Heating rate effects for the melting transition of Pt–Ag–Au nanoalloys

H¨useyin Yıldırım and Ali Kemal Garip

1Yenice Vocational School,Karabuk University,Karabuk,Turkey

2Department of Physics,Zonguldak Bulent Ecevit University,Zonguldak,Turkey

Keywords: chemical ordering,melting,optimization,nanoalloys

1. Introduction

Geometric shape, chemical ordering, size and composition dependent tunability of nanoalloys makes new nanoscale materials versatile and allows a fine tuning of specific properties such as optical, magnetic, and electronic properties.[1–3]In particular,chemical ordering of nanoalloys can help to design useful and inexpensive cost catalytic materials.[4]Therefore,high symmetry icosahedron nanoalloys organized in concentric core-shell structure are gaining increasing interest in catalysis applications due to the large surface-to-volume ratios that increase catalytic activity.[3,5,6]Also, it is important to know which atoms are located in the shell of a nanoalloy,because the surface strain between the core and shell atoms effects the catalytic activity.[4]In addition, if there is a coreshell nanoalloy in which shell atoms have the desired catalytic effects, it will be necessary to investigate the temperature range in which the nanoalloy remains thermally stable.[7]Some experimental studies in recent years show that Ag and Au surfaces change the catalytic activity. For example,Wanget al.reported that Ag surface segregation enhances the catalytic activity.[8]Liet al.obtained that more surface gold atoms have higher catalytic activity.[9]Christopheret al.studied the Ag (111) and (100) surfaces and found the higher selectivity of Ag (100) surface compared with Ag (111).[10]Zhuet al.examined the Ag (100), (110), (111) and (211)surfaces and found that the catalytic activity varied with the order of(110)>(100)>(111)>(211).[11]Woldu studied the Au (100), (110), and (111) surfaces and found that the (110)surface has the highest catalytic activity.[12]Mouet al.reported that the Au–Ag alloy catalyst has better catalytic activity than Au monometallic catalyst.[13,14]Zhenget al.found that the Au–Ag composition on the surface contributes more to the anaerobic benzyl alcohol dehydrogenation activity than the bulk.[15]

Direct methanol fuel cells(DMFC)and proton exchange membrane(PEM)fuel cells are promising technologies to reduce the dependence on fossil fuel energy due to its high energy conversion efficiency, clean energy and potential largescale applications.[6,16–18]The performance of these fuel cells depends on low cost and the efficiency of the electrocatalysts which is the key component for the oxygen reduction reaction(ORR) and methanol oxidation reaction (MOR) in the PEM and DMFC fuel cells.[16,17,19,20]The most effective electrocatalysts for ORR and MOR are platinum(Pt)based nanoalloys due to their excellent reactivity and stability.[18–20]However,a few major drawbacks associated with Pt as a catalyst are expensive Pt reserves and limited availability.[21,22]Compared to pure and bimetallic Pt catalysts,Pt based ternary catalysts exhibit excellent catalytic activities in ORR and MOR and lower costs.[22,23]In this sense, to integrate Pt with other metals,Pt-based binary[24–27]and ternary[21,28–30]nanocatalysts have been extensively studied experimentally.Especially,crossover nanoalloys between the catalytically active group 10 (Ni, Pd,Pt) and the less active group 11 (Cu, Ag, Au) are important due to the fact that they can vary their surface structures and catalytic activity.[3,31]Moreover, adding Pt to Ag–Au binary nanoalloys dramatically increases the catalytic activity.[32]Some experimental results have shown that Pt–Ag–Au ternary nanoalloys have improved catalytic activity.[21,33]Therefore,investigation of the structural and thermodynamic properties of Pt–Ag–Au ternary nanoalloys is important for future experimental studies in terms of their chemical and physical properties.

The reason for concentrating here on icosahedron structure is because the selected motif has highest symmetry of all discrete point groups and is only found in small clusters with a high surface to volume ratio.[34]Researchers chose 55-atom icosahedron as the model for the ternary nanoalloys due to the high symmetry and remarkable stabilization.[34,35]Furthermore,55 is a geometric magic number for icosahedron structures that have quasi-spherical shape and close-packed surface,and exhibit significant structural and electronic stability.[3,5]Although structural and dynamic properties of pure, binary and ternary nanoalloys with Pt, Ag and Au with 55 atoms have been investigated in detail,[3–7,36–44]there is still lacking of studies of heating rate effects on melting process, and structural properties of Pt–Ag–Au ternary core-shell nanoalloys with 55 atoms.

