Introduction

In recent years, due to the broad application prospects in the industry, bulk metallic glasses (BMGs) have attracted increasing attention [1,2,3,4,5]. Usually, the bulk metallic glass contains multicomponent elements with a dramatic difference in the atomic size of the elements [6, 7]. Afterward, it was found that some simple binary alloy systems also show high glass-forming ability, such as Ca-Al, Cu-Zr, and Cu-Hf [8, 9]. Among these, Cu-Zr is a popular representative of early transition metallic glasses due to its high glass-forming ability (GFA) for a broad range of compositions [10,11,12,13,14]. It is reported that Cu-Zr binary alloys with a wide glass-forming composition range (45 <  ×  < 60 at. %) can be prepared into metallic glasses up to 2 mm in diameter by a conventional Cu-mold casting method [15,16,17]. Furthermore, the binary composition of Cu-Zr reduces the complexity of the possible local atomic structures, making this system ideal for the study of the evolution of the spatial structure of liquids as they are supercooled to form a glass [18,19,20,21,22]. Numerous studies on the GFA of the Cu-Zr binary system have been carried out both by experiments and simulation [23,24,25,26].

The high glass-forming ability of Cu-Zr alloys is usually attributed to their icosahedral orders. Strong evidence has been found that the Cu-centered full icosahedra are responsible for the high glass-forming ability of Cu-Zr BMGs [18, 27, 28]. The existence of the icosahedra (ICO) cluster increases the energy barrier to form the crystalline structures and thus improves the glass-forming ability. More importantly, the ICO clusters can be connected to each other in the cooling process to form a string like icosahedral network, the so-called medium-range order [29, 30]. There are also results related to the GFA of the Cu-Zr system to the enhanced atomic packing density by Zr addition [31, 32].

It is well known that pure Cu liquid cannot be quenched to form bulk metallic glasses. Then there raises the question as to how the Zr addition modulates the GFA and liquid structure of Cu liquids. Besides, most of the previous research focused on the compositions with the best GFA determined, such as Cu50Zr50, Cu64.5Zr35.5, and Cu64Zr36 [33,34,35]. However, in such high Zr concentrations, the modulation mechanism of Zr to the liquid structure is hard to observe. It is necessary to check it from the minor Zr addition. Y. Zhang et al. studied the variation of atomic structure in Cu100−xZrx with minor Zr content (x < 10) [36]. They found that the addition of Zr can increase the ICO short-range order. Recently, the medium-range order is also believed to be an important structural factor in determining the GFA [37]. A detailed analysis of the modulation of minor Zr to the liquid structure, especially to the medium-range structure, is crucial to understanding the GFA of CuZr alloys.

In this paper, we address these issues by conducting a systematic study using molecular dynamics (MD) simulations. We tracked the atomic structure changes, caused by minor Zr addition, especially the changes in medium-range order, to uncover the role of Zr in the improvement of GFA.

Simulation methods

Molecular dynamic simulations were carried out using the large-scale atomic/molecular massively parallel simulator (LAMMPS) [38]. Embedded atom method (EAM) potentials were used to determine interatomic interactions [39]. The time step was fixed to 2 fs in all of the simulations. Cubic simulation boxes containing 32,000 atoms were constructed by randomly distributing Cu and Zr atoms according to the stoichiometry of Cu100−xZrx with x = 0, 0.5, 1.0, 2.0, 3.0, 5.0, 7.0, and 10.0, respectively. Periodic boundary condition was applied in all three dimensions. The simulations are performed under constant pressure and constant temperature (NPT ensemble) with zero pressure. The initial liquid state was obtained by holding the system at 1800 K for 20 ps to get a relaxed liquid state. The liquids were then quenched to 200 K with a cooling rate of 5 × 1011 \(\mathrm{K}\cdot {\mathrm{s}}^{-1}\) to obtain glassy structures for Cu100−xZrx (x = 2.0, 3.0, 5.0, 7.0, and 10.0). For Cu100Zr0, Cu99.5Zr0.5, and Cu99Zr1, the cooling rate is 5 \(\times\) 1012 \(\mathrm{K}\cdot {\mathrm{s}}^{-1}\). The structural information was recorded every 100 K during the cooling process. The atomic structures were characterized using radial distribution functions (RDF) and Voronoi tessellation analysis (VTA).

