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Scripta Materialia 68 (2013) 257–260

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Structural mechanism for ultrahigh-strength Co-basedmetallic glasses

X. Hui,a,⇑ D.Y. Lin,a X.H. Chen,a W.Y. Wang,a,b Y. Wang,b S.L. Shangb and Z.K. Liub

aState Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, ChinabDepartment of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA

Received 18 October 2012; accepted 23 October 2012Available online 26 October 2012

The atomic packing and electronic structure for Co43Fe20Ta5.5B31.5 metallic glass (MG) were explored by extended X-ray absorp-tion fine structure measurement and first-principles calculation. It is shown that the short-range order in this MG is of a (Co, Fe)B2-like, but not (Co, Fe)23B6-like, crystallographic structure. A network-like medium-range order can be formed via the build-up ofB-centered Z9 h0,3,6,0i Voronoi polyhedra. The intrinsic strengthening mechanism is attributed to the formation of strong covalentbonding between B and Co (Fe).� 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Metallic glass; Extended X-ray absorption fine structure; First-principles calculation; Short-range ordering

Metallic glasses (MGs) are intriguing condensedmaterials due to the random distribution of atoms in thestructure and the superior properties to their crystallinecounterparts. In 2003, Inoue et al. [1] reported that theCoFe20Ta5.5B31.5 MG had a fracture strength of5138 MPa, which set the record for the highest strengthamong known bulk crystalline or glassy alloys at thetime. Later, Fe71Nb6B23 MG [2], with a fracturestrength of 4850 MPa, was developed. Recently, it hasbeen found that the fracture strength of Co-basedMGs can even be increased to above 6000 GPa whenFe is removed from Co–Fe–Ta–B MGs [3].

Because of this extraordinary property, the strength-ening mechanism of this kind of MGs has attracted agreat deal of attention. Inoue et al. [1] deduced thatthe ultrahigh-strength of Co-based MGs results fromthe formation of local atomic ordering. Yao et al. [2]considered that the record high strength in Fe–Nb–BMGs is associated with the high Poisson’s ratio as wellas the formation of a network-like structure. Covalentbonding between metalloid and metallic elements inCo–Ta–B MG has been found via first-principles calcu-lations [4,5]. It has been further determined that Ta-based structural units with the composition close tothe stoichiometry of (Co, Fe)21Ta2B2 crystalline phaseexist in Co43Fe20Ta5.5B31.5 bulk metallic glass (BMG)

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⇑Corresponding author. Tel.: +86 10 62333066; fax: +86 106233447; e-mail: xdhui@ustb.edu.cn

[6]. Despite these findings, a number of basic questions,including what the substantial structural units are andhow the networks are constructed by these units, havenot been clarified. The structural origin for the ultra-high-strength of this kind of MGs is still a mystery. Inthis letter, we study the local atomic and electronicordering in a Co–Fe–Ta–B MG by extended X-rayabsorption fine structure (EXAFS) measurement andfirst-principles calculation. The short-range order(SRO) is explored by fitting the EXAFS spectra withspecific crystallographic data, and the complete distribu-tion of Voronoi polyhedra in this MG is acquired. Basedon the preferential coordinate polyhedron, we describethe network-like structure in the medium range. Thenature of the network-like structural ordering is ex-plained by the electronic structure. It is believed that thiswork has implications for understanding the strengthen-ing mechanism and developing a new generation ofultrahigh-strength metallic materials.

In this work, we chose Co43Fe20Ta5.5B31.5 MG as themodel alloy. The master alloy, with the nominal compo-sition, was first prepared by arc melting the mixture ofpure metals (P99.9 wt.%) under a Ti-gettered pure argonatmosphere. Glassy ribbons with a cross-section of0.04 � 4 mm2 were produced by the vacuum single-rollermelt-spinning technique. X-ray diffraction (Cu Ka, Phi-lips APD-10) and transmission electron microscopy witha Philips H800 transmission electron microscope wereused to check the structural nature of samples.

