First-principle study of the structural, electronic, and magnetic properties of amorphous Fe–B alloys

Physica B 407 (2012) 250–257

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First-principle study of the structural, electronic, and magnetic properties of amorphous Fe–B alloys Hua Tian a,b,c, Chong Zhang a,b,c, JiJun Zhao a,c,n, Chuang Dong a,b, Bin Wen b,d, Qing Wang a,b a

Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Dalian University of Technology, Ministry of Education, Dalian 116024, China School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China c College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China d State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 June 2011 Accepted 24 October 2011 Available online 31 October 2011

The structural, electronic, and magnetic properties of amorphous Fe100  xBx alloys (x ¼ 9, 17, 25, 27.3, 33.3, 36.3) are investigated using first-principles calculations. In these amorphous alloys, the shortrange order is manifested as a series of Fe- or B-centered polyhedra such as tricapped trigonal prism, icosahedron, and bcc-like structural unit. The electron densities of states of the amorphous alloys resemble those of crystalline Fe borides, which further confirm the similarity of the local order in the amorphous and crystalline phases. All B atoms carry small negative moments of about  0.1mB, while small negative moments are also found on very few Fe sites for the Fe-rich compositions (x ¼ 9, 17). The average magnetic moment per Fe atom decreases nonlinearly with increasing B composition, which can be associated with the nonlinear relationship between mass density and composition. & 2011 Elsevier B.V. All rights reserved.

Keywords: Metallic glasses Fe–B Short-range order Magnetic properties Electronic properties

1. Introduction Bulk metallic glasses (BMGs) [1,2] have attracted great interest from both industry and fundamental science. A prominent category of metallic glasses is the transition-metal (TM. such as Ni, Fe, Co) and metalloid (M. such as P, B) amorphous alloys. They usually exhibit good glass-forming ability due to strong chemical affinity between the TM and the metalloid species, as well as a deep eutectic in the phase diagram. The compositions of these glasses are usually close to an archetypal TM80M20. Among them, Fe–B binary metallic glasses provide an important prototype of the transition-metal–metalloid glasses. So far, the structures and physical properties of these Fe–B glasses have been extensively investigated from different aspects, including short-range order (SRO), electronic structure, and magnetism [3–22]. The structural properties of the TM–M glasses are characterized by the atomic SRO, which reflects the local nearest-neighbor structures. It is generally accepted that the trigonal-prism-related SRO structures stabilize the TM–M amorphous alloys without a long-range correlation in the network formation [23–25], and that the connectivity and spatial extension of these trigonal-prism structural units form a kind of medium-range order (MRO) structure in the TM–M amorphous structures [26]. Parallel to n Corresponding author at: College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China. Tel.: þ 86 0411 84709748; fax: þ 86 0411 84706100. E-mail address: [email protected] (J. Zhao).

0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.10.042

the experimental characterization of structural properties, atomistic simulations provides a powerful tool to explore the atomic order of TM–M metallic glasses [4,5,27–29] like Fe–B alloys. Besides the structural properties, the Fe–B metallic glasses are attractive because of their intriguing magnetic behavior. In contrast to the linear composition dependence in the Ni–M and Co–M amorphous systems, experiments revealed that Fe-based glasses alloys exhibit nonlinear behavior and shows a maximum of magnetic moment at approximately 80% Fe [3,10–13,30,31]. Strong magnetovolume effect was observed in the Fe-based alloys, that is, the magnetic phase in Fe100 xBx glasses has two distinct composition regions. With higher B content, the magnetic moment in the amorphous Fe–B alloys decreases with increasing B concentration and is only slightly lower than that of the crystalline iron borides [12]. In the Fe rich regime, experimental data show rather scattering behavior, depending on the preparation condition and on the thermal history of the samples. As a rule, the magnetic moment is lower in vapor-quenched amorphous ribbons and decreases rapidly with decreasing B concentration [12,14,15]. Recent experiment by magnetic Compton scattering [21] measured the induced magnetic moment on the boron atoms, which is about  0.04 mB for Fe80B20 and Fe76B24 samples. In addition to the tremendous experimental efforts, Bratkovsky and Smirnov [19] and Hafner et al. [20] have preformed theoretical calculations on the Fe100 xBx amorphous alloys and discussed the relationship between magnetic moment and composition. The electronic structures of Fe100  xBx amorphous alloys have also been investigated by experiments [16,32] and first-principles

