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The structural and dynamical properties of Al clusters adsorbed on Ni surface
Nuclear Instruments and Methods in Physics Research B 180 (2001) 251±256
www.elsevier.nl/locate/nimb
The structural and dynamical properties of Al clusters adsorbed on Ni surface Y.X. Wang a
a,b
, Z.Y. Pan
a,b,*
, Y.K. Ho
a,b
, Y. Xu
a,b
, A.J. Du
a,b
State Key Laboratory for Material Modi®cation by Laser, Ion and Electron Beams, Institute of Modern Physics, Fudan University, Shanghai 200433, People's Republic of China b Ion Beam Laboratory, Shanghai Institute of Metallurgy, Academic Sinica, Shanghai, People's Republic of China
Abstract The impact-induced deposition of Al13 clusters with icosahedral structure on Ni(0 0 1) surface was studied by molecular dynamics (MD) simulation using Finnis±Sinclair potentials. The incident kinetic energy (Ein ) ranged from 0.01 to 30 eV per atom. The structural and dynamical properties of Al clusters on Ni surfaces were found to be strongly dependent on the impact energy. At much lower energy, the Al cluster deposited on the surface as a bulk molecule. However, the original icosahedral structure was transformed to the fcc-like one due to the interaction and the structure mismatch between the Al cluster and Ni surface. With increasing the impinging energy, the cluster was deformed severely when it contacted the substrate, and then broken up due to dense collision cascade. The cluster atoms spread on the surface at last. When the impact energy was higher than 11 eV, the defects, such as Al substitutions and Ni ejections, were observed. The simulation indicated that there exists an optimum energy range, which is suitable for Al epitaxial growth in layer by layer. In addition, at higher impinging energy, the atomic exchange between Al and Ni atoms will be favourable to surface alloying. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The low-energy cluster beam deposition (LECBD) on solids has been found to exhibit a number of new eects which are not observed in collisions of atomic beams with the solids [1,2]. Along this line, the studies on metal-on-metal epitaxy are attracted much attention due to the potential applications [3,4]. Recent experimental evidence
*
Corresponding author. Fax: +86-21-65-10-49-49. E-mail address: [email protected] (Z.Y. Pan).
has shown that the structures resulting from metal heteroepitaxy are often complex and dicult to predict from the bulk material parameters [5]. For the Ni±Al system, Averback et al. [6] investigated the role of cohesive properties on cluster±solid interactions. Bilic et al. [7] simulated the adsorption and mixture of an Al atom on the Ni surface. In this paper, the impact-induced deposition of low-energy Al13 cluster with icosahedral structure (Ih ) on Ni(0 0 1) surface was studied by molecular dynamics (MD) simulation. Special attention was paid to study the characteristics of the deposition processes at various impact energy ranges.
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 4 2 5 - 6
252
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
2. Simulation methods The current simulation was performed using Finnis±Sinclair potentials for Ni±Al system. The potentials were developed by Ackland et al. [8], and further modi®ed at close atomic separations by Gao [9] through joining these potentials by a spline to the universal potential [10]. The potentials proved successful in describing the bulk properties of the Ni±Al system [9]. The MD program used in this study was similar to that in [11]. In this model, classical equations of motion were set at atomic level and integrated by using the leapfrog form of the Verlet algorithm [12] with variable time step. Periodic boundary conditions were applied in the [1 0 0] and [0 1 0] orthogonal directions. The Ni substrate with [0 0 1] surface consisted of 12 layers of atoms. Each layer contained 288 atoms (12 12 unit cell). The Al13 of Ih symmetry was initially located at a sucient distance above the surface and had negligible interaction with the Ni atoms. In order to study the dependence of the structural and dynamical properties on deposition energy, we set the temperature of the substrate at 0 K. The Al13 of Ih symmetry was selected as the projectile cluster which is more stable, compared with Oh symmetry [13]. 