Recently, the focus of clusters has been shifting toward nanoalloys consisting of two or more different metals within nanometer size.^[1] The size-dependent tunability of nanoalloys offers an excellent opportunity for tailoring new nanoscale materials.^[2] Besides, nanoalloys offer the opportunity for tailoring the structures and properties of materials through the choice of atom type and composition.^[3,4] Alloying of two or more metals at nanosize is of interest especially for catalysts since the combination of metals can increase the activity and/or the selectivity of catalysts.^[5] Since the activity and selectivity are closely associated with structure, their surface structures, compositions, and segregation properties are of particular interest.^[6] One promising route to determine and increase the catalytic performance is properly controlling of the size, structure, and composition of nanoalloys.^[7] In addition to the geometry and size of the particles, catalytic performance of nanoalloys depends on the chemical ordering.^[8] For this reason, a theoretical study of nanoalloys is important in order to find and develop the properties which they attain when their geometric structure and chemical composition varies.^[2]

The reason for concentrating here on truncated octahedron (TO) structure is that the selected motif possesses high symmetry,^[9] and frequently adopted in theoretical and experimental studies.^[10] The 38-atom TO was chosen as model for the trimetallic nanoalloys due to the high symmetry of the parent TO structure (O_h)^[11] with 8 (111) hexagonal and 6 (100) square faces.^[12] Besides, the size is interesting since it corresponds to magic number of atoms for the truncated octahedron^[13] and it is the only size below 50 atoms at which fcc structures are in competition with icosahedral fragments and amorphous structures.^[14] Furthermore, it was found that TO structures typically dominate 38-atom nanoclusters in several studies of literature and also they were obtained as the global minimum (GM) for many clusters for the Gupta many body potential,^[4,15,16] as well as the other many-body and pair potentials.^[17–19]

There have been many theoretical studies of mono and bimetallic nanoclusters with 38-atom TO structure to investigate the relationship between geometric structure, chemical ordering and segregation tendency.^{[2,4–11,14,15,20–25]} Zhu et al.^[7] investigated Pd–Au nanoalloys for 38-atom TO. Demiroğlu et al.^[11] performed a density functional theory (DFT) study to investigate the effect of the TiO₂ support on the structures of 38-atom AuRh nanoalloys and in another study nanoscale mixing properties of 38-atom Au–Rh were investigated.^[8] Roy et al.^[20] studied 38-atom Pd–Pt, Ag–Au, Pd–Au, and Ag–Pt binary clusters combining empirical potential (EP) and DFT calculations. Rodrigues et al.^[2] calculated the global optimization of Cu_nAu_m (n + m = 38) clusters. A study of chemical ordering in 38-atom Pd–Ir nanoalloys were reported by Davis et al.^[5] Cerbelaud et al.^[21] determined the optimal chemical ordering for binary AgAu cluster with 38-atom. Curley et al.^[6] studied the Ag–Au bimetallic nanoalloy clusters with 38 atoms using Gupta many-body potential. For chemical ordering in AgAu TO nanoalloys of 38 atoms, Rapetti et al.^[14] also reported a DFT global optimization study. Darby et al.^[4] reported that Cu₃₈ and Au₃₈ clusters have a TO structure. Molayem et al.^[22] found global minimum structures based on TO for some Cu–Ag nanoalloys with 38 atoms. A theoretical investigation of 38-atom CuPt clusters was performed by Guerrero-Jordan et al.^[23] using a genetic algorithm. Pittaway et al.^[24] also used genetic algorithm for global optimization of 38-atom PdAu clusters with TO structure. Fan et al.^[10] investigated the structural stability and chemical ordering of 38-atom TO Pd–Ir nanoalloys. Melting mechanism of Pd₂₄Pt₁₄ nanoalloy with TO was determined by Oderji et al.^[25] Negreiros et al.^[9] analyzed the kinetics of chemical ordering in a Ag–Pt TO nanoalloy particle via first principles simulations. TO structure and energetics of Ni, Ag, and Au nanoclusters of size 38 atoms were investigated by Michaelian et al.^[15]

