Geometric Structure and Chemical Ordering of Large AuCu Clusters: A

Jan 9, 2017 - We show that our potential is in good agreement with density-functional theory calculations, and use it to study the structure and chemi...
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Geometric Structure and Chemical Ordering of Large AuCu Clusters: A Computational Study Jing-Qiang Goh,†,‡ Jaakko Akola,*,†,‡ and Riccardo Ferrando*,§ †

Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland COMP Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland § Chemistry and Industrial Chemistry Department, University of Genoa, Via Dodecaneso 31, 16146 Genoa, Italy ‡

S Supporting Information *

ABSTRACT: Understanding the structure and composition of nanosized gold−copper (AuCu) clusters is crucial for designing an effective AuCu catalyst. Global optimization of AuCu clusters using atomistic force fields is a viable solution for clusters with at least a few nm sizes, because of its fast computation. Here we develop an atomistic many-body potential for AuCu on the basis of the second-moment approximation to the tight-binding model. We show that our potential is in good agreement with densityfunctional theory calculations, and use it to study the structure and chemical ordering of clusters of sizes up to ∼4 nm by means of global optimization searches. We show that the clusters present a surface enrichment in Au, while subsurface and central sites are enriched in Cu. Surface enrichment in Au and center enrichment in Cu are stronger in icosahedra. Surface Cu atoms prefer terrace sites on (111) facets. Both atomistic and DFT calculations show that L10 and L12 ordered phases are not favorable, even at their ideal compositions for these sizes, because of the tendency of Au to surface segregation. The stability range of icosahedral structures is wider in AuCu nanoalloys than in Au and Cu pure clusters. resolve the chemical ordering of AuCu and AuAg clusters.10 In addition to the available experimental characterization tools, theoretical studies of bimetallic clusters can provide us the complementary insights of cluster structure and chemical ordering.1,11−13 Structural search for energetically favored, large-sized clusters at the level of density functional theory (DFT) requires significant computational resources. At present, DFT global optimization of both structure and chemical ordering of nanoalloys is limited to a few tens of atoms,14 whereas optimization of chemical ordering for fixed geometry requires a smaller computational effort and can be performed for clusters of a few hundred atoms.15 For this reason, methods using empirical atomistic potentials are an important tool for optimizing nanoalloys of sizes of 3−5 nm, containing several thousand atoms. Among atomistic potentials, the secondmoment tight binding potential, known also as Gupta manybody potential,16−19 has been used for optimization of a series of nanoalloys in the range 3−5 nm.20−23 A method combining both Gupta and DFT simulations, in which the global search is made at the atomistic level and selected structures are locally reoptimized by DFT, is thus a feasible option to perform the

1. INTRODUCTION In recent years, research in bimetallic clusters has attracted the attention of the nanoscience community because of the potential wide range of interesting chemical and physical properties.1−3 In binary metallic clusters (often referred to as nanoalloys), one can combine the advantageous features of different materials into a nanosized entity by manipulating both cluster size and composition. The combination of Au and Cu atoms in a AuCu (gold−copper) nanoalloy can attain desired properties for effective catalysis processes.4 The introduction of some Cu in Au can effectively lead to a more stable catalyst for CO oxidation as compared to a monometallic Au system.5,6 Interestingly, AuCu nanoalloys have also been demonstrated to be a useful catalyst for the electrochemical reduction of CO2 to hydrocarbon fuels.7 This kind of nanoalloys can help to stabilize Cu and to reduce the cost of Au for the practical design of a catalytic material. A broad range of experimental techniques are available for the synthesis of AuCu clusters. Well-controlled formation of size-selected Au-rich/Cu-rich, Cu-rich/Au-rich core/shell clusters have been successfully realized via the cluster beam technique.8 One can also synthesize well-defined composition AuCu ordered phase nanocrystals by employing suitable Au and Cu precursors in a colloidal preparation method.9 To understand the structural effect, it is crucial to resolve the atomic ordering of a synthesized bimetallic cluster, and this is not a trivial task. Nonetheless, resonant high-energy X-ray diffraction combined with atomic pair distribution function analysis and computer simulation have been employed to © 2017 American Chemical Society

Special Issue: ISSPIC XVIII: International Symposium on Small Particles and Inorganic Clusters 2016 Received: November 28, 2016 Revised: January 6, 2017 Published: January 9, 2017 10809

