Atomic self-diffusion behaviors relevant to 2D homoepitaxy growth on stepped Pd(001) surface

Surface Science 624 (2014) 89–94

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Atomic self-diffusion behaviors relevant to 2D homoepitaxy growth on stepped Pd(001) surface Fusheng Liu a, Wangyu Hu b,⁎, Yifeng Chen a,⁎⁎, Huiqiu Deng b, Han Chen a, Xiyuan Yang c, Wenhua Luo d a

College of Metallurgical Engineering, Hunan University of Technology, Zhuzhou 412007, People's Republic of China Department of Applied Physics, Hunan University, Changsha 410082, People's Republic of China Department of Physics, Hunan University of Arts and Science, Changde 415000, People's Republic of China d Department of Physics and Electronic Information Science, Hunan Institute of Science and Technology, Yueyang 414006, People's Republic of China b c

a r t i c l e

i n f o

Article history: Received 17 July 2013 Accepted 15 January 2014 Available online 5 February 2014 Keywords: Adatom Diffusion Molecular dynamics Ehrlich–Schwoebel barrier Film growth

a b s t r a c t Using molecular dynamics, nudged elastic band and modified analytic embedded atom methods, the diffusion behaviors of Pd adatom on stepped Pd(001) surface have been investigated. Lower than 975 K, Pd adatom just hops along the perfect [110]-direction step. The diffusion dynamics equation is derived from the Arrhenius law between 875 and 975 K, and the corresponding migration energy and prefactor are 0.76 eV and 5.2 × 10−2 cm2/s respectively, which shows that they adhere to the step in case of adatom moving to the step. The adatom diffuses across the perfect step with an Ehrlich–Schwoebel barrier of 0.09 eV by exchange mechanism. Our calculations show the kink at step can markedly decrease the static energy barrier across the step with a negative Ehrlich–Schwoebel barrier, and it contributes to form layer-by-layer growth model in the epitaxial experiment. Our calculations show that the kink can also markedly improve the adatom's mass transport of interlayer, contributing to the formation of the compact film. Lastly, a quantitative result at 300 K shows that the kink affects tremendously the diffusion mobility of adatom near it, which indicates that the kink plays a key role in the formation of the compact and uniform film on Pd(001) surface in an epitaxial growth experiment. © 2014 Elsevier B.V. All rights reserved.

1. Introduction One of the challenges in recent studies of nanomaterials is the understanding of microscopic processes which control thin film growth, and this is not only a necessary task if we are to build materials of choice by design, but it is also a daunting task [1]. Atomic level processes in thin film growth involve complicated diffusion dynamics behaviors giving rise to an abundant variety of surface morphologies. In this wide field, the study of growth in the submonolayer regime is most worth paying attention due to the large impact of the initial dynamics on the resulting film structure. In an epitaxial growth experiment if atoms or molecules are deposited on a surface at a constant deposition rate, then they diffuse on various structural surfaces to meet other adspecies, resulting in nucleation of aggregates or attachment to already existing islands [2,3]. According to the Terrace Step Kink (TSK) model, the film surface consists of the terrace, step, kink, and so on. The atomic dynamics diffusion behaviors at the terrace, step and kink are a key for atom mass transport on the surface. If surface diffusion on terrace is not sufficient, it is impossible to gain the compact film. Moreover the diffusion dynamics behaviors of adatoms across a step play a crucial role in the crystal

⁎ Corresponding author. Tel./fax: +86 731 88823970. ⁎⁎ Corresponding author. Tel./fax: +86 731 22183466. E-mail addresses: [email protected] (W. Hu), [email protected] (Y. Chen). 0039-6028/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.susc.2014.01.011

