on Fe-based amorphous alloys by ab initio molecular dynamics ...

Study of the effects of metalloid elements (P, C, B) on Fe-based amorphous alloys by ab initio molecular dynamics simulations Wenbiao Zhang, Qiang Li, and Haiming Duan Citation: Journal of Applied Physics 117, 104901 (2015); doi: 10.1063/1.4914303 View online: http://dx.doi.org/10.1063/1.4914303 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/117/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Atomic packing and diffusion in Fe85Si2B9P4 amorphous alloy analyzed by ab initio molecular dynamics simulation J. Appl. Phys. 117, 17B705 (2015); 10.1063/1.4907230 Nano-crystallization and magnetic mechanisms of Fe85Si2B8P4Cu1 amorphous alloy by ab initio molecular dynamics simulation J. Appl. Phys. 115, 173910 (2014); 10.1063/1.4875483 The relationship between the stability of glass-forming Fe-based liquid alloys and the metalloid-centered clusters J. Appl. Phys. 112, 023514 (2012); 10.1063/1.4737613 Mechanical properties, glass transition temperature, and bond enthalpy trends of high metalloid Fe-based bulk metallic glasses Appl. Phys. Lett. 92, 161910 (2008); 10.1063/1.2917577 Study on the structural relationship between the liquid and amorphous Fe 78 Si 9 B 13 alloys by ab initio molecular dynamics simulation Appl. Phys. Lett. 90, 201909 (2007); 10.1063/1.2737937

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 124.117.210.67 On: Thu, 12 Mar 2015 02:35:10

JOURNAL OF APPLIED PHYSICS 117, 104901 (2015)

Study of the effects of metalloid elements (P, C, B) on Fe-based amorphous alloys by ab initio molecular dynamics simulations Wenbiao Zhang, Qiang Li,a) and Haiming Duana) School of Physics Science and Technology, Xinjiang University, Urumqi, Xinjiang 830046, China

(Received 10 December 2014; accepted 25 February 2015; published online 10 March 2015) In order to understand the effects of the metalloid elements M (M: P, C, B) on the atomic structure, glass formation ability (GFA) and magnetic properties of Fe-based amorphous alloys, Fe80P13C7, Fe80P14B6 and Fe80B14C6 amorphous alloys are chosen to study through first-principle simulations in the present work. The atomic structure characteristic of the three amorphous alloys is investigated through the pair distribution functions (PDFs) and Voronoi Polyhedra (VPs) analyses. The PDFs and VPs analyses suggest that the GFA of the three alloys dropped in the order of Fe80P13C7, Fe80P14B6, and Fe80B14C6, which is well consistent with the experimental results. The density of state (DOS) of the three amorphous alloys is calculated to investigate their magnetic properties. Based on the DOS analysis, the average magnetic moment of Fe atom in Fe80P13C7 and Fe80P14B6 amorphous alloys can be estimated to be 1.71 lB and 1.70 lB, respectively, which are in acceptable agreement with the experimental results. However, the calculated average magnetic moment of Fe atom in Fe80B14C6 amorphous alloy is about 1.62 lB, which is far less than the C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4914303] experimental result. V

I. INTRODUCTION

Recently, amorphous alloys have attracted great interest from both industry and fundamental science owing to their unique structure and excellent properties.1 In general, the stability and properties of material are closely related to their atomic structure. Nevertheless, the structure of amorphous alloys is still unclear so far due to the lack of the efficient atomic structure model and characterization technique. As a result, the glass forming ability (GFA) and many properties of amorphous alloys cannot be well understood and illustrated from the perspective of atomic-level structure. Recently, molecular dynamics simulations have been employed to provide an understanding of the GFA and properties of amorphous alloys. The Cu45Zr45Ag10 amorphous alloys with excellent GFA are investigated by simulations to study the effect of atomic structure on GFA.2 The relationships between the stability of glass-forming Fe-based liquid alloys and the metalloid-centered clusters has been investigated by simulations.3 Electronic and magnetic properties of Fe80P11C9 (Ref. 4) and Fe-B amorphous alloys5 have been investigated by first-principle simulations. And the local atomic ordering in Fe83M17 (M: C, B, P) amorphous alloys have also been studied by a computer simulation method.6 It is widely recognized that the metalloid elements (i.e., P, C, B) are essential to the formation of Fe-based amorphous alloys. Meanwhile, the content of metalloid elements also strongly affects the properties, including thermal stability, mechanical and magnetic properties, of Fe-based amorphous alloys.7 However, the effects of metalloid elements on the GFA and properties of Fe-based amorphous alloys have not been systematically investigated until now. In this study,