DOI: 10.1021/acs.jpcc.6b11958 J. Phys. Chem. C 2017, 121, 10809−10816

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The Journal of Physical Chemistry C structural search for large sizes.24,25 In this way, Gupta simulations guide the DFT simulations in exploring likely candidate clusters, and an accurate estimation of the relative energetic ordering for different structural families of a cluster can be evaluated at the DFT level. The energetic ordering of the structures determined at the Gupta level may coincide with that of DFT, as shown in several systems such as AgCu, AgNi, and AgCo,21,22,26,27 but there are cases (for example, AgAu, PdPt, and PdNi) in which atomistic and DFT calculations show significant differences in energetic ordering.24−26,28 For this reason, it is very important to check the validity of atomistic potentials against DFT for relatively small sizes before using the atomistic model for structural prediction at large sizes. In the first part of this work, we propose a new set of Gupta parameters for AuCu, whose results for describing the properties of bulk crystal phases are reported in the Supporting Information. We first perform several tests to check the global minima determined by the newly designed parameters against our DFT calculations, comparing also with the recent DFT results by Lysgaard et al.15 concerning icosahedral clusters of 309 atoms. We compare also with the results of other atomistic models, such as different Gupta parameter sets,11,19 and Effective Medium Theory (EMT) results.15 We demonstrate that our atomistic model is able to achieve a quite good agreement with DFT calculations, being thus a reliable tool to predict nanoparticle structures for large sizes. The specific analysis of chemical ordering in icosahedra of size 309 shows that the present model agrees much better with DFT than previous ones. The electronic structure (DOS, atomic charges) of the optimal icosahedra is also studied for selected compositions. In the second part of this work, global optimization of both structure and chemical ordering is made by means of this new set of Gupta parameters for large-sized AuCu clusters, with diameters in the range 3−4 nm. There we focus mostly on Au-rich and intermediate compositions whose importance for catalytic applications has been demonstrated in different cases.5,7

In the second type, chemical ordering only is optimized within a given structural motif by using exchange moves, from an initial configuration with random chemical ordering. Both random exchanges and tailored exchanges for intermixing systems31 are used. In each case, five simulations of 5 × 105 steps are made. Low acceptance temperatures (100−300 K) are used in the BH algorithm.3 Selected structures from atomistic BH searches are then locally relaxed by DFT until the maximum force acting on individual atoms is below 0.005 eV/ Å. To this end, we employ a parallelized DFT simulation package, the CP2K program.32 CP2K program adopts localized Gaussian and plane wave basis sets for the representation of electron density, and this dual representation is favorable for efficient simulations. We use a library of contracted m-DZVP basis sets33 for the Gaussianbased (localized) expansion of the Kohn−Sham orbitals, and a cutoff of 450 Ry for the electron density. Norm-conserving and separable pseudopotentials of Goedecker, Teter, and Hutter are used to describe valence electron−ion interaction,34 and the generalized gradient approximation of Perdew, Burke, and Ernzerhof (PBE)35 is adopted for the exchange-correlation energy functional. The AumCun clusters are optimized in a gas phase environment (a cubic simulation box with nonperiodic boundary condition) and valence configurations of 5d106s1, 3d104s1 are considered for Au and Cu.

3. ATOMISTIC MODEL The atomistic potential has the form proposed by Rosato et al.,18 which can be derived within the tight-binding second moment approximation.16 In this model, the potential energy E of a cluster is the sum over all the atoms of their bonding (Eb) and repulsive energy (Er) contributions: E=

∑ (Ejb + Ejr) (1)

j

The bonding energy term has the form of Ejb = −

2. COMPUTATIONAL METHODS Our global optimization searches are made using the atomistic force field described in the following section. The algorithm employed in these searches is Basin Hopping (BH).29 Two types of searches are made. In the first type, both geometric structure and chemical ordering of clusters are optimized staring from an initial random configurations. Different moves are used during the optimization. These comprise local displacement moves, such as the shake and the Brownian moves,30 and exchange moves, in which the identity of two randomly selected unlike atoms is swapped. In most cases, five simulations of 1 × 105 BH steps by shake moves, followed by 3 × 104 exchanges are made. In these simulations, the shake moves are performed by moving each atom randomly in a sphere of radius 1.4 Å. Further simulations are made by using Brownian and exchange moves simultaneously. Each Brownian move allows atoms to move according to Langevin dynamics (250 simulation steps, with a time step of 5 fs) at high temperature (2500 K). Brownian moves have been shown to be efficient for the optimization of large clusters. Hence, we assign probabilities of 0.8 for Brownian moves and 0.2 for exchange moves in each simulation with total number of 3 × 105 BH steps.

