Global Minimum Structures and Magic Clusters of CumAgn Nanoalloys

ARTICLE pubs.acs.org/JPCC

Global Minimum Structures and Magic Clusters of CumAgn Nanoalloys Mohammad Molayem,* Valeri G. Grigoryan, and Michael Springborg Physical and Theoretical Chemistry, Saarland University, D-66123, Saarbr€ucken, Germany ABSTRACT:

The putative global minimum structures of bimetallic CumAgn nanoalloys for all (m,n) with N = m + n from 2 to 60 atoms have been determined. The embedded-atom method was used for the description of the interatomic interactions in combination with the basin-hopping algorithm for the global structural optimization. The obtained global-minimum structures are mostly based on icosahedra, polyicosahedra as well as 5-fold pancakes. But also truncated octahedral are found for some clusters with 38 atoms. The bond-order parameter reveals the formation of CucoreAgshell clusters. The analysis of energetic properties, through stability functions, the excess and the mixing energies, gives that the clusters with more Ag atoms are energetically more favorable. Moreover, from our analysis we identify the most stable stoichiometries as a function of N. Finally, the results of the present study are compared with similar results on NimAgn clusters.

I. INTRODUCTION The aggregation on the nanoscale of two or more types of metal atoms results in structures called nanoalloys or alloyed clusters. Similar to their pure and homogeneous counterparts, these structures show very interesting properties with a nontrivial size dependence, which originate from their quantum-size effects and large surface/volume ratio and which are important for potential applications in catalysis and optics.13 For alloyed clusters one has an additional parameter that can be varied, i.e., not only the size but also the composition. Thereby it can become possible to use these systems as adjustable building blocks for nanodevices. However, this requires a detailed understanding of the relation between size and stoichiometry of the alloyed clusters on the one side and their properties on the other. The first and main step in understanding their properties is the determination of their structures. To this end, computational methods can provide valuable information. However, detailed computational studies face serious difficulties due to the huge number of possible structures of the nanoalloys, so that the potential energy surface (PES) is very complicated. In fact, even for a pure cluster the number of local total-energy minima grows exponentially with the total number of atoms, N. For bimetallic clusters the additional complexity due to the existence of homotops shows up. Homotops are AmBn clusters with the same number of atoms (N = m + n) and compositions (m/n) that have r 2011 American Chemical Society

similar geometries but different arrangements of the atoms. By considering an AmBn nanoalloy, the different possible homotops counts as (N!)/(m!n!).1 Despite these difficulties, some results for nanoalloys have appeared during the recent years (see ref 1 and citations therein). It has been suggested (see, e.g., ref 4) that differences in the strength of the chemical bonds, in the WignerSeitz radii, and in the bulk surface energies are important parameters in determining which types of structures will result for a given nanoalloy. In a recent study4 we considered NimAgn clusters using an approach similar to the one we shall use in the present paper for CumAgn clusters. The atomic radii for Ni, Cu, and Ag are 1.245, 1.28, and 1.445 Å, respectively, whereas the cohesive energies for their crystal structures are 4.44, 3.49, and 2.95 eV/atom, respectively, and the surface energies equal 149, 113.9, and 78.0 meV/Å2, respectively.1 Thus, these three parameters are much more similar for Cu and Ag than they are for Ni and Ag. In order to study how chemical similarity (or difference) affects the properties of the nanoalloys, it is the purpose of the present work to extend our earlier studied system of chemically two quite different elements to one of two much more similar elements. Received: May 30, 2011 Revised: September 11, 2011 Published: September 19, 2011 22148

dx.doi.org/10.1021/jp2050417 | J. Phys. Chem. C 2011, 115, 22148–22162

The Journal of Physical Chemistry C At first, it might be suggested that the similarity will lead to an increased mixing, but only more detailed studies can reveal whether this simple prediction is true. Coppersilver clusters have been the subject of some earlier studies. Thus, CushellAgcore clusters have been produced in Cu and Ag sulfate solutions5,6 and also by using thermal evaporation methods.7 On the other hand, sequential deposition of Cu and Ag on an amorphous substrate resulted in clusters with Cu forming the core and Ag the shell.8 Mass spectroscopy experiments on cationic Cu1Agn+ clusters were found to be in agreement with predictions based on the jellium model according to which particularly stable structures are found for n = 8, 20, 34, 40, and 58.9 Out of the many different chemical orderings that are possible for alloyed clusters, the formation of coreshell structure for CuAg clusters is in agreement with the properties of the pure Cu and Ag,1 i.e., the surface energies, the relative strength of homo- and heteroatomic bonds, the bulk lattice parameters and the atomic sizes, and the relative miscibility or immiscibility of the atomic species. Coreshell structures can form when the size mismatch between the atomic species is large. Then the core of the nanoalloy will be formed by that element that has the higher surface energy and the stronger homoatomic bonds. If the core element has also smaller atomic size, the formation of icosahedral motifs will be favored. This can be explained through the release of strain when the core is occupied by the smaller atoms.2,1012 On top of this, quantum effects may play a role, too. For example, electronic shell closure effects have been shown by Barcaro et al. for CuAg nanoalloys of size N = 40, which is a magic size according to the jellium model.13 For this cluster size, different structural motifs are possible, but since the shell closure occurs for the 5-fold pancake geometry, this is the one of the lowest total energy. Theoretical studies of the global total-energy minima structures for CuAg clusters were mostly carried through using the Gupta potential or the second moment approximation to the tight binding (SMATB) method.3,1315 Such studies have been performed for clusters with N = 34, 38, 40,3,13,14 as well as N = 98 atoms.15 In all of these studies genetic algorithms (GA) were employed for the global optimization, with the study of Barcaro et al.13 being the only exception. These authors applied three different algorithms, i.e., the basin-hopping (BH) method, the energy-landscape paving method, and the parallel excitable walkers method in determining the structures of the global total-energy minima. The most stable clusters were predicted to have coreshell polyicosahedra structures. A polyicosahedra (pIh) structure is formed by multi-interpenetrating 13-atomic icosahedra (Ih13). The results predicted that the Cu7Ag27 cluster is the most stable one for N = 34. This is the only cluster of this size for which a complete pentagonal bipyramid of Cu atoms can be formed in the core and be covered by a layer of Ag atoms as the shell. Different studies have focused on different stoichiometries of CuAg nanoalloys for N = 38. These include the studies of Rossi et al.3 and of Rapallo et al.14 who found that Cu8Ag30 is particularly stable (i.e., is a so-called magic cluster). On the other hand, Nu~ nez and Johnston found Cu9Ag29 to be the magic cluster for this size.15 For N = 40, different motifs have been found as the global minimum (GM) structures, including capped decahedral (c-Dh) and capped 5- or 6-fold pancakes (c-pc5 or c-pc6).13,16 The c-pc5 Cu13Ag27 was found to be particularly stable according to its formation energy or the so-called excess energy.

