0 Introduction

Metallic glasses have drawn wide attention for more than fifty years since originally synthesized in 1960. Much effort has been devoted to the study of amorphous alloys because they own excellent properties^[1-3]. However, there are still many longstanding issues to be solved, such as the influence of composition on the structure of amorphous alloys, and the nature of glass formation^[4-8]. For the sake of understanding the nature of the amorphous alloys, research has been conducted on the influence of composition on the structure and properties. There were many simulation and experiment results in the last few decades. Zhang et al.^[9] found that Zr₆₄Cu₂₆Al₁₀ alloy exhibited better compression performance compared with Zr₄₅Cu₄₅Al₁₀ by conducting molecular dynamics (MD) simulations. Wong^[10] revealed that the ZrCuAl ternary alloys had more icosahedra when the composition of Zr was less than that of Cu by conducting the simulations on the Zr_xCu_90-xAl₁₀ system. Yu^[11] used a novel approach to forecast the glass forming ability of different alloys and they successfully applied it to the (Zr_0.5Cu_0.5)_100-xAl_x ternary system. Deb Nath^[12] found that Zr composition had great influence on the mechanical properties of the ZrCuAl ternary alloys. Huang et al.^[13] investigated the local atomic structures of Cu₅₀Zr₄₅Al₅ and Zr₅₀Cu₄₅Al₅ amorphous alloys by conducting ab initio MD simulations. The difference in the atomic chemical property between Zr and Cu atom contributed to the difference in the GFA. MD simulations have been conducted on the Zr₅₀Cu_50-xAl_x alloys and Celtek et al.^[14] found that Al played a great important role in glass transition and icosahedral ordering. Zhao^[15-16] reported that ZrCuAl amorphous alloys with high Zr composition packed more loosely by analyzing the structure and energy distribution by conducting the MD simulations. Sha et al.^[17] provided the straightforward evidence that the electronic stability of the basic cluster in CuZrAl amorphous alloys is the origin of GFA. Wang^[18] found that as Cu content increases, the number of the ordered coordination polyhedron increases monotonically. Thus it is highly necessary to study the influence of the composition on the final structures and properties of the amorphous alloys.

In this paper, investigations were carried out in the Zr_xCu_90-xAl₁₀ (x=20, 30, 40, 50, 60, 70) ternary alloys. For the sake of clarifying the influence of the composition on these amorphous alloys, the coordination polyhedron structure, the coordination polyhedron connection structure and the energy distribution of these structures in the Zr_xCu_90-xAl₁₀ (x=20, 30, 40, 50, 60, 70) ternary alloys were described.

1 Simulation and Analysis 1.1 Simulation Method

The study was conducted using classic MD simulations^[19]. In our work, there were 16000 atoms in the unit cell, which were randomly arranged. The initial configuration of the Zr_xCu_90-xAl₁₀ (x=20, 30, 40, 50, 60, 70) alloys was heated up to 2000 K firstly, and then held for 10 ns. The liquid was cooled to 300 K with the speed of 5×10¹⁰ K/s.

1.2 Energy Analysis

E_{p, C} represents the cluster formation energy of the cluster with N atoms and the calculation method is as follows^[20-21]:

$E_{\mathrm{p}, \mathrm{C}}=(1 / N) \sum\limits_{i=1}^N\left(E_{\mathrm{p}, i}-E_{\mathrm{ref}, \alpha}\right)$

(1)

E_{p, i} represents the potential energy of the i-th atom and E_{ref, α} represents the reference energy of the type α atom. The reference energy is the crystal chemical PE (hcp Zr, fcc Cu and fcc Al).

