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Diffusions of small clusters on Pt(1 1 1) and Cu(1 1 1) surfaces
Applied Surface Science 254 (2008) 5822–5826
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Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Diffusions of small clusters on Pt(1 1 1) and Cu(1 1 1) surfaces Jianxing Jiang a, Peng Zhang a, Yiqun Xie a, Xijing Ning b, Min Zhuang c, Yufen Li a, Jun Zhuang a,* a State Key Lab for Advanced Photonic Materials and Devices, Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China b Institute of Modern Physics, Fudan University, Shanghai 200433, China c De´partement de Chimie, Universite´ de Montre´al, Case Postale 6128 Succursale Centre-ville, Montre´al, Que´bec H3C 3J7, Canada
A R T I C L E I N F O
A B S T R A C T
Article history: Received 30 June 2007 Accepted 16 March 2008 Available online 21 March 2008
Diffusions of small cluster Pt6 on Pt(1 1 1) surface and Cu6 on Cu(1 1 1) are studied by molecular dynamics simulation, respectively. The atomic interaction is modeled by the semiempirical potential. The results show that the diffusion processes in the two systems are far different. For example, on Pt(1 1 1) surface, the hopping of single atom and the shearing of two atoms of hexamer only occur on the adatom(s) adsorbed at B-step, while on Cu(1 1 1) surface they can appear on the adatom(s) either at Astep or B-step. To the concerted translation of the parallelogram hexamer, the anisotropy in the diffusion path is observed in the two systems, the mechanisms and then the preferential paths, however, are completely different. The reasons for these diffusion characteristics and differences are discussed. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Surface diffusion Clusters Metallic surfaces Molecular dynamics
1. Introduction The diffusion of single adatoms and small clusters on crystal surface is an important step in processes such as crystal growth, surface reconstruction, and thin-film formation, etc. In experiments, the tools for investigating surface diffusion include the field ion microscopy (FIM) [1,2] and scanning tunneling microscopy (STM) [3]. Based on the observation of FIM [4,5], interesting exchange mechanisms for the diffusion of Pt monomer, dimer, and trimer on Pt(0 0 1) surface are suggested. In theory, molecular dynamics (MD) simulation and molecular statics (MS) calculation are usually used for this task, and the calculations are sometimes based on the first-principle method [3,6,7]. Owing to the limitation of computing power, however, most studies, especially MD simulations, are often carried out on the semiempirical level [7– 11]. MD simulation is capable of giving the actual trajectories of the atoms, by which the unknown diffusion mechanisms or complicated diffusion processes could be revealed, for example, dislocation mechanism for diffusion of clusters on Ni(1 1 1) surface [10]. In our previous works, diffusion of single adatoms and structures of clusters on different metal surfaces were studied systematically with semiempirical potentials [11–14]. The results show that the case on Pt surface is far different from those on the others. For
* Corresponding author. E-mail address: [email protected] (J. Zhuang). 0169-4332/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2008.03.060
example, the diffusion of Pt monomer on Pt(0 0 1) surface is dominated by the exchange mechanism [11], and similar exchange process could also occur on Pt(1 1 1) surface [13], while on most other metal surfaces the dominant diffusion mechanism is hopping. As to the adatom clusters on Pt(1 1 1) surface, they usually have triangle-like structures instead of hexagon-like ones on the other metal surfaces [14]. These peculiar results motivate us to study the diffusion of small cluster further on Pt(1 1 1) surface. We consider the small cluster Pt6 in the present work. For comparison, the diffusion of Cu6 on Cu(1 1 1) surface is also investigated. 2. Calculation model The potential used in our simulation for platinum is obtained by the surface embedded-atom method (SEAM) which is developed from the conventional embedded-atom method (EAM) for the surface environment by Haftel and Rosen [15,16]. Based on this kind of potential, our previous works have revealed the exchange mechanism for the diffusion of Pt monomer and dimer on Pt(0 0 1) surface [11,12] and the triangle-like structures of Pt adatom clusters on Pt(1 1 1) surface [14], which are basically in accordance with the experiments [4,5,17]. In the present work, we still choose the SEAM potential for Pt system. For Cu system, Rosato– Guillope´–Legrand (RGL) potential is used, which is on the basis of the second-moment approximation to tight-binding model [18,19]. The substrate in our simulation is a (1 1 1) slab consisting of 30 layers,
J. Jiang et al. / Applied Surface Science 254 (2008) 5822–5826
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Table 1 The numbers of exchange, one-atom hopping, two-atom shearing and six-atom concerted translation processes for hexamer on Pt(1 1 1) and Cu(1 1 1) surfaces Surfaces (temperature)
Exchange
One-atom hopping
Shearing
Translation
Total
Pt (800 K) Cu (450 K)
57 (9.7%) 0
22 (3.7%) 88 (15.8%)
15 (2.5%) 163 (29.3%)
496 (84.1%) 306 (54.9%)
590 557
The total simulation time Ttot = 160 ns for Pt and Ttot = 12 ns for Cu. The numbers in the brackets are their percentages.