we do the research about atomic structure of Fe80P13C7, Fe80B14C6 and Fe80P14B6 amorphous alloys by ab inito molecular dynamics simulations. We chose the three alloys for the reasons that they are the typical ternary Fe-metalloid amorphous alloys, which had been widely investigated8,9 and were frequently chosen as the base alloys to develop Fe-based bulk metallic glasses.10 The present study will enable us to understand the effect of metalloid elements P, C, and B on the GFA and properties of Fe-based amorphous alloys from the perspective of atomic structure. The local environments around metalloid atoms and their roles in these amorphous alloys have also been discussed. Furthermore, we calculated the density of states (DOS) of the three amorphous alloys, based on which the effect of the metalloid elements on the magnetic properties of the three Fe-based amorphous alloys are discussed. II. EXPERIMENTAL

To verify the simulation results, Fe80P13C7, Fe80B14C6, and Fe80P14B6 melt-spun glassy ribbons were prepared by a melt-spinning technique and the thickness of the resultant glassy ribbons is 25 lm. The amorphous nature of the as-prepared glassy ribbons was confirmed by X-ray diffractometer (XRD) with Cu Ka radiation. The thermal behavior of the as-prepared glassy ribbons was investigated by Differential scanning calorimetry (DSC) under an Ar atmosphere at a heating rate of 0.33 K/s. Magnetic properties of the as-prepared glassy ribbons were measured by vibrating sample magnetometer (VSM) with the maximum of applied field of 800 kA/m at room temperature. III. COMPUTATIONAL METHODS

a)

Authors to whom correspondence should be addressed. Electronic addresses: [email protected] (Tel.: þ86-991-8583183) and [email protected] (Tel.: þ86-991-8582405).

0021-8979/2015/117(10)/104901/8/$30.00

The present calculations were performed by using the Vienna ab initio simulation package (VASP).11 The

117, 104901-1

C 2015 AIP Publishing LLC V


104901-2

Zhang, Li, and Duan

projected augmented wave (PAW) method was implemented and Perdew and Wang’s functional PW91 with a generalized gradient approximation (GGA) was used to describe electronic exchange and correlation effects.12,13 All the simulations were carried out in the canonical ensemble (NVT) with the temperature controlled by a Nose thermostat.14 A cubic supercell containing 100 atoms was employed and the size of the cell was estimated according to the density of alloys in the room temperature. The cell firstly melted and equilibrated at 1600 K and gradually cooled to 1250 K and then to 300 K with a cooling rate of 1.67 1014 K/s and the time step was 3 fs. The C point alone was used to sample the Brillouin zone of the supercell. The density of states (DOS) was calculated with spin polarization considered and magnetic properties of the samples were discussed based on the DOS analysis. IV. STRUCTURE PROPERTY AND GFA

The atomic structure characteristic is investigated mainly through the pair distribution functions, bond strength and Voronoi Polyhedra (VPs) analysis. We perform the pair distribution functions (PDFs) g(r) of Fe-Fe, Fe-M (M: P, C, B) and M-M in Fe80P13C7, Fe80B14C6 and Fe80P14B6 alloys at 1600 K and 300 K as shown in Fig. 1. It can be seen that, with the decrease of temperature, the height of the first peak obviously increases in all the PDFs, and most of the peaks shift toward larger distance and the second peak tends to split