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Figure 1. (a and b) EXAFS k3-weighted spectra measured (solid line)and fitted based on tetragonal Co2B and Fe2B crystallographicstructures (red solid circles); (c and d) the Fourier transform in R-space for the Co and Fe edge, respectively, of Co43Fe20Ta5.5B31.5 MG.(For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

258 X. Hui et al. / Scripta Materialia 68 (2013) 257–260

EXAFS measurements on the Co K-edge and Fe K-edge at room temperature were performed at theBL14W1 beamline of the Shanghai Synchrotron Radia-tion Facility. An Si (111) double-crystal monochroma-tor was used to reduce the harmonic content of themonochromator beam. The EXAFS data were extractedfrom the raw absorption spectrum with the ATHENAcode and further analyzed with the ARTEMIS code inthe IFEEFIT 1.2.11 package [7,8].

Ab initio molecular dynamics (AIMD) calculationswere performed by using Vienna Ab Initio SimulationProgram [9]. The electronic exchange and correlationfunctional were described by the generalized gradientapproximation parametrized according to Wang and Per-dew [10]. The generalized Kohn–Sham equations weresolved with an efficient iterative matrix diagonalizationroutine based on a sequential band-by-band residual min-imization method [11]. The electron–ion interactions weredescribed by Vanderbilt-type ultrasoft pseudopotentials[12]. The equation of motion was solved via the velocityVerlet algorithm with a time step of 1 fs. The C point alonewas used to sample the Brillouin zone of the supercell. Inthe AIMD calculations of Co43Fe20Ta5.5B31.5 MG, a cu-bic supercell containing 86 Co, 40 Fe, 11 Ta and 63 Bwas employed. The size of the supercell was initially as-signed according to the experimental density. The alloywas then melted and equilibrated at 2800, 2000 and1800 K, respectively, for 2000 time steps. The volume ofthe supercell was adjusted at every temperature plateauto satisfy the requirement of zero pressure of the inherentstructure of the liquid. The equilibrated liquid was thenquenched sequentially from 1800 to 1500, 1200, 1000,900, 800 and 300 K. At each temperature plateau, theensemble was relaxed for 1000 time steps. The totalquenching time was 67.5 ps, resulting in an average cool-ing rate of 2 � 1014 K s–1.

The EXAFS-measured (solid line) k3-weighted spectraand the Fourier transform in the R-space in the k-rangesof 3.336–9.129 and 3.160–8.162 A�1 for the Co and Feedge, respectively, of this MG are displayed in Figure 1.In order to derive the structural parameters around thecentral Co and Fe atoms, a fitting analysis for the mea-sured spectra was performed. We first fitted the EXAFSspectra with the cF116 Cr23C6 type of crystallographicdata [13]. However, we found that the calculated spectrawere not in agreement with the experimental ones. Thestructural parameters derived from the fitting are notsound, implying that the local structure in this MG is dif-ferent from that of the Cr23C6-type structure in the nearestneighbor. We then tried to adopt a structural model basedon tetragonal Co2B and Fe2B (which belong to the CuAl2type) crystallographic data to fit the experimental data[14,15]. Surprisingly, the calculated results (as shown inFigure 1 by red solid circles) coincided perfectly with theexperimental ones, indicating the possibility of Co2B-and Fe2B-like SROs in this MG. This supposition was ver-ified by comparing the measured structural parameterswith the crystallographic data, as shown below.

The displacement of nearest neighboring atoms (R1)and the coordinate number (CN) of this MG were ob-tained through the fitting of the experimental spectrabased on the structural models of Co2B and Fe2B, andare listed in Table 1. The composition ratio of the

metalloid to the sum of the metallic components is0.46, which is very close to that in the CuAl2 type ofstructure. Therefore, B atoms can occupy the positionsof Cu atoms, and Co, Fe and Ta can occupy the positionsof Al atoms, in the CuAl2-type crystallographic structure.It is shown in the table that, in this MG, the total CNsaround Co and Fe are 14.23 and 14.32, respectively, whilethe total CN in the CuAl2 type of structure is 15. The EX-AFS-measured CN of B around Co and Fe in MG are3.774 and 3.534, respectively, while the CN is 4 in theCuAl2 type of structure. It is also seen that the atomicpairs RCo–B, RFe–B, RCo–Ta and RFe–Ta in MG are veryclose to those in the CuAl2 type of structure. It is not dif-ficult to conclude from these parameters that there isCuAl2-like SRO in the structure of this MG. The slightdifference between the parameters of these two kinds ofstructure is reasonable because the atoms in MG are dis-tributed randomly and homogeneously in the long range.