each layer contains 12 12 atoms, and periodic boundary conditions are imposed along the direction ½2¯ 1 1 and ½0 1¯ 1. The cluster is placed on each surface of the slab. Molecular dynamics (MD) simulation for cluster diffusion is accomplished by the standard Verlet algorithm with a proper time step to ensure the total energy fluctuation less than 1.0 104 [20]. 3. Results and discussion On Pt(1 1 1) surface, MD simulation is performed at temperature 800 K. The results show that the diffusion processes are diverse and sometimes complicated. Besides the processes such as the concerted translation, the shearing of two atoms, and oneatom hopping, the exchange is also observed in our MD simulation. The statistic results from the simulation at temperature 800 K are given in Table 1. The diffusion processes generally result in the change of the cluster structures. In Fig. 1, four kinds of structures that appear in the simulation are given. For simplification, we call them A-type triangle, parallelogram, B-type triangle, and the crescent. ‘‘A’’ and ‘‘B’’ indicate the step type of the triangle edge. As we know, there are two different types of steps on fcc(1 1 1) surface, the so-called A-step ({1 0 0} microfaceted step) and B-step ({1 1 1} microfaceted step). The structures given in Fig. 1 are all adsorbed at fcc site, at which our calculation shows that the energy of the cluster is far lower than that at hcp site. For example, the relative energy of the parallelogram at fcc site is 0.05 eV, while it is 0.50 eV at hcp site (also see Fig. 6 in the following). Therefore, as we observed in MD simulation, the cluster basically does not stay at hcp site. For cluster Pt7, similar result is obtained in the experiment [2], which shows that the compact hexagonal heptamer always occupies fcc sites after diffusion. In Fig. 1, the diffusion processes between the structures are indicated by (A)–(E). The process (C) between the two parallelo-
grams means the concerted translation, by which the cluster diffuses as a whole. The transformation between the parallelogram and the crescent is through the shearing process (D), in which the two atoms hop together. The shearing is commonly observed in the diffusion of the clusters [9,21,22]. The process (A) from the A-type triangle to the parallelogram in Fig. 1 is a little complicated, we give the details in Fig. 2, which includes two steps. First, from the A-type triangle (1) to the configuration (a) in Fig. 2, one corner atom ‘‘a’’ hops to the nearest fcc site along the edge. Then, after a while, it enters into the nearest neighbor row of the substrate (dark gray balls in Fig. 2) and seems to disappear on the surface. As a result, strain is induced in the surface row and makes the atoms around ‘‘a’’ unstable and compete each other. The competition could last a certain time, after that the strain will finally be released when one atom ‘‘b’’ is pushed out from the surface. This process is very similar to the exchange diffusion of single adatom based on the strain induced and relaxed mechanism known on Cu(0 0 1) and Ag(0 0 1) surfaces [12]. The process (B) from the parallelogram to the B-type triangle in Fig. 1 is basically the same as the process (A). As shown in Fig. 2, the corner atom ‘‘c’’ hops first, and then it enters into the substrate. After the competition, atom ‘‘d’’ is finally pushed out. Corresponding to the processes in Fig. 2, the static energies are calculated by the standard approach: Choose and change a certain freedom according to the reaction path, then at each fixed
Fig. 2. Details of the diffusion processes between the configurations (1) and (3), and between (3) and (5) in Fig. 1.
Fig. 1. Structures of hexamer (black balls) observed on Pt(1 1 1) surface. (A), (B), (C), and (D) indicate the different diffusion processes (see details in text).
Fig. 3. The energy curve for the diffusion processes in Fig. 2.
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J. Jiang et al. / Applied Surface Science 254 (2008) 5822–5826 Table 2 In the total translations 496 and 306 given in Table 2 the numbers of the translations along the three paths on Pt(1 1 1) and Cu(1 1 1) surfaces Surfaces (temperature)
Translation in path (1)
Translation in path (2)
Translation in path (3)
Total
Pt (800 K) Cu (450 K)
464 (93.5%) 2 (0.6%)
32 (6.5%) 41 (13.4%)
0 263 (86.0%)
496 306
Their percentages are also given in the brackets.
Fig. 4. The different surroundings of the adatoms ‘‘a’’ and ‘‘b’’ at A-step and B-step, respectively.
increment of this freedom fully relax all the other freedoms of the active atoms. The results are given in Fig. 3. Finally, our MD simulation shows that the transfer between the two crescents in Fig. 1, i.e., process (E), is also by the exchange process. From the processes described above, we can find two interesting phenomena. One is that the exchange always occurs on the adatom adsorbed at A-step. Another is that the hopping, including one-atom hopping and the two-atom shearing, always appears on the adatom(s) at B-step. The reasons can be seen clearly from the configurations in Fig. 4. In the exchange process, as we described above, the adatom should enter into the surface row first. Owing to the difference between the structures of A-step and B-step, we can see from Fig. 4 that atom ‘‘a’’ of the cluster at A-step could enter into the ‘‘c–d’’ surface row near it, while atom ‘‘b’’ has no way to enter into the ‘‘d–e’’ row. Therefore, as we observed in MD simulation, the exchange only appears at A-step. As to the hopping, the different type of the step will certainly also affect its occurrence frequency like that for the exchange. But, from the structural characteristics in Fig. 4, it is easy to see that such influence could not cause the hopping to occur only at B-step. In our calculations, we find that the structures of the clusters on Pt(1 1 1) surface contract obviously (also see details in Fig. 8 in the following). More specifically, the corner atom ‘‘a’’ at A-step, as an example, deviates far from the normal fcc adsorption site and is closer to the surface atoms ‘‘c’’ and ‘‘d’’ as shown in Fig. 4. It obviously makes the hopping of atom ‘‘a’’ along A-step difficult. To atom ‘‘b’’ at B-step, however, the case is different. The structure contraction makes it closer to the surface atom ‘‘e’’ instead of ‘‘f’’ and ‘‘g’’, which then has less influence on the occurrence of the hopping. As a result, the possibility of the hopping occurring at Bstep increases relative to that at A-step. And, if the structure contraction is serious, it is possible that the hopping only occurs at B-step. Therefore, on Pt(1 1 1) surface, the structure contraction is the main reason which causes the hopping to appear only at B-step. While, for the exchange process, the structural characteristics of the steps determine that it could only occur at A-step. Another phenomenon that attracts us is that the concerted translations of the parallelogram are almost always along certain
Fig. 5. The three paths for the concerted translation of the parallelogram hexamer.