J. Appl. Phys. 117, 104901 (2015)

into two sub-peaks. These features indicate that the shortrange order (SRO) structure is becoming more dominant with the decrease of temperature. The positions of the first peaks for gFe-Fe(r) and gFe-M(r) at 1600 K and 300 K are listed in Table I. It can be found from Fig. 1 and Table I that the first peak of gFe-Fe(r) in all the three alloys moves to a larger distance, implying that the Fe-Fe bond length increases, with the decrease of temperature, which can be attributed to the larger bond length between Fe atoms in ferromagnetic iron than that in paramagnetic iron.15 Among the three alloys, the shift distance of the first peak position of ˚ for Fe80P13C7 and 0.10 A ˚ for gFe-Fe(r) is about 0.12 A ˚ Fe80P14B6, while that is merely 0.02 A for Fe80B14C6. The gFe-Fe(r) and gFe-M(r) PDFs all have the pronounced first peaks in smaller distance and the minor second peaks, however, the first peaks of gM-M(r) locate at a larger distance (except B-B) and the second peaks could not be neglected. These features in PDFs suggest that covalent bonding exists in Fe-M pairs, while M-M is likely to be the second neighbor. The B-B PDF shows a narrower peak in a small distance, suggesting that B-B bond may exist in the present B-containing Fe-based alloys. It can be seen from Figs. 2 and 3 that the P-P, P-C, C-C, P-B PDFs present the negligible first nearest peaks, demonstrating the absence of direct solute–solute contacts, i.e., the better solute-solute avoidance, which is benefit to the GFA of alloys.16 However, B-C pairs have relatively poor avoidance, which may promote the crystallization and degrade the GFA of Fe80B14C6.

FIG. 1. Partial PDFs at 1600 K and 300 K (a) Fe-Fe, (b) Fe-P, (c) Fe-C, and (d) Fe-B.


104901-3

Zhang, Li, and Duan

J. Appl. Phys. 117, 104901 (2015)

TABLE I. The positions of the first peaks for gFe-Fe(r) and gFe-M(r) at the temperature of 1600 K and 300 K. Fe80P13C7

rFe-Fe rFe-C rFe-P rFe-B

Fe80B14C6

Fe80P14B6

1600 K

300 K

1600 K

300 K

1600 K

300 K

2.45 1.92 2.25 —

2.57 1.95 2.30 —

2.45 1.90 — 2.10

2.47 1.95 — 2.10

2.45 — 2.25 2.08

2.55 — 2.27 2.10

We further evaluate the first peak position of gFe-M(r), i.e., rFe-M, to illustrate the strength of Fe-M bond in the three alloys. The rFe-P is about 25% shorter than the arithmetical mean of rP-P and rFe-Fe in both the liquid and amorphous states of Fe80P13C7 and Fe80P14B6 alloys. The rFe-C shows a similar shorter about 32% than the arithmetical mean of rC-C

FIG. 3. Partial PDFs at 1600 K and 300 K (a) P-P, (b) P-B, (c) C-C.

FIG. 2. Partial PDFs at 1600 K and 300 K (a) B-B, (b) P-C, (c) B-C.

and rFe-Fe in both Fe80B14C6 and Fe80P13C7 alloys, while the rFe-B is just 1.2% shorter than the arithmetical mean of rB-B and rFe-Fe in Fe80B14C6 and Fe80P14B6 alloys. These imply that Fe-P and Fe-C bonding was stronger than Fe-B bonding. Furthermore, we calculate and plot the charge density between the Fe-Fe, Fe-P, Fe-C, and Fe-B of selective slice in order to visually present the atomic bonds using the charge density as shown in Fig. 4. The results of charge density show that Fe-P and Fe-C bonding is stronger than Fe-B bonding, which is also in agreement on the analysis of the first peak position of gFe-M(r). These results are supported by the values of DHmix{AB} calculated by Miedema’s model for atomic pairs, in which the heat of mixing for Fe-C, Fe-P, and Fe-B atomic pairs is 50 kJ/mol, 39.5 kJ/mol, and 26 kJ/mol, respectively.17 To further study the role of the metalloid elements in the GFA of the present Fe-based alloys, we perform Voronoi


104901-4

Zhang, Li, and Duan

J. Appl. Phys. 117, 104901 (2015)

FIG. 4. Charge density between the (a) Fe-Fe, (b) Fe-P, (c) Fe-C, and (d) Fe-B.

