Materials Physics
Atomic Environment of Pt in Quasicrystal-Forming Zr70Cu29Pt1 Metallic Glass
2024 Volume 65 Issue 7 Pages 723-727
Details
2024 Volume 65 Issue 7 Pages 723-727
The atomic configurations of the quasicrystal-forming ternary Zr70Cu29Pt1 metallic glass were calculated by the combination of classical molecular dynamics (MD) and ab-initio MD simulations. The binary Zr70Cu30 was prepared by classical MD and then Pt atoms were inserted into the large voids of Zr70Cu30, followed by relaxation using ab-initio MD. The coordination number of Pt atoms increased due to relaxation and reached a level comparable to that of Cu. The obtained structural model of Zr70Cu29Pt1 was analyzed by Voronoi polyhedral analysis modified especially for shell structures. We then compared Pt-centered polyhedra and Bergman-type atomic clusters formed in quasicrystals. The combined method of classical and ab-initio MD simulations is effective for the construction of the complicated structural models for glassy materials.
The quasicrystal formation from metallic glasses has been extensively studied mainly in Zr-based alloy systems [1–12]. For example, Saida et al. reported that isothermal annealing induces the formation of the nanoscale icosahedral quasicrystal in Zr-Pt and Zr-Pd metallic glasses [5, 12]. In addition, they also found that the minor addition of noble metals (Pd, Pt, and Au) to the typical Zr-Cu metallic glasses leads to the quasicrystal formation [6], although no quasicrystal formation occurs in the original binary alloys. To understand a role of the noble metals in the quasicrystal formation, the environment of Pd in Zr70Cu29Pd1 metallic glass was investigated by Yang et al. using the extended x-ray absorption fine structure (EXAFS) technique [13]. It is suggested that Pd atoms do not substitute for Cu and Zr atoms that form the icosahedral atomic clusters, but rather contribute to connect these icosahedra. In addition, it is shown that Pd atoms are located at octahedral atomic sites and play a role in the formation of long-range quasiperiodic structures. Later, the same alloy was investigated using high-resolution x-ray diffraction techniques together with a reverse Monte Carlo simulation [14]. They showed that the pre-peak appeared in the x-ray structure factor originates from medium-range order around Pd atoms that occupy the octahedral atomic sites in metallic glasses. Additionally, it is also demonstrated that as the amount of Pd increases, if the medium-range order associated with Pd atoms cannot be formed, the pre-peak disappears. However, there are still unclear issues regarding the detailed connections to quasicrystals and the effects in cases of other noble metals.
In the present work, we focused on the addition of Pt as a noble metal and then examined the local atomic structures of glassy states of Zr70Cu29Pt1 by computational techniques. Our approach combines classical molecular dynamics (MD) simulation with ab-initio MD simulation [15, 16]. Following the previous studies [13, 14], we first prepare Zr70Cu30 metallic glass using classical MD, and then place Pt atoms in the large voids found in the structure, and subsequently relax it using ab-initio MD.
The structure models of glassy Zr70Cu29Pt1 were constructed by a combination of conventional and ab-initio MD simulations. Commercial codes of LAMMPS [17] and VASP [18–21] were utilized for conventional and ab-initio MD simulations, respectively. Two binary Zr70Cu30 models including 250 and 2000 atoms were initially constructed using a conventional MD simulation with embedded atom model potentials [22]. The initial structures, with Zr and Cu atoms randomly distributed on a bcc lattice, were cooled from 2000 K to 300 K at a cooling rate of 1.0 × 1012 K/sec. Large interstitial voids in the glassy structures were detected using a persistent homology method [23] with HomCloud software [24]. Then, Pt atoms were placed in the center of detected large voids in the binary Zr70Cu30. Subsequently, the obtained ternary configurations were isothermally relaxed for 2500 fs at 500 K using ab-initio calculation. The local atomic configurations of the glasses were analyzed by Voronoi polyhedral analysis.