∑ ξsw2 i

⎡ ⎞⎤ ⎛ rij exp⎢ −2qsw⎜ 0 − 1⎟⎥ ⎢⎣ ⎠⎥⎦ ⎝ rsw

(2)

meanwhile, the repulsive Born−Mayer term has the form of Ejr =

∑ A sw i

⎡ ⎞⎤ ⎛ rij exp⎢ −psw ⎜ 0 − 1⎟⎥ ⎢⎣ ⎠⎥⎦ ⎝ rsw

(3)

rij is the distance between atoms i and j. s (w) refers to the chemical species of the atom i (j), and r0sw is the nearestneighbor distance in the sw lattice. If the interaction is heteroatomic (s ≠ w) such as interaction between an Au−Cu atomic pair, r0sw is expressed as 0 0 rAuCu = rCuAu =

0 0 rAuAu + rCuCu 2

(4)

The empirical parameters p, q, A, and ξ can be fitted to the bulk properties of transition metals and alloys.19 Cutoff distances on the interactions are imposed as follows. The exponentials in eqs 2 and 3 are replaced by fifth-order polynomials of the form a3(r − rc2)3 + a4(r − rc2)4 + a5(r − rc2)5, between distances rc1 and rc2, with a3, a4, and a5 fitted in each case to obtain a function that is always continuous, with first and second derivative for all distances, and goes to zero at rc2. 10810

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The Journal of Physical Chemistry C Table 1. Metal−Metal Potential Parameters Fitted for AuCu Bimetallic Clusters in This Worka

a

sw

p

q

A

ξ

r0

rc1

rc2

Au−Au Cu−Cu Au−Cu

10.139 10.700 11.590

4.033 2.452 3.280

0.210120 0.088784 0.108500

1.8200 1.2785 1.4400

2.88 2.56 2.72

√2rAu 0 √2rCu 0 √2rAu 0

√3rAu 0 √3rCu 0 √3rCu 0

A and ξ are in eV, r0 in Å.

Table 1 presents the fitted parameters of the current work, together with the values of r0, rc1, and rc2 for homogeneous and heterogeneous pairs. At variance with the Gupta parameters of ref 19, which were fitted to reproduce specifically the properties of the L12 ordered phase for Au0.25Cu0.75 composition, the parameters of Table 1 aim at reproducing the overall behavior of the L12 phase for both Au0.25Cu0.75 and Au0.75Cu0.25 and of the L10 phase for Au0.50Cu0.50. Moreover, these parameters reproduce the asymmetry of Cu in Au and Au in Cu impurity dissolution energies. A comparison of the results obtained by this model with experimental data on bulk alloys is given in the Supporting Information. Further validation of the model is given by the comparison with DFT results reported in sections 4.1 and 4.2.

4. COMPARISON WITH DFT RESULTS 4.1. Chemical Ordering in the Icosahedron of Size 309. Chemical ordering in AuCu icosahedra of N = 309 atoms has been recently determined by using a combination of genetic-algorithm global optimization searches using both atomistic EMT potentials and DFT calculations.15 In these calculations, the excess energy Eexc * of clusters AumCun was calculated as an energetic stability index.3 E*exc is defined as1 * (m , n) = E(m , n) − m E(N , 0) − n E(0, N ) Eexc (5) N N

Figure 1. Excess energy per atom (in eV) for the AumCun icosahedron of m + n = N = 309 atoms.