Polyhedra (VPs) analysis in liquid state. The Voronoi polyhedral index is expressed as hn3 n4 n5 n6i, where ni denotes the number of i-edged faces of the Voronoi polyhedron.18 Fig. 5 exhibits the most dominated atom-centered VPs for the different atoms in the three alloys. We find that (1) polyhedron for Fe atoms with the index of h0 3 6 3i, h0 3 6 4i and h0 2 8 2i, h0 2 8 1i, h0 1 10 2i has larger amount in all three alloys, indicating that icosahedral-like cluster frequently occur in all three melts, even the index h0 0 12 0i of perfect icosahedron are also existed. (2) For P-centered clusters, the similar index h0 3 6 3i, h0 2 8 2i, h0 2 8 1i exist mostly in both Fe80P13C7 and Fe80P14B6 alloys, suggesting that P atoms has the similar environment with Fe atoms or locate at the substitute position of Fe atoms, so the shortrange ordering around P atoms is mainly icosahedral-like, which is accorded with that in binary Fe83P17 alloys.6 Additionally, the h0 4 4 0i and h0 4 4 3i cluster, which can be regarded as the Archimedean antiprism, also exist in Fe80P13C7 alloy and do not exist in Fe80P14B6 alloy. (3) C-centered polyhedron in Fe80P13C7 and Fe80B14C6 alloys are mainly composed of h0 5 2 0i, h0 4 4 0i, and h0 3 6 0i, which are regarded as distorted trigonal prisms covered with one, two, and three half-octahedrons, respectively. (4) While B-centered polyhedron shows different index in Fe80B14C6 and Fe80P14B6 alloys. In Fe80P14B6 alloy, the h0 3 6 0i, h0 4 4 0i, and h0 2 8 0i have a large proportion, indicating that B atoms are mostly located at the center of prism-like VPs. In Fe80B14C6 alloys, the main B-centered polyhedron index are h0 3 6 0i and h0 3 6 3i, which present prism-like, and little h0 3 6 4i, h0 2 8 2i, and h0 2 8 1i, which present icosahedral-like. Based on the PDFs and VPs analyses, the GFA of the three Fe-based alloys can be compared. First, the longer Fe-Fe bond length decides the larger size of Fe-centered cluster, in which more Fe atoms and metalloid atoms may be

contained. And the clusters with a larger size are unfavorable for the diffusion of atoms. As mentioned in PDFs analysis, compared with Fe80B14C6 alloy, Fe80P13C7 and Fe80P14B6 alloys have the larger Fe-Fe bond length, thus better GFA. Additionally, the PDFs analysis shows that the bonding of Fe-P, Fe-C is stronger than that of Fe-B in the three amorphous alloys. And the stronger bonding between constituent elements is benefit for the glass forming,1 so it can be expected that Fe80P13C7 and Fe80P14B6 alloys should have better GFA than Fe80B14C6 alloy. Second, it is indicated that the better solute-solute avoidance of P-P, P-C, C-C and poor avoidance of B-B and B-C are existed in the three Fe-based amorphous alloys. The poor avoidance of metalloid atoms leads the system to being in a higher free energy state, thus offers more opportunity for atomic migration and constituent segregation at atomic scale, which are favorable for the crystallization of alloy.19 Therefore, it is considered that the solute-solute avoidance of metalloid atoms may also play an important role for the GFA.20 The PDFs and VPs analyses indicate that Fe80P13C7 and Fe80P14B6 alloys, in which have better solute-solute avoidance, may have better GFA compared with Fe80B14C6 alloy, in which has poor solute-solute avoidance. Additionally, according to the results of P-centered VPs, P atoms of Fe80P13C7 alloy exist in the form of mainly icosahedral-like and partial antiprism-like VPs which induce the structure complexity of melts and increase the GFA of Fe80P13C7, while antiprism-like VPs are not showed in the Fe80P14B6 alloy. Based on the above discussion, we speculate that the GFA of the three alloys is dropped in the order of Fe80P13C7, Fe80P14B6, and Fe80B14C6. And as so far, bulk Fe80P13C7 glassy alloy rod with a maximum diameter of 2.0 mm has been prepared,21 while the preparation of bulk Fe80P14B6 and Fe80B14C6 glassy alloys has not been reported. These facts seem to support our speculation. It is well known that