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calculations [18–20,22,33]. According to these calculations, the electronic states in the vicinity of Fermi level are dominated by the strong hybridization of the 3d bands from iron and the 2p bands from boron. The decrease of magnetic moment with increasing B contents was attributed to a dilution effect, that is, the polarizable d–d interaction is replaced by magnetically inert p–d interactions. Meanwhile, the electronic structures of crystalline FeB, Fe2B, and Fe3B solids have been studied by firstprinciples calculations [34] and similar characteristics of the electronic states were observed. Despite the previous efforts, there are still many unclear issues in the relationship of atomic structures, electronic structures, and magnetic properties of Fe100  xBx amorphous alloys, as well as their dependence on the compositions, which deserve a comprehensive understanding from the atomistic point of view. In this paper, using first-principles methods we have explored the atomic structures, electronic, and magnetic properties of Fe100  xBx (x ¼9, 17, 25, 27.3, 33.3, 36.3) amorphous alloys. The local order in these amorphous alloys is discussed by analyzing the Fe- and B-centered polyhedra. The analogy of local structural order and electronic properties in the amorphous and crystalline Fe–B alloys is revealed. The composition dependence of magnetic moments is also investigated.

2. Theoretical methods Amorphous Fe100  xBx alloys of several representative compositions at x ¼9, 17, 25, 27.3, 33.3, 36.3 have been considered. These alloys were modeled by a series of 300-atom cubic supercells. The initial atomic positions were generated randomly to maximize the Fe–B mixing. For each composition, three random configurations were constructed and relaxed. Most of the theoretical results discussed in Section 3 were obtained by averaging three computational samples for each composition and the standard deviations due to three configurations were presented to ensure a reliable statistical analysis. Starting from those 300-atom supercells, we performed firstprinciples calculations to optimize the atomic coordinates and supercell parameters of these Fe–B amorphous alloys of different compositions. As a representative, the relaxed atomic configuration of Fe75B25 is displayed in Fig. 1. Here we employed the density functional theory (DFT) and the plane-wave pseudopotential technique, as implemented in the Vienna Ab-initio Simulation Program (VASP) [35]. The exchange-correlation functional was treated by the generalized gradient approximation (GGA) with the Perdew–Wang (PW91) parameterization [36]. The interaction between ions and electrons was described by the projector augmented-wave (PAW) method [37]. The structure optimization was conducted according to the Hellmann–Feynman forces with ˚ converge criteria of the force on each ion less than 0.001 eV/A. During geometry optimization, the Brillouin zone of the reciprocal space was sampled by the G point, while a 2  2  2 k-point mesh was used to further compute the electronic structures. In order to take into account the magnetic properties of the systems, the Kohn–Sham equation were solved in the spin-polarized manner during all DFT calculations.

3. Results and discussion 3.1. Glass structure 3.1.1. Mass density The mass densities of crystalline bcc-Fe, Fe3B, Fe2B, FeB solids from our calculations and experiments [38] are plotted in Fig. 2.

Fig. 1. Atomic structure of Fe75B25 amorphous alloy. Larger (purple color) balls denoted the Fe atoms and smaller (light red) ones for B atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2. Mass densities of amorphous Fe100  xBx alloys and of crystalline Fe–B compounds as function of composition. Filled dots are experimental data for glass alloys from Ref. [3]; filled triangles are experimental data for Fe (bcc), FeB, Fe2B, Fe3B crystals from Ref. [38]; open circles are our simulation results for glass alloys, open triangles are our simulation results for Fe (bcc), FeB, Fe2B, Fe3B crystals. Our theoretical mass densities of the amorphous Fe–B alloys were averaged from three configurations for each composition, and the standard deviations for each composition are within 0.05 g/cm3.

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Good agreement between theory and experiment is found with the maximum deviation less than 0.11 g/cm3. This suggests that our theoretical method is appropriate for describing the structural properties of Fe–B binary metallic glasses. As a well-known feature of metallic glass, the densities of the amorphous Fe–B alloys are always substantially lower than their crystalline counterparts by about 5%. As shown in Fig. 2, density D of amorphous Fe100 xBx alloys decreases with increasing boron concentration. However, the reduction rate of the mass density, i.e., dD/dx, is nonlinear and depends on the boron concentration, that is, dD/dx¼  0.013 g/cm3 in the Fe-rich region (x¼9, 17), and dD/dx¼  0.024 g/cm3 for the higher B contents (x¼25, 27.3, 33.3, 36.3), respectively. Similar two-slope trend was observed in experiment [3], where a noticeable change in the density slope occurs at 21 at% of B. The reduced dD/dx in the Fe rich region implies a possible change in the atomic structure, as suggested by previous studies [3,39,40]. 3.1.2. Pair correlation function The pair correlation function g(r) (PCF) and partial PCFs gij(r) are important quantities to characterize the structural properties of condensed matter, particularly for the liquids and amorphous solids. Fig. 3 shows the gij(r) of Fe–Fe, Fe–B, and B–B pairs for Fe–B

