Atomic and cluster level dense packing contributes to the high glass-forming ability in metallic glasses

Intermetallics 34 (2013) 106e111

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Atomic and cluster level dense packing contributes to the high glass-forming ability in metallic glasses L. Yang a, *, T. Ge a, G.Q. Guo a, C.L. Huang a, X.F. Meng a, S.H. Wei b, D. Chen a, L.Y. Chen c, ** a

College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29#, Nanjing 210016, PR China Department of Physics, Ningbo University, Ningbo, Zhejiang 315211, PR China c Department of Mechanical Engineering, University of WisconsineMadison, Madison, WI 53706, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 July 2012 Received in revised form 4 November 2012 Accepted 6 November 2012 Available online 10 December 2012

The microstructure features of a representative Zr48Cu45Al7 bulk metallic glass (BMG) were investigated via a series of simulations and calculations coupled with the synchrotron radiation-based experiments. It was revealed that bond shortening occurs in the atomic pairs, due to the strong interaction between the Al dopant atoms and their neighbors. The bond shortening leads to the atomic and cluster level dense packing in the local structures, which should be the structural mechanism of the high glass-forming ability in Al-microalloyed BMGs. This work not only reveals the atomic and cluster level microstructures in this class of glass materials, but also has implications for developing other BMGs with relatively large critical sizes. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: A. Ternary alloy systems B. Glasses, metallic D. Microstructure E. Simulations, Monte Carlo F. Diffraction

1. Introduction The underlying mechanism of the glass-forming ability (GFA) in alloys is the key for a broad application of these metallic glasses as engineering materials. However, this is a long-standing issue [1e7]. It has been well accepted that the formation and the macroscopic properties of materials are strongly influenced by their microstructures. Thus, great efforts have been devoted to investigating the microstructure in glassy alloys [8e13]. Unlike the crystalline alloys, it is still a challenge to establish the explicit structural pictures in amorphous alloys. So far, it has been realized that clusters (the convex polyhedra made up of one center atom and some shell atoms) should be the building blocks of microstructure in this class of glassy materials, based on which several structural models have been proposed [8e10]. These studies revealed the inherent short-range and medium-range ordering in glassy alloys, by building and stacking clusters topologically and chemically. It also has been suggested in these structural models that the dense packing principle is available for detecting the essential structural

* Corresponding author. Tel.: þ86 25 52112903. ** Corresponding author. E-mail addresses: [email protected] (L. (L.Y. Chen).

Yang),

[email protected]

0966-9795/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.intermet.2012.11.009

nature of glassy alloys, which enhances understanding of the glassforming mechanism in alloy systems. Recently, at the macroscopic scale, it has been enunciated that the mass density difference between a glassy alloy to its corresponding crystal alloy reaches the local minimum at a pinpointed composition with the best GFA. This implies that high dense packing efficiency in microstructure may significantly contribute to the relatively high GFA in a composition-pinpointed bulk metallic glass (BMG) [14]. The above-mentioned structural models indicate that dense packing is a universal phenomenon in the glassy alloy, However, in the atomic and cluster level microstructure, it has not been found that how dense the atoms pack in the clusters and how dense the clusters fill in space. Thus, it is difficult to reveal the packingeGFA relationship by using these structural models. In this work, a series of simulations and calculations coupled with the synchrotron radiation-based experiments were performed to address this issue. A representative Zr48Cu45Al7 BMG and a corresponding Zr50Cu50 binary alloy were selected as the research prototypes. Zr48Cu45Al7 has a critical casting size of 8 mm [15], which is higher than that (1.5 mm) of Zr50Cu50 composition [16]. It was found that bond shortening caused by strong atomic interactions occurs in the Al-containing atomic pairs, which leads to a relatively high dense packing the atoms in clusters and a high space-filling efficiency of the clusters themselves. The atomic and cluster dense packing is the structural origin of the high GFA in the