growth modes. If adatoms descend easily from an upper terrace to a low terrace, the growth mode is likely layer-by-layer. If having the positive Ehrlich–Schwoebel (ES) barrier [4,5], adatoms cannot easily descend from an upper terrace to a low terrace, and the growth is likely to proceed with formations of 3D model. On the other hand, the shape of the growing two-dimensional islands depends on how fast is the mobility of adatom along steps [6–8]. For atomic diffusion relevant to nucleation and early stage of thin film growth, a great many experiments based on field ion microscope (FIM), scanning tunneling microscope (STM), low energy electron microscopy (LEEM) and quasi-elastic helium atom scattering have been devoted to the determination of surface diffusion coefficients [9]. By using FIM, the dynamics behaviors of adatom or clusters can directly be derived from the Arrhenius law according to the diffusion coefficient as a function of temperature. However, it only can measure some highlighting or hard materials, such as Re, W, Pt, Ir, and so on. STM measures indirectly the dynamics behaviors of adatoms based on the nucleation theory, although it is much more successful in looking at soft materials for example Cu and semiconductors than FIM. In other measurement techniques, such as helium atom scattering, work function determination can also measure the dynamics diffusion behaviors of adatoms. However, these experimental methods which may have the atomic spacial resolution find it very difficult to gain the detailed diffusion processes in transition state because of the very low time resolution (no more than 103 Hz).

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Multi-scale modeling which has become popular these days remains as yet a challenge. Nonetheless, the field is advancing fast. Based on macroscopic continuum mechanics the films are treated as elastic solids [10]. Models based on mean field theory and rate equations [11] make more explicit reference to microscopic processes through scaling laws. Not just as a useful complement, the theoretical calculation even can obtain some results which the experiment methods cannot arrive at. For example, the first principles can calculate the static diffusion barriers on complex surface, even under the stress field [12–14]. Molecular dynamic (MD) simulation not only traces the dynamical trajectories of adatom and clusters on various complex surfaces, but also gives the available diffusion mechanisms directly, especially for more complicated diffusion processes, such as detailed steps during the nucleation [6,8,15,16]. In atomic level, kinetic Monte Carlo (KMC) simulations have been used successfully to study qualitative, even quantitative behavior of growth in limited cases in long time scale [17,18], whose rates are ideally obtained from first principles and MD calculations [19,20]. Although a lot of experimental and theoretical results are now available on the dynamic diffusion behaviors of adatom and clusters on perfect surfaces, rather little is known about the dynamic behaviors of adatom nearby the step. Based on the TSK model, the diffusion behaviors of adatom nearby the step play a key role for the surface morphologies of film in epitaxial growth experiment. Palladium (Pd) is a rare metal, which has wide application in catalysis and hydrogen storage [21–23]. However, there is a considerable lack of studies about nucleation and growth mechanism that controlled the surface morphology which significantly affects the catalytic capability itself [24–26]. In this series of papers, the atomic self-diffusion dynamics behaviors relevant to nucleation and growth mechanism on perfect Pd(001) and Pd(111) surfaces had been studied [27,28], and the corresponding diffusion mechanisms had been discussed. In this study, we investigate atomic self-diffusion behaviors relevant to 2D homoepitaxy growth on the stepped Pd(001) surface with the combination of MD method, nudged elastic band (NEB) method and a modified analytic embedded atom method (MAEAM) developed from the analytic embedded atom method by Hu [29]. Finally, we analyze quantificationally the impact of the step and kink on Pd(001) surface in an epitaxial growth experiment at T = 300 K. 2. Computational methodology In this paper, the interactions among Pd atoms are described by the MAEAM potentials. The corresponding details and parameters can be found in Refs. [29–31], and MAEAM potentials have been successfully applied in the calculations of nanoparticles and bulk materials [29,32–35]. Recently our researches [32,36,37] have indicated clearly that the MAEAM combined with the MD simulations is a powerful tool for studying the phenomenon of the self-diffusion on the metal surface. Using identical Pd MAEAM potential parameters and MD simulations, the migration energy (Em = 0.62 eV) of the single Pd adatom on Pd(001) surface has been deduced from the Arrhenius law in the range from 600 to 900 K [27], which is in good agreement with the experimental result (Em = 0.60 eV) [38], and the diffusion dynamics behaviors about 2D clusters on Pd(111) surface, the surface energy and the vacancy migration energy [28] are in good agreement with other theoretical data [39–41]. These results indicate that Pd MAEAM potential parameters can provide a reasonable description of surface dynamics properties. Our systems which are shown in Fig. 1 are the Pd(001) slabs with enough thickness in the z direction, normal to the surface. On the surface plane, where periodic boundary conditions have been applied, the size of the slab is 12 rows and 16 columns, as illustrated in Fig. 1(a). The top layer of slab consists of a smaller terrace of 8 columns, delimiting a step along [110] direction on Pd(001) surface, as shown in Fig. 1(b). And then, half of the atoms in the rightmost atomic column are removed on the top layer, forming a typical kink, as illustrated in

