Molecular dynamics simulation of deposition of nickel nanocluster on copper surface

Transcription

1 J Nanopart Res (2011) 13: DOI /s RESEARCH PAPER Molecular dynamics simulation of deposition of nickel nanocluster on copper surface Lingqi Yang Yuwen Zhang J. K. Chen Received: 15 September 2010 / Accepted: 26 April 2011 / Published online: 11 May 2011 Ó Springer Science+Business Media B.V Abstract The burrowing of nickel nanocluster deposited onto the copper surface is investigated by molecular dynamics (MD) simulation. The simulation is carried out at different temperatures for 40.1 ns with three different lattice orientations Cu(100), Cu(110), and Cu(111) that have , , and lattice units, respectively. The Ni(100) nanocluster consists of 249 atoms (five lattices diameter) and the initial kinetic energy is assigned to be 0 ev. The results show that the burrowing process goes extremely slow as temperature is at or under 900 K. There is virtually no burrowing observed when the system temperature is below 500 K. The burrowing processes at different temperatures are discussed in terms of kinetic energy of the cluster exerted by the strong capillary force. It is found that the kinetic energy will play a key role in the acceleration of the burrowing process. Keywords Molecular dynamics Nanocluster Burrowing Modeling and simulation List of symbols E i Potential energy of atom i (J) F a Embedding energy required to place atom of type a (J) L. Yang Y. Zhang (&) J. K. Chen Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA zhangyu@missouri.edu H Length of a unit fcc structure of gold (Å) M Total mass of atoms (kg) MSD Mean square displacement (Å 2 ) N Number of total atoms r i Coordinate of atom i (Å) r ij Distance from atom i to atom j (Å) t Time (ps) Y cm Y coordinate of the centroid of nanoparticle pair (Å) Greek symbols / ij Pair-wise potential interaction (J) q j Contribution to the electron charge density from atom j to atom i Subscripts cm Center-of-mass i Atom i j Atom j Introduction There are numerous applications in nanosintering, which uses the laser beam to fuse the nanoparticle into a desired three-dimensional object (Pan et al. 2008). Variety of structure behaviors after the deposition of nanoclusters onto a thin film, which is also referred to as burrowing, can be observed. One of the most important mechanisms during the burrowing process has been demonstrated as the

2 4480 J Nanopart Res (2011) 13: site-exchange process between atoms in the nanocluster and the substrate (Nouvertné et al. 1999; Stepanyuk et al. 2000; Tafen and Lewis 2008). Surface alloys can be formed as a result even for metals immiscible in bulk form. Cluster as a whole buried under the substrate as the burrowing takes sufficient time is found in several reports. For example, Ag atom and clusters can be embedded completely into Pd(100, 111) substrates (Nacer et al. 1997), Co nanoclusters can burrow into Au(111), Cu(001), and Ag(001) substrates (Zimmermann et al. 1999; Padovani et al. 1999; Frantz et al. 2003) and so as the Ni nanoclusters on Au(001, 110, 111) substrate (Tafen and Lewis 2008). Due to the extraordinary property exhibited, Co and Ni have become very promising coating materials in the industry. Padovani et al. (1999) experimentally studied the burrowing of Co clusters into Au(111) substrate at a temperature of 450 K. The clusters remain globally undisturbed until the temperature over 600 K when irreversible cluster fragmentation and dissolution occur. Several researchers have investigated the deposition of Co on Cu surfaces in different ways (Nouvertné et al. 1999; Zimmermann et al. 1999; Frantz and Nordlund 2003; Zimmermann et al. 2001). An experiment carried out by Yeadon et al. (1997) demonstrated that particles reorientation proceeds by a mechanism involving classical neck growth by surface diffusion, followed by migration of the grain boundary through the particle during the sintering of copper nanoparticles on Cu(001) surface. Zimmermann et al. (1999, 2001) provided the experimental evidence that the deposition of Co clusters on Cu(001) and Ag(001) substrates fails to show either burrowing or reorientation at room temperature. At temperature of 600 K, the burrowing, which can lead to surface smoothing along the cluster substrate interface, is a result of the strong capillary forces and surface tension associated with a nanoparticle. They also suggested that burrowing