Investigation of thermal, structural and dynamical properties of (Au_x–Cu_y–Ni_y)_N=32,108,256 ternary nanosystems: effect of Au addition to Cu–Ni bimetallic nanoclusters via MD simulation

Abstract

In this work, we have investigated the heating and cooling processes for ternary (Au_x–Cu_y–Ni_y)_N=32,108,256 nanoclusters with different Au mole fractions (x = 0, 0.1, 0.3, 0.5, 0.7, and 0.9) using molecular dynamics simulation. We have examined the effect of addition of Au atoms to Cu–Ni nanoclusters on the different thermodynamic, structural, and dynamical properties. Our thermodynamic results showed that the most stable structures (which correspond to the maximum melting points) for the sizes of N = 32, 108, and 256 are at x_Au = 0.7, 0.5, and 0.33, respectively. Our structural results showed that the ternary nanoclusters have almost homogeneous structures and core–shell regimes cannot be seen for them. The Au atoms tend to lie at outermost layers and so, Cu and Ni atoms lie at innermost layers. Also, our dynamical results indicated that as the Au mole fraction increases, the self-diffusion decreases.

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1. Introduction

Metallic nanoclusters have received considerable attention from the scientific community because of their unique physical and chemical properties.^1–3 Nanoclusters generally possess different properties from bulk materials as a result of their large surface-to-volume ratio. Many investigations have been directed toward bimetallic nanoclusters in recent years.^4–6 Nowadays, besides their continued use in jewelry, Au–Cu alloys have emerged prominently in the nanosciences, mostly for catalysis (such as carbon monoxide oxidation^7–9 and selective oxidation of alcohols^10,11). Cu–Ni nanoparticles have been widely used as catalysts,¹² hyperthermic magnetic fluids,¹³ electrode materials in solid oxide fuel cells, in multilayer ceramic capacitors,¹⁴ and as condenser tubing in marine applications.¹⁵ Ni–Au catalysts have been found to be superior materials for the steam reforming reaction, in which methane or other hydrocarbons react with water to produce H₂ and CO.^16,17

Molecular dynamics (MD) simulation has been used to investigate the thermal and structural properties of bimetallic nanoparticles including the effects of size, composition, and structure on the melting and thermodynamic properties.^18–20 For example, Z. Kuntová et al.²¹ investigated the melting of binary metallic Ag–Ni and Ag–Co nanoclusters. They find that the core–shell structure is especially stable for compositions at which the external shell is completely made of silver. Oviedo et al.²² investigated the formation of binary core–shell nanoparticles composed of Au, Ag, and Pt atoms. They showed that it is possible to obtain different degrees of decoration of the core nanostructure. Xiao et al.²³ studied the size effect on alloying ability and phase stability of immiscible bimetallic nanoparticles. Akbarzadeh and Abbaspour⁶ simulated the heating and cooling processes of Ag–Au alloy nanoclusters of 256 atoms with the different mole fractions supported on single walled carbon nanotube with the different diameters.

Gold–copper–nickel alloys are basic materials in jewellery.²⁴ Recently, Shiraishi et al. reported that Cu_0.5Au_0.5−xNi_x alloys containing nickel up to about 12% at possess sufficient age hardenability for use as dental restorative alloys.²⁵ The Cu–Au–Ni braze alloy is commonly used for vacuum electronic brazing applications where the Ni addition is needed to wet surfaces.²⁶ The Cu–Au–Ni alloys were also used with a high degree of success in microwave tubes with braze joints to metallized sapphire windows, which withstood 700 °C bake-out temperatures.²⁷ The gold–copper–nickel ternary system possesses a pronounced age-hardenability and used as the dental metal alloys.²⁸

