Structural evolution and energy landscape of Zr55Cu35Al10 ternary alloy during glass transition

Journal of Alloys and Compounds 825 (2020) 154109

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Structural evolution and energy landscape of Zr55Cu35Al10 ternary alloy during glass transition Jingfeng Zhao , Xuxiang Xie , Ying Xu , Xuefeng Zhou * School of Chemistry and Materials Engineering, Changshu Institute of Technology, Changshu, 215500, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 July 2019 Received in revised form 26 January 2020 Accepted 28 January 2020 Available online 3 February 2020

In this work, classic molecular dynamics simulations were employed to study the glass transition of Zr55Cu35Al10 ternary alloy. According to the structure and energy analysis, during quenching to the glass transition temperature (Tg) of the Zr55Cu35Al10 alloy, by quantitatively analyzing the cluster, i-zone and free volume atom pairs based on the tight-bond cluster model, it was found that the fraction of the cluster and i-zone atom pairs increased while the fraction of the free volume atom pairs decreased continuously. The Zr-centered first shell clusters tend to transform to the coordination polyhedra with high coordination number (CN) owning low cluster energy and the Cu- and Al-centered clusters tend to become the coordination polyhedra with CN ¼ 12 presenting the lowest cluster energy in the short-range structure. The medium-range structure of the coordination polyhedra connection sharing three atoms with the lowest energy increased significantly. Furthermore, it was confirmed that the significance of Al addition on the increase in glass forming ability (GFA) in the ZrCuAl ternary alloys. © 2020 Elsevier B.V. All rights reserved.

Keywords: Molecular dynamics simulations Glass transition Tight-bond cluster model Short-range structure Medium-range structure Energy landscape

1. Introduction Bulk metallic glasses (BMGs) have good application prospects because they own excellent physical and mechanical properties [1e4]. However, many common materials cannot be used for engineering applications for lacking of theoretical criteria to evaluate the glass forming ability (GFA) of alloys. As a result, revealing the nature of glass transition and predicting the GFA of different alloys have been a vital issue and a great challenge in the research of metallic glasses [5,6]. It is known that the local atomic structure of the BMGs has great effect on the GFA of the BMGs [7e10]. In the past decades, scientists have devoted much effort on studying the short and medium-range structure of the BMGs. It has been reported that short-range clusters, especially the icosahedron, can stabilize the liquid and glassy structure and restrain the crystallization [11e18]. Sheng et al. found that icosahedral medium-range structure could further make the local atoms pack more closely [19e21]. Lopez et al. proposed that chemical interactions contribute to the different GFA in NieZr and CueZr systems [22]. Liu et al. suggested that the structure in metallic glass presented a combination of local translational symmetry and spherical-

* Corresponding author. E-mail address: [email protected] (X. Zhou). https://doi.org/10.1016/j.jallcom.2020.154109 0925-8388/© 2020 Elsevier B.V. All rights reserved.

periodical order [23]. Ma et al. proposed a new packing scheme and considered that the MRO presented a fractal framework of 2.31-dimensional [24]. Feng et al. introduced the change ratio of polyhedral volume, correlated to dynamic heterogeneities to describe to the microstructure in metallic glass [25]. More recently, Ebner et al. found that high pressure torsion modified the structure of the Cu45Zr45Al5Ag5 bulk metallic glass samples by increasing the mean atomic volume characterized using synchrotron X-ray diffraction, nanoindentation, differential scanning calorimetry, atomic force and transmission electron microscopy [26]. Qiao et al. explained the relationship between the structural heterogeneities in metallic supercooled liquids and the overall mechanical properties in amorphous alloys [27]. Kosiba et al. revealed the interfaces between the relaxed and rejuvenated glass retard shear localization by analyzing the structural heterogeneities in monolithic metallic glasses using molecular dynamics simulations [28]. The properties of the metallic glasses essentially lie on differences of their structures, including not only geometric arrangements of the local atoms but also their energy distributions. Surely, the structural evolution and energy landscape of the local atoms are believed to be the origin of the metallic glass transition [29,30]. Yao et al. calculated the energies icosahedral SROs in supercooled liquid and glass Al systems and found that the energies of local clusters in liquid or glass can be very different from isolated clusters [31]. Wu et al. have found that the icosahedral cluster had the lowest energy

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J. Zhao et al. / Journal of Alloys and Compounds 825 (2020) 154109

Fig. 1. The variation of the average potential energy (PE) of Zr55Cu35Al10 alloy as a function of the temperature during the cooing process.