ARTICLE

The GM structures of CuAg clusters with N = 98 are quite different from those of palladiumplatinum and platinum aluminum nanoalloys. Leary tetrahedra were predicted as the GM of the PdPt and PtAl clusters,17,18 while different types of icosahedron structures, i.e., incomplete anti-Mackay, Mackay, and polyicosahedron, were found for CuAg nanoalloys.15 Parameter-free density functional theory (DFT) methods have also been applied to CuAg clusters. These calculations have identified a jellium shell-closure effect for N = 34 and 40 through a large gap between highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO, respectively). Also the particular stability of c-pc5 Cu7Ag27, pIh Cu8Ag30, and c-pc5 Cu13Ag27 clusters was found through DFT studies.3,16,19 Different types of icosahedra have also been proposed recently for some selected but quite large sizes of CuAg clusters.20 The favorable structure were anti-Mackay icosahedra for Cu55Ag72 and Cu147Ag132 and chiral icosahedra for Cu309Ag200 and Cu561Ag312. For small CumAg (m = 1 7) clusters detailed studies of structural and vibrational properties have been performed using DFT for both cationic and neutral systems.21 The formation of three-dimensional geometries was seen at m > 6 for neutral clusters while for cationic ones it occurred already for m > 5. A DFT study of the properties of Cu7Ag27 clusters in comparison to CuAg bulk alloys showed that a hierarchy of bond strengths is the key factor in determining the global minimum structures.22 From molecular dynamic simulations it has been found that at intermediate to high temperatures (300600 K) the deposition of Ag on Cu will result in perfect coreshell structures.23,24 It was also shown that a face-centered cubic core of Ag can result in the formation of AgCuAg multishell structures at different temperature ranges, but by deposition on Ih cores only core shell structures are obtained.25 Large nanoalloys with some hundreds to thousands of atoms have been studied numerically by using lattice gas models. Segregation isotherms were determined for cuboctahedral and icosahedral lattices.26,27 Various stages of segregation phases in CuAg clusters were also found for different Ag concentrations.28 Despite the many computational studies for CuAg nanoalloys only a few selected sizes have been studied systematically, and their structures are well-known in only a few cases. A complete understanding of clusters requires a complete knowledge of their structures. However, a global structure optimization for a large set of sizes and/or stoichiometries cannot be obtained through ab initio calculations. Instead, putative global minimum structures can be obtained by using model potentials. Ultimately, these structures can be studied more precisely with the help of first-principles methods,16 which, however, is beyond the scope of the present work. Instead we shall study the development of structural and energetic properties as a function of size and stoichiometry for all stoichiometries of CumAgn clusters for N = m + n between 2 and 60. We use the embedded atom method (EAM) for the description of the interatomic interactions.29 This approach is combined with the basin-hopping (BH) global structure-optimization algorithm.30 The results are subsequently thoroughly analyzed by using different tools in order to identify particularly stable clusters, structural motifs, and mixing patterns. The stability of a given cluster is studied by comparing its total energy either with those of stoichiometric neighbors by using stability functions or with those of all other clusters of the same size. Also other analytical tools like the bond-order parameter 22149

dx.doi.org/10.1021/jp2050417 |J. Phys. Chem. C 2011, 115, 22148–22162

The Journal of Physical Chemistry C and the mixing energies are used to study the properties of the CuAg nanoalloys. Finally, we shall throughout the paper compare with the results from our earlier study on NimAgn clusters.4 The remaining parts of the paper are organized as follows. In section II, a brief description of the potential model and the global optimization method is presented. Section III contains our results and discussion. Finally, our conclusions are summarized in section IV.

II. CALCULATIONS Total-Energy Expression. In the present study, all global optimization studies on CuAg clusters were performed using the EAM model in describing the interatomic interactions. The EAM was originally developed by Daw and Baskes29,31 and has been applied successfully to various metallic systems.29,3133 Also metallic clusters have been studied successfully with the EAM, and a good agreement with available experimental data was found.3439 Within this method, any atom is considered as an impurity embedded in a host comprising all the other atoms. The energy of this atom becomes then a functional of the electron density, Fhi , provided by the other (host) atoms at its position. Thereby, the total energy of the system of interest contains one term that is the sum of the embedding energies of its individual atoms. In addition to this a correction due to the corecore interactions must be included. This takes the form of short-ranged pair potentials. Accordingly, the functional form of the total energy for an N-atomic system relative to the noninteracting atoms is given by31 2 3 N N 1 4Fi ðFh Þ þ E¼ Φij ðrij Þ5 ð1Þ i 2 j ¼ 1, ði6¼ jÞ i¼1

∑

∑

Here, Fi(Fhi ) is the embedding energy and Φij(rij) is the pair potential between atoms i and j with an interatomic distance of rij. The values of the parameters of the embedding functions and pair potentials are determined by fitting to experimental data of the bulk system, including heat of solution, elastic constants, and sublimation and vacancy-formation energies. An important advantage of the EAM is that the embedding functions depend only on the local electron densities but not on the type of atoms which provide those densities. As a technical detail we add that for computational/mathematical reasons it is important that the pair potentials are continuous and differentiable. We have taken care of this by extrapolating those beyond their cutoff distances. This extrapolation does not affect the conclusions of our results. We use a geometric mean of the pure pair potentials in order to obtain the heteroatomic ones,32 i.e. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2Þ ΦAB ðrÞ ¼ ΦAA ðrÞ 3 ΦBB ðrÞ The same parametrization has also been used by different authors for potentials based on second moment approximation to the tight binding method,14,15,24 and it was found that an average value of homoatomic parameters for the heteroatomic interactions yields a good agreement to experimental data.40 Additionally, the validity of this selection was also checked generally for various types of (pair) potentials, and the accuracy of it was found to be about 1%.41

ARTICLE

The constraints on pair potentials require them to change monotonically and vanish beyond certain distances. We used cutoff distances equal to 4.95 and 5.55 Å for Cu and Ag, respectively. Evaluation of heteroatomic interactions shows the smaller cutoff is large enough for them to turn off. Therefore the cutoff distances considered for these heteroatomic interactions were set to the smallest value of the homoatomic interactions. By this selection the following cases are possible for each pair of atoms i and j: (i) rij g rAg cut, then no interactions and no contributions of electron density at sites i and j; (ii) rij e rCu cut, the atoms interact with each other and both contribute electron density at the site of the other one. Four other cases are also Ag possible when rCu cut < rij < rcut; (iii) i = Cu, j = Cu, the case is similar to (i); (iv) i = Ag, j = Ag, then it is as (ii); (v) for i = Cu, j = Ag, there are no interactions between atoms, atom j contributes electron density at site i, contribution to the total energy via embedding function Fi(Fhi ) (eq 1); (vi) i = Ag, j = Cu, the atoms do not interact, atom i contributes electron density at site j, contribution to the total energy via the embedding function Fj(Fhj ) (eq 1). This approach has been tested by us in our previous studies4,39 and is consistent with the original EAM method. Global Optimization Method. The basin-hopping (BH) algorithm, which we use to determine the global minimum structures of CuAg clusters, is a stochastic global optimization method based on Monte Carlo simulations and was developed by the Wales group.30,42,43 It has been found that this method is able to identify the structures of the global total-energy minima for many different types of systems including atomic and molecular clusters and both for pure30 and binary clusters.4447 With the BH method, the complex PES of the system under study is mapped onto a simpler surface for which the energy is stepwise a constant. Thus, the value of this energy for a given structure is taken as the total energy that is obtained after relaxing the structure to its nearest local total-energy minimum structure. Subsequently, a Monte Carlo simulation is performed on this transformed total-energy surface. Then in each Monte Carlo step a new structure is accepted if its energy, Enew, is lower than the previous one, Eold, or otherwise with a probability given by exp[(Eold Enew)/kBT]. The nonphysical temperature T is an adjustable parameter and should not be confused with an annealing temperature. In addition, an acceptance ratio is used that defines the number of accepted trials. For this, we use the commonly used value of 1/2. Both the finite probability of leaving a given funnel and the fact that we, in addition, use slightly changed coordinates as starting point of each iteration help in increasing the possibility that we ultimately will identify the structure of the global total-energy minimum. Finally, the value of the temperature T that is used in the Monte Carlo search was set so that for pure Ag clusters we could identify the (known) structures of the global total-energy minima with the lowest computational time. Thereby, we found T = 0.8 to be a good value. Subsequently, we performed 5000 Monte Carlo iterations for each bimetallic cluster to find the GM. In all cases, the starting configuration was completely random.

