J. Phys. Chem. B 2005, 109, 13743-13754
13743
Melting and Freezing Characteristics and Structural Properties of Supported and Unsupported Gold Nanoclusters Chin-Lung Kuo and Paulette Clancy* School of Chemical and Biomolecular Engineering, Cornell UniVersity, Ithaca, New York 14853 ReceiVed: April 12, 2005; In Final Form: May 26, 2005
Molecular dynamics simulations in conjunction with MEAM potential models have been used to study the melting and freezing behavior and structural properties of both supported and unsupported Au nanoclusters within a size range of 2 to 5 nm. In contrast to results from previous simulations regarding the melting of free Au nanoclusters, we observed a structural transformation from the initial FCC configuration to an icosahedral structure at elevated temperatures followed by a transition to a quasimolten state in the vicinity of the melting point. During the freezing of Au liquid clusters, the quasimolten state reappeared in the vicinity of the freezing point, playing the role of a transitional region between the liquid and solid phases. In essence, the melting and freezing processes involved the same structural changes which may suggest that the formation of icosahedral structures at high temperatures is intrinsic to the thermodynamics of the clusters, rather than reflecting a kinetic phenomenon. When Au nanoclusters were deposited on a silica surface, they transformed into icosahedral structures at high temperatures, slightly deformed due to stress arising from the Au-silica interface. Unlike free Au nanoclusters, an icosahedral solid-liquid coexistence state was found in the vicinity of the melting point, where the cluster consisted of coexisting solid and liquid fractions but retained an icosahedral shape at all times. These results demonstrated that the structural stability in the structures of small Au nanoclusters can be enhanced through interaction with the substrate. Supported Au nanoclusters demonstrated a structural transformation from decahedral to icosahedral motifs during Au island growth, in contrast to the predictions of the minimum-energy growth sequence: icosahedral structures appear first at very small cluster sizes, followed by decahedral structures, and finally FCC structures recovered at very large cluster sizes. The simulations also showed that island shapes are strongly influenced by the substrate, more specifically, the structural characteristic of a Au island is not only a function of size, but also depends on the contact area with the surface, which is controlled by the wetting of the cluster to the substrate.
Introduction Understanding and predicting the properties of small metal clusters is of fundamental importance. This is mainly due to innovative applications of nanoclusters in science and technology, such as heterogeneous catalysis and the fabrication of nanoelectronic devices. However, before such practical applications can be achieved, a good knowledge of the optical, magnetic, and electronic properties of these clusters, as well as their thermodynamic properties, must be established. This requires a complete characterization of the cluster’s geometrical structure and its dependence on size.1,2 Accordingly, the study of how free metal clusters develop as a function of size is being extensively investigated with both experimental and theoretical methods (see detailed reviews in refs 1 and 2). Unlike bulk materials, nanometer-sized clusters can exhibit various structural motifs, including both crystalline and noncrystalline structures. For instance, in the case of noble and transition metal clusters, experimental images have commonly observed truncated octahedra or cuboctahedra with facecentered-cubic (FCC) local environments, and multiply twinned particles (MTP), which have icosahedral or decahedral structures with 5-fold symmetry characteristics (see Figure S1 in the Supporting Information). Other types of structures have also * Address correspondence to this author. E-mail: pc@ pcnet.cheme.cornell.edu. Phone: 1-607-255-6331. Fax: 1-607-255-9166.
been observed, including twinned FCC (containing one or several parallel twin planes), twinned HCP, or even amorphous clusters.3-8 In most commonly accepted models, icosahedra and decahedra are considered to be assemblies of single-crystal tetrahedra with (111)-like facets and twins related on their adjoining faces. An icosahedron is formed by 20 tetrahedra sharing the same central vertex and three twin boundaries. It has six 5-fold symmetry axes and a quasispherical shape with 20 (111)-like facets so that its surface energy can be efficiently minimized. However, because each tetrahedral unit has to be distorted to make three of its edges about 5% shorter than the one on the surface, the icosahedral structures have relatively high internal strain, either homogeneous or inhomogeneous, that may lead to structural modifications and defects.9 Therefore icosahedra are expected to be favorable at small cluster sizes where the minimization of surface energy prevails over the internal strain. On the other hand, decahedral structure is obtained by packing five tetrahedra together like a pentagonal bipyramid with 10 (111) facets. Since the resulting cluster shape is far from spherical, a better decahedral structure can be obtained by introducing five rectangular (100)-like facets, as suggested by Ino,10 to make the cluster more rounded. This idea was employed by Marks who calculated the lowest energy configuration for each tetrahedral unit using a modified Wulff construction.11 This new structure corresponds to a truncated decahedron in which the (111)-like re-entrant facets are created
10.1021/jp0518862 CCC: $30.25 © 2005 American Chemical Society Published on Web 06/24/2005
13744 J. Phys. Chem. B, Vol. 109, No. 28, 2005 to decrease the exposure of the energetically expensive (100)like facets while the cluster shape remains close to a sphere. Even though the Marks-type decahedra have a higher surface energy than the icoscahedra, they have less internal strain and thus become more favorable than the icosahedra at increasing cluster sizes. Finally, crystalline clusters with FCC local order are expected to be the most favorable structure in the macroscopic limit. One of the most stable structures for FCC clusters is the truncated octahedron, which has large exposures of (100)-like facets with a quasispherical shape. Although truncated octahedra have higher surface energy than icosahedra and decahedra, FCC structures have no internal strain and thus become dominant for large clusters due to their low surface-to-volume ratios. Therefore, based solely on the energetics of these clusters, the interplay between internal strain and the minimization of surface energy determines the dominant structural motif over specific size ranges, i.e. icosahedra are favored at small sizes, decahedra at intermediate sizes, and FCC structures in the limit of large clusters. Theoretical studies that focused on an exhaustive search for the lowest energy configurations of free metal clusters and calculations that employed continuum models were all in accord with these general predictions of the minimum-energy growth sequence.12-14 For example, Cleveland et al. applied the Embedded Atom Method (EAM) potential model and the energy-minimization methods to determine the optimal structures of Au nanoclusters comprised of 100 to 1000 atoms (equivalent to 1.4-3.0 nm).12,13 They found that Marks-type decahedra and truncated octahedra dominate across the entire size range. Similar results have been obtained by Baletto et al.,14 who investigated the general trends of crossover sizes among these three different structural motifs using quenched Molecular Dynamics simulations with a potential model proposed by Rosato, Guillope´, and Legrand (RGL model) and the EAM potential models. Their results showed that the crossover sizes strongly depend on the type of metals studied. For copper clusters, icosahedral structures can persist for clusters containing up to 1000 atoms, followed by a very wide decahedral window (1 000 < N < 30 000). For silver, decahedra were favored over a wide interval covering 300 to 20 000 atoms. In the case of gold clusters, icosahedral structures were energetically noncompetitive even at very small sizes and the optimal structures became truncated octahedra at a size of around 600 atoms. However, these theoretical studies do not always agree with experimental observations. One of the most puzzling results in the field of free cluster growth is the observation of large gold icosahedra generated in the laboratory by various methods.9,15-17 Similar results were obtained for free copper and silver clusters produced in an inner-gas aggregation source, where a great abundance of large icosahedra was found while small clusters (∼2 nm) are mainly decahedra.18,19 Recent Molecular Dynamics simulations regarding the melting and freezing behavior of gold nanoclusters also showed a preferential formation of icosahedral structures for various cluster sizes (459-3000 atoms).20,21 These observations suggest that the final atomic arrangement of a cluster may be the result of a competition between thermodynamic and kinetic factors, i.e. the conditions of growth may play a role rather than thermodynamic considerations alone. This would imply that the minimum-energy growth sequence is not always followed, and the formation of large icosahedra could be interpreted as a consequence of kinetic factors arising from the fact that processing conditions may make it hard to achieve thermodynamically equilibrium structures in the experiments.