in both supercooled liquid and glassy samples by analyzing the energy distribution of ten types of Voronoi clusters at temperatures above and below the Tg [32]. Nevertheless, such studies on the energy landscape of the liquid and glass structure are still rare, especially in the ternary alloy system. Therefore, it is very meaningful to study the structural evolution and energy landscape of the local atomic structure during the glass transition. The ZreCueAl ternary alloy system, owns high GFA and shows excellent mechanical properties, is the most fundamental one in a number of stable bulk glassy alloys and has been researched extensively [33e35]. Therefore, In this paper, Zr55Cu35Al10 ternary alloy was selected as the research object to study the structural evolution (including the atom pairs, coordination polyhedra shortrange structure and coordination polyhedra connection mediumrange structure) and their energy distributions during the rapid cooling process, further and profoundly understanding the nature of glass transition. 2. Computational method 2.1. Simulation method The investigation we conducted is carried out using classic molecular dynamics simulations with embedded atom method (EAM) potentials proposed by Sheng et al. [11]. In our work, the unit cell is made up of 16000 atoms, in which 8768 Zr atoms, 5632 Cu atoms and 1600 Al atoms are randomly arranged. Periodic boundary conditions are imposed on the cubic supercell and time step is set to be 1fs. The initial structure is heated up to 2000 K, which is about 800 K higher than the melting temperature of Zr55Cu35Al10, and then the temperature is hold at 2000 K for 10 ns to break the initial configuration and obtain the equilibrium liquid state. The cooling process is conducted according to the following method. The system is cooled from 2000 K to 300 K with a total time of 170 ns and suspended for 5 ns to obtain the configuration for the corresponding temperature with a temperature interval of 100 K. The effective average cooling rate is 1010 K/s. The whole process is carried out in the NPT ensemble with a Nose-Hoover thermostat for temperature control and a Nose-Hoover barostat for pressure control. The external pressure is set as zero.

Fig. 2. The pair distribution functions of the Zr55Cu35Al10 alloy quenching from 1900 K to 300 K.

with short and strong directional bonding; the regions of free volume are between the clusters and have liquid-like loose bonding; the interconnecting zones connect the cluster and free volume with bonds that are shorter than the free volume bonds and longer than the bonds in the structure of the corresponding crystallized structure. The three components of the model are quantified by comparing the pair distribution functions (PDFs) and radial distribution functions (RDFs) for the nearest atom pairs for the ascast Zr55Cu35Al10 bulk metallic glass and its completely crystallized counterpart [39,40]. The radii of Zr, Al and Cu are 1.62 Å, 1.43 Å and 1.28 Å, respectively, which are obtained according to the periodic table of chemical elements. The ZreZr has the largest atom pair distance with the characteristic value 3.24 Å. Beyond 3.33 Å, which is 2.8% larger than 3.24 Å, there are almost no ZreZr nearest atom pairs existing within the PDF for the crystallized counterpart. As a result, the initial distances for the i-zone atom pairs are set at least 2.8% greater than their characteristic atomic radii. The initial distances for the atomic pairs in the free volume region are set at 9.6% larger than their characteristic atomic radii because the free volume regions do not exist in the crystallized counterpart and the terminal of the RDF for the crystallized counterpart is 9.6% greater than the ZreZr characteristic atomic radius. The end of the first peaks in the RDF for the as-cast bulk metallic glass is about 20% greater than the ZreZr characteristic atomic radius. So the final atom distances for the free volume atom pairs are 120% of their characteristic atomic radii [39,40]. 2.2.2. Energy analysis The potential energy (PE) for every atom can be obtained from the classic molecular dynamics simulations. The atom pair formation energy for different atoms is also calculated and can be expressed as:


Ep;B ¼


 Ep;a  Eref ;a þ Ep;b  Eref ;b 2

;

(1)

where Ep;a and Ep;b are the PE. In addition, the cluster formation energy Ep;C for an N-atom cluster is defined as:

,

XN


!

2.2. Structure and energy analysis method

Ep;C ¼ 1

2.2.1. Structure analysis The tight-bond cluster model for amorphous alloys proposed by Refs. [36e42] consists of clusters, interconnecting-zones (i-zones) and regions of free volume. The clusters are formed from atoms

Ep;i is the PE for the ith atom in the cluster and Eref ;a is the reference energy for the type a atom [32,41]. The crystal chemical PE (hcp Zr, fcc Cu and fcc Al) is used as the reference energy. We use Ep;C to analyze the energy distribution of the local clusters. We

N

i¼1

Ep;i  Eref ;a



;

(2)

J. Zhao et al. / Journal of Alloys and Compounds 825 (2020) 154109

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Fig. 3. The change of the fraction of the cluster, interconnecting zone (i-zone) and free volume atom pairs in the whole system and the Zr, Cu and Al-centered first shell coordination polyhedra as a function of the temperature.

3. Results and discussion

define the effective radius for an N-atoms cluster as:

3.1. Glass transition

, reff ¼ 1

! XN1 ðN  1Þ i¼1 dc;i ;

(3)

where dc;i is the distance between the central atom and the shell atom.

