Atomic packing and fractal behavior of Al-Co metallic glasses

Journal of Alloys and Compounds 735 (2018) 464e472

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Atomic packing and fractal behavior of Al-Co metallic glasses M. Kbirou a, *, M. Mazroui a, **, A. Hasnaoui b a b

Laboratoire de Physique de la Mati
ere Condens ee, Facult e des Sciences Ben M'Sik, University Hassan II of Casablanca, B.P. 7955, Casablanca, Morocco LS3M, Facult e Poydisciplinaire Khouribga, Univ. Hassan 1, B.P.: 145, 25000, Khouribga, Morocco

a r t i c l e i n f o

a b s t r a c t

Article history: Received 26 July 2017 Received in revised form 5 October 2017 Accepted 7 November 2017 Available online 10 November 2017

The rapidly solidified Al-Co alloy is studied in a favored composition range of 25e75 at.% of aluminum (Al) by performing a set of classical molecular dynamics simulations (MD) based on the Embedded Atom Method (EAM). We have examined particularly the structure using several analyzing techniques such as: the radial distribution function (RDF), the Voronoi tessellation analysis and the structure factor. We observed a splitting in the second peak of both the RDF and the structure factor, indicating metallic glass formation. The Voronoi analysis shows that it is difficult to define a dominant type of coordination polyhedra for all compositions, manifesting two different Voronoi polyhedral (VP): < 0; 3; 6; 4 > and < 0; 2; 8; 4 > , and this distribution varies with increasing Al content. The structure factor is further examined via illustrating two of their important parameters: the full width at half maximum (FWHM) and the positon of the first sharp peak (FSP) as a function of the composition and the atomic volume, respectively. The first parameter showed a maximum for the Al50 Co50 alloy according to the dominance of unlike pairs, while the second one revealed a power law that allowed to compute the fractal dimension which is almost comparable to that found out from the analysis of the cumulative coordination number (CN). © 2017 Elsevier B.V. All rights reserved.

Keywords: Binary metallic glass Molecular dynamics Radial distribution function Voronoi tessellation Structure factor Fractal dimension

1. Introduction Metallic glasses have sparked widespread attention since the first glassy alloy was synthetized in 1960 due to their unique combination of properties in comparison with other amorphous materials and thus becoming the cutting edge of materials research and the key for a broad application such as engineering materials [1e4]. In the field of metallic glass's study, one of the important scientific terminologies is the so-called glass-forming ability (GFA), which is defined as the ease or difficulty of the metallic glass formation [5,6]. The main structural factors that can affect the GFA or the preparation of a metallic glass are the mixing entropy and size mismatch between main constitutional elements [5,6]. There exist also thermodynamic ones such as: the crystallization-glass transition temperature difference DTxg ¼ Tx  Tg (where Tx is the onset temperature of the crystallization and Tg stands for the glass transition temperature) and the ratio Trg ¼ Tg =Tl (Tl is the liquidus

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (M. Kbirou), mazroui.m@gmail. com (M. Mazroui). https://doi.org/10.1016/j.jallcom.2017.11.109 0925-8388/© 2017 Elsevier B.V. All rights reserved.

temperature) [7e9]. Furthermore, the atomic structure of MGs has a clear correlation with GFA and gives rise to a great influence on the formation and mechanical properties in MGs. Therefore, understanding the atomic structure might be helpful to predict metallic glasses with good GFA. On the other hand, binary metallic alloys compared with monatomic metal systems [10e12], are known as good glass forming systems, provided that heterogeneous nucleation can be avoided. Indeed, these systems exhibit in general a much slower and complicated growth kinetics than monatomic metallic glasses [13e16]. Moreover, Binary metallic systems have been shown to present a good GFA and a wide glass-forming composition range. Several studies have been devoted to the correlation between the local structure, the atomic diffusivity and the GFA in Cu-Zr glasses [17e19]. However, the change in the local structure with composition and its relationship to GFA is still unclear. In comparison with other amorphous alloys, Al-based metallic glasses represent one group of disordered materials, which is different from most of the well-known bulk glass formers. They show poor GFA, disappointing performance and unsatisfactory structure. From another side, aluminum and its alloys have excellent engineering performance, wide applications and abundant sources [20]. Therefore, we need new theories and approaches in

