Molecular Dynamics Simulations of the Coalescence of Iridium Clusters

J. Phys. Chem. C 2007, 111, 6713-6719

6713

Molecular Dynamics Simulations of the Coalescence of Iridium Clusters Tiffany Pawluk* and Lichang Wang* Department of Chemistry and Biochemistry, Southern Illinois UniVersity, Carbondale, Illinois 62901 ReceiVed: January 19, 2007; In Final Form: March 10, 2007

The coalescence of small iridium clusters was studied using a molecular dynamics (MD) technique with a cluster Sutton-Chen potential. MD simulations were carried out on the reaction of two clusters from 1 to 7 atoms at various incident angles and initial kinetic energies. The threshold energy of product formation was investigated for the various systems, and the effect of initial orientation between two clusters on the product was also studied. A comparison of diffusion and Ostwald-ripening coalescence mechanisms was performed for 8-atom cluster formation, and Ostwald-ripening led to cluster formation with higher initial energies. An atom-to-bond collision resulted in the formation of a larger cluster more often and at higher energies than an atom-to-atom collision.

1. Introduction The study of nanosize clusters has become one of the dominant areas of research throughout the fields of chemistry, physics, and biology. The potential applications of these materials include catalysis, data storage, medical diagnosis, and biosensing,1-4 and an understanding of the structure and resulting properties is fundamental to exploiting their value. In particular, clusters containing metal have received great attention in recent years because they exhibit electronic and magnetic properties that differ from those of bulk metals. These properties are highly dependent on size.5-11 Therefore, to make use of the unique properties of small clusters, the buildup of clusters must be well controlled and reproducible to obtain the desired cluster size. To achieve this, it is important to understand the mechanism of cluster coalescence to make practical use of it. Cluster growth and stability have been studied both experimentally and theoretically.5-8,10-52 When placed on surfaces, cluster buildup can be accomplished by diffusion of smaller clusters into larger ones.19,20,24,26,27 This diffusion can also lead to aggregation and a loss of size-based activity, known as sintering.40,53 Previous studies on the coalescence of metal nanoparticles have employed molecular dynamics (MD) and Monte Carlo (MC) methods.31-39,51,52 Hawa et al. used MD with a Stillinger-Weber potential to study the coalescence of both equal36 and unequal37 sized silicon nanoparticles. Zeng et al. studied Au and Cu nanoparticle sintering using MD with an embedded atom potential.38 Raut et al. investigated the sintering of aluminum by MD, including the influence of temperature and orientation.39 These studies show that metal nanoparticles do coalesce, often with sintering as a result. The diffusion of iridium atoms has been studied only by a limited number of groups.20-23,26,27,54 Wang and Ehrlich used field ion microscopy (FIM) to find that iridium clusters from 18 to 39 atoms diffuse across the Ir(111) surface.54 Chen and Tsong also found by FIM that the step atoms of the Ir(011) surface diffuse along the steps.22 From a theoretical perspective, Shiang and Tsong used MD to study the diffusion of Ir dimers on Ir surfaces,26 and Habar et al. studied adatoms on Ir(111).23 These studies confirm the diffusion of iridium atoms on surfaces. * Authors to whom correspondence should be addressed. E-mail: (T.P.) [email protected]; (L.W.) [email protected].