Fig. 1(c). The slabs used here are large enough so that the finite size effects, which have been tested, can be ignored in the present cases. The six-value Gear predictor–corrector algorithm and the Nosé constanttemperature technique are employed during the MD simulations. For diffusion dynamics behavior of Pd adatom along compact [110] direction, an adatom is placed on the step of the slab first, under the conditions of constant temperature and constant volume (NVT ensemble), and then the MD simulation at desired temperature is done. The classical equations of motion are solved by the standard Verlet algorithm with a time step of 2 fs. Data are recorded after a thermalization of 10,000 steps, which are enough to achieve equilibration. After that the simulation is performed for a considerable number of steps, of the order of 107, in order to accumulate reliable statistical data. In the present work, the static energy barriers (Es) of atomic diffusion are calculated by using quenched MD and the NEB method [42,43]. At 0 K, quenched MD consists of canceling the velocity of a particle whenever its product with the force acting on the particles is negative. The NEB method allows one to find the minimum energy path for a rearrangement of a group of atoms from a given initial position to a given final position and to estimate the static energy barriers of a diffusion process. The initial and final states are determined from quenched MD simulation. Ea is defined as Ea = Esad − Emin, where Esad and Emin are the total system energy with the adatom or dimer at the saddle point and at the initial or final site, respectively.

3. Results 3.1. Self-diffusion dynamic behavior along the [110]-direction step When a Pd adatom is placed at the step of slab, the adatom vibrates in fourfold equilibrium site because of the thermal fluctuations. Movement of the adatom away from the step at the low temperature range is very difficult because it requires breaking more bonding with surrounding atoms. Essentially, this is a process where a two-dimensional cluster containing (N + 1) atoms dissociates a cluster containing N atoms and a dissociated adatom, and the adatom needs to overcome binding coming from the cluster except for spanning the surface saddle, which requires much higher energy. If an adatom always diffuses along the [110]-direction step in a certain temperature range, the selfdiffusion dynamics behavior can be derived from the Einstein equation and Arrhenius law. A Pd adatom is placed at the step of slab as shown in Fig. 1(b). MD simulations are performed in the temperature range from 875 to 975 K with the interval of 25 K, and the simulation time varied from 20 to 30 ns according to the simulation temperature. The lower end of the range corresponds to the limit for appropriate diffusion mobility by way of economizing computation time, while the upper end of the onset of the surface disordering, such as the disordering of step atoms, spontaneous creation of adatom-vacancy of step atoms, adatom away from the step, and so on. The detailed analysis of the trajectories shows that Pd adatom diffuses along the [110]-direction by bridge hopping mechanism in the temperature range from 875 to 975 K, in contrast to the simple exchange mechanism with the substrate atoms on Pd(001) terrace [27,44–46]. With simulation temperature increasing, when T = 1000 K, a little diffusion events away from the [110]-direction step appear by exchange mechanism with substrate atoms, and the exchange direction is along the [001]-direction. The diffusion dynamics equation between 875 and 975 K is shown in Fig. 2; the corresponding prefactor and migration energy are 5.2 × 10−2 cm2/s and 0.76 eV. Compared with the adatom's prefactor (D0 = 6.2–8.7 × 10−1 cm2/s) and migration energy (Em = 0.63 eV) on Pd(001) terrace, not only is the migration energy along the [110]-direction step more than 0.13 eV, but also is the prefactor lower than 1 order of magnitude. Therefore, the adatom diffusion is more difficult along the step than on Pd(001) terrace at the same temperature. In other words, once a Pd adatom

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a) Terrace

b) Step

c) Kink

Fig. 1. Top view of the hard-sphere model of Pd (001) surface.

adheres at the step of 2D cluster on Pd(001) surface, this is a process that the cluster coarsens and grows.