path or direction. As shown in Fig. 5, between fcc site and hcp site, there are three paths for the parallelogram to move, for convenience, we denote them as ‘‘1’’, ‘‘2’’, and ‘‘3’’. From MD simulation, the numbers of the concerted translations in the three paths are given in Table 2, in which most of the translations are along path ‘‘1’’, only a few are along path ‘‘2’’, but none is observed along path ‘‘3’’. The static energy calculation gives the correspondence results as shown in Fig. 6a, the activation energy of the concerted translation in path ‘‘1’’ is the lowest (0.49 eV), while in path ‘‘3’’ it is the highest (1.27 eV). To explain this phenomenon, we compare the surface structures before and after the adsorption of the cluster. It is found that the deformation of the surface induced by the cluster is obvious. More specifically, a marked concavity is formed in the surface as shown in Fig. 7. When the parallelogram diffuses in path ‘‘3’’, as shown in Fig. 5, the two surface atoms under the cluster ‘‘a’’ and ‘‘b’’ will change to ‘‘d’’ and ‘‘e’’. In path ‘‘2’’, only one atom is changed, ‘‘a’’ and ‘‘b’’ to ‘‘b’’ and ‘‘c’’. When the parallelogram diffuses in path ‘‘1’’, however, the two surface atoms under the cluster remain unchanged. The results mean that the change of the surface deformation or concavity is largest when the parallelogram diffuses in path ‘‘3’’, while it is smallest in path ‘‘1’’. Or, in other words, the diffusion in path ‘‘3’’ demands that the
Fig. 6. The energy curves for the concerted translation of the parallelogram in the different paths ‘‘1’’, ‘‘2’’, and ‘‘3’’ shown in Fig. 5 on Pt(1 1 1) (a) and Cu(1 1 1) surfaces (b).
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Fig. 7. Deformation of the surface under the cluster of the parallelogram hexamer. On Pt(1 1 1) surface, a marked concavity is formed. Fig. 8. Contractions of hexamers on Pt(1 1 1) and Cu(1 1 1) surfaces.
parallelogram jumps out of the concavity completely. While, in path ‘‘1’’, the diffusion occurs approximately within the concavity. Therefore, the activation energy of the translation in path ‘‘1’’ is the smallest, and then almost all translations occur in this path as we observed in MD simulation. For the long-range diffusion, the parallelogram moving only in path ‘‘1’’ is not enough, which just results in the translation between the fcc and hcp sites. On Pt(1 1 1) surface, another diffusion path is ‘‘2’’. If the parallelogram translates alternately in ‘‘1’’ and ‘‘2’’ paths, the long-range diffusion can be realized. The interesting is that the particular translation paths ‘‘1’’ and ‘‘2’’ result in the long-range diffusion of the parallelogram only along the ‘‘a–b–c’’ atom row as shown in Fig. 5. Certainly, owing to the existence of the other diffusion mechanisms, the cluster can diffuse freely over the surface. In Fig. 1, we can see that besides the parallelogram translation (C), the processes (A), (B), and (D) also have contributions to the diffusion. From Figs. 3 and 6a, the activation energies of the processes (A), (B), (C), and (D) are (0.66; 0.86 eV), (0.82; 0.81 eV), (0.70; 0.70 eV) and (0.83; 0.77 eV), respectively, which are close to the result 0.89 0.04 eV obtained in experiment [2]. As we mentioned above, the single adatom diffusion and the structural characteristics of adatom clusters on Pt(1 1 1) surface are far different from those on the others. Therefore, for the diffusion of small cluster studied here, it is interesting to compare the results on Pt(1 1 1) surface with those on the others. As an example, we choose Cu(1 1 1) surface for comparison. MD simulation is done at temperature 450 K. The diffusion processes observed in the simulation and their numbers are also given in Table 1, from which one obvious difference from the results on Pt(1 1 1) surface is that there is no exchange diffusion process on Cu(1 1 1) surface. On Pt(1 1 1) surface, the activation energy of the exchange process between the two crescents is 0.62 eV, which is smaller than those of the one-atom hopping processes shown in Fig. 2(1)-(a) and (3)-(c), they are 0.66 eV and 0.82 eV from Fig. 3. While on Cu(1 1 1) surface, the activation energy of the exchange is about 1.62 eV, which is far larger than that of the one-atom hopping, about 0.21 eV. This is the reason why on Cu(1 1 1) surface no exchange process is observed. In addition, we can also understand this difference from the structural characteristics of the clusters on the two surfaces. As mentioned above, the adsorbed Pt cluster will make the Pt(1 1 1) surface form a marked concavity, it means that the cluster can be closer to the surface, or be embedded in the surface to a certain degree. Meanwhile, the cluster on Pt(1 1 1) surface is usually bended obviously as described in our previous work [14], in which the border atoms of the cluster, specifically the corner atoms are much closer to the substrate than the inner atoms. It is not difficult to imagine that these structural characteristics will make the exchange possible or
easy. While, on Cu(1 1 1) surface, these characteristics are not obvious (see Fig. 7), and then no exchange is observed. Certainly, our calculations are based on the semiempirical potentials, so whether the exchange really appears or not needs further studies. However, from our comparison between the two surfaces, we can see that when the exchange could be possible. Besides the exchange, the relative occurrence frequencies of the other diffusion processes are also different on the two surfaces. In Table 1, we can see that from Pt(1 1 1) to Cu(1 1 1) surface the percentages of the shearing and one-atom hopping increase, while the percentage of the concerted translation decreases. In addition, different from those on Pt(1 1 1) surface, our MD simulation on Cu(1 1 1) surface shows that one-atom hopping and the shearing appear on the adatoms either at A-step or B-step. As mentioned above, on Pt(1 1 1) surface the hopping only occurring at B-step is mainly owing to the contraction of the cluster. For more clear, the percentages of the contraction (l l0)/l0 between any two adatoms are given in Fig. 8, where l0 