104901-5

Zhang, Li, and Duan

J. Appl. Phys. 117, 104901 (2015)

FIG. 6. DSC thermal scans of as-prepared Fe80P14B6, Fe80P13C7, and Fe80B14C6 melt-spun glassy ribbons at a heating rate of 0.33 K/s.

FIG. 5. Number of Voronoi polyhedra with central (a) Fe, (b) C, and (c) P atoms at 1600 K.

the GFA of amorphous alloys can be generally evaluated by some indicators for GFA, such as the reduced glass transition temperature Trg (¼Tg/Tl), the supercooled liquid region DTx x (¼Tx Tg) and the parameter c ( ¼ TgTþT ), in which Tg is the l glass transition temperature, Tx is the onset crystallization temperature, and Tl the liquids temperature. To further verify the validity of simulation results, we do the DSC scan of the three Fe-based amorphous alloy ribbons at a heating rate of 0.33 K/s as shown in Fig. 6. The corresponding thermal parameters determined from DSC scans together with the three common indicators for GFA (i.e., Trg, DTx, and c) are summarized in Table II. All the three indicators for GFA indicate that the GFA of Fe80P13C7, Fe80P14B6, and Fe80B14C6 alloys decrease successively, which is consistent with our speculation based on the simulation calculation. Further the structure features of the glass states are investigated using the bond pair analysis technique, which is an efficient method to describe the SRO features of the atomic clusters in the liquid or solid states.22 Honeycutt and

Anderson23 used four index number i, j, l, m to classify bonded pairs of atomic clusters. If atom A and atom B form a bond, i ¼ 1, and otherwise i ¼ 2. j denotes the number of near-neighbors which form bonds with atom A and atom B. l represents the number of bonds formed among the neighboring atoms. m is a special classifying index parameter. Two atoms are thought to form a bond if they are within a cutoff distance. Here, we use the distance to the first minimum in the pair correlation functions as the cutoff distances in our analysis. We count the bond pair distribution in the three Febased amorphous alloys at 300 K as shown in Fig. 7. It can be seen from Fig. 5 that the 1551 and 1541 bond pairs, which are corresponding to icosahedral cluster, have a large proportion, and the 1441 and 1661 bond pairs, which are related with bcc structure, also make up a considerable percentage. The bond pair distribution analysis indicates that the more orderly icosahedrons and bcc type SRO are mainly existed in the glass states of the three Fe-based amorphous alloys. V. DENSITY OF STATES AND MAGNETIC PROPERTIES

Based on the equilibrium structures, the spin polarized total and partial electronic density of states (DOS) of Fe80P13C7, Fe80P14B6, and Fe80B14C6 amorphous alloys are calculated. The DOSs of all the three amorphous alloys show the similar shapes. As an example, the DOS of the Fe80P13C7 amorphous alloy is showed in Fig. 8 and is then discussed in detail. The electronic states near the Fermi level for all the TABLE II. Summary of the thermal parameters of Fe80P14B6, Fe80P13C7, and Fe80B14C6 amorphous alloys determined from the DSC curves and the corresponding indicators of GFA. (Tm: the melting temperature; Tl: the liquids temperature; Trg ¼ Tg/Tl; DT ¼ Tx Tg; c ¼ Tx/Tg þ Tl). Amorphous alloys

Tc (K)

Tg (K)

Tx (K)

Tm (K)

Tl (K)