Despite of many investigations on the bimetallic nanoclusters, there is not sufficient experimental and theoretical data about ternary metallic nanoclusters and a little knowledge has been understood about their properties. Recently, Subbaraman et al.²⁹ used MD simulation in order to study the effect of Ag addition on Cu–Ni bimetallic nanoclusters and evaluated structure of Ag–Cu–Ni ternary nanoclusters with 4 nm diameter. Their results showed that Ag atoms are located at low-coordination sites such as edges, corners, and faces. Also, they found that alteration of melting point and crystalline structure of the nanocluster is strongly depended on the Ag concentration. It is therefore expected that the ternary alloy properties would be significantly different from those of the constituent elements as well as their binary alloys. In particular, the effect of systematic addition of the third component on the melting characteristics and structural evolution of binary alloy nanoclusters has been rarely investigated.²⁹ In this work, effect of Au addition on Cu–Ni nanoclusters is studied by MD simulation. The importance of the addition of Au to the bimetallic Cu–Ni cluster is well-known for different researchers. Au is one of the most malleable and flexible metals. When Au adds to an alloy, it can be expanded or compressed very much. Also, the different properties of Au are dependent on its size very much. Therefore, by Au addition on a cluster, we can improve the catalytic and other properties of the nanocluster.^30–37 The availability and recyclability of precious transition metals such as Au used for catalysis in various emerging energy technologies have been identified as a significant bottleneck toward successful deployment of electrochemical energy storage or conversion devices.³⁷ The investigation of structural and dynamical changes of the Au–Cu–Ni clusters during the heating–cooling cycles is an important goal of this work. It is obvious that melting and freezing processes of these nanoclusters indicate important structural changes of them which can be useful for other experimental and theoretical studies on these types of nanomaterials.

2. Simulation method

The MD simulations were performed in canonical ensemble (NVT) using Nóse–Hoover thermostat.^38,39 All of the simulations were performed by DL_POLY classic software.⁴⁰ Then, Ni_0.5Cu_0.5, Au_0.1Ni_0.45Cu_0.45, Au_0.3Ni_0.35Cu_0.35, Au_0.5 Ni_0.25Cu_0.25, Au_0.7Ni_0.15Cu_0.15, and Au_0.9Ni_0.05Cu_0.05 nanoclusters with total number of atoms N = 32, 108 and 256 were selected for MD simulations (totally 18 initial structures have been selected). Each nanocluster was treated by annealing in order to exclude the effect of their initial configuration on the phase transition temperature and also to reach its stable structure. At the beginning, the heating process was performed for all nanoclusters in the range of 300 to 1200 K with increasing 100 K steps. Close to melting points, the temperature increments were reduced to 10 K. Similar simulations were performed in cooling process in the range of 1200 to 300 K. Each melting or cooling process was performed for 2 ns of simulation time with time step of 1 fs. In order to confirm the phase transition temperature, three cycles of heating cooling processes have been performed and the average of the results have been considered. Also, cutoff radius for all of the simulations was selected 15 Å.

The metal–metal interactions were modeled by quantum Sutton–Chen (QSC) potentials.^41,42 The QSC potential has been widely applied in simulation studies of nanoclusters and the simulated results using this potential are consistent with the experiments for low-dimensional systems and bulk.^41–46 The potential energy in the QSC model is:

The first term is the pair repulsion potential and the second term represents the metallic bonding energy associated with the local density, ρ_i which is calculated by:

where r_ij is the distance between atoms i and j, c is a dimensionless parameter, also ε and a are parameters with dimensions of energy and length, respectively. The QSC parameters for the Ni, Cu and Au are listed in Table 1. The geometric mean was used to obtain the energy parameter ε and the arithmetic mean was used for the remaining parameters. Recently, Guisbiers et al.⁴⁴ used the QSC potential for the Au–Au, Au–Cu, and Cu–Cu interactions and simulated the melting temperatures of the Au–Cu nanoalloys, as well as bulk Au and Cu in good agreement with experimental data. Also, Davoodi and Katouzi⁴⁵ used the QSC potential for the Au–Au, Au–Ni, and Ni–Ni interactions and successfully simulated thermodynamic properties and melting temperatures of the Au–Ni nanoalloys (and bulk Au and Ni) in good agreement with experiment. Akbarzadeh et al.⁴⁶ also used the QSC potential for the Ni–Ni interactions to calculate thermodynamic properties of Ni nanoclusters. Subbaraman and Sankaranarayanan²⁹ also investigated the effect of Ag addition on the thermal characteristics and structural evolution of Ag–Cu–Ni ternary alloy nanoclusters using the QSC potential.