The relationship between the average PE of all atoms and the temperature is shown in Fig. 1. Crystallization is often accompanied by energy mutation. However, there is no abrupt change in PE here. The PE of the system decreases basically in a linear trend as the temperature drops, and the turning point can be observed between 700 K and 800 K. Through linearly fitting and extrapolating the two

Fig. 4. The change of the fraction of the cluster, i-zone and free volume atom pairs in the ZreZr,ZreCu,ZreAl,CueCu,CueAl and AleAl atom pairs as a function of the temperature.

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Fig. 5. The change of the fraction and the energy of the ZreZr,ZreCu,ZreAl,CueCu,CueAl and AleAl atom pairs as a function of the atomic pair distance.

Table 1 The compression ratio of different kinds of atom pairs. Atom pair

L(Å)

L0 (Å)

△¼(L0 -L)/L0 (%)

ZreZr ZreCu ZreAl CueCu CueAl AleAl

3.17 2.83 2.98 2.53 2.55 2.75

3.24 2.9 3.05 2.56 2.71 2.86

2.16 2.41 2.30 1.17 5.90 3.85

parts of the PE curve in the temperature range of 1200 Ke900 K and 300 Ke600 K, the Tg in the simulation is identified at 730 K. It is basically in line with the experiment Tg with the value of 657 K measured by differential scanning calorimetry [20], if the cooling rate difference is taken into consideration. According to the Tg, the PE curve is classified into two stages, 1900 Ke800 K and 700 Ke300 K. Fig. 2 shows the distribution function curves of Zr55Cu35Al10 alloy at different temperatures. For better contrast, the curve is shifted vertically. It can be seen from figure that, decreasing from

Fig. 6. The fractions of the different kinds of Zr, Cu and Al-centered coordination polyhedra at 1300 K, 800 K and 300 K.

J. Zhao et al. / Journal of Alloys and Compounds 825 (2020) 154109

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Table 2 The fraction, energy, cluster radius, the number of the cluster bond, i-zone and free volume bond in the different kinds of the Zr-centered coordination polyhedra. Coordination Polyhedron

Sub-type

Fraction

Energy

Cluster radius

Cluster

I-zone

Free Volume

Zr-centered (CN ¼ 13)

Zr8Cu6 Zr9Cu5 Zr10Cu4 Zr8Cu5Al1 Zr9Cu4Al1 Zr10Cu3Al1 Zr11Cu2Al1 Zr7Cu5Al2 Zr8Cu4Al2 Zr9Cu3Al2

0.005 0.010 0.010 0.013 0.020 0.014 0.004 0.005 0.012 0.010

0.089 0.075 0.060 0.102 0.086 0.071 0.055 0.125 0.111 0.096

3.052 3.093 3.130 3.064 3.103 3.141 3.178 3.035 3.077 3.116

9.558 9.018 8.703 9.381 9.010 8.713 8.449 9.697 9.276 9.026

2.329 2.621 2.824 2.474 2.709 2.818 2.945 2.461 2.593 2.720

1.111 1.360 1.470 1.143 1.278 1.467 1.606 0.840 1.131 1.254

Zr-centered (CN ¼ 14)

Zr9Cu6 Zr10Cu5 Zr8Cu6Al1 Zr9Cu5Al1 Zr10Cu4Al1 Zr11Cu3Al1 Zr7Cu6Al2 Zr8Cu5Al2 Zr9Cu4Al2 Zr10Cu3Al2

0.017 0.023 0.027 0.045 0.040 0.014 0.012 0.030 0.035 0.020

0.085 0.069 0.110 0.095 0.082 0.064 0.132 0.121 0.107 0.094

3.128 3.165 3.103 3.139 3.179 3.214 3.076 3.115 3.152 3.190

8.524 8.215 8.775 8.536 8.143 7.971 9.137 8.823 8.478 8.098

3.333 3.366 3.344 3.335 3.414 3.442 3.378 3.266 3.429 3.524

2.142 2.418 1.880 2.129 2.443 2.585 1.494 1.910 2.092 2.377

Zr-centered (CN ¼ 15)

Zr10Cu6 Zr8Cu7Al1 Zr9Cu6Al1 Zr10Cu5Al1 Zr11Cu4Al1 Zr8Cu6Al2 Zr9Cu5Al2 Zr10Cu4Al2 Zr8Cu5Al3 Zr9Cu4Al3

0.016 0.023 0.043 0.043 0.019 0.032 0.046 0.031 0.016 0.014

0.077 0.117 0.105 0.089 0.075 0.128 0.114 0.102 0.139 0.125

3.197 3.140 3.172 3.209 3.243 3.147 3.184 3.221 3.160 3.197

7.751 8.135 8.015 7.644 7.391 8.220 7.894 7.578 8.205 7.820

3.844 3.993 3.874 3.920 3.932 4.042 4.017 4.036 4.059 4.108

3.404 2.871 3.110 3.437 3.675 2.737 3.089 3.386 2.736 3.072

Zr-centered (CN ¼ 16)