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order to improve their GFA and properties that can promote greatly the development of Al-based amorphous alloys. According to the Al-Co phase diagram [21], Al3 Co or AlCo3 alloys are intermetallic phases that located well away from their eutectic points. These alloys are of a great importance in technological industries [22,23] and their metallic glasses would open a new horizon to technological applications. Zhang et al. [24] have prepared experimentally a metallic glass based on the Al-Co alloy with an addition of Zirconium by means of rapid solidification techniques [25] of copper mould section casting, the most used method to fabricate BMGs. Although, this alloy contains a third element (Zr) it will interesting to study the Al-Co binary first and then try to understand the effect of Zr addition. On the other hand, the chemical and structural heterogeneity of the glass crystallization of Zr60Cu30xCoxAl10 amorphous alloys are recently investigated by Wang et al. [26] using high-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM), indicating the initial formation of a nanoscale metastable icosahedral phase upon the early stage of the crystallization. More precisely, it is of a great help to study the local order in this binary amorphous system Alx Co100x where x ¼ 25.0, 33.5, 50.0, 66.5 and 75.0 to find out the good glass former composition and illustrate the correlation between the local structure and composition. Because of the very small scale involved in BMGs, describing the atomic packing directly by experiment is very difficult. Therefore, numerical methods such as the molecular dynamics (MD) remain the preferred ones because these methods can assist in clarifying the physical information gained from experimental results. It is an effective approach to predict the arrangement of alloys at the atomic level once the atomic interaction potentials that accurately describe the interatomic interaction are available. In this paper, using the embedded atom method (EAM) potential for the Al-Co system, we carried out classical MD simulations to address the atomic structural change caused by adding Co to the AlCo binary MGs. A set of structural characterization methods focused on the Pair Distribution Function (PDF), structure factor and Voronoi indices have been employed to theoretically study the effect of alloying compositions on short-to-medium range order of the AlCo MGs. In section 2, we summarize details of the calculations method with a description of the EAM potential that models the binary Al-Co alloy and describe the MD approaches used here. The results are presented and discussed in section 3, with a focus on the correlation between local atomic structure and the composition in the system. Finally, a summary is given in Section 4.

465

total electron density calculated from the summation of densities of all neighboring atoms j. While the second one 4ij ðrij Þ is recognized as the pair potential where rij is the distance between atoms i and j. The aim of the work of Pun et al. [35] was essentially developing an EAM potential that is valid for pure Al, pure Co and the mixed AleCo interactions, via performing a fit of the mixed-pair potential function represented by a generalized Morse function:

i o r  r  n h c VAlCo ðrÞ ¼ E0 eqb1 ðrr1 Þ  qeqb1 ðrr1 Þ þ d j h

(2)

Where the cutoff function jðxÞ is given by:

jðxÞ ¼

x4 1 þ x4

if x < 0

(3)

jðxÞ ¼ 0 if x  0 whereas E0, q, b1, r1, d, rc and h are fitting parameters of the VAlCo function. All details of EAM fitting procedure have recently presented in the study [35]. As a first step, 6912 Co atoms are arranged in an fcc structure end enclosed in cubic box using periodic boundary conditions (PBCs) along the three Cartesian directions [36]. To make an alloy, an amount of aluminum is added each time to reach the wanted fraction as shown in Fig. 1, in a volume where Newton equations are discretized using a Verlet algorithm with a time step of 1 fs. The system is firstly heated up to a sufficiently high temperature (2500 K) in order to remove the memory effects from the initial configuration under isothermal-isobaric ensemble NPT [37]. Then, we let the system run 105 fs at the same temperature under the canonical ensemble (NVT) in order to guarantee the equilibrium liquid state of the system and to obtain the initial configuration for the cooling process [38]. After the equilibration period, the system is quenched to a lower temperature of 200 K in the NPT at a cooling rate of 1013 K=s. This cooling rate value is used because it allows the formation of the glassy state from one side and is not heavy time consuming from another side. Many methods have been used to characterize the short-range order and describe the local structures in MGs. Here, we will focus on three representative methods that characterize the atomic structure: the radial distribution function, the Voronoi tessellation analysis and the structure factor. We will first give an atomic description of the vitrification process and glass formation during the rapid quenching process of alloys and illustrate the relationship between the composition and the atomic structure.