Table 1 Potential parameters used in MD simulations for metal nanoclusters

QSC	ε (eV)	a (Å)	n	m	c
Ni	0.0073767	3.5157	10	5	84.745
Cu	0.0057921	3.6030	10	5	84.843
Au	0.0078052	4.0651	11	8	53.581

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3. Results and discussion

3.1 Thermodynamic properties

We have presented the internal energies for the (Au_x–Cu_y–Ni_y)_N=32,108,256 nanoclusters with the different Au mole fractions (x = 0, 0.1, 0.3, 0.5, 0.7, and 0.9) at different temperatures in the heating process in Fig. 1 (x is for the Au mole fraction and y is for the Cu and Ni mole fractions). According to this figure, we can identify a simple jump in every panel for every nanocluster which indicates the temperature range of the phase transition. Paying attention to these curves we recognized the melting points exactly. The internal energies for the (Au_x–Cu_y–Ni_y)_N=32,108,256 nanoclusters during the cooling process have been also presented in Fig. 1. In order to specify the melting points with more accuracy, the temperature increments in the annealing processes have been reduced to 10 K ns⁻¹ near the melting points, but (because of preventing of plots from crowd), we have shown the heating and cooling processes in Fig. 1 with the rate of 100 K ns⁻¹. We have also presented the internal energies for the (Au_x–Cu_y–Ni_y)_N=32 nanocluster with the different Au mole fractions in heating and cooling processes with the rate of 10 K ns⁻¹ close to the melting points in Fig. S1 in the ESI.† According to Fig. 1 and S1,† a hysteresis (due to the existence of the difference in heating and cooling curves below the melting point temperatures) in the course of the cooling process can be recognized. It is also shown that the hysteresis increases with increasing the Au mole fraction. The presence of hysteresis in melting–freezing transition is not unusual and is expected both theoretically and experimentally, as reported in the cases of different nanoclusters.^6,29,47,48 It is also shown that the melting temperature increases as the size of the nanoalloy increases. This is due to the fact that the smaller nanocluster has the larger surface-to-volume ratio of atoms. Therefore, the smaller nanocluster has smaller cohesive energy and so it has smaller melting temperature than the bigger cluster.

Fig. 1 The internal energies for the (Au_x–Cu_y–Ni_y)_N=32,108,256 nanoclusters with the different Au mole fractions at different temperatures in the heating and cooling processes.

According to Fig. 1, for the (Au_x–Cu_y–Ni_y)_N=32 nanocluster, it is shown that the addition of Au to the Cu–Ni alloy induces thermal stability in the ternary nanoclusters from x = 0 to x = 0.7 and later on that, this addition makes the cluster a little unstable (x = 0.9). In the other words, the most stable composition for the ternary (Au_x–Cu_y–Ni_y)_N=32 nanocluster is at the x = 0.7 and y = 0.15 composition. The increasing of the stability (decreasing of energy) of the nanocluster can be due to the stronger interactions of the Au atoms than the Cu and Ni atoms (Table 1). For the (Au_x–Cu_y–Ni_y)_N=108 nanocluster, the addition of Au to the Cu–Ni alloy makes stable the ternary nanoclusters from x = 0 to x = 0.5. It means that the x = 0.5 and y = 0.25 is the most stable composition for the ternary (Au_x–Cu_y–Ni_y)_N=108 nanocluster. It is also shown that the x = y = 0.33 is the most stable composition for the (Au_x–Cu_y–Ni_y)_N=256 nanoalloy.

To specify the melting points with more accuracy, we have presented the specific heat capacity at constant volume (C_V) for the nanoclusters at different temperatures in the heating process in Fig. 2. According to this figure, the first order phase transition can be identified. We have determined the melting points of the nanoclusters using the heat capacity graphs and presented them in Fig. 3. According to this figure, for the (Au_x–Cu_y–Ni_y)_N=32 nanocluster, the melting temperature increases as the Au mole fraction increases in the ternary nanoclusters from x_Au = 0 to x = 0.7, then the addition of Au decreases a little the melting point (x = 0.9). The maximum melting temperature for the ternary (Au_x–Cu_y–Ni_y)_N=32 nanocluster is at x = 0.7 and y = 0.15 composition. This result is in agreement with the energy results in Fig. 1. In the other words, the addition of Au to the Cu–Ni alloy induces thermal stability in the ternary nanoclusters from x_Au = 0 to x = 0.7, and therefore, increases the melting point. This can be due to the stronger interactions of the Au atoms than the Cu and Ni atoms. For the (Au_x–Cu_y–Ni_y)_N=108 and (Au_x–Cu_y–Ni_y)_N=256 nanoclusters, the maximum of the melting temperatures are at x = 0.5 and x = 0.33 compositions, respectively. These results are also in agreement with the thermal stability of the ternary nanoclusters presented in Fig. 1. According to Fig. 1 to 3, the melting temperature ranges do not exhibit considerable change between x = 0.0 and x = 0.9. This result indicates that melting point of these ternary nanoclusters are more strongly depended on their size not to their composition.