Kuo and Clancy The nature of the substrate may also influence the morphology and the internal structure of a supported cluster. This is a major concern for the controlled growth of nanostructured materials since preferred morphologies and crossover sizes may change when clusters are deposited on different substrates. For example, Au clusters deposited on an MgO (100) surface, either from gas-phase epitaxial growth or low energy cluster beam deposition, were observed to be single crystals and have half-octahedral shape with (100) truncations in a size range between 1 and 4 nm.22,23 On the other hand, decahedral structures were predominant when Au atoms were deposited on an amorphous carbon substrate within a similar size range.24 As another example, Ag islands on a Si (100) surface25 showed that octahedral structures were favored and only a few icosahedral clusters were found. However, after exposure to air, the silicon surface was oxidized into an amorphous structure accompanied by an increase in the number of icosahedra. The difference in these observations can be explained by a decrease in the stability of the icosahedral clusters due to the additional strain from the crystalline substrate. Other investigations regarding the effect of the cluster-substrate interaction on the morphology of clusters have been reported.26-28 In this study, we have investigated the melting and freezing characteristics and related structural transformations of Au nanoclusters within a size range of 2 and 5 nm. In the first part of this paper, a microscopic description of the melting and freezing behavior of free Au nanoclusters, as well as the influence of a supporting silica substrate, will be addressed. Molecular dynamics simulations were performed on both the supported and unsupported Au nanoclusters containing 300 to 3000 atoms (2-4.6 nm) to study their thermodynamic properties and observe any structural changes that occurred during the heating and cooling processes. In the second part of this paper, we discuss the effect of the substrate on the structural properties of deposited Au nanoclusters focusing on Au island formation, preferred structures and size-dependent morphological transformations. We will demonstrate a structural transformation from decahedral to icosahedral structures during Au island growth that does not follow the trend suggested by the minimum-energy growth sequence. Finally, we will show that structural transformations depend on the contact area between the cluster and the substrate. Simulation Methods Molecular dynamics simulations were performed at constant temperature and effectively at constant pressure to investigate the behavior of supported and unsupported Au nanoclusters of different sizes, providing detailed insight into their structural properties and growth behavior. The temperature of the systems was kept constant via the Nose´-Hoover thermostat.29 Equations of motion were integrated by using a fifth-order predictorcorrector algorithm with a time step of 1 fs. Modified Embedded Atom Method (MEAM) models30-32 that we developed for the Au-Si-O ternary system33 were used to describe the interactions between atoms in the simulations. The functional form of the total configuration energy E in MEAM is written as the sum of direct contributions from all neighboring atoms and is given by
E)
∑i
{
Fi(Fij) +
1
∑φij(Rij)
2 i* j
}
(1)
The first term in eq 1 is the embedding function for atom i embedded in a background electron density Fij, while the second term is the conventional pair potential. Since a detailed
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J. Phys. Chem. B, Vol. 109, No. 28, 2005 13745
explanation of the MEAM potential has been well documented, the interested reader is referred to refs 30-32. The performance and transferability of these atomic potentials have been validated through a series of tests.33,34 For the AuAu interaction, some fundamental physical properties, such as the elastic constants, vacancy formation energies, surface energies, and the fcc-bcc/fcc-hcp structural energy differences, were calculated and compared to experimental data or prior theoretical studies. The Au-Si atomic potential successfully reproduced the results of LDA calculations such as the prediction of properties for Au/Si in the L12 structure, binding energies and bond lengths for two isolated Au-Si clusters, and the energy barrier for a Au atom migrating in the (110) channel of c-Si.33 For the Si-O and O-O interactions, our potential models were able to predict the optimal lattice parameters, internal atomic coordinates, bulk modulus, densities, and binding energies for several important polymorphs of crystalline silica, such as Rand β-quartz, R- and β-cristobalite, and β-tridymite. As a further stringent test, the dynamic stability of crystalline silica was tested by using Molecular Dynamics simulations.34 For the Au-O interaction, the model predicted the adsorption energies and bond distances of Au adatoms on various sites of a R-quartz slab. The agglomeration behavior and the contact angle of a gold overlayer deposited on a silica substrate were examined by using Molecular Dynamics simulations, showing generally satisfactory agreement with ab initio calculations and experimental data. For the interested reader, detailed explanations regarding the development and validation of these atomic potentials are provided in refs 33 and 34. A (100) R-quartz slab, prepared from a bulk crystal and containing 3888 atoms in dimensions of 57.4 Å × 49.7 Å × 15.2 Å was used to represent a silica substrate in the simulations. The bulk R-quartz crystal was first equilibrated at 300 K for 100 ps and then the periodic boundary condition along the [001] direction was removed. The system was heated from 300 to 1000 K with a temperature step of 100 K and equilibrated at each temperature for 100 ps. After the heating process was completed, the system was quenched to room temperature instantaneously and equilibrated at that temperature for 100 ps. The bottom 1296 atoms were held fixed at their bulk lattice positions during substrate preparation to represent an underlying bulklike substrate. Although the bulk crystal is stable in the simulations and retains its R-quartz structure, the structure of the surface altered significantly during the heating process such that it should be considered to be a distorted, but still largely crystalline surface. Order Parameters The bond order parameter method developed by Steinhardt et al. to study supercooled liquids and metallic glasses35 was employed here to help identify the internal structure of Au nanoclusters. Bonds are defined as the vectors connecting a pair of neighboring atoms within a given cutoff radius. The general idea of bond order parameters is to capture the symmetry of bond orientations regardless of the bond length. The orientation of a bond r with respect to some reference system is specified by the spherical harmonics functions
Qlm(r) ) Ylm(θ(r);φ(r))
(2)
where θ(r) and φ(r) are the polar and azimuthal angles of the bond r in this reference system. Only even-l spherical harmonics are considered here because the bond order parameters will not be changed by the permutation of a pair of atoms.
