Theoretical study of AuCu nanoalloys adsorbed on MgO(001)

Surface Science 606 (2012) 938–944

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Theoretical study of AuCu nanoalloys adsorbed on MgO(001) M. Cerbelaud a, 1, G. Barcaro b, A. Fortunelli b, R. Ferrando a,⁎ a b

Dipartimento di Fisica dell'Università di Genova, via Dodecaneso 33, 16146 Genova, Italy CNR-IPCF, Istituto per i Processi Chimico-Fisici, Via G. Moruzzi 1, Pisa, I56124, Italy

a r t i c l e

i n f o

Article history: Received 9 December 2011 Accepted 10 February 2012 Available online 20 February 2012 Keywords: Copper Gold Magnesium oxide Nanoalloys

a b s t r a c t The structures of AuCu clusters adsorbed on the (001) face of MgO are searched for by a two-step methodology. In a first step, the relevant structural motifs are singled out by global optimization searches within an atomistic model. In a second step, the lowest energy structures of each motif are relaxed by density-functional calculations. Three different sizes (30, 40 and 50 atoms) are considered. For each size, three compositions are analyzed. For size 30, a competition between fcc pyramids and a new motif (the daisy structure) is found. For 40 and 50 atoms, icosahedral fragments prevail. The results are discussed in connection with experimental data related to clusters of larger sizes. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Compared to monometallic clusters, bimetallic clusters are very interesting because their physical and chemical properties can be tuned not only by varying their size but also by varying their composition and atomic ordering. During the last years, one of the systems which has received considerable interest is AuCu. The AuCu system has three ordered alloys in bulk crystals: Au0.5Cu0.5 (fcc, L10), Au0.25Cu0.75 and Au0.75Cu0.25 (both fcc, L12). It has been shown in experiments that the stoichiometry of bulk alloys can be well reproduced in the clusters [1,2]. Several theoretical studies have been devoted to free AuCu clusters in recent years. These studies often consist in searching the geometry of the lowest-lying isomer by global minimization algorithms using an atomistic interaction potential, in most cases the so-called Gupta potential [3], derived within the second-moment approximation to the tightbinding model [4–10]. According to this model, the global minima (GM) are found to be icosahedral packing structures for most nuclearities, with a tendency in favor of gold segregation to the surface. Lordeiro et al. and Darby et al. have pointed out that some structures of small clusters found by means of the Gupta potential are in disagreement with experimental ones [5,4,11]. For small clusters, where quantum effects are more significant, the Gupta potential appears to be not accurate enough and studies at a higher level of theory, such as density functional theory (DFT), are needed [12].

⁎ Corresponding author. Fax: + 39 010311066. E-mail address: ferrando@fisica.unige.it (R. Ferrando). 1 Present address: CNRS, Institut des Matériaux Jean Rouxel, 2 rue de la Houssinière, 44322 Nantes CEDEX 3, France. 0039-6028/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2012.02.010

To study the medium-sized clusters at a higher level of theory than the Gupta level, one method combining empirical potential and DFT calculations (EP-DF method) has recently been proved feasible [13]. The EP-DF consists in searching candidate structures of minimum energy at the Gupta level. These structures are then minimized at the DFT level. Such a method has recently been applied by Tran et al. to study Au 38−n Cun clusters [14]. They have shown that for the AuCu clusters of size N = 38 atoms, the truncated octahedral structure is less energetically favored at the DFT than at the Gupta level, suggesting that the energetic ordering of AuCu medium-sized clusters should be analyzed at a higher level of theory than the Gupta one. From the experimental point of view, Pauwels et al. have reported an analysis performed by electron diffraction and high resolution electron microscopy of 1–4.5 nm AuCu clusters generated by laser vaporization and deposited at low energy on amorphous carbon and MgO substrates [1]. In the case of deposition on carbon substrate, it was found that AuCu nanoparticles can adopt various morphologies such as cuboctahedra, decahedra and various quasi-spherical geometrical structures. In the case of deposition on the MgO substrate, only the truncated octahedral morphology has been observed. On MgO, the clusters with the stoichiometric compositions Au0:25 Cu0:75 , Au0:5 Cu0:5 and Au0:75 Cu0:25 were all found to have an fcc structure and to be in cubeon-cube epitaxy relation with MgO(001) substrate. Pauwels et al. also performed Monte Carlo simulations on free constrained clusters using an embedded-atom atomistic potential. Simulations showed that clusters have an ordered core surrounded by a disordered shell, which disagrees with the experiment. Several reasons were then advocated for this disagreement. One reason is about the fact that clusters are generated far out of thermodynamic equilibrium and then cooled out, which may give disordered cold structures. Another reason concerned