Fig. 2 The specific heat capacity at constant volume (C_V) for the different nanoclusters at different temperatures in the heating process.

Fig. 3 The melting points of the different nanoclusters at different Au mole fractions.

3.2 Structural properties

In order to investigate the structural changes of the ternary nanoclusters during the heating and cooling processes, we have calculated the Au–Au, Au–Ni, Au–Cu, Ni–Ni, Cu–Cu, and Ni–Cu radial distribution functions (RDFs) for the (Au_x–Cu_y–Ni_y)_N=32,108,256 nanoclusters at different Au mole fractions (from x = 0.1 to the Au mole fraction corresponding to the maximum melting point) and presented in Fig. 4, S2, and S4.† According to Fig. 4, the RDF peaks at x = 0.1 in the cooling process are smaller and broader than those of the heating process. This can be due to the fact that after heating and then cooling the nanocluster, it loses the ordered initial structure. It is also shown for the Ni–Ni and Ni–Cu RDFs at x = 0.7 that the peaks in the cooling process are stronger and sharper than those of the heating process. This can be due to the higher degree of structural order (and interactions) between the Ni–Ni and Cu–Ni atoms than the initial structure. It is also shown that the position of the first RDF peaks of similar and dissimilar pairs are very close together. This means that the ternary nanocluster has almost homogeneous structure and it is not seen a core–shell regime for it.

Fig. 4 The different RDFs for the (Au_x–Cu_y–Ni_y)_N=32 nanocluster at initial at 300 K (the solid lines) and at 300 K after cooling process (the dashed lines) at the different Au mole fractions.

According to Fig. 4, the addition of Au to the Cu–Ni alloy from x = 0.1 to x = 0.7 signifies the Ni–Ni and Cu–Ni RDF peaks and also make them sharper. This result indicates a higher degree of structural order and presence of long range order in the ternary nanocluster. This result is also in agreement with the energy and melting point results in Fig. 1 and 3. In the other words, the addition of Au to the Cu–Ni alloy induces thermal stability in the ternary nanoclusters and therefore increases the melting point. It is also shown that the addition of Au to the nanoalloy from x = 0.1 to x = 0.7 shifts the Au–Au, Au–Cu, Au–Ni, and Cu–Cu RDFs to the larger distances. We can also distinguish more peaks at larger distances for the x = 0.7 relative to the x = 0.1. It seems that the increasing of the Au mole fractions shifts them to the outer layers of the ternary nanoalloy. It can be also observed that the first Ni–Ni RDF peak at the x = 0.7 after the cooling process is stronger than that of the Au–Au and Cu–Cu RDFs. In order to examine this point, we have presented the number of the Au, Ni, and Cu surface atoms in the (Au_x–Cu_y–Ni_y)_N=32 nanocluster with the different Au mole fractions in Fig. 5. According to this figure, with increasing the Au mole fraction, the Au surface atoms increase but the Cu and Ni surface atom decrease. This can be also found better if we compare the first RDF peaks in Fig. 4: we observe that Ni–Ni RDF > Cu–Cu RDF > Au–Au RDF. This means that the Au atoms tend to lie at outermost layers, the Ni atoms tend to lie at innermost layers, and the Cu atoms lie between the Ni and Au atoms in the ternary nanocluster. Of course, due to the lack of the core–shell structure, this classification is not very obvious, but it can be distinguished to some extent in Fig. 6 in which we have presented the snapshots of the ternary nanoalloy with the different Au mole fractions at the initial at 300 K, at the melting point, and at 300 K after cooling process. According to Fig. 6, with increasing the Au mole fraction, the Au atoms present in the outer layers but the Ni and Cu atoms present in the inner layers of the nanocluster. It means that Au atoms located at the surface sites of nanoalloys are favorable. This result is in good agreement with previous studies.^49–52 This is mainly attributed to the lower surface energy of Au than Cu and Ni. In addition, the lattice parameters of bulk Au, Cu, and Ni are 4.08, 3.61, and 3.52 Å, respectively, and thus the smaller Ni atoms tend to occupy the center of the cluster and the Au atoms tend to locate on the cluster surface.

Fig. 5 The number of the Au, Ni, and Cu surface atoms in the (Au_x–Cu_y–Ni_y)_N=32 nanocluster at the initial at 300 K (the solid lines) and at 300 K after cooling process (the dashed lines) at the different Au mole fractions.