Despite of these investigations on the monometallic and bimetallic nanoclusters with 38-atom TO structure, there are not sufficient data about trimetallic 38-atom nanoclusters. Pacheco-Contreras et al.^[13] investigated Ag–Au–Pt trimetallic clusters contain a total of 38 atoms at Gupta and DFT levels. Wu et al.^[26] investigated geometrical and energetic properties in 38-atom Au–Pd–Pt clusters. The structrures of Cu₈Au_nPt_{30 – n} clusters were analyzed by Wu et al.^[27] Besides, many above-mentioned investigations performed simulation searches by combining EP and DFT approaches. Since there is still lacking a thorough study presenting the relationship between geometric structure, chemical ordering, and segregation tendency of trimetallic nanoalloys with 38-atom TO, we have focused on 38-atom Pd–Pt–Ag trimetallic nanoalloys with TO structure in this study. Although some investigations^[28,29] on clusters present comparisons with available experimental results, it is not always possible to directly compare theoretical results with experimental data for clusters. To study small clusters with rather accurate methods from the theoretical point of view, DFT calculations could be an alternative choice. Thus, we have performed DFT re-optimization for the best chemical ordering structures of Pd_nAg_{32 – n}Pt₆ trimetallic nanoalloys obtained at Gupta level.

In order to model the metallic bonding between Pt, Pd, and Ag atoms in Pd–Ag–Pt trimetallic naoalloys, Gupta potential^[30,31] has been used. Gupta potential can be written in terms of repulsive () and attractive () many-body terms and the functional form is given by

Table 1.

Table 1.

Table 1. The Gupta potential parameters for Pt–Pd–Ag trimetallic clusters. . A/eV ς/eV p q r0/Å Pd–Pd 0.1746 1.7180 10.867 3.742 2.7485 Pd–Pt 0.2300 2.2000 10.740 3.870 2.7600 Pd–Ag 0.1610 1.5597 10.895 3.492 2.8200 Pt–Pt 0.2975 2.6950 10.612 4.004 2.7747 Pt–Ag 0.1750 1.7900 10.730 3.570 2.8330 Ag–Ag 0.1031 1.1895 10.850 3.180 2.8921

Table 1. The Gupta potential parameters for Pt–Pd–Ag trimetallic clusters. .

The best chemical ordering structures of Pd_nAg_{(32 – n)}Pt₆ nanoalloys with TO structure were carried out using Monte Carlo Basin–Hopping algorithm.^[34,35] The best chemical ordering structures obtained at Gupta level were chosen as initial configurations and re-optimized DFT searches were performed for the chemical ordering in Pd_nAg_{(32 – n)}Pt₆ nanoalloys. The DFT calculations with Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional^[36] were made by using the Quantum ESPRESSO package.^[37,38] In Quantum ESPRESSO, the energy cutoff for wavefunctions was used as 45.0 Ry (1 Ry = 13.6056923(12) eV) and the cutoff energy for charge density was used as 448.0 Ry.

In the current study, chemical ordering in 38-atom trimetallic Pd–Ag–Pt nanoalloys with TO structure has been studied and a systematic search was performed for the best chemical ordering structures. Besides, structure and chemical ordering effect on stability of trimetallic nanoalloys are explored. Structural details of trimetallic nanoalloys are analyzed as a function of their chemical compositions. We mainly focus here on the Pd_nAg_{(32 – n)}Pt₆ nanoalloys with fixed six Pt atoms where the fixed number 6 represents inner atoms of the 38-atom TO structure. The high-symmetry structure is taken as initial atomic configurations.