is the normal distance between the two nearest neighbor atoms, and l is the distance between the two adatoms after full relaxation. The results show that the contraction on Cu(1 1 1) surface is much less than that on Pt(1 1 1) surface, so it is understandable that on Cu(1 1 1) surface the hopping and shearing can also occur on the adatom(s) at A-step. Furthermore, the large contraction implies that the attractions among the adatoms are strong relative to the drag from the adsorption site. Therefore, the results in Fig. 8 also clearly show that the atoms of the cluster on Pt(1 1 1) surface are bound more tightly than that on Cu(1 1 1) surface. The tight binding makes the cluster tend to move as a whole, while the loose binding will make the shearing and oneatom hopping easy. This is the reason why from Pt(1 1 1) to Cu(1 1 1) surface the relative number of the concerted translation decreases, while the relative numbers of the shearing and oneatom hopping increase. Moreover, on Pt(1 1 1) surface, there is only the two-atom shearing. While, on Cu(1 1 1) surface, the shearing processes are diverse. Besides the two-atom shearing, the three-atom shearing and four-atom shearing are also observed. The reason is also the loose binding of the adatoms on Cu(1 1 1) surface. Another interesting difference between the two surfaces is the preferential path of the parallelogram translation. On Cu(1 1 1) surface, the numbers and percentages of the translation in the three paths are also given in Table 2. From Pt(1 1 1) to Cu(1 1 1) surface, the preferential path changes from ‘‘1’’ to ‘‘3’’. In above, we point out that on Pt(1 1 1) surface the anisotropy in the diffusion path is due to the marked concavity or deformation of the surface under the cluster. On Cu(1 1 1) surface, however, the concavity is not obvious as shown in Fig. 7, and the preferential path is ‘‘3’’
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J. Jiang et al. / Applied Surface Science 254 (2008) 5822–5826
Fig. 9. The partial concerted translation process for the parallelogram hexamer diffusion on Cu(1 1 1) surface.
instead of ‘‘1’’. Then we can conclude that on this surface the anisotropy in the diffusion path is not due to the surface concavity. In Fig. 9, we show the process of the translation in the preferential path ‘‘3’’ on Cu(1 1 1) surface, comparing with the translations in the other paths, we can see that the hopping processes of the six atoms are obviously not synchronous, ‘‘a’’ and ‘‘b’’ atoms move first, then ‘‘c’’ and ‘‘d’’, and finally ‘‘e’’ and ‘‘f’’. But the processes are still correlative because the movements are overlapped in time. Therefore, we call this diffusion process as partial concerted translation for convenience. The key of this partial concerted translation is that its activation energy is lower than that of the conventional one, in which the six atoms hop synchronously. The former is 0.16 eV, while the latter is about 0.23 eV. From the energy curves in Fig. 6b, the activation energies in path ‘‘1’’ and ‘‘2’’ are 0.35 and 0.26 eV, respectively. So far it is clear that why on Cu(1 1 1) surface the translation in path ‘‘3’’ is dominant. That is, in path ‘‘3’’, the parallelogram can diffuse by the partial concerted translation, which has the lower activation energy than the conventional one. As shown in Fig. 9, the dislocation is needed in the partial concerted translation, which implies that the appearance or the lower activation energy of this diffusion process is also a result of the loose binding of the adatoms on Cu(1 1 1) surface. Recently, also on Cu(1 1 1) surface, Flores et al. [23] report the same process. They call it double rotation mechanism, and the activation energy is 0.15 eV, which is in good accordance with ours 0.16 eV. Finally, from Table 2, we can see that the translation in path ‘‘1’’ can be neglected on Cu(1 1 1) surface. As a result, with the paths ‘‘2’’ and ‘‘3’’, the long-range diffusion of the parallelogram will along the ‘‘e–b’’ atom row as shown in Fig. 5 instead of the ‘‘a–b–c’’ atom row on Pt(1 1 1) surface. 4. Conclusion Diffusions of hexamers Pt6 and Cu6 adsorbed, respectively, on Pt(1 1 1) and Cu(1 1 1) surfaces are studied by molecular dynamics with the semiempirical potentials. It is shown that the diffusion process on Pt(1 1 1) surface is far different from that on Cu(1 1 1) surface. Two factors are found to be the reasons for the differences. One is the surface deformation; the other is the cluster contraction. On Pt(1 1 1) surface, the deformation or the concavity of the surface under the cluster is more obvious than that on Cu surface, it makes the exchange process possible on Pt(1 1 1) surface. Owing to
the structural characteristics of the steps, the exchange only appears on the adatom at A-step. As to the contraction of the cluster, it is shown that on Pt(1 1 1) surface the contraction is much larger than that on Cu(1 1 1) surface, which also means the adatoms are bound loosely on Cu(1 1 1) surface comparing with that on Pt(1 1 1) surface. The marked contraction on Pt(1 1 1) surface makes one-atom hopping and two-atom shearing only occur on the adatom(s) adsorbed at B-step. While, on Cu(1 1 1) surface, they can appear on the adatom(s) either at A-step and Bstep. On Cu(1 1 1) surface, the loose binding of the adatoms leads to the increment of the shearing process comparing with that on Pt(1 1 1) surface. In the two systems, the anisotropy of the translation of the parallelogram hexamer is all observed, but the reasons and then the preferential paths are completely different. On Pt(1 1 1) surface, it is due to the marked concavity of the surface, while on Cu(1 1 1) surface it is owing to the appearance of the partial concerted translation resulting from the loose binding. The different anisotropy of the parallelogram will lead the different long-rang diffusion on the two surfaces.
Acknowledgements This work was supported by Chinese NSF (Grant No. 10004002), Technology Development Foundation of Shanghai (Grant No. 02QA14007) and ‘973’ project of China (Grant No. 2001CB610506).Some of the calculations are performed on NHPCC of Fudan University.