3. Results and discussion By using the potentials, the binding energy of the Al13 of Ih symmetry was found to be 36.28 eV, which was consistent with other theoretical values [14±18]. Thus, we considered that it was appropriate to adopt the potentials to study the behavior of Al13 impacting on Ni surface. According to the structural and dynamical feature of the cluster on the surface, three impact energy regions have been identi®ed in the low-energy period. The ®rst one is de®ned as low±low energy (LLE), which is from 0.01 to 1 eV per atom, the second, low±medium energy (LME) from 2 to 10 eV per atom, and the third, low±high energy (LHE) from 11 to 30 eV per atom. At LLE, the cluster and the substrate surface are compressed slightly by the collision. Fig. 1
shows the snapshots of a typical event of softlanding with deposition energy of 0.01 eV/atom. At t 1:0 ps, the lower part of the cluster begins to change its structure. After relaxation, the Al cluster rearranges its structure from Ih symmetry into fcc-like structure without dissociation and resides on the Ni substrate as a bulk molecule. In Fig. 2, Ectr ; Ecin and Etin denote the kinetic energy of the cluster center of mass (CM), the internal energies of the cluster and the substrate, respectively; and DEcp and DEtp design the potential energy changes of the cluster and the substrate, respectively. It can be seen that, due to the attractive interaction between the cluster and the substrate, Ectr reaches the maximum value at t 0:9 ps, which is more than 20 times of its initial translational energy. Meanwhile, the potential energy of the cluster decreases rapidly until it reaches the minimum after t 2 ps, which is in accordance with the atomic position distribution presented in Fig. 1. It can be clearly seen from Figs. 1 and 2 that the structure rearrangement of the cluster occurs during 1±2 ps. The kinetic energy for rearrangement mainly comes from the decrease of DEcp which is attributed to the advantageous Ni±Al cohesive over the Al±Al [9] at the distance of the Al cluster approaching the Ni surface. Therefore, we conclude that the rearrangement of the cluster re¯ects the competition between the Ni±Al and Al±Al interaction. In addition, the stress, induced by the incommensurate structures between the cluster and the surface, is another factor to drive the cluster atoms to move into the stable sites. As a typical LME event, Figs. 3 and 4 present the snapshots, and the energy dissipation for a deposition with impinging energy of 6 eV/atom, respectively. In contrast to LLE, as the Al13 reaches the Ni surface at about 0.1 ps, it is deformed severely and then broken up. Some cluster atoms are migrated long distance outward from the impact point. The enhancement in DEcp , which corresponds to the severe deformation of the cluster, is compensated by the decrease of Ectr . We can see from Fig. 4 that the energy transfer takes place chie¯y in the short time interval (0.1±0.25 ps), which demonstrates that the energy transfer stems mainly from the collision cascade. This is
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
253
Fig. 1. Snapshots of an Al13 cluster of Ih symmetry impacting on an Ni(0 0 1) surface. The incident energy is 0.01 eV per atom. At each instant, the left shows the side view and the right for the top view. The black dots represent Ni atoms, and open circles for Al atoms.
Fig. 2. The variations of energies versus time for a 0.01 eV/atom Al13 cluster impacting on a Ni substrate. Ectr ; Ecin ; Etin ; DEcp and DEtp denote the translational energy, the internal energy of the Al cluster and the substrate, and the potential energy changes of the cluster and the substrate, respectively. The initial values of DEtp 0 and DEcp 0 at t 0 are adopted.
254
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
Fig. 3. The same as in Fig. 1, but for impact energy of 6 eV/atom.
Fig. 4. The same as in Fig. 2, but for impact energy of 6 eV/atom.
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
255
Table 1 The mean number of the adatoms, substitutions, sputtered atoms and re¯ected atoms observed at the end of the simulations for each eventa Ein (eV/atom) Ni adatoms Al adatoms Alsub in the 1st layer below surface Alsub in the 2nd layer below surface Alsub in the 3rd layer below surface Al re¯ected atoms Ni sputtered atoms a
12 4.6 5.9 4.4
15 6.8 6.1 5.8
0.5
0.8 0.2
18 8.8 8.9 6.0 1.1 0.1 0.9
20 8.4 4.3 5.1 1.0
25 10.0 3.5 5.5 2.4
1.3 0.2
1.1 1.5
30 9.3 3.7 5.0 2.0 0.6 1.7 4.4
Alsub denotes the Al subsitution.