The radial distribution function (RDF) which measures the probability of finding a particle at a distance r away from a given reference particle is widely used to detect the structural characteristics of glass and liquid microstructures [40, 41]. This function is defined as

$$\mathrm g\left(\mathrm r\right)=\frac V{N^2}\left\langle\sum\nolimits_{i=1}^N\frac{n(r)}{4\pi^2\Delta r}\right\rangle$$
(1)

where N is the number of atoms in the simulation box, V is the volume of the box, and n(r) is the number of particles located between r and r+∆r

The partial radial distribution function (PRDF) is defined as

$${\mathrm{g}}_{\alpha \beta }\left(\mathrm{r}\right)=\frac{V}{{N}_{\alpha }{N}_{\beta }}{\sum}_{i}^{N}{\sum}_{j\ne i}^{N}\delta (r-{r}_{ij})$$
(2)

where \(\delta (r-{r}_{ij})\) is the Dirac delta function, V is the volume of the system, and \({N}_{\alpha }\) and \({N}_{\beta }\) represent the number of \(\alpha\) atoms and \(\beta\) atoms, respectively.

One of the most frequently used techniques to characterize the topological short-range order in liquid and glass structures is the VTA [42]. In this technique, the atomic arrangement around each central atom is described by four indices < \({n}_{3}\),\({n}_{4}\),\({n}_{5}\),\({n}_{6}\)> to differentiate between different types of the polyhedron, where \({n}_{k}\) is the number of K-edged faces of the Voronoi polyhedron (VP). The sum of these \({n}_{k}\) numbers represents the number of nearest-neighbor atoms, namely the coordination number (CN) for each central atom. For example, the full icosahedral motif < 0, 0, 12, 0 > is described by twelve pentagons (\({n}_{3}\)=0, \({n}_{4}\)=0, \({n}_{5}\)=12, and \({n}_{6}\)=0).

The Bergman packing order can be confirmed by the angle distribution function (ADF) of the first and the second shell [43]. The angle is calculated according to

$${\theta }_{\text{ijk}}={\mathit{cos}}^{-1}\left(\frac{{r}_{ij}^{2}+{r}_{ik}^{2}-{r}_{jk}^{2}}{2{r}_{ij}{r}_{ik}}\right)$$
(3)

where rjk is the distance between atoms \(j\) and \(k\). \(j\), \(k\) is the atom at the shell of the central atom \(i\). Usually, a Bergman-type cluster is defined as one center atom-icosahedral-dodecahedral-icosahedral arrangement.

Results

The enhanced GFA by Zr addition

Figure 1 shows the radial distribution function g(r) of the Cu100−xZrx binary alloy at 200 K. The samples were obtained by quenching the liquids from 1800 K under the cooling rates of 5.0 × 1011 \(\mathrm{K}\cdot {\mathrm{s}}^{-1}\). From Fig. 1, the second peak exhibits pronounce split under the cooling rate of 5.0 × 1011 \(\mathrm{K}\cdot {\mathrm{s}}^{-1}\) when the Zr atom content is greater than 3%, which indicates that the system formed typical glass structures. However, when Zr content is less than 3%, the g(r) of CuZr alloys shows sharp peaks which is the typical pattern of crystallized structure. The inset in Fig. 1 displays the g(r) of Cu100Zr0, Cu99.5Zr0.5, and Cu99Zr1 alloy under the cooling rates of 5.0 × 1012 \(\mathrm{K}\cdot {\mathrm{s}}^{-1}\). We found that all the alloys transformed to glassy structures when we further increased the cooling rate to 5.0 × 1012 \(\mathrm{K}\cdot {\mathrm{s}}^{-1}\). It shows that addition of Zr decreased the critical cooling rate and thus increased the GFA.