The best chemical ordering structures obtained at Gupta level for Pd_nAg_{(32 – n)}Pt₆ nanoalloys are presented in Fig. 1. As can be seen from the figure our simulations did not break the initial symmetry and in general, Pt atoms are preferentially placed in the inner part of the nanoalloys. In Pd₁₈Ag₁₄Pt₆ and Pd₂₀Ag₁₂Pt₆ compositions one Pd atom locates at core with 5 Pt atoms by replacing one Pt atom. Since the number of Pt atoms is constant to 6, the compositions except Pd₁₈Ag₁₄Pt₆ and Pd₂₀Ag₁₂Pt₆ exhibit a octahedral Pt core. For Ag₃₂Pt₆ bimetallic nanalloy, Ag atoms tend to segregate to the surface and Pt atoms tend to segregate into the structure core. In Pd_nAg_{(32 – n)}Pt₆ trimetallic nanoalloys, with the increase of Pd atoms from 1 to 8, the Pd atoms locate at the center of hexagonal facets of TO. It is well known that 38-atom TO structure has 8 (111) hexagonal and each (111) facets has 7 atoms composed of 6 sites on the vertexes of hexagon and 1 central site. Besides, 38-atom TO structure has six (100) square facets and each (100) facets has 4 atoms. At n_Pd = 9–14, each of the added six Pd atoms locates on one of the six (100) facets. With the further increase of Pd atoms, the locating tendency of Pd atoms can be identified as growing on the sites on the adjoining edges of (100) and (111) facets.

Fig. 1.

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	Fig. 1. The best chemical ordering structures of 38-atom trimetallic PdnAg32 – nPt6 nanoclusters. The dark blue, light blue, and grey colors represent Pd, Ag, and Pt atoms, respectively.

In the nanoscale, the energetic stability among a family of nanoalloys is determined by calculating the excess energy (ΔE_exc). For trimetallic Pd_nAg_{(32 – n)}Pt₆ nanoalloys with fixed size but different compositions excess energy is defined as^[39]

In order to provide more useful structural information about the chosen nanoalloy system, Gupta and DFT approaches were combined. The best chemical ordering structures at Gupta level were recalculated with DFT relaxations to crosscheck the lowest energy structures. Since there is not occurrence of any discrepancies on nanoalloy structures, it can be interpreted as DFT results confirm the Gupta level calculations with small shifts on bond lengths. Also, DFT calculations indicate that the truncated octahedron structure is indeed the lowest energy ones for Pd_nAg_{(32 – n)}Pt₆ nanoalloys. Figure 2 shows the plots of excess energy as a function of composition for 38-atom nanoalloys at Gupta and DFT levels. It is worth mentioning that the lowest excess energy values were obtained at the same composition of Pd₈Ag₂₄Pt₆ at Gupta and DFT levels since Gupta and DFT excess energy variations exhibit quite compatible behaviors. In Pd₈Ag₂₄Pt₆ composition, 8 Pd atoms are central sites of 8 (111) hexagonal facets of TO, 24 Ag atoms locate on surface, and 6 Pt atoms locate at the core of the structure.

Fig. 2.

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	Fig. 2. Excess energy of 38-atom trimetallic PdnAg32 – nPt6 nanoclusters at Gupta and DFT levels.

The structure of the most stable composition Pd₈Ag₂₄Pt₆ for Pd_nAg32 – nPt₆ nanoalloys is illustrated in detail in Fig. 3. It is clear from the figure that, Pd, Ag, and Pt atoms of the Pd₈Ag₂₄Pt₆ composition are located more symmetrically. Figure 4 shows the two different chemical orderings of Pd₁₈Ag₁₄Pt₆ and Pd₂₀Ag₁₂Pt₆ nanoalloy structures at DFT level. Since one Pd atom locates at core with 5 Pt atoms for these two compositions, we researched what would be their energies if the surface Pt atom is in the core. The top row represents the re-optimization structures obtained at Gupta level and the bottom row represents the structures with Pt atoms forming core for Pd₁₈Ag₁₄Pt₆ and Pd₂₀Ag₁₂Pt₆ nanoalloys in Figs. 4(a) and 4(b), respectively. For Pd₁₈Ag₁₄Pt₆ composition, the DFT analysis shows that the structure obtained at Gupta level is 0.026-eV higher in energy than the structure which has 6 Pt atoms in its core. However, the DFT analysis is also found in close competition for Pd₂₀Ag₁₂Pt₆ as the re-optimization structure obtained at Gupta level is only 0.001-eV higher in energy. According to these results, it seems that the chemical orderings which correspond to Gupta level minima are energetically favorable for both Pd₁₈Ag₁₄Pt₆ and Pd₂₀Ag₁₂Pt₆ nanoalloys.