Global bond order parameters can be constructed by averaging over all bonds in the Au nanocluster:
Qlm )
1
∑ Qlm(r)
(3)
Nb bonds
where the sum runs over all Nb bonds in the system. In a similar way, the local bond order parameters for a given atom can be defined by averaging all bonds with its nearest neighbors. To avoid any dependence on the choice of the reference system, rotationally invariant combinations can be constructed as
Ql )
(
4π
l
∑
2l + 1 m)-l
| |)
1/2
Qlm
2
(4)
and
Wl )
∑ m ,m ,m 1
2
3
[
]
l l l m1 m2 m3 ‚Qlm1Qlm2Qlm3
(5)
m1+m2+m3)0
where Ql and Wl are called the second-order and third-order invariants, respectively, and the coefficients [‚‚‚] are the Wigner 3j symbols. Because the magnitude of nonzero {Ql} and {Wl} elements can be affected by altering the definition of nearest neighbors and by including the surface bonds in the average, it is useful to have a reduced order parameter set, which can be constructed as
Wl
W ˆl) (
|Qlm| ) ∑ m
(6)
2 3/2
Since this quantity is normalized, it is almost insensitive to the precise definition of the nearest neighbors. In this way, it provides a quantitative measurement for the prevalent crystal structure of the system under study. Because of symmetry reasons, the first nonzero values occur at l ) 4 for clusters with cubic symmetry, and at l ) 6 for clusters with icosahedral atomic arrangements. This property makes global bond order parameter Q4 a very useful tool to distinguish between icosahedral-shaped multiple-domain FCC particles and truly icosahedral clusters. In the latter case, the value of Q4 should be close to 0. Since the order of magnitude of bond order parameter Q6 is the same for some structures of interest and can be affected by the existence of defects or the elastic deformation due the internal strain, Q6 is not an ideal tool in the determination of prevalent structures inside the clusters. However, it can play a role in measuring the crystallinity and the symmetry of a cluster. For example, in a cluster with FCC structure, all atoms have the same local bond orientation and the global bond order parameter Q6 is very close to its bulk FCC crystal value (Q6 ∼ 0.42). An “ideal” icosahedron is considered to consist of 20 distorted tetrahedra joined at the center of the cluster with different orientations, which results in a low degree of crystallinity for an icosahedral cluster (Q6 ∼ 0.1). However, the value of Q6 may increase due to the deformation of an icosahedral cluster. This usually happens when the size of a cluster is not coincident with its particular “magic number”2 or for large icosahedra in which the internal strain is relieved by elastic deformation or the appearance of defects. In this study, we employed two local bond order parameters, W ˆ 4 and W ˆ 6, in concert to determine the internal structures of
13746 J. Phys. Chem. B, Vol. 109, No. 28, 2005
Kuo and Clancy
TABLE 1: The Values of Bond Order Parameters for 13-Atom Icosahedral, fcc, and hcp Clusters, as Well as for 15-Atom bcc and 7-Atom sc Clustersa geometry
Q4
Q6
W ˆ4
W ˆ6
icosahedral FCC HCP BCC SC liquid
0 0.19094 0.09722 0.03637 0.76376 0
0.66332 0.57452 0.48476 0.51069 0.35355 0
0 -0.159317 0.134097 0.159317 0.15937 0
-0.169754 -0.013161 -0.012442 0.013161 0.013161 0
a
Bonds at the surface are excluded here.
Au nanoclusters based on the relative percentages of atoms having a given local atomic arrangement. The values of bond order parameters for a number of simple geometries, such as 13-atom icosahedral, FCC, and HCP clusters, as well as 15atom BCC and 7-atom SC clusters are listed in Table 1, serving as criteria to characterize the local environment of each atom. For example, a truncated octahedron (TO) or other FCC cluster should have around 99% atoms with a FCC local environment, whereas in an icosahedral cluster, only atoms located in the tetrahedral units have local FCC symmetry. Other atoms in the icosahedral cluster, such as the central atoms and the atoms on the internal twinning planes, have local 5-fold symmetry and HCP local order, respectively. For amorphous clusters and metallic glasses, a relatively high percentage of atoms should be found having an icosahedral local environment. The structure of a cluster will also be reflected in its diffraction pattern.36 The Debye scattering equation was used to calculate the intensity of the elastically scattered diffraction, I(s), corresponding to a rotationally averaged ensemble as a function of the scattering variable, s ) 2 sin θ/λ:
I(s) )
f2(s) ∑ i,j
sin(2πsrij) 2πsrij
(7)
where rij is the distance between atoms i and j in the cluster, θ and λ are the angle and wavelength of the incident X-rays, and f(s) is the atomic scattering factor. Results and Discussion 1. Thermal Behavior of Free and Supported Gold Clusters. In the first part of this study, we investigated the melting and freezing behavior of free (unsupported) Au nanoclusters with sizes ranging from 2.0 to 4.6 nm (Au333, Au682, Au1184, Au1713, and Au3055), and compared the results to those of supported Au nanoclusters having the same size range. For each cluster, the initial configuration was constructed such that it possessed FCC structures comprising a spherical shape. Each cluster was heated from 300 K with a temperature step of 100 K and equilibrated at each temperature for 100 ps. In the vicinity of the melting point (approximately 100 K below), the temperature step was reduced to 20 K. All clusters were heated to at least 200 K above their melting temperatures to ensure complete melting. The final configurations of these liquid clusters were further equilibrated to generate several initial configurations for the freezing runs, which were then cooled to 300 K at a rate of 2 × 1011 K/s. Conventionally, melting and freezing transitions can be identified in several ways. The simplest one is to examine the variation of potential energy with changes in cluster temperature. One such example is illustrated in Figure 1 for a cluster containing 3055 atoms, where the melting transition can be identified by a change in potential energy at a temperature of
Figure 1. Potential energy (per atom) as a function of temperature for the 3055-atom cluster; solid and dotted curves correspond to heating and cooling, respectively.
TABLE 2: Calculated Melting and Freezing Temperatures for Free and Supported Au Nanoclusters of Various Sizes free Au clusters
supported Au clusters
cluster size
Tm (K)
Tf (K)
Tm (K)
Tf (K)
Au333 Au682 Au1184 Au1713 Au3055
1150 1190 1230 1260 1280
1040 1070 1090 1110 1120
1220 1250 1290 1290 1320
1040 1070 1090 1110 1120
about 1280 ( 10 K. Table 2 summarizes the melting and freezing temperatures for both the supported and unsupported Au nanoclusters, where the well-established increased depression of the melting temperature as the cluster size reduces was observed for all clusters. The melting temperature of bulk gold was predicted to be around 1500 K with use of the present MEAM potential model, which is about 200 K higher than the experimental value.37 The depression of the melting and freezing points between clusters and bulk shown by the MEAM potential is around 280-450 K for free clusters and between 180 and 450 K for supported clusters, comparable to that found experimentally58 (see Figure S2 in the Supporting Information). 1.1. Melting of Free Au Nanoclusters. Several theoretical models have been proposed to account for the depression of melting points with thermodynamic approaches. Pawlow considered the triple-point equilibrium between a solid and a liquid particle of equal mass in contact with the vapor.38 Neglecting the second-order term, he derived the following equation for quasispherical solid particles of radius rs:
∆T ) -
[ ()]
2VsT0 Fs σ - σl Lrs s Fl
2/3
(8)
where ∆T is the melting point depression, L is the molar latent heat of fusion, Vs is the molar volume of solid, T0 is the bulk melting point, Fs and Fl are the mass densities, and σs and σl are the surface tensions of the solid and liquid phase, respectively. In a similar approach developed by Sambles,39 the solid cluster is assumed to be surrounded by a thin liquid layer of thickness t during melting, and the depression of the melting point for a cluster of radius r is expressed as follows:
∆T ) -
[
( )]
σl Fs 2VsT0 σsl - 1L r-t r Fl
(9)
where σsl represents the solid-liquid interfacial tension. This approach relies on the existence of surface melting, which has
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J. Phys. Chem. B, Vol. 109, No. 28, 2005 13747
Figure 2. Snapshots of (a) Au333, (b) Au1184, and (c) Au3055 clusters at 1000 K, showing that they have each transformed into icosahedralshaped clusters prior to melting.