Fig. 1
figure 1

Radial distribution functions g(r) of the simulated Cu100−xZrx (x = 0, 0.5, 1.0, 2.0, 3.0, 5.0, 7.0, and 10.0) alloys at 200 K. The inset presents the g(r) of Cu100Zr0, Cu99.5Zr0.5, and Cu99Zr1 alloy under the cooling rates of 5.0 × 1012 \(\mathrm{K}\cdot {\mathrm{s}}^{-1}\)

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The temperature dependence of the atomic volume during cooling is presented in Fig. 2. At the same temperature, the atomic volume increases with increasing Zr atoms content, which is due to the larger size of Zr atoms (1.60 Å) with respect to Cu atoms (1.28 Å). The glass transition temperature, Tg, which is defined as the inflection temperature in volume-T curves can be determined and the results are also shown in Fig. 2. We can see that Tg increased monotonously from 697 to 760 K along with the Zr content increase from 0 to 10%. Although the reduced glass transition temperature Trg is a more suitable parameter to evaluate GFA, the quick increase of Tg with minor Zr addition still provided the enhanced GFA information in CuZr alloys. For Cu-Zr system, it was found that increasing the Zr content from 0 to 10% can both decrease the critical cooling rate and increase Tg, which resulted in the increase of GFA [36].

Fig. 2
figure 2

Evolution of volume with temperature during cooling of Cu100−xZrx (x = 0, 0.5, 1.0, 2.0, 3.0, 5.0, 7.0, and 10.0). The lines are linear fits in the low and high-temperature regions. The glass transition temperature Tg is determined by the intersection of the two curves

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Partial radial distribution function (PRDF)

The partial RDFs of Cu100−xZrx MGs at 200 K are shown in Fig. 3. According to Fig. 3a, little difference in the Cu-Cu partial RDFs can be observed among all the samples. Only the height of the first peak decreases as the Zr content increases. It is due to the size mismatch between the Cu and Zr atoms which will cause positions of atoms at the nearest neighbor to become more dispersed. It also can be found that a slight bump at 3.6 Å disappears with the increase of Zr which shows the transformation of the liquid structure from a crystalline characteristic to a homogeneous liquid structure. For Cu-Zr partial RDFs which is shown in Fig. 3b, an increase in the amplitudes of the first maxima shows that Cu atoms prefer to bond with Zr atoms. Besides these, we cannot get further structure information caused by Zr addition from the partial RDFs.

Fig. 3
figure 3

The partial RDFs of the simulated Cu100−xZrx systems at 200 K. a Cu-Cu partial RDFs; b Cu-Zr partial RDFs

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Voronoi tessellation analysis

We employ the Voronoi tessellation analysis method to characterize the local atomic structure of configurations. In Fig. 4, we show the fractions of the top ten of the most dominant Voronoi polyhedron (VP) in CuZr metallic glass at 200 K. In general, the types of VP can be divided into three categories. The “crystal-like” represents a quasi-crystalline structure and is indexed by Voronoi polyhedral type < 0, 4, 4, x > with x = 5, 6, 7. The “Mixed” type is a category that consisted of < 0, 3, 6, x > with x = 4, 5, and 6. The “ICO-like” type, such as < 0, 1, 10, 2 > , < 0, 0, 12, 0 > , < 0, 2, 8, 2 > , < 0, 1, 10, 3 > and < 0, 2, 8, 4 > , are the VPs with high \({n}_{5}\) value (\({n}_{5}\)=8, 10, or 12) which characterizes perfect and defective icosahedral structures [44]. From Fig. 4, we found that the fraction of “ICO-like” VPs increases significantly with the Zr addition. While the fraction of “mixed” VPs, which is < 0, 3, 6, 4 > , < 0, 3, 6, 5 > , and < 0, 3, 6, 6 > and the “crystal-like” VPs, which is < 0, 4, 4, 6 > and < 0, 4, 4, 7 > decrease with increasing Zr atom content. These results indicate the ability of Zr atoms to promote the formation of ICO clusters and strongly increase the icosahedral short-range order in the system.