Our purpose is to construct a plausible structural model of ternary Zr70Cu29Pt1. Since it has been reported that the local structures of Zr70Cu30 are not significantly changed by the 1 at% addition of a noble metal [13], we first construct Zr70Cu30 metallic glass with a relatively slow cooling rate as a base structure, before adding Pt atoms. Figure 1(a) shows a structure model of the Zr70Cu30 metallic glass containing 250 atoms. Note that this image is a snapshot of the MD trajectory. To compare the MD results with the experiment, the x-ray structure factors S(Q) were calculated from the Zr70Cu30 models containing 250 and 2000 atoms as shown in Fig. 1(b). The S(Q) profiles of both models basically reproduce the experimental one. However, the height of the first peak for the 250 atoms model is lower than that of the others. Since this is probably due to the effect of the small cell size, we consider the structure models of Zr70Cu30 to be reasonable. To insert Pt atoms into the binary model with 250 atoms, we detect the large holes in the model using a persistent homology technique. This technique can search for different types of holes. Figure 1(c) shows a persistence diagram obtained from the Zr70Cu30 model with 250 atoms. The details are described in the previous papers [23, 24]. The plot in the diagram corresponds to each hole, and the plot away from the diagonal tends to represent a larger hole. Using the plots away from the diagonal marked in the diagram, it is possible to detect the larger holes in the structure. An example of the detected holes surrounded by 8 atoms is shown in Fig. 1(d). We then place 4 Pt atoms in the centers of 4 large holes corresponding to plots 1 to 4 in the persistence diagram of Fig. 1(c).
(a) Structure model of the Zr70Cu30 metallic glass containing 250 atoms. (b) X-ray structure factor S(Q) profiles of the MD results and the experiment of the previous work [14]. (c) The persistence diagram obtained from the Zr70Cu30 model with 250 atoms. (d) The detected large voids surrounded by 8 atoms. The atoms of Zr and Cu atoms are denoted by circles in green and blue, respectively.
It is necessary to relax the Zr70Cu30 model, in which Pt atoms are inserted, to obtain more stable and reasonable glass structures. We then kept the ternary model at 500 K lower than the glass transition temperature of this system (∼620 K [6]). Due to the lack of EAM potentials for the ternary Zr-Cu-Pt system, we applied ab-initio MD simulation to the relaxation of the initial structure. Figure 2(a) shows the changes in coordination numbers for Zr, Cu, and Pt atoms during the relaxation process. While the coordination numbers for Zr and Cu atoms do not change significantly, the coordination number for Pt atoms gradually increases and reaches about 10.5, the same level as that of Cu atoms after 1000 fs. In addition, the x-ray structure factor S(Q) changes slightly after relaxation as shown in Fig. 2(b). In particular, the second peak is split into two peaks after relaxation, marked with an arrow, and this feature is shared with the experimental S(Q) profile of Zr70Cu29Pd1 [14]. However, due to the oscillations in the calculated S(Q) profile, it was difficult to confirm the presence of a pre-peak. Figure 2(c) shows a representative atomic environment around a Pt atom. Although the central Pt atom has coordination number 10, a distorted octahedron can be found inside. The coordination polyhedron with a central Pt atom seems to be different from an icosahedron.
(a) The changes in average coordination numbers for Zr, Cu, and Pt atoms during the relaxation. (b) Structure factor S(Q) profiles of the before relaxation, after relaxation and the experiments of the previous work [14]. Note that the experimental S(Q) profiles were obtained from Zr70Cu29Pd1 and Zr70Cu30. (c) The atomic environment centered on Pt atoms, with a distorted octahedron inside. The atoms of Zr, Cu, and Pt atoms are denoted by circles in green, blue, and gray, respectively. The white circles represent atoms that do not belong to the distorted octahedron.
