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The connection of icosahedral and defective icosahedral clusters in medium-range order structures of CuZrAl alloy
Journal of Non-Crystalline Solids 521 (2019) 119475
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The connection of icosahedral and defective icosahedral clusters in mediumrange order structures of CuZrAl alloy ⁎
T
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Lei Rena,b, Tinghong Gaob,c, , Rui Maa,b, , Quan Xieb,c, Zean Tianb,c, Qian Chenb,c, Yongchao Liangb,c, Xuechen Hub,c a
College of Materials and Metallurgy, Guizhou University, Guiyang 550025, China Institute of New Type Optoelectronic Materials and Technology, Guizhou University, Guiyang 550025, China c College of Big Data and Information Engineering, Guizhou University, Guiyang 550025, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Medium-range order Cu50Zr40Al10 alloy Connection mode Icosahedral cluster Defective icosahedral clusters
Medium-range order structure is the one of the important local structural units in the field of bulk metallic glasses. The rapid solidification of Cu50Zr40Al10 ternary alloy is investigated by molecular dynamics simulation. Simultaneously, the connections between the full icosahedral and defective icosahedral clusters in mediumrange order structures of Cu50Zr40Al10 alloy are characterized systematically by the quantitative method and visualization analysis. The results reveal that the icosahedral clusters as the main structures with high structural stability are bonded with each other by interpenetrating connection, and form the triangle, double triangle, triple triangle, tetrahedron and chain connected icosahedral medium-range order clusters. Moreover, the icosahedral and defective icosahedral clusters prefer to link with each other and form the bigger medium-range order clusters with different configurations in this system. These structures keep the high structural stability of icosahedral medium-range order section and the structural variability of chain-like medium-range order structures.
1. Introduction Since Pd-Ni-P bulk metallic glasses (BMGs) were successfully prepared by Turnbull group in 1982 [1], BMGs have became one of the most potential research materials due to their extraordinary strengths, elasticity, high yield strength, and excellent nanoprocessability [2–4]. The macro properties of materials are determined by their microstructures, which is an important topic in the materials science [5]. It is worth mentioning that alloys play a key role in the research of the relationship between the microstructures and the properties of materials [6–8]. Cu-Zr-Al alloy as a new kind of materials for BMGs, its mechanical properties and glass forming ability get greatly improved [9,10]. The research on clusters of Cu-Zr-Al basic alloy has attracted much attention in order to understand its properties [11,12]. The characteristics of various clusters in materials are the basis for developing advanced alloys. In BMGs, the icosahedral (ICO) cluster has very good structural stability and configural continuity [13,14], and the existence of ICO cluster increases the barrier to form the crystalline structures and improves the glass-forming ability (GFA) [15]. The medium-range order (MRO) structures belong to the length scale between short-range order (SRO) and long-range order [15]. The ICO ⁎
clusters are considered as the main structural units for studying MRO structure [16,17], and it is also an important factor affecting the properties of metallic glass. Among the MRO structures, the icosahedral medium-range order (IMRO) structures are more stable than others [18,19]. In 2007, Shimono and Onodera found that the network-like ICO clusters existed in metallic glass and it was the origin of MRO structure [20,21]. Wakeda and Shibutani analyzed that the interpenetrating connection of IMROs had higher local elastic modulus in Cu-Zr binary alloy [19]. Foroughi et al. showed that the < 0 2 8 2 > polyhedron was the dominant cluster and the intercross connection of icosahedra was the most stable in Cu50Zr50 BMG [22]. Nevertheless, the evolution of MRO structures and the ICO cluster with MRO structural feature have not been researched comprehensively. Therefore, it is of great significance to analyze the MRO structures in Cu50Zr40Al10 amorphous alloy. However, under existing experimental conditions, the evolution process of MRO structures has not been well observed. With the development of computer technology, computer simulations have become an indispensable method in the structural researches of materials. Many kinds of materials, including various alloys, semiconductors, ceramics, have been simulated at the atomic or molecular level by computer [23–25]. More recently,
Corresponding authors at: Institute of New Type Optoelectronic Materials and Technology, Guizhou University, Guiyang 550025, China. E-mail addresses: [email protected] (T. Gao), [email protected] (R. Ma).
https://doi.org/10.1016/j.jnoncrysol.2019.119475 Received 29 March 2019; Received in revised form 19 May 2019; Accepted 29 May 2019 Available online 10 June 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
Journal of Non-Crystalline Solids 521 (2019) 119475
L. Ren, et al.
Molecular dynamics (MD) simulation is applied as an effective tool to investigate the evolution of clusters and widely used in studying glass formation processes of CuZrAl alloys during rapid solidification [26–28]. In this study, MD simulation is employed to explore the connections of clusters during the quenching process in liquid Cu50Zr40Al10 alloy. Completed structural information is necessary to understand the MRO structures. The radial distribution function (RDF) is adopted to indicate the interaction of different type of atoms. The structural evolution of clusters has been detected by the Voronoi polyhedron index [29]. Moreover, the connection modes of MRO structures are further investigated by the Open Visualization Tool (Ovito) [30]. Based on the MD simulation results, the structural characterization of MRO clusters in Cu50Zr40Al10 alloy is discussed in detail. Fig. 1. Evolution of the main Voronoi polyhedrons in Cu50Zr40Al10 alloy.