Zr8Cu8Al1 Zr9Cu7Al1 Zr10Cu6Al1 Zr11Cu5Al1 Zr8Cu7Al2 Zr9Cu6Al2 Zr10Cu5Al2 Zr11Cu4Al2 Zr8Cu6Al3 Zr9Cu5Al3

0.005 0.012 0.015 0.008 0.008 0.015 0.013 0.005 0.006 0.008

0.119 0.106 0.094 0.078 0.132 0.118 0.104 0.087 0.139 0.130

3.177 3.209 3.240 3.277 3.185 3.219 3.252 3.291 3.196 3.229

7.669 7.473 7.144 6.950 7.587 7.321 6.995 6.784 7.482 7.278

4.273 4.086 4.227 4.118 4.466 4.290 4.420 4.134 4.578 4.441

4.058 4.441 4.629 4.932 3.947 4.388 4.585 5.082 3.940 4.280

1900 K to 300 K, no sharp peaks appear in all the curves, and with the increase of r, the peak strength decreases rapidly while the peak width increases rapidly. It means that as r increases, the structure becomes more and more disordered. During cooling, the peak value of the first peak increases and the width decreases, indicating that the atomic structure becomes more ordered as the temperature decreases. As can be seen from the figure, starting from 700 K, the second peak splits, and as the temperature decreases, the split becomes more and more obvious, proving the formation of glassy structure. 3.2. The structure and energy analysis of the atom pairs Based on the tight-bond cluster model and the quantitative definition, the change of the cluster, i-zone and free volume atom pairs in Zr55Cu35Al10 alloy during the rapid cooling process was analyzed. Fig. 3 shows the change in the fractions of the cluster, izone and free volume atom pairs as the temperature decreases in the simulation. It is found that in the whole system the fraction of the cluster atom pairs increases while the fraction of the free volume atom pairs decreases with the temperature decreasing, it can be seen clearly that both present linear variation trend below the Tg. The fraction of the i-zone atom pairs increases above the Tg and remain basically unchanged below the Tg. As a result, the Tg (730 K in this simulation) can be roughly inferred by the different

changing trend in the fraction of the cluster, i-zone and free volume atom pairs with the temperature decreasing. Atoms are bonded mainly in the form of cluster atom pairs at 300 K, accounting for about 60%. By calculating the change in the fractions of the atom pairs containing Zr, Cu and Al atoms respectively (Fig. 3 (b), (c) and (d)), their changing trend with the temperature decreasing is basically the same as the whole system. It can be seen in Fig. 3(b), (c) and (d) that the fraction of Al cluster atom pairs is the largest, while that of the free volume atom pairs is the smallest among the three elements at different temperatures, indicating that it is easier to form short bonds with Al atoms even if the radius of Al is not the smallest. The Al content is the least in the ternary alloy, but the fraction of Al cluster atom pairs is the largest, indicating that the bonding between Al and Zr or Cu tend to be strong. Furthermore, the variation in Al atom pairs with decreasing temperature is the most dramatic, increasing from 0.4631 to 0.6821 for cluster atom pairs and decreasing from 0.3533 to 0.1087 for free volume atom pairs. Obviously, during cooling, a portion of the Al free volume atom pairs transforms to cluster atom pairs, resulting in the formation of more dense clusters in the first shell. Fig. 4 shows the variation of fractions of the cluster, i-zone and free volume atom pairs as a function of the temperature in different types of atom pairs. It can be seen from Fig. 4(a) that the fraction of the CueAl cluster atom pairs is the highest, followed by the AleAl cluster atom pairs and ZreAl cluster atom pairs. It can be seen that

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J. Zhao et al. / Journal of Alloys and Compounds 825 (2020) 154109

Table 3 The fraction, energy, cluster radius, the number of the cluster bond, i-zone and free volume bond in the different kinds of the Cu-centered coordination polyhedra. Coordination Polyhedron

Sub-type

Fraction

Energy

Cluster radius

Cluster

I-zone

Free Volume

Cu-centered (CN ¼ 10)

Zr7Cu4 Zr8Cu3 Zr9Cu2 Zr6Cu4Al1 Zr7Cu3Al1 Zr8Cu2Al1 Zr9Cu1Al1 Zr6Cu3Al2 Zr7Cu2Al2 Zr8Cu1Al2

0.026 0.063 0.039 0.015 0.053 0.065 0.019 0.014 0.022 0.010

0.071 0.053 0.031 0.097 0.085 0.071 0.050 0.110 0.097 0.087

2.803 2.844 2.894 2.763 2.810 2.856 2.902 2.772 2.823 2.871

6.948 6.817 6.467 7.324 7.078 6.778 6.544 7.343 7.017 6.696

1.905 1.977 2.127 1.737 1.847 2.012 2.108 1.804 1.898 2.081

1.146 1.206 1.405 0.939 1.074 1.209 1.348 0.850 1.085 1.224

Cu-centered (CN ¼ 11)