Our previous coalescence study on Ir55 including only 3-atom systems showed that the formation of clusters was very sensitive to the initial kinetic energy given to the system, as well as the orientation of the coalescing particles. Despite those findings, a number of issues remain to be answered. For instance, cluster buildup can be accomplished through diffusion or Ostwaldripening. In contrast to diffusion coalescence (i.e., larger clusters formed as two diffusing clusters come in contact), the Ostwaldripening mechanism is single atom transfer from one nanoparticle to another. Between these two growth mechanisms, which mechanism is dominant for iridium coalescence? How does the growth mechanism depend on the initial kinetic energies, incident angles, and the parent cluster size? To answer these questions, we chose to study the coalescence of iridium clusters from 1 to 7 atoms in the gas phase using MD simulations with a modified Sutton-Chen potential.56 2. MD Simulation Details To further investigate the kinetics and mechanism of the coalescence of iridium nanoparticles, constant energy MD studies were carried out over a range of energies on three iridium systems. The smallest system studied is a single atom colliding with a dimer. The incident angle was varied to study cluster formation following atom-to-atom and atom-to-bond collisions. The results are presented and discussed in section 3.1. The second test case is a system of two squares. This was chosen as a test system because our previous density functional theory (DFT) work has shown that the square is a prominent feature in stable iridium clusters,5 and also by the ab initio MD simulations discussed below. The initial orientation of the squares was varied to study the interaction of a face-to-face orientation and edge-to-edge in the same plane. The results are discussed in Section 3.2. The third test system was a single atom colliding with the most stable 7-atom structure from our previous DFT investigations.5 Again here, the incident angle was varied and a range of initial kinetic energies was tested. The results are discussed in section 3.3. The initial coordinates of the dimer, square, and 7-atom clusters were chosen as the relaxed structures from our previous DFT studies of iridium.5 Greater detail of the initial conditions for each system is provided in the results section.

10.1021/jp070494n CCC: $37.00 © 2007 American Chemical Society Published on Web 04/13/2007

6714 J. Phys. Chem. C, Vol. 111, No. 18, 2007

Pawluk and Wang

Figure 1. Potential energy, V (eV), versus time, t (fs), for two trajectories of a 4-atom system. The initial geometries were two dimers parallel (bottom curve) and approaching perpendicularly (top curve).

TABLE 1: Comparison of Binding Energy Obtained Using the Original Bulk and Cluster Optimized Parameters of Sutton-Chen Potential and DFT Calculationsa binding energy (eV) dimerc linear trimerc trianglec square tetrahedron cube bulk-like 8-atom

cluster PES

DFTb

original PES

-5.06 -8.09 -9.46 -13.33 -14.18 -32.31 -31.35

-5.06 -9.63 -9.09 -15.08 -13.68 -39.20 -36.24

-2.73 -0.15 -8.56 -10.83 -14.24 -11.75 -13.74

a The reference point of the energy is the asymptotic region of isolated atoms. bDFT binding energy published in ref 5. cData for these structures published in ref 55.

We studied the coalescence of the above systems by solving the equations of motion for position, xi, yi, zi,

dxi pxi ) , dt mi

dyi pyi ) , dt mi

dzi pzi ) dt mi

(1)

and momentum, pxi, pyi, pzi,

dpxi dt

)-

dpyi

∂V , ∂xi

dt

)-

dpzi

∂V , ∂yi

dt

)-

∂V ∂zi

(2)

based on the Cartesian coordinates x, y, and z for each atom, i, with i ) 1-8. We adopted Cartesian coordinates because our intention of building the dynamics code is for studying systems consisting of more than 100 metal atoms where the Cartesian coordinates are the most practical choice. mi is the mass of the ith atom, and V is the potential energy surface (PES). Here we use the Sutton-Chen potential

V)

[∑ 1

2

V(rij) - c

ij

]

∑i xFi

() a rij

n

Ecom )

pcom2 2mcom

(∑ i

)

) (∑

px,i(t ) 0) 2 +

) (∑

py,i(t ) 0) 2 +

i

i

pz,i(t ) 0)

)

2

∑i mi

(3)

2

(4)

As defined above, the internal kinetic energy is the energy of the motion of the atoms without the translational energy of the entire system. This is directly proportional to the temperature N of the system by T(t) ) ∑i)1 (miV2i (t))/(kB(3N - 6)), where Vi is the velocity of the ith iridium atom.

where the pair potential is given by

V(rij) )