III. RESULTS AND DISCUSSION Structural Properties. Structural Motifs and Growth Pattern. We find different types of structures for the GM, although they all are based on icosahedral geometries. These are the 13-atom 22150


The Journal of Physical Chemistry C

ARTICLE

Figure 1. Structures of some CumAgn nanoalloys with different compositions (m,n). Dark red and gray spheres represent Cu and Ag atoms, respectively.

icosahedron (Ih13), the 19-atom double icosahedron (Ih19), the caped 5-fold pancake structures with 34 and 39 atoms (c-pc534 and c-pc539), the 6-fold pancake with 40 atoms (c-pc640), the 55atom icosahedron (Ih55), and polyicosahedron structures that are made of multi-interpenetrating Ih13 motifs. A pancake is a structure consisting of pentagons or hexagons caped with two single atoms at both ends. Accordingly, the c-pc534 structure contains layers of 1 + 5 + 1 + 5 + 10 + 5 + 1 + 5 + 1 atoms and the c-pc539 has 1 + 5 + 1 + 10 + 5 + 10 + 1 + 5 + 1 atoms. Both of these structures are fragments of the Ih55 structure. The c-pc640 structure with 1 + 6 + 6 + 1 + 12 + 1 + 6 + 6 + 1 atoms consists of

six Ih13 icosahedra for which each pair have common atoms and for which the two atoms on the symmetry axis are shared by all icosahedra. Figure 1 shows putative GM structures of some selected CumAgn clusters. For all clusters with 13 atoms we find the GM structure to be based on the Ih13, although in many cases they possess some distortions due to the differences in the bond lengths (AgAg > CuAg > CuCu). This structure forms the core for all putative global minimum structures of larger clusters. New atoms are added to the T sites, i.e., the top center of the triangular faces formed by the atoms of the inner shell, and the 22151



ARTICLE

Figure 2. The bond order parameter as a function of composition (number of Cu atoms, m) for the global minima of five sizes (N = 34, 38, 39, 55, and 60) of CuAg clusters. The inserts show the number of the three possible types of bonds versus m. Solid squares and triangles refer to the numbers of CuCu and AgAg bonds, respectively, whereas open circles are for the number of CuAg bonds.

second icosahedron is formed at N = 19. This growth continues through the formation of new Ih13 icosahedra on the sides of the Ih19. The next, symmetric structure is formed for some clusters with N = 34. The GM structure of smaller clusters, 23 < N < 34, belong to the pIh category. However, an incomplete part of the c-pc534 motif is also formed for many clusters in this range. The GM structures of clusters with N = 34 and m = 515 are c-pc534, but again, differences in the atomic sizes lead in many cases to distortions from a perfect 5-fold pancake. All other clusters of this size are pIh. The c-pc534 is also formed for many clusters with N > 34, but the addition of new atoms causes the symmetry of the structures to be broken and makes them all pIh. We find three different types of structures as GM for clusters with 38 atoms. For m = 1, 2 or m = 3134 the structures are all c-pc539, and for the Cu-richest clusters, i.e., m = 3537, we find face-centered cubic (fcc)-based, truncated octahedron (TO) structure. Other stoichiometries for N = 38 all have the pIh structure. Although a part of the 5-fold structure is also formed

for these clusters, the extra atoms and a tendency toward a coreshell arrangement prevent the formation of the completely symmetric 5-fold structure. In contrast to the results of previous studies, we do not recognize any symmetric structure for the Cu6Ag32. The c-pc539 structure is the GM of many Ag-rich (m = 13) and Cu-rich (m = 2438) clusters for N = 39. The GM of Cu6Ag33 is c-pc640 which is not capped from one side along the symmetry axis. The c-pc539 with one extra atom on the surface is the putative global minimum structure of many stoichiometries for N = 40, i.e., for m = 13 and m = 2839. An exception is Cu33Ag7 which has the c-pc640 structure. Our results show that the global-minimum structures of all Cuor Ag-rich clusters in the range N = 4150 are based on the c-cp539 motif with, however, some exceptions. The extra atoms are added to the pancake structures so that the Ih55 structure is formed for N = 55. For other stoichiometries, the structures are based on pIh’s. Even for these pIh’s one can identify at least parts of the c-pc640 structure. But the tendency toward the formation 22152


The Journal of Physical Chemistry C of coreshell motifs and the presence of additional atoms lead to reductions in the symmetry so that these clusters belong to the pIh’s. For even larger sizes, the incomplete Ih55 is more frequently formed for the CuAg clusters with more Cu or Ag atoms.

Figure 3. Ratio of the average radial distance of the Cu atoms to that of the Ag atoms in CumAgn clusters as a function of (m,n) for N = m + n from 2 to 60.

ARTICLE

For N = 51 we find the structure of clusters with m = 16 and or with m = 4250 to be based on the Ih55 motif with some unoccupied sites. For N = 52 this structure is seen for m = 19 and m = 3451. For N = 53 many clusters have an incomplete Ih55 structure, i.e., for m = 18 and m = 3252. This structure is found even more frequently for N = 54, i.e., for m = 18 and m = 2553. All other clusters of these sizes have the pIh structure. The GM structures for N = 55 atoms and m = 19 are Ih55. Substituting more Ag atoms with Cu causes larger distortions and pIh structures become the GM of clusters for 10 < m < 27. But again we find the Ih55 as the GM of clusters of this size with m = 2754. The Ih55 with extra atoms on the surface is the GM of many stoichiometries of clusters with N = 5660, in particular when the cluster contains only few Cu or Ag atoms. In the other cases, the putative global minima become pIh. In total we see that the interplay between a tendency toward coreshell formation and the differences between the bond lengths leads to more symmetric structures mainly for those clusters that contain many more atoms of the one type than of the other type.

Figure 4. The stability function NΔ2 for selected sizes of CuAg nanoalloys vs number of Cu atoms (m). 22153



ARTICLE

Figure 5. The stability function nΔ2 for selected sizes of CuAg nanoalloys vs number of Cu atoms (m).

Figure 6. The stability function mΔ2 for selected sizes of CuAg nanoalloys vs number of Cu atoms (m).

Bond Order Parameter. Although the formation of the core shell structures can be identified by looking at the structures, it is very helpful to make use of the concept of the bond order parameter (σ) which gives a quantitative measure for segregation (i.e., for coreshell structures). The bond order parameter of a AmBn cluster is defined as σ ¼

NAA þ NBB NAB NAA þ NBB þ NAB

ð3Þ

Here, N ij (with i and j being A and/or B) is the number of nearest-neighbor bonds between atoms of type i and j. Positive values of σ indicate segregation of the atoms in the cluster while σ would be zero for disorderly mixed clusters. Mixed and onion-like phases of clusters result in negative values of σ. Here and in most of what follows we have chosen to limit ourselves to the discussion of some few selected cluster sizes (N = 34, 38, 39, 55, and 60). The nanoalloys with 34, 22154



ARTICLE

Figure 7. The stability function mnΔ(1) 2 for selected sizes of CuAg nanoalloys vs number of Cu atoms (m).