been proposed based on simulations for lead40 and experimental results using dark field electron microscopy.41 According to this concept, a quasiliquid wetting layer is formed on the surface of a cluster, and thickens as the temperature increases until the whole cluster melts. Although the existence of such an effect is quite plausible, supportive experimental evidence is not very strong at present.1 According to Pawlow’s first-order triple-point theory, a linear dependence of the melting temperatures on N-1/3 is implied in eq 8; however, this linear dependence does not hold in Shambles’ approach due to the existence of a quasiliquid wetting layer. The melting points obtained in our simulations scale linearly with N-1/3, which is in better agreement with Pawlow’s approach than the liquid shell model (see Figure S3 in the Supporting Information). In addition, we did not observe any surface melting or the thickening of a quasiliquid wetting layer during the heating process even though some groups have reported such a phenomenon for simulated Ni and Au clusters using different potential models.42-45 The melting scenario of Au nanoclusters observed in our simulations involves a structural transformation from the initial FCC configuration to an icosahedral structure at elevated temperatures followed by a transition to a “quasimolten” state54 in the vicinity of the melting point, in which the clusters were found to continuously fluctuate between different structural motifs. Such a solid-to-solid structural transformation occurred at a temperature between 800 and 1000 K, and is illustrated by the slope change in the potential energy curve shown in Figure 1. Illustrative instantaneous snapshots of Au333, Au1184, and Au3055 clusters at 1000 K are presented in Figure 2. We can see that these clusters have transformed into icosahedral-shaped particles prior to melting. This is a surprising result because icosahedral structures are not the lowest energy configurations for Au clusters within this size range. To avoid any confusion with the icosahedral-shaped multiple-domain FCC particles routinely observed in some experiments,46 X-ray diffraction patterns and the bond order parameter analysis were used to identify the internal structures of the Au nanoclusters obtained
Figure 3. Calculated X-ray diffraction powder patterns for clusters (a) Au3055, (b) Au1184, and (c) Au333 at 1000 K.
TABLE 3: Calculated Heat of Fusion for Free and Supported Au Nanoclusters of Various Sizes latent heat of fusion (eV/atom) cluster size
free Au clusters
supported Au clusters
Au333 Au682 Au1184 Au1713 Au3055
0.144 0.156 0.165 0.178 0.186
0.160 0.150 0.140 0.170 0.192
in our simulations. For the purpose of reducing vibrational noise effects on the structural analysis, the clusters were relaxed to a local minimum energy configuration by using the conjugated gradient method before they were analyzed. Figure 3 presents the calculated X-ray diffraction patterns for Au333, Au1184, and Au3055 clusters, where the unresolved {220}, {311}, and {222} reflection peaks clearly demonstrate the noncrystalline characteristic of icosahedra. Since these diffraction patterns did not reflect the FCC characteristic of individual domains within the particles, we can conclude that these clusters are indeed geometrically icosahedra. The results of the bond order analysis for these Au clusters are summarized in Table 4 and show that these Au clusters are mainly composed of atoms with three different local bond orders, i.e., FCC, HCP and icosahedral
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Kuo and Clancy
TABLE 4: Results of Bond Order Analysis for Au Nanoclusters of Various Sizes, Na N
PFCC
PHCP
Picosahedral
Punclass
333 682 1184 1713 3055
0.366 0.374 0.413 0.447 0.480
0.270 0.320 0.309 0.283 0.256
0.190 0.127 0.080 0.092 0.083
0.174 0.179 0.198 0.178 0.181
a Bond order parameters W ˆ 4 and W ˆ 6 were used together to determine the internal structures of Au nanoclusters based on the relative percentages of atoms within different local atomic arrangements. Punclass denotes the percentage of atoms not belonging to either of these classifications, which may result from defects or surface atoms.
symmetry, which are in accord with the main characteristics of icosahedral clusters. However, it can be noticed that the relative percentage of icosahedral atoms reached a plateau for Au1713 and Au3055 clusters, which is in contrast to the expectation that this percentage should continue to decrease. We think this was mainly due to the relaxation of large internal strains by the elastic deformation in a large icosahedron, which can lead to an asymmetric morphology and the partial amorphization in the constituent tetrahedral units within an icosahedron. As noted above, the melting scenario revealed in our simulations differs from most other theoretical works to date,40,42-45 where no such structural transformation was found and the thermal evolution involved only surface melting or the thickening of a quasiliquid wetting layer. However, there is growing evidence that this kind of solid-to-solid structural transformation is possible in metal clusters at high temperatures. Cleveland et al. investigated the melting of gold nanoclusters using the EAM potential model47,48 and showed that the melting process involved a solid-to-solid structural transformation from low-temperature optimal configurations (truncated octahedra for Au459, and truncated decahedra for Au75 and Au146) to hightemperature icosahedral structures followed by an icosahedral solid-liquid coexistence state in the vicinity of the melting point. They interpreted these structural transformations as being identified with the intrinsic thermodynamic properties of the clusters driven by vibrational and configurational entropy at elevated temperature. A recent theoretical study done by Doye and Calvo49 also pointed out that vibrational entropy plays a crucial role in determining the equilibrium structure of a cluster. They calculated the temperatures of structural transitions for clusters at a given size using the superposition method and constructed the phase diagrams for silver and Lennard-Jones clusters based on these calculations. Their results showed that the crossover sizes between different structural motifs increase with temperature, indicating that the structural change in a cluster from FCC or decahedral configurations to an icosahedral structure could occur as the temperature increases. Doraiswamy et al.50 also constructed a morphology map for Au clusters using a probability model based on thermodynamics and continuum elastic theory. According to their morphology map (Figure 6a in ref 50), icosahedral structures are dominant at high temperatures (800-1250 K) within a size range between 2 and 5 nm, where the optimal structures are single crystals at low temperatures. However, these results conflict with those predicted from the phase maps constructed according to the inert gas aggregation experiments, where the formation of icosahedral and decahedral particles (MTPs) was a low-temperature phenomenon while the clusters formed at high temperatures were mainly single crystals. In that case, the warm metal vapor was thermalized by an inert gas, like helium or argon, at a lower
Figure 4. Snapshots of a Au1184 cluster at 1200 K in different configurations showing that the cluster did not have a fixed structure but fluctuated between different structural motifs: (a and b) the Au1184 cluster in a decahedral motif; (c) the cluster in a truncated octahedral motif; and (d) the cluster in a configuration that cannot readily be identified.