Trg

DT (K)

c

Fe80P13C7 Fe80P14B6 Fe80B14C6

588 606 664

678 688 722

701 708 742

1236 1314 1404

1318 1380 1468

0.548 0.524 0.494

23 20 20

0.351 0.342 0.338


104901-6

Zhang, Li, and Duan

FIG. 7. The distribution of main bond pairs in 300 K. (a) Fe80P13C7; (b) Fe80B14C6; (c) Fe80P14B6.

three amorphous alloys are dominated by the Fe-d states, and the d band of Fe split into two main peaks t2g and eg, which is similar with bcc Fe.24 The DOS of the Fe80P13C7 amorphous alloy indicates that this alloy is weak ferromagnetism (i.e., both spin bands are partially filled at the Fermi energy). And the DOSs of Fe80P14B6 and Fe80B14C6 alloys also show the same characteristic of weak ferromagnetism. It can be seen in Fig. 8 that the Fermi level locates near the local maximum of the DOS of the majority spin band and close to the local minimum of the DOS of the minority side. Ferromagnetism occurs when the Fermi level falls in the gap of spin-down band, and the deeper gap of spin-down band results in the stronger magnetism.25 Therefore, Fe80P13C7 alloy is ferromagnetic, which is consistent with the experimental result. Additionally, we evaluate the split between spin-up (majority) and spin-down (minority) Fe-d bands, which are 1.09 eV, 1.15 eV, and 1.25 eV for Fe80P13C7, Fe80P14B6, and Fe80B14C6, respectively. It is known that the band splitting is due to the exchange interaction of the band

J. Appl. Phys. 117, 104901 (2015)

electrons, and the stronger exchange interaction leads to the larger split between spin-up and spin-down bands. Further, based on the mean field theory,26 the Curie temperature (Tc) sensitively dependents on the strength of exchange interaction, and thus the larger band splitting corresponds to the higher Tc. It can be seen in Table II that the Tc of Fe80P13C7, Fe80P14B6, and Fe80B14C6 glassy ribbons are 588 K, 608 K, and 664 K, respectively. So the simulation results about the band splitting for the three amorphous alloys can account for the experimental results of Tc. It can be clearly seen from the partial DOS of Fe80P13C7 amorphous alloy that the magnetization is dominated by Fe 3d states, followed by a small contribution from 3p states of P and 2p states of C. We list the average magnetic moments of Fe and M (P, B, C) in Table III. Fe has the magnetic moment of 1.86 lB, 1.89 lB, and 1.80 lB in Fe80P13C7, Fe80P14B6, and Fe80B14C6 amorphous alloys, respectively. The metalloid elements (P, B, and C) have the similar magnetic moment in the three Fe-based amorphous alloys. Among the three metalloid elements, B has the largest negative magnetic moment of 0.12 lB, which is similar with the B average magnetic moment of 0.1 lB in Fe1xBx amorphous alloy,5 followed by C that has the average magnetic moment of about 0.11 lB, which is also similar with C with the average magnetic moment of about 0.12 lB in Fe80P11C9.4 P contributes to a minimum negative magnetic moment of about 0.06 lB. Therefore, we can see from the DOS results that Fe80P13C7 has the largest magnetic moment, followed by Fe80P14B6, and Fe80B14C6 has the smallest magnetic moment. Based on the magnetic valence theory,27 it is considered that the valence electrons, i.e., sp electrons, of the metalloid elements will transfer to the minority-spin band of Fe host. Hence, the metalloid elements with more sp electrons results in the more decrease of the saturation magnetization compared to the metalloid elements with less sp electrons. However, our simulation results do not seem to support the magnetic valence theory and suggest that the electrons do not transferred from metalloid elements to Fe. The average magnetic moment per Fe atom of Fe80P13C7, Fe80P14B6, and Fe80B14C6 amorphous alloys has been determined both from the total DOS simulation results and by VSM measurement at room temperature of the meltspun glassy ribbons, which are summarized in Table IV. The average magnetic moments per Fe atom of the measurement results are 1.77 lB, 1.81 lB, and 1.85 lB for Fe80P13C7, Fe80P14B6, and Fe80B14C6 glassy ribbons, respectively, while those of the simulation results are 1.71 lB, 1.70 lB, and 1.62 lB, respectively. It is indicated that the simulation results are within a basic acceptable range compared with the experimental results. Additionally, we also investigate the charge transfer in the three alloys using the Mulliken population analysis and the corresponding results are summarized in Table V. As shown in Table V, Fe atom transfer the charge to metalloid atoms in Fe80B14C6 amorphous alloy, while the opposite charge transfer occurs in Fe80P13C7 and Fe80P14B6 amorphous alloys, which may account for the DOS results that Fe80B14C6 amorphous alloy has the lower saturated magnetic moment than that of the other two