Fig. 3.

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	Fig. 3. The location of Pt, Pd, and Ag atoms of the most stable Pd8Ag24Pt6 composition for PdnAg32 – nPt6.

Fig. 4.

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	Fig. 4. Two different chemical orderings of (a) Pd18Ag14Pt6 and (b) Pd20Ag12Pt6 nanoalloy structures at DFT level. The top row represents the re-optimization structures obtained at Gupta level and the bottom row represents the structures with Pt atoms forming core.

In order to better discuss about the atomic mixing degree of different type atoms in Pd–Ag–Pt nanoalloys, the order parameter (R_A)^[40] is adopted. R_A can be defined by the average distance of a type of atoms from the center of a cluster, i.e.,

Figure 5 shows the order parameter (R) variation of trimetallic Pd_nAg32 – nPt₆ nanoalloys. As can be seen from the figure R_Ag value is larger than R_Pd and R_Pd is larger than R_Pt for most of the compositions. It indicates that there is a clear tendency for Ag atoms to segregate to the surface of the nanoalloys and also Pt atoms prefer to locate at core. For n_Pd = 1–8, R_Pd parameter values keep constant as 8 Pd atoms occupy the central sites of 8 (111) hexagonal facets. In the size range of n_Pd = 9–31, R_Pd parameter values gradually increase with the increasing concentration of surface Pd atoms. The change reason of the R_Pt parameter at n_Pd = 18 and 20 is that the replacement of one Pt atom in the core with one Pd atom on the surface.

Fig. 5.

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	Fig. 5. The order parameter (R) variation of trimetallic PdnAg32 – nPt6 nanoalloys.

The strain effects are more important in the bimetallic and trimetallic systems, because of the size mismatch between different atomic species. Also, the strain becomes different in different geometries, indicating that the chosen geometry and chemical ordering are interrelated. Since nanoparticles with strained surfaces may present important catalytic properties, we decided to investigate the local atomic pressure values for Pd–Ag–Pt nanoalloys. The local pressure P_i acting on atom i is proportional to the trace of the tensor given as follows:^[41,42]

Figure 6 shows the local atomic pressures for Ag₃₂Pt₆, Pd₃₂Pt₆, and Pd₈Ag₂₄Pt₆ nanoalloys to compare the most stable structure of trimetallic (Pd₈Ag₂₄Pt₆) and bimetallic (Ag₃₂Pt₆, Pd₃₂Pt₆) nanoalloys. For Ag₃₂Pt₆ bimetallic nanoalloy, 6 Pt atoms locate at the core and their pressure values are strongly positive. The 32 Ag atoms locate on the surface due to lower surface energy. The 8 Ag atoms on surface are central sites of 8 (111) hexagonal facets and they present positive pressure value as remaining Pd atoms present negative local atomic pressure. The pressure on the surface is in the range between –4 GPa and 3 GPa for Ag₃₂Pt₆ bimetallic nanoalloy. As for Pd₃₂Pt₆ bimetallic nanoalloy, Pd atoms fully occupy the surface and 6 Pt atoms occupy the core of the structure. The pressure of the inner Pt atoms is also strongly positive. The 8 Pd atoms at central sites of 8 (111) hexagonal facets have positive pressure values and pressure becomes negative for remaining 24 Pd atoms. The pressure on the surface is in the range between –6 GPa and 2 GPa for Pd₃₂Pt₆ bimetallic nanoalloy. Pd₈Ag₂₄Pt₆ trimetallic nanoalloy is also has a core composed of 6 Pt atoms which have strongly positive pressure values, similar to these two bimetallic compositions. The 8 Pd atoms especially locate at central sites of 8 (111) hexagonal facets and the pressure at the central sites becomes more positive than bimetallic ones indicating the strain is more compressive. For Pd₈Ag₂₄Pt₆ nanoalloy, the pressure on the surface is in the range between –5 GPa and 4 GPa. The 24 Ag atoms locate on the adjoining edges of (100) and (111) facets and they exhibit negative pressure. As can be seen from the pressure scale, it can be interpreted as that the substituted atoms on surface present mildly pressure range for trimetallic nanoalloy.