Zr7Cu5 Zr8Cu4 Zr9Cu3 Zr6Cu5Al1 Zr7Cu4Al1 Zr8Cu3Al1 Zr9Cu2Al1 Zr6Cu4Al2 Zr7Cu3Al2 Zr8Cu2Al2

0.017 0.040 0.032 0.011 0.041 0.057 0.026 0.012 0.024 0.014

0.075 0.058 0.038 0.097 0.090 0.072 0.052 0.111 0.099 0.083

2.847 2.891 2.938 2.813 2.860 2.902 2.946 2.824 2.871 2.916

6.547 6.245 6.007 6.771 6.386 6.276 6.080 6.770 6.445 6.286

2.279 2.435 2.381 2.257 2.482 2.408 2.428 2.324 2.395 2.341

2.175 2.320 2.612 1.972 2.132 2.315 2.492 1.906 2.160 2.372

Cu-centered (CN ¼ 12)

Zr8Cu5 Zr9Cu4 Zr7Cu5Al1 Zr8Cu4Al1 Zr9Cu3Al1 Zr6Cu5Al2 Zr7Cu4Al2 Zr8Cu3Al2 Zr9Cu2Al2

0.016 0.019 0.036 0.049 0.029 0.011 0.027 0.031 0.009

0.070 0.056 0.103 0.087 0.067 0.124 0.118 0.105 0.087

2.912 2.953 2.873 2.916 2.963 2.840 2.879 2.922 2.974

5.652 5.473 5.960 5.675 5.334 6.307 5.952 5.633 5.207

3.425 3.249 3.519 3.484 3.438 3.557 3.574 3.655 3.614

2.923 3.279 2.521 2.841 3.228 2.136 2.474 2.712 3.179

Al atoms are easy to form short and tight bonding with Zr, Cu and Al atoms in the system. For the atom pairs containing Zr atom, the fraction of the cluster atom pairs is the lowest at 300 K, and 90% of the free volume atom pairs are related to Zr atom pairs (ZreZr,

ZreCu and ZreAl atom pairs), suggesting that the bonding between Zr atom pairs tend to be weaker, especially for ZreZr and ZreCu atom pairs. According to Fig. 4(c), the fraction of the free volume atomic pair of ZreZr, ZreCu and ZreAl is relatively high. It can be

Table 4 The fraction, energy, cluster radius, the number of the cluster bond, i-zone and free volume bond in the different kinds of the Al-centered coordination polyhedra. Coordination Polyhedron

Sub-type

Fraction

Energy

Cluster radius

Cluster

I-zone

Free Volume

Al-centered (CN ¼ 11)

Zr6Cu5Al1 Zr7Cu4Al1 Zr8Cu3Al1 Zr9Cu2Al1 Zr10Cu1Al1 Zr6Cu4Al2 Zr7Cu3Al2 Zr8Cu2Al2 Zr9Cu1Al2 Zr6Cu3Al3

0.003 0.016 0.037 0.024 0.006 0.005 0.018 0.023 0.006 0.002

0.108 0.099 0.088 0.072 0.046 0.113 0.107 0.098 0.077 0.139

2.843 2.888 2.933 2.982 3.018 2.855 2.904 2.952 2.995 2.855

8.744 8.536 8.162 7.894 7.723 8.671 8.372 8.185 7.902 9.303

1.488 1.624 1.943 2.019 1.901 1.747 1.833 1.865 2.000 1.182

0.767 0.836 0.895 1.088 1.376 0.582 0.794 0.950 1.098 0.515

Al-centered (CN ¼ 12)

Zr7Cu5Al1 Zr8Cu4Al1 Zr9Cu3Al1 Zr10Cu2Al1 Zr6Cu5Al2 Zr7Cu4Al2 Zr8Cu3Al2 Zr9Cu2Al2 Zr7Cu3Al3 Zr8Cu2Al3

0.047 0.118 0.091 0.027 0.030 0.092 0.121 0.067 0.029 0.029

0.120 0.109 0.084 0.063 0.147 0.134 0.115 0.105 0.145 0.130

2.886 2.931 2.981 3.028 2.856 2.899 2.947 2.993 2.916 2.956

8.943 8.440 7.890 7.480 9.204 8.924 8.370 7.946 8.795 8.512

2.263 2.550 2.809 3.016 2.160 2.342 2.679 2.954 2.533 2.729

0.794 1.009 1.291 1.503 0.637 0.733 0.952 1.100 0.672 0.759

Al-centered (CN ¼ 13)