temperature, which can lead to the direct formation of solid particles from the gas phase. Consequently, the predicted structural transformations (gas phase f solid phase) might be different from what we are discussing here (solid phase T liquid phase). Another interesting phenomenon revealed in our study, which was not found in previous simulations regarding the melting of Au nanoclusters, is the presence of what has been termed a “quasimolten” state54 in the vicinity of the melting point in which the clusters continuously fluctuate between different structural motifs such as icosahedral, decahedral, and octahedral, or some hybrid structures that cannot readily be identified. Care should be taken when using this terminology. This is not a liquid phase but an ensemble of a set of transient, fluctuating different structural moieties. Figure 4 presents instantaneous snapshots of a Au1184 cluster at 1200 K at different time steps, showing that the cluster did not have a fixed stable structure at this stage. The evidence of “quasimelting” in small particles has been disclosed when the particles were exposed to intense electronbeam irradiation.51,52 There, a continual change of cluster shapes accompanying a reorganization of internal atomic arrangements was observed with use of high-resolution electron microscopy. This kind of behavior in small particles can be explained by a theoretical model proposed by Ajayan and Marks, who considered that the distribution of particle structures was best represented by a potential energy surface.53 In this case, the structure of a small particle is not necessarily the lowest energy configuration, but instead is controlled by the shape of its potential energy surface. On the basis of this model, one can calculate a temperature at which thermal fluctuations will be large enough for a cluster to overcome the energy barrier and transform into other structural motifs. Ajayan and Marks extended this model to include entropy effects, which allowed them to calculate the Gibbs free energy surface as a function of cluster morphology.54 They predicted the presence of a “quasimolten” phase at a temperature well below the melting
Supported and Unsupported Gold Nanoclusters
Figure 5. Phase map for particle structures versus size and temperature, as constructed by Ajayan and Marks in ref 49.
Figure 6. A comparable phase map for particle structures versus size and temperature according to the melting scenario observed in our simulations.
point, and constructed a phase map for particle structures versus size and temperature (see Figure 5). Our simulation results predict a phase map similar in spirit to their predictions and confirm the likelihood for a “quasimolten” phase in the vicinity of the melting point. However, there are differences between these two approaches: Multiply twinned particles were considered as low-temperature products in their phase map, which can transform into single crystals at elevated temperatures. This is the exact opposite of what we have observed here. A phase map that better reflects our results is proposed in Figure 6, which is very similar to the phase diagram constructed by Doye and Calvo49 for silver clusters using the Sutton-Chen potential model with the exception that, in our case, a “quasimolten” state is included between the liquid phase and the stable solid structures. In this map, although the optimal structures may be decahedral or FCC structures at lower temperatures, they will transform into icosahedral or decahedral structures as the temperature increases, depending on the size of the cluster. This kind of phase map is important because it allows us to understand the critical role of temperature in cluster growth. For instance, spherically shaped nanoclusters are preferred for the fabrication of nonvolatile memory cells because the resulting three-dimensional symmetry can provide the best charge confinement and physical stability from surface energy minimization. Therefore, we would expect that the ideal growth condition for spherical nanoclusters will be at elevated temper-
J. Phys. Chem. B, Vol. 109, No. 28, 2005 13749 atures where the “quasimolten” state and the icosahedral phase are contiguous, or we can choose an annealing temperature that is high enough to transform a preformed cluster into an icosahedral structure. 1.2. Freezing of Free Au Liquid Clusters. According to classical nucleation theory based on macroscopic concepts of the solid-liquid interface,55 one would expect that crystallization starts at a nucleation center and then proceeds smoothly throughout the whole cluster, just like a reverse process of surface melting. However, Valkealahti et al. drew a different conclusion based on their simulations for the crystallization of liquid copper clusters using the effective-medium theory model.56 Their results showed that the crystallization of copper clusters is a collective transformation phenomenon, which takes place almost simultaneously all over the cluster. Nam et al. investigated the structural change of Au nanoclusters upon cooling from the liquid phase using the EAM potential model.21 They reported a surface-induced mechanism for the formation of icosahedral structures, where surface ordering, with the formation of (111)-type facets and 5-fold symmetry axes, took place abruptly followed by the rearrangement of interior atoms proceeding inward from the surface. They concluded that the reason icosahedral structures always dominate during freezing in their simulations is mainly due to kinetic factors rather than thermodynamic ones, where the reduction of surface energy more efficiently contributes to the determination of the cluster structure than the internal energy. However, according to the phase map constructed based on the melting scenario revealed in our simulations, the formation of icosahedral structures during the freezing process appears more likely to be the result of thermodynamics rather than kinetics. However, a clear resolution of this matter is essentially precluded by the inability of MD to follow the system for time scales long enough to match the experimental scenario. To investigate the freezing mechanism of Au liquid clusters and further validate the phase map constructed based on our observation in the melting process, we studied the structural transformations of Au nanoclusters produced upon cooling from the liquid phase and examined the reversibility of the meltingand-freezing cycle. The freezing transitions of Au liquid clusters were identified by the same method used for the melting transitions. As illustrated in Figure 1 for a cluster containing 3055 atoms, the system undergoes a liquid-solid transition at a temperature of around 1100 K upon cooling from 1500 K, where hysteresis in the melt-and-quench cycle can clearly be observed. In addition, the final configuration of the cluster had a lower potential energy than that of the initial phase at 300 K, which indicates that the annealing process transformed the Au3055 cluster into a more stable state than that of the initial configuration. The freezing of Au liquid clusters revealed in our simulations showed that morphological changes or structural transformation of the gold clusters during freezing are the same, in reverse, as those we observed during melting, with no abrupt transition from liquid to a solid phase. Instead, the quasimolten state appeared again in the freezing process, playing the role of a transitional region between the liquid and solid phase. When the temperature was well above the freezing point, the cluster was not always spherical but fluctuated rapidly between different shapes, resembling a combination of icosahedra, decahedra, and octahedra with disordered surfaces (see Figure S4 in the Supporting Information). In contrast to the “quasimolten” state, the residence time in a specific shape in the liquid phase was much shorter. This can be explained in terms of Ajayan and Marks’ model,
13750 J. Phys. Chem. B, Vol. 109, No. 28, 2005 where the Gibbs free energy surface becomes flat at high temperatures so that the cluster can transform easily between different structural motifs. When these clusters (Au333, Au682, Au1184, Au1713, and Au3055) were cooled from the “quasimolten” state to a temperature just below the freezing point, they all froze into an icosahedral structure (see Figure S5 in the Supporting Information), suggesting that the formation of icosahedral structures at high temperatures appears to us to have a thermodynamic origin, though it is difficult to be sure, rather than being a kinetic phenomenon. As we decreased the temperature to 300 K, we did not observe any structural transformation from icosahedral to low-temperature optimal configurations such as decahedral or FCC structures for clusters within this size range. Despite the use of a slower cooling rate (∼1011 K/s), we were still unable to induce the icosahedral clusters to undergo any structural transformation for a period of around 1 ns, though it is possible that, given access to experimental time scales, we may have observed structural changes. One possible explanation is that the energy barrier for an icosahedron to transform into a decahedron is intrinsically large. Baletto et al.57 studied the solid-state growth of free silver clusters using Molecular Dynamics simulations. Their results showed that it is possible to transform a decahedron into an icosahedron at low or intermediate temperatures but, on the contrary, a quasimelted and short-life intermediate structure must be formed to induce such an icosahedral to decahedral transformation, which can happen only when the temperature is close to the melting point. On the other hand, the kinetics of structural transformations could be retarded due to the decrease in temperature and the resultant increase of free energy barriers between different structural motifs. In this case, even though the system has reached a point where decahedral or FCC structures become more favorable, the thermal fluctuation of an icosahedral cluster may not be large enough to overcome the free energy barriers to transform into other configurations. Therefore the final structures will be composed of a set of “frozen in” structures representative of clusters formed at high temperatures. Similarly, we can infer that if the clusters are formed or annealed at a temperature within the “quasimolten” phase followed by a rapid cooling process, the final structures will become a combination of different cluster morphologies. In this situation, the final distribution of different cluster morphologies will be determined not only by the relative energies of different configurations, but also by the magnitudes of the energy barriers between different structural motifs together with the kinetics of structural transformations. 1.3. Melting and Freezing of Supported Au Nanoclusters. In this section, we focus on the thermal behavior of supported Au nanoclusters to form a contrast, where appropriate, to the behavior of free Au clusters. Au nanoclusters of various sizes as discussed in the previous section (Au333, Au682, Au1184, Au1713, and Au3055) were deposited on a crystalline silica surface, heated, and then recrystallized according to the same procedure described above for free clusters to reveal the influence on cluster characteristics due to the presence of a substrate. The melting and freezing points of these supported Au nanoclusters are summarized in Table 2, where we can see that the melting temperatures of the supported Au nanoclusters are somewhat higher than those for free clusters. In particular, as the size of the cluster decreases, the influence from the substrate on the melting points appears to become more significant. However, this effect was not observed for the latent heats and freezing points of all supported Au nanoclusters (see Tables 2 and 3),
Kuo and Clancy
Figure 7. Snapshots of a supported Au1184 cluster at 1260 K, showing that the cluster consisted of coexisting solid and liquid fractions but retained an icosahedral shape at all times.