By using the AIMD method, the atomic configurationof this Co-based MG was obtained. To ensure that thisconfiguration can mimic the realistic atomistic packingof this MG, we fitted the EXAFS-measured k3-weightedspectra and the Fourier transform in the R-space withthe AIMD configuration (as shown in the Supplementaryfigure). It is shown that the AIMD calculated spectra canreproduce both the shape and the position of the mainpeak of experimental spectra well. Therefore, it is reason-able for us to characterize the real structure by the atomicconfiguration obtained from the AIMD simulation.

The AIMD-calculated generalized and partial paircorrelation functions (GPCF and PPCF) of the MG at300 K are shown Figure 2. It is observed that there issplitting in the first GPCF peak, resulting in the appear-ance of two subpeaks around 2.1 and 2.5 A. The dis-placement of the first subpeak is very close to the firstshell of the CuAl2 type of crystallographic structure.Therefore, it is likely that these two subpeaks corre-spond to B-related pairs and metal–metal pairs, respec-tively. In contrast to the first peak, the second peak ofGPCF does not exhibit splitting. However, this doesnot mean that there is no local ordering in the structure.This deduction can be made from the PPCFs. It is

Table 1. EXAFS-measured and AIMD-fitted parameters of the first coordination shell for Co43B31.5Fe20Ta5.5 MG.

Centeratoms

Pairs R1 CN E0 r2

AIMD EXAFS AIMD EXAFS

Co Co–B 2.075 2.139 (0.006) 3.889 3.774 (0.243) 4.780 (0.801) 0.006 (0.001)Co–Co 2.525 2.547 (0.003) 6.324 6.287 (0.213) �9.072 (0.346) 0.015 (0.000)Co–Fe 2.475 2.418 (0.004) 2.897 2.919 (0.147) �19.869 (0.582) 0.011 (0.001)Co–Ta 2.625 2.682 (0.011) 1.215 1.254 (0.185) 20.000 (0.008) 0.013 (0.002)

Fe Fe–B 2.075 2.090 (0.006) 3.626 3.534 (0.251) �13.473 (0.933) 0.007 (0.001)Fe–Co 2.475 2.516 (0.006) 6.228 6.767 (0.496) �10.387 (0.646) 0.030 (0.000)Fe–Fe 2.475 2.435 (0.004) 3.469 4.033 (0.221) �15.145 (0.531) 0.019 (0.001)Fe–Ta 2.675 2.665 (0.007) 0.923 0.986 (0.091) 19.997 (0.000) 0.009 (0.001)

E0, the absorption edge energy shift; R1, the fitted neighboring interatomic distance; CN, the coordination number of neighboring atoms; r2, themean-square disorder in the distribution of interatomic distances. Values in parentheses are the fitted error bars.

X. Hui et al. / Scripta Materialia 68 (2013) 257–260 259

shown that there is obvious splitting on all of the secondpeaks of the PPCFs except for that of the Ta–Ta atomicpair. It is also found that, for the PPCF of B–B and Ta–Ta pairs, both the height and width of the first peak aresmaller than those of the second peak, illustrating thatmost of the B and Ta atoms cannot form nearest neigh-bors with their congeneric atoms. These results demon-strate that the local atomic configuration of the SROresembles a compound with a composition near thatof the CuAl2 type of crystallographic structure.

Through the Voronoi tessellation method, the localnearest-neighbour coordination can be defined to identifythe possible clusters [16]. We use the Voronoi indexhn3,n4,n5,n6, . . .i to designate and differentiate the typeof the coordinate polyhedron, where ni denotes thenumber of i-edged faces of the Voronoi polyhedron andP

ni is the total coordinate number. The Voronoi polyhe-dra with the average frequency in the range from 1.5% to10% in this MG are shown in Figure 3. It is seen that all thepolyhedra are of the Kasper type, which are deltahedrathat involve the minimum number of disclinations [17].The tricapped trigonal prism (TTP) packing, correspond-ing to the Voronoi index of Z9 h0,3,6,0i, has the highestfrequency of 6.5%. The next is Z13 h0,1,10,2i, at 3.5%.No other type of polyhedron has a frequency higher than3%. This is contrast to the Voronoi polyhedra in MGs thatare composed only of metallic elements, of which icosahe-dra are predominant [18,19]. The formation of the prefer-ential type of TTP polyhedra results from the effectiveatomic size ratio, R*, and the strong bonding nature ofmetal–metalloid atomic pairs in the clusters. It can be cal-culated that the R* between B and Fe, Co and Ta are 0.784,

Figure 2. AIMD-calculated generalized and partial pair correlationfunctions of Co43Fe20Ta5.5B31.5 MG at 300 K.