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Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Diffusions of small clusters on Pt(1 1 1) and Cu(1 1 1) surfaces Jianxing Jiang a, Peng Zhang a, Yiqun Xie a, Xijing Ning b, Min Zhuang c, Yufen Li a, Jun Zhuang a,* a State Key Lab for Advanced Photonic Materials and Devices, Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China b Institute of Modern Physics, Fudan University, Shanghai 200433, China c De´partement de Chimie, Universite´ de Montre´al, Case Postale 6128 Succursale Centre-ville, Montre´al, Que´bec H3C 3J7, Canada
A R T I C L E I N F O
A B S T R A C T
Article history: Received 30 June 2007 Accepted 16 March 2008 Available online 21 March 2008
Diffusions of small cluster Pt6 on Pt(1 1 1) surface and Cu6 on Cu(1 1 1) are studied by molecular dynamics simulation, respectively. The atomic interaction is modeled by the semiempirical potential. The results show that the diffusion processes in the two systems are far different. For example, on Pt(1 1 1) surface, the hopping of single atom and the shearing of two atoms of hexamer only occur on the adatom(s) adsorbed at B-step, while on Cu(1 1 1) surface they can appear on the adatom(s) either at Astep or B-step. To the concerted translation of the parallelogram hexamer, the anisotropy in the diffusion path is observed in the two systems, the mechanisms and then the preferential paths, however, are completely different. The reasons for these diffusion characteristics and differences are discussed. ß 2008 Elsevier B.V. All rights reserved.
Keywords: Surface diffusion Clusters Metallic surfaces Molecular dynamics
1. Introduction The diffusion of single adatoms and small clusters on crystal surface is an important step in processes such as crystal growth, surface reconstruction, and thin-film formation, etc. In experiments, the tools for investigating surface diffusion include the field ion microscopy (FIM) [1,2] and scanning tunneling microscopy (STM) [3]. Based on the observation of FIM [4,5], interesting exchange mechanisms for the diffusion of Pt monomer, dimer, and trimer on Pt(0 0 1) surface are suggested. In theory, molecular dynamics (MD) simulation and molecular statics (MS) calculation are usually used for this task, and the calculations are sometimes based on the first-principle method [3,6,7]. Owing to the limitation of computing power, however, most studies, especially MD simulations, are often carried out on the semiempirical level [7– 11]. MD simulation is capable of giving the actual trajectories of the atoms, by which the unknown diffusion mechanisms or complicated diffusion processes could be revealed, for example, dislocation mechanism for diffusion of clusters on Ni(1 1 1) surface [10]. In our previous works, diffusion of single adatoms and structures of clusters on different metal surfaces were studied systematically with semiempirical potentials [11–14]. The results show that the case on Pt surface is far different from those on the others. For
* Corresponding author. E-mail address: [email protected] (J. Zhuang). 0169-4332/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2008.03.060
example, the diffusion of Pt monomer on Pt(0 0 1) surface is dominated by the exchange mechanism [11], and similar exchange process could also occur on Pt(1 1 1) surface [13], while on most other metal surfaces the dominant diffusion mechanism is hopping. As to the adatom clusters on Pt(1 1 1) surface, they usually have triangle-like structures instead of hexagon-like ones on the other metal surfaces [14]. These peculiar results motivate us to study the diffusion of small cluster further on Pt(1 1 1) surface. We consider the small cluster Pt6 in the present work. For comparison, the diffusion of Cu6 on Cu(1 1 1) surface is also investigated. 2. Calculation model The potential used in our simulation for platinum is obtained by the surface embedded-atom method (SEAM) which is developed from the conventional embedded-atom method (EAM) for the surface environment by Haftel and Rosen [15,16]. Based on this kind of potential, our previous works have revealed the exchange mechanism for the diffusion of Pt monomer and dimer on Pt(0 0 1) surface [11,12] and the triangle-like structures of Pt adatom clusters on Pt(1 1 1) surface [14], which are basically in accordance with the experiments [4,5,17]. In the present work, we still choose the SEAM potential for Pt system. For Cu system, Rosato– Guillope´–Legrand (RGL) potential is used, which is on the basis of the second-moment approximation to tight-binding model [18,19]. The substrate in our simulation is a (1 1 1) slab consisting of 30 layers,
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Table 1 The numbers of exchange, one-atom hopping, two-atom shearing and six-atom concerted translation processes for hexamer on Pt(1 1 1) and Cu(1 1 1) surfaces Surfaces (temperature)
Exchange
One-atom hopping
Shearing
Translation
Total
Pt (800 K) Cu (450 K)
57 (9.7%) 0
22 (3.7%) 88 (15.8%)
15 (2.5%) 163 (29.3%)
496 (84.1%) 306 (54.9%)
590 557
The total simulation time Ttot = 160 ns for Pt and Ttot = 12 ns for Cu. The numbers in the brackets are their percentages.
