases on approaching the surface of the slab. It is reported that the magnetic moment increases due to the decrease of the number of magnetic atoms in the first shell and the increase of the bond length among magnetic atoms and that the bond length usually has a larger effect on the magnetic moment than that of the coordination number.6,12 However, it is observed that the average Fe magnetic moment increases with the decrease of the average coordination number of Fe−Fe in the surface component (shown in Figure 5) and that the average Fe−Fe bond length does not exhibit an obvious trend along the Z-axis (not shown here). Therefore, we can speculate that the surface component has a larger average magnetic moment (2.23 μB) than that for the interior component (2.01 μB) because of the low coordination number of Fe−Fe in the surface component. To further understand the variation of the magnetic moment, the partial local density of states of Fe in the surface and interior components is shown in Figure 6. The Fermi level EF is set to zero as the reference energy state. It is clear that the electronic states are dominated by the Fe d states, indicating that Fe d states make a major contribution to the magnetization. The Fe d spin-up states below the Fermi level in the surface component are obviously higher than those in the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Tao Zhang: 0000-0002-9561-3242 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was carried out by TianHe-1(A) at the National Supercomputer Center in Tianjin and supported by the National Key Research and Development Program of China (Grant No. 2016YFB03005) and the National Natural Science Foundation of China (Grant No. 51571005).

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REFERENCES

(1) Lu, Z. P.; Liu, C. T.; Thompson, J. R.; Porter, W. D. Structural amorphous steels. Phys. Rev. Lett. 2004, 92, No. 245503. (2) Inoue, A.; Shen, B. New Fe-based bulk glassy alloys with high saturated magnetic flux density of 1.4−1.5 T. Mater. Sci. Eng. A 2004, 375−377, 302−306. (3) Suryanarayana, C.; Inoue, A. Iron-based bulk metallic glasses. Int. Mater. Rev. 2013, 58, 131−166. (4) 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. (5) Wang, F.; Inoue, A.; Han, Y.; Zhu, S. L.; Kong, F. L.; Zanaeva, E.; Liu, G.; Shalaan, E.; Al-Marzouki, F.; Obaid, A. Soft magnetic FeCo-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.

Figure 6. Partial local density of states (DOS) of Fe of surface and interior components in the Fe78B13Si9 amorphous slab. E


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The Journal of Physical Chemistry C (6) Wang, Y.; Takeuchi, A.; Makino, A.; Liang, Y.; Kawazoe, Y. Nano-crystallization and magnetic mechanisms of Fe85Si2B8P4Cu1 amorphous alloy by ab initio molecular dynamics simulation. J. Appl. Phys. 2014, 115, No. 173910. (7) 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. (8) Yu, Q.; Wang, X. D.; Lou, H. B.; Cao, Q. P.; Jiang, J. Z. Atomic packing in Fe-based metallic glasses. Acta Mater. 2016, 102, 116−124. (9) Dobromir, M.; Neagu, M.; Popa, G.; Chiriac, H.; Pohoaţa,̆ V.; Hison, C. Surface and bulk magnetic behavior of Fe−Si−B amorphous thin films. J. Magn. Magn. Mater. 2007, 316, e904−e907. (10) Lee, S. H.; Stephens, J. A.; Hwang, G. S. On the nature and origin of Si surface segregation in amorphous AuSi alloys. J. Phys. Chem. C 2010, 114, 3037−3041. (11) Zhang, W. B.; Liu, J.; Lu, S. H.; Zhang, H.; Wang, H.; Wang, X. D.; Cao, Q. P.; Zhang, D. X.; Jiang, J. Z. Size effect on atomic structure in low-dimensional Cu-Zr amorphous systems. Sci. Rep. 2017, 7, No. 7291. (12) Liu, F.; Press, M. R.; Khanna, S. N.; Jena, P. Magnetism and local order: Ab initio tight-binding theory. Phys. Rev. B 1989, 39, 6914. (13) Spencer, M. J.; Hung, A.; Snook, I. K.; Yarovsky, I. Density functional theory study of the relaxation and energy of iron surfaces. Surf. Sci. 2002, 513, 389−398. (14) Chrissafis, K.; Maragakis, M. I.; Efthimiadis, K. G.; Polychroniadis, E. K. Detailed study of the crystallization behaviour of the metallic glass Fe75Si9B16. J. Alloys Compd. 2005, 386, 165−173. (15) Qin, J.; Gu, T.; Yang, L.; Bian, X. Study on the structural relationship between the liquid and amorphous Fe78Si9B13 alloys by ab initio molecular dynamics simulation. Appl. Phys. Lett. 2007, 90, No. 201909. (16) Ramanujan, R. V.; Zhang, Y. R. Solid state dendrite formation in an amorphous magnetic Fe77.5Si13.5B9 alloy observed by in situ hot stage transmission electron microscopy. Appl. Phys. Lett. 2006, 88, No. 182506. (17) 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. (18) Wang, Y.; Perdew, J. P. Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling. Phys. Rev. B 1991, 44, 13298. (19) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758. (20) Zhang, X.; Li, R.; Zhang, T. Ab initio molecular dynamics simulation of the surface composition of Co54Ta11B35 metallic glasses. J. Non-Cryst. Solids 2015, 425, 199−206. (21) Blaineau, S.; Jund, P.; Drabold, D. A. Physical properties of a GeS2 glass using approximate ab initio molecular dynamics. Phys. Rev. B 2003, 67, No. 094204. (22) Danilov, D.; Hahn, H.; Gleiter, H.; Wenzel, W. Mechanisms of Nanoglass Ultrastability. ACS Nano 2016, 10, 3241−3247. (23) Cheng, Y. Q.; Ma, E. Atomic-level structure and structure− property relationship in metallic glasses. Prog. Mater. Sci. 2011, 56, 379−473. (24) Takeuchi, A.; Inoue, A. Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element. Mater. Trans. 2005, 46, 2817−2829. (25) Jóvári, P.; Saksl, K.; Pryds, N.; Lebech, B.; Bailey, N. P.; Mellergård, A.; Delaplane, R. G.; Franz, H. Atomic structure of glassy Mg60Cu30Y10 investigated with EXAFS, x-ray and neutron diffraction, and reverse Monte Carlo simulations. Phys. Rev. B 2007, 76, No. 054208. (26) Honeycutt, J. D.; Andersen, H. C. Molecular dynamics study of melting and freezing of small Lennard-Jones clusters. J. Phys. Chem. 1987, 91, 4950−4963.

(27) Steinhardt, P. J.; Nelson, D. R.; Ronchetti, M. Bondorientational order in liquids and glasses. Phys. Rev. B 1983, 28, 784. (28) Lechner, W.; Dellago, C. Accurate determination of crystal structures based on averaged local bond order parameters. J. Chem. Phys. 2008, 129, No. 114707. (29) Mickel, W.; Kapfer, S. C.; Schröder-Turk, G. E.; Mecke, K. Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter. J. Chem. Phys. 2013, 138, No. 044501. (30) Ganesh, P.; Widom, M. Ab initio simulations of geometrical frustration in supercooled liquid Fe and Fe-based metallic glass. Phys. Rev. B 2008, 77, No. 014205. (31) 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, No. 104901.

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Atomic Structure And Magnetic Properties Of The Fe78B13Si9

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