Fig. 4
figure 4

Distribution of the top ten most dominant Voronoi polyhedral at 200 K for Cu100−xZrx (x = 0, 0.5, 1.0, 2.0, 3.0, 5.0, 7.0, and 10.0)

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The evolution of the three types of VPs as a function of the temperature during the cooling process is presented in Fig. 5. Figure 5a shows the increased fraction of “crystal-like” VPs with decreasing temperature. We can divide the curves into two groups according to their variation behavior below Tg. When the Zr content is higher than 3%, the “crystal-like” VPs increase slowly with temperatures; while the Zr content is lower than 3%, the “crystal-like” VPs increase much faster. It confirms that crystallization is impeded by the higher content of Zr addition. These two categories can also be clearly observed in Fig. 5b and c, in which the variation of the “Mixed” VPs and “ICO-like” VPs is plotted. It shows that there exists a critical Zr content which is 3%. When the Zr content is lower than 3%, the Zr addition only slightly modifies the liquid structure of copper. However, when the Zr addition is higher than 3%, the liquid turns rapidly to ICO-dominated glass-forming liquids. It indicates that there exist two distinct glass states before and after 3% Zr contents.

Fig. 5
figure 5

a The fraction of “crystal-like” clusters with decreasing temperature for Cu100−xZrx. b The fraction of “mixed-like” clusters. c The fraction of “ICO-like” clusters

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The two distinct glassy states can also be confirmed from the angle distribution function (ADFs), which are shown in Fig. 6. When the Zr content is lower than 3%, there are four characteristic angles in the ADFs, which are 43°, 58°, 92°, and 117°, respectively. These angles demonstrate that there are plenty of crystalline-like clusters of the liquids. When the Zr content is higher than 3%, the angle of 43° disappears and the angles of 92° and 117° merged into a new angle of 112°. We should note that the two peaks in higher Zr content are consistent with the characteristic peak of ICO short-range order, which is 58° and 112° [45]. This suggests that the glass-forming liquid with strong ICO short-range order can only be obtained when the Zr addition is higher than the critical content of 3%.

Fig. 6
figure 6

ADFs of the first shell of Cu100−xZrx MGS at 200 K. The characteristic angle of ICO is also plotted in dashed lines

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Medium-range order

Next, we checked how the Zr addition affects the medium-range order of the icosahedral cluster in CuZr binary alloy. First, we analyzed the network formed by < 0, 0, 12, 0 > VPs. The number of ICO clusters in the cooling process in Cu100−xZrx alloy is calculated and shown in Fig. 7. In Fig. 7, two distinct ICO-connected paths can also be observed. The number of ICO clusters is almost maintained constant when Zr content is less than 3%. However, in the case of Zr content higher than 3%, the number of icosahedral clusters first increases rapidly with decreasing temperatures and then decreases rapidly as the temperature decreases from 1000 K. It shows the pic of the increasement and connection of ICO VPs in the cooling process. Zr contents contribute to the formation of ICO clusters and then help the ICO clusters to aggregate into a larger network, which will create ICO medium-range order (MRO) in the liquids.

Fig. 7
figure 7

The amounts of icosahedra cluster with temperature in Cu100−xZrx (x = 0, 0.5, 1.0, 2.0, 3.0, 5.0, 7.0, and 10.0)

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There are four different linkages between two icosahedra, which is intercross-sharing (IS), face-sharing (FS), edge-sharing (ES), and vertex-sharing (VS) cluster respectively. The variation of the four linkages numbers in the system at 200 K is shown in Fig. 8. The connected ICO populations are close to zero when Zr atomic content is less than 3%, while the connections of ICO increase rapidly when Zr atomic content is greater than 3%. Among the four linkages, the IS linkage mode is the dominant one. The ICO clusters connected by IS can exhibit a more locally ordered structure and show a higher atomic packing density than other linkages and make the structure more stable to resist crystallization [46].

