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Structural and Chemical Orders in Ni64.5Zr35.5 Metallic Glass by Molecular Dynamics Simulation

The atomic structure of Ni64.5Zr35.5 metallic glass has been investigated by molecular dynamics (MD) simulations. The calculated structure factors from the MD glassy sample at room temperature agree well with the X-ray diffraction (XRD) and neutron diffraction (ND) experimental data. Using the pairwise cluster alignment and clique analysis methods, we show that there are three types dominant short-range order (SRO) motifs around Ni atoms in the glass sample of Ni64.5Zr35.5, i.e., Mixed-Icosahedron(ICO)-Cube, Twined-Cube and icosahedron-like clusters. Furthermore, chemical order and medium-range order (MRO) analysis show that the Mixed-ICO-Cube and Twined-Cube clusters exhibit the characteristics of the crystalline B2 phase. Our simulation results suggest that the weak glass-forming ability (GFA) of Ni64.5Zr35.5 can be attributed to the competition between the glass forming ICO SRO and the crystalline Mixed-ICO-Cube and Twined-Cube motifs.

Meanwhile, SRO and medium-range order (MRO) also govern the mechanical response to deformation in the MG systems [18]. Hence, investigating such atomic SRO and MRO structures in metallic liquids and glasses is a key to understanding structure-properties relationship of MG materials.
Among all Ni-Zr alloys with different compositions, it is believed that Ni 64.5 Zr 35.5 could be the most promising candidate for forming bulk MG, since Ni 64.5 Zr 35.5 is close to a eutectic point in Ni-Zr binary phase diagram [19][20][21]. Because the melting temperature is at a local minimum at the eutectic composition, the kinetics associated with crystal nucleation and growth would be relatively easily suppressed, leading to a relatively higher GFA compared to the same alloy system at other compositions. In particular, it has been shown that critical cooling rate for glass formation is minimal for the Ni-Zr alloy containing about 35 at.% Zr [22], which suggests that Ni 64.5 Zr 35.5 has the highest GFA in Ni-Zr system. However, compared to well-known Cu-Zr system which has been commonly regarded as good glass former in binary metallic alloys [23,24], experimental synthesis of bulk MG of Ni 64.5 Zr 35.5 is still very challenging.
Although Ni and Cu differ only by one electron, the GFA of Cu 64.5 Zr 35.5 and Ni 64.5 Zr 35.5 is very different. Cu 64.5 Zr 35.5 glassy samples with mm size can be fabricated by copper mold casting method [23], while glassy Ni 64.5 Zr 35.5 ribbon can only be obtained by careful melt-spinning process [20]. The cooling rate in meltspinning method is typically 10 5 -10 6 K/s which is much faster (about 2 orders of magnitude) than that of casting method. This difference indicates that the GFA of Ni 64.5 Zr 35.5 is much weaker relative to that of Cu 64.5 Zr 35.5 system. This weaker GFA nature of Ni 64.5 Zr 35.5 could be attributed to the difference in the short-to mediumrange order in the atomistic structures between the two systems. For example, it is believed that crystal-like motif can facilitate the crystal nucleation and growth to prevent the glass formation if the cooling rate is not high enough. Therefore, investigating the differences of short-to medium-range ordered structure and chemical order between Ni 64.5 Zr 35.5 and Cu-Zr system would provide useful insights into the origin of weak GFA in Ni 64.5 Zr 35.5 .
Using the experimental X-ray diffraction (XRD) and neutron diffraction (ND) experimental data, the atomic structure of Ni 64.5 Zr 35.5 MG has been studied by reverse Monte-Carlo (RMC) method and Voronoi tessellation analysis [25,26]. These studies have suggested that a large number of icosahedral-like and prismatic-like SRO structures exist in Ni 64.5 Zr 35.5 glass. Moreover, a significant degree of chemical ordering has also been observed in Ni 64.5 Zr 35.5 glass samples [26]. However, compared to the RMC method, MD simulation has a great advantage in obtaining more reliable atomic structure as long as the interatomic potentials are accurate. Fortunately, the interatomic potential of Ni-Zr system has been developed recently [27], which allows us to perform direct MD simulations for Ni 64.5 Zr 35.5 . To our knowledge, although the MD simulations for liquid Ni-Zr binary alloys have been reported [27], MD simulation of metallic glass at the composition around Ni 64.5 Zr 35.5 is still lacking.