In eqs 3-5, rij is the distance between two atoms, and , a, c, m, and n are constant parameters. In our previous work with this potential, we found the bulk parameters originally determined by Sutton and Chen56 did not accurately represent the interaction of atoms in a small cluster. We therefore optimized the parameters , a, and c for small iridium clusters. The cluster optimized parameters that were used in this work are  ) 0.00255 eV, a ) 3.45 Å, c ) 328.22, m ) 6, and n ) 14.55 We tested the accuracy of the cluster (optimized) potential by comparing the binding energy of clusters from 2 to 8 atoms with our previous DFT results and those from the original potential. The results are summarized in Table 1. As the data shows, the cluster potential in general provides good agreement with the DFT results for these small clusters. We intend to continue our study of appropriate PESs for describing larger systems of Ir atoms, but the current PES is suitable for our present work. Ab initio MD simulations58-60 were performed for a system of 4 Ir atoms to further examine the interactions among atoms when the system is not at the minima such as those provided in Table 1. The electron-ion interactions were described by ultrasoft pseudopotentials.61 The exchange and correlation energies were calculated with the Perdew-Wang 91 form of the generalized gradient approximation (GGA).62 A planewave basis set with a cutoff energy of 300 eV was used. The electronic part of the simulation is the same as our previous DFT calculations on Ir clusters.5 The Vienna ab initio simulation package (VASP) was used in the ab initio MD simulations.63-65 Two trajectories were obtained for a 4-atom system. A timestep of 3 fs was used59 with an initial temperature of 500 K. The starting geometries are one with two parallel Ir dimers and one with two dimers approaching perpendicularly. The results of the potential energy as a function of time are plotted in Figure 1. Some representative structures were also provided. It is clear that a square structure is more stable than a tetrahedron structure. The above set of coupled equations of motion (i.e., eqs 1 and 2) was solved using the sixth-order Runge-Kutta method.57 The trajectories were propagated at a time step of 0.01 fs for a total of 1 000 000 steps. Any complex lasting more than these 10 ps is considered long-lived. During the entirety of the simulations, the total energy and the total angular momentum of the system were monitored for their conservation. The total energy is E ) ET + V, where the kinetic energy is given by ET 2 ) ∑i (p2x,i + p2y,i + pz,i )/2mi. We also calculate the internal kinetic energy, Ti ) ET - Ecom, where

and the local electron density is given by

Fi )

∑j

() a

rij

3. Results

m

(5)

3.1. 3-Atom Coalescence. Coalescence of a single Ir atom, C, colliding with an Ir dimer, A-B, was studied as the incident

MD Simulations of the Coalescence of Ir Clusters

J. Phys. Chem. C, Vol. 111, No. 18, 2007 6715

Figure 2. The initial configuration of the 3-atom interaction, AB + C. The third iridium atom, C, is initially 10 Å from the dimer centerof-mass, while the angle, θ (°), is varied from 0 to 90°.

Figure 3. Plot of original dimer (black triangle), new dimer (blue square), and trimer (red circle) formation as a function of incident angle, θ, and initial internal kinetic energy, Ti(t ) 0).

angle of the single atom was varied from collinear with the dimer, θ ) 0°, to perpendicular, θ ) 90°. The dimer bond distance was set at the equilibrium distance found in our previous DFT studies.5 The single atom was placed 10 Å from the dimer center-of-mass (com) to ensure no initial interaction. A cluster schematic is shown in Figure 2. The initial kinetic energy (i.e., kinetic energy at t ) 0, ET(t ) 0)) was varied over the range of 0.02 to 2.0 eV. The ET(t ) 0) was given to the single atom, C, in the direction of com of the dimer (i.e., ET(t 2 ) 0) ) p2c /2mc ) (p2x,c + p2y,c + pz,c )/2mc with px,c ) pc × cos θ, py,c ) pc × sin θ, pz,c ) 0. The important kinetic energy for the system and consequent formation of bigger clusters, however, is the internal kinetic energy, Ti. The resulting products and final internal kinetic energy, Ti, as a function of angle and of initial internal kinetic energy, Ti(t ) 0), are presented in Table 2. The results for all energies at θ ) 0° and for ET(t)0) ) 1.0 and 0.1 eV at all angles were previously reported.55 Our findings showed that trimer product formation was highly influenced by incident angle and initial kinetic energy. The current study builds upon our previous findings by varying the incident angle for all energies to see the extent of the trend.

