Structures of Nanoalloy Clusters Au n Al n (n= 1â10) and the Growth

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Structures of Nanoalloy Clusters AuAl (n=1-10) and the Growth Patterns to the Bulk Phase Xiao Wang, Adebayo Adeleke, Wei Cao, Youhua Luo, Meng Zhang, and Yansun Yao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07401 • Publication Date (Web): 18 Oct 2016 Downloaded from http://pubs.acs.org on October 25, 2016

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The Journal of Physical Chemistry

Structures of Nanoalloy Clusters AunAln (n=1-10) and the Growth Patterns to the Bulk Phase

Xiao Wang1, Adebayo A. Adeleke2, Wei Cao3, Youhua Luo1, Meng Zhang1*, and Yansun Yao2,4* 1

Department of Physics, East China University of Science and Technology,

Shanghai 200237, China 2

Department of Physics and Engineering Physics, University of Saskatchewan,

Saskatoon, Saskatchewan, S7N 5E2, Canada 3

Nano and Molecular Systems Research Unit, P.O. Box 3000, FIN-90014, Finland

4

Canadian Light Source, Saskatoon, Saskatchewan, S7N 2V3, Canada

Corresponding Authors *Phone: 86-21-64253964. E-mail: [email protected]. (M.Z.) *Phone: 1-306-9666430. E-mail: [email protected]. (Y.Y.)

1

ACS Paragon Plus Environment


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ABSTRACT Gold nanoclusters have attracted intense interests due to their unique applications as catalysts. The properties of the gold clusters can often be extended through alloying with other metals, by virtue of adding new degrees of freedom and increasing the versatility of bonding.

Here we reported a new series of bimetallic clusters AunAln (n =

1−10) determined from the density functional calculations.

Particle swarm global

minimum searches, coupled with density functional optimization, were used to identify low-lying structures of the AunAln clusters and the crystalline phase, in addition to the experimentally known AuAl and Au2Al2 structures.

Significantly enhanced binding

energies were calculated in stable AunAln clusters compared with their pure Au or Al counterparts as a result of polarized Au-Al interactions. The polarization is due to a high electron affinity of gold induced by strong relativistic and shell structure effects. In addition, an Au2Al2 unit was identified as the common motif for lowest-energy structures from Au2Al2 – Au10Al10, and up to the crystalline phase.

This information serves to the

understanding of new clusters formation and their growth mechanism to the corresponding bulk phase. The present results welcome experimental studies of the predicted clusters which may lead to the discovery of novel properties in this microscopic form of matter, bridging between free atoms and the bulk matter.

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INTRODUCTION Small atomic clusters often exhibit structures and properties that are strikingly Since the discovery of fullerenes,1 the

different from those of bulk materials.

investigations of small atomic clusters have been strongly motivated and have led to growing applications of the clusters in nanoelectronics and catalysis industry.

Currently,

a great deal of the research is being devoted to the understanding of structures and stabilities of the clusters, and to growth mechanism relating this microscopic form of matter to their bulk counterparts.2,

3

Among these investigations, gold clusters and

nanoparticles have been featured prominently. Progressive studies unearthed the atomic structures of Aun clusters, in particular, for those with size (n < ~32 atoms),4-10 and the links between the sizes and structures of the clusters with catalytic activity11, 12.

When

the size increases, gold clusters undergo a remarkable evolution from 2D planes to 3D tetrahedrons and to empty cage structures.13−16 Some of the larger clusters, for example the anionic Au16 and Au17, have peculiar tetrahedral structures with the inner diameter similar to those of the fullerenes (‘golden buckyballs’).14 Such a large void inside the Au clusters immediately suggest the possibility that they may be doped with foreign atoms. It is well established that the structures and properties of gold clusters can be modified by doping with other metals.17,18 Particular metals, such as Ag, Cu or Al, have structures very different from Au clusters, and the onsets of 3D structures at smaller cluster sizes.

Alloying Au clusters with these metals may be considered as a possible

route connecting the microscopic phenomena of clusters to bulk properties of solid state materials. Among the dopants, Al received considerable attention due to its low cost and interesting behaviors at low dimensions.