each layer contains 12 12 atoms, and periodic boundary conditions are imposed along the direction ½2¯ 1 1 and ½0 1¯ 1. The cluster is placed on each surface of the slab. Molecular dynamics (MD) simulation for cluster diffusion is accomplished by the standard Verlet algorithm with a proper time step to ensure the total energy fluctuation less than 1.0 104 [20]. 3. Results and discussion On Pt(1 1 1) surface, MD simulation is performed at temperature 800 K. The results show that the diffusion processes are diverse and sometimes complicated. Besides the processes such as the concerted translation, the shearing of two atoms, and oneatom hopping, the exchange is also observed in our MD simulation. The statistic results from the simulation at temperature 800 K are given in Table 1. The diffusion processes generally result in the change of the cluster structures. In Fig. 1, four kinds of structures that appear in the simulation are given. For simplification, we call them A-type triangle, parallelogram, B-type triangle, and the crescent. ‘‘A’’ and ‘‘B’’ indicate the step type of the triangle edge. As we know, there are two different types of steps on fcc(1 1 1) surface, the so-called A-step ({1 0 0} microfaceted step) and B-step ({1 1 1} microfaceted step). The structures given in Fig. 1 are all adsorbed at fcc site, at which our calculation shows that the energy of the cluster is far lower than that at hcp site. For example, the relative energy of the parallelogram at fcc site is 0.05 eV, while it is 0.50 eV at hcp site (also see Fig. 6 in the following). Therefore, as we observed in MD simulation, the cluster basically does not stay at hcp site. For cluster Pt7, similar result is obtained in the experiment [2], which shows that the compact hexagonal heptamer always occupies fcc sites after diffusion. In Fig. 1, the diffusion processes between the structures are indicated by (A)–(E). The process (C) between the two parallelo-
grams means the concerted translation, by which the cluster diffuses as a whole. The transformation between the parallelogram and the crescent is through the shearing process (D), in which the two atoms hop together. The shearing is commonly observed in the diffusion of the clusters [9,21,22]. The process (A) from the A-type triangle to the parallelogram in Fig. 1 is a little complicated, we give the details in Fig. 2, which includes two steps. First, from the A-type triangle (1) to the configuration (a) in Fig. 2, one corner atom ‘‘a’’ hops to the nearest fcc site along the edge. Then, after a while, it enters into the nearest neighbor row of the substrate (dark gray balls in Fig. 2) and seems to disappear on the surface. As a result, strain is induced in the surface row and makes the atoms around ‘‘a’’ unstable and compete each other. The competition could last a certain time, after that the strain will finally be released when one atom ‘‘b’’ is pushed out from the surface. This process is very similar to the exchange diffusion of single adatom based on the strain induced and relaxed mechanism known on Cu(0 0 1) and Ag(0 0 1) surfaces [12]. The process (B) from the parallelogram to the B-type triangle in Fig. 1 is basically the same as the process (A). As shown in Fig. 2, the corner atom ‘‘c’’ hops first, and then it enters into the substrate. After the competition, atom ‘‘d’’ is finally pushed out. Corresponding to the processes in Fig. 2, the static energies are calculated by the standard approach: Choose and change a certain freedom according to the reaction path, then at each fixed
Fig. 2. Details of the diffusion processes between the configurations (1) and (3), and between (3) and (5) in Fig. 1.
Fig. 1. Structures of hexamer (black balls) observed on Pt(1 1 1) surface. (A), (B), (C), and (D) indicate the different diffusion processes (see details in text).
Fig. 3. The energy curve for the diffusion processes in Fig. 2.
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J. Jiang et al. / Applied Surface Science 254 (2008) 5822–5826 Table 2 In the total translations 496 and 306 given in Table 2 the numbers of the translations along the three paths on Pt(1 1 1) and Cu(1 1 1) surfaces Surfaces (temperature)
Translation in path (1)
Translation in path (2)
Translation in path (3)
Total
Pt (800 K) Cu (450 K)
464 (93.5%) 2 (0.6%)
32 (6.5%) 41 (13.4%)
0 263 (86.0%)
496 306
Their percentages are also given in the brackets.
Fig. 4. The different surroundings of the adatoms ‘‘a’’ and ‘‘b’’ at A-step and B-step, respectively.
increment of this freedom fully relax all the other freedoms of the active atoms. The results are given in Fig. 3. Finally, our MD simulation shows that the transfer between the two crescents in Fig. 1, i.e., process (E), is also by the exchange process. From the processes described above, we can find two interesting phenomena. One is that the exchange always occurs on the adatom adsorbed at A-step. Another is that the hopping, including one-atom hopping and the two-atom shearing, always appears on the adatom(s) at B-step. The reasons can be seen clearly from the configurations in Fig. 4. In the exchange process, as we described above, the adatom should enter into the surface row first. Owing to the difference between the structures of A-step and B-step, we can see from Fig. 4 that atom ‘‘a’’ of the cluster at A-step could enter into the ‘‘c–d’’ surface row near it, while atom ‘‘b’’ has no way to enter into the ‘‘d–e’’ row. Therefore, as we observed in MD simulation, the exchange only appears at A-step. As to the hopping, the different type of the step will certainly also affect its occurrence frequency like that for the exchange. But, from the structural characteristics in Fig. 4, it is easy to see that such influence could not cause the hopping to occur only at B-step. In our calculations, we find that the structures of the clusters on Pt(1 1 1) surface contract obviously (also see details in Fig. 8 in the following). More specifically, the corner atom ‘‘a’’ at A-step, as an example, deviates far from the normal fcc adsorption site and is closer to the surface atoms ‘‘c’’ and ‘‘d’’ as shown in Fig. 4. It obviously makes the hopping of atom ‘‘a’’ along A-step difficult. To atom ‘‘b’’ at B-step, however, the case is different. The structure contraction makes it closer to the surface atom ‘‘e’’ instead of ‘‘f’’ and ‘‘g’’, which then has less influence on the occurrence of the hopping. As a result, the possibility of the hopping occurring at Bstep increases relative to that at A-step. And, if the structure contraction is serious, it is possible that the hopping only occurs at B-step. Therefore, on Pt(1 1 1) surface, the structure contraction is the main reason which causes the hopping to appear only at B-step. While, for the exchange process, the structural characteristics of the steps determine that it could only occur at A-step. Another phenomenon that attracts us is that the concerted translations of the parallelogram are almost always along certain
Fig. 5. The three paths for the concerted translation of the parallelogram hexamer.