Our interest is whether Pt atoms can be placed at the center of the atomic clusters found in quasicrystals toward the quasicrystal formation. To confirm this, we compare the Pt-centered structures with an atomic cluster of the quasicrystal using a Voronoi polyhedral analysis. Following previous studies [25–27], we assume a Bergman-type atomic cluster for quasicrystals. To clarify the shell structure, we employ a neighboring Voronoi polyhedral analysis, which is especially designed for shell structures, as described in Fig. 3(a). We then focus on a large atomic cluster around Pt and investigate the Voronoi polyhedra formed with the atoms in the first and second shells acting as centers. For the Bergman atomic cluster, as shown in Fig. 3(b), it is understood that each atom on the first shell forms an icosahedron (⟨0 0 12 0⟩), and each atom on the second shell forms a 16-coordination polyhedron (⟨0 0 12 4⟩), with 12 of each type. Table 1 shows the count for ⟨0 0 12 0⟩, ⟨0 0 12 4⟩, and others at the first and second shells for Pt-centered polyhedra in the metallic glass. For comparison, the count for the Bergman-type atomic cluster is also shown in the table. Note that ⟨0 2 8 1⟩ and ⟨0 2 8 2⟩ are similar with the icosahedron, while ⟨0 2 8 3⟩ and ⟨0 2 8 4⟩ resemble the 16-coordination polyhedron. We immediately understand that in the first and second shells of the Pt-centered polyhedra in the metallic glass, there is only one icosahedron and no 16-coordination polyhedron, respectively. The fractions for the similar polyhedra are also quite small. These facts imply that Pt atoms are not placed in the center of Bergman-type atomic clusters, even if the Bergman-type atomic clusters can be formed in the metallic glass [26, 27]. It should be noted that even in the present model, the atomic environments around Zr also tend to be much closer to the Bergman-type atomic cluster than those around Pt.
(a) Schematic diagram of the neighboring Voronoi polyhedral analysis designed for shell structures. (b) Bergman atomic cluster with an icosahedron centered on the atoms in its first shell, and a 16-coordination polyhedron centered on the atoms in its second shell.
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Finally, we consider where the Pt atoms are located in the Bergman atomic cluster. Figure 4(a) shows the network of central Cu and Zr atoms of icosahedral-like coordination polyhedra with Pt atoms in the Zr70Cu29Pt1 metallic glass. It can be seen that most of the central atoms of the polyhedra are connected at the first nearest distance to each other. This type of connection implies the presence of the interpenetrating icosahedral-like polyhedra. As shown in Fig. 4(b), the similar network is also found in the Bergman atomic cluster. In this figure, two Bergman atomic clusters are connected to each other, which can be found in quasicrystals [28]. From this comparison, it is considered that the Pt atoms are not located in the center of the Bergman atomic cluster, but are positioned on the outside. In particular, the Pt atom marked with an arrow is located at the interface between two Bergman atomic clusters.
(a) The network of central Cu and Zr atoms of icosahedral-like coordination polyhedra with Pt atoms in the Zr70Cu29Pt1 metallic glass. (b) The similar network found in the Bergman atomic cluster. Note that the gray and yellow atoms are the centers of icosahedra and 16-coodination polyhedra, respectively.
In the previous studies [13, 14] of Zr70Cu29Pd1, Pd atoms are not involved in replacing Cu and Zr in icosahedral clusters. Rather, Pd atoms assist in linking these clusters. Moreover, Pd atoms occupy octahedral sites, contributing to the development of long-range quasicrystal order. In the case of Zr70Cu29Pt1, it can be said that our calculations indicate that Pt is in a similar situation to Pd in Zr70Cu29Pd1. Rather than occupying the centers of Bergman atomic clusters, Pt atoms are possibly located at the outer edges, where they could play a role in connecting these atomic clusters.
In this work, we employed the combination method of classical MD and ab-initio MD simulations to construct the complicated ternary Zr70Cu29Pt1 system. The base binary structure of Zr70Cu30 was calculated by classical MD with a relatively slow cooling rate and then the Pt-added glass structure was relaxed by ab-initio MD considering the electronic states. As a result, it was shown that Pt atoms in Zr70Cu29Pt1 are not located at the center of Bergman-type atomic clusters, but rather play a role in connecting the atomic clusters. This approach combines the strength of the two different MD methods and enables us to obtain the reasonable structural models of the complicated systems. This study is an initial trial, but the advantages of this method are expected to become more pronounced with an increase in the number of atoms and a decrease in the cooling rate for complicated glassy materials.
This work was partially supported by a JSPS Grant-in-Aid for Transformative Research Areas (A) “Hyper-Ordered Structures Science” Grant No. 20H05881 and a JSPS Grant-in-Aid for Challenging Research Exploratory Grant No. 23K17837.