When the single atom approaches the dimer collinearly, the atom-to-atom collision results in new B-C dimer formation, reactive scattering, for all energies tested. At 15°, the A-B dimer is only preserved at Ti(t ) 0) ) 0.013 and 0.067 eV. However, the product is very sensitive to the incident angle and energy when the collision is atom-to-bond. This type of collision results in varied products for angles above 15°. The frequency of new dimer and trimer formation as a function of incident angle and initial internal kinetic energy is shown in Figure 3. A long-lived trimer complex is regularly formed, occurring 40% of the time for the angles from 30 to 90° and 50% of the time for 45, 75, and 90°. For the energies below Ti(t ) 0) ) 0.27 eV at 75° and below Ti(t ) 0) ) 0.33 eV at 90°, a trimer is formed exclusively. This trend is again due to the elastic nature of the atom-to-bond collision. Above Ti(t ) 0) ) 0.33 eV, the cluster has sufficient energy to dissociate, regardless of impact angle. These results show that the conditions of the impact are critical to cluster formation. In cases where the final internal kinetic energy is greater than initial, Ti(f) > Ti(t ) 0), the product clusters remain in a “hot” vibrationally excited state. The results in Table 2 show this trend for the trimer products. Above Ti(t ) 0) ) 0.27 eV, none of

TABLE 2: The Final Product(s) and Final Internal Kinetic Energy, Ti(f), for the Iridium AB + C Reaction as a Function of Initial Kinetic Energy and Incident Angle, θ (see Figure 2) θ (°) ET(t ) 0) (eV)

Ti(t ) 0) (eV)

0.020

0.013

0.050

0.033

0.10c

0.067

0.20

0.13

0.30

0.20

0.40

0.27

0.50

0.33

1.0c

0.67

1.5

1.0

2.0

1.3

0 Ti(f) (eV) product Ti(f) (eV) product Ti(f) (eV) product Ti(f) (eV) product Ti(f) (eV) product Ti(f) (eV) product Ti(f) (eV) product Ti(f) (eV) product Ti(f) (eV) product Ti(f) (eV) product

c

0.14 A + BC 0.070 A + BC 0.070 A + BC 0.11 A + BC 0.18 A + BC 0.19 A + BC 0.26 A + BC 0.57 A + BC 0.97 A + BC 1.2 A + BC

15

30

45

60

75

90

0.58 AB + C 0.018 A + BC 0.065 AB + C 0.097 A + BC 0.18 A + BC 0.21 A + BC 0.21 A + BC 0.47 A + BC 0.80 A + BC 1.3 A + BC

0.34 AB + C 1.8 A-B-C 2.1 B-A-C 0.10 A + BC 0.14 AB + C 0.22 AB + C 0.31 AB + C 0.61 A + BC 0.51 A + BC 1.3 AC + B

0.046 A + BC 0.015 AB + C 2.1 A-B-C 3.0 B-A-C 0.17 A-B-C 1.2 BA...Ca 2.4 A-B-C 0.36 AB + C 1.0 AC + B 1.0 AB + C

0.55 A + BC 1.5 A-B-C 0.069 A + BC 0.31 A + BC 0.19 AC + B 0.60 AB...Ca 0.32 AB + C 0.66 AB + C 0.99 AB + C 1.2 AB + C

0.097 AC...Ba 0.086 AC...Ba 0.24 AC...Ba 2.9 ABCb 0.66 AC...Ba 0.27 A + BC 0.30 AC + B 0.63 AC + B 1.0 AC + B 1.1 AB + C

3.1 A-C-B 1.3 A...BCa 0.69 A...BCa 0.92 A...BCa 1.3 A...BCa 0.78 AB...Ca 0.34 A + BC 0.65 A + BC 0.59 AB + C 1.3 A + BC

a A...B indicates an interatomic distance greater than 3.0 and less than 5.0 Å, so that these atoms do not form a real bond but rather a van der Waals complex. bABC indicates a triangular complex. cThese results were previously published in ref 55.

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Figure 5. The initial configurations of Ir4 + Ir4. (a) Two squares are initially in the same plane. (b) Two squares are initially parallel. The numbers 1-8 in (a) and (b) refer to the initial positions of atoms 1-8.