Fig. 6.

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	Fig. 6. Local atomic pressure for Ag32Pt6, Pd32Pt6, and Pd8Ag24Pt6 nanoalloys.

Figure 7 shows the local atomic pressure for Pd₁₈Ag₁₄Pt₆ and Pd₂₀Ag₁₂Pt₆ nanoalloys. As can be seen from the side views of these two nanoalloys, one Pt atom locates on central site of (111) hexagonal facet and presents highly positive pressure which is close to each other. For Pd₁₈Ag₁₄Pt₆ nanoalloy, Pd core atom has pressure value about 8 GPa which is the lowest positive pressure in the core. The pressure value of surface Pd atoms exhibits in the range between –5 GPa and 1 GPa. Also, Ag atoms exhibit negative pressure about –7 GPa. For Pd₂₀Ag₁₂Pt₆ nanoalloy, Pd core atom has pressure value about 6 GPa which is the lowest positive pressure in the core. The pressure value of surface Pd atoms exhibits in the range between –5 GPa and 0 GPa. Also, Ag atoms exhibit negative pressure about –7 GPa similar to Pd₁₈Ag₁₄Pt₆ nanoalloy. According to pressure results of these two compositions, the location of one Pd atom at core with 5 Pt atoms can be attributed to the relaxation of strained core structure.

Fig. 7.

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	Fig. 7. The local atomic pressure for Pd18Ag14Pt6 and Pd20Ag12Pt6 nanoalloys.

In this study, we have performed a systematic investigation of Pd_nAg32 – nPt₆ trimetallic nanoalloys and we have focused on 38-atom Pd–Pt–Ag trimetallic nanoalloys with truncated octahedron (TO) structure. The best chemical ordering structures were obtained using Monte Carlo basin-hopping algorithm within Gupta potential. The structures with the lowest energy at Gupta level are then re-optimized by DFT relaxations and DFT results confirm the Gupta level calculations with small shifts on bond lengths, indicating TO structure is favorable for 38-atom of Pd_nAg32 – nPt₆ trimetallic nanoalloys.

In Pd_nAg_{(32 – n)}Pt₆ trimetallic nanoalloys, all the compositions except Pd₁₈Ag₁₄Pt₆ and Pd₂₀Ag₁₂Pt₆ nanoalloys exhibit a octahedral Pt core. From the order parameter variations of trimetallic Pd_nAg32 – nPt₆ nanoalloys, it was observed that Ag atoms exhibit a clear tendency to segregate to the surface. DFT level investigations showed that two chemical orderings corresponding Gupta level minima with 5 Pt atoms at core (for Pd₁₈Ag₁₄Pt₆ and Pd₂₀Ag₁₂Pt₆) are energetically favorable than the chemical orderings with 6 Pt atoms at core. Moreover, DFT and Gupta excess energy analysis show that Pd₈Ag₂₄Pt₆ composition has the lowest excess energy value which corresponds to more stable structure. In Pd₈Ag₂₄Pt₆ composition, 8 Pd atoms are central sites of 8 (111) hexagonal facets of TO, 24 Ag atoms locate on surface and 6 Pt atoms locate at the core of the structure. Furthermore, it was observed that 8 Pd atoms at central sites of hexagonal facets exhibit more positive pressure than the atoms at central sites of bimetallic Ag₃₂Pt₆ and Pd₃₂Pt₆ nanoalloys in relation to mismatch between three different atomic species and also chemical ordering.