Thus, in this study the structural properties and heating rate effect on the melting behaviors of 55-atom icosahedron Pt13AgnAu42−n(n=0–42)ternary nanoalloys are investigated systematically. The platinum atom number is fixed at 13 and the silver and gold atom numbers are varied for all other compositions. As a result of the structural optimization of 55-atom Pt13AgnAu42−n(n=0–42) ternary nanoalloys, the most stable composition is found. Then, in order to present the heating rate effect on the melting behaviors in detail,three different icosahedron compositions corresponding to Pt13Ag42, the most stable composition of Pt13AgnAu42−n(n=0–42)ternary nanoalloys and Pt13Au42are selected.Thus,melting processes of Ag-rich, Au-rich and the most stable compositions are investigated.

2. Material and methods

The most stable chemical ordering of Pt13AgnAu42−n(n=0–42) ternary nanoalloys was obtained with the GMIN program[45]using the Basin–Hopping algorithm. The local relaxations for optimizing the chemical ordering were performed. The interatomic interactions were modeled by the Gupta potential[46,47]and Gupta parameters are given in Table 1.[48]

Table 1. The Gupta potential parameters for Pt–Ag–Au ternary nanoalloys.

The melting behaviors of nanoalloys were carried out by molecular dynamics (MD) simulations under canonical ensemble(NVT)conditions. All MD simulations have been carried out using the DL POLY 4 package.[49,50]The temperature was controlled by an Andersen thermostat with a relaxation time of 1.0 ps. Each nanoalloy was heated from 0 K to 1300 K with a temperature increment of 5 K. The best chemical ordering structures obtained as a result of the optimization of Pt13AgnAu42−n(n=0–42) ternary nanoalloys were taken as the initial configurations for MD simulations,and the melting temperatures of the nanoalloys were obtained to be dependent on the heating rate. Newton’s equations of motion were integrated in 400000 steps using the velocity Verlet algorithm with 0.003 ps,0.005 ps and 0.008 ps time steps. These simulation setups corresponds to a heating rate of 4.2 K/ns,2.5 K/ns and 1.6 K/ns,respectively. To realize thermal equilibrium in MD,the total relaxation times for 1.6 K/ns, 2.5 K/ns and 4.2 K/ns heating rates are 3200 ps,2000 ps and 1200 ps,respectively.

3. Results and discussion

In the current study, optimizing the chemical ordering was performed using the Basin–Hopping algorithm for 55-atom Pt13AgnAu42−n(n=0–42) ternary nanoalloys with an icosahedron structure. We mainly concentrate here on the Pt13AgnAu42−n(n=0–42)nanoalloys with fixed 13 Pt atoms where the fixed number 13 represents inner atoms of the 55-atom core-shell icosahedron structure.

Mixing energy(Emix)analysis is a useful analysis method to the energetic stability among a family of nanoalloys with respect to composition.Emixis defined as[5,51]

whereE(Pt13AgnAu42−n) represents the total energy of the ternary nanoalloy,E(Pt13Ag42) andE(Pt13Au42) represent the total energies of the bimetallic Pt–Ag and Pt–Au nanoalloys. Among all the compositions of nanoalloys,the structure in which the mixing energy takes the minimum value is more stable than the others. The mixing energies of Pt13AgnAu42−n(n=0–42)nanoalloys as a function of the number of Ag atoms(n)are shown in Fig.1. From the mixing energy analysis,the lowest mixing energy value was obtained at the composition of Pt13Ag21Au21in Pt13AgnAu42−n(n=0–42)nanoalloys. In Fig.1,blue,gray and yellow spheres represent platinum,silver and gold atoms,respectively.

Also,comparing the changing tendency of the number of Ag–Au bonds and the mixing energies as a function of Ag atoms in Fig.1,we find that the two tendencies are adverse. In other words,the structures which contain more Ag–Au bonds have lower mixing energies. This result indicates that composition with more Ag–Au bonds is more stable.

Fig. 1. Mixing energy variation and the number of Ag–Au bonds in Pt13AgnAu42−n (n=0–42)nanoalloys as a function of Ag atoms.

In order to better discuss the atomic mixing degree of different types of atoms in Pt–Ag–Au nanoalloys, the order parameter(RA)[4]is adopted.RAcan be defined by the average distance of a type of atoms from the center of a cluster

wherenAis the number of atoms in each type in the ternary nanoalloys, andxi,yiandzishow the positions of the atoms.LargeRvalues indicate that the atoms are at the shell, while smallRvalues indicate that the atoms are located in the core.