Figure 4. Potential energy, V (eV), versus time, t (fs), for the coalescence of three Ir2 + Ir1 systems with Ti(t ) 0) ) 0.13 eV and various incident angles. See Figure 2. (a) θ ) 0°; (b) θ ) 45°; and (c) θ ) 75°.

the products are vibrationally excited. Figure 4 shows the potential energy, V (eV), versus time, t (fs), for three cases with Ti(t ) 0) ) 0.067 eV. In Figure 4a, the collinear impact results in immediate dissociation at 2.4 ps, after which time there is no interaction between the dimer and single atom and the potential energy does not fluctuate. In Figure 4b,c, incident angles of 45 and 75°, respectively, result in trimer complexes

Figure 6. The initial configurations of Ir7 + Ir1. (a) Single atom approaches a side bond on the cluster. (b) Single atom approaches an end bond. (c) Single atom approaches an atom in the cluster. (d) Single atom approaches a face center in the cluster. The dashed line represents the path of the single atom toward the cluster. The numbers 1-8 in (a) refer to the initial positions of atoms 1-8, with atoms 1, 2, and 5 in the foreground.

forming upon association. The complexes remain for the entire 10 ps and both are vibrationally hot. 3.2. 8-Atom Diffusion Coalescence: Ir4 + Ir4. To represent a diffusion-based coalescence mechanism, the interaction of Ir4

TABLE 3: The Final Product(s) and Final Internal Kinetic Energy, Ti(f), for the Reaction Ir4 + Ir4 as a Function of Initial Kinetic Energy (The Superscripts 1-8 Identify the Atoms, Initially Ir41-4 + Ir45-8 (see Figure 5))a (a) Ir4 + Ir4: two squares initially in same plane 2.8-5.8 6.0 6.3-8.9 1.4-2.9 3.0 3.1-4.4 3.1-5.4 4.0 2.8-6.0 Ir8 Ir51,2,4,6-7 Ir8 Ir33,5,8

ET(t ) 0) (eV) Ti(t ) 0) (eV) Ti(f) (eV) product

0.048-2.3 0.038-1.1 1.8-5.5 Ir8

2.5 1.3 2.5 Ir62,4-8 Ir21,3

ET(t ) 0) (eV) Ti(t ) 0) (eV) Ti(f) (eV) product

0.048-3.4 0.028-1.7 1.2-6.1 Ir8

3.5 1.8 3.2 Ir41-4 Ir45-8

a

Table 3 sections a,b correspond to Figure 5a,b.

(b) Ir4 + Ir4: two squares initially parallel 3.8 4.0 4.3 1.9 2.0 2.1 4.2 2.9 4.6 Ir41-4 Ir41-4 Ir8 Ir45-8 Ir45-8

9.0 4.5 3.9 Ir51-4,8 Ir35-7

9.3 4.6 3.2 Ir71,2,4-8 Ir13

4.5 2.3 4.9 Ir8

5.0 2.5 2.1 Ir41,3,5,8 Ir42,4,6,7

9.5 4.8 3.7 Ir61,3-5,7,8 Ir22,6

MD Simulations of the Coalescence of Ir Clusters + Ir4 was studied. The atoms were placed in an initial geometry of 2 squares with the structural information from our DFT calculations.5 A distance of 10 Å separates the com of the two squares. Kinetic energy ET(t ) 0) ) 0.048-10.0 eV was distributed evenly among the x, y coordinates of four atoms of 4 one square in the direction of the other (i.e., ET(t ) 0) ) ∑i)1 2 4 2 2 (pi )/(2mi) ) ∑i)1 (px,i + py,i)/(2mi) with px,i ) pi × cos θ and py,i ) pi × sin θ). Two initial configurations were studied: the interaction from a side-to-side orientation (planar), θ ) 0°, to a face-to-face impact (parallel), θ ) 90°, as shown in Figure 5. A total of 69 trajectories were run. The results are summarized in Table 3, with the superscript numbers identifying the atoms 1-8. For the planar orientation, much of the kinetic energy given to the system is converted to out-of-plane motion if even a small amount of energy is given to the out-of-plane direction (i.e., z-direction). The threshold energy for 8-atom cluster formation is Ti(t ) 0) ) 1.1 eV. The planar instances of Ti(t ) 0) ) 1.3 and 3.0 eV dissociated before the 10 ps time limit was reached, giving a resonance feature to the dissociation pattern of the larger clusters. From the parallel orientation, an 8-atom cluster is formed exclusively up to Ti(t ) 0) ) 1.7 eV. For the initial energies of Ti(t ) 0) ) 1.8-2.0 eV, the collision is nonreactive, and the product clusters maintain the original atoms. An 8-atom cluster is formed for Ti(t ) 0) ) 2.1-2.3 eV, again showing a resonance pattern to the dissociation. Above this energy, the products are two 4-atom clusters, although not the original atom distribution. Also shown in Table 3, Ti(f) > Ti(t ) 0) when 8-atom clusters are formed. The parallel orientation leads to hot products even after dissociation. 3.3. 8-Atom Ostwald Ripening Coalescence: Ir7 + Ir1. To investigate an Ostwald-ripening coalescence mechanism, an Ir atom was propelled toward a 7-atom cluster. The most stable Ir7 cluster from our previous DFT studies5 was chosen as the initial geometry, a square bonded to two atoms above and one atom below. Four incident angles were investigated (i.e., two instances of atom-to-bond, one atom-to-atom, and one atom-