3.2. Atomic self-diffusion behaviors across the [110]-direction step To explore the most probable diffusion path of the adatom across the [110]-direction step on Pd(100) surface, a Pd adatom is placed in fourfold site on the upper terrace near step, and several MD simulations are performed in NVT ensemble in the temperature range from 750 to

Fig. 2. Arrhenius plots of the diffusion coefficients of Pd adatom along the [110]-direction step on Pd(001) surface. The solid lines are Arrhenius fits to the molecular dynamics data.

1000 K, then the diffusion trajectories of adatom have been tracked. The analysis of trajectories shows that Pd adatom diffuses across the step by the combination mechanism of exchange and hopping. When Pd adatom A in fourfold equilibrium site gains enough internal energy, it interacts with the substrate atoms causing the neighboring substrate atoms to relax out from their normal lattice sites. Adatom A gradually enters into the outermost layer, and forces out substrate atom B moving toward the saddle point, as shown in Fig. 3(a). When atom B arrives at the saddle point, atoms A and B form a transitional dumbbell dimer, as shown in Fig. 3(b). Finally, adatom A entirely enters into the outermost layer of the upper terrace, and atom B jumps to a new fourfold equilibrium site on the low terrace along the [001]-direction, as shown in Fig. 3(c). According to the diffusion path, using quenched MD method and the minimum energy path (MEP) in NEB method, we have obtained that the static energy is 0.74 eV from Fig. 3(a) to (c). Compared with the static energy 0.65 eV in terrace by NEB method, the ES barrier is 0.09 eV. In reverse, the static energy is 1.14 eV from Fig. 3(c) to (a), which shows that Pd adatom located on step is more stable than that on terrace because of more bonding with substrate atoms. For the self-diffusion of the Pd dimer across the step, several MD simulations are also performed in the temperature range from 750 to 1100 K. MD trajectories' analysis shows atoms of the dimer exchange with substrate atoms by the atom-by-atom pattern from the upper terrace to the low terrace, as shown in Fig. 4. In Fig. 4(a), the dimer containing atoms A and B occupies fourfold equilibrium sites on the upper terrace near the step. From Fig. 4(a) to (b), atom A of the dimer enters into the outermost layer on the upper terrace, and forces out substrate atom 1 jumping to a new fourfold equilibrium site on the low terrace, forming a loose dimer (containing atom B and atom 1). Then, atom B enters into the outermost layer, and atom 2 merges and jumps to a new equilibrium site on the low terrace, forming a new dimer at the step, as shown in Fig. 4(c). Using quenched MD and NEB methods, we have

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Fig. 3. Schematic of the most possible diffusion path of Pd adatom across compact step on Pd(001) surface. Circle balls represent atoms of top terrace.

obtained that the static energy barrier Ea = 0.88 eV from Fig. 4(a) to (b), and the lower barrier Ea = 0.61 eV from Fig. 4(b) to (c) because of the existence of the kink (atom 1). The static energy barrier of the Pd dimer has also been calculated on Pd(001) terrace by the atom-byatom exchange mechanism, and Ea = 0.59 eV. The ES barrier of the dimer is 0.29 eV across the step. In addition, we have also calculated the static energy barrier of the dimer by concert exchange mechanism

with substrate atoms, as shown in Fig. 4(a) to (c) directly, and the corresponding Ea = 1.23 eV. Compared with the atom-by-atom pattern, the probability of diffusion events may almost ignore by concert exchange mechanism in the low temperature range. Our results are in agreement with other theoretical studies [47–49] which show that the clusters diffuse across the step from the upper terrace to the low terrace by the atom-by-atom pattern.

Fig. 4. Schematic of the diffusion mechanism of Pd dimer across compact step on Pd(001) surface. Circle balls represent atoms of top terrace.