Figure 8. The stability function mnΔ(2) 2 for selected sizes of CuAg nanoalloys vs number of Cu atoms (m).

39, and 55 atoms are interesting since for these sizes we have seen many stoichiometries with 5-fold, symmetric structures. N = 38 is also selected since three different structures were found as its GM’s, i.e. pIh, c-pc539 with one atom removed, and TO. The N = 60 is considered since it is the largest size of our study. Accordingly, Figure 2 shows σ together with the numbers of different types of nearest-neighbor bonds as functions of the

number of Cu atoms (m) for N = 34, 38, 39, 55, and 60. σ is in all cases positive suggesting some degree of segregation of one species (which turns out to be Ag) toward the surface and the formation of coreshell structures. The formation of such CucoreAgshell structures can be also identified by looking at the number of different types of bonds. Thus, in Figure 2 we also see that the number of AgAg bonds decreases and becomes zero not only for pure Cu clusters but also for some clusters 22155


The Journal of Physical Chemistry C with a nonvanishing number of Ag atoms. In the latter case, the Ag atoms are well separated on the surface of the Cu core without forming AgAg bonds. On the other hand, the number of CuCu bonds is not vanishing even when the number of Cu atoms is very small. This is in agreement with the formation of a Cu core and the tendency to maximize the number of the stronger CuCu bonds. Finally, Figure 2 shows,

ARTICLE

which may not be a surprise, that the maximum number of CuAg bonds is found for clusters with approximately equal numbers of Cu and Ag atoms. When compared with our previous results for Ni mAgn clusters, 4 the results of Figure 2 are very similar to those for the Ni mAg n clusters. Thus, even if one may consider Ni and Ag as being more different than Cu and Ag (when comparing atomic radii, cohesive energies, and surface energies), the closer similarity between Cu and Ag does not result in more mixed structures, but segregation prevails. Radial Distances. Further information on the construction of coreshell structures can be identified by analyzing the distances of the atoms to their center. Thus, for each atom we calculate its radial distance Ri B R0 j, ri ¼ j B

i ¼ 1, 2, :::, N

ð4Þ

with B R0 ¼

Figure 9. The excess energy per atom for CumAgn clusters as a function of (m,n) for N = m + n from 2 to 60.

1 N B Ri N i¼1

∑

ð5Þ

being the center of the cluster of interest. Subsequently, for each cluster the ratio between the average radial distance of the Cu atoms and the average radial distance of

Figure 10. The excess energy of the CuAg nanoalloys for some selected sizes (N = 34, 38, 39, 55, and 60) vs the number of Cu atoms (m). 22156



ARTICLE

Figure 11. Energy difference between the first and second stable isomers for five selected sizes of CuAg nanoalloys vs number of Cu atoms (m).

the Ag atoms rðm, nÞ ¼

ÆrCu æ ÆrAg æ

ð6Þ

gives information on whether a coreshell structure has been formed. Thus, this ratio being smaller than 1 indicates a CucoreAgshell structure, whereas it being larger than 1 indicates a AgcoreCushell and if being close to 1 suggests mixing or multishell structures. This ratio is shown in Figure 3. It is clear that the average radial distance of the Ag atoms is larger than that of the Cu atoms, supporting that CucoreAgshell structures have been formed. Moreover, it is interesting to notice that Figure 3 is very similar to the analogous figure for NimAgn clusters.4 Energetic Properties. An important issue is the identification of stoichiometries that are particularly stable. To this purpose many different tools have been introduced and applied, including

the stability function, the energy difference between the first and second isomers for a given cluster size, and the excess energy. We shall here discuss those for the CuAg clusters. Stability Function. The stability function, i.e., the second difference in energy Δ2 as a function of number of atoms, compares neighboring cluster sizes. This property is uniquely defined for monatomic clusters, but for binary clusters more different definitions may be proposed. These include N

n

Δ 2 ¼ Eðm 1, n þ 1Þ þ Eðm þ 1, n 1Þ 2Eðm, nÞ

Δ 2 ¼ Eðm þ 1, nÞ þ Eðm 1, nÞ 2Eðm, nÞ

m

Δ 2 ¼ Eðm, n þ 1Þ þ Eðm, n 1Þ 2Eðm, nÞ

mn

22157

ð1Þ

Δ2

¼ Eðm, n þ 1Þ þ Eðm 1, nÞ 2Eðm, nÞ dx.doi.org/10.1021/jp2050417 |J. Phys. Chem. C 2011, 115, 22148–22162


ARTICLE

Figure 12. The mixing coefficient (upper panel) and mixing energy (lower panel) for CuAg clusters vs the number of Cu (m) and Ag (n) atoms for N = m + n from 2 to 60. ð2Þ

¼ Eðm þ 1, nÞ þ Eðm, n 1Þ 2Eðm, nÞ

ð2Þ

¼ Eðm þ 1, nÞ þ Eðm, n 1Þ 2Eðm, nÞ

mn

Δ2

mn

Δ2

ð7Þ 48

of which the first one was proposed by Rossi et al. In all definitions, E(m,n) is the total energy for the binary AmBn cluster. Particularly stable clusters (i.e., magic clusters) are then identified as those with particularly large, positive values of Δ2. Since it is not possible to show all stability functions for all clusters of the present study, we restrict ourselves to the discussion of some selected cases. Thus, Figure 4 depicts NΔ2 for clusters with N = 34, 38, 39, 55, and 60 atoms. The most stable cluster for N = 34, i.e., Cu7Ag27 as well as five other magic clusters, m = 11, 13, 17, 19, and 22, are all 5-fold c-pc534 structures. The enhanced stability of Cu7Ag27 is in agreement with the finding of previous studies.3 This cluster is formed by a central pentagonal bipyramid of Cu atoms covered with a one-atom thick shell of Ag atoms. Also in our earlier study on NiAg clusters4 we found this stoichiometry to be particularly stable. We find the Cu8Ag30 with a pIh structure as the most stable cluster of the size N = 38. The stability of this stoichiometry is in agreement with the results of other studies.3,19 In Figure 4 one can also identify Cu1Ag37 and Cu32Ag6 among the energetically favorable clusters of this size. These two have completely different structures compared to other stable stoichiometries, as both are c-pc539 with one vacant site whereas the other clusters of this size all are pIh. The pIh Cu9Ag30, which is made by a c-pc534 and five extra atoms on the surface, has the highest value of NΔ2 for N = 39 (Figure 4b). Three further, symmetric structures are also particularly stable clusters for N = 39, i.e., m = 1, 6, and 24. Figure 4d shows that the coreshell pIh Cu12Ag43 cluster corresponds to a magic cluster for N = 55. Both GMs of Cu11Ag44 and Cu13Ag42 have Cu atoms which are segregated to the surface, and this can be a cause for the high stability for m = 12. Three