Colloquially known as ‘superatoms’, some

Al clusters have been found to behave analogously to the halogen, alkaline earth, and other multivalent species.19 Alloyed AuxAly clusters have been actively explored and a rich spectrum of structures was discovered, ranging from Au-rich Au5Al to Al-rich AuAl12, through various techniques including photoelectron spectroscopy (PES), 3



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high-resolution photoelectron imaging, and first principles calculations.20-24 In this group, the clusters with (nearly) equal composition, i.e., x ≈ y, were relatively less studied until the recent discovery of Al2Au2,25 followed by a series of new alloyed clusters AuxAly− (x + y = 7, 8; x = 1−3; y = 4−7).26 Motivated by these new findings, in this paper we theoretically investigated the AunAln clusters, where the Al and Au have equal composition, in the range n = 2 − 10.

We chose this size range specifically to probe the

structure evolution of the AunAln clusters with increasing size, moving from small atomic clusters to the onset of crystalline phase. The goal is to understanding the connection between molecular-like phenomena of bimetallic clusters to bulk properties of alloys. Toward this end, we predicted the global minimum structures of the AunAln clusters up to n = 10, as well as the solid state structure of crystalline AuAl, using an ex nihilo structure search methodology based on particle swarm optimization (PSO) algorithm.27

We

analyzed the size-dependent structural characteristics from clusters to crystalline phase and the underlining bonding strategies, and proposed a new building block for nanomaterials composed of Au and Al.

To the best of our knowledge, this is the first

systematic theoretical investigation of the structures and properties of the AunAln clusters beyond n = 2. COMPUTATIONAL METHODS Candidate structures of AunAln clusters were generated using the CALYPSO method, which has been proved to be an efficient method for cluster structure prediction27. A local version of particle swarm optimization (PSO) algorithm was implemented to explore potential energy surface for non-periodic systems. Gaussian package28 with PBEPBE/LANL2DZ basis set29, 30 is used to perform structure relaxation with medium precision. The proportion of the structures generated by PSO is 0.8 and the population size is set as 20. More than 3000 distinct isomers (local energy minima) were selected from the energy surface for finer optimization using all-electron spin-unrestricted calculation with the DMOL3 program,31 and the Perdue-Burke-Ernzerhof (PBE) 4


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functional32. Relativistic calculations were carried out with scalar relativistic corrections to valence orbitals, i.e., orbitals that participate in bonding, via a local pseudopotential (VPSR) employing double numerical plus polarization with addition of diffuse functions (DNP+).

Convergence of self-consistent field (SCF) was set with a criterion of 1×10-5

Hartree on total energy and electron density, 2×10-3 Hartree/Å on the gradient, and 5×10-3Å on the displacement.

Harmonic vibrational analysis was carried out at the same

level of theory to examine the stability of low-energy isomers and estimate zero-point energy (ZPE) corrections. A benchmark calculation was carried out on AuAl dimer using hybrid BLYP33, PW9134 and PBE functionals in DMOL3 for bond length and vibrational frequencies. The results (Table S1) show that the PBE functional yields the best agreement with the experimental values. We therefore chose the PBE functional for the present study. It should be noted that for pure coinage metal cluster, the PW91 functional tends to yield closer match to the experiment35. To further test the reliability of the methods, vibrational frequencies of previously known clusters, e.g., Au2, Al2, Au7, AuAl, Au2Al2, Au2Al2─, were calculated using PBE functional, DNP+ basis and VPSR pseudopotential (see Supporting Information (SI) Table S2 for results). The comparison of the calculated frequencies to the experimental data yields an excellent agreement.16, 23, 25, 36

Crystalline AuAl structures were also obtained using the CALYPSO method and fully optimized using the CASTEP package37 and PBE functional, with the van der Waals corrections38 included for treating the dispersion interactions. Brillouin zone integration was carried out on a 10×10×10 Monkhorst−Pack k-points mesh in geometry optimizations along with a kinetic energy cutoff of 600 eV.

Phonons were calculated

with a supercell method, using a 2×3×3 supercell as implemented in the PHONOPY program.39

The interatomic forces were calculated from the optimized supercell through

the VASP package40 with a kinetic energy cutoff of 500 eV, and a 7×7×7 k-point mesh. A projector augmented wave (PAW) potential41 with the PBE functional were used. 5



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Convergence was achieved when the energy difference between two successive iterations was less than 10-6 eV. RESULTS AND DISCUSSION A. Structures of AunAln Clusters and Crystalline AuAl

Figure 1. Predicted ground-state structures and low-lying isomers of the AunAln (n = 1-10) clusters.

Numbers in the brackets are the energies (in eV) of the clusters relative

to the ground-state energies. atoms, respectively.