2 Results and Discussion 2.1 Glass Transition

Fig. 1 represents variation in potential energy(PE) of Zr_xCu_90-xAl₁₀ (x=20, 30, 40, 50, 60, 70) alloys with the temperature during cooling. The PE basically changes linearly with the temperature, and there is a turning point between the temperature of 700 K and 800 K, indicating the occurrence of glass transition. The glass transition temperatures (T_g) of these alloys were obtained by linear fitting PE curves from 1200 K to 800 K and from 700 K to 300 K. T_g of Zr₅₀Cu₄₀Al₁₀ alloy obtained in the experiment is 670 K-679 K^[22], which is roughly consistent with the simulation result. As the cooling rate of simulation is much faster than that of the experiment (the cooling rate of experiment is generally lower than 10⁶K/s), T_g obtained in the simulations is generally higher than the value obtained in the experiments. Fig. 2 shows variation of T_g with the Zr composition. It can be seen that T_g tends to increase first and then decrease with Zr composition increasing. When the Zr composition is 30%, T_g reaches the maximum value and the alloy owns high GFA, which is consistent with the results of relevant literature^[10-12].

2.2 Pair Distribution Functions

Fig. 3 shows the pair distribution functions of Zr_xCu_90-xAl₁₀ (x=20, 30, 40, 50, 60, 70) amorphous alloys at 300 K. The curves are shifted vertically for better comparison. It can be seen that the first peak of each curve exhibits short-range order. When the Cu composition is higher than the Zr composition, the first peak splits. With the increase of Zr composition, the splitting phenomenon becomes less and less obvious. When the composition of Zr is higher than the composition of Cu, the splitting phenomenon disappears. In addition, with the increase of Zr composition, the first shell peak position shifts to the right.

Fig. 4 shows the partial PDFs of like atomic pairs and unlike atomic pairs. For better comparison, the curves are shifted vertically. As shown in the figure, the PDF curves of like atomic pairs are sensitive to the composition of the alloy. For the Zr-Zr partial PDF, with Zr composition increasing, the first peak strength increases. Partial PDFs for Cu-Cu atom pairs present strong short-range order when Cu composition is large. For the partial PDFs of unlike atomic pairs, the composition has little effect on the strength of their peaks.

The first shell peak position and cut-off distance are extracted from the partial PDFs and are listed in Tables 1, 2, 3 and 4, which is basically consistent with the data obtained in the simulations conducted by Deb Nath^[12].

2.3 Short-Range Structure and Energy Analysis

Fig. 5 shows the fractions and energy of the Al, Cu and Zr-centered nearest shell coordination polyhedron. It is found that CN = 16 occupies the most fraction in the Zr₂₀Cu₇₀Al₁₀, Zr₃₀Cu₆₀Al₁₀ alloys, CN = 15 occupies the most fraction in the Zr₄₀Cu₅₀Al₁₀, Zr₅₀Cu₄₀Al₁₀ alloys and the coordination polyhedron number with CN=14 is the largest in the Zr₆₀Cu₃₀Al₁₀ and Zr₇₀Cu₂₀Al₁₀ alloys. As the Zr composition increases, the corresponding CN of the coordination polyhedron with the highest fraction in the alloy decreases. The energy distribution of the Zr-centered coordination polyhedron shows that as the CN increases, the energy of the coordination polyhedron declines and then climbs up. When CN reaches 16, the energy of the coordination polyhedron is the lowest. Dowling et al.^[23-26] proposed that the decrease of the polyhedron with high coordination number stands for the increase of the atomic structures packing loosely. It is found that the proportion of the Cu-centered 12 coordination polyhedron increases and then decreases with the increase of Zr composition. As the Zr composition increases from 20% to 30%, the proportion of the Cu-centered 12 coordination polyhedron increases from 55% to 56%, while the fraction decreases to 12% as the Zr composition increases to 70%. By calculating the energy of the coordination polyhedron, the variation trend in the energy of Cu-centered coordination polyhedron is the same as that of the Zr-centered polyhedron. When CN reaches 12, the energy of the coordination polyhedron is the lowest. Different from the Zr-centered coordination polyhedron, the energy distribution of the Cu-centered polyhedron with CN=12 differs greatly from that of other polyhedron, which should be caused by the formation of stable icosahedral structure. Among the Al-centered coordination polyhedron, the proportion of the 12 coordination polyhedron is the highest. The energy distribution is similar with the Cu-centered polyhedron. The 12 coordination polyhedron have the minimum energy and are the most stable. In the Zr₃₀Cu₆₀Al₁₀ alloy, there are more Zr-centered high-coordination polyhedron (especially the coordination polyhedron with CN=16), Al and Cu-centered 12 coordination polyhedron, forming more tightly packed and low-energy short-range structure. As a result, Zr₃₀Cu₆₀Al₁₀ alloy owns higher GFA.