where E(m,n) is the binding energy of the AumCun cluster. In ref 15, E(m,n) was the energy of the AumCun cluster icosahedron with the optimal chemical ordering. Compositions with lower Eexc * correspond to stronger stability. The DFT results of ref 15 showed that the lowest Eexc * is obtained for composition Au170Cu139, corresponding to m/N = 0.550. On the other hand, the EMT calculations gave a rather different optimal composition, corresponding to m/N = 0.63. Also, the optimal excess energy per atom Eexc * /N was quite different: −0.122 eV for DFT and −0.065 eV for EMT. According to DFT calculations, the surface of the cluster at the optimal composition contained 24 Cu atoms, placed in nonsymmetric way in sites on the terraces. The interior of the cluster was found to be of full icosahedral symmetry, with a Cu atom in the central site. The EMT results gave only eight Cu surface atoms at the optimal composition. We have performed the same calculation using our Gupta model, whose results about E*exc are reported in Figure 1. We obtain results in much better agreement with DFT. Our optimal composition is Au174Cu135, corresponding to m/N = 0.563, with Eexc * /N = −0.114 eV. Our optimal cluster has 20 Cu atoms on its surface, which are placed in a nonsymmetric way, while the interior of the cluster has a full icosahedral symmetry with a Cu atom in the central site, in agreement with DFT results.15 The structure of the optimal Au174Cu135 is shown in Figure 2. Our Gupta parameter set performs better than previous ones. For example, the Gupta set used in ref 11 gives an optimal composition m/N = 0.498, with 40 Cu atoms in the surface layer. We have also recalculated the excess energies at

Figure 2. Structure of the optimal icosahedral cluster of composition Au174Cu135. The different panels show the different icosahedral shells of the cluster, from the second shell in the top left panel, to the fifth (surface) shell in the bottom right panel. Inner shells preserve the full icosahedral symmetry, while the surface shell symmetry is broken by the placement of the 20 Cu atoms in the terraces. There is a single atom on each terrace, but it is not possible to place them in a way which preserves the full symmetry of the icosahedron due to geometric frustration.

the DFT-PBE level for a few compositions. The results are given in Table 2, showing that the agreement between DFT and Gupta results is quite good for intermediate and Au-rich compositions, while it is less satisfactory in the Cu-rich case. The electronic density of states (eDOS) of the clusters of Table 2 is shown in Figure 3. From the results in this figure, one can observe that the p-orbital states of Au and Cu mainly dominate in the electronic states adjacent to the band edges. 10811

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The Journal of Physical Chemistry C Table 2. Excess Energy per Atom Eexc * /N (in eV) Evaluated for AuCu Icosahedra Using the PBE Functional and the Gupta Potential composition

m/N

E*exc/N (PBE)

E*exc/N (Gupta)

Au77Cu232 Au155Cu154 Au174Cu135 Au232Cu77

0.249 0.502 0.563 0.751

−0.0970 −0.1195 −0.1214 −0.0969

−0.0781 −0.1120 −0.1143 −0.0976

affect adsorption properties for reactant molecules, such as CO and O2.6 4.2. Preferential Placement of Single Cu Impurities. Here we consider the placement of single Cu impurities in Au host clusters. This is an important subject for catalytic applications in which the catalytic activity and stability of Au clusters is improved by introducing Cu atoms.5,7 Specifically, we consider several sites in an icosahedron of 309 atoms, in a decahedron of 192 atoms and in a truncated octahedron of 201 atoms. The sites where the impurity is placed are shown in Figure 4 and the energies calculated by DFT and Gupta local relaxations are given in Table 3. For all clusters, the zero of the energy corresponds to placing the impurity in the central site A (not shown in the figure). The calculations show that a single Cu impurity is better placed in the interior of the cluster. Surface sites are always less favorable. The most favorable inner site in the icosahedron is the central site by a large amount of energy, as the small Cu impurity fits very well in that compressed site.20 In the truncated octahedron, the best site is a subsurface site, which is below one of the vertices, but energy difference with other internal sites are smaller. On the surface, terrace sites are more favorable than edge and vertex sites, the latter being the highest in energy. In the truncated octahedron, there is a slight preference for (111) terraces, while in the decahedron the best placement is at the bottom of the Marks re-entrance, while (100) and (111) terrace sites are somewhat higher in energy and almost degenerate.