Moreover, no detailed explanation of experimental results by MD simulation has been reported yet. Reliable MD simulation for this system will enable us to look into the structures of the alloy at undercooled liquid and glass states at atomistic level, and provide very useful insights into the GFA in this system.
In this paper, the atomic structure of Ni 64.5 Zr 35.5 glass is studied by MD simulation using the Finnis-Sinclair-type potential recently developed [27,28]. The pairwise cluster alignment method and clique analysis algorithm [29,30] are used to identify the dominant structure order in MD Ni 64.5 Zr 35.5 sample . This approach can extract a clique of similar clusters from atomic structure of MD sample without knowing the details of packing motif in advance. Meanwhile, the cluster alignment method can also calculate the populations of SRO clusters and explore the MRO in metallic liquid and glass systems. In addition to a large fraction of the Twined-Cube (similar to prismatic-like structure) and icosahedron-like clusters around Ni atoms as previously observed, we found significant populations of Ni-centered Mixed-ICO-Cube cluster which is composed of half icosahedron and half cube in Ni 64.5 Zr 35.5 glass sample obtained from the MD simulations. Furthermore, we show that the cubic part of Mixed-ICO-Cube cluster and the Twined-Cube cluster have excellent chemical ordering, indicating the emergence of metastable crystalline B2 phase [31]. Our results show that the suppression of glass formation by crystalline B2 phase could be responsible for the weak GFA of Ni 64.5 Zr 35.5 .

II. Method
The sample used in MD simulation of Ni 64.5 Zr 35.5 contains 3225 Ni and 1775 Zr atoms. The simulations are performed using the isothermal-isobaric (NPT) ensemble with the Nosé-Hoover thermostat in LAMMPS code [28]. The semi-empirical Finnis-Sinclair-type interatomic potential developed by Wilson and Mendelev is employed [27]. The time step in the MD simulations is 2.5 fs. Before the cooling process, the sample is held at 2000K for 2.5ns to achieve equilibrium. After that, the sample is cooled down to 300K continuously with different cooling rates at 10 13 , 10 12 , 10 11 and 10 10 K/s, respectively. In order to eliminate the effect of atomic thermal motions, the structural and chemical orders in the glass sample at 300 K are averaged over 500ps, which is sufficient to obtain the convergent results for the structural and physical properties studied in this paper.
In order to compare with the experimental data, the total structure factors S(q) of where b i and b j are the coherent neutron scattering length of the relevant atom species [34].
The SROs in Ni 64.5 Zr 35.5 MD samples are analyzed by the pairwise cluster alignment method [29,30]. In this method, a cluster can be assigned to each atom in the MD sample by extracting this atom and its first neighbor cell atoms along with it from the MD sample. Then each cluster extracted from the MD sample is used as a template and all other clusters with the same chemical element at the center are aligned against it. The similarity between the aligned cluster and the template is measured by an alignment score defined as where N is the number of the neighbor atoms in the template. %H and %Z are the atomic positions in the aligned cluster and template, respectively. To obtain optimal alignment, is chosen between 0.8 and 1.2 to vary the size of the template. Once we have all the alignment scores between any two clusters in the glass sample, we can obtain a clique of clusters whose pairwise alignment scores are smaller than a cutoff value of 0.15. The clusters belong to the same clique are very similar with each other and have the common SRO.

III. Results and Discussions
Fig . 1 shows the evolution of instantaneous potential energy E-3k B T as function of temperature with a continuous cooling rate of 10 10 K/s. In harmonic systems, the temperature dependence of both kinetic energy and potential energy are 3/2 k B T.
Therefore, E-3k B T will be a constant for all temperatures in harmonic systems. By subtracting 3k B T from the total energy obtained from MD simulations, the temperature dependence of anharmonicity in the system can be seen more clearly [35]. In particular, the plot in Fig. 1 shows that the anharmonicity in liquid and glass are different, which enables us to see the glass transition and estimate the glass transition temperature T g from the plot. From Fig. 1 one can see that at temperature higher than 975K the energy decreases significantly with decreasing temperature, whereas at low temperature region with T<975K the energy has only a slight decrease and is nearly constant around room temperature. Clearly, it shows a transition from liquid to glass and the obtained glass transition temperature is T g ≈975K, which agrees with the experimental result [19].