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3.3. Self-diffusion behaviors of the adatom near the kink at the step In fact, there are plenty of kinks in a real surface, which occupy a very important position in TSK model. Differing from 2D terrace and 1D step, structurally the kink is zero dimension. So the diffusion behavior of adatom nearby a kink may be different from that on 2D terrace or along 1D step. To simplify our simulation, the slab containing only one kink has been build, so the interaction among kinks along the step is not considered, as shown in Fig. 1(c). Four typical diffusion paths are shown in Fig. 5, and the corresponding static energy barriers have been calculated using the quenched MD and NEB methods. Specific paths are as follows: a) a Pd adatom diffuses from site E to site C by hopping mechanism, abbreviated as EC path; b) a Pd adatom located in the site B enters into the site of atom 2 with exchange mechanism, and atom 2 jumps to the site C, abbreviated as B2C path, and others analogizing; c) A1C path; and d) A1D path. Corresponding to these diffusion paths, the system energy curves as a function of the reaction coordinate are shown in Fig. 6. Reaction coordinates 0.0 and 1.0 correspond to the initial and final configurations of the diffusion process, respectively. As shown, several results stand out from the present simulation. As can be seen from Fig. 6, along A1D path, the static energy barrier is 1.0 eV which is the highest value because the adatom not only overcomes the saddle barrier, but also adds bonding energy coming from the kink. In the point of view of energy, the diffusion is impossible to happen by along A1D path. Through EC path, the static energy barrier (0.47 eV) is lower than that (0.72 eV) along the step, and the reason lies on atom 1 near the kink that can attract adatom located in site E, decreasing the total energy of system, and forming a more stable cluster. For A1C and B2C diffusion paths, as shown in Fig. 5, a Pd adatom located in site A or B exchanges with a substrate atom near the kink first, Pd adatom enters into the substrate, and a substrate atom (later forming a new adatom) emerges, moves to saddle site, and finally arrives in site C; the corresponding static energy barriers are 0.70 and 0.64 eV respectively. For the difference of barrier in A1C and B2C diffusion paths, we can explain it qualitatively in the view of bonding with the second neighbor atoms located on the upper terrace. From Fig. 6, one can find that the first parts of the energy curves about A1C and B2C diffusion paths are almost same before the new adatom moves to the saddle site. It is because adatom breaks the same number of bonds in this diffusion process. When adatom moves to the saddle point, both new adatoms have the three nearest-neighbor atoms (two substrate atoms beside the saddle point and an original adatom) in A1C and B2C paths. For A1C path, there are only two the second-neighbor atoms (atoms 2 and 3) at the saddle point. However, for B2C path, there are three second-neighbor atoms (atoms 1, 3 and 4), so the adatom only requires less energy to break less bonds in this diffusion process. Along A1C diffusion path, the ES barrier is 0.05 eV; along B2C diffusion path, the ES barrier is −0.01 eV numerically, generally as zero. Compared with the ES barrier (0.09 eV) across the step, the kink can decrease the ES barrier,

Fig. 5. Schematic of the diffusion paths of Pd adatom across compact step near a kink on Pd(001) surface. Circle balls represent atoms of top terrace.

Fig. 6. The system energy as a function of reaction coordinates corresponding to the diffusion path shown in Fig. 5. The reaction coordinates have been normalized by the distance between the initial and final configurations.