2. Simulation conditions and methods MD simulation was performed with the Large-scale Atomic/ Molecular Massively Parallel Simulator (LAMMPS) [31] for ternary alloy. In this study, the system consisted of 10,000 atoms (5000 Cu atoms, 4000 Zr atoms and 1000 Al atoms, which corresponds to the composition of Cu50Zr40Al10 alloy) in the cubic box (side lengths = 5.58 nm) with the three dimensional periodic boundary condition. Simulations conducted in the NPT (constant atom number, system pressure and temperature) ensemble with zero pressure, and based on the newly-developed embedded atom model (EAM) potential by Y. Q. Cheng et al., the reliable potential file (see the supplemental material [32]) described the interaction between atoms in Cu-Zr-Al system [33]. The potential function could be fitted to represent the potential energy surfaces of more than 600 configurations obtained by ab initio calculations. Meanwhile, the initial configuration of Cu50Zr40Al10 alloy was generated randomly, and the simulation was started to melt at 2000 K which is higher than the melting point of Cu50Zr40Al10 alloy [34]. The system was run for 100 ps at 2000 K to guarantee an equilibrium liquid state, using 2.0 fs time step and NPT ensemble. Subsequently, the system gradually cooled down to 200 K at a cooling rate of 1012 K/s. The atomic configurations were recorded with an interval of 20 K during the rapid solidification. Finally, several structural characterization methods were applied to indicate the structural properties of the MRO clusters in Cu50Zr40Al10 alloy.
number of < 0 3 6 3 > Voronoi polyhedrons increased with the decreasing temperature and almost maintained unchanged at low temperature. According to the statistical numbers, the microstructures of solidified Cu50Zr40Al10 alloy were dominated by full ICO and defective ICO clusters under cooling rate of 1012 K/s.
3.2. Formation of Cu50Zr40Al10 amorphous alloy Radial distribution function (RDF) is a major structural characterization method widely used to detect the structural properties of liquid and glass microstructures. The g(r) curve represents the average number of atoms on the sphere at a distance ‘r’ centered on any atom. The g(r)min/g(r)max is defined as the Wendt-Abraham parameter, of which the g(r)min (g(r)max) is the first minimum (maximum) of RDF. This is an important parameter used to further analyze and estimate the glass transition temperature (Tg) [40,41]. Fig. 2 showed the trend of g (r)min/g(r)max at cooling rate of 1012 K/s. There was a notable inflection point of the fitting curve at 728 K, namely the Tg ≈ 728 K, which was close to the result obtained by Inoue et al. in the study of Cu60-xZr40Alx alloy (x = 0 to 10 at%). According to the scanning calorimetry curves, the Tg increased monotonously from 717 K at 0% Al to 741 K at 10% Al [42]. At the end of rapid solidification, Cu50Zr40Al10 alloy formed amorphous structure. Fig. 3 showed the RDFs of Voronoi polyherdrons in Cu50Zr40Al10 alloy at 200 K. From the evolution of the main polyhedrons during quenching process in Fig. 1, the number of < 0 1 10 2 > , < 0 3 6 4 > , < 0 2 8 4 > and < 0 0 12 0 > Voronoi polyhedrons was most in the Cu50Zr40Al10 amorphous system at the end of the solidification process. Notably, the first peak of g < 0 0 12 0 > (r) curve were higher and sharper compared with the g < 0 1 10 2 > (r), g < 0 2 8 4 > (r) and g < 0 3 6
3. Results and discussion 3.1. Voronoi polyhedron The Voronoi ployhedron analysis [29,35] is carried out to characterize the microstructures in Cu50Zr40Al10 alloy. The Voronoi polyhedral index is expressed as < n3, n4, n5, n6 > , where ni denotes the number of i-edged faces of the Voronoi polyhedron, to specify the characteristics of the atomic clusters surrounding an atom. The Voronoi polyhedron index of the full ICO clusters is defined as < 0 0 12 0 > [36,37], the < 0 1 10 2 > , < 0 2 8 2 > , < 0 2 8 4 > , and < 0 3 6 4 > polyhedron indexes denote the defective ICO clusters [38]. Fig. 1 demonstrated the largest number of eight main Voronoi polyhedrons in Cu50Zr40Al10 alloy during the quenching process. The number of < 0 3 6 4 > , < 0 1 10 2 > , < 0 2 8 4 > , < 0 0 12 0 > and < 0 2 8 2 > Voronoi polyhedrons increased remarkably, especially the number of < 0 0 12 0 > Voronoi polyhedrons increased more significantly. It can be clearly seen that the number of < 0 0 12 0 > Voronoi polyhedrons was least in the eight main Voronoi polyhedrons in high temperature liquid. However, it became one of the major Voronoi polyhedrons in the microstructures of Cu50Zr40Al10 alloy at the end of the rapid solidification. The < 0 0 12 0 > clusters as the major structural unit exist in most metallic liquids and glasses [39]. Moreover, the number of < 0 2 8 3 > and < 0 2 8 1 > Voronoi polyhedrons slightly increased with the decrease of temperature. While the
Fig. 2. Correlations of the Wendt-Abraham radio with temperature during quenching process. 2
Journal of Non-Crystalline Solids 521 (2019) 119475
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Fig. 3. RDFs of Voronoi polyhedrons in Cu50Zr40Al10 alloy at 200 K. (a) A large number of polyhedrons. (b) Others.