In order to see how good are the glass samples obtained from our MD simulations in comparison with experiment, we calculated the total and partial structure factors using Faber-Ziman formalism [32] for the samples at 300K prepared by different cooling rates. As shown in Figs. 2(a) and 2(b), although there is a slight shift of the height of the main peak, one can observe that the structure factors calculated from our MD simulations using the Eq. (3) and Eq. (4) agree well with the experimental XRD and ND data [26], respectively. It should be noted that as the same problem in RMC method, the agreement between the calculated and experimental S(q) does not always guarantee the correct description of the three-dimensional atomistic structures in the glass sample. Nevertheless, this good agreement of total structure factors is an essential requirement of the reliable MD simulation.
We can see from Figs. 2(a) and (b) that the height of main peak increases with lowering cooling rate, indicating more order developed with lower cooling rate. In Figs. 2(b) the experimental ND data and the simulated ND spectrum exhibit a prepeak [25] around q≈1.8Å -1 in addition to other peaks. Because the low q region in reciprocal space is corresponding to large distance in real space, the pre-peak would indicate certain medium-range correlations in the glass structure. However, the prepeak is not well seen in the in XRD spectra from both experiment and simulation.
Therefore, the origin of this small pre-peak needs further investigation.
The comparisons between the calculated and experimental partial structure factors [26] are shown in Fig. 3. The overall agreements between the calculated and experimental spectra are reasonably good but some discrepancies present, especially for the partial S(q) of the Zr-Zr pairs. Although the peak positions agree with each other, the peak intensity of the first peak from the calculation is much higher than that seen in experiment. It should be noted that the experimental partial structure factors are calculated from the different total structure factors of isotopic substitutions. The differences of total structure factors among the isotopic substitutions may be very small, so that the uncertainty of the obtained partial structure factors could be relative larger. Another source of the differences may also be attributed to the inaccuracy the interatomic potential used in the simulation, but we also would like to note that the potential has been successfully applied to explain several phenomena in Ni 50 Zr 50 (see Ref. [36]) Nevertheless, the main discrepancy is in the intensity of the peak at small q value which affects the degree of MRO in the system. The peaks of Ni-Ni and Ni-Zr show the distribution of alignment scores for Ni-and Zr-centered clusters from MD glass sample at 300K, respectively. As shown in Fig. 5(a), compared to the other motifs of Ni-centered cluster, the distribution of scores for Mixed-ICO-Cube, Twined-Cube and ICO-like motifs have relatively larger portion in the region with small score. It indicates that the local structures in the sample can be better described by these motifs than the others. Similarly, Fig. 5(b) shows the Z15 cluster is the major motif of Zr-centered cluster in Ni 64.5 Zr 35.5 .
To describe the SRO of glass sample quantitatively, we use alignment score 0.15 as a cutoff to assign the clusters to the given template. If a cluster has alignment score less than 0.15 for more than one template, the lowest alignment score is used to assign the motif of the cluster. The choice of cutoff value of 0.15 for determining the fraction of the SRO motif is a bit arbitrary but it is guided by considering the thermal motion of the atoms at given temperature. This cutoff value is inferred from the width of the first peak in the calculated pair correlation g(r) which reflects the atomic displacements due to thermal motion. At 300K, the width of the first peak of g(r) is roughly 0.15 d 0 , where d 0 is the averaged nearest neighbor bond length.  Recently, it has been demonstrated that performing MD simulated annealing below but close to the glass transition temperature (i.e., sub-T g annealing) can accelerate structural relaxation since the structural relaxation and glass formation is much more efficient in the vicinity of T g [38,41,42]. To investigate the effects of sub-T g annealing in Ni-Zr systems, the initial Ni 64.5 Zr 3 5.5 sample at 2000K is continuously cooled down to 925K at 10 10 K/s, then the as-quenched sample is annealed for 1400ns at 925K. Finally, the annealed sample was continuously cooled down to 300K at 10 10 K/s. The MD steps used for such a cooling-annealing-cooling cycle is equivalent to a cooling rate of 1.08×10 9 K/s. Fig. 8(a) shows the potential energy at 300K for different cooling rates including result from the sub-T g annealing cycle. It can be seen that the potential energy for the samples with continuous cooling linearly depends on logarithm of cooling rates, which is similar to the case of other binary alloy systems such as Cu-Zr [41], Al-Sm [42] and Ni-Nb [43]. When considering the error bar of the fitting, the potential energy for Ni 64.5 Zr 35.5 from the sub-T g annealing simulation is actually not far away from the extrapolation of the least-square fitting line based on the energies of the continuously cooled samples.