Gold and purple spheres represent gold and aluminum

Space groups were determined with a tolerance of 0.1 Å. 6


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The predicted ground-state and metastable structures of AunAln isomers up to n = 10 are presented in Figure 1, with the structures ordered according to their relative energies (see Fig. S1 in SI for more isomers and coordinates of the predicted structures.).

Clearly,

the AunAln clusters have more diverse structures than singly doped counterpart Au2n-1Al due to greater degrees of freedom available to each element.

An interesting feature

revealed in the geometries of the ground-state AunAln clusters is that the onset of the 3D structures occurs at a small cluster size, i.e., n = 2. For pure Aun clusters, on the contrary, the 2D planar structures are predicted to exist until Au12, only beyond which the For anionic Aun− cluster, a previous

3D structures emerge (Fig. S2 in SI).

experiment-theory combined study established that the 2D to 3D transition occurs at Au12−.42

This comparison highlights the strong Au-Al interactions in the AunAln clusters,

where electrons tend to move from Al to Au, forming nominal Alδ+ and Auδ- (see later). As such, the Au-Al interactions stabilize the clusters by strong electrostatic attractions. The ground-state AunAln clusters, not surprisingly, all have enclosed structures with alternating arrangement of Al and Au atoms – such geometries maximize the Au-Al interactions as well as minimize the Al-Al repulsions. Pure Aun clusters are predicted to have 2D structures in small size range (Fig. S2). An interpretation is that the strong relativistic effects of Au lowers the s orbital and enhances the s-d hybridization, which favors fewer, but more directional covalent bonds in small clusters43. For pure Al clusters, 2D planar structures were found to be favored until Al5,44 beyond which the 3D caged structures occur, and when n is greater than 11, an interior Al atom emerges in the middle of the cage (Fig. S2). This type of structure evolution is consistent to the change of the Al valency, that when n < 6, Al behaves similarly to monovalent alkali metal, which indeed prefer 2D clusters, while at larger cluster size, Al becomes trivalent and prefer 3D structures. At n = 13, in particular, the Al13 cluster with 39 valence electrons behaves in analogy with a halogen atom (both need one more electron to close the outermost shell) according to the implementation of the 7



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spherical shell jellium model. The diatomic AuAl has a C∞v symmetry with the calculated vibrational frequencies of 332.6 cm−1, which is in excellent agreement with the experimental results of 333 cm−1 20

.

The ground-state geometry of the Al2Au2 cluster has a tetrahedral structure with the

C2v symmetry, identical to the experimentally identified structure by high-resolution PES.25

The C2v structure has an enclosed structure of alternating Au and Al, which is in

fact a preferred geometry for all AunAln clusters. The ‘open’ structures, for example, the Y shape C2v structure, is energetically unfavorable for Au2Al2, Au4 and Al4, but it may be preferred in Au4−.45

Our predicted ground-state geometries of Aln, Aun, AuAl and

Au2Al2 clusters are in good agreement with those reported in the literature.4,16, 46-48 The predicted ground-state structure of Au3Al3 has an enclosed book structure (Fig. 1). Again, this geometry is suited to maximize the Au-Al interactions. Other predicted isomers, such as the rectangle (C1), distorted benzene analogue (C3v) structure, or distorted triangular structures, either have less Au-Al interactions or engage unfavorable Al-Al repulsions, and therefore are higher in energies. has a square antiprism with D2d symmetry. Al-Au bonds, forming an empty cage.

The ground-state Au4Al4 cluster

Such a structure yields maximum twelve

This is an interesting finding that the cage

structures can form in AunAln at a smaller threshold (8 atoms) compared with pure Aun clusters.

The latter requires at least 16 atoms to form an empty cage, as shown for

example in Au16− or Au17− by electron diffraction experiments.49 For alkali metals, on the other hand, the cage structures tend to form at a lower threshold.

Similar cage structures

have previously been found in V@Cs8, V@Na8, and V@Li8 clusters, where the alkali metals form cages (named as ‘superatoms’) with dopant V atom situated in the center.50-52 The empty cage structures from Au4Al4 to Au8Al8 are facilitated by the same bonding strategy, however, the sizes of the cages are not sufficient to adopt another atom in the center.

The Au9Al9 cluster has a filled cage structure with one interior Au atom in the

center.