preferred because of the similar microstructures between the < 0 1 10 2 > and < 0 0 12 0 > clusters. The variation of the number of ICO clusters linking with < 0 3 6 4 > and < 0 2 8 2 > clusters were similar, which went up first and then kept moderate growth below the Tg. These connections are moderated due to the quite a few number of < 0 3 6 4 > and < 0 2 8 2 > clusters and the increasing trend with the decreasing temperature shown in Fig. 1. The slight connections appeared between ICO and < 0 2 8 3 > , < 0 3 6 3 > , < 0 2 8 1 > clusters. These connections increased slightly during the rapid solidification and kept a small amount. The reasons are the slight increasing trend of < 0 2 8 3 > , < 0 3 6 3 > clusters and fewer number of < 0 2 8 1 > clusters with the decreasing temperature shown in Fig. 1.
4 > (r)
curves, which manifested the increasing of SRO structures in Fig. 3(a). And the splitting of the second peak in g < 0 0 12 0 > (r) curve was a well-known characteristic feature of glass formation [43]. In Fig. 3(b), the first peak of g(r) curve of eight main Voronoi polyhedrons was the highest among the three g(r) curves and the obvious split on the second peak of g(r) curve. While the g(r) curve of the total atoms showed no split, this was because the atomic interactions in the thermodynamic metastable amorphous system promoted the uniformity of the Cu, Zr and Al atoms. And the second peak of g(r) curve of except eight main Voronoi polyhedrons also did not split. This behavior of the second peak of RDFs without splitting was also observed when X. Ou et al. investigated the Cu50Zr45Al5 metallic glass and Y. Y. Cui et al. studied amorphous state Cu50Zr65Al10 [44,45]. The results indicated that the eight main Voronoi polyhedrons played an important role in the study of the microstructures formation and evolution of Cu50Zr40Al10 amorphous alloy during the rapid solidification. According to the Voronoi polyhedrons and RDF analysis, we observed the eight main clusters are the characteristic configurations in the microstructures of Cu50Zr40Al10 alloy during quenching process. Moreover, the connections relationship among the clusters was also a significant factor affecting the amorphous structure. In amorphous alloys, ICO clusters as the main characteristic structural unit represented the stability of BMGs to some extent [14,46]. In order to further analyze the MRO structures formed by ICO clusters and eight main clusters, the number of the connections between ICO clusters and eight main clusters in Cu50Zr40Al10 alloy was obtained as illustrated in Fig. 4. It is obvious that the connections can be divided into three parts of preferred, moderated and slight connections. The number of ICO connecting with < 0 1 10 2 > , < 0 0 12 0 > and < 0 2 8 4 > clusters increased significantly with the decrease of temperature and keep the highest rate in the system when temperature below 728 K. The connections are
3.3. Visualization analysis According to the previous analysis, the ICO clusters preferred to connect to the < 0 1 10 2 > , < 0 0 12 0 > , < 0 2 8 4 > , < 0 3 6 4 > and < 0 2 8 2 > clusters in Cu50Zr40Al10 amorphous alloy during the rapid solidification. In Fig. 5, the central atoms of < 0 1 10 2 > clusters were bonding together to form the relatively compact morphologies, which was similar to the < 0 0 12 0 > and < 0 2 8 4 > clusters. Although the number of < 0 2 8 2 > clusters was more than < 0 0 12 0 > clusters, many lonely center atoms of < 0 2 8 2 > clusters existed in the system. However, the connected center atoms of < 0 3 6 4 > clusters were very rare and dispersed in the system randomly, which were favorable to form shorter chains as shown in Fig. 5(d). It could be concluded that the < 0 1 10 2 > , < 0 0 12 0 > and < 0 2 8 4 > clusters were easier to form larger size nanoclusters that could be seen as the main structures in Cu50Zr40Al10alloy. MRO cluster has been defined as an important structure beyond SRO. A comprehensive understanding of characteristics of MRO structures is one of the most important purposes in MG researches [47]. IMRO clusters consist of many < 0 0 12 0 > clusters to be bonded by their center atoms, which are also known as interpenetrating connection. Shimono and Onodera reported that the configuration formed by the ICO clusters through the interpenetrating connection is statistically dominant among the other types [20]. And the interpenetrating ICO clusters were not only energetically more favorable, but also structurally more stable [16]. The Ovito is used to show the various morphologies results from the different connection styles between the central atoms of ICO clusters. The triangle, double triangle, triple triangle, tetrahedron and chain connected ICO structures that were important MRO structures in Cu50Zr40Al10 alloy as shown in Fig. 6 (a), (b), (c), (d) and (e). The triangle, double triangle, triple triangle and tetrahedron connected MRO clusters were more condensed than the chain connected MRO clusters. The ICO clusters connected by triple triangle interlocked with other clusters in order to improve the stability of the structures and became the backbone structures in this system. In