Zr7Cu6Al1 Zr8Cu5Al1 Zr9Cu4Al1 Zr10Cu3Al1 Zr7Cu5Al2 Zr8Cu4Al2 Zr9Cu3Al2 Zr10Cu2Al2 Zr7Cu4Al3 Zr8Cu3Al3

0.005 0.013 0.013 0.006 0.010 0.019 0.014 0.002 0.005 0.006

0.110 0.098 0.079 0.062 0.113 0.098 0.099 0.068 0.118 0.113

2.952 2.994 3.029 3.075 2.966 3.008 3.050 3.104 2.991 3.025

7.797 7.517 7.173 6.908 7.648 7.329 7.004 6.706 7.337 7.204

3.063 2.872 3.154 3.102 2.937 3.030 3.027 3.118 3.337 3.269

2.139 2.611 2.673 2.990 2.409 2.641 2.969 3.176 2.325 2.527

J. Zhao et al. / Journal of Alloys and Compounds 825 (2020) 154109

7

Fig. 7. The change of the effective radius and energy of the Zr, Cu and Al-centered coordination polyhedra as a function of the coordination number.

seen that the bonding strength between atom pairs containing Zr is weak, while the bonding strength between the atomic pairs containing Cu is between atomic pairs containing Al and atomic pairs containing Zr. According to the above analysis, compared with Zr and Cu atoms, Al atoms are more likely to form tight bonding with other atoms, leading to the formation of the Al-centered first shell

clusters packing more closely and becoming more stable, inhibiting crystallization and promoting the glass transition in the process of cooling. Fig. 5 shows the fraction and energy distribution of ZreZr, ZreCu, ZreAl, CueCu, CueAl and AleAl atom pairs. The red, orange and purple lines represent the characteristic distance of

Fig. 8. The change of the fractions of the cluster bond, the i-zone bond, and the free volume bond and the energy of the Zr, Cu and Al-centered coordination polyhedra as a function of the coordination number.

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J. Zhao et al. / Journal of Alloys and Compounds 825 (2020) 154109

Fig. 9. The change of the average number of the coordination polyhedra connections with the number of shared atoms from one to four as a function of the temperature.

different atomic pairs, the initial distance of the i-zone atom pairs and the initial distance of the free volume atom pairs respectively. It can be seen that the fraction distribution of different atom pairs is basically gaussian. The distances corresponding to the peak value of their atom pairs are less than the characteristic distances of their atom pairs. It can be seen that many compressed atom pairs exist in the glassy structure at 300 K, and the stretched atomic pairs also exist. Then the compression ratio was calculated and shown in Table 1. △¼(L’ -L)/L0 , L0 is the characteristic distance of atom pair, and L is the atom pair distance corresponding to the peak value. It is found that the compression ratio of the CueAl atomic pair is the largest, followed by AleAl atomic pair and ZreAl atomic pair. As a result, Al atoms tend to form tight bonding with other atoms. The compression ratios of ZreZr, ZreCu and ZreAl atoms are relatively small, so it is easy to form loose bonding in atom pairs containing Zr atom. The energy of different atom pairs decreases first and then increases as the atom pair distance increases. In addition to CueAl atom pairs, other i-zone atom pairs have lower energy than cluster and free volume atom pairs. It can be seen that the presence of izone atom pairs can reduce the energy of the system and make the system more stable.

3.3. The structure and energy analysis of the coordination polyhedra Fig. 6 shows the fraction distribution of Zr, Cu and Al-centered coordination polyhedra at 1300 K, 800 K and 300 K. For the Zrcentered coordination polyhedron, when the temperature drops from 1300 K to 800 K in supercooled liquid, the fractions of the coordinate polyhedra with CN ¼ 15, 16 increase and the fractions of the coordinate polyhedra with CN ¼ 13, 14 decrease, while the fractions do not change significantly when the temperature decreaes from 800 K to 300 K. Finally, Zr-centered coordination polyhedra is mainly made up of the high coordination polyhedra with CN ¼ 14, 15, 16. For the Cu-centered coordination polyhedron, with the temperature decreasing from 1300 K to 800 K, the fractions of the coordination polyhedra with CN ¼ 10, 11 do not change significantly while the coordination polyhedra wtih CN ¼ 12 increases significantly. When the temperature drops to 300 K, the fractions of the coordinate polyhedra with CN ¼ 10, 12 increase while the fraction of the coordination polyhedra with CN ¼ 11 decreases. At 300 K, the polyhedra with CN ¼ 10, 11 and 12 become the most important clusters. For the Al-centered coordination polyhedra, when the temperature drops from 1300 K to 300 K, the fractions of the coordination polyhedra with CN ¼ 11, 13 keep

Fig. 10. The average energy of the coordination polyhedra connections with the number of shared atoms from one to four at 300 K.