fairly dierent from the LLE processes presented in Figs. 1 and 2. Also, at the end of the relaxation, the side-face atoms in the upper part (UP) of the cluster spread far away compared with those of the lower part (LP). The transverse mean spread [6] relative to the impact point is calculated to be 3:81a0 (a0 is the lattice constant of pure Ni metal) for the UP atoms and 1:94a0 for the LP atoms. We recall the mean separation of a free cluster is 0:73a0 . This feature can be understood as follows. The LP atoms reach the surface ®rstly. When the UP atoms arrive, they will also collide with the scattered LP atoms. Thus they may get more transverse momentum and move far away [19]. We perform the same simulation again, but ignore the interactions among the cluster atoms. In this case, the mean spread for atoms in the UP and the LP atoms are 1:38a0 and 1:59a0 , respectively. It suggests that the interactions among the cluster atoms play an important role on the transverse migration of the cluster atoms. It is worthwhile to note that only a few defects were observed at the deposition with LME condition. It means that a good Al epitaxy will be expected to grow in layer by layer at LME. At LHE, Al substitutions can be observed, whose number and depth distribution in the substrate increase with the impact energy. Consequently, some Ni atoms are ejected into the epitaxial layer. Due to the Al substitutions appearing in the second layer below the surface, vacancies are presented. Furthermore, re¯ected Al atoms and sputtered Ni atoms are also observed. The statistical results for eight events of each incident energy are listed in Table 1. It illustrates
that the energy for sputtering to occur is higher than that for re¯ecting. Meanwhile, no interstitial defects are created in our simulations, which is consistent with the expected by [6]. Substitutions generated in the simulations indicate that increasing energy can be helpful for surface alloying. Substrate temperature is another important factor, which will be discussed in our further work.
4. Conclusion This paper concentrated on exploring the structural and dynamical characteristics of Al cluster deposition on the Ni surface. We have found that the deposition energy can be divided into three ranges namely LLE, LME and LHE. At LLE, the cluster transforms into the fcc-like structure due to the strong Ni±Al cohesion. At LME, the collision cascade causes the cluster breaking up and spreading. When the deposition energy reaches LHE, the defects, such as Al substitutions and Ni ejections are observed. The atomic exchange between Al and Ni atoms indicates that increasing impact energy will be favourable to surface alloying.
Acknowledgements This work was mainly supported by National Nature Science Foundation of China under grant number 19875011, Postdoctoral Foundation of
256
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
China, and Engineering-physics Research Institute Foundation of China. References [1] I. Yamada, H. Takaoka, H. Usui, T. Takagi, J. Vac. Sci. Technol. A 4 (1986) 722. [2] R. Beuhler, L. Friedman, Chem. Rev. 86 (1986) 521. [3] P. Beccat, J. Massardier, Catal. Lett. 9 (1991) 183. [4] J. Hayoz, D. Naumovic, R. Fasel, P. Aebi, L. Schlapbach, Surf. Sci. 373 (1997) 153. [5] W.G. Cullen, P.N. First, Surf. Sci. 420 (1999) 52. [6] H. Hsieh, R.S. Averback, H. Sellers, C.P. Flynn, Phys. Rev. B 45 (1992) 4417. [7] A. Bilic, B.V. King, D.J. O'Connor, Surf. Sci. 442 (1999) 256.
[8] G.J. Ackland, M.W. Finnis, V. Vitek, J. Phys. F 18 (1988) L153. [9] F. Gao, D.J. Bacon, G.J. Ackland, Philos. Mag. A 67 (1993) 275. [10] J.P. Biersack, J.F. Ziegler, J. Nucl. Instr. and Meth. 141 (1982) 93. [11] R.W. Lee, Z.Y. Pan, Y.K. Ho, Phys. Rev. B 53 (1996) 4156. [12] L. Verlet, Phys. Rev. A 159 (1967) 98. [13] D.Y. Sun, X.G. Gong, J. Phys.: Condens. Matter 9 (1997) 10555. [14] V. Kumar, V. Sundararajan, Phys. Rev. B 57 (1998) 4939. [15] X.C. Gong, V. Kumar, Phys. Rev. Lett. 70 (1993) 70. [16] S.N. Khanna, P. Jena, Phys. Rev. B 57 (1995) 705. [17] H.P. Cheng, R.S. Berry, R.L. Whetten, Phys. Rev. B 43 (1991) 10647. [18] J.Y. Yi, D.J. Oh, Bernholc, R. Car, Chem. Phys. Lett. 174 (1990) 461. [19] Z.Y. Pan, Phys. Lett. A 172 (1993) 378.