Fig. 4. Evolution of the connections between ICO clusters and eight main clusters during rapid solidification. 3
Journal of Non-Crystalline Solids 521 (2019) 119475
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Fig. 5. Snapshots of the connected center atoms of the five clusters in Cu50Zr40Al10 alloy at 200 K. The dark blue, red, light green, light blue and orange balls represent the (a) < 0 1 10 2 > clusters, (b) < 0 0 12 0 > clusters, (c) < 0 2 8 4 > clusters, (d) < 0 3 6 4 > clusters, (e) < 0 2 8 2 > clusters, respectively (The individual atoms in the Fig. 5 can be bonded to each other by periodic boundary conditions). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
connected with ICO clusters to formed MRO structures by the triangle and tetrahedron modes, as shown in Fig. 7 (d), (e), and (f). The typical MRO structures consisted of the ICO and < 0 3 6 4 > clusters as illustrated in Fig. 7 (g), (h), and (i). Although the number of < 0 2 8 2 > clusters were very rare, most of them were favorable to connect the surface of IMRO clusters to make these structures more stronger as shown in Fig. 7 (j), (k), and (l). Among the connection modes, the < 0 3 6 4 > and < 0 2 8 2 > clusters connected with the stable IMRO structures to form longer chain-like MRO structures that the IMRO structures were the backbone structures. These MRO structures kept the high structural stability of IMRO section and the structural variability of chain-like MRO structures.
addition, the chain connection was a significant way for ICO clusters to link others to form MRO structures. Moreover, the tetrahedron connected ICO structures in which center atoms of ICO clusters formed a tetrahedron were shown in Fig. 6 (d). The tetrahedron connected ICO structure was closely linked with the nearby extended ICO clusters, which made these structures more compact after the rapid cooling process. Tanaka believed that the stable ICO clusters in supercooled liquids prevented the formation of longrange crystalline structures [48]. So, the IMRO clusters formed by triangle, double triangle, triple triangle, tetrahedron, chain connections are more likely to hinder nucleation and growth of the nucleus, resulting in enhanced GFA. In order to further investigate the connection modes between ICO and defective ICO clusters in Cu50Zr40Al10 alloy, it is necessary to understand the formation of MRO structures in detail. Fig. 7 demonstrated that MRO clusters were mainly the combination structures connected by the center atoms of the ICO and < 0 1 10 2 > , < 0 2 8 4 > , < 0 3 6 4 > or < 0 2 8 2 > clusters. In Fig. 7 (a), (b), and (c), the < 0 1 10 2 > clusters connected with ICO clusters to form the triangle, tetrahedron and pentagon structures with higher structural stability, and connected these combination structures to form the bigger MRO structures. The < 0 1 10 2 > clusters have combined with ICO clusters very well because of the similar fivefold structures in these two clusters. There were many < 0 2 8 4 > clusters in this system, which
4. Conclusions The structural properties of the various clusters and the connection modes of the MRO in Cu50Zr40Al10alloy were investigated in this study based on the MD Simulation. According to the results of liquid Cu50Zr40Al10 alloy during the quenching process and the detailed investigation by several structural analysis methods, the following conclusions are obtained: (1) At the end of rapid solidification, the full ICO and distorted ICO clusters are dominant in liquid Cu50Zr40Al10alloy. Moreover, the
Fig. 6. Schematic of common IMRO clusters. The purple, green and cream-coloured balls represent Al, Cu and Zr center atoms, respectively. The red balls represent the central atoms of ICO clusters. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 4
Journal of Non-Crystalline Solids 521 (2019) 119475
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Fig. 7. Schematic of center atoms of MRO clusters and MRO clusters under cooling rate of 1012K/s. The schematic configurations of central atoms are at the left corner of each figure. The dark blue, red, light green, light blue and orange balls represent the < 0 1 10 2 > , < 0 0 12 0 > , < 0 2 8 4 > , < 0 3 6 4 > and < 0 2 8 2 > clusters, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Conflict of interest form
most of ICO clusters tend to connect with the < 0 1 10 2 > , < 0 0 12 0 > , < 0 2 8 4 > , < 0 3 6 4 > and < 0 2 8 2 > clusters. (2) ICO clusters are bonded with each other by interpenetrating connection, forming the triangle, double triangle, triple triangle, tetrahedron and chain connected IMRO clusters as the main structures in this system. The ICO and defective ICO clusters prefer to link with each other and form the bigger MRO clusters with different configurations. (3) The stable IMRO structures connected with other clusters to form bigger MRO structures. These MRO structures kept the high structural stability of IMRO section and the structural variability of chain-like MRO structures.
The authors declare no conflict of interest.
Declaration of interset statement No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.