L. Yang et al. / Intermetallics 34 (2013) 106e111

Al-microalloyed glassy alloys. This work may extend to other multicomponent BMGs, and has implications for searching more BMGs with relatively large critical sizes. 2. Experimental and simulation methods 2.1. Synchrotron radiation-based experiments The selected Zr48Cu45Al7 ternary and Zr50Cu50 binary alloy ingots were prepared by arc melting the mixture of Zr (99.9 wt.%), Cu (99.9 wt.%), and Al (99.9 wt.%) elements in Ti-gettered high purity argon atmosphere. The amorphous ribbons having a cross section of 0.04  2 mm2 were prepared by Melt-spinning on these ingots. The synchrotron radiation-based X-ray diffraction measurements were performed for all samples at the beam line, BW5, of Hasylab in Germany. A high-energy X-ray (about 100 keV) was used in this measurement, ensuring that the diffraction signals have a wide range of values in Q (the wave vector transfer) space. The two-dimensional diffraction raw data were recorded using a Mar345 image plate, and integrated to Q-space data after subtracting its background by program Fit2D [17]. The diffraction data were normalized via software PDFgetX to obtain the structure factor S(Q). Subsequently, after calculating the proper thickness for each measurement, their Zr and Cu K-edge extended X-ray absorption fine structure (EXAFS) spectra were measured at the beam lines BL14W1, in Shanghai Synchrotron Radiation Facility (SSRF) of China, and U7C, in National Synchrotron Radiation Laboratory (NSRL) of China. The measured data were further normalized via a standard procedure, using software Viper [18]. 2.2. Reverse Monte-Carlo (RMC) simulation The RMC simulation technique is an iterative method extensively used for building structural models in disordered systems

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that agree quantitatively with experimental data (such as the synchrotron radiation-based x-ray diffraction, EXAFS, and neutrondiffraction data). In particular, it is available for glassy alloys [19]. In this work, the synchrotron radiation-based diffraction and EXAFS data were simulated simultaneously, using software RMCA [20]. The initial cubic boxes containing 40,000 random-distributed Cu, Zr, and Al atoms were built, matching the Zr50Cu50 binary and the Zr48Cu45Al7 ternary compositions. During the RMC simulation, the experimental diffraction and EXAFS data were compared with the simulation spectra using the iterative calculation expression [21]:

d2 ¼

2 1 X 1 X cm;Cu ðkn Þ Sm ðQn Þ  Sexp ðQn Þ þ 2 2 ε n εCu n 2 2 1 X cm;Zr ðkn Þ  cexp;Zr ðkn Þ  cexp;Cu ðkn Þ þ 2 εZr n

(1)

2

where d denotes the deviation between the experimental and simulation data, the ε parameters can regulate the weight of the data set given in the fitting procedure, the S(Q) and cðkÞ parameters are the XRD structural factor and the EXAFS signal, respectively. Once an experiment-simulation convergence is obtained, the simulation is stopped, and all the atoms are “frozen” with determined three-dimensional positions in the cubic box. As a result, an atomic-structural model is obtained, which is available for further analyses. 2.3. Voronoi tessellation According to the Voronoi original algorithm [22], each convex Voronoi polyhedron (VP) is formed by connecting the perpendicular bisectors between a center atom and all of its neighboring atoms. A VP is usually indexed as , where ni denotes the number of i-edged faces on its surface. Each VP is

Fig. 1. (a) The two-dimensional diffraction pattern of Zr48Cu45Al7, (b) the structure factor S(Q) of Zr48Cu45Al7 and Cu50Zr50, (c) the Zr and Cu K-edge EXAFS spectra of Zr50Cu50, and (d) the corresponding EXAFS data in Zr48Cu45Al7. The red and green solid lines denote the simulation and experimental data, respectively. (For interpretation of colour in this figure legend, the reader is referred to the web version of this article.)