www.elsevier.nl/locate/nimb
The structural and dynamical properties of Al clusters adsorbed on Ni surface Y.X. Wang a
a,b
, Z.Y. Pan
a,b,*
, Y.K. Ho
a,b
, Y. Xu
a,b
, A.J. Du
a,b
State Key Laboratory for Material Modi®cation by Laser, Ion and Electron Beams, Institute of Modern Physics, Fudan University, Shanghai 200433, People's Republic of China b Ion Beam Laboratory, Shanghai Institute of Metallurgy, Academic Sinica, Shanghai, People's Republic of China
Abstract The impact-induced deposition of Al13 clusters with icosahedral structure on Ni(0 0 1) surface was studied by molecular dynamics (MD) simulation using Finnis±Sinclair potentials. The incident kinetic energy (Ein ) ranged from 0.01 to 30 eV per atom. The structural and dynamical properties of Al clusters on Ni surfaces were found to be strongly dependent on the impact energy. At much lower energy, the Al cluster deposited on the surface as a bulk molecule. However, the original icosahedral structure was transformed to the fcc-like one due to the interaction and the structure mismatch between the Al cluster and Ni surface. With increasing the impinging energy, the cluster was deformed severely when it contacted the substrate, and then broken up due to dense collision cascade. The cluster atoms spread on the surface at last. When the impact energy was higher than 11 eV, the defects, such as Al substitutions and Ni ejections, were observed. The simulation indicated that there exists an optimum energy range, which is suitable for Al epitaxial growth in layer by layer. In addition, at higher impinging energy, the atomic exchange between Al and Ni atoms will be favourable to surface alloying. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The low-energy cluster beam deposition (LECBD) on solids has been found to exhibit a number of new eects which are not observed in collisions of atomic beams with the solids [1,2]. Along this line, the studies on metal-on-metal epitaxy are attracted much attention due to the potential applications [3,4]. Recent experimental evidence
*
Corresponding author. Fax: +86-21-65-10-49-49. E-mail address: [email protected] (Z.Y. Pan).
has shown that the structures resulting from metal heteroepitaxy are often complex and dicult to predict from the bulk material parameters [5]. For the Ni±Al system, Averback et al. [6] investigated the role of cohesive properties on cluster±solid interactions. Bilic et al. [7] simulated the adsorption and mixture of an Al atom on the Ni surface. In this paper, the impact-induced deposition of low-energy Al13 cluster with icosahedral structure (Ih ) on Ni(0 0 1) surface was studied by molecular dynamics (MD) simulation. Special attention was paid to study the characteristics of the deposition processes at various impact energy ranges.
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 1 ) 0 0 4 2 5 - 6
252
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
2. Simulation methods The current simulation was performed using Finnis±Sinclair potentials for Ni±Al system. The potentials were developed by Ackland et al. [8], and further modi®ed at close atomic separations by Gao [9] through joining these potentials by a spline to the universal potential [10]. The potentials proved successful in describing the bulk properties of the Ni±Al system [9]. The MD program used in this study was similar to that in [11]. In this model, classical equations of motion were set at atomic level and integrated by using the leapfrog form of the Verlet algorithm [12] with variable time step. Periodic boundary conditions were applied in the [1 0 0] and [0 1 0] orthogonal directions. The Ni substrate with [0 0 1] surface consisted of 12 layers of atoms. Each layer contained 288 atoms (12 12 unit cell). The Al13 of Ih symmetry was initially located at a sucient distance above the surface and had negligible interaction with the Ni atoms. In order to study the dependence of the structural and dynamical properties on deposition energy, we set the temperature of the substrate at 0 K. The Al13 of Ih symmetry was selected as the projectile cluster which is more stable, compared with Oh symmetry [13]. 3. Results and discussion By using the potentials, the binding energy of the Al13 of Ih symmetry was found to be 36.28 eV, which was consistent with other theoretical values [14±18]. Thus, we considered that it was appropriate to adopt the potentials to study the behavior of Al13 impacting on Ni surface. According to the structural and dynamical feature of the cluster on the surface, three impact energy regions have been identi®ed in the low-energy period. The ®rst one is de®ned as low±low energy (LLE), which is from 0.01 to 1 eV per atom, the second, low±medium energy (LME) from 2 to 10 eV per atom, and the third, low±high energy (LHE) from 11 to 30 eV per atom. At LLE, the cluster and the substrate surface are compressed slightly by the collision. Fig. 1