M. Cerbelaud et al. / Surface Science 606 (2012) 938–944

the fact that the interactions with the substrate may lead to both structural and chemical ordering rearrangements in the cluster. The interaction with MgO might force the system to adopt a solid solution chemical ordering with fcc geometric structure. In this article we perform a search for the most stable structures of AuCu clusters deposited on MgO(001) by an EP-DF method. We consider sizes up to N = 50 atoms. For each size the three stoichiometries Au 0:25 Cu0:75 , Au 0:5 Cu0:5 and Au 0:75 Cu0:25 are studied. Different structural motifs and chemical ordering patterns are singled out. In particular, a new motif, the ‘daisy structure’, is found. This motif has no counterpart in free gas-phase clusters, its stability being induced by the interaction with the substrate. Our calculations cannot presently explore the size range which has been considered in the experiments, but only smaller sizes. However we believe that the comparison of the morphologies that are obtained at small sizes with those obtained in the experiments for larger sizes can be interesting because they can suggest possible size-dependent morphology transitions. The paper is structured as follows. In Section 2 we describe our model and computational methodology. In Section 3 we report on the results, first focusing on chemical ordering in fcc clusters and then comparing different geometric motifs. The results are discussed in comparison with the available experimental information. Section 4 contains the conclusions. 2. Computational details 2.1. Empirical energy potential model: Gupta level The empirical atomistic potential has been fully described in Ref. [15], therefore only a brief summary will be presented here. The energy of a cluster of N atoms is written as the sum of single-atom terms: E¼

N  X

mm

Ei

mo 

þ Ei

;

ð1Þ

i¼1

with Eimm and Eimo respectively the metal–metal and metal–oxide interactions. Eimm is expressed by the expression derived within the secondmoment approximation to the tight-biding model: mm

Ei

b

r

¼ Ei þ Ei ;

ð2Þ

with r

Ei ¼

∑

j≠j;r ij br c

   r ij A exp −p −1 ; r0

( b

Ei ¼ −

∑

j≠i;r ij br c

ð3Þ

  )1=2 r ij 2 ξ exp −2q −1 ; r0

ð4Þ

where rij is the distance between atoms i and j, rc is the cutoff radius and r0 the nearest-neighbor distance. (A, ξ, p, q) is a set of parameters fitted to experimental bulk quantities. In this paper, parameters fitted by Cleri and Rosato have been used (see Table 1) [3].

Table 1 Metal–metal potential parameters for AuCu bimetallic cluster [3]. ij

p

q

a

ξ

Au–Au Cu–Cu Au–Cu

10.229 10.960 11.050

4.036 2.278 3.04757

0.2061 0.0855 0.1539

1.7900 1.2240 1.5605

939

Eimo is a many-body potential energy surface for metal–MgO(001) interactions fitted on first principles calculations in the case of nonreactive interfaces [16,15]. It is expressed as: mo

Ei ðxi ; yi ; zi ; Z i Þ n o −2a ðx ;y ;Z Þ½z −a ðx ;y ;Z Þ −a ðx ;y ;Z Þ½z −a ðx ;y ;Z Þ ¼ a1 ðxi ; yi ; Z i Þ e 2 i i i i 3 i i i −2e 2 i i i i 3 i i i ; ð5Þ with −Z i =bj3 ðxi ;yi Þ

aj ðxi ; yi ; Z i Þ ¼ bj1 ðxi ; yi Þ þ bj2 ðxi ; yi Þe

;

bjk ðxi ; yi Þ ¼ cjk1 þ cjk2 fcosðχxi Þ þ cosðχyi Þg þ cjk3 fcosðχ ðxi þ yi ÞÞ þ cosðχ ðxi −yi ÞÞg:

ð6Þ

ð7Þ

where Zi is the number of metal nearest neighbors of atom i, χ = 2π/a with a the oxygen–oxygen distance in the substrate, x and y are the coordinates parallel to the 〈110〉 directions, and the terms cjkl are 27 parameters which are fitted on first principles calculations, as described in Ref. [15]. A discussion of the physical meaning of the present model of metal–MgO interactions is given in Ref. [16]. Here we briefly recall that this model is developed to reproduce the DFT energetics of adsorbed atoms. In particular, the model reproduces the weakening of the interaction between an adsorbed metal atom and the substrate with increasing number of metal neighbors (number Z in the equations). The model includes polarization effects but it does not include dispersion forces. As for charge transfer, we expect that it should be small. In fact it has been shown that for an isolated Au atom on a thick oxide film, charge transfer is negligible [17]. For Cu charge transfer should be even smaller. 2.2. Global optimization algorithm Global optimization searches are performed using the basinhopping algorithm [18] and the parallel excitable Walkers algorithm (PEW) [19,20]. The optimization consists of two steps. First, extensive searches of geometric motifs are performed. These searches start from random initial configurations, in which atoms are randomly placed in a cubic box above the substrate. The elementary move used in these searches is the shake move. This move consists in displacing randomly each atom within a sphere of radius 1.4 Å centered on its present equilibrium position. In the PEW searches, the (555) signature of the common-neighbor analysis or the fraction of atoms in contact with the substrate are used as order parameters. For any cluster, at least 10 unseeded searches of length from 3000 to 10,000 Monte Carlo steps are performed. In the second step of the procedure, for each motif, several isomers are selected for further simulation runs in which the optimal chemical ordering is searched for (optimization of the homotops). During the search of homotops, only exchange moves are performed. In an exchange move, the positions of two atoms of different species are interchanged. For each structure, at least 2000 exchange moves are made. To complete the search, the lowest-lying structures obtained for a given composition are tested for the other compositions. In this case, the nature of atoms is changed in order to reproduce the new compositions, and then chemical ordering is optimized by exchange runs. Full global optimization at the DFT level would be extremely cumbersome for these cluster sizes on a substrate. Of course, our procedure cannot warrant that all significant structural motifs are singled out by the search procedures at the Gupta level. For example, it is well known that Au pure clusters tend to form leaflet or cage structures at small sizes [21–26]. These structures are not even local minima at the Gupta level. However, cage and leaflet structures are significant at small sizes and should be much less favorable for mixed clusters than for pure Au clusters. With this in mind, we remark that within each

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motif singled out by the Gupta searches, we consider several isomers and homotops for local relaxation at the DFT level (not all of them are shown in the following). In any case, even a full DFT global optimization would not warrant that all significant structures are found, due to the NP-hard nature of the optimization problem [27,28]. 2.3. Density functional calculations DFT local relaxation calculations are performed using the PWscf (plane wave self-consistent field) computational code [29]. The Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional has been used [30]. The MgO(001) surface is modeled by a two-layer slab, which contains 72 Mg and 72 O atoms in the lattice positions of the MgO bulk structure. During the optimization, the atoms of the slab are fixed. It has been previously shown that the relaxation of substrate atoms has very small effects [31]. The energy cutoff of the wave function is fixed at 40 Ry (1 Ry= 13.606 eV). Calculations are performed by applying a smearing procedure of the energy levels with a Gaussian broadening of 0.002 Ry. 3. Results and discussion 3.1. Influence of atomic ordering in copper–gold pyramidal clusters with N = 30 atoms A factor which increases the complexity of the energy landscape of nanoalloys is the existence of ‘homotops’. Homotops are Am Bn isomers having a fixed number of atoms, the same composition (m/n ratio) and the same geometrical structure, but different arrangements of the A and B atoms [32]. In order to discuss this issue in a simple geometry, we consider size 30, at which it is possible to build up a perfect pyramidal structure. For this structure, we search for the best homotops (i.e. we optimize chemical ordering by exchange runs) for the three different compositions. Examples of the most stable homotops found at the Gupta level for pyramidal clusters of compositions Au 7 Cu23 , Au 15 Cu15 and Au 23 Cu7 are shown in Fig. 1. At this level of description, it is found that gold has a tendency to segregate at the surface. As already mentioned, this tendency has already been reported by several authors in free AuCu clusters [10,5,7,9]. Gold surface segregation is currently explained first by the fact that gold has a smaller surface energy than copper (96.8 meV Å− 2 for gold and 113.9 meV Å− 2 for copper) [4] and also by the fact that copper should also prefer inner sites because of its smaller size. In fact, smaller atoms in inner positions help to relieve strain [33]. However, the description at the atomistic potential level has to be confirmed at the higher level of theory. Therefore, the study of homotops in the copper–gold pyramidal clusters with 30 atoms has also been carried out at the DFT level. Thus, atoms of different kinds are permuted “by hand” in the pyramidal structure and the new cluster is then minimized at the DFT level.