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L. Yang et al. / Intermetallics 34 (2013) 106e111

embeded into a corresponding convex Voronoi cluster (VC) having a solute (the center) atom and some solvent (the shell) atoms (Configurations of some VCs and corresponding VPs are in Fig. 1 of P Ref. [23] and Fig. 6 of Ref. [24]). Therefore, ni also equals the number of the shell atoms in one VC, i.e., coordination number (CN) of the center atom. The Voronoi algorithm requires that all VCs are formed by piling up a set of Delaunay tetrahedrons sharing the common vertex at one atom (the center atom) [25]. As a result, their surface should be only made up of triangle faces. In other words, they are regarded as deltahedra [10]. In the RMC simulated structural model, all the VCs can be extracted and indexed according to the Voronoi tessellation. 3. Results and discussion 3.1. The atomic-level structural information Fig. 1aed shows the experimental two-dimensional diffraction data, the structural factor, S(Q), and the Zr and Cu K-edge EXAFS data, along with their corresponding simulation spectra (we only show the data of Zr48Cu45Al7 here). The observations that the twodimensional diffraction spectra have some halos and the S(Q) curves has no sharp peaks after the first strong peak adequately indicate the amorphous nature of the present samples [26]. It is found in Fig. 1bed that all the simulated data are consistent with their experimental spectra, which ensures the success of this RMC simulation. The reliable atomic-level structural information can be obtained from the simulated atomic-structural model, within which three-dimensional positions of atoms have been determined. The atomic-pair distances (APDs) for both samples are shown in Table 1. In addition, another set of interatomic bond lengths (DASSESSED) were obtained by summing the assessed radii of atoms deduced from the efficient packing model [27]. It is worth noting in Zr48Cu45Al7 that although the APD values of ZreZr, ZreCu, and CueCu are very similar with those from the DASSESSED values, the other APDs around the Al centers are apparently smaller than their counterparts. In particular, the ZreAl bond shortened by 7.7 percent is observed. It indicates that strong interaction may occur between the Al atoms and their neighbors, resulting in the bond shortening behavior. The AleAl bond length is not provided here, because they are avoided to connect with each other due to the rather low Al concentration. Since there is no obvious bond shortening in the ZreZr, ZreCu, and CueCu pairs for both samples, it indicates that it is the Al addition that causes the “non-spherical” atoms [28] and the corresponding bond shortening in the Zr48Cu45Al7 ternary composition. The bond shortening in glassy alloys was observed elsewhere [21,28e30].

Table 1 The atomic-pair distances in both Zr50Cu50 and Zr48Cu45Al7 samples, which are obtained from the RMC (DRMC), and from the assessed radii of atoms (DASSESSED). (DRMC  DASSESSED)/DASSESSED is listed too. Compositions

Atomic pairs

DRMC ( A)

DASSESSED ( A)

Distance change (%)

Zr48Cu45Al7

ZreZr ZreCu ZreAl CueCu CueAl

3.18 2.85 2.76 2.55 2.57

3.16 2.84 2.99 2.52 2.67

þ0.63 þ0.35 7.69 þ1.19 3.75

Zr50Cu50

ZreZr ZreCu CueCu

3.19 2.85 2.56

3.16 2.84 2.52

þ0.95 þ0.35 þ1.59

Fig. 2. Distribution of the major VCs, centered with (a) Zr, (b) Cu, and (c) Al atoms. Note only VCs possessing a weight over 2.0% are selected.