104901-7

Zhang, Li, and Duan

J. Appl. Phys. 117, 104901 (2015)

FIG. 8. Spin polarized total and partial DOS of Fe80P13C7 amorphous alloy. (a) Total DOS, (b) Fe DOS, (c) P DOS, and (d) C DOS. TABLE III. Average magnetic moment of s, p, and d states and the total magnetic moment of Fe, P, C and B atoms in Fe80P14B6, Fe80P13C7 and Fe80B14C6 amorphous alloys. atoms

s (lB)

p (lB)

d (lB)

Total (lB)

Fe80P13C7

Fe P C

0.0069 0.0025 0.0105

0.0221 0.057 0.098

1.886 0 0

1.86 0.0595 0.1085

Fe80P14B6

Fe P B

0.007 0.003 0.02

0.023 0.061 0.1

1.92 0 0

1.89 0.064 0.12

Fe B C

0.008 0.021 0.0117

0.03 0.099 0.0938

1.837 0 0

1.80 0.12 0.1055

Alloys

Fe80B14C6

TABLE IV. Comparison of the calculated and experimental magnetic moments of Fe atom at room temperature. Amorphous alloys Fe80P13C7 Fe80P14B6 Fe80B14C6

Experimental(lB)

Calculated(lB)

1.77 1.81 1.85

1.71 1.70 1.62

TABLE V. The mulliken population analysis of three amorphous alloys.

Fe80P13C7 Fe80B14C6 Fe80P14B6

Fe

P

C

B

0.077 0.108 0.098

0.424 – 0.542

0.09 1.00 –

– 0.190 0.042

amorphous alloys. However, it should be noted that, based on the magnetic valence theory,7,27 the saturation magnetization of the three Fe-based amorphous alloys should increase in order of Fe80P13C7, Fe80P14B6, and Fe80B14C6. The experimental results coincide with the magnetic valence theory, while the simulation results are just the opposite. The further studies on this problem are required. VI. CONCLUSION

The atomic structure and DOS of Fe80P13C7, Fe80P14B6, and Fe80B14C6 amorphous alloys were investigated by ab inito molecular dynamics simulations. Based on the simulation results, the effects of the metalloid elements M (M: P, C, B) on the atomic structure, GFA and magnetic properties of the three Fe-based amorphous alloys are studied and the following conclusions may be drawn: (1) The Fe-Fe bond length is larger in Fe80P13C7 and Fe80P14B6 amorphous alloys, and the bonding of Fe-P and Fe-C is stronger than that of Fe-B, both which are considered to be favorable for the GFA. And the B atom in Fe80B14C6 amorphous alloy show poor solute-solute avoidance, which degrades the GFA of the alloy. Additionally, the P induces the structure complexity of melts, thus increasing the GFA. Based on the above simulation results, we conclude that the GFA of the three alloys is dropped in the order of Fe80P13C7, Fe80P14B6, and Fe80B14C6. (2) The DOS simulation results indicate that the magnetization of the three Fe-based amorphous alloys increases in