Fig.2. The order parameter(R)variation of Pt13AgnAu42−n(n=0–42)nanoalloys.

From Fig. 3, it can be seen thatRAgandRAuare larger thanRPtfor all compositions,indicating that the locating tendencies of Ag and Au atoms to segregate to the shell and Pt atoms prefer to locate at core. Forn=1–12,RAgparameter keeps constant as 12 Ag atoms occupying the central sites of the shell. Forn=13–41,with the increase of Ag atoms,RAgdecreases gradually and becomes closer toRAuwhileRAualmost remains constant. In addition, forn=1–41,RPtalmost remains constant. This means that the Pt atoms located at the core and Ag and Au atoms prefer to mix at the shell. Also,the segregation degrees of Pt, Ag and Au atoms in 55-atom Pt–Ag–Au ternary nanoalloys are mainly dependent on their surface energies,cohesive energies and atomic radii.

Table 2. Properties of Pt,Ag and Au.[31]

Owing to the large surface energy and cohesive energy,Pt atoms prefer to located in the core,while Ag and Au atoms prefer to locate on the shell as they have smaller surface energy and cohesive energy, in Pt13Ag42and Pt13Au42nanoalloys,respectively. Similarly,the core segregation of Pt is also associated with the lower atomic radius of Pt compared with Ag and Au. As a result,the Ag and Au atoms on the shell and the segregation of Pt atoms at the core enable minimization of the nanoalloy surface energy. The optimization results in general support the Ptcore(AgAu)shellthat is proposed in this study.Also,Pacheco-Contreraset al.found the similar results for 13-and 19-atom icosahedron ternary Ag–Au–Pt nanoalloys.[48]

The melting temperature of a nanoalloy can be estimated by MD simulations. Also, the heating rate in MD simulations effects the melting transition of nanoalloys.[52]In this study,MD simulations were performed at three different heating rates for 55 atom Pt13Ag42, Pt13Ag21Au21and Pt13Au42nanoalloys to investigate the effect of heating rate on the melting transition. The literature values of heating rate vary between 0.8 and 100 K/ns.[53–57]In the literature, the melting dynamics of the nanoalloy consisting of gold and silver atoms have studied with a heating rate of 10 K/ns.[54]In the present study, the heating rates were used as 1.6 K/ns, 2.5 K/ns and 4.2 K/ns. The caloric curve and the Lindemann index were used to clarify the melting transition.

The caloric curve and Lindemann index are commonly used in MD simulations to investigate melting behavior of nanoalloys. The caloric curve represents the total energy as a function of temperature and, melting temperature of the nanoalloy corresponds to distinguishable increase in total energy.[7]The melting temperatures of nanoalloys obtained from the caloric curve were also supported with the Lindemann index criteria. When the index is in the range of about 0.1–0.15,the melting occurs in nanoalloys,whereas the critical value can vary between 0.05–0.20 due to,e.g.,the nature of interactions between atoms,the magnitude of quantum effects and the crystal structure.[5]For each layer,the Lindemann index is expressed as follows:[58,59]

whereNL(i)is the atom numbers in thei-th layer.rjkis the distance between thej-th andk-th atoms. The 55-atom icosahedron nanoalloy consists of three layers starting from its center of mass. The 55-atom icosahedron nanoalloys have a single atom in the first layer, 12 atoms in the following second layer, and 42 atoms in the third layer.[7,44]The caloric curve and Lindemann index vary as a function of temperature during the heating processes for Pt13Au42, Pt13Ag21Au21, Pt13Ag42nanoalloys with different heating rates,as shown in Figs.3,5 and 6,respectively.