2.4 Medium-Range Structure and Energy Analysis

Researchers introduced three classical connected clusters to explain the splitting of sub-nearest neighbor peaks, i.e., the cluster connection sharing one atom, two atoms and three atoms^[27-30]. The main peak of the sub-nearest neighbor is mainly derived from the connection with three sharing atoms, the splitting peak is principally derived from the connection sharing one atom, and the peak valley between the two peaks is mainly derived from the connection sharing two atoms^[27-30]. It can be seen from the PDFs of Zr₃₀Cu₆₀Al₁₀ and Zr₆₀Cu₃₀Al₁₀ amorphous alloys that the second peak of PDF for Zr₃₀Cu₆₀Al₁₀ amorphous alloy shifts to left in Fig. 6. The main peak of the second peak mainly results from the coordination polyhedron connection with three sharing atoms, revealing that the structure is closely concerned with the cluster connection sharing three atoms. The splitting of the second peak is mainly caused by the coordination polyhedron connection sharing one atom. For crystals, coordination polyhedrons are generally connected with one, two and four sharing atoms, and the cluster connection with two and four sharing atoms are the main connection mode in crystals. In the rapid cooling process, the formation of the cluster connection with two and four sharing atoms are inhibited. Therefore, the amount of the polyhedron connections with three sharing atoms can represent the GFA to a certain extent.

It can be seen from Fig. 7 that in the studied Zr_xCu_90-xAl₁₀ (x=20, 30, 40, 50, 60, 70) alloy system, the number of connection sharing an atom is the largest, followed by the connection with three sharing atoms, and then the connection with two sharing atoms, and the number of the connection with four sharing atoms is the lowest. With Zr composition increasing, the amount of the connections sharing one atom and three atoms increases first and then decreases, while the amount of the connections with two and four sharing atoms decreases first and then increases. For the Zr₃₀Cu₆₀Al₁₀ ternary alloy, the amount of connection with three sharing atoms is the highest and the amount of connection sharing two atoms is the lowest. Further calculating the different polyhedron connections with three sharing atoms with different central atoms, as shown in Fig. 8, as the Zr composition increases (Cu composition decrease), the amount of Zr-Al and Zr-Zr polyhedron connections sharing three atoms increases continuously, while the amount of the Cu-Al and Cu-Cu polyhedron sharing three atoms decreases continuously. The amount of Zr-Cu polyhedron connection with three sharing atoms increases first and then decreases, reaching the high value when the Zr composition is 30% and 40%. This change mainly contributes to that Zr₃₀Cu₆₀Al₁₀ having the maximum amount of the connection with three sharing atoms.

Fig. 9 shows energy distribution of the alloys with different compositions and connection modes. It can be seen that, regardless of the composition, the connection with three sharing atoms presents the lowest energy, followed by the connection sharing one atom, and then the connection with four sharing atoms, and the connection with two sharing atoms presents the highest energy. The energy landscape indicates that the amorphous alloy tends to form the coordination polyhedron connection with three sharing atoms. When Zr composition is 30% and 40%, the energy of different connections is the lowest. The amount of the connection with three sharing atoms is the most for the Zr₃₀Cu₆₀Al₁₀ alloy. Therefore, the Zr₃₀Cu₆₀Al₁₀ has more tightly connected, lower energy and more stable medium-range structure, owning higher GFA.

3 Conclusions

The results of the classical molecular dynamics simulations show that when the Zr composition is 30%, the glass transition temperature reaches the maximum value and the Zr₃₀Cu₆₀Al₁₀ owns high glass forming ability. There are more Zr-centered polyhedron with high CN, Al and Cu-centered 12 coordination polyhedron and coordination polyhedron connections sharing three atoms in Zr₃₀Cu₆₀Al₁₀ alloy. The existence of the stable structures has great impact on the high GFA of the Zr₃₀Cu₆₀Al₁₀ alloy.