104901-8

Zhang, Li, and Duan

the order of Fe80B14C6, Fe80P14B6, and Fe80P13C7. The metalloid elements of B, C, and P have the similar average magnetic moment in the three Fe-based amorphous alloys, which are about 0.12 lB, 0.11 lB, and 0.06 lB, respectively. The calculated average magnetic moment per Fe atom of Fe80P13C7 and Fe80P14B6 amorphous alloys can be estimated to be 1.71 lB and 1.70 lB, respectively, which are in acceptable agreement with the measurement results, while the calculated average magnetic moment per Fe atom of Fe80B14C6 amorphous alloy is about 1.62 lB, which is less than the measurement result. ACKNOWLEDGMENTS

This research was sponsored by the National Natural Science Foundation of China (No. 51261028) and Xinjiang Graduate Student Research Innovation Project (XJGRI2014015). 1

A. Inoue, Acta Mater. 48, 279–306 (2000). T. Fujita, K. Konno, W. Zhang, V. Kumar, M. Matsuura, A. Inoue, T. Sakurai, and M. W. Chen, Phys. Rev. Lett. 103, 075502 (2009). 3 S. X. Zhou, B. S. Dong, J. Y. Qin, D. R. Li, S. P. Pan, X. F. Bian, and Z. B. Li, J. Appl. Phys. 112, 023514 (2012). 4 H. Wang, T. Hu, and T. Zhang, Physica B: Condens. Matter 411, 161–165 (2012). 2

J. Appl. Phys. 117, 104901 (2015) 5

H. Tian, C. Zhang, J. Zhao, C. Dong, B. Wen, and Q. Wang, Physica B: Condens. Matter 407, 250–257 (2012). 6 A. V. Evteev, A. T. Kosilov, and E. V. Levtchenko, Acta Mater. 51, 2665–2674 (2003). 7 S. Meng, H. Ling, Q. Li, and J. Zhang, Scr. Mater. 81, 24–27 (2014). 8 T. A. Donnelly, T. Egami, and D. G. Onn, Phys. Rev. B 20, 1211 (1979). 9 S. N. Kaul and V. Srinivasa Kasyapa, J. Mater. Sci. 24, 3337–3344 (1989). 10 C. Suryanarayana and A. Inoue, Bulk Metallic Glasses (CRC Press, 2010). 11 G. Kresse and J. Furthm€ uller, Comput. Mater. Sci. 6, 15–50 (1996). 12 G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). 13 Y. Wang and J. P. Perdew, Phys. Rev. B 44, 13298 (1991). 14 S. Nose, J. Chem. Phys. 81, 511–519 (1984). 15 E. G. Moroni, G. Kresse, J. Hafner, and J. Furthm€ uller, Phys. Rev. B 56, 15629 (1997). 16 W. K. Luo, H. W. Sheng, and E. Ma, Appl. Phys. Lett. 89, 131927 (2006). 17 A. Takeuchi and A. Inoue, Mater. Trans. 46, 2817–2829 (2005). 18 N. N. Medvedev, J. Comput. Phys. 67, 223–229 (1986). 19 B. S. Dong, S. X. Zhou, D. R. Li, J. Y. Qin, S. P. Pan, Y. G. Wang, and Z. B. Li, J. Non-Cryst. Solids 358, 2749–2752 (2012). 20 K. Lu and J. T. Wang, J. Cryst. Growth 112, 525–530 (1991). 21 Q. Li, J. Li, P. Gong, K. Yao, J. Gao, and H. Li, Intermetallics 26, 62–65 (2012). 22 L. Hui, B. Xiufang, and W. Guanghou, Mater. Sci. Eng.: A 298, 245–250 (2001). 23 J. D. Honeycutt and H. C. Andersen, J. Phys. Chem. 91, 4950–4963 (1987). 24 N. F. Mott, Adv. Phys. 13, 325–422 (1964). 25 A. P. Malozemoff, A. R. Williams, and V. L. Moruzzi, Phys. Rev. B 29, 1620 (1984). 26 B. D. Cullity and C. D. Graham, Introduction to Magnetic Materials (John Wiley & Sons, 2011). 27 A. R. Williams, V. L. Moruzzi, A. P. Malozemoff, and K. Terakura, IEEE Trans. Magn. 19, 1983–1988 (1983).