path or direction. As shown in Fig. 5, between fcc site and hcp site, there are three paths for the parallelogram to move, for convenience, we denote them as ‘‘1’’, ‘‘2’’, and ‘‘3’’. From MD simulation, the numbers of the concerted translations in the three paths are given in Table 2, in which most of the translations are along path ‘‘1’’, only a few are along path ‘‘2’’, but none is observed along path ‘‘3’’. The static energy calculation gives the correspondence results as shown in Fig. 6a, the activation energy of the concerted translation in path ‘‘1’’ is the lowest (0.49 eV), while in path ‘‘3’’ it is the highest (1.27 eV). To explain this phenomenon, we compare the surface structures before and after the adsorption of the cluster. It is found that the deformation of the surface induced by the cluster is obvious. More specifically, a marked concavity is formed in the surface as shown in Fig. 7. When the parallelogram diffuses in path ‘‘3’’, as shown in Fig. 5, the two surface atoms under the cluster ‘‘a’’ and ‘‘b’’ will change to ‘‘d’’ and ‘‘e’’. In path ‘‘2’’, only one atom is changed, ‘‘a’’ and ‘‘b’’ to ‘‘b’’ and ‘‘c’’. When the parallelogram diffuses in path ‘‘1’’, however, the two surface atoms under the cluster remain unchanged. The results mean that the change of the surface deformation or concavity is largest when the parallelogram diffuses in path ‘‘3’’, while it is smallest in path ‘‘1’’. Or, in other words, the diffusion in path ‘‘3’’ demands that the
Fig. 6. The energy curves for the concerted translation of the parallelogram in the different paths ‘‘1’’, ‘‘2’’, and ‘‘3’’ shown in Fig. 5 on Pt(1 1 1) (a) and Cu(1 1 1) surfaces (b).
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Fig. 7. Deformation of the surface under the cluster of the parallelogram hexamer. On Pt(1 1 1) surface, a marked concavity is formed. Fig. 8. Contractions of hexamers on Pt(1 1 1) and Cu(1 1 1) surfaces.
parallelogram jumps out of the concavity completely. While, in path ‘‘1’’, the diffusion occurs approximately within the concavity. Therefore, the activation energy of the translation in path ‘‘1’’ is the smallest, and then almost all translations occur in this path as we observed in MD simulation. For the long-range diffusion, the parallelogram moving only in path ‘‘1’’ is not enough, which just results in the translation between the fcc and hcp sites. On Pt(1 1 1) surface, another diffusion path is ‘‘2’’. If the parallelogram translates alternately in ‘‘1’’ and ‘‘2’’ paths, the long-range diffusion can be realized. The interesting is that the particular translation paths ‘‘1’’ and ‘‘2’’ result in the long-range diffusion of the parallelogram only along the ‘‘a–b–c’’ atom row as shown in Fig. 5. Certainly, owing to the existence of the other diffusion mechanisms, the cluster can diffuse freely over the surface. In Fig. 1, we can see that besides the parallelogram translation (C), the processes (A), (B), and (D) also have contributions to the diffusion. From Figs. 3 and 6a, the activation energies of the processes (A), (B), (C), and (D) are (0.66; 0.86 eV), (0.82; 0.81 eV), (0.70; 0.70 eV) and (0.83; 0.77 eV), respectively, which are close to the result 0.89 0.04 eV obtained in experiment [2]. As we mentioned above, the single adatom diffusion and the structural characteristics of adatom clusters on Pt(1 1 1) surface are far different from those on the others. Therefore, for the diffusion of small cluster studied here, it is interesting to compare the results on Pt(1 1 1) surface with those on the others. As an example, we choose Cu(1 1 1) surface for comparison. MD simulation is done at temperature 450 K. The diffusion processes observed in the simulation and their numbers are also given in Table 1, from which one obvious difference from the results on Pt(1 1 1) surface is that there is no exchange diffusion process on Cu(1 1 1) surface. On Pt(1 1 1) surface, the activation energy of the exchange process between the two crescents is 0.62 eV, which is smaller than those of the one-atom hopping processes shown in Fig. 2(1)-(a) and (3)-(c), they are 0.66 eV and 0.82 eV from Fig. 3. While on Cu(1 1 1) surface, the activation energy of the exchange is about 1.62 eV, which is far larger than that of the one-atom hopping, about 0.21 eV. This is the reason why on Cu(1 1 1) surface no exchange process is observed. In addition, we can also understand this difference from the structural characteristics of the clusters on the two surfaces. As mentioned above, the adsorbed Pt cluster will make the Pt(1 1 1) surface form a marked concavity, it means that the cluster can be closer to the surface, or be embedded in the surface to a certain degree. Meanwhile, the cluster on Pt(1 1 1) surface is usually bended obviously as described in our previous work [14], in which the border atoms of the cluster, specifically the corner atoms are much closer to the substrate than the inner atoms. It is not difficult to imagine that these structural characteristics will make the exchange possible or
easy. While, on Cu(1 1 1) surface, these characteristics are not obvious (see Fig. 7), and then no exchange is observed. Certainly, our calculations are based on the semiempirical potentials, so whether the exchange really appears or not needs further studies. However, from our comparison between the two surfaces, we can see that when the exchange could be possible. Besides the exchange, the relative occurrence frequencies of the other diffusion processes are also different on the two surfaces. In Table 1, we can see that from Pt(1 1 1) to Cu(1 1 1) surface the percentages of the shearing and one-atom hopping increase, while the percentage of the concerted translation decreases. In addition, different from those on Pt(1 1 1) surface, our MD simulation on Cu(1 1 1) surface shows that one-atom hopping and the shearing appear on the adatoms either at A-step or B-step. As mentioned above, on Pt(1 1 1) surface the hopping only occurring at B-step is mainly owing to the contraction of the cluster. For more clear, the percentages of the contraction (l l0)/l0 between any two adatoms are given in Fig. 8, where