which is in good agreement with the other theoretical calculations [50–52]. 4. Discussion Based on our calculated results, further we discuss the homoepitaxial growth of film on Pd(001) surface. The self-diffusion parameters such as the migration energy, prefactor and static energy barrier about adatom and dimer at various surface structures are listed in Table 1. If Pd adatom diffuses by exchange mechanism with substrate atom, we suppose that the diffusion prefactor equals that of adatom on Pd(001) terrace, which has a certain rationality. For the prefactor of the adatom diffusing to the kink along the [110]-direction step, we suppose that it is equal to that of the adatom along the [110]-direction step. For the prefactor of the dimer diffusing across the step, we suppose that it is equal to that of the dimer on Pd(001) terrace. From the data in Table 1 and the Arrhenius law, we can simply assess the atomic mobility about various diffusion processes and the corresponding characteristic temperature (TD) which an adatom or cluster moves one nearest-neighbor distance per second [53,54], as listed in Table 2. As shown in Table 2, TD of Pd adatom along the step is the highest in all of the diffusion paths, which arrives at 268 K. Because the ES barrier exists, TD across the step is higher about 30 K than that on Pd(001) terrace, which indicates that the adatom diffusion is more difficult across the step than on terrace. If there is a kink in the step, and the corresponding TD decreases dramatically (see B2C and A1C diffusion paths), which states that the kink can increase the mobility of Pd adatom markedly. For interlayer diffusion of adatom along the step to the kink (EC path), TD is only 165 K far lower than that on Pd(001) terrace. Therefore, the kink plays a key role on the diffusion of adatom on Pd(001) surface. To understand deeply the diffusion mobility (Dr) about all the diffusion processes, we calculate quantificationally the diffusion mobility under the different diffusion paths when the substrate temperature T = 300 K, which is just in the epitaxial temperature range. For comparison, we suppose that the relative amount of Dr which the adatom diffuses across the perfect step is 1. From Table 2, we can see that the diffusion mobility of adatom along the perfect step is lower by about 1600 times than that on the terrace. So once the adatom diffuses to the step, it will adhere the step, forming a new kink, which greatly enhances the diffusion mobility of Pd adatom across the step, and the corresponding diffusion mobility increases from ten to hundreds of times according to the different diffusion paths. The kink can markedly decrease the additional ES barrier, even to a negative ES barrier, and the adatom descends easily from the upper terrace to a low terrace, and the growth mode is likely layer-by-

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Table 1 Self-diffusion parameters of adatom and dimer on Pd(001) surface. Type

Diffusion path

Static energy barrier and migration energy (eV)

Prefactor (cm2/s)

ES (eV)

Pd1

On terrace Across step B2C path A1C path Along step Along EC path On terrace Across step

Es Es Es Es Es Es Es Es

(6.2–8.7) × 10−1 – – – 5.2 × 10−2 – (1.1–1.9) × 10−1 –

– 0.09 0 0.05 – – – 0.29

Pd2

= = = = = = = =

0.65, Em = 0.63 ± 0.02 0.74 0.64 0.70 0.7, Em = 0.76 0.47 0.59, Em = 0.58 ± 0.02 0.88

layer. From Table 2, through EC path, we can also see that the adatom diffuses more quickly about 2 orders of magnitude than that on terrace. Such quick diffusion mobility of adatom in interlayer can form the compact film in low temperature range. In short, based on Pd(001) surface, plenty of kinks in all kinds of steps contribute to the formation of the compact and uniform film in epitaxial growth experiment. 5. Conclusion In this paper, we have studied the diffusion behaviors of Pd adatom on stepped Pd(001) surface by MD method with the combination of NEB method and a MAEAM potential. MD simulations show that Pd adatom only diffuses along the [110]-direction step by hopping mechanism in the low temperature range. The migration energy (0.76 eV) and prefactor (5.2 × 10−2 cm2/s) are derived from the Arrhenius law, which show that they adhere to the step if adatom once moves to the step. The static energy barrier of the adatom is 0.74 eV across the perfect step, and the corresponding ES barrier is 0.09 eV. If a kink exists at the step, the static energy barrier of the adatom near the kink across the step decreases markedly. So the kink at the step contributes to form layerby-layer growth model in homoepitaxial experiment, and it can also markedly increase the mass transport of the adatom in interlayer, contributing to the formation of the compact film. The diffusion mobility about some typical processes on the stepped Pd(001) surface at T = 300 K shows that plenty of kinks at step contribute to the formation of the compact and uniform film in homoepitaxial growth experiment. Acknowledgments This work is financially supported by the Hunan Provincial Natural Science Foundation of China (No. 13JJ3108) and the NSFC (No. 51274094 and No. 51271075) as well as by the Natural Science Foundation of Hunan University of Technology (No. 2011HZX22). We would also like to acknowledge a grant of computer time from the National Super Computer Center of Changsha.

Table 2 The characteristic temperature (TD) and relative diffusion mobility (Dr) of adatom and dimer on Pd(001) surface at 300 K. It supposed that the relative amount of Dr is 1 for the adatom across the step. Type

Diffusion path

TD (K)

Dr

Adatom

On terrace Across step B2C path A1C path Along step Along EC path On terrace Across step

205 233 201 220 268 165 190 287

32.5 1 47.9 4.7 0.02 5515.5 142.8 0.001

Dimer

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