Fig. 6 The snapshots of the (Au_x–Cu_y–Ni_y)_N=32 ternary nanoalloy with the different Au mole fractions at the initial at 300 K, at the melting point, and at 300 K after cooling process (Cu is in brown, Ni is in blue, and Au is in yellow).

According to Fig. S2,† the RDFs of the bigger cluster, (Au_x–Cu_y–Ni_y)_N=108, develop in the more extended distance than the smaller one, (Au_x–Cu_y–Ni_y)_N=32. This is due to the fact that there are more atomic layers and interactions in the bigger cluster than the smaller one (for example the Au–Au RDF). It is also shown that the position of the first RDF peaks of similar and dissimilar pairs are very close together. This means that the ternary nanocluster has almost homogeneous structure and it is not seen a core–shell regime for it (such as the smaller cluster). According to Fig. S2,† the addition of Au to the Cu–Ni alloy from x = 0.1 to x = 0.5 signifies the first peak of Au–Au RDF but decrease it for other RDFs. Of course the order of Ni–Ni RDF > Cu–Cu RDF > Au–Au RDF for the first peaks also exists. Therefore, the same layering order for the smaller cluster also exists for this bigger one. It is also shown that the addition of Au to the nanoalloy from x = 0.1 to x = 0.5 shifts the different RDFs to the larger distances, especially for Au–Au RDF (i.e. to the outer layers of the ternary nanoalloy). In order to examine this point, we have also presented the number of the Au, Ni, and Cu surface atoms in the (Au_x–Cu_y–Ni_y)_N=108 nanocluster with the different Au mole fractions in Fig. S3.† According to this figure, with increasing the Au mole fraction, the Au surface atoms increase but the Cu and Ni surface atom decrease (such as the Fig. 5). In the other words, as the Au mole fraction increases, the Au atoms tend to lie at outermost layers and so, the Ni and Cu atoms lie at innermost layers. We have also presented the snapshots of the ternary (Au_x–Cu_y–Ni_y)_N=108 nanoalloy with the different Au mole fractions at the initial at 300 K, at the melting point, and at 300 K after cooling process in Fig. 7.

Fig. 7 The snapshots of the (Au_x–Cu_y–Ni_y)_N=108 nanocluster with the different Au mole fractions at the initial at 300 K, at the melting point, and at 300 K after cooling process (Cu is in brown, Ni is in blue, and Au is in yellow).

We have also presented the different RDFs of the (Au_x–Cu_y–Ni_y)_N=256 ternary nanoalloy in Fig. S4.† According to this figure, the addition of Au to the Cu–Ni alloy from x = 0.1 to x = 0.33 signifies the first peak of Au–Au RDF but decrease it for other RDFs. This situation is similar to the (Au_x–Cu_y–Ni_y)_N=108 cluster. Of course, the order of Ni–Ni RDF > Cu–Cu RDF > Au–Au RDF for the first peaks also exists. Therefore, the same layering order exists for all the three ternary nanoalloys. We have also presented the number of the Au, Ni, and Cu surface atoms in the (Au_x–Cu_y–Ni_y)_N=256 nanocluster with the different Au mole fractions in Fig. S5.† Such as the Fig. S3 and S5,† as the Au mole fraction increases, the Au atoms tend to lie at outermost layers and so, the Ni and Cu atoms lie at innermost layers. We have also presented the snapshots of the ternary (Au_x–Cu_y–Ni_y)_N=256 nanoalloy with the different Au mole fractions at the initial at 300 K, at the melting point, and at 300 K after cooling process in Fig. 8. Therefore, by overall considering of RDF plots for simulated nanoclusters in can be concluded that when three miscible metals forms a nanocluster, total and local order regimes can be occurred which depend strongly on the cluster size and composition.

Fig. 8 The snapshots of the (Au_x–Cu_y–Ni_y)_N=256 nanocluster with the different Au mole fractions at the initial at 300 K, at the melting point, and at 300 K after cooling process (Cu is in brown, Ni is in blue, and Au is in yellow).

3.3 Dynamical properties

In order to examine the dynamical changes of the ternary nanoclusters during the heating process, we have calculated the self-diffusion coefficients of the (Au_x–Cu_y–Ni_y)_N=32,108,256 nanoclusters at different Au mole fractions and presented versus temperature in Fig. 9. At lower temperatures, the nanoalloys have solid structures and so, they have very smaller values of the self-diffusion coefficients than those values at higher temperatures. At melting temperatures, the values of diffusion coefficient exhibit a considerable jump in the cluster melting point which this sudden increase of diffusion coefficient for the bigger nanoalloys are more than the smaller sizes because of lower mass and higher mobility of the smaller nanoclusters.