decreasing while the fraction of the coordination polyhedra with CN ¼ 12 keeps increasing, accounting for 67.5% at 300 K. It can be seen that in the cooling process, the Zr-centered coordination polyhedra tend to transfer to the high coordination polyhedra while Cu and Al-centered coordination polyhedra prefer to form the coordination polyhedra with CN ¼ 12. Tables 2e4 list the fraction, energy, cluster radius, the number of the cluster bond, i-zone and free volume bond of the Zr, Cu and Alcentered coordination polyhedra whose fractions are in the top 10. Taking the Al-centered coordination polyhedra with CN ¼ 12 as an example, the fraction, energy, cluster radius, the number of the cluster bond, i-zone and free volume bond were analyzed. In the case that the number of Al atom is the same, as the number of Zr atoms increases, the effective radius increases, the number of cluster bonds and i-zone bonds decreases, the number of free volume bonds increases, and finally the energy increases. In the case that the number of Zr atom is the same, the increase of Al atoms will lead to the increase of the effective radius, the decrease of the number of cluster bonds, the increase of the number of izone bonds, the decrease of the number of free volume bonds, and finally the reduction of the energy of the coordination polyhedra. In the case of the same number of Cu atoms, the increase of Al atoms will lead to the reduction of the effective radius of the coordination polyhedron, the increase of the number of cluster bonds, the decrease of the number of i-zone bonds, the decrease of the number of free volume bonds, and finally the reduction of the energy of the coordination polyhedra. It can be seen that the number of free volume bonds plays an important role in the energy of coordination polyhedra. The addition of Al atoms can reduce the number of free volume bonds, reduce the energy of coordination polyhedra and obtain a more stable structure, improving the glass forming ability of the ZrCuAl alloys. Increasing the number of the Zr atoms has the opposite effect, increasing the number of free volume bonds and increasing the energy of coordination polyhedra. Fig. 7 shows the variation of the effective radius and energy of the coordination polyhedra with increasing the CN. For the Zrcentered coordination polyhedra, the energy decreases first and then increases and the lowest energy corresponds to CN ¼ 16, while the effective radius increases basically linearly with the increase of the CN. For the Cu-centered coordination polyhedra, the energy also decreases first and then increases with increasing the CN, which is similar with that of the Zr-centered coordination polyhedra. However, the lowest energy corresponds to CN ¼ 12 and the energy presents an obvious decrease compared with the other coordination polyhedra. By analyzing the variation of the effective radius, it is found that when the CN is 12, the effective radius

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Fig. 11. The change of the average number of the ZreZr,ZreCu,ZreAl,CueCu,CueAl,AleAl coordination polyhedra connection with two shared atoms as a function of the temperature.

Fig. 12. The change of the average number of the ZreZr,ZreCu,ZreAl,CueCu,CueAl,AleAl coordination polyhedra connections with three shared atoms as a function of the temperature.

experiences obvious deviation from the linearly increasing curve with the coordination number increasing from 9 to 11, obtaining a relatively small effective radius. For the Al-centered coordination polyhedra, the variation trend of the energy and effective radius is the same with that of the Cu-centered coordination polyhedra. When the CN is 12, relatively small effective radius and minimum polyhedra energy are also obtained. It can be seen that the energy of the coordination polyhedroa is closely related to the CN and the effective radius. The effective radius of polyhedra affects the fractions of the cluster, i-zone and free volume bond. Therefore, the variation of the fractions of the cluster bond, i-bond, free volume bond and energy with the CN was further studied. As can be seen from Fig. 8(a), the fractions of the cluster bonds and free volume bonds in the Zr-centered coordination polyhedra changes linearly with the increase of the CN, while the fraction of the i-zone bonds increases first and then decreases with the increase of the CN, corresponding to the variation trend of the polyhedra energy. As for the Cu-centered coordination polyhedra, when the coordination number is 12, the fraction of the i-zone bonds presents an obvious increase, while the fraction of the free volume bonds decreases obviously. Similar to the Cu-centered coordination polyhedra, for Al-centered coordination polyhedra, the fraction of the cluster and i-zone bonds experiences a sudden increase, the fraction of the free volume bonds shows a sudden decrease. It can be seen that the increase of the fraction of the i-zone bonds is the main factor for obtaining the coordination polyhedra with low energy. From the above analysis, it is concluded that the energy of the coordination polyhedra is closely related to the CN. The energy of the polyhedra tends to decrease with the increase of the CN, in addition, the energy is also affected by the effective radius of the polyhedra. The effective radius has effect on the fractions of the cluster, i-zone and free volume bonds. The change of the fraction of the i-zone bond has a great impact on the energy of polyhedra. The increase of i-zone bonds would make the atomic packing more compact and form a more stable structure, which is in line with the above point that the presence of i-zone atom pairs can reduce the energy of the system and make the system more stable.