This bonding situation is similar to the highly stable W@Au12 cluster, which has 8


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an icosahedral structure with the W atom encapsulated in the cage yielding particularly efficient radial bonding.53, 54

When the Au atom emerges in the center of the Au8Al9

cage, its interactions with surrounding Al atoms are maximized and the coordination number undergoes a significant increase to near the bulk value (the bond of ambient Al and the center Au are depicted with thin stick radius in Fig.1). At n = 10, the cluster adopts a three dimensional network, showing the onset of periodicity and the characteristics of an extended crystalline structure.

This manifestation is also found in

pure Au20, where the highly stable tetrahedral pyramid structure Au20 cluster can be viewed as a fragment of the face centered cubic (FCC) lattice of bulk gold (Fig. S2). Previous studies suggested that the cluster-to-bulk transformation in gold is likely to occur at the medium size range, i.e., at Au38−, with the emergence of the pyramidal Au20− fragment.55

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Figure 2. Optimized crystal structures of the lowest-energy AuAl crystalline phase. The structures are ordered by their relative energies from the lowest (a) to the highest (f). Gold and purple spheres represent gold and aluminum atoms, respectively.

Lattice

parameters for these structures are listed in Table S3.

Figure 3. Structural evolution from neutral AunAln (n=1-10) clusters toward bulk structure. Gold and purple spheres represent gold and aluminum atoms, respectively. The AunAln becomes an extended crystalline structure when n approaches infinity. Au and Al are known to form solid solutions, and several single-phase structures, including the AuAl phase, have been recovered from the annealed liquid.56

To this end,

we also searched for the stable crystalline AuAl structures with the swarm-intelligence structure search method.

The predicted ground-state crystalline phase has a monoclinic

unit cell with the P21/m space group (Fig. 2), which is consistent to the experimentally identified unit cell of AuAl by X-ray and electron diffraction patterns.56 The calculated structure parameters of the P21/m structure are very close to the experimental values (~ 2% discrepancy or less) within the accuracy of the DFT method (Table. S3 in SI).57 Other predicted AuAl structures with higher energies do not reproduce the experimental 10


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diffraction patterns (Fig. 2).

The P21/m structure can be viewed as a monoclinically

distorted NiAs structure for AB alloys, with the coordination numbers for Al and Au increased to 8 and 9, respectively.

Interestingly, a common feature shared by the

crystalline AuAl and its cluster counterparts is the existence of an Au2Al2 unit, which may be considered as the ‘building block’ for structural growth (Fig. 3).

All AunAln

clusters, from n = 1 to 10, can be viewed as low-energy edge-sharing arrays of the Au2Al2 units.

In the crystalline phase, the trace of Au2Al2 motif is also clearly visible

(highlighted by dotted ecliptics, Fig. 3).

These units interconnect to each other and

extend to three dimensions, resulting in the lowest-energy crystalline phase. A major goal of nanoscience has been dedicated to finding the stable fragments as the building blocks for a rational design of new nanomaterials.

The Au4 tetrahedron, for

example, has been viewed as a building block for pyramid Au20 cluster. The stacking of the Au4 tetrahedrons in the Au20 cluster is stabilized by multiple electron deficient bonds (4c-2e) located at the center of the tetrahedrons comprising the cluster. If the stacking continues in the same manner to infinity, the FCC lattice of bulk gold would result. For the AunAln series, the Au2Al2 unit may be viewed as a building block. It starts as a relaxed tetrahedron, at which Au and Al occupy alternative corners, in neutral Au2Al2, and then undergoes various distortions in larger clusters and bulk AuAl.

The finding of

the Au2Al2 as a possible building block provides insights into how the geometrical structures of bimetallic AunAln clusters evolve toward the bulk, which hopefully can lead to the discovery of novel properties in this cluster series. B. Thermodynamic Stability and Electronic Structures To analyze the thermodynamic stability of the AunAln clusters, we calculated the average binding energy (Eb), defined as the difference between the energy of the cluster, E(AunAln), and the energy sum of individual atoms, nE(Au) + nE (Al), averaged by the total number of atom n, e.g., 11



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Eb ( Au n Al n )  nE ( Au )  nE ( Al )  E ( Au n Al n ) / 2n .

(1)

From the results (Table 1), the Eb of AunAln clusters increases monotonically with the cluster size, from 1.96 eV for Au1Al1 to 3.37 eV for Au10Al10, indicating an energetically favorable process for the cluster growth. In comparison, the measured enthalpy of formation (∆fH) for the AuAl crystal is about -39.2 kJ/mol.56

It is noteworthy that at the

same cluster size, the Eb of an alloyed AunAln cluster is significantly higher than the Eb of pure Al2n or Au2n cluster.