other pIh’s are found to be magic clusters for this size, m = 10, 20, and 24. The Ag-rich clusters for N = 60 atoms have a more complicated stability pattern, suggesting that the addition of just one atom can cause a noticeable change in the stability. Most of the magic clusters for N = 60 are pIh’s. Just three clusters with an Ih55 core covered by five extra atoms on the surface are seen to be of significant stability (m = 1, 4, and 6). Among the most stable clusters are Cu12Ag48 and Cu17Ag43 with pIh structures. On comparison with our previous results for NiAg clusters,4 significant differences are found. Thus, for N = 60, we find particularly stable clusters for many different values of m for the whole range 0 < m < 60 for NiAg, whereas these are found mainly for small m for CuAg. On the other hand, for N = 34, there are more different particularly stable clusters for CuAg than for NiAg. In addition, |NΔ2| tends to take larger values in general for NiAg than for CuAg, suggesting that the larger similarity in the properties of Cu and Ag compared with Ni and Ag reduces the stability function. Ultimately, this may suggest that more different stoichiometries are stable and can be produced for CuAg than for NiAg. To compare the different definitions of the stability functions, we show those in Figures 58 for some selected values of N. It is seen that many of those clusters that are found to be particularly stable according to NΔ2 also are so according to the other definitions of the stability function. For N = 34, the most stable cluster according to mΔ2 and mnΔ(2) 2 is found for Cu17Ag17. This cluster and Cu2Ag32 are stable according to all of the Δ2 functions for N = 34. For N = 38 the enhanced stability of the pIh Cu8Ag30 cluster is also given according to nΔ2 and mΔ2. However, for this size the prediction of which cluster is the most stable one depends sensitively on which Δ2 function is used. Thus, the following clusters are found by the different definitions: nΔ2 gives Cu1Ag37 (c-pc539), mΔ2 gives Cu8Ag30 (pIh), mnΔ(1) gives Cu7Ag31 2 (c-pc539), and mnΔ(2) 2 gives Cu18Ag20. Moreover, (m,n) = (12,26) is the only composition which is magic according to all of the stability functions. The Cu9Ag30 cluster with pIh structure is the only cluster of size N = 39 which is found to be magic according to all stability functions. This cluster is the most stable one when we use NΔ2 and nΔ2. The other stability functions find different stoichiometries, all with pIh structures, to be the most stable ones, i.e., mΔ2, mn (1) Δ2 , and mnΔ(2) give Cu14Ag25, Cu10Ag29, and Cu13Ag26 2 respectively. A comparison of the stability functions for N = 55 shows that many clusters of this size are stable independent of the definition of the stability function. Clusters with m = 7, 12, 42, and 47 are magic according to all Δ2 functions. All these clusters are Ih55 except for the Cu12Ag43 cluster which is a pIh. Finally, it is again interesting to compare with our previous results on NiAg clusters.4 This comparison confirms that for both systems there are larger similarities between the results found by using different definitions of the stability function than between the two different systems. Thus, the stability function clearly identifies a difference between the two different types of bimetallic clusters, a difference that was not identified by the bond order parameter. Excess Energy. Whereas the stability functions compare the total energies of neighboring cluster stoichiometries, the excess energy, Eexc, compares the total energies of the binary clusters with those of the pure ones and, thus, gives information about the 22158



ARTICLE

Table 1. The Most Stable Compositions, (m, n), for CuAg Nanoalloys within the Size Range of N = 2 60a N

N

Δ2

Δ2

Δ2

n

m

mn

Δ(1) 2

mn

Δ(2) 2

ΔEisom

2

Eexc

Δ2

N

N

Δ2

n

m

Δ2

mn

Δ(1) 2

mn

Δ(2) 2

ΔEisom

Eexc

(1, 1)

32

(8, 24)

(11, 21)

(4, 28)

(4, 28)

(11, 21)

(7, 25)

(11, 21)

3

(2, 1)

(1, 2)

(2, 1)

(1, 2)

(2, 1)

(2, 1)

33

(5, 28)

(13, 20)

(5, 28)

(5, 28)

(7, 26)

(17, 16)

(7, 26)

4

(3, 1)

(3, 1)

(3, 1)

(1, 3)

(3, 1)

(2, 2)

34

(7, 27)

(7, 27)

(17, 17)

(5, 29)

(17, 17)

(7, 27)

(7, 27)

5

(3, 2)

(3, 2)

(3, 2)

(1, 4)

(3, 2)

(3, 2)

35

(7, 28)

(7, 28)

(8, 27)

(7, 28)

(9, 26)

(10, 25)

(9, 26)

6

(2, 4)

(5, 1)

(5, 1)

(1, 5)

(5, 1)

(5, 1)

(2, 4)

36

(9, 27)

(33, 3)

(30, 6)

(6, 30)

(30, 6)

(20, 16)

(12, 24)

7

(2, 5)

(2, 5)

(1, 6)

(1, 6)

(5, 2)

(1, 6)

(2, 5)

37

(8, 29)

(9, 28)

(8, 29)

(9, 28)

(8, 29)

(8, 29)

(9, 28)

8

(2, 6)

(4, 4)

(4, 4)

(2, 6)

(7, 1)

(4, 4)

(4, 4)

38

(8, 30)

(1, 37)

(8, 30)

(7, 31)

(18, 20)

(19, 19)

(10, 28)

9 10

(1, 8) (1, 9)

(1, 8) (1, 9)

(3, 6) (7, 3)

(1, 8) (1, 9)

(7, 2) (7, 3)

(1, 8) (1, 9)

(4, 5) (5, 5)

39 40

(9, 30) (7, 33)

(9, 30) (12, 28)

(14, 25) (11, 29)

(10, 29) (11, 29)

(13, 26) (12, 28)

(1, 38) (13, 27)

(9, 30) (12, 28)

11

(1, 10)

(1, 10)

(9, 2)

(1, 10)

(9, 2)

(1, 10)

(5, 6)

41

(8, 33)

(15, 26)

(30, 11)

(7, 34)

(29, 12)

(21, 20)

(12, 29)

12

(1, 11)

(1, 11)

(1, 11)

(1, 11)

(9, 3)

(1, 11)

(4, 8)

42

(31, 11)

(12, 30)

(17, 25)

(12, 30)

(17, 25)

(16, 26)

(12, 30)

13

(1, 12)

(1, 12)

(12, 1)

(1, 12)

(12, 1)

(12, 1)

(3, 10)

43

(15, 28)

(11, 32)

(10, 33)

(2, 41)

(15, 28)

(2, 41)

(15, 28)

14

(1, 13)

(1, 13)

(4, 10)

(1, 13)

(10, 4)

(1, 13)

(4, 10)

44

(11, 33)

(8, 36)

(22, 22)

(8, 36)

(22, 22)

(21, 23)

(11, 33)

15

(1, 14)

(1, 14)

(3, 12)

(1, 14)

(14, 1)

(1, 14)

(5, 10)

45

(11, 34)

(13, 32)

(14, 31)

(13, 32)

(13, 32)

(11, 34)

(11, 34)

16

(1, 15)

(1, 15)

(4, 12)

(1, 15)

(7, 9)

(1, 15)

(7, 9)

46

(31, 15)

(1, 45)

(37, 9)

(1, 45)

(33, 13)

(37, 9)

(15, 31)

17 18

(2, 15) (2, 16)

(2, 15) (1, 17)

(5, 12) (2, 16)

(1, 16) (2, 16)

(15, 2) (8, 10)

(8, 9) (16, 2)

(5, 12) (8, 10)

47 48

(17, 30) (30, 18)

(20, 27) (8, 40)