should occur where the surface energy of the nanoparticle is significantly higher than the substrate. Similar results are also reported by Stepanyuk et al. (2001) that larger capillary forces, vacancy mechanism during the deposition and lower energy of the total system after burrowing are recognized via molecular dynamics (MD) simulations. Another mechanism termed as disordered motion of atoms (Frantz and Nordlund 2003; Frantz et al. 2003) is observed beside the vacancy migration due to the burrowing of nonaligned clusters by applying MD method. Kolesnikov et al. (2009) applied kinetic Monte Carlo (KMC) and MD methods to investigate the evolution of Co nanostructure embedded into a Cu(100) surface at the atomic scale. The key role of substrate vacancies in the motion of embedding Co atoms is identified and self-organization of Co atoms is discussed in details in different conditions. Apart from this, Ni, which is widely used in thin film technology today, has also drawn plenty of attentions because of its unique magnetostrictive, electronic, thermal, and corrosion resistance properties (Tafen and Lewis 2008; Niwa et al. 2004; Mirabbaszadeh et al. 2008). Jiménez-Sáez et al. (2005) applied MD method to simulate the deposition of Ni clusters on Cu(001) surfaces by low energy cluster beam deposition (LECBD) technique. Results with 1 ev/atom of the bombardment energy were compared with systems in which the energy per atom was 0 ev. They conclude that kinetics effects play less important role when difference between lattice parameters of clusters and substrate are small. Instead of Ni cluster, the deposition for Ni thin film growth on Al substrates of various orientations associated with low adatom incident energy of 0.1 ev are also studied by MD simulation (Lee and Chung 2006a, b). Interfacial features are quantitatively investigated with different substrate temperatures and deposition rates which determine the growth behavior and structural characteristics in the interface region for the Al/Ni(001) system (Lee and Chung 2006a). The steering effect (Lee and Chung 2006b), which cause the remarkable rougher surface for Ni adatom on Al(111) compared to the cases of Al(001, 011), was observed especially with low incident energy. A large-scale MD simulation of energetic Ni nanoclusters impact onto Ni surfaces was performed by Mirabbaszadeh et al. (2008). The purpose of this simulation was to activate other kinds of lateral mass transport mechanism to complete the deposition by accelerating the incoming particles to high kinetic energies instead of heating some materials which, however, are not resistant of high temperature. Another surprising phenomenon came from the result of Tafen and Lewis (2008) that Ni could penetrate into Au surfaces, whereas Au nanoclusters do not burrow into Ni surfaces. They suggested that these results are attributed to the difference of exchange

3 J Nanopart Res (2011) 13: energy barriers and also adsorption energy for Ni atoms on Au surfaces and Au atoms on Ni surfaces. In this article, the depositions of Ni(100) nanocluster with 249 atoms on Cu(100) ( lattices), Cu(110) ( lattices), and Cu(111) ( ) surfaces at different temperatures are modeled using the MD method. The whole system will be studied with periodic boundary condition along the x y plane and free boundary condition along the z-coordinate. The effect from the lattice orientation of the substrate will be systematically investigated. In addition, the site-exchange mechanism will also be identified and discussed in details. Simulation procedure During the simulation procedure, LAMMPS, a parallel program explored by Sandia National Laboratories, is applied run MD simulations. Spherical Ni(100) nanoclusters and Cu(100, 110, 111) substrate were created with a initial face centered cubic (fcc) lattice structure. The Ni cluster has 249 atoms and 0 ev initial kinetic energy. The number of lattice units for different lattice structures are different: (1) the Cu(100) substrate has lattice units (24,800 atoms), (2) the Cu(110) substrate has lattice units (24,304 atoms), and (3) Cu(111) substrate has lattice (24,262 atoms). And the last two layers of the Cu atoms in the substrate are fixed to mimic the rigidity that would be introduced by the bulk of the substrate that is not explicitly modeled. The embedded atoms method (EAM) potential developed by Foiles et al. (1986) is employed to describe the