The caloric curve and Lindemann index of Pt13Au42nanoalloys at heating rates of 1.6 K/ns,2.5 K/ns vs. 4.2 K/ns,respectively, are shown in Fig. 3. In Fig. 3(a), the melting temperature of Pt13Au42nanoalloy is 703 K due to the sudden jump in total energy. Pt13Au42nanoalloy in Fig.3(a)has dangling surface Au atoms at some temperatures according to Fig.4(a). The dangling of these atoms effects the Lindemann index.The behaviors of the Lindemann index of each layer for Pt13Au42and Pt13Ag21Au21are given in Fig.4 to understand the melting mechanism with respect to layers. As shown in Fig. 4(a), the Lindemann index of the atoms on the shell of the nanalloy is greater than atoms in the core of the nanoalloy,which indicates that the shell atoms have large amplitude from their original lattice positions while the core atoms of nanoalloys remain their original lattice positions. It is also evident that an increase in temperature (595 K and 640 K)leads to a dangling in shell atoms. For Pt13Au42nanoalloys in 2.5 K/ns and 4.2 K/ns heating rates,variations of the caloric curve and Lindemann index occur within a temperature range.Figures 3(b)and 3(c)show that this temperature range is small(60 K) for the heating rate of 4.2 K/ns and large (75 K) for the heating rate of 2.5 K/ns. Also, caloric curves and Lindemann indexes have abrupt changes in melting transition for the heating rates of 2.5 K/ns and 4.2 K/ns. This situation indicates that there is an isomerization caused by solid-liquid and liquid-solid transitions during the melting transition.

Fig.3. The caloric curve and Lindemann index variation for Pt13Au42 nanoalloys at(a)1.6 K/ns,(b)2.5 K/ns and(c)4.2 K/ns heating rates.

Fig. 4. Behavior of the layered Lindemann index for (a) Pt13Au42 and (b) Pt13Ag21Au21 nanoalloys at 1.6 K/ns heating rate with respect to temperature.

Figure 5 shows the caloric curve and Lindemann index of Pt13Ag21Au21nanoalloys at heating rates of 1.6 K/ns,2.5 K/ns and 4.2 K/ns, respectively. According to Figs. 5(a)–5(c), the melting temperature of the Pt13Ag21Au21nanoalloys is 698 K,678 K, and 709 K due to the sudden jump in the Lindemann index and caloric curves. As shown in Fig. 5, melting temperature of Pt13Ag21Au21is lowest(678 K)in heating rate 2.5 K/ns. Also, there is no isomerization in Figs. 5(a)–5(c). The common characteristic of Pt13Ag21Au21nanoalloys with different heating rates is that they have dangling surface atoms before reaching the melting temperature. As shown in Fig.4(b),it is observed that there are small movements in the Lindemann index and caloric curve because the melting sign of Pt13Ag21Au21nanoalloy starts from the surface.

The caloric curve and Lindemann index of Pt13Ag42nanoalloys at heating rates of 1.6 K/ns,2.5 K/ns and 4.2 K/ns,respectively, are shown in Fig. 6. The common characteristic of Pt13Ag42nanoalloys with different heating rates is that melting takes place within a temperature range. According to the Lindemann index in Fig. 6(a), the melting of Pt13Ag42nanoalloy occurs between 668 K and 750 K, and there is an on-going isomerization in a range of 82 K.This is the smallest isomerization range for 55-atom Pt13Ag42nanoalloys. As shown in Fig.6(b),when the heating rate is 2.5 K/ns,the isomerization range is 168 K. There is a solid–liquid transition between 632 K and 800 K.In this temperature range of 168 K,the nanoalloy passed into the liquid phase and then turned into the solid phase again. This is the largest isomerization range for 55-atom Pt13Ag42nanoalloys. In addition,when the heating rate is 4.2 K/ns, the isomerization range is 146 K. There is a solid-liquid transition between 708 K and 854 K.As a result,the temperature range where melting occurs are varies at different heating rate for Pt13Ag42nanoalloys.

Fig.5. The caloric curve and Lindemann index variation for Pt13Ag21Au21 nanoalloys at(a)1.6 K/ns,(b)2.5 K/ns and(c)4.2 K/ns heating rates.

Fig.6. The caloric curve and Lindemann index variation for Pt13Ag42 nanoalloys at(a)1.6 K/ns,(b)2.5 K/ns and(c)4.2 K/ns heating rates.

In order to investigate the size effect, we selected some compositions for 147 and 309 atom clusters.The melting transitions have been examined by the caloric curves and Lindemann index variations for 400000 MD steps. The results are shown in Figs.7 and 8.The outstanding behavior is the sudden jump behavior for selected Pt–Au and Pt–Ag–Au nanoalloys with 55,147 and 309 atoms. There are other melting mechanisms which do not include sudden jump behavior,and a few examples are given in Figs.3(b),3(c),6(a),6(b),and 6(c). In addition, the melting temperatures of the 147 and 309 atoms were found to be relatively higher for the examined compositions as seen from Figs.7 and 8.

Fig.7. The caloric curve and Lindemann index variation for nanoalloys of(a)Pt55Au92,(b)Pt55Ag46Au46,and(c)Pt55Ag92.