For example, the calculated Eb for Au10Al10 is 3.37 eV, which

is about 0.5 eV higher than those of Au20 (2.88 eV) and Al20 (2.82 eV). This finding clearly shows that the Al-Au interactions are energetically favorable and stabilize the bimetallic clusters. Table 1. Calculated average binding energies per atom (Eb) and the HOMO−LUMO energy gap (Egap) in bare Au2n, Al2n and AunAln clusters, as well as the estimated charge transfer (Mulliken charge) per atom from Al to Au in the AunAln clusters. System

Eb

Egap

(eV)

(eV)

Al2

0.97

0.34

Al4

1.68

Al6

System

Eb

Egap

(eV)

(eV)

Au2

1.28

1.78

0.48

Au4

1.82

2.19

0.44

Au6

Al8

2.39

0.61

Al10

2.48

Al12

System

Eb

Egap

Charge

(eV)

(eV)

Transfer

Au1Al1

1.96

2.47

0.44 e−

1.00

Au2Al2

2.51

1.96

0.35 e−

2.25

1.73

Au3Al3

2.72

1.54

0.29 e−

Au8

2.37

0.94

Au4Al4

2.87

0.72

0.37 e−

0.41

Au10

2.49

1.17

Au5Al5

3.07

0.96

0.44 e−

2.62

0.42

Au12

2.60

1.05

Au6Al6

3.10

0.62

0.46 e−

Al14

2.78

0.91

Au14

2.67

1.49

Au7Al7

3.19

0.72

0.48 e−

Al16

2.80

0.79

Au16

2.72

0.75

Au8Al8

3.24

0.33

0.41 e−

Al18

2.79

0.35

Au18

2.81

1.01

Au9Al9

3.31

0.26

0.57 e−

Al20

2.82

0.30

Au20

2.88

1.42

Au10Al10

3.37

0.46

0.46 e−

12


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Figure 4. Calculated DED of the Au4Al4 and Au5Al5 clusters. where the charges are accumulated in the clusters.

Blue regions indicate

The surface isovalue for electron

density is 0.03 e/Å3. The Au-Al interactions in the AunAln clusters are illustrated using the deformation electron density (DED), defined as the difference between the charge density of the cluster and the sum of charge densities of individual atoms. as examples, the DED are analyzed in Fig. 4.

Using Al4Au4 and Al5Au5

In both clusters, electron accumulation is

clearly revealed around midway of the Au-Al contacts, showing covalent characteristics. Notably, in all AunAln clusters we found a substantial amount of charge transferred from Al to Au, which indicates the presence of polarity in the Al-Au interactions.

Strong

relativistic effect contributes to a high electron affinity of Au, and a tendency to forming negatively polarized valence states in gold alloys.58

Here the amount of charge transfers

in the AunAln clusters were estimated using Mulliken population analysis59 (Table 1, for details see Table S5 in SI).

Clearly, in all clusters the Au atoms are partially anionized,

gaining an amount of charge ranging from 0.35 ~ 0.57 e-/atom. The notable charge transfer reflects the strong polarization in the Au-Al bonds, inducing a mixture of covalent and ionic characteristics. In the crystalline phase (the aforementioned P21/m structure), the charge transfer was estimated using the Bader Charge Analysis60, which shows a greater amount of charge transfer ranging from 0.67 to 0.68 e-/atom.

It should

be noted, however, that assigning charges to the atomic constituents of an alloyed 13



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compound involves partitioning of either real or reciprocal space for which no conclusive scientific approach can be given. Our estimated charge transfer only gives a trend, that Au tends to exist as anionic in AunAln clusters and AuAl crystals. Previous studies showed that anionic Au exhibits similar chemical properties to those of the halide ions, or act as an acceptor in hydrogen bonds.58

Figure 5. (a) Relative potential energy (eV) of the Au4Al4 and Au5Al5 clusters during 20 ps of molecular dynamics simulation. (b) Phonon dispersion of the P21/m crystalline structure calculated at ambient pressure. The kinetic stability of AunAln clusters is examined by the energy gap (Egap) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).

The calculated energy gap of AunAln clusters decreases with odd-even

oscillations (Table 1), and eventually vanishes in the crystalline AuAl phase (see Fig. 3 in SI for band structure of the P21/m phase).