interatomic interaction between metallic atoms: E i ¼ F i X N j6¼i! q j r ij þ 1 X N / 2 ij r ij ; ð1þ j6¼i where E i is the energy of atom i, r ij is the distance between atoms i and j, F i is the embedding energy function of the electron density, q j is the electron density at atom i contributed from atom j, and / ij is a short-range pair potential function. The nanoclusters and substrate were first prepared and relaxed at 0 K via molecular statics (MS) minimization separately. Then each of them was thermally equilibrated under NVT ensemble for 40 ps and NVE ensemble for another 40 ps at 300 K. In those ensembles, N denotes number of atoms, V is volume, T stands for temperature, and E means the total energy. In NVT ensemble, the volume and temperature will be constant, whereas in NVE ensemble, the volume and total energy will be constant. Periodic boundary condition along the x y plane and free boundary condition along the z-coordinate are applied. Empirically, if the temperature and potential energy are stable during the subsequent NVE ensemble stage just after the NVT ensemble stage, the system can be treated in the thermal equilibration status. Afterward, Ni naoncluster and Cu substrate are assembled to establish the initial MD simulation model as sketched in Fig. 1. The centroids of cluster and substrate have the same x and y coordinates and the gap distance between them along the z-coordinate is 3.5 Å. Throughout the simulations, the system temperature is computed and monitored every 25 and 10 steps under NVT and NVE ensembles, respectively. For NVT, temperature is relaxed every 25 steps to reach the desire value. For NVE, if the difference between the computed and desired temperatures is[1 K, the atomic velocities are rescaled such that the system temperature is reset to exactly the desired value. For all simulations, a times step of 2 fs is adopted and periodic boundary condition along x y plane and free boundary condition along z-coordinate are applied again. In addition, a heuristic method is used to monitor the deformation of local lattice structure during the simulations. This method differentiates the local crystal structure by the angles between the bonds, instead of the interatomic distance, and is stable under high temperature. The structures of bcc (body centered cubic), fcc, hcp (hexagonal close packed), and ico (icosahedra) are marked by the colors of green, yellow, red, and cyan, respectively. The blue color is used to present the unknown types of structure. Considering the lattice structure transformation, the change of color is dramatically around the interfacial area between Ni cluster and Cu substrates. Results and discussion Thermal equilibration Thermal equilibration is significant for MD simulation. In order to confirm that the system is well

4 4482 J Nanopart Res (2011) 13: lattices of Cu(100) 2 lattices of Cu(100) Fig. 1 Physical model 5 lattices of Ni(100) 3.5Å 20 lattices of Cu(100) Ni Lattice units: 3.52 Å Cu Lattice units: Å 20 lattices of Cu(100) balanced before the simulation starts, thermal equilibration for Ni cluster and Cu substrate, respectively, is compulsory. If the temperature and potential energy are stable after the NVT ensemble, the system will be treated as an equilibrated system. Figure 2 shows the potential energy and temperature history of Ni cluster and Cu(100) substrate in the thermal equilibration. Apparently, after 40 ps of NVT ensemble, the potential energy and temperature are stable for both Ni and Cu(100). Compared to Fig. 2a c, the concussion of temperature in Fig. 2d is a little severe due to the small amount number of atoms in Ni cluster. It is expected that the concussion of temperature will be attenuated as the size of Ni cluster increases. Cu(110) and Cu(111) also exhibit similar trend during the equilibration stage. Burrowing process snapshots and vector plots After the thermally equilibrating the system well, the simulation of burrowing process starts. Figure 3 shows the snapshots of the cross-sectional view from Fig. 2 Thermal equilibration of Ni(100) and Cu(100) with both NVE and NVT stages. a Potential energy of Cu(100), b temperature of Cu(100), c potential energy of Ni(100), and d temperature of Ni(100)