which indicated that the presence of the substrate only slows the kinetics of structural transformation from the ordered to the disordered phase, but did not significantly change the thermodynamic properties of the clusters. The melting mechanism of supported Au nanoclusters observed in our simulations was very similar to that of free clusters. Supported Au nanoclusters all transformed into icosahedral structures at high temperatures, but were slightly deformed due to the strain arising from the gold-silica interface (see Figure S6 in the Supporting Information). However, as the temperature approached the melting point, we did not observe the “quasimolten” phase found for the free Au nanoclusters, in which the clusters continuously fluctuated between different structural motifs. Instead, an icosahedral solid-liquid coexistence state was observed, where the cluster consisted of coexisting solid and liquid fractions but retained its icosahedral shape at all times (see Figure 7). After the temperature exceeded the melting point, the clusters started fluctuating rapidly between different shapes, similar to that found for free Au liquid clusters. Overall, these results demonstrated that the structural stability of small Au nanoclusters was enhanced by interaction with the substrate, which also implied that the formation of the interface reduced the free energy of the system and trapped the clusters in a deep potential well. Our results agree well with Ajayan et al.’s experiments52 in which Au clusters were deposited on a MgO substrate and exposed to intense electron-beam irradiation. They found that the particles became unstable and started fluctuating between different structures after the particles were lifted from the original substrate by a pillar-like structure grown from the substrate overlayers. It was noticed that as the height of the pillar increased, the frequency of the structural fluctuations also increased, but after the pillar-like structure collapsed, the particle
Supported and Unsupported Gold Nanoclusters became stable again and crystallized on the substrate into the Wulff polyhedron shape with well-defined surface facets. These results implied that the stability of small particles can increase due to interactions with a substrate, as observed here in our simulations. The freezing process of supported Au liquid clusters was very close to being the reverse process of the melting scenario except that the “quasimolten” state appeared again before the temperature reached the freezing point. Upon cooling from the liquid phase, all of the supported Au nanoclusters froze into icosahedral structures, but the morphologies of the clusters were slightly distorted due to the stress arising from the goldsilica interface. This effect was found to be more significant as the size of the cluster increased. 2. The Effect of the Substrate on the Structural Properties of Deposited Gold Clusters. It has been shown that deposited clusters may have different structural properties to those of free clusters due to the interactions with the substrate. However, the exact role of the substrate is often obscure. For example, Doraiswamy et al.50 studied the morphological transformations of Au particles supported on silica substrates over a size regime from 2 to 9 nm using real-time high-resolution microscopy. They used intense electron beams to induce morphological transformations and determined the preferred structure region in terms of the relative probabilities of occurrences among different structural motifs. Their experimental results showed that icosahedral structures were not confined to very small sizes and had the highest probability of occurrence for clusters with a size smaller than 4 nm. After that, the probability of observing icosahedra decreased with increasing size, leading to a broad transition regime between 5.5 and 7.0 nm, in which the icosahedral and decahedral clusters almost had equal probability. For decahedral structures, the probability of occurrence was relatively low for clusters with a size smaller than 4 nm, but a gradual increase of the decahedral phase with cluster size can be found over a broad size regime. This is an unexpected result in terms of energetics and was not found in the growth of free noble metal clusters, where large icosahedra were much more abundant than large decahedra. Therefore, in the second part of this study, we attempted to investigate the influence of the substrate on the structural properties of deposited Au clusters via the simulation of Au island formation and growth. In particular, we focused on the morphological transformations of Au islands with a diameter between 2 and 4 nm during growth as well as the dependence of such morphological transformations on the contact areas of the cluster with the substrate. We simulated the formation of Au islands using two different methods: (1) the crystallization of a series of liquid clusters and (2) solid-state growth via atomic deposition. In the first method, four Au nanoclusters of different sizes, containing 565, 786, 965, and 1758 atoms, respectively, were heated and then recrystallized to mimic a Au island at different stages during the growth period. For these systems, we assumed that the Au islands can only grow in the z-direction because we intend to study the interface-size dependence of the structural transition later on. Thus the initial contact area of the cluster with the substrate was set to be the same in these simulations, corresponding to a diameter of 3.6 nm. The initial configurations of these four clusters were chosen to be approximately a domed shape with FCC local order (see Figure S7 in the Supporting Information). Each cluster was heated from 300 K in a temperature step of 100 K and equilibrated at each temperature for 100 ps. After these clusters were completely melted, the liquid clusters were further equilibrated and then cooled to 300 K at a rate of 2 × 1011 K/s.
J. Phys. Chem. B, Vol. 109, No. 28, 2005 13751
Figure 8. Side views of (a) Au565, (b) Au786, (c) Au965, and (d) Au1758 clusters at 1100 K during heating.
Figure 9. Top views of (a) Au565, (b) Au786, (c) Au965, and (d) Au1758 clusters at 1100 K during heating. The re-entrant facets are indicated by the arrows.