0.784 and 0.78, respectively. According to Miracle’s for-mulation [20], with decreasing R*, the preferred polyhedratype changes from the Frank–Kasper type (for R* > 1.2)to the icosahedral type (R* < 0.902), then to the bicappedsquare Archimedean antiprism type (R* < 0.835) and fi-nally to the TTP packing type (R* < 0.732). From Fig-ure 3a, it is seen that these TTP coordinate polyhedrawere formed by setting a B atom at the center. It is note-worthy that B atoms also occupy the positions of coordi-nate atoms due to topological and chemical effects.

In previous works, trigonal prism and chemical twin-ning models have been developed for metalloid elementscontaining MGs [21,22]. Densely packed clusters [23]and quasi-equivalent clusters model [24] have been alsoproposed to describe medium-range ordering (MRO)for MGs. These models are too ideal to satisfy all real-istic MGs. In this work, the geometric/topological pack-ing beyond the nearest coordinate shell for the currentMG can be described by using the above informationof Voronoi polyhedra. As shown in Figure 3a, TTPcoordinate polyhedra with CN = 9 are preferential.The TTP polyhedra are the ideal blocks for constructing

Figure 3. (a) Average frequencies of Voronoi polyhedra in Co43Fe20-

Ta5.5B31.5 MG alloy; (b) the network-like MRO formed by B-centeredclusters. The orange, green, blue and red balls represent B, Co, Fe, andTa atoms, respectively. (For interpretation of the references to colour inthis figure legend, the reader is referred to the web version of this article.)

Figure 4. The charge density distribution in Co43Fe20Ta5.5B31.5 MGalloy, generated using VESTA. (a) 0.05qmax isosurface structure in threedimensions; (b–d) 2-D contour plots of the (001), (010) and (100)Miller planes with 0.05 e A�3 intervals. The different types of atoms in(a) are identified with various colors: B in red, Co in blue, Fe in pinkand Ta in gold. (For interpretation of the references to colour in thisfigure legend, the reader is referred to the web version of this article.)

260 X. Hui et al. / Scripta Materialia 68 (2013) 257–260

network-like MRO. To prove this deduction, we ex-tracted 10 TTP coordinate B-centered polyhedra andpresented them in 3-D configuration, as shown in Fig-ure 3b. It is seen that these polyhedra are linked via ver-tex-, edge-, face- and intercross-shared atoms, and formsa network-like MRO. Among these kinds of connec-tions, the intercross-shared type of linkage is the mostcommon. All four kinds of component elements canserved as glue atoms. The formation of this kind of net-work is attributed not only to the necessity of densepacking, but also to the chemical interaction betweenthe metalloid and metallic elements.

To shed light on the local atomistic ordering of thisBMG, we calculated the distribution of charge densityusing Venus software [25,26]. Figure 4 shows the poten-tial chemical bonding morphology in this MG alloy cap-tured through different views of charge densitydistribution. As shown in Figure 4a, the 0.05qmax onthe surface structures projected by the (001), (010)and (100) Miller planes display a bonding networkformed by B-bonding chains. The chemical bonding inthis MG can be further understood quantitativelythrough the two-dimensional (2-D) contour plots ofcharge density on the (001), (010) and (100) Millerplanes with 0.05 e A–3 intervals. From Figure 4b–d, itcan be seen that there is clear overlapping among thecharge densities of elemental B and Co or Fe. The Batoms have a high charge density and connect with otheratoms as nuclei. The distribution of charge densityexhibits specific directionality, indicating that covalentbonding between B and Co (Fe) has been formed. Thisdemonstrates that the addition of B results in an in-crease in the amount of covalent bonding in this MG,thus providing ultrahigh strength and hardness. There-fore, the physical nature of the formation of B-centered

network-like MRO (shown in Fig. 3) is that there is astrong bonding tendency between Co, Fe with B atoms.