5 J Nanopart Res (2011) 13: Fig. 3 Sintering snapshots of Ni(100) and Cu(100) at 1,000 K. a t = 0 ns, T = 0K,b t = 0.1 ns, T = 1,000 K, c t = 14.5 ns, T = 1,000 K, and d t = ns, T = 1,000 K (a) (b) (c) (d) the center of Ni cluster along the x z plane at t = 0, 0.1, 14.5, and ns for the case of Cu(100) at 1,000 K. The yellow and blue colors stand for the substrate and cluster, respectively. The snapshot in Fig. 3a shows the system s structure after the MS minimization but before burrowing process starts. Figure 3b is at the end of the NVT ensemble stage which lasts 0.1 ns. It is clearly seen that the cluster moves toward and lays down on the Cu(100) surface. Several atoms are implanted into the substrate. At t = 14.5 ns (Fig. 3c), most of atoms penetrate into the substrate due to the atom-vacancy exchange (Kolesnikov et al. 2009) and atoms from the Cu(100) has wrapped the whole cluster. This wrapping phenomenon is mainly attributed to the surface diffusion. At t = ns, the Ni cluster has already been embedded completely into the Cu(100) substrate. In reality, compared with the cluster, the substrate barely rotates during the simulation. As a result, the burrowing process is sensitive to the initial crystallographic lattice direction. Therefore, the system of Ni cluster and Cu(110, 111) substrate is also considered and simulated. Results of snapshots are plotted in Fig. 4. It is seen that it takes longest time for Ni burrowed completely into the Cu(100) at 1,000 K. For Cu(111), it only takes about ns. For the system at 900 K, the burrowing process is relatively slow but it is expected to be complete if the simulation lasts long enough. For all groups during the simulation at temperature below 900 K, the burrowing processes are not complete. Most of Ni cluster still remains on the surface when temperature is 700 K. Simulation at 500 K of the system Ni(100) and Cu(100) is also carried out but burrowing barely takes place if temperature drops below 500 K. According to Zimmermann et al. (1999), Ni cluster with surface energy larger than Cu substrate is capable to lead the burrowing process but the strong capillary force added on the cluster is the core reason for pushing the Ni cluster burrowing into the Cu substrate. Zhang et al. (2004) provided the exact values of the surface energy of Ni and Cu with different lattice orientations which are provided in the

6 4484 J Nanopart Res (2011) 13: T = 700 K, t = 40.1 ns T = 700 K, t = 40.1 ns T = 700 K, t = 40.1 ns T = 900 K, t = 40.1 ns T = 900 K, t = 40.1 ns T = 900 K, t = 40.1 ns T = 1000 K, t = 24.58ns T = 1000 K, t = 22.5 ns T = 1000 K, t = ns Fig. 4 Sintering snapshots of Ni(100) and Cu(100, 110, 111) at 1,000, 900, and 700 K Table 1 Surface energies of Ni and Cu Lattice orientation Cu (10-7 J/cm 2 ) Ni (10-7 J/cm 2 ) (100) (110) (111) Table 1. Apparently, Ni(100) has a larger surface energy than Cu(100), Cu(110) and also Cu(111) which implies the capability of the occurrence of the burrowing process. In addition, Cu(111) has the lowest surface energy and Ni(100) has a largest surface energy which result in a largest different of surface energy between Ni(100) and Cu(111) compared with other two cases. This is perfectly matched by the fact that burrowing is faster with the system of Ni(100) and Cu(111) at 1,000 K. For the system temperature under 1,000 K, the effect of the surface energy is attenuated dramatically. It is interesting to notice that for system at 900 K, more atoms remain above the Cu(111) surface at the end of the simulation. And for system at 700 K, each group has a very similar status when the Ni cluster only wets the Cu substrate. Based on the work from Kim et al. (2008), the kinetic energy and local acceleration of the deposited atoms could be the explanation of such differences among groups at different temperatures. In order to illustrate this phenomenon, Fig. 5 is plotted to show the time evolution (0.1 ns) of the kinetic energy of group Ni(100) and Cu(100) at four different temperatures. The Ni cluster has 0 ev initial kinetic energy. Due to the large capillary forces added on the cluster, its kinetic energy increases