This result suggests that in order to get the same potential energy, the simulation time used for sub-T g annealing is almost the same as that used in continuously cooling.
This result is very different from the case of strong glass forming system like Cu 64.5 Zr 35.5 , where the sub-T g annealing approach can help to speed up the glass formation process [41]. Our results indicate that in weak glass forming system like the present case of Ni 64.5 Zr 35.5 , sub-T g annealing is not very effective owing to the relatively stronger crystalline nucleation tendency.
To study the influence of cooling rate on the SRO clusters, we show the fractions of Mixed-ICO-Cube, Twined-Cube and ICO-like clusters in the sample of 300K with different cooling rates in Fig. 8(b). When the cooling rate is lowered, the fraction of

ICO-like clusters is nearly constant while that of Twined-Cube clusters increases
considerably. The fraction of the Mixed-ICO-Cube clusters also increases slightly with lowering the cooling rate. The open symbols shown in Fig. 8(b) are the fractions of SRO clusters for the samples after sub-T g annealing process with an effective cooling rate of 1.08×10 9 K/s. Since the Twined-Cube cluster has the character of crystalline phase while ICO-like cluster is more related to glass phase, our results suggest that even in the very fast quench process the crystalline phase motifs are still the dominant SRO in Ni 64.5 Zr 35.5 system. Therefore, Ni 64.5 Zr 35.5 should not be a good glass former.
To further investigate the competition among different SRO motifs, we also examine the evolution of SRO clusters during the sub-T g annealing at 925K. During the annealing process, for every 200ns the sample is quenched to 10K to obtain the inherent structure for SRO analysis.

IV. Conclusions
In summary, the atomic structure of Ni 64. 5 1. The instantaneous energy E-3k B T as function of temperature with continuous cooling process, where the cooling rate is 10 10 K/s. It is clear that there is a phase transition from liquid to glass and the obtained glass transition temperature _ ≈ 975 agrees with the experimental data [19].  [26], respectively. One can observe that the calculated total structure factors from MD simulations agree well with the XRD and ND experimental data. The maximal discrepancy between MD simulations and experiments locates at the main peak in low-q region, as shown in the insets. In addition, the ND data from our MD simulation also produce well the characteristic pre-peak [25] around q≈1.8Å -1 , which generally corresponds to medium-range correlations in real space.   (3,4,9,8) and (7,8,9,10) form three nearly orthogonal squares, respectively. The other portion of surfaces are 10 triangles constituting a slightly distorted half ICO. (b) Twined-Cube cluster can be viewed as two interpenetrating cubes with common (111) plane formed by sites (Zr3, Zr4, Zr5). The sites (Ni3, Ni4, Ni5, Zr2, Zr3, Zr4, Zr5) and (Ni1, Ni2, Ni6, Zr1, Zr3, Zr4, Zr5) form the two half cubic surfaces C1 and C1', respectively. Here the usage of Ni or Zr as the site's name is to imply that the corresponding sites could be mostly occupied by Ni or Zr as revealed in the following investigation.  In the cubic part of Mixed-ICO-Cube clusters, the chemical composition at sites 2, 4, 8, 10 is Ni-rich (although it is a bit weak in site 8) while at sites 3, 7, 9 is Zr-rich, exhibiting the trend of B2 chemical order. This trend of B2 chemical order is even more pronounced in the Twined-Cube clusters. Our results demonstrate that the crystalline-like clusters have much more pronounced chemical order than that of ICO, implying that the crystalline phase could still emerge in Ni 64.5 Zr 35.5 sample even by fast cooling process.