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Journal of Non-Crystalline Solids 521 (2019) 119475
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Acknowledgments [23]
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51761004, 60766002 and 51661005), the Guizhou Province Science and Technology Fund (Grant No. J[2015] 2050), and the Cooperation Project of Science and Technology of Guizhou Province (Grant No. LH[2016] 7430).
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
The connection of icosahedral and defective icosahedral clusters in mediumrange order structures of CuZrAl alloy ⁎
T
⁎
Lei Rena,b, Tinghong Gaob,c, , Rui Maa,b, , Quan Xieb,c, Zean Tianb,c, Qian Chenb,c, Yongchao Liangb,c, Xuechen Hub,c a
College of Materials and Metallurgy, Guizhou University, Guiyang 550025, China Institute of New Type Optoelectronic Materials and Technology, Guizhou University, Guiyang 550025, China c College of Big Data and Information Engineering, Guizhou University, Guiyang 550025, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Medium-range order Cu50Zr40Al10 alloy Connection mode Icosahedral cluster Defective icosahedral clusters
Medium-range order structure is the one of the important local structural units in the field of bulk metallic glasses. The rapid solidification of Cu50Zr40Al10 ternary alloy is investigated by molecular dynamics simulation. Simultaneously, the connections between the full icosahedral and defective icosahedral clusters in mediumrange order structures of Cu50Zr40Al10 alloy are characterized systematically by the quantitative method and visualization analysis. The results reveal that the icosahedral clusters as the main structures with high structural stability are bonded with each other by interpenetrating connection, and form the triangle, double triangle, triple triangle, tetrahedron and chain connected icosahedral medium-range order clusters. Moreover, the icosahedral and defective icosahedral clusters prefer to link with each other and form the bigger medium-range order clusters with different configurations in this system. These structures keep the high structural stability of icosahedral medium-range order section and the structural variability of chain-like medium-range order structures.
1. Introduction Since Pd-Ni-P bulk metallic glasses (BMGs) were successfully prepared by Turnbull group in 1982 [1], BMGs have became one of the most potential research materials due to their extraordinary strengths, elasticity, high yield strength, and excellent nanoprocessability [2–4]. The macro properties of materials are determined by their microstructures, which is an important topic in the materials science [5]. It is worth mentioning that alloys play a key role in the research of the relationship between the microstructures and the properties of materials [6–8]. Cu-Zr-Al alloy as a new kind of materials for BMGs, its mechanical properties and glass forming ability get greatly improved [9,10]. The research on clusters of Cu-Zr-Al basic alloy has attracted much attention in order to understand its properties [11,12]. The characteristics of various clusters in materials are the basis for developing advanced alloys. In BMGs, the icosahedral (ICO) cluster has very good structural stability and configural continuity [13,14], and the existence of ICO cluster increases the barrier to form the crystalline structures and improves the glass-forming ability (GFA) [15]. The medium-range order (MRO) structures belong to the length scale between short-range order (SRO) and long-range order [15]. The ICO ⁎
clusters are considered as the main structural units for studying MRO structure [16,17], and it is also an important factor affecting the properties of metallic glass. Among the MRO structures, the icosahedral medium-range order (IMRO) structures are more stable than others [18,19]. In 2007, Shimono and Onodera found that the network-like ICO clusters existed in metallic glass and it was the origin of MRO structure [20,21]. Wakeda and Shibutani analyzed that the interpenetrating connection of IMROs had higher local elastic modulus in Cu-Zr binary alloy [19]. Foroughi et al. showed that the < 0 2 8 2 > polyhedron was the dominant cluster and the intercross connection of icosahedra was the most stable in Cu50Zr50 BMG [22]. Nevertheless, the evolution of MRO structures and the ICO cluster with MRO structural feature have not been researched comprehensively. Therefore, it is of great significance to analyze the MRO structures in Cu50Zr40Al10 amorphous alloy. However, under existing experimental conditions, the evolution process of MRO structures has not been well observed. With the development of computer technology, computer simulations have become an indispensable method in the structural researches of materials. Many kinds of materials, including various alloys, semiconductors, ceramics, have been simulated at the atomic or molecular level by computer [23–25]. More recently,
Corresponding authors at: Institute of New Type Optoelectronic Materials and Technology, Guizhou University, Guiyang 550025, China. E-mail addresses: [email protected] (T. Gao), [email protected] (R. Ma).
https://doi.org/10.1016/j.jnoncrysol.2019.119475 Received 29 March 2019; Received in revised form 19 May 2019; Accepted 29 May 2019 Available online 10 June 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
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Molecular dynamics (MD) simulation is applied as an effective tool to investigate the evolution of clusters and widely used in studying glass formation processes of CuZrAl alloys during rapid solidification [26–28]. In this study, MD simulation is employed to explore the connections of clusters during the quenching process in liquid Cu50Zr40Al10 alloy. Completed structural information is necessary to understand the MRO structures. The radial distribution function (RDF) is adopted to indicate the interaction of different type of atoms. The structural evolution of clusters has been detected by the Voronoi polyhedron index [29]. Moreover, the connection modes of MRO structures are further investigated by the Open Visualization Tool (Ovito) [30]. Based on the MD simulation results, the structural characterization of MRO clusters in Cu50Zr40Al10 alloy is discussed in detail. Fig. 1. Evolution of the main Voronoi polyhedrons in Cu50Zr40Al10 alloy.