Fig. 9 The self-diffusion coefficients of the (Au_x–Cu_y–Ni_y)_N=32,108,256 nanoclusters at different Au mole fractions.

According to Fig. 9, the bigger clusters has smaller values of the self-diffusion coefficient. This is due to the fact that the surface atoms can move more freely than the atoms in the inner part of nanocluster. Therefore, the bigger nanocluster (which has a small fraction of atoms on its surface) has smaller value of the self-diffusion. It is also shown that as the Au mole fraction increases, the self-diffusion decreases. This is in agreement with our previous results. In the other words, the addition of Au to the Cu–Ni alloy induces thermal stability in the ternary nanoclusters and therefore, decreases the diffusion values. This can be due to the stronger interactions of the Au atoms than the Cu and Ni atoms.

4. Conclusions

In this work, we have investigated the heating and cooling processes of the ternary (Au_x–Cu_y–Ni_y)_N=32,108,256 nanoclusters with the different Au mole fractions (x = 0, 0.1, 0.3, 0.5, 0.7, and 0.9) at different temperatures in the heating and cooling processes. We have examined the effect of addition of Au atoms to Cu–Ni nanoclusters to the different thermodynamic, structural, and dynamical properties and the following important results have been summarized:

(1) According to the energy results, a hysteresis in the course of the cooling process of the nanoclusters can be recognized. It is also shown that the hysteresis increases with increasing the Au mole fraction.

(2) The melting temperature decreases as the size of the nanoalloy decreases. This is due to the fact that the smaller nanocluster has the larger surface-to-volume ratio of atoms.

(3) For the (Au_x–Cu_y–Ni_y)_N=32 nanocluster, the addition of Au to the Cu–Ni alloy induces thermal stability in the ternary nanoclusters from x = 0 to x = 0.7 and later on that, this addition makes the cluster a little unstable (x = 0.9). In the other words, the most stable composition for the ternary (Au_x–Cu_y–Ni_y)_N=32 nanocluster is at x = 0.7 and y = 0.15.

(4) For the (Au_x–Cu_y–Ni_y)_N=108 nanocluster, the addition of Au to the Cu–Ni alloy makes stable the ternary nanoclusters from x = 0 to x = 0.5. It means that the x = 0.5 and y = 0.25 is the most stable composition for the ternary (Au_x–Cu_y–Ni_y)_N=108 nanocluster. It is also shown that the x = y = 0.33 is the most stable composition for the (Au_x–Cu_y–Ni_y)_N=256 nanoalloy.

(5) According to the structural results, the position of the first RDF peaks of similar and dissimilar pairs are very close together. This means that the ternary nanoclusters have almost homogeneous structures and the core–shell regimes cannot be seen for them.

(6) For the (Au_x–Cu_y–Ni_y)_N=32 nanocluster, the addition of Au to the Cu–Ni alloy signifies the RDF peaks and also make them sharper. This result indicates a higher degree of structural order and presence of long range order in the ternary nanocluster which increases the melting point.

(7) The addition of Au to the Cu–Ni nanocluster, shifts the RDFs to the larger distances.

(8) With increasing the Au mole fraction, the Au surface atoms increase but the Cu and Ni surface atom decrease. In the other words, the Au atoms tend to lie at outermost layers and so, Cu and Ni atoms lie at innermost layers.

(9) We observed the following order in the first peak: Ni–Ni RDF > Cu–Cu RDF > Au–Au RDF. This observation approves the layering order described.

(10) For the (Au_x–Cu_y–Ni_y)_N=108,256 nanoclusters, the addition of Au to the Cu–Ni alloy signifies the first peak of Au–Au RDF and shifts the different RDFs to the larger distances. The order of Ni–Ni RDF > Cu–Cu RDF > Au–Au RDF for the first peaks also exists.

(11) At melting temperatures, the values of diffusion coefficient exhibit a considerable jump in the cluster melting point which this sudden increase for the bigger nanoalloys are more than the smaller sizes.

(12) The smaller nanocluster has higher value of the self-diffusion coefficient than the bigger one. This is due to the fact that the surface atoms can move more freely than the atoms in the inner part of nanocluster.

(13) As the Au mole fraction increases, the self-diffusion decreases. This can be due to the stronger interactions of the Au atoms than the Cu and Ni atoms.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra13057g

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