2. Computational details 3. Results and discussion In the current study, Al-Co MGs with five different compositions (Al25 Co75 , Al33:5 Co66:5 , Al50 Co50 , Al66:5 Co33:5 and Al75 Co25 ) were analyzed using classical molecular dynamics (MD) simulations within the LAMMPS [27] package and based on an optimized embedded-atom-method (EAM) interatomic potential [28e30]. This potential gives a realistic description of interatomic interactions between aluminum and cobalt atoms in the liquid and amorphous states. We adopt the EAM potential form that is widely used provide various surface phenomena such as vibrations, relaxations, and adatom diffusion [31] in metallic systems [28] and glasses [13e15,32e34] where the system energy is approximated as:

Etot ¼

X   1X   Fi rh;i þ 4 r ; 2 isj ij ij i

(1)

The first term Fi ðrh;i Þ is the embedding function where rh;i is the

In this section, we investigated five compositions where the system was cooled each time at the same rate. The glass transition is further examined via monitoring the volume (or the enthalpy) versus temperature for all five compositions during the amorphization process and the results are shown in Fig. 2. In contrast to the heating process (not shown here), we see that along the cooling, the volume decreases in a continuous manner as the temperature decreases accompanied with a change in the slope determined as the glass transition temperature, where the gradients of V=T(H=T) are small because of the lower thermal expansion of solids [39,40]. This indicates that there is no occurrence of crystallization in the system and that the solid (a discontinuous change in the curve VðTÞ), which was expected to be formed at lower temperature, becomes a glass for all compositions. However, the glass transition of the AlCo3 , which corresponds to the eutectic point of the phase diagram, is more observable than the other

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Fig. 1. Configuration of Al-Co alloy obtained at 200 K for two selected compositions Al25Co75 and Al75Co25. The Al atoms are grey and the Co atoms are black.

Fig. 2. The average volume of Al-Co alloys as a function of temperature for different compositions during the cooling process at the rate of 1013 K/s.

compositions indicating that the GFA of the eutectic alloy [41] is higher than that of the other alloys suggesting that the addition of Al atoms prevents the glass transition. In general, the Radial Distribution Function (RDF) is widely used as a basic description of the structures of crystal, liquid and amorphous structures [42,43]. It is defined as the probability to find atoms over an interval of n time steps of integration of the equations of motion, the mean volume V and the mean number of atoms N at a distance r from an atom [44]. The resulting total RDF and partial PRDF curves for Al-Al, Al-Co and Co-Co pairs in the binary alloy AlCo with five compositions are shown in Fig. 3. The “total” RDF which refers to all pairs are similar to those of other MGs [42,44,45]: a double peak at the second maximum “the well-known characteristic of amorphous state”, a sharper symmetrical single first peak containing the short range order (SRO) information in the system [44,46]. We observe from Fig. 3 that as Al content decreases, the sharpness of this peak becomes weak and a shoulder peak starts to appear on the right region and becomes much significant. The Al-Al and Co-Co PRDF

curves show two peaks, the height of the first one increases and its position is almost unchanged, while the second peak becomes more split with the increase respectively of Al and Co concentrations. Indicating that the RDF of like bonds (Al-Al and Co-Co) shows sensitivity to the atomic composition and that there is an increasing degree of the short and medium range order as the composition increases. For the Al-Co RDF curve, the same behavior observed before for the Al-Al and Co-Co bonds is observed here with the exception that the atomic concentration does not affect them. The position of the first peak differs from that of the Al-Al and Co-Co bonds, while the splitting in the second peak becomes more pronounced with the decrease of Al fraction. This indicates that the interactions are more intensive and strong among the unlike than like bonds and play a governing role in the frame of amorphous structure pairs even for low Al compositions. Furthermore, the local atomic packing in Al-Co simulated glass configuration is monitored by conducting Voronoi tessellation analysis on their corresponding inherent structures [47]. It is a

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Fig. 3. Total RDF curve and partial RDFs of Al-Al, Al-Co and Co-Co bonds for Al-Co metallic glasses obtained at 200 K and at cooling of 1013 K/s.