2. Simulation conditions and methods MD simulation was performed with the Large-scale Atomic/ Molecular Massively Parallel Simulator (LAMMPS) [31] for ternary alloy. In this study, the system consisted of 10,000 atoms (5000 Cu atoms, 4000 Zr atoms and 1000 Al atoms, which corresponds to the composition of Cu50Zr40Al10 alloy) in the cubic box (side lengths = 5.58 nm) with the three dimensional periodic boundary condition. Simulations conducted in the NPT (constant atom number, system pressure and temperature) ensemble with zero pressure, and based on the newly-developed embedded atom model (EAM) potential by Y. Q. Cheng et al., the reliable potential file (see the supplemental material [32]) described the interaction between atoms in Cu-Zr-Al system [33]. The potential function could be fitted to represent the potential energy surfaces of more than 600 configurations obtained by ab initio calculations. Meanwhile, the initial configuration of Cu50Zr40Al10 alloy was generated randomly, and the simulation was started to melt at 2000 K which is higher than the melting point of Cu50Zr40Al10 alloy [34]. The system was run for 100 ps at 2000 K to guarantee an equilibrium liquid state, using 2.0 fs time step and NPT ensemble. Subsequently, the system gradually cooled down to 200 K at a cooling rate of 1012 K/s. The atomic configurations were recorded with an interval of 20 K during the rapid solidification. Finally, several structural characterization methods were applied to indicate the structural properties of the MRO clusters in Cu50Zr40Al10 alloy.
number of < 0 3 6 3 > Voronoi polyhedrons increased with the decreasing temperature and almost maintained unchanged at low temperature. According to the statistical numbers, the microstructures of solidified Cu50Zr40Al10 alloy were dominated by full ICO and defective ICO clusters under cooling rate of 1012 K/s.
3.2. Formation of Cu50Zr40Al10 amorphous alloy Radial distribution function (RDF) is a major structural characterization method widely used to detect the structural properties of liquid and glass microstructures. The g(r) curve represents the average number of atoms on the sphere at a distance ‘r’ centered on any atom. The g(r)min/g(r)max is defined as the Wendt-Abraham parameter, of which the g(r)min (g(r)max) is the first minimum (maximum) of RDF. This is an important parameter used to further analyze and estimate the glass transition temperature (Tg) [40,41]. Fig. 2 showed the trend of g (r)min/g(r)max at cooling rate of 1012 K/s. There was a notable inflection point of the fitting curve at 728 K, namely the Tg ≈ 728 K, which was close to the result obtained by Inoue et al. in the study of Cu60-xZr40Alx alloy (x = 0 to 10 at%). According to the scanning calorimetry curves, the Tg increased monotonously from 717 K at 0% Al to 741 K at 10% Al [42]. At the end of rapid solidification, Cu50Zr40Al10 alloy formed amorphous structure. Fig. 3 showed the RDFs of Voronoi polyherdrons in Cu50Zr40Al10 alloy at 200 K. From the evolution of the main polyhedrons during quenching process in Fig. 1, the number of < 0 1 10 2 > , < 0 3 6 4 > , < 0 2 8 4 > and < 0 0 12 0 > Voronoi polyhedrons was most in the Cu50Zr40Al10 amorphous system at the end of the solidification process. Notably, the first peak of g < 0 0 12 0 > (r) curve were higher and sharper compared with the g < 0 1 10 2 > (r), g < 0 2 8 4 > (r) and g < 0 3 6
3. Results and discussion 3.1. Voronoi polyhedron The Voronoi ployhedron analysis [29,35] is carried out to characterize the microstructures in Cu50Zr40Al10 alloy. The Voronoi polyhedral index is expressed as < n3, n4, n5, n6 > , where ni denotes the number of i-edged faces of the Voronoi polyhedron, to specify the characteristics of the atomic clusters surrounding an atom. The Voronoi polyhedron index of the full ICO clusters is defined as < 0 0 12 0 > [36,37], the < 0 1 10 2 > , < 0 2 8 2 > , < 0 2 8 4 > , and < 0 3 6 4 > polyhedron indexes denote the defective ICO clusters [38]. Fig. 1 demonstrated the largest number of eight main Voronoi polyhedrons in Cu50Zr40Al10 alloy during the quenching process. The number of < 0 3 6 4 > , < 0 1 10 2 > , < 0 2 8 4 > , < 0 0 12 0 > and < 0 2 8 2 > Voronoi polyhedrons increased remarkably, especially the number of < 0 0 12 0 > Voronoi polyhedrons increased more significantly. It can be clearly seen that the number of < 0 0 12 0 > Voronoi polyhedrons was least in the eight main Voronoi polyhedrons in high temperature liquid. However, it became one of the major Voronoi polyhedrons in the microstructures of Cu50Zr40Al10 alloy at the end of the rapid solidification. The < 0 0 12 0 > clusters as the major structural unit exist in most metallic liquids and glasses [39]. Moreover, the number of < 0 2 8 3 > and < 0 2 8 1 > Voronoi polyhedrons slightly increased with the decrease of temperature. While the
Fig. 2. Correlations of the Wendt-Abraham radio with temperature during quenching process. 2
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Fig. 3. RDFs of Voronoi polyhedrons in Cu50Zr40Al10 alloy at 200 K. (a) A large number of polyhedrons. (b) Others.