shows the snapshots of a typical event of softlanding with deposition energy of 0.01 eV/atom. At t 1:0 ps, the lower part of the cluster begins to change its structure. After relaxation, the Al cluster rearranges its structure from Ih symmetry into fcc-like structure without dissociation and resides on the Ni substrate as a bulk molecule. In Fig. 2, Ectr ; Ecin and Etin denote the kinetic energy of the cluster center of mass (CM), the internal energies of the cluster and the substrate, respectively; and DEcp and DEtp design the potential energy changes of the cluster and the substrate, respectively. It can be seen that, due to the attractive interaction between the cluster and the substrate, Ectr reaches the maximum value at t 0:9 ps, which is more than 20 times of its initial translational energy. Meanwhile, the potential energy of the cluster decreases rapidly until it reaches the minimum after t 2 ps, which is in accordance with the atomic position distribution presented in Fig. 1. It can be clearly seen from Figs. 1 and 2 that the structure rearrangement of the cluster occurs during 1±2 ps. The kinetic energy for rearrangement mainly comes from the decrease of DEcp which is attributed to the advantageous Ni±Al cohesive over the Al±Al [9] at the distance of the Al cluster approaching the Ni surface. Therefore, we conclude that the rearrangement of the cluster re¯ects the competition between the Ni±Al and Al±Al interaction. In addition, the stress, induced by the incommensurate structures between the cluster and the surface, is another factor to drive the cluster atoms to move into the stable sites. As a typical LME event, Figs. 3 and 4 present the snapshots, and the energy dissipation for a deposition with impinging energy of 6 eV/atom, respectively. In contrast to LLE, as the Al13 reaches the Ni surface at about 0.1 ps, it is deformed severely and then broken up. Some cluster atoms are migrated long distance outward from the impact point. The enhancement in DEcp , which corresponds to the severe deformation of the cluster, is compensated by the decrease of Ectr . We can see from Fig. 4 that the energy transfer takes place chie¯y in the short time interval (0.1±0.25 ps), which demonstrates that the energy transfer stems mainly from the collision cascade. This is
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
253
Fig. 1. Snapshots of an Al13 cluster of Ih symmetry impacting on an Ni(0 0 1) surface. The incident energy is 0.01 eV per atom. At each instant, the left shows the side view and the right for the top view. The black dots represent Ni atoms, and open circles for Al atoms.
Fig. 2. The variations of energies versus time for a 0.01 eV/atom Al13 cluster impacting on a Ni substrate. Ectr ; Ecin ; Etin ; DEcp and DEtp denote the translational energy, the internal energy of the Al cluster and the substrate, and the potential energy changes of the cluster and the substrate, respectively. The initial values of DEtp 0 and DEcp 0 at t 0 are adopted.
254
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
Fig. 3. The same as in Fig. 1, but for impact energy of 6 eV/atom.
Fig. 4. The same as in Fig. 2, but for impact energy of 6 eV/atom.
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
255
Table 1 The mean number of the adatoms, substitutions, sputtered atoms and re¯ected atoms observed at the end of the simulations for each eventa Ein (eV/atom) Ni adatoms Al adatoms Alsub in the 1st layer below surface Alsub in the 2nd layer below surface Alsub in the 3rd layer below surface Al re¯ected atoms Ni sputtered atoms a
12 4.6 5.9 4.4
15 6.8 6.1 5.8
0.5
0.8 0.2
18 8.8 8.9 6.0 1.1 0.1 0.9
20 8.4 4.3 5.1 1.0
25 10.0 3.5 5.5 2.4
1.3 0.2
1.1 1.5
30 9.3 3.7 5.0 2.0 0.6 1.7 4.4
Alsub denotes the Al subsitution.