between coordination polyhedra. In general, two coordination polyhedra are mainly connected by sharing one atom (vertex connection), two atoms (edge connection), three and four atoms (plane connection) [43e48]. The four common coordination polyhedra connections are used to describe the structural evolution of the medium-range structure during the cooling process. It can be seen from Fig. 9 that the number of the coordination polyhedra connection with one shared atom is the largest while the connection with four shared atoms is the lowest. However, the numbers of the connections sharing one and four atoms do not change obviously, just have a slight increase and decrease respectively during the cooling process. The number of coordination polyhedra connection sharing three atoms and sharing two atoms increases and decreases significantly respectively quenching from 1900 K to 700 K, while the temperature decreases from 700 K to 300 K, their numbers basically remain unchanged. The number of connection with three shared atoms is much higher than that of the connection with two shared atoms at 300 K. As the temperature decreases, the density of the system increases. As a result, the number of more closely packed medium-range structure will increase. Comparing with the edge connection (sharing two atoms), the plane connection (sharing three and four atoms) have a closer atomic packing. In addition, the coordination polyhedra connections sharing two and four atoms are the main connection modes of the crystal structure. As a result, the formation of the connections sharing two and four are restrained in the rapid cooling process. It can be seen that the variation trend in the number of connections sharing two atoms and three atoms is different in the two stages of supercooled liquid and glassy state. In the supercooled liquid, there is a very significant decrease in the number of connection sharing two atoms and a very significant increase in the number of connection sharing three atoms. When entering the glassy state, their numbers do not change significantly. By calculating the number of all connections at different stages it is found that the connection sharing three atoms is mainly obtained by consuming the connection sharing two atoms. Therefore, the medium-range structure develops towards the connection sharing three atoms during the glass transition. Fig. 10 shows the average energy of the coordination polyhedra connections with the number of shared atoms from one to four at 300 K. It can be seen that the energy of the coordination polyhedra with three shared atoms is the lowest while the energy of the coordination polyhedra with two shared atoms is the highest, the energy of the connections sharing one atom and four atoms is in between, which explains that although the packing density of the connection with four shared atoms is the largest, the medium-

3.4. The structure and energy analysis of the medium-range structure The medium-range structure is much more complex than the short-range structure. In order to describe the medium-range structure, it is necessary to understand the relationship between atoms in the sub-neighbor. Therefore, this paper describes the medium-range structure by studying the connection schemes

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range structure develops towards the connection sharing three atoms by consuming the connection sharing two atoms rather than the connection sharing one atom during the glass transition. Thus, in terms of energy, the medium range structure transfers to the coordination polyhedra connection sharing there atoms during the glass transition. In order to further investigate the different coordination polyhedra connection with different central atoms, the change of the average number of the ZreZr,ZreCu,ZreAl,CueCu,CueAl,AleAl coordination polyhedra connection with two and three shared atoms as a function of the temperature was shown in Fig. 11 and Fig. 12. ZreZr, ZreCu and ZreAl coordination polyhedra connections account for a large proportion in the connection sharing three atoms, indicating that it is easy for Zr-centered coordination polyhedra to form the stable connection with low energy. The number of ZreCu coordination polyhedra connection is the largest in the connection sharing two atoms, while the number of CueCu coordination polyhedra connection exceeds the number of ZreAl coordination polyhedra connection. Considering the composition of Zr and Cu in the alloy studied here, it can be seen that Cu-centered coordination polyhedra have great contribution to the formation of high-energy connection with two shared atoms. In the cooling process, the increase in the number of connection sharing three atoms is mainly caused by the increase in the number of ZreZr, ZreCu and ZreAl coordination polyhedra connections. The corresponding reduction in the number of coordination polyhedra connections sharing two atoms is also mainly caused by the decrease in the number of ZreZr, ZreCu and ZreAl coordination polyhedra connections. 4. Conclusions According to the structure and energy analysis, during quenching to the glass transition temperature (Tg) of the Zr55Cu35Al10 alloy, by quantitatively analyzing the cluster, i-zone and free volume atom pairs in the tight-bond cluster model, it was found that the fraction of the cluster and i-zone atom pairs increased while the fraction of the free volume atom pairs decreased continuously. The Zr-centered first shell clusters tend to transform to the coordination polyhedra with high coordination number (CN) owning low cluster energy and the Cu- and Alcentered clusters tend to become the coordination polyhedra with CN ¼ 12 with the lowest cluster energy in the short-range structure. The medium-range structure of the coordination polyhedra connection sharing three atoms with the lowest energy increased significantly. Furthermore, in terms of their structure and energy landscape, it was confirmed that the addition of Al atoms improved the glass forming ability of the ZrCuAl ternary alloys.

Writing - original draft, Writing - review & editing. Xuxiang Xie: Investigation. Ying Xu: Data curation. Xuefeng Zhou: Writing review & editing.

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Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Jingfeng Zhao: Data curation, Formal analysis, Software,

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