Figures 8 and 9 present instantaneous snapshots of these Au islands at 1100 K during heating. Unlike the free Au nanoclusters, these simulations showed that the Au1758 cluster was the only one that could transform into an icosahedral structure at 1100 K before melting; the other three clusters all transformed instead into a pentagonal pyramid with five (111)-like twin facets around a common 5-fold axis (half-decahedra). Re-entrant facets at the twin boundaries in Marks-type decahedra can clearly be observed in the Au965 cluster, which was first found in Marks et al.’s experiment for annealed particles,1 and was predicted to be the minimum energy configuration for decahedral-type clusters by the modified Wulff construction. For the other two smaller clusters, Au565 and Au786, even though such re-entrant facets are not as clearly defined as those in Au965, they can still be identified in the snapshots. A similar trend can be seen in the freezing process, as shown in the final configurations of the frozen clusters (see Figures S8 and S9 in the Supporting Information). The only one that crystallized into an icosahedron was Au1758; the other three Au clusters all crystallized into a half decahedron. The (111)-like re-entrant facets also appear in these decahedra, which become more evident as
13752 J. Phys. Chem. B, Vol. 109, No. 28, 2005
Figure 10. The relationship between the morphologies of Au islands and their aspect ratios. Type 1 represents the decahedral motif and type 2 represents the icosahedral motif.
the Au island grows bigger. These simulations clearly demonstrate a morphological transition from decahedral to icosahedral structures as the size of the Au island increased from 565 to 1758 atoms; this is the opposite scenario to that suggested by the minimum-energy growth sequence, i.e., icosahedral clusters appear at very small sizes, followed by decahedral particles and finally single crystals recovered at large sizes. To clarify the role of the interface in the structural transition, four new clusters, containing 360, 576, 792, and 936 atoms, respectively, were heated and then re-crystallized according to the same procedure described in our previous simulations. The initial configurations of these new clusters were chosen to have a tetragonal shape with FCC local symmetry. The initial contact areas with the substrate are identical for these new clusters, corresponding to a diameter of 2.4 nm, and are about 56% smaller than those in the previous simulations (d ) 3.6 nm). We then compared the morphology between these two series of simulations (see Figures S10 to S12 in the Supporting Information for Au565 vs Au576, Au786 vs Au792, and Au965 vs Au936, respectively). The Au576, Au792, and Au936 clusters all transformed and crystallized into icosahedral structures, instead of decahedral ones, during the heating and cooling processes, reflecting the effect of the contact area on the morphology of Au islands. The only one that turned into a half decahedron was Au360, which indicated that the crossover size of such a morphological transition has been shifted to a smaller size (see Figure S13 in the Supporting Information). These results demonstrated that the preferred structures and morphological transitions of supported Au nanoclusters during heating and cooling are different from those of free clusters. In this case, the structural property of a Au island is not only a function of its size, but also depends on the contact area of the cluster, i.e. the lateral size of the interface, and hence involves issues related to the adhesion and wetting of a cluster on the substrate. We discovered that these structural transitions can be characterized as a function of the “aspect ratio” of a Au island, defined here as the ratio of the height to the diameter of an island. The relationship between the morphologies of these Au islands and their aspect ratios are presented in Figure 10. Even though Au islands in these two series of simulations have different sizes and different contact areas with the substrates, they exhibit a common trend in structural transitions, i.e. the transformation of a Au island from a decahedron into an icosahedron began when the aspect ratio was between 0.55 and 0.65, as shown in Figure 10. To understand if a different growth method can alter the structural properties of a deposited cluster, we simulated the solid-state growth of Au islands via atomic deposition of Au
Kuo and Clancy atoms on a silica substrate, thus serving as a complementary study to the formation of Au islands via freezing of liquid droplets. For simplicity, we omitted processes such as surface diffusion, nucleation, and aggregation of Au adatoms during the growth period because it is infeasible to perform such simulations within a reasonable time frame with Molecular Dynamics. Here we adopted an indirect way to circumvent these problems. Before starting the growth simulation, three layers of Au atoms with a diameter of 3.6 nm were deposited and then annealed on the surface of a silica substrate, serving as a base for further deposition. During the growth simulation, the temperature of the cluster was kept constant at 1100 K. Five Au atoms were introduced onto the base every 50 ps with an incident velocity of 0.5 Å/ps, which was chosen to be small enough to avoid any bouncing off from the cluster surface. The initial positions of the deposited Au atoms were randomly picked from an area with a diameter of 3.6 nm at a distance of 10 Å above the island so that the radius of the Au cluster would remain close to 1.8 nm during the growth period to allow a clear comparison to the results from the previous simulations where islands were formed by solidification from the melt. Instantaneous snapshots of a Au island at different stages during the growth period (see Figures S14 to S16 in the Supporting Information) showed that a pentagonal pyramid with five (111) twin facets (half decahedron) was first formed as the number of Au atoms reached 536. After that, we observed a wide decahedral window up to 1000 atoms followed by a transition zone between 1000 and 1300 atoms, in which the Au island looked like hybrid structures and did not appear to fall into any simple structural classification. While it was clearly not a decahedron at that moment, it was not classifiable as an icosahedron even though the Au island started showing a hexagonal shape with more than one 5-fold symmetry axis. Finally, when the number of deposited Au atoms reached 1345, the Au island transformed fully into an icosahedron (see Figure S16b in the Supporting Information). Another growth simulation was performed with the same procedure mentioned above but for a Au island with a diameter of 2.4 nm. This system showed that a decahedron has already formed by the time that 320 Au atoms had been deposited (see Figure S17 in the Supporting Information). After that, a smaller decahedral window up to a size containing around 420 Au atoms was observed for this growth process, implying that the decahedral window can be shifted and become narrower as the size of the interface is reduced. These solid-state growth simulations also present a morphological transformation from decahedral to icosahedral structures during the growth period, and illustrate that there is a dependence of the decahedral window on the contact area of the cluster with the substrate, which are consistent with what we observed in our previous simulations for the crystallization of liquid clusters. Since this kind of simulation is very computationally demanding, we have only performed the solid-state growth of Au islands at one temperature, i.e. 1100 K. However, we do not rule out the possibility that the preferred structures and the growth sequence could be different at a lower temperature, or for Au islands with a larger diameter. For example, a Au island might turn into an octahedron when it was grown at room temperature or when it has a diameter larger than 5 nm. To summarize the results in this section, including both the crystallization of liquid clusters and the deposition-growth simulations, we observed a morphological transformation from decahedral to icosahedral structures during Au island growth in which a half decahedron was always formed first, which then