(9, 38) (8, 40)

(13, 34) (8, 40)

(30, 17) (16, 32)

(13, 34) (21, 27)

(13, 34) (14, 34)

19

(1, 18)

(11, 8)

(18, 1)

(1, 18)

(18, 1)

(1, 18)

(4, 15)

49

(18, 31)

(36, 13)

(37, 12)

(12, 37)

(33, 16)

(47, 2)

(14, 35)

20

(2, 18)

(3, 17)

(2, 18)

(1, 19)

(2, 18)

(2, 18)

(7, 13)

50

(21, 29)

(18, 32)

(19, 31)

(18, 32)

(17, 33)

(32, 18)

(19, 31)

21

(2, 19)

(9,12)

(9, 12)

(1, 20)

(20, 1)

(3, 18)

(6, 15)

51

(12, 39)

(12, 39)

(12, 39)

(12, 39)

(12, 39)

(30, 21)

(22, 29)

22

(3, 19)

(3, 19)

(3, 19)

(1, 21)

(18, 4)

(11, 11)

(6, 16)

52

(15, 37)

(4, 48)

(31, 21)

(31, 21)

(4, 48)

(30, 22)

(22, 30)

23

(3, 20)

(3, 20)

(12, 11)

(3, 20)

(13, 10)

(3, 20)

(7, 16)

53

(17, 36)

(17, 36)

(19, 34)

(17, 36)

(19, 34)

(22, 31)

(21, 32)

24

(3, 21)

(3, 21)

(3, 21)

(1, 23)

(19, 5)

(6, 18)

(5, 19)

54

(10, 44)

(10, 44)

(10, 44)

(6, 48)

(10, 44)

(1, 53)

(16, 38)

25 26

(10, 15) (3, 23)

(10, 15) (8, 18)

(2, 23) (3, 23)

(2, 23) (3, 23)

(10, 15) (8, 18)

(2, 23) (3, 23)

(6, 19) (7, 19)

55 56

(12, 43) (44, 12)

(1, 54) (12, 44)

(33, 22) (14, 42)

(1, 54) (12, 44)

(37, 18) (44, 12)

(1, 54) (18, 38)

(20, 35) (18, 38)

27

(4, 23)

(18, 9)

(4, 23)

(4, 23)

(18, 9)

(7, 20)

(8, 19)

57

(15, 42)

(9, 48)

(9, 48)

(9, 48)

(9, 48)

(9, 48)

(19, 38)

28

(3, 25)

(6, 22)

(7, 21)

(3, 25)

(27, 1)

(6, 22)

(7, 21)

58

(13, 45)

(15, 43)

(16, 42)

(15, 43)

(13, 45)

(8, 50)

(23, 35)

29

(6, 23)

(5, 24)

(6, 23)

(5, 24)

(6, 23)

(6, 23)

(6, 23)

59

(13, 46)

(6, 53)

(6, 53)

(7, 52)

(6, 53)

30

(7, 23)

(13, 17)

(7, 23)

(4, 26)

(13, 17)

(10, 20)

(9, 21)

60

(12, 48)

31

(6, 25)

(6, 25)

(8, 23)

(6, 25)

(8, 23)

(5, 26)

(8, 23)

(23, 36)

(20, 39)

(17, 43)

(22, 38)

These compositions are defined by all of the proposed stability criteria, i.e., the stability functions (eq 7), as well as the first and second isomers energy difference, and the excess energy (eq 8). a

alloying processes19,49 Eexc ¼ Eðm, nÞ m

EðAgN Þ EðCuN Þ n N N

ð8Þ

Here, E(CuN) and E(AgN) are the energies of the putative GMs of pure Cu and Ag clusters with N = m + n atoms, respectively. The form of (eq 8) implies that the excess energies of pure clusters are zero, whereas negative values indicate that mixing is energetically preferred. In Figure 9 we show Eexc/N. As can be seen in the figure, Eexc/N is negative for almost all sizes and stoichiometries, which indicates that mixing is favorable. There is a certain range of stoichiometries, i.e., for m between m = 6 and 15 and n between n = 17 and 30, where the excess energy per atom is taking the most negative values. This indicates that these are sizes for which the most stable clusters are found. In order to analyze the excess energy in more detail, the excess energy versus the number of Cu atoms is shown in Figure 10 for five selected sizes. In all cases, the overall behavior of the excess energy gives that it has a minimum for Ag-rich clusters. On top of the overall trend, Eexc shows an oscillatory behavior, which can be ascribed to smaller structural changes. That Cu7Ag27 is of enhanced stability, as was found above, is recovered here.

For N = 38, Cu10Ag28 is found to be particularly stable when studying the excess energy as is the case for Cu9Ag29. Both clusters have pIh structures similar to Cu8Ag30, which is found to be magic by four definitions of the stability functions. The particular stability of the Cu9Ag30 cluster is also identifiable through its excess energy which has the lowest value for N = 39 for exactly this cluster size. For N = 55, Cu20Ag35 has the lowest excess energy. That this pIh cluster should be the most stable one is not found when using the concept of stability functions. However, as seen in Figure 10, the excess energy for N = 55 is low for a whole range of clusters, a result that is different from the findings for the smaller clusters in Figure 10. The lowest value of Eexc for N = 60 is found for m = 22. Also this cluster has a pIh structure with many Cu atoms segregated to the surface. In general, the excess energy is lowest for Ag-rich clusters. This tendency is more pronounced for smaller sizes, i.e., for N = 34, 38, and 39, and was also found in our earlier studies on NiAg clusters.4 However, in the present study, the fact that, for N = 55 and N = 60, Eexc changes only little for a larger range of m, was not found for the NiAg clusters. Thus, this may be related to the closer similarity between Cu and Ag than between Ni and Ag. 22159



ARTICLE

For N = 60 the thermally stable clusters are found for (m, n) = (13, 47), (24, 36), (26, 34), (34, 26), (37, 23), (39, 21), (42, 18), (45, 15), (49, 11), and (51, 9). All these clusters have pIh structures except for the last three clusters which consist of the Ih55 motif with five extra atoms added to the T sites above the outer atomic shell. Mixing Energy And Mixing Coefficient. The effect of substituting atoms in a pure cluster with another type of atom can be quantified through the so-called mixing energy. This is defined as50,51 Emix ¼ Eðm, nÞ ½EðA m =A m A n Þ þ EðBn =Bm Bn Þ

ð9Þ

where E(Am/AmAn) is the total energy of a cluster structurally similar to the AmBn cluster but with the n B atoms replaced by A atoms. Only the effects of the n A atoms on the remaining m A atoms are included, whereas their mutual interactions are not calculated. Finally, from the mixing energy one can define a mixing coefficient according to50,51 M ¼

Figure 13. The quantity D(m, n) for (upper panel) the ratio of the average distances and (lower panel) the excess energy per atom for clusters with N = m + n atoms ranging from 2 to 60.