J. Phys. Chem. C, Vol. 111, No. 18, 2007 6717 to-face center) as shown in Figure 6, with initial kinetic energies ET(t ) 0) ) 0.05-15.0 eV. All energy was given to the single atom in the direction of the cluster. A total of 39 trajectories were studied, and the results are presented in Table 4. The atom-to-bond collisions result in a long-lived 8-atom cluster for energies up to Ti(t ) 0) ) 4.4 and 4.6 eV, depending on the location of the bond in the cluster. When the single atom collided with another atom, the 8-atom cluster dissociated above Ti(t ) 0) ) 2.5 eV. These results are similar to the findings for the 3-atom case discussed above and show that the atom-tobond collision is more able to absorb the energy of the impact across the cluster. When the single atom approaches a face center in the cluster, the 8-atom structures begin to dissociate with Ti(t ) 0) ) 2.8 eV. For an atom-to-bond collision, the position of the impacted bond in the cluster also plays a role in the products of dissociation. When the bond is on the top of the cluster, the original 7-atom cluster remains intact. When the single atom hits a bond in the center of the structure, the original cluster is broken apart and a dimer or trimer is frequently formed. This is likely due to the greater rigidity atoms of the middle bond, stabilized by a higher-bond order. The collision is therefore reactive. Figure 7 shows the fluctuation of potential energy versus time for three trajectories of the coalescence of Ir7 + Ir1. In the top picture, Ti(t ) 0) ) 0.9 eV results in an 8-atom product cluster. The potential energy remains constant with oscillation throughout the time. In the middle and bottom figures, the energies of Ti(t ) 0) ) 5.3 and 6.1 eV, respectively, result in dissociation of the 8-atom cluster within 2 ps. This is reflected by the increase in potential energy in both cases. This indicates that to isolate the larger clusters, energy would need to be removed from the system before the 2 ps time is reached. In the case of the 8-atom cluster formation, the final internal kinetic energy is very high compared with the initial, and these clusters will eventually dissociate as well. Our future studies will include methods to remove energy from the system to isolate the larger clusters, such as the use of a carrier gas. The use of argon as a carrier

TABLE 4: The Final Product(s) and Final Internal Kinetic Energy, Ti(f), for the Reaction Ir7 + Ir1 as a Function of Initial Kinetic Energy (The Superscripts 1-8 Identify the Atoms, Initially Ir71-7 + Ir18, (see Figure 6))a ET(t ) 0) (eV) Ti(t ) 0) (eV) Ti(f) (eV) product

0.54-5.0 0.46-4.4 3.7-5.7 Ir8

ET(t ) 0) (eV) Ti(t ) 0) (eV) Ti(f) (eV) product

1.0-5.0 0.98-4.6 3.7-6.2 Ir8

ET(t ) 0) (eV) Ti(t ) 0) (eV) Ti(f) (eV) product

1.0-3.0 0.82-2.5 3.2-4.1 Ir8

ET(t ) 0) (eV) Ti(t ) 0) (eV) Ti(f) (eV) product

1.0-3.0 0.96-2.8 3.4-4.8 Ir8

a

(a) Ir7 + Ir1: single atom collision with side bond 6.0 7.0 8.0 9.0 5.3 6.1 7.0 7.9 4.2 3.8 5.2 6.1 Ir61-6 Ir52,4,6-8 Ir62-7 Ir61-6 Ir27,8 Ir31,3,5 Ir21,8 Ir27,8