Similar oscillation has been previously

observed, and also reproduced in our calculations, in pure Al2n and Au2n clusters (Table 1), whereas the decrease of Egap indicates a gradual delocalization of the electrons with increasing quantity of states.

When the cluster grows toward the bulk, the finely

separated orbital states form valence (bonding) and conduction (anti-bonding) bands. A general trend for the AunAln series is that the Eb increases with the cluster size (Table 1). This indicates that for large clusters the energy differences between bonding and 14


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antibonding interactions are greater, which leads to larger widths for the two bands.

The

bandwidth expansion in energy is a key ingredient for the metallization when the AunAln clusters grow to the bulk.

In the bulk phase, a large band expansion forces the valence

and conduction band to overlap near the Fermi level, leading to a metallic state.

The

dynamic stabilities of the AunAln clusters were examined using molecular dynamics simulation (MD) implemented in the CASTEP code37 at room temperature (T = 300 K). The Nosé-Hoover-Langevin (NHL) thermostat61 was used for NVT dynamics. Figure 5a shows the MD results for the Au4Al4 and Au5Al5 clusters.

Within the employed

simulation time of 20 ps, no structural changes were detected in any structure while the instantaneous values of the relative potential energy fluctuate due to thermal fluctuations but the average values stay constant. stable at room temperature.

Thus, the ground-state clusters are expected to be

In addition, the stability of the crystalline AlAu phase (for

the aforementioned P21/m structure) were examined by the phonon dispersion relations (Fig. 5b).

Notably, none of the vibrational modes contains imaginary frequency,

suggesting that the crystalline AuAl structure is mechanically stable and dynamically stable at ambient conditions. CONCLUSIONS In conclusion, the size-dependent structural and electronic properties of bimetallic AunAln (n = 1−10) clusters and crystalline AuAl phase have been systematically investigated by using density functional theory.

The ground-states structures for the AunAln clusters and

bulk phase were predicted and analyzed.

In these structures, Au exhibits strikingly high

electron affinity due to relativistic and shell structure effects, and forms negatively valence states Auδ−.

The Au−Al interactions are therefore stabilized by strong

polarization which results in the AunAln clusters significantly more stable than pure Au2n and Al2n clusters.

Theoretical evidence shows that an Au2Al2 unit can be viewed as a

common motif for low-energy structures of Au2Al2 – Au10Al10, which helps clarifying the growth mechanism for cluster-assembled nanomaterials in this group. 15


We have further


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shown that the trace of Au2Al2 motif is also clearly visible in the bulk state.

Since the

properties of nanomaterials depend strongly on their sizes and shapes, this work illustrates a bottom-up approach of manipulating the cluster structures, which may lead to the discovery of novel physical and chemical properties in these new materials in the future. Supporting Information Available: Details of structures and parameters of bare Al2n, Au2n, AunAln clusters; lattice parameters and band structure of bulk AuAl; vibrational frequencies of Au2, Al2, Au7, AlAu, Al2Au2, Al2Au2─; Mulliken atomic charges of AunAln clusters. . ACKNOWLEDGMENTS This work is financially supported by the National Natural Science Foundation of China (Grant no. 21303054), Natural Sciences and Engineering Research Council of Canada (NSERC), and Strategic Grant of University of Oulu.

A. A. Adeleke gratefully

acknowledges the financial support from African Institute for Mathematical Sciences (AIMS) under the POST AIMS program.

Part of the calculations have been performed

through the use of the computing resources provided by the University of Saskatchewan, WestGrid and Compute Canada. Notes The authors declare no competing financial interest. REFERENCES (1) Kroto, H. W.; Heath, J. R.; O'Brien, S. C.; Curl, R. F.; Smalley, R. E. C60: Buckminsterfullerene. Nature 1985, 318, 162-163. (2) Rohmer, M.-M.; Bénard, M. Structure, Reactivity, and Growth Pathways of Metallocarbohedrenes M8C12 and Transition Metal/Carbon Clusters and Nanocrystals: A Challenge to Computational Chemistry. Chem. Rev. 2000, 100, 495-542. (3) Einax, M.; Dieterich, W.; Maass, P. Colloquium: Cluster Growth on Surfaces: 16


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Structures of Nanoalloy Clusters Au n Al n (n= 1â10) and the Growth

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Structures of Nanoalloy Clusters Au n Al n (n= 1â10) and the Growth