geometric method that serves to reflect the characteristic arrangement of near neighbors (its coordination number) enclosing an atom and forming the Voronoi polyhedron (VP) by counting the number of polygonal facets having three, four, five and six vertices/ edges, leading to a vector of four integers < n3, n4, n5, n6> that identifies the structural type [48,49]. Hwang et al. [50] have grouped these VP into three types: crystal-like, icosahedral-like and mixed-like clusters. The top five dominant local VP including the icosahedral and mixed-like, with increasing concentration for the Al-Co alloy are depicted in Fig. 4(b) It shows the evolution of the icosahedral clusters < 0; 0; 12; 0 > ; < 0; 1; 10; 2 > and < 0; 2; 8; 4 > with two of mixed-like clusters < 0; 3; 6; 4 > and < 0; 3; 6; 5 > as the concentration changes from 25% to 75%. Fig. 4(a) illustrates the simulated atomic model of these basic clusters. Each polyhedron has its own symmetry, characteristic and CN. It is observed from Fig. 4(b) that the types of mixed-like pairs show a continuous decreasing while that of icosahedral-like increases along with Al concentration. Therefore, our system results in two different dominant cluster types. For Al25 Co75 and Al33:5 Co66:5 glasses, < 0; 3; 6; 4 > VP is the most dominant VP. While the other compositions exhibit < 0; 2; 8; 4 > as the abundant VP in the system rather than the full icosahedra < 0; 0; 12; 0 > and Kasper polyhedral Z10 and Z11 (not shown here), defined as polyhedra that are formed of fragments of incomplete, irregular or distorted icosahedra [51], where his fraction is approximately close to 0 (not shown here). Those are the populous structural unit in other multicomponent metallic glasses [52,53], this leads to say that the local ordering is found to strongly depend on the composition. However, the connection schemes that link two basic types of < 0; 2; 8; 4 > , which are simultaneously present in the system, were analyzed in Fig. 5. The connections that constitute the extended ordering of the medium range order (MRO) are generally presented in four types: first, the Interpenetrating Connection of Icosahedra

(ICOI), concerning two icosahedral-like VP where their two central atoms are first nearest neighbors of each other and share 5 common neighbor atoms. While the three others have these basic clusters connected via vertex sharing (VS), edge-sharing (ES) and face-sharing (FS). Despite the great success in understanding the structureeproperty relation in MGs, answers on some questions are still missing such as: how the improvement of mechanical/physical properties of MGs is related essentially to the overall structural amorphousness, how this atomic structure is composed and how such a composition can be built into the structure [54,55]. In response to these questions, the percolation in particular the fractal dimension has been proposed [56]. In this model, the strong correlation between the mass M(r) and volume V has been extensively observed and was directly confirmed by: MðrÞ ¼ r df (where r is the radius of a region within the atom and df is the fractal dimension expected to be a non-integer number) [57]. The RDFs curve that are initially computed, are then integrated to calculate the cumulative CN, in order to measure the local dimension in MGs. Fig. 6 shows lnðCN þ 1Þ plotted as a function of Ln(r), where CN þ 1 is the average number of atoms within the system which supposed as a sphere of radius r and “1” is added to represent the center atom of the sphere. It is calculated at special positions rcenter ; r1shell ; r2shell ; r3shell and r4shell in order to characterize the MGs structure at the SRO and MRO. In general, the CN increases in a discontinuous way between the center atom and the first coordination shell to continue increasing sharply from the first shell to the fourth one. The fractal dimension is obtained as the slope of two linear fittings, the first is between rcenter and r1shell and the second is between r2shell and r4shell. The resulting estimation of fractal dimensions are listed in Table 1. The linear fit of points beyond the outer radius of the second coordination shell leads to dimensions around 3.01 for all glass compositions, indicating that the composition have no effect on the

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Fig. 4. (a) Schematic configurations of five typical basic clusters taken rom Al25Co75 metallic glass at 200 K. Grey balls stand for Al atoms and Black balls for Co atoms. (b) Fractions of the five typical VP as a function of composition.

Fig. 5. Schematics of two typical cluster of <0,2,8,4> linked by ICOI, VS, ES and FS in Al25Co75 metallic glass at 200 K.

fractal dimension at the MRO even if the free volume change decreasingly with the increase of Al compositions. However, the short-range dimension d changes from 2.54 (almost close to the fractal dimension of liquid) to 2.68 (the fractal dimension of glass) that do not reflect the same trend as that from the free volume [57] suggesting that d is mostly composition-dependent since the shortto-medium range order and atomic packing topology change with the changing of composition. And that the interactions of Al prevent perhaps the system from the formation of glass. The g(r) method that is able to characterize the local environment surrounding each atomic pair by giving the probability of finding atoms as a function of distance r from an average center atom in real space, is directly related to the structure factor in reciprocal space which is achieved via Fourier transformation according to [58]:

Z∞ r 2 gðrÞ

SðqÞ ¼ 1 þ 4pr

sinðqrÞ dr qr

0

where gðrÞ is already calculated above, q is the variable in the reciprocal space which is the absolute value of the scattering vector in X-ray or neutrons experiment and r is the atomic density of the system [58]. Fig. 7 depicts the total structure factor SðqÞ calculated from the MD simulations of Al-Co MGs at 200 K for Al different concentrations (25, 33.5, 50, 66.5 and 75). It can be clearly seen that the shape of the SðqÞ curves change with the composition. When we look in more detail at the total structure factor SðqÞ of Al25 Co75 and compare it to that of the other compositions, we observe three interesting features: first, the split of the second peak in the RDF

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469

Fig. 6. Log-log plots of total atom coordination number (CN þ 1) versus radius, r, showing the local dimension in metallic glasses with different compositions. Short-range dimension d results from a linear fit taken from the center atom to the outer radius of the first coordination shell. Long-range dimension is computed out from a linear fit of points beyond the outer radius of the second coordination shell.

Table 1 the local fractal dimensions calculated from a linear fit taken from the center atom to the outer radius of the first coordination shell, for the different compositions. Composition

Al25Co75

Al33.5Co66.5

Al50Co50

Al66.5Co33.5

Al75Co25

df

2.68

2.58

2.54

2.59

2.58

curve [51,59] is also found in the structure factor and this splitting becomes more pronounced with the increase of the Al concentration. Second, the location of first peak shifts a little to the higher r side at lower concentration of Al. Finally, the shape of the second and third maxima becomes sharper as a function of the Al concentration, which means that the structure factor is strongly dependable on the composition. In MGs or generally amorphous solids, the structure factor and RDF indicates the existence of SRO into the medium-range-order (MRO) regime and the lack of long-range periodicity makes the

glass structure looks ‘disordered’ [51]. This ‘disordered’ structure has manifested itself in the unclearly shown peaks from the structure factor and RDF and as a replacement the emergence of a few ones such us the first sharp (q1 or r1) and the second splitted peaks [58,60,61]. We have focused our study on the FSP, or the first maximum of the structure factor curve [62] and on the sharpest peak. This can yield a direct structural information about the order at the atomic level structure in MGs. Based on the strong correlation between q1 and d, the interatomic distance apparently described by the well-known Ehrenfest relation [63]. It is found that the position of the FSDP is closely related to the average atomic volume (Va) via Va ¼ ð1=qÞD where the power D is expected to be 3 for liquids, gases, crystalline and randomly-ordered amorphous materials [64]. The atomic volume dependence of the position of the first sharp peak (FSP) for metallic glasses where Al concentration ranging from 25 to 75 is then plotted using double logarithmic scale in Fig. 8. It is observed that the value of q shifts linearly from

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Fig. 7. Computed structure factor for Al-Co metallic glasses with different compositions at 200 K.

2.95 to 3.13 with decreasing the atomic volume from 14.41 to 11.61 and that all five data points fall on a line despite the diversity of composition of MGs, validating the universal scaling behavior [64,65]:

 q¼

1 Va

0:38±0:08

This scaling behavior allows to get an insight into the MRO which is therefore not dependent on the quenching rate but on the composition. The computed fractal dimension is given by df ¼ 1=0:38 ¼ 2:63. We note that the found value of 2.63 is

comparable to the fractal dimension determined above by the linear fit of r versus lnðCN þ 1Þ. As we said before, all information concerning the order in the glass state is contained in the first sharp peak including its parameters such as the intensity, position and broadening or the full width at half maximum (FWHM) [66]. We have already seen that the position of FSP increases with the increase of Al concentration, this change is accompanied by an additional change of the FWHM and intensity. The composition dependence of the intensity (height or amplitude) of the FSP of the structure factor is shown in Fig. 9(a) where we observe that the peak monototically increases when increasing Al-content, indicating an increasing of the ordering in the system. Fig. 9(b) presents the behavior of the FWHM determined by a Gaussian fit of the FSP of the structure factor. The FWHM shows a continuous increase of the width versus the composition with a maximum at about 50% of Al, and then a decrease to reach a minimum of 0.23 at the composition of 75%. This behavior of the FWHM as a function of composition is explained essentially by the contribution of the partial structure factors Sij (given via a Fourier transform of the partial RDFs) where the FSP is located at different positions [64,66]. In the regions where Al fractions is lower (or higher), the main participation comes from like pairs Co-Co (or Al-Al). While for Al fraction equal to 50%, all three partial structure factors including the like an unlike pairs contribute strongly to the structure factor.