fairly dierent from the LLE processes presented in Figs. 1 and 2. Also, at the end of the relaxation, the side-face atoms in the upper part (UP) of the cluster spread far away compared with those of the lower part (LP). The transverse mean spread [6] relative to the impact point is calculated to be 3:81a0 (a0 is the lattice constant of pure Ni metal) for the UP atoms and 1:94a0 for the LP atoms. We recall the mean separation of a free cluster is 0:73a0 . This feature can be understood as follows. The LP atoms reach the surface ®rstly. When the UP atoms arrive, they will also collide with the scattered LP atoms. Thus they may get more transverse momentum and move far away [19]. We perform the same simulation again, but ignore the interactions among the cluster atoms. In this case, the mean spread for atoms in the UP and the LP atoms are 1:38a0 and 1:59a0 , respectively. It suggests that the interactions among the cluster atoms play an important role on the transverse migration of the cluster atoms. It is worthwhile to note that only a few defects were observed at the deposition with LME condition. It means that a good Al epitaxy will be expected to grow in layer by layer at LME. At LHE, Al substitutions can be observed, whose number and depth distribution in the substrate increase with the impact energy. Consequently, some Ni atoms are ejected into the epitaxial layer. Due to the Al substitutions appearing in the second layer below the surface, vacancies are presented. Furthermore, re¯ected Al atoms and sputtered Ni atoms are also observed. The statistical results for eight events of each incident energy are listed in Table 1. It illustrates
that the energy for sputtering to occur is higher than that for re¯ecting. Meanwhile, no interstitial defects are created in our simulations, which is consistent with the expected by [6]. Substitutions generated in the simulations indicate that increasing energy can be helpful for surface alloying. Substrate temperature is another important factor, which will be discussed in our further work.
4. Conclusion This paper concentrated on exploring the structural and dynamical characteristics of Al cluster deposition on the Ni surface. We have found that the deposition energy can be divided into three ranges namely LLE, LME and LHE. At LLE, the cluster transforms into the fcc-like structure due to the strong Ni±Al cohesion. At LME, the collision cascade causes the cluster breaking up and spreading. When the deposition energy reaches LHE, the defects, such as Al substitutions and Ni ejections are observed. The atomic exchange between Al and Ni atoms indicates that increasing impact energy will be favourable to surface alloying.
Acknowledgements This work was mainly supported by National Nature Science Foundation of China under grant number 19875011, Postdoctoral Foundation of
256
Y.X. Wang et al. / Nucl. Instr. and Meth. in Phys. Res. B 180 (2001) 251±256
China, and Engineering-physics Research Institute Foundation of China. References [1] I. Yamada, H. Takaoka, H. Usui, T. Takagi, J. Vac. Sci. Technol. A 4 (1986) 722. [2] R. Beuhler, L. Friedman, Chem. Rev. 86 (1986) 521. [3] P. Beccat, J. Massardier, Catal. Lett. 9 (1991) 183. [4] J. Hayoz, D. Naumovic, R. Fasel, P. Aebi, L. Schlapbach, Surf. Sci. 373 (1997) 153. [5] W.G. Cullen, P.N. First, Surf. Sci. 420 (1999) 52. [6] H. Hsieh, R.S. Averback, H. Sellers, C.P. Flynn, Phys. Rev. B 45 (1992) 4417. [7] A. Bilic, B.V. King, D.J. O'Connor, Surf. Sci. 442 (1999) 256.
[8] G.J. Ackland, M.W. Finnis, V. Vitek, J. Phys. F 18 (1988) L153. [9] F. Gao, D.J. Bacon, G.J. Ackland, Philos. Mag. A 67 (1993) 275. [10] J.P. Biersack, J.F. Ziegler, J. Nucl. Instr. and Meth. 141 (1982) 93. [11] R.W. Lee, Z.Y. Pan, Y.K. Ho, Phys. Rev. B 53 (1996) 4156. [12] L. Verlet, Phys. Rev. A 159 (1967) 98. [13] D.Y. Sun, X.G. Gong, J. Phys.: Condens. Matter 9 (1997) 10555. [14] V. Kumar, V. Sundararajan, Phys. Rev. B 57 (1998) 4939. [15] X.C. Gong, V. Kumar, Phys. Rev. Lett. 70 (1993) 70. [16] S.N. Khanna, P. Jena, Phys. Rev. B 57 (1995) 705. [17] H.P. Cheng, R.S. Berry, R.L. Whetten, Phys. Rev. B 43 (1991) 10647. [18] J.Y. Yi, D.J. Oh, Bernholc, R. Car, Chem. Phys. Lett. 174 (1990) 461. [19] Z.Y. Pan, Phys. Lett. A 172 (1993) 378.