Fig. 3. Partial pair correlation functions gij(r) (ij¼ Fe–Fe, Fe–B, B–B) of Fe100  xBx amorphous alloys of different compositions.

Table 1 Nearest-neighbor distance Rij and nearest-neighbor numbers Nij for different pairs of atoms (Fe–Fe, Fe–B, B–Fe ) in the amorphous of Fe–B alloys with different compositions, compared to the experimental values (Expt.) [7] for amorphous Fe83B17. (Theoretical results were averaged from three configurations for each composition. Standard deviations of the Nij and the Rij for each composition are ˚ respectively.). within 0.4 and 0.02 A, Fe63.7 B36.3

Fe66.7 B33.3

Fe72.7 B27.3

Fe75 B25

Fe83 B17

Fe83B17 (Expt.)

Fe91 B9

10.24 4.28 1.32 8.81 14.52 2.58 ˚ RFe–B (A) 2.15 ˚ RFe–Fe (A)

10.58 3.83 1.26 8.92 14.31 2.58

10.99 3.08 0.77 8.96 14.07 2.57

11.45 2.71 0.78 8.92 14.16 2.56

12.06 1.81 0.27 9.12 13.87 2.55

12.2 1.9 – – – 2.58

12.52 0.87 0.07 8.89 13.39 2.54

2.17

2.17

2.17

2.17

2.10

2.20

NFe–Fe NFe–B NB–B NB NFe

amorphous alloys with different compositions. For each composition, the three configurations exhibit similar PCF, thus the one with the lowest energy is chosen as a representative. By definition, gij(r) is the number of atom j that can be found at distance r from atom i. We determined the nearest-neighbor numbers NFe–Fe, NFe–B, NB–B by counting the number of atoms in the first-coordination shells in the equilibrium configurations, which are equivalent to integrating the first peak of radial distribution functions RDFij(r)¼cj4prr2gij(r) (r is the atomic density). Then the numbers of nearest neighbor for the Fe and B atoms can be calculated as NFe ¼NFe–Fe þNFe–B and NB ¼NB–Fe þNB–B, respectively. The nearest-neighbor distances RFe–Fe and RFe–B for different ij pairs of atoms can be estimated from the first peaks of the gij(r)’s. The nearest-neighbor numbers Nij as well as the nearest-neighbor distances RFe–Fe and RFe–B averaged for the three configurations of each composition are summarized in Table 1. Experimental data of Fe83B17 glass [7] are also listed for comparison. As shown in Fig. 3, the location and height of the first Fe–Fe and Fe–B peaks in the partial PCFs are insensitive to the Fe–B composition. Accordingly, in Table 1 one can see that the partial nearest-neighbor distance RFe–Fe and RFe–B only exhibit weak variations with composition (with amplitude less than ˚ For Fe83B17, the theoretical RFe–Fe and RFe–B are 2.55 A˚ 0.09 A). ˚ respectively, consistent with the experimental values and 2.17 A, ˚ [7]. Meanwhile, the height of (RFe–Fe ¼2.58 A˚ and RFe–B ¼ 2.10 A) the first B–B peak reduces with decreasing B content while the position of this peak remains invariant. When the B content is less than 9 at%, the first B–B peak almost disappears in the partial PCFs. As presented in Table 1, the nearest-neighbor number NFe–Fe decreases with increasing B concentration, while NFe–B increases. For Fe83B17, our simulations gave NFe–Fe ¼12.06 and NFe–B ¼1.8, which are in excellent agreement with measured values (NFe–Fe ¼12.2 and NFe–B ¼1.9, respectively) [7]. Overall speaking, the average nearest-neighbor number of Fe atom (NFe) is about 1470.5 and moderately changes with B concentration, whereas that of B atom (NB) is about 9 and nearly invariant with B concentration (variation less than 0.08). NB–B gradually decreases with decreasing B content and approach zero at the lower-boron region, e.g. NB–B ¼0.07 with 9 at% of B content. This is consistent with the change of the first B–B peak of gBB(r) in Fig. 3. Since the pair-correlation functions (Fig. 3) and the nearestneighbor numbers (Table 1) only describe the average structural characteristics, they show less correlation with Fe–B composition. To gain deeper insight into the variation of local structures with composition, we further counted the coordination numbers (CNs) for each atom and examine the distribution of coordination polyhedra in the next subsection.