10.0 8.8 4.4 Ir71,3-8 Ir12

11.0 9.6 4.4 Ir71,3-8 Ir12

(b) Ir7 + Ir1: single atom collision with top bond 7.0 8.0 9.0 6.4 7.3 8.1 4.0 4.0 5.0 Ir71-7 Ir71-7 Ir71-7 Ir18 Ir18 Ir18

10.0 9.0 5.3 Ir71-7 Ir18

15.0 13.5 10.6 Ir71-7 Ir18

8.0 7.2 4.2 Ir52-6 Ir31,7,8

9.0 8.1 8.2 Ir71-7 Ir18

6.0 5.5 3.0 Ir71-7 Ir18

(c) Ir7 + Ir1: single atom collision with cluster atom 4.0 5.0 10.0 15.0 3.4 4.2 8.5 12.8 2.6 3.5 5.2 4.5 Ir61,3-7 Ir61-4,7,8 Ir71-7 Ir31,3,8 Ir22,8 Ir25,6 Ir18 Ir32,5,6 Ir24,7 (d) Ir7 + Ir1: single atom approaches face center 4.0 5.0 6.0 7.0 3.6 4.5 5.4 6.3 3.2 3.4 4.4 3.2 Ir71,3-7 Ir8 Ir51,2,7,8 Ir51,2,5,7,8 Ir12 Ir33-5 Ir33,4,6

Table 4 sections a-d correspond to Figure 6a-d.

15.0 13.1 5.5 Ir51,3,4,6,8 Ir25,7 Ir12

10.0 9.0 9.6 Ir61,3,5-8 Ir22,4

6718 J. Phys. Chem. C, Vol. 111, No. 18, 2007

Pawluk and Wang 4. Conclusions Our studies investigated the formation of trimers and 8-atom clusters by coalescence of 1-7 atoms using molecular dynamics simulations. A range of initial orientations and initial kinetic energy was tested. Trimer formation is very sensitive to both. The Ostwald-ripening coalescence mechanism yielded 8-atom clusters to a much higher energy than a diffusion-based model. An atom-to-bond collision will also lead to cluster formation at higher initial energies than an atom-to-atom or atom-to-face center collision. Acknowledgment. We acknowledge the Donors of the American Chemical Society Petroleum Research Fund for the support of this research under Grant No. ACS PRF 41572-G5. References and Notes

Figure 7. Potential energy, V (eV), versus time, t (fs), for the coalescence of three Ir7 + Ir1 systems. (a) Ti(t ) 0) ) 0.9 eV results in Ir8. (b) Ti(t ) 0) ) 5.3 eV results in Ir6 + Ir2. (c) Ti(t ) 0) ) 6.1 eV results in Ir5 + Ir3. All cases are an atom-to-bond impact, as shown in Figure 6a.

gas has been shown to be an effective method of thermally stabilizing metal clusters in MD simulations by Lummen and Kraska.51,52 The results of Ir4 + Ir4 and Ir7 + Ir1 indicate that the growth of clusters will be dominated by the Ostwald-ripening mechanism. Clusters begin to dissociate at Ti(t ) 0) ) 1.3 eV for the planar interaction of Ir4 + Ir4, and at Ti(t ) 0) ) 1.8 eV for the parallel configuration. For the Ostwald-ripening model, an 8-atom cluster is formed with initial energy as high as Ti(t ) 0) ) 4.4 or 4.6 eV, when the impact occurs at a side or top bond, respectively. The interaction of these clusters with a substrate will play a large role in the overall mechanism of cluster formation, and work in this area is forthcoming. We expect, however, that the substrate will enhance the Ostwaldripening growth mechanism. The 4-atom structure will more strongly adhere to the surface compared with a single atom, making diffusion difficult. The growth mechanism of clusters is also dependent on the probability of cluster collision. Our future study of the substrate effect will address this aspect of cluster growth as well.

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