Fig. 8
figure 8

Population of IS, FS, ES, and VS linkages with Zr content at 200 K

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We also calculated the sharing coordination atoms (SCA) between the central atom and one of its second shell atoms. It is an indicator parameter of MRO and can be used to describe packing feathers in the second neighbor shells. The details of SCA methods can be found in ref [47]. In ICO-type metallic glass, the SCA-3 is the characteristic index of Bergman MRO while the SCA-2 is more related to the Mackay MRO [48]. Figure 9 shows the variation of the SCA index with increasing Zr atom content at 200 K. We found that the SCA-1 index is almost kept constant with Zr addition. However, the SCA-2 and SCA-4 index decrease with increasing Zr content, while the SCA-3 index increases. Meanwhile, the SCA-3 index is higher than the SCA-2 index, which demonstrates that the addition of Zr enhances the Bergman MRO in the system [47]. Since the SCA-4 corresponds to a much looser packing method, the decreasing of SCA-4 methods shows the atomic packing become denser with the Zr addition.

Fig. 9
figure 9

Variation of the four main SCA indexes with increasing Zr content at 200 K

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To analyze the detailed MRO change in the system by Zr addition, we picked all the ICO-centered atoms and calculated their RDFs which are shown in Fig. 10. The RDFs show sharp first peaks which correspond to the IS connection of ICO VPs. And the RDFs also show clearly four or five following peaks beyond the first sharp peaks which show MRO structures formed in the liquid. We normalized all the peak positions in RDFs with the position of the first peak, and we get the normalized peak positions. The results are shown in Table 1. We found that the normalized peaks show a sequence of 1, 1.66, 2.01, 2.5, 2.6, and 3.04 in Cu100−xZrx binary alloy. This sequence corresponds well to the six shells of the Bergman structure, which are 1.0, 1.58, 2.00, 2.42, 2.67, and 3.00 [47]. These results confirm that enhanced Bergman-ICO type of MRO with the Zr additions.

Fig. 10
figure 10

The RDFs of the ICO-center system for the Cu100−xZrx (x = 0, 0.5, 1.0, 2.0, 3.0, 5.0, 7.0, and 10.0)

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Table 1 Comparison of the RDF peaks with hierarchical ICO structure of the Cu100−xZrx. All the peak positions are normalized by the position of the first peak of RDF
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Discussion

As illustrated above, the addition of Zr content can decrease the critical cooling rate and increase Tg. From Voronoi analysis results, we find that the Zr addition leads to the enhancement of ICO short-range order. More importantly, the addition of Zr can enhance interpenetrating ICO connection which will give rise to the Bergman-ICO medium order in the glasses. As a result, the addition of Zr makes the Cu-Zr binary alloy not only energetically more favorable but also structurally more stable [49]. The ICO order with a fivefold environment can increase the barrier for nucleation and cause slower structural rearrangement [50, 51] and therefore retard the nucleation of crystals, leading to the enhancement of GFA [52, 53]. This is the structural origin of Zr to improve the GFA of CuZr alloys. Our results also found that there exists a critical Zr content which is 3%. The glass states show distinct structural characters before and after 3%.

Conclusions

In summary, molecular dynamics simulation is performed to investigate the structural behavior of CuZr binary alloy by minor Zr addition. Various techniques have been used to characterize the atomic-level structure in terms of short-to-medium range order. Our results demonstrate that the slight change in the composition of Zr can significantly influence the microstructure of CuZr metallic glass. We found that the GFA can be greatly enhanced by minor Zr additions. The Zr addition can enhance the ICO short-range order (SRO) of the system, and the main connection method of ICO clusters is IS linkage. In the medium range, Bergman MRO becomes stronger with Zr addition. The improvement of SRO and MRO is responsible for the enhanced GFA in CuZr alloys, and we also found a critical Zr content which is 3%. When the Zr content is lower than 3%, the effect of Zr on the structures is not obvious. However, when the Zr content is higher than 3%, the Zr can rapidly change the structures of the liquid and glassy structure. Our results help to elucidate the role of Zr in CuZr metallic glasses from the atomic level.