In summary, we have clarified that the SROs in thisCo-based MG are of the Co2B- and Fe2B-type crystallo-graphic structures by using EXAFS measurement andAIMD calculation. Through the Voronoi tessellationmethod, we have identified all of the polyhedra to beof the Kasper type, of which B-centered TTP Voronoipolyhedra with Z9 h0,3,6,0i accounts for the highestfrequency of 6.5%. These preferential TTP polyhedraare linked via vertex-, edge-, face- and intercross-sharedatoms, and form a network-like MRO. This kind of net-work-like structure should be attributed not only to thenecessity of dense packing but also to chemical interac-tions. The electronic structure shows that the formationof a network of B-centered clusters is due to the strongbonding tendency between Co and Fe with B atoms.

The authors are grateful for the financial sup-port of the National Nature Science Foundation ofChina (51071018 and 51271018). We would like tothank Shanghai Synchrotron Radiation Facility andBeijing Synchrotron Radiation Facility for the beamlineand technical support.

Supplementary data associated with this article canbe found, in the online version, at http://dx.doi.org/10.1016/j.scriptamat.2012.10.030.

[1] A. Inoue, B. Shen, H. Koshiba, H. Kato, A. Yavari, Nat.Mater. 2 (2003) 661.

[2] J.H. Yao,J.Q. Wang,Y. Li, Appl. Phys. Lett. 92 (2008) 251906.[3] J.F. Wang, R. Li, N.B. Hua, T. Zhang, J. Mater. Res. 26

(2011) 2072.[4] J.F. Wang, R. Li, R.J. Xiao, T. Xu, Y. Li, Z.Q. Liu, L.

Huang, N.B. Hua, G. Li, T. Zhang, Appl. Phys. Lett. 92(2008) 251906.

[5] C. Hostert, D. Music, J. Bdnarcik, J. Keches, J.M.Schneider, J. Phys.: Condens. Matter 24 (2012) 175402.

[6] I. Kaban, P. Jovari, M. Stoica, J. Echert, W. Hoyer, B.Beuneu, Phys. Rev. B 79 (2009) 212201.

[7] M. Newville, J. Synchrotron Radiat. 8 (2001) 322.[8] B. Ravel, M. Newville, J. Synchrotron Radiat. 12 (2005) 537.[9] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15.

[10] Y. Wang, J.P. Perdew, Phys. Rev. B 44 (1991) 298.[11] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 169.[12] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892.[13] A. Hirata, Y. Hirotsu, K. Amiya, N. Nishiyama, A.

Inoue, Phys. Rev. B 80 (2009) 10201(R).[14] K.H.J. Buschow, P.G. Van Engen, R. Jongebreur, J.

Magn. Magn. Mater. 38 (1983) 1.[15] C. Gianoglio,C. Badini, J. Mater. Sci. 21 (12) (1986) 4331–4334.[16] V.A. Borodin, Philos. Mag. A 79 (1999) 1887.[17] J.P.K. Doye, D.J. Walse, J. Phys. B 29 (1996) 4859.[18] X. Hui, H.Z. Fang, G.L. Chen, S.L. Shang, Y. Wang,

Z.K. Liu, Appl. Phys. Lett. 92 (2008) 201913.[19] H.Z. Fang, X.D. Hui, G.L. Chen, Z.K. Liu, Appl. Phys.

Lett. 94 (2009) 091904.[20] D.B. Miracle, W.S. Sanders, Philos. Mag. 83 (2003) 2409.[21] P.H. Gaskell, Nature 276 (1978) 484.[22] J.M. Dubois, P.H. Gaskell, G. Le Caer, Proc. R. Soc.

London A402 (1985) 323.[23] D.B. Miracle, Nat. Mater. 3 (2004) 69721.[24] H.W. Sheng, W.K. Luo, F.M. Alamgir, J.M. Bai, E. Ma,

Nature 439 (2006) 419.[25] K. Momma, F. Izumi, J. Appl. Crystallogr. 41 (2008) 653.[26] K. Momma, F. Izumi, J. Appl. Crystallogr. 44 (2011) 1272.