Isomer Energy Difference. Usually for small clusters, the fact that there is only few total-energy minima makes the energy difference between the energetically lowest and next-lowest structure relatively large. This is not the case for larger clusters for which many clusters with close energies may exist. When studying stability of a given cluster, it is, therefore, also relevant to compare its energy to that of the energetically next-lying isomer. This energy difference, ΔEisom, is a measure of thermal stability of the lower energy isomer. In Figure 11 we show ΔEisom for the CuAg clusters with N = 34, 38, 39, 55, and 60 atoms versus the number of Cu atoms. Many of the particularly stable clusters with N = 34 that were identified above are also thermally stable. This is the case for m = 7, 13, 16, and 22 which all are c-pc534. Furthermore, we find two other thermally stable clusters, Cu10Ag24 (c-pc534) and Cu28Ag6 (pIh), that are not identified through other stability criteria. On the other hand, there are also cases where clusters, which are particularly stable according to other criteria, are not thermally stable. This is, e.g., the case for m = 5, 9, and 30. Also for N = 38 many of the particularly stable clusters are found to be thermally stable, too. In addition two clusters, Cu9Ag29 and Cu15Ag23, are thermally stable, although they are not particularly stable according to other criteria. In this case, one may also notice that the two isomers of Cu4Ag30 are essentially energetically degenerate. The thermally stable stoichiometries for N = 39 are those that are stable according to other criteria, too, whereas the magic Cu32Ag7 and Cu35Ag4 clusters are not thermally stable. For N = 55, the interesting cases are m = 7, 12, 42, and 47, which correspond to maxima for all Δ2 functions. Differences are seen for Cu15Ag40, Cu32Ag23, and Cu33Ag22, where the isomer energy difference essentially vanishes. This can be contrasted by their enhanced stability according to the Δ2 functions.

Emix 100% Eðm, nÞ

ð10Þ

The mixing energy is large and negative if the binary clusters prefer a mixed and not segregated arrangement of the atoms. The mixing coefficient, M, and the mixing energy per atom for CuAg clusters are shown in Figure 12. In particular for Ag- or Cu-rich clusters M takes low values, i.e., lower than 6%. But even for most other cases, M stays in most cases below 12% and only in few cases we find M to be larger than 30%. These results are in agreement with our finding of noticeable segregation effects in the CuAg clusters, where the Ag atoms segregate to the surface of clusters and the Cu atoms form a core. Not surprisingly, the behavior of Emix is similar to that of M. Starting with pure clusters, the mixing energy becomes increasingly negative when introducing a growing amount of Ag (Cu) atoms to the cluster. The most negative values of Emix are found for Ag-rich clusters, suggesting the existence of a stabilizing effect of the Cu atoms when being added to the Ag-rich clusters, whereas a similar effect for the addition of Ag atoms to Cu-rich clusters is not observed. This can be related to the differences in the strength of the interatomic bonds, for which AgAg bonds are weaker and CuCu bonds are stronger than CuAg bonds. When comparing Figure 12 with our earlier results for NiAg clusters,4 we find that the figures look very different, although the structures of the clusters as such are very similar. This suggests that a figure like Figure 12 does not directly give information on the overall structures of the clusters. Rather, as also is obvious from the definition of Emix and M, the figure gives information on energetic properties. Thus, the fact that Emix and M in general are smaller for the CuAg clusters than for the NiAg clusters is in accord with the closer similarity in the energetic properties of Cu and Ag compared with those of Ni and Ag.

IV. CONCLUSIONS In this work the structural and energetic properties of bimetallic CuAg clusters were explored thoroughly. The putative global minimum structures were determined for CumAgn clusters with all possible stoichiometries, i.e., (m, n), with N = m + n from 2 to 60. The atomatom interactions were described within the embedded-atom method, which was combined with the basinhopping algorithm for global structure optimization. We found that the growth of CuAg clusters is based on the formation of icosahedra, polyicosahedra, and two types of 5-fold pancakes with 34 and 39 atoms. The exceptions were some 22160


The Journal of Physical Chemistry C clusters of size N = 38 that were found to have truncated octahedron structures. The analysis of the bond order parameter indicated the formation of CucoreAgshell structures in agreement with experiments7 and other previous studies.3,13,16,19 There is some value in taking into consideration that we used a potential which contains a pair interaction term to obtain these structures. It is known that all potentials of this type have a bias toward compact structures and therefore this bias should be considered for further analysis of the results. Also the range of pair potentials affect the structural motifs of favored geometries, where at intermediate ranges of pair potentials icosahedra are dominant. Decahedra and fcc are then favored at short and very short ranges, respectively.52 Clusters with enhanced stability were identified by using various definitions of stability functions, the excess energy and the energy difference between the first and the second isomers. We found, similar to our earlier results on NiAg clusters,4 that Ag-rich clusters are more stable in many cases. Moreover, the definition of the stability functions was found to be of importance when applied to the bimetallic clusters. Cu7Ag27 was identified as being particularly stable according to four different definitions of the stability tools, which is in agreement with previous studies.3,14,15 Also for N = 38, the enhanced stability of the Cu8Ag30 is in agreement with results of previous studies.3,14 We identified different structures including 5-fold capped pancakes with 39 atoms, pIh, and 6-fold pancakes as those of the global minimum for the clusters with N = 40. These findings are similar to those of Barcaro et al.,13 whereas in the present study we did not recognize any capped decahedron. Clusters of enhanced stability for this size were (7, 33), (11, 29), (12, 28), and (13, 27). The enhanced stability of the (13, 27) cluster was also found in other studies.13,16 The magic Cu13Ag32 with N = 45 was also found in previous studies.3,19 In general, Ag-rich clusters were found more frequently to be particularly stable stoichiometries than is the case for Cu-rich clusters. This behavior was particularly recognizable through the excess and mixing energies. As a summary, Table 1 gives a list of all the energetically favorable stoichiometries for each cluster size considered in this study. The difficulty in determining the stable clusters for bimetallic clusters is reflected in different magic clusters when comparing different descriptors for stability. Despite this, we see that some clusters are found to be particularly stable by more tools. Most notably are (m, n) = (3, 2), (1, 11), (6, 23), (12, 39), and (9, 48) that are found to be particularly stable according to no less than five different stability measures. For another set of 16 clusters, (2, 1), (3, 1), (5, 1), (4, 4), (1, 8), (1, 9), (, 110), (1, 13), (1, 14), (1, 15), (2, 18), (3, 20), (3, 23), (7, 27), (8, 29), and (10, 44), four criteria identify those as being of enhanced stability. Finally, for a quantitative comparison between the results of the present study and those of our earlier study on NiAg clusters4 it is useful to proceed as follows. For a certain property, Z, we calculate its average ÆZæ, for all the clusters of our study. Subsequently, we can study the quantity 0 1 Z ðm, nÞ Z ðm, nÞ NiAg CuAg A ð11Þ Dðm, nÞ ¼ log@1 þ ÆZNiAg æ ÆZCuAg æ D(m, n) approaches 0 if the dependence of Z on cluster stoichiometry, (m, n), for NiAg and for CuAg clusters is very similar to each other. On the other hand, larger values of