L. Yang et al. / Intermetallics 34 (2013) 106e111

3.2. The cluster level structural information At the cluster scale, distributions of the Zr-, Cu-, and Al-centered VCs (the so-called local structures) in both samples are shown in Fig. 2aec. In previous wok [23], it has been proved that besides the so-called ideal icosahedron (the <0,0,12,0> cluster), other units (such as those indexed as <0,2,8,2>, <0,3,6,3>, <0,4,4,4>, <0,1,10,2>, and so on) also are icosahedral or icosahedral-like clusters. Thus, as shown in Fig. 2a, Zr atoms in Zr48Cu45Al7 are prone to be centered in some icosahederal-like VCs, such as those indexed as <0,2,8,2> and <0,3,6,3>. It is coincident with the widely accepted viewpoint that the microstructure containing abundant icosahedral clusters may ease the formation of glassy alloys [31e34]. Concerning both Cu- and Al-centered VCs, the most popular VC is indexed as <0,2,8,1>, which has a CN of 11. Because the assessed radius of Cu atoms (1.26  A) is smaller than that of Al atoms (1.41  A) [27], it is expected that the Cu atoms should have a smaller average CN than the Al counterparts according to the efficient packing model [9]. It is found that some Cu and Al atoms may be centers in VCs with relatively small CNs (such as the <0,3,6,0>, <0,2,8,0>, and <0,3,6,1> VCs with CNs of 9, 10, and 10, respectively). However, it is the Al-centered ones that have obviously higher fractions. It suggests that Al atoms may have a smaller average CN than that of Cu ones. Why? It is found that the

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Al atom-containing bonds are apparently shortened compared with the assessed Al atom, resulting in less neighbor atoms surrounding Al centers. On the other hand, the length of CueCu bond is a little bit larger than the CueCu DASSESSED value. Thus, it is possible that the Al atoms have a smaller average CN than the Cu atoms. To deduce more structural features of VCs, another cluster level analysis was performed by calculating the volumes of VCs in both samples, as shown in Fig. 3a and b. It is worth noting that all the volumes of Zr- and Cu-centered VCs are smaller in the Zr48Cu45Al7 BMG, compared with their counterparts in the Zr50Cu50 binary alloy. The volume changes of various VCs are also shown in Fig. 4a and b. The volume changes (1e2%) indicate that although some of the cluster level structural characters (such as the Voronoi index) are similar in both samples, atoms are more densely packed in Zrand Cu-centered clusters of the Zr48Cu45Al7 ternary alloy. To examine whether it is the Al minor addition that contributes to the volume shrinkage of local structures, a further calculation was performed for the fractions of Zr- and Cu-centered clusters containing Al atoms in Zr48Cu45Al7, as listed in Table 2. It is shown that about a half of these clusters contain at least one Al atom. This indicates that the Zr or Cu centers are prone to connect with Al atoms, forming the VCs having Al shell atoms. The shortened ZreAl or CueAl bonds contained in the Zr- or Cu-centered clusters decrease the average distances between the centers and the shell atoms, leading to the volume shrinkage. 3.3. The origin of bond shortening The bond shortening leads to the volume shrinkage in clusters. It is required to reveal the origin of the bond shortening. Therefore, the electronic basis in Zr48Cu45Al7 was studied. The DMol3 cluster method was performed based on the density functional theory [35]

Fig. 3. The volume distributions of the VCs centered with (a) Zr and (b) Cu atoms.

Fig. 4. The volume differences in the (a) Zr- and (b) Cu-centered VCs between Zr48Cu45Al7 and Zr50Cu50, i.e., [(VZr48Cu45Al7  VZr50Cu50)/VZr50Cu50].

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Table 2 The fractions of the Zr- or Cu-centered clusters containing n (n ¼ 0,1,2,3.) Al atoms.

Fractions

Clusters

The number of Al-containing atoms 0

1

2

3

Zr-centerd Cu-centerd

44.03% 55.05%

35.10% 32.11%

15.94% 10.38%

4.93% 2.46%

Fig. 5. The total DOS and partial DOS in (a, b) <0,3,6,1>, and (c, d) <0,2,8,0> VCs. Partial DOS were selected, which were originated from the representative atoms of Al0, Cu4, Cu5, Zr6, Zr8 in <0,3,6,1>, and Al0, Al1, Cu4, Cu5, Zr7, Zr10 in <0,2,8,0>, respectively. The partial DOS were displayed in threefold magnification. The number behind the atoms denotes their serial number in these clusters. The Fermi energy level possesses a position of 0 eV.