Fig.8. The caloric curve and Lindemann index variation for nanoalloys of(a)Pt147Au162,(b)Pt147Ag81Au81,and(c)Pt147Ag162.

The composition effect on the melting temperatures has been examined for 55-atom Pt–Ag–Au nanoalloys.The results are given in Fig. 9. It is found that the melting temperatures fluctuate between 653 K and 721 K depending on the composition. In this fluctuation,the highest and lowest melting temperatures belong to Pt13Ag7Au35and Pt13Ag8Au34compositions, respectively. In addition, two different melting mechanisms have been observed in binary nanoalloys as in ternary nanoalloys.

Fig. 9. The caloric curve and Lindemann index variation for Pt13AgnAu42−n nanoalloys.

We used the Ackland–Jones analysis to see the structural changes (isomerization) during melting transitions of Pt13Au42and Pt13Ag42nanoalloys.The Ackland–Jones analysis is a tool to distinguish ICO,BCC,HCP,and FCC coordination structures based on analysis of the distribution of angles formed by the pairs of neighbors of a central atom.[60–62]In this method, at beginning, inner shell atoms of nanoalloy are described as HCP coordinated and all surface atoms are described as disordered.

We chose the configurations with isomerization which characterizes the structural evolution. The Ackland–Jones analysis of the configurations which are corresponding to Pt13Au42and Pt13Ag42compositions is presented in Tables 3 and 4, respectively. When we analyze the tables with the melting transition,the number of HCP coordinated atoms decreases and the number of disordered atoms increases. While this change in HCP coordinated atoms is slower in Pt13Au42nanoalloys, it is abruptly decreased in Pt13Ag42nanoalloys.Transitions from HCP coordinated atoms to BCC and FCC coordinated atoms correspond to isomerization at temperatures determined with the Lindemann criterion where the melting transition occurs. During the melting transition, the number of HCP coordinated atoms decreases and the number of BCC coordinated atoms changes. We also see that the number of FCC coordinated atoms varies slightly. This clearly shows that some of the HCP coordinated atoms change their local structure to BCC and FCC coordinations,as we do not see any important change in disordered atoms. In general,disordered atoms also dominate after the melting transitions.

Table 3. Structural evolution through the Lindemann index of Pt13Au42 nanoalloy in different heating rates.

Table 4. Structural evolution through the Lindemann index of Pt13Ag42 nanoalloy in different heating rates.

4. Conclusions

In summary,we have performed a theoretical study of different compositions of icosahedral Pt–Ag–Au ternary nanoalloys using many-body Gupta potential. Using the chemical ordering optimization results of Pt13AgnAu42−n(n= 0–42)nanoalloys, we have performed bond number and mixing energy analysis. The results show that the most stable composition is Pt13Ag21Au21, which has the lowest mixing energy with highest number of Ag–Au bonds. Also,order parameter analysis indicates that Ag and Au atoms generally segregate at the shell and Pt atoms locate at the core of the nanoalloys, which is further explained by the atomic radius, surface energy and cohesive energy of bulk values of those elements. The chemical ordering optimization results in general support the Ptcore(AgAu)shell, which is proposed in this study. MD simulations are used to investigate the heating rate effect on the melting transition of Pt13Au42,Pt13Ag21Au21and Pt13Ag42ternary nanoalloys under NVT conditions.Also,in order to investigate the size effect, MD simulations of selected some compositions for 147 and 309 atom clusters have been performed. The melting transitions of selected Pt–Ag–Au nanoalloys are explored using caloric curves and Lindemann parameters. There have been two identified types of melting mechanisms, one includes sudden jump behavior in the caloric curve and the other includes some isomerisation through melting transition. A detailed investigation for melting transitions for the first type shows that just before transition temperature the surface atoms begin to dangle before core atoms.The temperature range in which the isomerization takes place depends on the heating rate value.Also,the melting temperatures of the 147 and 309 atoms are found to be relatively higher than 55 atoms for the examined compositions. In addition,the simulation results show that the melting temperatures of Pt13AgnAu42−n(n=0–42)nanoalloys fluctuate,depending on the composition. These results are of great importance for multifunctional properties of Pt–Ag–Au ternary nanoalloys.

Acknowledgement

DLPOLY 4 is a molecular dynamics simulation package written by I. T. Todorov and W. Smith, and has been obtained from STFC’s Daresbury Laboratory via the website http://www.ccp5.ac.uk/DLPOLY.