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Fig. 4. Distribution of coordination numbers (CN) for the central B and Fe atoms in the amorphous Fe100  xBx alloys.

BFe9

B2Fe8

BFe8

B2Fe7

BFe10

B2Fe9

Fe12B

Fe13

Fe10B4

Fe11B3

Fe12B2

Fe14

Fe14B

Fe15

Fe12B3

Fe13B2

Fe13B3

Fe14B2

Fig. 5. Atomic structures of the representative B-centered clusters taken from the structures of amorphous Fe100  xBx alloys. Larger blue balls denote for Fe atoms; smaller pink balls for B atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.1.3. Coordination number and polyhedron To examine the short-range order and local structures of the amorphous Fe–B alloys, we first counted the local coordination numbers, which are defined as the numbers of first shell atoms for each central atom. The cutoff distances for the first shell were determined from the first valley of the corresponding partial PCFs for the Fe–Fe, Fe–B, and B–B pairs. By such definition, the central atom together with its first-shell atoms constitutes a coordination polyhedron. At each composition, we counted all B-centered and Fe-centered coordination polyhedra for the three configurations considered. The statistic distributions of these B- and Fe-centered polyhedra are displayed in Fig. 4. Some typical B- and Fe-centered polyhedra taken from the equilibrium structures are displayed in Figs. 5 and 6. As shown in Fig. 4(a), the most abundant type of local polyhedron surround B atom is the CN9 one for all compositions. These B-centered CN9 polyhedra (such as BFe9 and B2Fe8) can be related to the tricapped trigonal prisms (TTP) (see Fig. 5). For most compositions (except Fe83B17), the second dominant B-center polyhedra are

Fig. 6. Atomic structures of the representative Fe-centered clusters taken from the structures of amorphous Fe100  xBx alloys. Larger blue balls denote for Fe atoms; smaller pink balls for B atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

CN¼8, which correspond to the monocapped square antiprism with one atom missing on the base square, e.g., BFe8 and B2Fe7 in Fig. 5. The third abundant B-center polyhedra are CN¼10, which come from either the bicapped square antiprism (BFe10 in Fig. 5) or the tetracapped trigonal prism (B2Fe9 in Fig. 5). In our simulation supercells, these six polyhedra constitute most proportion of the B-centered polyhedra (e.g., 66.7% for Fe72.7B27.3 and 88.9% for Fe91B9), and the population for the rest polyhedra is nearly negligible. Note that the tricapped trigonal prism and square antiprism are the building blocks in the Fe3B and Fe2B crystals [41], respectively. Such similarity in the local structural units in amorphous and

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crystalline structures is also reflected in their electronic states, as we will show in the next subsection. In the Fe-centered case (see Fig. 4(b)), at larger B contents (x¼36.3, 33.3, 27.3, and 25) the four most abundant types of CN polyhedron are CN13, CN14, CN15, and CN16. As the B concentration decreases, the number of CN12 polyhedra increases. At Fe rich region (x¼9, 21), the CN12, CN13, CN14, and CN15 polyhedra are the four most abundant types of local polyhedra. As shown in Fig. 6, the Fe-centered CN12 polyhedra such as Fe12B, Fe13 are distorted icosahedra. As the coordination number of central Fe atom increases (CN13 or CN14), the majority of polyhedra such as Fe10B4, Fe12B2, Fe14, Fe14B, and Fe15 can be viewed as deformed bcc-like structural units. Moreover, there are several polyhedra like Fe11B3, Fe12B3 that can be considered as intermediate structures between icosahedron and bcc unit. Note that Fe13B2 polyhedron is a bicapped icosahedron rather than bcc structure. The larger CN15 polyhedra like Fe13B3 and Fe14B2 are analogous to the Frank–Kasper (FK) polyhedron, but with one convex less on the surface. In the simulation supercells, the above mentioned structural units constitute the majority of Fecentered polyhedra (e.g., 72.2% for Fe72.7B27.3 and 68.7% for Fe91B9). It is noted that the portion of distorted icosahedra increases with decreasing B content (form 0.08% for Fe63.7B36.3 to 14% for Fe91B9), which can be attributed to the increase in NFe–Fe (see Table 1) as well