under the generalized gradient approximation [36]. Unlike the crystalline alloys, which have the determined unit cells that can be stacked periodically to form the long-rang ordering, the corresponding glassy alloys only possess the short-range ordering. It is difficult to calculate the electronic density of state (DOS) for all the atoms or clusters in the microstructure of glassy alloys. However, because it has been found that some VCs with abundant five-fold symmetry features are the backbones of the microstructure in Zr48Cu45Al7, the electronic basis of these preferred VCs needs to be revealed and extrapolate to the whole microstructure. Two typical Al-centered VCs, indexed as <0,3,6,1> and <0,2,8,0>, were selected to perform the calculation of DOS. The total DOS and the partial DOS from some representative atoms are shown in Fig. 5aed. All the partial DOS were threefold magnified while the

total DOS were not. The Al:3s electron is a leading contributor in the total DOS located at about 7.0 eV in Fig. 5a and b, and 6.4 eV in Fig. 5c and d. But only about 20% of the total DOS is made up of the Al:3s electron, the rest is contributed by other atoms, such as the Cu:4s4p and Zr:4d5s5p. Similar results can be obtained that the Al:3s electron is a leading contributor in the total DOS located at about 4.7 eV (4.2 eV or 2.1 eV) in Fig. 5a and b, and 4.4 eV (3.9 eV or 1.9 eV) in Fig. 5c and d. These results indicate that there are strong hybridization interactions between the Al center atoms and their neighbor Cu or Zr atoms, leading to the bond shortening. Furthermore, the average mulliken charges (AMCs) were calculated for four representative Al-centered VCs (<0,3,6,0>, <0,3,6,1>, <0,2,8,0>, and <0,2,8,1>) in Zr48Cu45Al7, as listed in Table 3. As observed, all the Zr atoms donate charges (0.1e0.2) and all the Cu atoms are “donees” (0.1 to 0.2), some of the Al atoms are contributors while the others are not. These observations are reasonable, because the Pauling’s electronegativities of Zr, Al, and Cu elements are 1.33, 1.61, and 1.90 [37], respectively. However, the calculated AMC values of Zr or Cu atoms in several selected VCs for Zr50Cu50 are much lower, which are not shown here due to the page limitation in Table 3. These results further indicate that it is the Al addition atoms that cause the strong hybridization interactions in the AleCu and AleZr atomic pairs. Whereas, such strong interaction is absent in the ZreZr, CueCu or CueZr atomic pairs. By studying the electronic basis of VCs, the origin of the strong bonding effect between the Al atoms and their neighbors is revealed. 3.4. The atomic and cluster level dense packing Based on the results deduced above, the atomic and cluster level dense packing in the representative Zr48Cu45Al7 BMG can be revealed. At the atomic level, the Al addition leads to the bond shortening in the AleZr and AleCu pairs, resulting from their strong atomic interactions. Thus, the Al centers and their neighbor atoms should be regarded as “non-spherical” atoms rather than “spherical” spheres [28]. Compared with the “spherical” atoms, less space allows “non-spherical” atoms to move, leading to atomic dense packing in the Al-centered local structures. In addition, some of the Zr- and Cu-centered clusters contain at least one Al atom at their shell sites, the bond shortening of the AleZr or AleCu atomic pairs contributes to the volume shrinkage in these clusters. Therefore, the atomic-level dense packing also occurs in the Zr- and Cu-centered local structures. At the cluster scale, the Zr-centered icosahedral clusters are popular in microstructures of both

Table 3 The average mulliken charges (AMCs) for four representative Al-centered VCs in Zr48Cu45Al7. Al(1) stands for the Al center atom, the others are the atoms containing in these VCs. The number in sharp bracket and round bracket denote the Voronoi index of clusters and the serial number of an atom respectively. “e” denotes that this atom obtains charges. Al2Cu4Zr4<0,3,6,0>