7 J Nanopart Res (2011) 13: Fig. 5 Kinetic energy of Ni(100) cluster on Cu(100) at 1,000, 900, and 700 K rapidly as the cluster approaching to the surface of the substrate. After it reaches to the maximum, it slightly decreases and then tends to be stable. The fact that the average magnitude of the kinetic energy of system at 1,000 K is larger than any other groups brings the fastest burrowing process. For systems at temperature below 900 K, the dramatic reduction of the kinetic energy is the main reason for the absence of the burrowing process. For the other two groups, Ni(100) and Cu(110), Ni(100) and Cu(111), their kinetic energies have a very similar performances. Figure 6 shows the snapshots with the same system at the same time as Fig. 3 but via tracking the change of lattice structure. Apparently, yellow and blue are two major colors which means the fcc lattice and some unknown lattice structures are dominant during the simulation. As the burrowing process goes on, more atoms of blue, green, and red colors appear in the whole system due to the continuous lattice structure deformation mainly caused by the interaction between Ni cluster and Cu(100) substrate especially at high temperature. In Fig. 6 Lattice deformation snapshots of Ni(100) and Cu(100) at 1,000 K. a t = 0 ns, T = 0 K, b t = 0.1 ns, T = 1,000 K, c t = 14.5 ns, T = 1,000 K, and d t = 24.1 ns, T = 1,000 K

8 4486 J Nanopart Res (2011) 13: T = 700 K, t = 40.1 ns T = 700 K, t = 40.1 ns T = 700 K, t = 40.1 ns T = 900 K, t = 40.1 ns T = 900 K, t = 40.1 ns T = 900 K, t = 40.1 ns T = 1000 K, t = 24.58ns T = 1000 K, t = 22.5 ns T = 1000 K, t = ns Fig. 7 Lattice deformation snapshots of Ni(100) and Cu(100, 110, 111) at 1,000, 900, and 700 K addition, the numerical results also indicate that there are slight evidences of the ico (cyan) lattice structures which barely can be recognized from the snapshots. Figure 7 shows the snapshots of the lattice deformation for groups at different temperature and lattice orientations. Compared the snapshots at same temperature but different lattice orientation, it is seen that for the system at 1,000 K, the deformation of lattice structure from Cu(111) is slightly intense than Cu(100). This phenomenon can be confirmed by the fact that the burrowing process of Cu(111) complete faster than the other two cases. On the contrary, for the system at 900 K, the lattice deformation is not as obvious as the other two cases which also coincides the fact presented in Fig. 4. Less lattice deformation is observed for the system at 700 K. In order to illustrate the qualitative features of burrowing, atoms movement vectors are plotted in Fig. 8 for the system of Ni cluster and Cu(100) substrate. The arrow heads of the vectors are the current positions of the atoms collected within the range of ðy cm H=2Þ to ðy cm þ H=2Þ and the tails are the positions from the last output data. Thus, the length of a vectors represent the distance that the atoms have moved in 4 ps for NVT and 160 ps for NVE. It is evident from Fig. 7a that the Ni cluster moves toward the substrate due to the strong attracting force from the substrate. As a result, almost half of atoms of the Cu(100) substrate also show a moving direction toward the Ni cluster. For the atoms far from the surface, the atoms vectors remain in chaos which could be explained by the weakened effect from the cluster. Figure 8b isa typical status during the burrowing process that part of the cluster has already been burrowed into the surface. The other part that still stands above the

9 J Nanopart Res (2011) 13: Fig. 8 Atoms movement vector plots of Ni(100) and Cu(100) at 1,000 K. a t = ns, T = 1,000 K, b t = 4.1 ns, T = 1,000 K, c t = 12.1 ns, T = 1,000 K, and d t = ns, T = 1,000 K surface is covered by the atoms from the Cu(100) according to the snapshots mentioned above which has shown a strong movement due to the surface diffusion. For the interface of Ni cluster and Cu(100) surface, the atoms vectors are not as obvious as the surface of the system because atoms from the cluster and substrate exchange randomly. For Fig. 8c, only a small part of the cluster stays above the surface. A small number of atoms vectors at surface exhibit a clear moving direction behavior which means the burrowing of the Ni cluster is almost complete. Few vectors direction of atoms at the surface can be recognized in Fig. 8d when burrowing is complete. The whole system appears in a very stable status compared with other three vector plots. Number of atoms implanted During the burrowing process, the vacancy migration will result in the implanted atoms of Ni cluster below the surface and sputtered Cu substrate above the surface. Therefore, the number of atoms implanted under the Cu surface is important to understand the atoms exchange between the cluster and substrate. The height of the substrate surface is obtained by calculating the average