preferred because of the similar microstructures between the < 0 1 10 2 > and < 0 0 12 0 > clusters. The variation of the number of ICO clusters linking with < 0 3 6 4 > and < 0 2 8 2 > clusters were similar, which went up first and then kept moderate growth below the Tg. These connections are moderated due to the quite a few number of < 0 3 6 4 > and < 0 2 8 2 > clusters and the increasing trend with the decreasing temperature shown in Fig. 1. The slight connections appeared between ICO and < 0 2 8 3 > , < 0 3 6 3 > , < 0 2 8 1 > clusters. These connections increased slightly during the rapid solidification and kept a small amount. The reasons are the slight increasing trend of < 0 2 8 3 > , < 0 3 6 3 > clusters and fewer number of < 0 2 8 1 > clusters with the decreasing temperature shown in Fig. 1.
4 > (r)
curves, which manifested the increasing of SRO structures in Fig. 3(a). And the splitting of the second peak in g < 0 0 12 0 > (r) curve was a well-known characteristic feature of glass formation [43]. In Fig. 3(b), the first peak of g(r) curve of eight main Voronoi polyhedrons was the highest among the three g(r) curves and the obvious split on the second peak of g(r) curve. While the g(r) curve of the total atoms showed no split, this was because the atomic interactions in the thermodynamic metastable amorphous system promoted the uniformity of the Cu, Zr and Al atoms. And the second peak of g(r) curve of except eight main Voronoi polyhedrons also did not split. This behavior of the second peak of RDFs without splitting was also observed when X. Ou et al. investigated the Cu50Zr45Al5 metallic glass and Y. Y. Cui et al. studied amorphous state Cu50Zr65Al10 [44,45]. The results indicated that the eight main Voronoi polyhedrons played an important role in the study of the microstructures formation and evolution of Cu50Zr40Al10 amorphous alloy during the rapid solidification. According to the Voronoi polyhedrons and RDF analysis, we observed the eight main clusters are the characteristic configurations in the microstructures of Cu50Zr40Al10 alloy during quenching process. Moreover, the connections relationship among the clusters was also a significant factor affecting the amorphous structure. In amorphous alloys, ICO clusters as the main characteristic structural unit represented the stability of BMGs to some extent [14,46]. In order to further analyze the MRO structures formed by ICO clusters and eight main clusters, the number of the connections between ICO clusters and eight main clusters in Cu50Zr40Al10 alloy was obtained as illustrated in Fig. 4. It is obvious that the connections can be divided into three parts of preferred, moderated and slight connections. The number of ICO connecting with < 0 1 10 2 > , < 0 0 12 0 > and < 0 2 8 4 > clusters increased significantly with the decrease of temperature and keep the highest rate in the system when temperature below 728 K. The connections are
3.3. Visualization analysis According to the previous analysis, the ICO clusters preferred to connect to the < 0 1 10 2 > , < 0 0 12 0 > , < 0 2 8 4 > , < 0 3 6 4 > and < 0 2 8 2 > clusters in Cu50Zr40Al10 amorphous alloy during the rapid solidification. In Fig. 5, the central atoms of < 0 1 10 2 > clusters were bonding together to form the relatively compact morphologies, which was similar to the < 0 0 12 0 > and < 0 2 8 4 > clusters. Although the number of < 0 2 8 2 > clusters was more than < 0 0 12 0 > clusters, many lonely center atoms of < 0 2 8 2 > clusters existed in the system. However, the connected center atoms of < 0 3 6 4 > clusters were very rare and dispersed in the system randomly, which were favorable to form shorter chains as shown in Fig. 5(d). It could be concluded that the < 0 1 10 2 > , < 0 0 12 0 > and < 0 2 8 4 > clusters were easier to form larger size nanoclusters that could be seen as the main structures in Cu50Zr40Al10alloy. MRO cluster has been defined as an important structure beyond SRO. A comprehensive understanding of characteristics of MRO structures is one of the most important purposes in MG researches [47]. IMRO clusters consist of many < 0 0 12 0 > clusters to be bonded by their center atoms, which are also known as interpenetrating connection. Shimono and Onodera reported that the configuration formed by the ICO clusters through the interpenetrating connection is statistically dominant among the other types [20]. And the interpenetrating ICO clusters were not only energetically more favorable, but also structurally more stable [16]. The Ovito is used to show the various morphologies results from the different connection styles between the central atoms of ICO clusters. The triangle, double triangle, triple triangle, tetrahedron and chain connected ICO structures that were important MRO structures in Cu50Zr40Al10 alloy as shown in Fig. 6 (a), (b), (c), (d) and (e). The triangle, double triangle, triple triangle and tetrahedron connected MRO clusters were more condensed than the chain connected MRO clusters. The ICO clusters connected by triple triangle interlocked with other clusters in order to improve the stability of the structures and became the backbone structures in this system. In
Fig. 4. Evolution of the connections between ICO clusters and eight main clusters during rapid solidification. 3