Fig. 1. Most stable homotops found at the Gupta level for pyramidal nanoparticles. Yellow (light gray) and red (dark gray) spheres refer to Au and Cu atoms in the cluster, respectively. In the substrate, big and small spheres correspond to Mg and O atoms, respectively.

Details of the DFT level energy comparison between pyramidal homotops for Au 7 Cu23 and Au 23 Cu7 absorbed on MgO(001) are shown respectively in Figs. 2 and 3. The most stable homotops found at the atomistic level are not the most stable homotops at the DFT level (see Fig. 2(h) and (c)). The differences between the orderings obtained at Gupta and DFT levels can be explained by the fact that Gupta potential does not take into account electronic effects such as charge transfer in the cluster which can have an influence in the AuCu system, in analogy to what has been found for AgAu [34–36]. We note that the number of possible homotops in this cluster is of the order of 2 · 106 (this number might be reduced by one order of magnitude by taking symmetry into account). Therefore it is impossible to sample all of them at the DFT level. However, the inspection of a few ten homotops is already sufficient (a) to reveal that DFT and Gupta present different trends, (b) to produce low-energy DFT homotops, even though it is not warranted that the best DFT homotop is singled out. For the gold-rich composition, the DFT analysis confirms the tendency of gold to segregate at the surface. The cluster with an Au-core (see Fig. 3(e)) has in fact a much higher energy than the others. Nevertheless, putting all the gold atoms on the surface does not give the most stable homotop. That structure (see Fig. 3(b)) is in fact 0.68 eV higher than the global minimum, which has two gold atoms in its core. We note also that the homotop which maximizes the number of heterogeneous bonds (see Fig. 3(d)) is 0.94 eV higher in energy than the global minimum, so that energy minimization is not driven by the maximization of intermixing. Placing copper in under-coordinated sites is always unfavorable, even when these sites are at interface with the substrate. For the copper-rich composition, the DFT analysis clearly shows the tendency of gold segregation at the surface. The most stable homotops are obtained by putting all gold atoms on the surface. The energy varies considerably according to the position of gold atoms in the structure. For example, the most stable homotop obtained at the atomistic level analysis, where all gold atoms are situated at the middle-edge and center-face positions, is 2.50 eV higher in energy than the global

Fig. 2. Energetics of homotops in Au7Cu23/MgO pyramidal nanoparticles at the DFT level (relaxed structures). Symbols as in Fig. 1.

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Fig. 3. Energetics of homotops in Au23Cu7/MgO pyramidal nanoparticles at the DFT level (relaxed structures). Symbols as in Fig. 1.