Supported and Unsupported Gold Nanoclusters transformed into an icosahedron, instead of an octahedron or full decahedron, as the number of Au atoms increased. This kind of transformation seems to be independent of the choice of potential models since Baletto et al.57 also reported a similar result for the growth of free Ag clusters using the tight-binding model, which they applied to explain why large icosahedra are much more abundant than large decahedra in some experiments. However, the preferred structure and the morphological transition for a deposited cluster could be more complicated. Our simulations showed that the island shapes are strongly influenced by the substrate: the structural property of a Au island is not only a function of cluster size, but also depends on the contact area between an island and the substrate, leading to a mixed morphology growth within a certain size range (2-4 nm in this study), i.e. Au islands could be a combination of decahedra and icosahedra at a given size, depending on growth conditions such as the initial film thickness, surface defects, annealing temperature, and annealing time. Comparing the potential energies of Au576, Au792, and Au936 clusters to those of Au565, Au786, and Au965 clusters (see Figure S18 in the Supporting Information), we find that the icosahedral structure is still a more stable configuration for clusters within this size range. However, the substrate can stabilize a nonequilibrium structure via its interaction with the cluster so that the energy barriers for Au565, Au786, and Au965 clusters to transform into an icosahedron could be prohibitively large. Consequently, they transformed into other local minima having lower energy barriers in the free energy surface like the decahedral type structures. In addition, we can infer from our simulations that the probability of observing icosahedral structures will decrease with increasing diameter of a Au island since its decahedral window will be enlarged. Similarly, we can expect a predominance of the decahedral phase among Au islands with larger diameters or interfaces for the same reason. Finally, we have to point out that these results might conflict with those obtained by using gas-phase annealing and cluster beam deposition, in which the clusters are fabricated in a cluster source and attain a stable morphology like free clusters before arriving at the substrate. In that case, the configurations of the clusters are mainly determined by the experimental conditions in the cluster source, and the pressure and temperature of the carrier gas. After the preformed clusters interact with the substrate, their structures may change, all depending on the incident energy of the preformed clusters and the strength of the cluster-support interaction. Conclusion Molecular Dynamics simulations in conjunction with the MEAM potential models have been applied to study the thermal behavior and the structural properties of both supported and unsupported Au nanoclusters within a size range between 2 and 5 nm. These simulations have suggested the following conclusions: (1) Regarding the thermal behavior of free Au nanoclusters, our study revealed some interesting phenomena which were not shown in previous simulations for the melting and freezing mechanism of Au or other transition metal clusters. The melting scenario of Au nanoclusters observed in our simulations involved a structural transformation from the initial FCC configuration to an icosahedral structure at elevated temperatures followed by a transition to a so-called “quasimolten” state in the vicinity of the melting point, in which the clusters were found to continuously fluctuate between different structural motifs that nucleated in this region. Such a solid-to-solid structural transformation has been reported by Cleveland et
J. Phys. Chem. B, Vol. 109, No. 28, 2005 13753 al.47,48 for Au clusters containing 75-459 atoms using the EAM potential models but it conflicted with the results of other previous simulation studies regarding the melting of metal clusters, where no such structural transformation has been found. Some people may question the validity of this kind of structural transformation since it contradicts the minimum-energy growth sequence. However, as Doye and Calvo pointed out recently, entropic effects should be considered for clusters at a higher temperature (>0 K), and thus the equilibrium structure of a cluster corresponds to its lowest free energy, rather than the potential energy. According to their calculations for the equilibrium structures of silver and Lennard-Jones clusters using the superposition method, this kind of structural transformation is quite plausible at high temperatures.49 The presence of a “quasimolten” state in the vicinity of the melting point is another interesting phenomenon revealed in our simulations. Although this phenomenon was not observed in previous simulations for the melting of Au nanoclusters, the existence of such a “quasimolten” state at a temperature well below the melting point has been predicted by Ajayan and Marks using a theoretical model that allowed them to calculate the Gibbs free energy surface as a function of cluster morphology.54 Our simulation results confirmed the likelihood for the existence of such a “quasimolten” phase in the vicinity of the melting point but the multiply twinned particles (MTPs) were considered as the low-temperature products in their phase map, which is exactly the opposite to what we have observed here. During the freezing of Au liquid clusters, we observed neither an abrupt transition from liquid to solid phase nor the formation of a nucleation center in the interior of a liquid cluster. Instead, the “quasimolten” state reappeared in the vicinity of the freezing point, playing the role of a transitional region between the liquid and solid phase. When the liquid Au clusters were cooled from the “quasimolten” state to a temperature just below the freezing point, they all froze into an icosahedral structure. We believe that the similarity in morphological changes occurring in melting and freezing supports the idea that thermodynamics dominates over kinetic processes in the formation of icosahedral structures during growth, but the time scale of MD simulations precludes a definitive statement. (2) The effect of a substrate on the melting and freezing behavior of Au nanoclusters showed that the structural stability of small Au nanoclusters was enhanced by interaction with a substrate, which slowed the kinetics of structural transformation from ordered to disordered phases but did not significantly change the thermodynamic properties of the clusters. During the heating process, supported Au nanoclusters also transformed into icosahedral structures at high temperature like free clusters, but were slightly deformed due to the strain arising from the gold-silica interface. Rather than observing a “quasimolten” phase, we found an icosahedral solid-liquid coexistence state in the vicinity of the melting point, in which the cluster consisted of coexisting solid and liquid fractions but remained an icosahedral shape at all times. Upon cooling from the liquid phase, the freezing points of supported Au nanoclusters were found to be very close to those of free Au clusters and the “quasimolten” state appeared again before the temperature reached the freezing point, indicating that the presence of a substrate did not have significant influence on the freezing of Au nanoclusters. (3) The influence of the substrate on the structural properties of deposited Au clusters was revealed by simulations of Au island formation on a silica surface. We observed a morphological transformation from decahedral to icosahedral structures
13754 J. Phys. Chem. B, Vol. 109, No. 28, 2005 during Au island growth at high temperatures, in which a half decahedron was always formed first and then transformed into an icosahedron, instead of an octahedron or full decahedron, as the number of Au atoms increased. More importantly, our simulations demonstrated that, unlike free Au nanoclusters, the structural property of a Au island is not only a function of cluster size but also depends on the contact area between an island and the substrate, which can be characterized as a function of the “aspect ratio”, defined here as a ratio of the height to the diameter of an island. For instance, Au islands can transform into an icosahedron at high temperature only when their aspect ratios exceed a critical value of around 0.6; otherwise, they tend to exhibit a decahedral-type configuration. In other words, we can say that the morphology of an island is controlled by its growth rate in the lateral direction vs that in the z-direction, depending on growth conditions such as the initial film thickness, surface defects, nucleation rate, and annealing profiles. Acknowledgment. The authors thank the financial support of the NSF MRSEC program via the Cornell Center for Materials Research (CCMR), as well as CCMR’s computing facilities for access to their resources. Supporting Information Available: Supplemental figures regarding the structural and morphological transformations of Au nanoclusters at different stages. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Marks, L. D. Rep. Prog. Phys. 1994, 57, 603. (2) Martin, T. P. Phys. Rep. 1996, 273, 199. (3) Smith, D. J.; Marks, L. D. J. Cryst. Growth 1981, 54, 433. (4) Jose´-Yacaman, M.; Herrera, R.; Gomez, A. G.; Tehuacanero, S.; Schabes-Retchkiman, P. Surf. Sci. 1990, 237, 248. (5) Garzon, I. L.; Posada-Amarillas, A. Phys. ReV. B 1996, 54, 11796. (6) Oviedo, J.; Palmer, R. E. J. Chem. Phys. 2002, 117, 9548. (7) Michaelian, K.; Rendon, N.; Garzon, I. L. Phys. ReV. B 1999, 60, 2000. (8) Michaelian, K.; Beltran, M. R.; Garzon, I. L. Phys. ReV. B 2002, 65, 041403. (9) Ascencio, J. A.; Perez, M.; Jose´-Yacaman, M. Surf. Sci. 2000, 447, 73. (10) Ino, S. J. Phys. Soc. Jpn. 1969, 27, 941. (11) Marks, L. D. J. Cryst. Growth 1984, 61, 556. (12) Cleveland, C. L.; Landman, U.; Shafigullin, M. N.; Stephens, P. W.; Whetten, R. L. Z. Phys. D 1997, 40, 503. (13) Cleveland, C. L.; Landman, U.; Schaaff, T. G.; Shafigullin, M. N.; Stephens, P. W.; Whetten, R. L. Phys. ReV. Lett. 1997, 79, 1873. (14) Baletto, F.; Ferrando, R.; Fortunelli, A.; Montalenti, F.; Mottel, C. J. Chem. Phys. 2002, 116, 3856. (15) Allpress, J. G.; Sanders, J. V. Surf. Sci. 1967, 7, 1. (16) Komoda, T. Jpn. J. Appl. Phys. 1968, 7, 27. (17) Marks, L. D.; Smith, D. J. Cryst. Growth 1981, 54, 425.
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