Al2Cu4Zr5<0,2,8,0>

AlCu5Zr5<0,3,6,0>

AlCu5Zr6<0,2,8,1>

Atom

AMC

Atom

AMC

Atom

AMC

Atom

AMC

Al(1) Al(2) Cu(3) Cu(4) Cu(5) Cu(6) Zr(7) Zr(8) Zr(9) Zr(10)

0.030 0.090 0.096 0.158 0.117 0.103 0.130 0.083 0.208 0.113

Al(1) Al(2) Cu(3) Cu(4) Cu(5) Cu(6) Zr(7) Zr(8) Zr(9) Zr(10) Zr(11)

0.042 0.139 0.211 0.128 0.144 0.118 0.061 0.137 0.230 0.122 0.148

Al(1) Cu(2) Cu(3) Cu(4) Cu(5) Cu(6) Zr(7) Zr(8) Zr(9) Zr(10) Zr(11)

0.118 0.108 0.157 0.138 0.108 0.091 0.102 0.097 0.098 0.117 0.069

Al(1) Cu(2) Cu(3) Cu(4) Cu(5) Cu(6) Zr(7) Zr(8) Zr(9) Zr(10) Zr(11) Zr(12)

0.059 0.141 0.168 0.126 0.142 0.130 0.092 0.157 0.082 0.195 0.130 0.110

L. Yang et al. / Intermetallics 34 (2013) 106e111

Zr50Cu50 and Zr48Cu45Al7. These clusters do not lead to very high cluster level dense packing, because it has been recognized that the space can not be completely filled only by icosahedral clusters due to their symmetry features, leaving some voids in space [38]. However, it has been deduced that some smaller Al-centered clusters (such as <0,3,6,0> and <0,2,8,0>) are favored in the Zr48Cu45Al7 sample, which may occupy the voids to connect the larger Zr-centered icosahedral clusters and enhance the spacefilling efficiency. As a result, the relatively high cluster level dense packing achieves. According to Miracle’s dense cluster packing model [9], some solute atoms (such as the so-called b atoms) having small radius and low concentration are prone to enter small local structures, enhancing the connection of the neighboring larger clusters. In our case, some of the Al atoms should be regarded as the b atoms. Because the Al addition leads to the formation of high atomic and cluster dense packing, most of the Zr, Cu, and Al atoms are relatively tightly nailed in the local structures, like some “frozen” spheres having the reduced mobility. During rapid quenching, these “frozen” atoms (clusters) are preserved to avoid obvious rearrangement of atoms and clusters, and the crystallization is accordingly retarded. This should be the structural mechanism of the high GFA in the selected Zr48Cu45Al7 BMG.

Science Foundation of Zhejiang Province (Grant No. Y607546), the open fund of National Engineering Research Center of Near-netshape Forming for Metallic Materials (Grant No. 2012005) and the Fundamental Research Funds for the Central Universities are gratefully acknowledged.

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4. Conclusion [18]

In summary, the microstructure of a representative Zr48Cu45Al7 BMG was investigated at both atomic and cluster scales. It was revealed that the Al dopant atoms have strong interactions with their neighbor atoms, leading to the bond shortening behavior and the cluster-volume shrinkage. These factors contribute to the atomic and cluster dense packing in the local structures. Such dense packing should be the structural origin of the high GFA caused by Al-microalloying in the ZrCu system. This work has implications for designing a dense packing scheme for developing more BMG compositions in the multicomponent alloy systems. Acknowledgements The authors would like to thank the HASYLAB in Germany, the SSRF in Shanghai, and the NSRL in Hefei for the use of the advanced synchrotron radiation facilities. Financial supports from the National Natural Science Foundation of China (Grants No. 10805027 and 10804058), the Natural Science Foundation of Jiangsu Province (Grant No. BK2011071), the NUAA Research Funding (Grant No. NS2010168), the Funding for Outstanding Doctoral Dissertation in NUAA (Grant No. BCXJ12-08), the Natural

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