Compared to the eDOS of clusters at intermediate compositions, the introduction of more Au atoms (as in Au232Cu77, whose surface is pure Au) enhances the d-orbital states in the band region of −12 to −7 eV. On the other hand, the introduction of more Cu atoms (as in Au77Cu232, whose core is pure Cu) does not result in a significant change to the eDOS profile. The d-band centers are deeper for Au than for Cu. The variation of their position for the different compositions of Figure 3 is negligible. On the other hand, HOMO−LUMO gaps are of marginal size for each case, as can be expected for clusters of this size, containing thousands of electrons. The Bader charge analysis shows that in Au77Cu232, Au155Cu154, and Au174Cu155, where the surface contains both types of metals, Au surface atoms get negatively charged (with charges of the order of −0.3 e), while surface Cu atoms become positive. On the other hand, in Au232Cu77, the surface contains only Au atoms that are almost neutral. These features crucially

Figure 3. Electron density of states for the optimal icosahedral clusters of compositions Au77Cu232, Au155Cu154, Au174Cu135, and Au232Cu77. The top part of each panel shows the decomposed orbital states for Au and Cu, with the symmetries of states listed in parentheses. s- and p-symmetric states were multiplied by a factor of 10. The bottom parts of each panel shows the total density of states for Au and Cu. The HOMO levels are positioned at the zero-energy level. The positions of the d-band centers are indicated for both species in each panel. The vertical scales are arbitrary and not to be compared between the different panels. 10812

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overestimates the stability of other subsurface sites compared to DFT calculations. 4.3. Ordered versus Disordered Phases. The phase diagram of bulk Au−Cu presents stable ordered phases for compositions Au0.25Cu0.75, Au0.75Cu0.25 (L12 phase), and Au0.50Cu0.50 (L10 phase).36 The L10 phase presents an alternating sequence of (100) planes of pure Au and pure Cu, whereas in the L12 phase (100) planes of pure Cu (Au) alternate with mixed planes in which Au and Cu atoms are placed in a checkerboard pattern. It is interesting to check whether these ordered phase are stable in nanoalloys. To this end, we have considered truncated octahedral clusters of size 201 in which we have built up the three perfect ordered phases of compositions Au57Cu144, Au105Cu96, and Au144Cu57 (see the left column of Figure 5).

Figure 4. Sites for placing single Cu impurities in Au clusters. Top row: icosahedron of 309 atoms. In the left panel, subsurface sites are shown. The Au atoms covering these subsurface sites are shown as small spheres. In the right panel, surface sites are shown. Middle row: Marks decahedron of 192 atoms. Bottom row: fcc truncated octahedron of 201 atoms. In the left panel, subsurface sites are shown. The Au atoms covering these subsurface sites are shown as small spheres. In the right panel, surface sites are shown. For all clusters, site A is the central site of the cluster (not shown). The energies related to the different placement of the impurities are given in Table 3.

Table 3. Energies (in eV) for Single Cu Impurities in Au Clustersa cluster

position

DFT-PBE

Gupta

Ih309

A center B subvertex C subedge D subterrace E terrace F edge G vertex A center B re-entrance C (100) terrace D (111) terrace A center B subvertex C subedge D subterrace E (111) terrace F (100) terrace

0.000 0.748 0.951 1.077 1.426 1.440 1.532 0.000 0.313 0.438 0.441 0.000 −0.108 0.039 0.111 0.352 0.416

0.000 0.868 0.959 0.996 1.323 1.350 1.392 0.000 0.267 0.330 0.320 0.000 −0.055 −0.044 −0.053 0.203 0.240

Dh192

TO201

Figure 5. Ordered phases (left column) and optimized chemical ordering according to the Gupta potential (right column) for truncated octahedra of size 201. For compositions Au57Cu144 and Au144Cu57, the ordered phase is of L12 type, whereas for Au105Cu96, the ordered phase is of L10 type.

These clusters have been locally relaxed both at the Gupta and at the DFT level. Then we have considered the same TO geometry and compositions but optimizing chemical ordering by basin-hopping searches at the atomistic level, obtaining the minima represented in the right column of Figure 5, which strongly differ from those of the ordered phases. The main difference is a smaller number of Cu atoms at the cluster surface. These minima have been locally relaxed also by DFT. The results of our calculations show that the phase-ordered minima are always unfavorable for size 201. For Au57Cu144, the phase-ordered minimum is higher in energy by 3.514 and 4.897 eV, according to DFT-PBE and Gupta calculations, respectively. On the other hand, the energy differences are 3.892 and 3.842 eV for Au105Cu96 and 11.916 and 8.605 eV for Au144Cu57. DFT and Gupta calculations are therefore in good agreement for all cases.

a

The sites in which the impurities are placed are shown in Figure 4. For all clusters, the zero of the energy is the cluster with the impurity placed in the central site A.