minimum (see Fig. 2(h)). According to Fig. 2, it appears that the energy of this pyramidal structure is reduced when the gold atoms occupy in sequence vertex (corner), edge and face positions, i.e. the sites with lower coordination numbers. The corner sites at the interface with the substrate are all occupied by gold atoms, while copper atoms occupy the inner sites of the interface. Other tests carried out with the Au15 Cu15 pyramidal structure and with Au7 Cu23 , Au 15 Cu15 , Au 23 Cu7 sixfold symmetry structures have also confirmed this tendency of gold surface segregation at positions of low coordination. To sum up, the chemical order found at the Gupta level analysis is not the most stable at the level of DFT analysis. The DFT analysis confirms the tendency of gold atoms to segregate at the surface and it shows that gold atoms prefer occupying the sites with low coordination. This is true both for the free cluster facet and for the facet in contact with the substrate. The tendency of gold segregation on the surface in gas-phase AuCu clusters has already been observed at the DFT level by Tran and Johnston [14] and Rodrigues et al. [9]. 3.2. Structural competition at the DFT level In the following, we are interested in determining the stable structures of copper–gold nanoparticles supported by MgO(001) with N = 30, 40 and 50 atoms for the three compositions Au0:25 Cu0:75 , Au0:5 Cu0:5 and Au0:75 Cu0:25 , without any restriction on the nanoparticle shape. We follow the method already used by Tran and Johnston, performing an analysis which combines approaches at different levels. The global minimization approach is used for searching potential lowest-lying motifs within the atomistic potential model. Then the DFT is used to reoptimize selected structures belonging to the different motifs. As already demonstrated in paragraph 1, DFT analysis does not confirm the chemical order found at the atomistic level. Therefore different homotops will be tested for each geometrical structure at the DFT level analysis. Homotops will preferentially be chosen according to the previous remarks on site preferences of gold atoms. 3.3. Results for copper–gold clusters with N = 30 atoms Simulations have been carried out for the compositions Au7 Cu23 , Au15 Cu15 and Au23 Cu7 . Fig. 4 shows the comparison of the relevant structural motifs at the DFT level. For each structure, only the homotop which was found as the lowest in energy is considered. For the copper-rich composition, the global minimum is an fcc pyramidal structure in (001) epitaxy with the substrate. This global minimum is in close competition with a new structure called by the

Fig. 4. AuCu/MgO nanoparticles of size N = 30. Symbols as in Fig. 1.

following ‘daisy structure’, which is only 0.12 eV higher in energy (see Figs. 4(I-b) and 5). The other fcc-based structures (Fig. 4(I-c) and (I-d)) and the polyicosahedral ‘six-fold pancake’ structure [37] (Fig. 4(I-e)) are higher in energy. Looking now at the results for the composition Au15 Cu15 , an analogous trend is observed. The fcc pyramidal structure in (001) epitaxy with the substrate and the daisy structure are in competition for the global minimum, with the latter being slightly more stable. The other structures are somewhat higher in energy. As for the composition Au 23 Cu7 , it appears that the fcc pyramidal structure in (001) epitaxy with the substrate is much lower in energy than all the other structures. The daisy structure is in this case 0.90 eV higher in energy than the global minimum, and structures with icosahedral or six-fold pancake motif appear more stable at this composition (Fig. 4(III-b) and (III-c)). In summary, for size N = 30, we show that the fcc pyramidal structure is energetically favorable for all the compositions, being the lowest

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Fig. 5. Top, side and bottom views of the daisy structure for Au7Cu23. It presents a sixfold ring in the top layer and nine atoms in contact with the substrate. Symbols as in Fig. 1.

isomer in Au7 Cu23 and Au23 Cu7 , and the second-lowest in Au15 Cu15 by only 0.07 eV. For Au 15 Cu15 the daisy structure is the lowest in energy, and for Au7 Cu23 it is in close competition with the fcc structure. Let us inspect more closely the daisy structure in order to understand how it is stabilized by the interaction with the substrate. The daisy structure is shown in Fig. 5 in different views for Au7 Cu23 . The structure in Fig. 5 has 9 atoms in contact with the substrate. Five of them are Cu atoms which occupy the inner part of the bottom layer. The remaining four are under-coordinated Au atoms at the periphery of the bottom layer. The five copper atoms form a rectangle with one atom at its center. The rectangle has sides of 0.399 and 0.323 nm, so that the five Cu atoms are reasonably close to on-top positions above substrate oxygens (that are arranged on a square). Now we detach the daisy structure from the substrate and locally minimize it by DFT. In this way we can quantify the strain induced by the substrate on the structure. After this relaxation, the arrangement of the atoms which were in contact with the substrate clearly changes so that the sides of the rectangle now become 0.431 and 0.276 nm i.e. much farther from a square arrangement. Also the positions of the peripheral gold atoms become less symmetric. Now the detached daisy structure can be recognized as a distorted fragment of the 55-atom icosahedron. To obtain this structure, we cut the 55-atom icosahedron by a plane which is perpendicular to one of its twofold rotation axes and passes through its center. Let us choose the coordinates in such a way that this plane is z = 0. Now we keep all 21 atoms for z > 0, while we keep only 9 of the 13 atoms at z = 0 and eliminate all 21 atoms for z b 0. Moreover, we displace the four peripheral atoms at z = 0 to break the symmetry of the structure.