z-coordinate of the top layer of the substrate. Figure 9 shows three groups with same model but different temperatures and different lattice orientations. As mentioned in the snapshots, the Ni cluster can be completely burrowed into the Fig. 9 Number of Ni(100) atoms implanted under the Cu(100, 110, 111) surface at 1,000, 900, and 700 K Cu substrate at 1,000 K, which can also be demonstrated by the black lines in Fig. 9. There is a rapid growth within the initial period, then the burrowing becomes slower. Afterward, the whole Ni cluster is completely burrowed into the substrate and the number of atoms implanted remains stable around 249 which is exactly the number of the Ni cluster. Moreover, the plot also proves that the fulfillment of the burrowing process of the system Cu(111) at 1,000 K is earlier than other two cases. For the same system at 900 K, the burrowing process is relatively slow and not complete within the whole simulation time of 40.1 ns. However, the continuous growth of

10 4488 J Nanopart Res (2011) 13: the amount of exchanged atoms suggests that the burrowing could be complete if the duration of the simulation is longer enough. In addition, the fact that less atoms of the Ni cluster have been exchanged into the Cu(111) substrate also proves the interesting phenomenon observed from the snapshots Fig. 4, which can be explained by the attenuation of the effect from the surface energy due to the reduction of the kinetic energy. For the system at 700 K, the number of atoms implanted keeps almost the same after the initial growth for all cases. Under this circumstance, the Ni cluster simply wets the Cu substrate. For the system at 500 K, burrowing barely occurs and no obvious atoms exchange is observed. Mean square displacement Fig. 10 MSD of Ni(100) and Cu(100, 110, 111) at 1,000, 900, and 700 K The mean square displacement (MSD) is a measure of the average distance a molecule travels in the burrowing process: MSD ¼ 1 N X N i¼1 ½r i ðþ r t i ð0þš 2 ; ð2þ where N is the number of atoms sampled, t is time, and r is the position of each atom. Figure 10 shows the MSD for different lattice structure of copper and temperature. It is obvious that for the system at higher temperature, the movement of atoms is more intense. For the system of Ni(100) and Cu(111) at 1,000 K, the MSD is apparently much higher than the other two cases at the same temperature, which is also because of the larger difference of the surface energy between Ni(100) and Cu(111). For the system at 900 and 700 K, the differences between the MSD values at different temperatures are not very clear. When the temperature descends below 700 K, the movement of atom can be ignored. In order to capture the mechanism of surface diffusion of the substrate, surface MSD of all the atoms within or above the top layer (with one lattice thickness) of the substrate (see Fig. 11). The MSD at surface of the system at 1,000 K reaches to a stable value after about 25, 22, and 16 ns for Cu(100, 110, 111), respectively, which imply that the burrowing process completes and surface diffusion fades away. For the system at 900 and 700 K, the amplitude of the MSD of surface decreases dramatically. Unlike the MSD of the whole system, the MSD at surface at Fig. 11 MSD at surface of substrate of Ni(100) and Cu(100, 110, 111) at 1,000, 900, and 700 K 700 K still increases but considerably slow. This is because the stronger movement at the surface compared to the whole system which also indicates the existence of the intermixing of a very small amount of atoms between Ni cluster and Cu substrate. In addition, for the system at 1,000 K, the atoms movement is more intense which brings a larger concussion of the MSD of surface compared to other two groups. As temperature descends, the curve is smoother which suggests that the atoms movement is also attenuated. All groups from Cu(100, 110, 111) have a very similar behavior for MSD at surface. Conclusion The deposition of Ni cluster on Cu substrate is systematically studied by MD simulation. The