ARTICLE

D indicate that there are materials-specific differences in the property of interest. In Figure 13 we show D(m, n) for Z being the ratio of the average radial distance, (eq 6), and for Z being the excess energy per atom, Eexc/N; cf. eq 8. The upper panel supports that the structures are very similar. Thus, even if Cu and Ag have more similar atomic radii, surface energies, and cohesive energies than is the case for Ni and Ag, this difference does hardly manifest itself in structural differences. On the other hand, properties related to the energies of the clusters are less similar for the two types of systems, as can be seen in the lower panel in Figure 13. In particular, the mixing energy and the mixing coefficient were very different. Moreover, the energetic properties for the CuAg clusters possessed a weaker dependence on stoichiometry than was the case for those of the NiAg clusters, which ultimately may suggest that for the former many more different stoichiometries can be made stable.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work was supported by the German Research Foundation (DFG) through project Sp 439/24. ’ REFERENCES (1) Ferrando, R.; Jellinek, J.; Johnstom, R. L. Chem. Rev. 2008, 108, 845. (2) Baletto, F.; Ferrando, R. Rev. Mod. Phys. 2005, 77, 371. (3) Rossi, G.; Rapallo, A.; Mottet, C.; Fortunelli, A.; Baletto, F.; Ferrando, R. Phys. Rev. Lett. 2004, 93, 105503. (4) Molayem, M.; Grigoryan, V. G.; Springborg, M. J. Phys. Chem. C 2010, 115, 7179. (5) Belloni, J.; Mostafavi, M.; Remita, H.; Marignier, J. L.; Delcourt, M. O. New J. Chem. 1998, 22, 1239. (6) Henglein, A.; Tausch-Treml, R. J. Colloid Interface Sci. 1981, 80, 84. (7) Langlois, C.; Alloyeau, D.; Bouar, Y. L.; Loiseau, A.; Oikawa, T.; Mottet, C.; Ricolleau, C. Faraday Discuss. 2008, 138, 375. (8) Cazayous, M.; Langlois, C.; Oikawa, T.; Ricolleau, C.; Sacuto, A. Phys. Rev. B 2006, 73, 113402. (9) Janssens, E.; Neukermans, S.; Wang, X.; Veldeman, N.; Silverans, R.; Lievens, P. Eur. Phys. J. D 2005, 34, 23. (10) Yang, L.; Raeker, T. J.; DePristo, A. E. Surf. Sci. 1993, 290, 195. (11) Hsu, P. J.; Lai, S. K. J. Chem. Phys. 2006, 124, 044711. (12) Wang, G.; Hove, M. A. V.; Ross, P. N.; Baskes, M. I. J. Chem. Phys. 2005, 122, 024706. (13) Barcaro, G.; Fortunelli, A.; Rossi, G.; Nita, F.; Ferrando, R. J. Phys. Chem. B 2006, 110, 23197. (14) Rapallo, A.; Rossi, G.; Ferrando, R.; Fortunelli, A.; Curley, B. C.; Lloyd, L. D.; Tarbuck, G. M.; Johnston, R. L. J. Chem. Phys. 2005, 122, 194308. (15) Nu nez, S.; Johnston, R. L. J. Phys. Chem. C 2010, 114, 13255. (16) Ferrando, R.; Fortunelli, A.; Johnston, R. L. Phys. Chem. Chem. Phys. 2008, 10, 640. (17) Paz-Borbon, L. O.; Mortimer-Jones, T. V.; Johnston, R. L.; Posada-Amarillas, A.; Barcaro, G.; Fortunelli, A. Phys. Chem. Chem. Phys. 2007, 9, 5202–5208. (18) Logsdail, A.; Paz-Borbon, L. O.; Johnston, R. L. J. Comput. Theor. Nanosci. 2009, 6 (April), 857. (19) Ferrando, R.; Fortunelli, A.; Rossi, G. Phys. Rev. B 2005, 72, 085449. 22161



ARTICLE

(20) Bochicchio, D.; Ferrando, R. Nano Lett. 2010, 10, 4211. (21) Jiang, Z. Y.; Lee, K. H.; Li, S. T.; Chu, S. Y. Phys. Rev. B 2006, 73, 235423. (22) Ortigoza, M. A.; Rahman, T. S. Phys. Rev. B 2008, 77, 195404. (23) Baletto, F.; Mottet, C.; Ferrando, R. Eur. Phys. J. D 2003, 24, 233. (24) Baletto, F.; Mottet, C.; Ferrando, R. Phys. Rev. B 2002, 66, 155420. (25) Baletto, F.; Mottet, C.; Ferrando, R. Phys. Rev. Lett. 2003, 90, 135504. (26) Lequien, F.; Creuze, J.; Berthier, F.; Legrand, B. J. Chem. Phys. 2006, 125, 094707. ~ l’glia, G.; (27) Moreno, V.; Creuze, J.; Berthier, F.; Mottet, C.; TrA Legrand, B. Surf. Sci. 2006, 600, 5011. (28) Lequien, F.; Creuze, J.; Berthier, F.; Braems, I.; Legrand, B. Phys. Rev. B 2008, 78, 075414. (29) Daw, M. S.; Baskes, M. I. Phys. Rev. Lett. 1983, 50, 1285. (30) Wales, D. J.; Doye, J. P. K. J. Phys. Chem. A 1997, 101, 5111. (31) Daw, M. S.; Baskes, M. I. Phys. Rev. B 1984, 29, 6443–6453. (32) Foiles, S. M.; Baskes, M. I.; Daw, M. S. Phys. Rev. B 1986, 33, 7983. (33) Daw, M. S.; Foiles, S.; Baskes, M. I. Mater. Sci. Rep. 1993, 9, 251. (34) Grigoryan, V. G.; Springborg, M. Phys. Rev. B 2004, 70, 205415. (35) Grigoryan, V. G.; Alamanova, D.; Springborg, M. Phys. Rev. B 2006, 73, 115415. (36) Hoof, T. V.; Hou, M. Phys. Rev. B 2005, 72, 115434. (37) Medasani, B.; Park, Y. H.; Vasiliev, I. Phys. Rev. B 2007, 75, 235436. (38) Tafen, D. N.; Lewis, L. J. Phys. Rev. B 2008, 77, 075429. (39) Hristova, E.; Dong, Y.; Grigoryan, V. G.; Springborg, M. J. Phys. Chem. A 2008, 112, 7905. (40) Massen, C.; Mortimer-Jones, T. V.; Johnston, R. L. J. Chem. Soc., Dalton Trans. 2002, 4375. (41) Abrahamson, A. A. Phys. Rev. 1964, 133, A990. (42) Wales, D. J.; Scheraga, H. A. Science 1999, 285, 1368. (43) Wales, D. J. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses; Cambridge University Press: Cambridge, 2004. (44) Doye, J. P. K.; Meyer, L. Phys. Rev. Lett. 2005, 95, 063401. (45) Hristova, E.; Grigoryan, V. G.; Springborg, M. J. Chem. Phys. 2008, 128, 244513. (46) Munro, L. J.; Tharrington, A.; Jordan, K. D. Comput. Phys. Commun. 2002, 145, 1. (47) Calvo, F.; Yurtsever, E. Phys. Rev. B 2004, 70, 045423. (48) Rossi, G.; Ferrando, R.; Rapallo, A.; Fortunelli, A.; Curley, B. C.; Lloyd, L. D.; Johnston, R. L. J. Chem. Phys. 2005, 122, 194309. (49) Fortunelli, A.; Velasco, A. J. Mol. Struct.: THEOCHEM 1999, 487, 251. (50) Jellinek, J.; Krissinel, E. B. Chem. Phys. Lett. 1996, 258, 283. (51) Jellinek, J. Theory of Atomic and Molecular Clusters, With a Glimpse at Experiments; Springer-Verlag: Berlin and Heidelberg, 1999. (52) Doye, J. P. K.; Wales, D. J.; Berry, R. S. J. Chem. Phys. 1995, 103, 4234.

22162


Global Minimum Structures and Magic Clusters of CumAgn Nanoalloys

Recommend Documents