3.4. Results for copper–gold clusters with N = 40 atoms For size N = 40 atoms, the compositions Au 10 Cu30 , Au 20 Cu20 and Au 30 Cu10 have been studied. The comparison between the most relevant structures at the DFT level is shown in Fig. 6. For the composition Au 10 Cu30 , the global minimum is a ‘six-fold pancake’ structure [37]. An icosahedral structure is also found in close competition, only 0.08 eV higher in energy. The most stable fcc-based structure found for this composition is 0.44 eV higher in energy and therefore it is not favored (Fig. 6(I-d)). Let us now look at the composition Au20 Cu20 . The global minimum is an icosahedral structure. This structure is in very close competition with an fcc-based structure (piece of fcc truncated octahedron) in (001) epitaxy with the substrate. The energy difference is only 0.03 eV. For this composition the ‘six-fold pancake’ structure (not shown) is much higher in energy. As for the composition Au30 Cu10 , three structures are found in very close competition: the icosahedral structure (GM), the ‘six-fold pancake’ structure (0.07 eV higher) and a decahedral motif structure in (111) epitaxy with the substrate (0.08 eV higher). No fcc cluster has been found to be in close competition with these structures.

Fig. 6. AuCu/MgO nanoparticles of size N = 40. Symbols as in Fig. 1.

3.5. Results for copper–gold clusters with N = 50 atoms An energy comparison among the structures obtained for the compositions Au 13 Cu37 , Au 25 Cu25 and Au 37 Cu13 is shown in Fig. 7. Compared to results obtained with N = 30 and 40 atoms, the differences in energy between the various structures are larger. For the three compositions, it turns out clearly that the global minimum is a mixed motif between icosahedral and decahedral structures. As in the case of N = 40 atoms, some fcc based clusters are found as the 4th lowest energy structures for compositions Au 0:25 Cu0:75 and Au 0:5 Cu0:5 (see Fig. 7(I-b) and (I-c) for Au 13 Cu37 and Fig. 7(II-c) and (II-d) for Au25 Cu25 ). 4. Discussion Pauwels et al. have investigated AuCu clusters by electron microscopy, finding that all the AuCu clusters deposited on MgO substrate have an fcc structure [1]. Let us examine the fcc structures found in our searches. First of all, we focus on interplanar distances in fcc structures. The experimental results show that lattice spacings tend to increase with increasing Au content [1], and are scattered in a wide range of values, from 0.372 to 0.422 nm [38]. We have measured the distances between (001) planes in our AuCu pyramids of 30 atoms finding that the interplanar distances (the interplanar distance is half of the lattice spacing in bulk crystals) are significantly variable, however with the

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Pauwels et al. are indeed larger than those analyzed in this paper. This leads us to think that a transition between icosahedral and fcc structures is likely to take place at sizes larger than N = 50. The fact that some fcc structures are found in close competition with icosahedral ones for the compositions Au0:25 Cu0:75 and Au0:5 Cu0:5 may indicate that the transition size for copper-rich compositions is rather close to N = 50 atoms, while for composition Au0:75 Cu0:25 the transition is likely to take place at larger sizes. This hypothesis needs to be verified. However, calculations at the DFT level are very cumbersome for clusters with more than N = 50 atoms. On the other hand, the accuracy of the atomistic potential is not really satisfactory to be confident in its predictions without DFT verification. Therefore, to study clusters in the experimental size range (several hundred atoms), it would be necessary to develop more accurate atomistic potentials, introducing for example charge-transfer effects [34]. Another point that should be considered when comparing with the experiments is that in many cases several different isomers are found within a narrow energy range from the lowest minimum. In the experimental conditions, either entropic or electron beam heating effects may cause transitions between these isomers [38], so that the experimentally observed structures may differ from the minimum-energy ones. Quantifying these effects is quite difficult, especially for what concerns beam heating. Also the calculation of thermodynamic effects would need a more reliable atomistic model. 5. Conclusions