The agreement between DFT and Gupta results is quite good in the icosahedron and in the decahedron, for which the energetic ordering of the sites is very well reproduced by the Gupta potential. In the truncated octahedron, Gupta potential is right in singling out the most favorable site (i.e., the subvertex site) and in the energetic ordering of surface sites, but it 10813

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5. OPTIMIZATION OF LARGER CLUSTERS AT THE ATOMISTIC LEVEL 5.1. Global Optimization of AuCu Clusters with N = 586. Clusters of size 586 have been fully optimized at the atomistic level for three compositions, Au0.25Cu0.75, Au0.50Cu0.50, and Au0.75Cu0.25. These clusters have diameters in the range 2.5−2.7 nm. The results are shown in Figure 6. Even though

Figure 7. Optimal chemical ordering for TO, Dh, and Ih clusters of composition Au0.50Cu0.50. Each cluster is shown in two views: cluster surface (left column) and cross section (right column).

Figure 6. Optimized structures for Au−Cu clusters of size 586 for three different compositions.Each cluster is shown in two views: cluster surface (left column) and cross section (right column).

586 is a magic size for the regular truncated octahedron, the optimal geometric structure is always icosahedral for the three compositions considered here. This structure consists of a 561atom icosahedron capped by an island with atom in antiMackay stacking. This is at variance with the results for pure Au and Cu clusters of size 586, for which the TO is indeed the lowest energy structure according to our optimization searches. For pure Au, the TO is in close competition with a Marks Dh, whereas for pure Cu it is in close competition with the capped Ih. These results show that the tendency to form icosahedral structures in binary clusters with size mismatch, which has been found for a series of different systems,22 is confirmed also for Au−Cu. Referring to the subshells of Au293Cu293 clusters, some of the Au atoms are distributed sparsely in the cluster core. In this manner, the Au−Cu mixing can be enhanced together with those surface Cu atoms in the Au-rich shell. The Cu-rich Au146Cu440 cluster has a clear Cu-rich/Au-rich core/shell structure. In the Au-rich Au440Cu146 cluster, Au−Cu mixing within the cluster core is favored, and some subsurface enrichment in Cu is observed. This last point is discussed in more details in section 5.2. 5.2. Optimization of Chemical Ordering in Larger Icosahedra, Decahedra, and Truncated Octahedra. Here we deal with the optimization of chemical ordering for TO, Dh and Ih clusters of larger sizes (1289, 766, and 923 atoms, respectively), whose diameters are in the range between 3 and 4 nm. For all geometries, we consider compositions Au0.50Cu0.50 and Au0.60Cu0.40, which correspond to Au645Cu644 and Au773Cu516 for the TO, Au383Cu383, and Au460Cu306 for the Dh, and Au462Cu461 and Au554Cu369 for the Ih. Images of the clusters with optimal chemical ordering are given in Figures 7 and 8.

Figure 8. Optimal chemical ordering for TO, Dh, and Ih clusters of composition Au0.60Cu0.40. Each cluster is shown in two views: cluster surface (left column) and cross section (right column).

For each cluster, we analyze chemical ordering in the following way. We define the cluster surface as the collection of atoms that have less than 11 nearest neighbors. Then we remove surface atoms and define the cluster subsurface as the surface of the resulting cluster after removal. Then we remove surface atoms again and define the cluster core as the remaining part of the cluster. In this way, cluster surface and subsurface are both shells of monatomic thickness. In Table 4, we report the concentrations cAu and cCu of the two different species. Our results show the following: • The surface is always very strongly enriched in Au (from 25% to more than 33% compared to the average composition of the whole cluster), the subsurface is strongly enriched in Cu (from 20% to 25%), and the core is enriched in Cu too (from 11% to 14%). The surface enrichment in Au is due to the lower surface energy and larger atomic size of Au. On the other hand, subsurface 10814