l0 is the normal distance between the two nearest neighbor atoms, and l is the distance between the two adatoms after full relaxation. The results show that the contraction on Cu(1 1 1) surface is much less than that on Pt(1 1 1) surface, so it is understandable that on Cu(1 1 1) surface the hopping and shearing can also occur on the adatom(s) at A-step. Furthermore, the large contraction implies that the attractions among the adatoms are strong relative to the drag from the adsorption site. Therefore, the results in Fig. 8 also clearly show that the atoms of the cluster on Pt(1 1 1) surface are bound more tightly than that on Cu(1 1 1) surface. The tight binding makes the cluster tend to move as a whole, while the loose binding will make the shearing and oneatom hopping easy. This is the reason why from Pt(1 1 1) to Cu(1 1 1) surface the relative number of the concerted translation decreases, while the relative numbers of the shearing and oneatom hopping increase. Moreover, on Pt(1 1 1) surface, there is only the two-atom shearing. While, on Cu(1 1 1) surface, the shearing processes are diverse. Besides the two-atom shearing, the three-atom shearing and four-atom shearing are also observed. The reason is also the loose binding of the adatoms on Cu(1 1 1) surface. Another interesting difference between the two surfaces is the preferential path of the parallelogram translation. On Cu(1 1 1) surface, the numbers and percentages of the translation in the three paths are also given in Table 2. From Pt(1 1 1) to Cu(1 1 1) surface, the preferential path changes from ‘‘1’’ to ‘‘3’’. In above, we point out that on Pt(1 1 1) surface the anisotropy in the diffusion path is due to the marked concavity or deformation of the surface under the cluster. On Cu(1 1 1) surface, however, the concavity is not obvious as shown in Fig. 7, and the preferential path is ‘‘3’’
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Fig. 9. The partial concerted translation process for the parallelogram hexamer diffusion on Cu(1 1 1) surface.
instead of ‘‘1’’. Then we can conclude that on this surface the anisotropy in the diffusion path is not due to the surface concavity. In Fig. 9, we show the process of the translation in the preferential path ‘‘3’’ on Cu(1 1 1) surface, comparing with the translations in the other paths, we can see that the hopping processes of the six atoms are obviously not synchronous, ‘‘a’’ and ‘‘b’’ atoms move first, then ‘‘c’’ and ‘‘d’’, and finally ‘‘e’’ and ‘‘f’’. But the processes are still correlative because the movements are overlapped in time. Therefore, we call this diffusion process as partial concerted translation for convenience. The key of this partial concerted translation is that its activation energy is lower than that of the conventional one, in which the six atoms hop synchronously. The former is 0.16 eV, while the latter is about 0.23 eV. From the energy curves in Fig. 6b, the activation energies in path ‘‘1’’ and ‘‘2’’ are 0.35 and 0.26 eV, respectively. So far it is clear that why on Cu(1 1 1) surface the translation in path ‘‘3’’ is dominant. That is, in path ‘‘3’’, the parallelogram can diffuse by the partial concerted translation, which has the lower activation energy than the conventional one. As shown in Fig. 9, the dislocation is needed in the partial concerted translation, which implies that the appearance or the lower activation energy of this diffusion process is also a result of the loose binding of the adatoms on Cu(1 1 1) surface. Recently, also on Cu(1 1 1) surface, Flores et al. [23] report the same process. They call it double rotation mechanism, and the activation energy is 0.15 eV, which is in good accordance with ours 0.16 eV. Finally, from Table 2, we can see that the translation in path ‘‘1’’ can be neglected on Cu(1 1 1) surface. As a result, with the paths ‘‘2’’ and ‘‘3’’, the long-range diffusion of the parallelogram will along the ‘‘e–b’’ atom row as shown in Fig. 5 instead of the ‘‘a–b–c’’ atom row on Pt(1 1 1) surface. 4. Conclusion Diffusions of hexamers Pt6 and Cu6 adsorbed, respectively, on Pt(1 1 1) and Cu(1 1 1) surfaces are studied by molecular dynamics with the semiempirical potentials. It is shown that the diffusion process on Pt(1 1 1) surface is far different from that on Cu(1 1 1) surface. Two factors are found to be the reasons for the differences. One is the surface deformation; the other is the cluster contraction. On Pt(1 1 1) surface, the deformation or the concavity of the surface under the cluster is more obvious than that on Cu surface, it makes the exchange process possible on Pt(1 1 1) surface. Owing to
the structural characteristics of the steps, the exchange only appears on the adatom at A-step. As to the contraction of the cluster, it is shown that on Pt(1 1 1) surface the contraction is much larger than that on Cu(1 1 1) surface, which also means the adatoms are bound loosely on Cu(1 1 1) surface comparing with that on Pt(1 1 1) surface. The marked contraction on Pt(1 1 1) surface makes one-atom hopping and two-atom shearing only occur on the adatom(s) adsorbed at B-step. While, on Cu(1 1 1) surface, they can appear on the adatom(s) either at A-step and Bstep. On Cu(1 1 1) surface, the loose binding of the adatoms leads to the increment of the shearing process comparing with that on Pt(1 1 1) surface. In the two systems, the anisotropy of the translation of the parallelogram hexamer is all observed, but the reasons and then the preferential paths are completely different. On Pt(1 1 1) surface, it is due to the marked concavity of the surface, while on Cu(1 1 1) surface it is owing to the appearance of the partial concerted translation resulting from the loose binding. The different anisotropy of the parallelogram will lead the different long-rang diffusion on the two surfaces.
Acknowledgements This work was supported by Chinese NSF (Grant No. 10004002), Technology Development Foundation of Shanghai (Grant No. 02QA14007) and ‘973’ project of China (Grant No. 2001CB610506).Some of the calculations are performed on NHPCC of Fudan University.
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