11 J Nanopart Res (2011) 13: numerical results show that the burrowing process is very sensitive to the initial lattice orientation and temperature. The effect from the lattice orientation is significant when temperature is very high. For the system at 1,000 K, the burrowing process is much faster than the other group, which is mostly because of the larger kinetic energy brought by the higher temperature. In addition, it is expected that the burrowing can be complete at 900 K if it takes sufficient time. For the system at temperature 700 K, the Ni cluster only wets the Cu substrate by exchanging few atoms with the substrate rather than penetrating into the substrate. For temperatures at or below 500 K, burrowing barely exists. Besides, vacancy migration mechanism is captured during the burrowing process and it is the surface diffusion that leads the strong atoms movement at the surface of the whole system. The number of atoms implanted below the Cu surface also confirms the burrowing process at different temperatures with different lattice orientations. The characteristic of MSD reveals that the atoms movement is extraordinarily strong for the system of Ni(100) and Cu(111) at 1,000 K. From the MSD at surface, the atoms movement at surface region is more intense than the bulk and the evidence of a small amount of atoms exchange at 700 K are also captured. Acknowledgments Support for this work by the U.S. National Science Foundation under Grant No. CBET is gratefully acknowledged. The authors thank the University of Missouri Bioinformatics Consortium (UMBC) for providing supercomputing time. References Foiles SM, Baskes MI, Daw MS (1986) Embedded-atommethod functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 33:7983 Frantz J, Nordlund K (2003) Mechanism of Co nanocluster burrowing on Cu(100). Phys Rev B 67: Frantz J, Nordlund K, Keinonen J (2003) Burrowing of cobalt nanoclusters in copper. Nucl Instrum Methods Phys Res B 206:66 70 Jiménez-Sáez JC, Pérez-Martín AMC, Said-Ettaoussi M, Jiménez-Rodríguez JJ (2005) Molecular dynamics simulation of Ni cluster deposition on Cu(001) surfaces. Nucl Instrum Methods Phys Res B 228:64 68 Kim S-P, Lee S-C, Lee K-R, Chung Y-C (2008) Asymmetric surface intermixing during thin-film growth in the Co Al system: role of local acceleration of the deposited atoms. Acta Mater 56: Kolesnikov SV, Klavsyuk AL, Saletsky AM (2009) Atomicscale self-organization of Co nanostructures embedded into Cu(100). Phys Rev B 79: Lee S-G, Chung Y-C (2006a) Atomic investigation of Al/ Ni(001) by molecular dynamics simulation. Jpn J Appl Phys 45: Lee S-G, Chung Y-C (2006b) Surface characteristics of epitaxially grown Ni layers on Al surfaces: molecular dynamics simulation. J Appl Phys 100: Mirabbaszadeh K, Zaminpayma E, Nayebi P, Saramad S (2008) Large-scale molecular dynamics simulations of energetic Ni nanocluster impact onto the surface. J Clust Sci 19: Nacer B, Massobrio C, Félix C (1997) Deposition of metallic clusters on a metallic surface at zero initial kinetic energy: evidence for implantation and site exchanges. Phys Rev B 56: Niwa D, Homma T, Osaka T (2004) Deposition mechanism of Ni on Si(100) surfaces in aqueous alkaline solution. J Phys Chem B 108: Nouvertné F, May U, Bamming M, Rampe A, Korte U, Güntherodt G, Pentcheva R, Scheffler M (1999) Atomic exchange processes and bimodal initial growth of Co/ Cu(001). Phys Rev B 60: Padovani S, Scheurer F, Bucher JP (1999) Burrowing selforganized cobalt clusters into a gold substrate. Europhys Lett 45: Pan H, Ko SH, Grigoropoulos CP (2008) The solid-state neck growth mechanisms in low energy laser sintering of gold nanoparticles: a molecular dynamics. J Heat Transf 130: Stepanyuk VS, Hergert W, Rennert P (2000) Co adatoms on Au(100): energetics of site exchange. Comput Mater Sci 17: Stepanyuk VS, Tsivline DV, Bazhanov DI, Hergert W, Katsnelson AA (2001) Burrowing of Co clusters on the Cu(001) surface: atomic-scale calculations. Phys Rev B 63: Tafen DN, Lewis LJ (2008) Structure and energetics of Ni and Au nanoclusters deposited on the (001), (110), and (111) surfaces of Au and Ni: a molecular dynamics study. Phys Rev B 77: Yeadon M, Yang JC, Averback RS, Bullard JW, Olynick DL, Gibson JM (1997) In situ observations of classical grain growth mechanisms during sintering of copper nanoparticles on (001) copper. Appl Phys Lett 71: Zhang J-M, Ma F, Xu K-W (2004) Calculation of the surface energy of fcc metals with modified embedded-atom method. Chin Phys 13: Zimmermann CG, Yeadon M, Nordlund K, Gibson JM, Averback RS (1999) Burrowing of Co nanoparticles on clean Cu and Ag surfaces. Phys Rev Lett 83: Zimmermann CG, Nordlund K, Yeadon M, Gibson JM, Averback RS, Herr U, Samwer K (2001) Burrowing of nanoparticles on clean metal substrates: surface smoothing on a nanoscale. Phys Rev B 64:085419