Fig. 7. AuCu/MgO nanoparticles of size N = 50. Symbols as in Fig. 1.

expected increasing trend with increasing gold content. For example, in Au 7 Cu23 , the distance between the bottom and the first planes is 0.168 nm, whereas the distance between the second and the third planes is 0.174 nm. These distances increase to 0.176–0.184 nm in Au 15 Cu15 , and to 0.199–0.191 nm in Au 23 Cu7 . Our clusters are very small, with most atoms in surface positions, so that an overall contraction of distances is expected with respect to larger clusters and bulk crystals. Let us now discuss the cluster structures. For size N = 30 atoms, the DFT results show that fcc pyramidal structures are generally energetically favored for the three compositions Au0:25 Cu0:75 , Au0:5 Cu0:5 and Au0:75 Cu0:25 . This is due to the fact that size 30 is a magic geometric size for the fcc pyramid. However we find that fcc structures are in close competition with a new motif (the daisy structure) for copper-rich and intermediate compositions. For sizes N = 40 and 50 atoms the situation is different. For gold-rich compositions, it turns out that icosahedral fragments are more energetically favored and no fcc structure was found in competition with them. For compositions Au 0:25 Cu0:75 and Au 0:5 Cu0:5 , icosahedral packing structures are also more energetically favored than fcc structures even if some fcc structures are in close competition with them. According to these results, it seems that for medium-sized clusters (at least for 40≤ N ≤ 50) the fcc-structures are generally not favored. The interactions with the substrate are not sufficient to induce an fcc structure reorganization. The differences between the structures experimentally observed by Pauwels et al. and the structures found in our calculations may be due to the different size ranges of the clusters. The clusters analyzed by

In this paper, we have shown the results of an EP-DF method applied on AuCu clusters deposited on MgO(001) substrate. Structures have been first selected by global minimization searches using an atomistic potential, before being minimized by DFT. Our results show that the chemical ordering predicted by atomistic potential is not verified at the DFT level. At the DFT level, we have shown that there is a tendency of gold surface segregation at sites with low coordination numbers. However core–shell structures are not always favored. The structural competition for clusters of sizes N = 30, 40 and 50 atoms has been analyzed at a DFT level. The analysis has been carried out for the three stoichiometries Au 0:25 Cu0:75 , Au 0:5 Cu0:5 and Au 0:75 Cu0:25 . Whatever the composition, we find that icosahedral structures are more stable than fcc ones for clusters containing 40 and 50 atoms, whereas for 30 atoms (a magic size for the fcc pyramid) fcc structures are favorable. At size 30, a new low-energy structural motif (the daisy structure) has been singled out. This motif is in close competition with fcc structures. In summary, it seems that the interactions with the substrate are not sufficient to induce an fcc-structure for these small clusters. The comparison with the experimental results of Pauwels et al. suggests that a transition to fcc clusters should take place for sizes larger than 50 atoms. For copper-rich compositions, there is some indication that the transition size is indeed close to 50 atoms. Acknowledgments The authors acknowledge support from CINECA for the project HP10C4VX3O and CASPUR for the project Structures of Au clusters adsorbed on CaO(001). The authors acknowledge the networking support of the COST Action MP0903 NANOALLOY. References [1] B. Pauwels, G. van Tendeloo, E. Zhurkin, M. Hou, G. Verschoren, L.T. Kuhn, W. Bouwen, P. Lievens, Phys. Rev. B 63 (2001) 165406. [2] A.K. Sra, T.D. Ewers, R.E. Schaak, Chem. Mater. 17 (2005) 758. [3] F. Cleri, V. Rosato, Phys. Rev. B: Condens. Matter Mater. Phys. 48 (1993) 22. [4] S. Darby, T.V. Mortimer-Jones, R.L. Johnston, C. Roberts, J. Chem. Phys. 116 (2002) 1536. [5] R.A. Lordeiro, F.F. Guimarães, J.C. Belchior, R.L. Johnston, Int. J. Quantum Chem. 95 (2003) 112. [6] D. Cheng, S. Huang, W. Wang, Eur. Phys. J. D 39 (2006) 41.

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