4. Conclusion

Fig. 8. Power-law scaling in MD-simulated Al-Co MGs: The location of the First Sharp Peak (FSP) as a function of the average atomic volume.

Employing an Embedded Atom Method of the Al-Co interatomic potential, Molecular dynamics simulations are conducted in order to investigate the structural and thermal behavior of rapidly quenched Al-Co amorphous alloys in a wide composition range between 25 and 75% of Al. Radial distribution function, Voronoi tessellation analysis, structure factor and fractal dimension exhibit monotonic changes with Al composition. It is found that the glass formation is clearly observed at the eutectic and near-eutectic point. Total and partial RDFs have been computed indicating that unlike pairs (Al-Co) are the responsible of the decomposition of the second peak and that the increase of Al concentration contribute essentially to the weakness of order in MGs. The same performance is observed in the structure factor that gives a good statistical

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Fig. 9. Relative changes of the FSP parameters: peak Height (a), peak full width at half maximum (b) as a function of Al concentration at cooling rate of 1013 K/s.

analysis with the exception that the first maximum becomes sharper and the decomposition in the second peak is more significant as the Al concentration increases. According to the Voronoi analysis performed for all simulated glasses, it is observed that there is no single dominant structural unit exhibiting two different types with two different coordination numbers including the icosahedral and icosahedral-coordination which is always present. The mixed-like clusters of index < 0; 3; 6; 4 > that decrease with increasing Al content while the < 0; 2; 8; 4 > of icosahedral-like is found to be in Al-rich glasses larger than the full icosahedra < 0; 0; 12; 0 > , the previously known as the most found VP in multicomponent MGs, including the binary ones. These polyhedra make up the higher population of that of all system and their content increases as Al content increases, indicating a sort of improvement of the icosahedral short-range ordering in Al-rich AlCo glasses. However, the investigation of the fractal dimension computed by the linear fitting of the L lnðCN þ 1Þ versus r curve, confirm that there is a composition effect and that a higher fraction of Al can prevent the vitrification of the system. The position of the FSP of structure factor is analyzed as a function of the atomic volume, and revealed a power law close to that proposed by Ma et al. [64]. Finally, another parameter of the structure factor which consists in the FWHM is discussed and showed a maximum in the AL50 Co50 which is attributed to the unlike pairs that is larger than that of like pairs and indicating that the GFA is lower in this system. References [1] E. Axinte, Metallic glasses from ‘ alchemy’ to pure science: present and future of design, processing and applications of glassy metals, Mater. Des. 35 (2012) 518e556. [2] K. Mivsek, Metallic Glass, Seminar, University of Ljubljana Faculty of Mathematics and Physics, 2006. [3] W. Zhang, A. Inoue, X.M. Wang, Developments and applications of bulk metallic glasses, Rev. Adv. Mater. Sci. 18 (2008) 1e9. [4] A. Inoue, A. Takeuchi, Recent development and application products of bulk glassy alloys, Acta Mater. 59 (2011) 2243e2267. [5] A. Inoue, Stabilization of metallic supercooled liquid and bulk amorphous alloys, Acta Mater. 48 (2000) 279e306. [6] A. Inoue, High strenght bulk amorphous alloys with low critical cooling rates (overview), Mater. Trans. 36 (1995) 866e875. [7] A.L. Greer, Metallic glasses...on the threshold, Mater. Today 12 (2009) 14e22. [8] X.H. Du, J.C. Huang, C.T. Liu, Z.P. Lu, New criterion of glass forming ability for bulk metallic glasses, J. Appl. Phys. 101 (2007) 23e25. [9] B. Yang, Y. Du, Y. Liu, Recent progress in criterions for glass forming ability, Trans. Nonferrous Metals Soc. China 19 (2009) 78e84. [10] M.H. Bhat, V. Molinero, E. Soignard, V.C. Solomon, S. Sastry, J.L. Yarger, C.A. Angell, Vitrification of a monatomic metallic liquid, Nature 448 (2007)

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