as the bigger radius of Fe atom with regard to B. The above analysis also indicates the co-existence of polyhedral close-packing (icosahedron and KP polyhedron) and bcc-like structural patterns in these amorphous Fe–B alloys. Our present results agree well with recent simulations of the FeB amorphous alloys [7,8], which found that most of the Fe-centered polyhedra are deformed bcc units or icosahedra for the composition around Fe83B17.

3.2. Electronic structure and magnetic properties 3.2.1. Density of states Based on the equilibrium structures, we discuss the electronic properties of these amorphous Fe–B alloys. Spin-polarized electronic densities of states (DOS) for the Fe100–xBx glasses with 9rxr36.3 are shown in Fig. 7; and the partial DOS for Fe66.7B33.3, Fe75B25 and Fe91B9 are shown in Fig. 8. Overall speaking, the electronic states near the Fermi level for all these Fe–B amorphous alloys are dominated by the Fe-d states forming a spin-split two-peaked band. The Fermi level is pinned right above the majority spin band and locates close to the minimum of the DOS of the minority side. The spin-polarized DOS of crystalline Fe3B, Fe2B calculated with the same method are shown in Fig. 9

Fig. 7. Spin-polarized electron density of states of amorphous Fe100  xBx alloys.

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Fig. 8. Spin polarized total and partial electron density of states in amorphous Fe–B alloys: (a) Fe63.7B33.3, (b) Fe75B25, (c) Fe91B9. Black lines: total DOS; green lines: s states; red lines: p state; blue lines: d state. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 9. Spin polarized total and partial electron density of states in amorphous Fe–B alloys in the Fe–B crystalline solids: (a) Fe2B, (b) Fe3B. Black lines: total DOS; green lines: s states; red lines: p state; blue lines: d state. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

for comparison. Interestingly, the electron DOS of the amorphous Fe–B alloys are close to those of their crystalline counterparts. The similarity of DOS for the crystalline and amorphous alloys is important, which can be related to the resemblance of local order in the crystalline and amorphous phase. For example, B-centered TTP is the building unit of crystalline Fe3B compound [41], while the B-centered TTP-like polyhedra are abundant in the amorphous Fe75B25 alloy. According to the analysis of partial DOS (Fig. 8), the B-s states form a fully occupied, non-bonding band and interact only weakly

with the Fe-d band. The B-s and B-p are well separated by a distinct pseudogap at 5–6 eV below Fermi level. The Fe–B bonding is dominated by hybridization between the 2p states from B and the 3d states from Fe. Such covalent coupling between B-p and Fe-d states is stronger in the spin-down (minority) band, resulting in a slightly larger occupation of the B spin-down states and small negative moments on the B sites. This ferrimagnetism induced by strong covalent coupling in the spin-down band is a rather general phenomenon in many glassy and crystalline transitionmetal–metalloid alloys [38,42,43].

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Table 2 Composition x, average magnetic moment mFe on the Fe atoms, average magnetic moment mB on the B atoms, and average magnetic moments per atom m for the amorphous Fe–B alloys (m ¼ ð1xÞmFe þ xmB ). The theoretical values of crystalline Fe2B and Fe3B solids are also listed for comparison. x (at% B)

mFe (mB)

mB (mB)

m (mB)