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surf subs subs core core Table 4. Composition of Surface (csurf Au , cCu ), subsurface (cAu , cCu ) and Core (cAu , cCu ) in the TO, Dh, and Ih Clusters of Figures 7 and 8

structure

cluster

csurf Au

csurf Cu

csubs Au

csubs Cu

ccore Au

ccore Cu

TO TO Dh Dh Ih Ih

Au645Cu644 Au773Cu516 Au383Cu383 Au460Cu306 Au462Cu461 Au554Cu369

0.784 0.869 0.753 0.846 0.829 0.928

0.216 0.131 0.247 0.154 0.171 0.072

0.256 0.379 0.252 0.342 0.298 0.377

0.744 0.621 0.748 0.658 0.702 0.623

0.388 0.484 0.363 0.486 0.282 0.398

0.612 0.516 0.637 0.514 0.718 0.602

calculations, and obtained a quite good agreement, which is much better than the agreement obtained by using previous Gupta parameter sets or other atomistic models. Our atomistic model agrees very well with DFT results15 for optimal chemical ordering in icosahedral clusters. Moreover, it reproduces most features of the preferential placement of isolated Cu impurities in a host Au cluster, and the correct energetic ordering of phase-ordered and disordered clusters for the compositions Au0.25Cu0.75, Au0.75Cu0.25 (L12 phase), and Au0.50Cu0.50 (L10 phase). These results show that our atomistic model is a reliable tool for a wide range of compositions, including at least Au-rich and intermediate compositions, which have been investigated more deeply here because of their importance for catalysis.5,7 Due to the difference in electronegativity between Au and Cu, some charge transfer from Cu to Au is expected in this system. Our calculations however show that satisfactory results can be obtained without including charge-transfer terms explicitly in the potential. Indeed, charge transfer would simply reinforce the tendency of Au to surface segregation, a tendency that is already effectively taken into account. This is different from AgAu,38 in which the correct segregation profile is obtained only when charge-transfer terms are explicitly included.39 The model has then been used to fully optimize clusters of several hundred atoms and to optimize chemical ordering in clusters up to about 1300 atoms. Our results for AuCu clusters have shown that the stability domain of the icosahedron is enlarged compared to pure Au and Cu clusters. For what concerns chemical ordering, there is an overall tendency toward Au surface enrichment and Cu subsurface and core enrichment, which is stronger in the icosahedral motif compared to decahedra and truncated octahedra.

placement of Cu helps in decreasing the atomic pressure.3,20,37 • There are some differences between the motifs. The Ih cluster shows the strongest Cu enrichment of the core and the strongest Au enrichment of the surface. This is consistent with the fact that the core of the icosahedron is compressed, so that the smaller Cu atoms are better placed there, while the Ih surface suffers tensile strain, so that placing small atoms there is a disadvantage. • Cu surface atoms are preferentially placed at highcoordination sites, such as terrace sites of (111) facets and Marks re-entrances. Moreover, these surface Cu atoms tend to be completely surrounded by Au surface neighbors. Finally, in Figure 9 we report the plot of E*exc/N for the TO of 1289 atoms. Comparing with the plot of Eexc * /N of Figure 1,

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b11958.

Figure 9. Excess energy per atom (in eV) for the AumCun truncated octahedron of m + n = N = 1289 atoms.

we note that the minimum shifts to compositions which are closer to 50−50%, which is the optimal composition in the bulk crystal limit.36 The results is understandable in terms of the reduced surface-to-volume ratio for the 1289-atom cluster. Moreover, even for finite sizes, in the TO there is no icosahedral strain preferring Cu in the core and Au on the surface. These factors both contribute in approaching the bulk limit.

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Comparison of Gupta potential results and experimental data for AuCu bulk alloys (PDF).

AUTHOR INFORMATION

Corresponding Authors

*E-mail: jaakko.akola@tut.fi. *E-mail: ferrando@fisica.unige.it. ORCID

Riccardo Ferrando: 0000-0003-2750-9061

6. CONCLUSION In this paper we have proposed a new parameter set for the Gupta potential, compared its results to those of DFT

Notes

The authors declare no competing financial interest. 10815

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ACKNOWLEDGMENTS J.-Q.G. and J.A. acknowledge financial support from the Academy of Finland through its Centres of Excellence Program (Project 284621). J.-Q.G. acknowledges the graduate student scholarship by Magnus Ehrnrooth foundation. The computational resources were provided by CSC, the IT Center for Science Ltd., Espoo, Finland.

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DOI: 10.1021/acs.jpcc.6b11958 J. Phys. Chem. C 2017, 121, 10809−10816