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Fig. 5. Snapshots of the connected center atoms of the five clusters in Cu50Zr40Al10 alloy at 200 K. The dark blue, red, light green, light blue and orange balls represent the (a) < 0 1 10 2 > clusters, (b) < 0 0 12 0 > clusters, (c) < 0 2 8 4 > clusters, (d) < 0 3 6 4 > clusters, (e) < 0 2 8 2 > clusters, respectively (The individual atoms in the Fig. 5 can be bonded to each other by periodic boundary conditions). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
connected with ICO clusters to formed MRO structures by the triangle and tetrahedron modes, as shown in Fig. 7 (d), (e), and (f). The typical MRO structures consisted of the ICO and < 0 3 6 4 > clusters as illustrated in Fig. 7 (g), (h), and (i). Although the number of < 0 2 8 2 > clusters were very rare, most of them were favorable to connect the surface of IMRO clusters to make these structures more stronger as shown in Fig. 7 (j), (k), and (l). Among the connection modes, the < 0 3 6 4 > and < 0 2 8 2 > clusters connected with the stable IMRO structures to form longer chain-like MRO structures that the IMRO structures were the backbone structures. These MRO structures kept the high structural stability of IMRO section and the structural variability of chain-like MRO structures.
addition, the chain connection was a significant way for ICO clusters to link others to form MRO structures. Moreover, the tetrahedron connected ICO structures in which center atoms of ICO clusters formed a tetrahedron were shown in Fig. 6 (d). The tetrahedron connected ICO structure was closely linked with the nearby extended ICO clusters, which made these structures more compact after the rapid cooling process. Tanaka believed that the stable ICO clusters in supercooled liquids prevented the formation of longrange crystalline structures [48]. So, the IMRO clusters formed by triangle, double triangle, triple triangle, tetrahedron, chain connections are more likely to hinder nucleation and growth of the nucleus, resulting in enhanced GFA. In order to further investigate the connection modes between ICO and defective ICO clusters in Cu50Zr40Al10 alloy, it is necessary to understand the formation of MRO structures in detail. Fig. 7 demonstrated that MRO clusters were mainly the combination structures connected by the center atoms of the ICO and < 0 1 10 2 > , < 0 2 8 4 > , < 0 3 6 4 > or < 0 2 8 2 > clusters. In Fig. 7 (a), (b), and (c), the < 0 1 10 2 > clusters connected with ICO clusters to form the triangle, tetrahedron and pentagon structures with higher structural stability, and connected these combination structures to form the bigger MRO structures. The < 0 1 10 2 > clusters have combined with ICO clusters very well because of the similar fivefold structures in these two clusters. There were many < 0 2 8 4 > clusters in this system, which
4. Conclusions The structural properties of the various clusters and the connection modes of the MRO in Cu50Zr40Al10alloy were investigated in this study based on the MD Simulation. According to the results of liquid Cu50Zr40Al10 alloy during the quenching process and the detailed investigation by several structural analysis methods, the following conclusions are obtained: (1) At the end of rapid solidification, the full ICO and distorted ICO clusters are dominant in liquid Cu50Zr40Al10alloy. Moreover, the
Fig. 6. Schematic of common IMRO clusters. The purple, green and cream-coloured balls represent Al, Cu and Zr center atoms, respectively. The red balls represent the central atoms of ICO clusters. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 4
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Fig. 7. Schematic of center atoms of MRO clusters and MRO clusters under cooling rate of 1012K/s. The schematic configurations of central atoms are at the left corner of each figure. The dark blue, red, light green, light blue and orange balls represent the < 0 1 10 2 > , < 0 0 12 0 > , < 0 2 8 4 > , < 0 3 6 4 > and < 0 2 8 2 > clusters, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Conflict of interest form
most of ICO clusters tend to connect with the < 0 1 10 2 > , < 0 0 12 0 > , < 0 2 8 4 > , < 0 3 6 4 > and < 0 2 8 2 > clusters. (2) ICO clusters are bonded with each other by interpenetrating connection, forming the triangle, double triangle, triple triangle, tetrahedron and chain connected IMRO clusters as the main structures in this system. The ICO and defective ICO clusters prefer to link with each other and form the bigger MRO clusters with different configurations. (3) The stable IMRO structures connected with other clusters to form bigger MRO structures. These MRO structures kept the high structural stability of IMRO section and the structural variability of chain-like MRO structures.
The authors declare no conflict of interest.
Declaration of interset statement No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.
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Acknowledgments [23]
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51761004, 60766002 and 51661005), the Guizhou Province Science and Technology Fund (Grant No. J[2015] 2050), and the Cooperation Project of Science and Technology of Guizhou Province (Grant No. LH[2016] 7430).
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