Amorphous

Fe63.7B36.3 Fe66.7B33.3 Fe72.7B27.3 Fe75B25 Fe83B17 Fe91B9

36.3 33.3 27.3 25 17 9

1.87 1.94 2.07 2.11 2.17 2.09

 0.07  0.08  0.10  0.10  0.12  0.12

1.16 1.26 1.48 1.56 1.78 1.89

Crystal

Fe2B Fe3B

33.3 25

1.99 2.14

 0.10  0.13

1.29 1.57

Fig. 10. Average magnetic moment per Fe atom in amorphous of Fe100  xBx alloys as function of composition. Red filled dots are out theoretical values. Experimental data include open triangles from Ref. [13], filled squares from Ref. [10], crosses from Ref. [30]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.2.2. Magnetic properties Table 2 summarizes the average magnetic moments on the Fe sites ðmFe Þ and B sites ðmB Þ, and average magnetic moments for all atoms ðmÞ in the amorphous Fe100  xBx alloys with different composition x. Clearly, the magnetic moment comes from the Fe atoms [44]. The theoretical moments for the crystalline Fe2B and Fe3B solids are also listed in Table 2 for comparison. In general, the magnetization is slightly weaker in the amorphous solids than in their crystalline counterparts, for example, a reduction of magnetic moment per atom from m ¼ 1:29 mB in the crystalline Fe2B to m ¼ 1:26 mB in the amorphous Fe66.7B33.3. Fig. 10 compares the theoretical and experimental magnetic moments [10,13,30] as a function of composition. Our theroretical results are in good agreement with the experimental data measured by Hiroyoshi et al. [10]. Interestingly, the magnetic moment does not show linearly relationship with all composition. Within higher B content (x¼25, 27.3, 33.3, and 36.3), the magnetic moment decreases with increasing B concentration, whereas the magnetic moment in the Fe rich region (x¼9, 17) decreases with decreasing B concentration. In other words, the magnetic phase in Fe100 xBx glasses exhibit two distinct regions as a function of composition. This phenomenon can be related to the nonlinear relationship between mass density and composition, as discussed in the Section 3.1.1. The distributions of the local magnetic moments for different Fe– B compositions are shown in Fig. 11. The distribution of both B and Fe moments becomes narrower with decreasing B concentration. In most of the cases, the Fe moments exhibit positive moments, ranging between 1mB and 3mB (see Fig. 11(b) and Table 2), and their mean value for each composition decreases monotonically with increasing B content. In higher Fe regime (x¼ 9, 17), the most striking results are the appearance of negative (antiferromagnetic) moments on very few Fe sites (e.g., about 4.3% of Fe atoms in Fe91B9). This phenomenon was also found by previous first-principles calculations [20]. Meanwhile, all B atoms carry small negative moments of about  0.1mB (see Fig. 11(a) and Table 2). The composition dependence of the magnetic moments of amorphous Fe100 xBx is dominated by the following two competing effects: (1) competition between ferro- and antiferromagnetic exchange interactions, which results in a decrease of net magnetic

Fig. 11. Distribution of the local magnetic moments on the (a) B sites and (b) Fe sites in amorphous Fe–B alloys. The theoretical results are averaged from three configurations for each composition.

H. Tian et al. / Physica B 407 (2012) 250–257

moment in the Fe-rich regime (x¼9, 17) [20]; (2) dilution effect [20]: at larger B content the magnetic moment decreases due to the substitution of Fe by B, which reduces the number of Fe–Fe neighbors, as illustrate in Section 3.1.2. As a consequence of the reduced number of Fe–Fe bonds, the d bonding is weakened. The hybridization between the Fe-d states and the B-p states pulls the Fe minority band down, as shown in Fig. 5.

[3] [4] [5] [6] [7] [8] [9] [10]

4. Conclusion We have conducted a comprehensive study on the structural, electronic, and magnetic properties of amorphous Fe–B alloys using first-principles simulations. The local environment of B is dominated by the TTP-like polyhedra, while the Fe-centered polyhedra can be related to icosahedron, bcc-like structural units, and Frank-Kasper polyhedron, depending on the composition of the Fe–B alloys. The electron densities of states of the amorphous Fe–B alloys exhibit similar features as their crystalline counterparts, which also confirm the similarity of the local order in the crystalline and amorphous phase. The calculated magnetic moment does not vary linearly with composition. For the lower B contents, the reduction of magnetic moment with increasing Fe composition arises from the competition between ferro- and antiferromagnetic exchange interactions. Meanwhile, the decrease of magnetism in the higher-B region is due to a dilution effect, i.e., polarizable d–d bonds replaced by magnetically inert p–d bonds. The present theoretical results provide some useful insights into the local structural order, bonding, electronic state, and magnetism of these Fe–B amorphous alloys.

Acknowledgments

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The work was financially supported by the 973 Program (No. 2007CB613902), the National Natural Science Foundation of China (No. 50901012, 40874039, 51041011 and 50901012), and the Fundamental Research Funds for the Central Universities of China (No. DUT10ZD211). References [1] A. Inoue, Acta Mater. 48 (2000) 279. [2] W.H. Wang, C. Dong, C.H. Shek, Mater. Sci. Eng., R 44 (2004) 45.

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