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Investigation of Lin, O–Lin and H–Lin interactions by molecular dynamics simulation methods
Journal of Physics and Chemistry of Solids 61 (2000) 689–694 www.elsevier.nl/locate/jpcs
Investigation of Lin, O–Lin and H–Lin interactions by molecular dynamics simulation methods I. Kara a,*, N. Kolsuz b a
Department of Physics, Burdur Education Faculty of S.D.U., 15100 Burdur, Turkey b Department of Physics, Pamukkale University, 20017 Denizli, Turkey Received 11 December 1998; accepted 15 September 1999
Abstract We have investigated the structures and energies of lithium microclusters containing 3–10 atoms in the bcc(100) and bcc(110) surface symmetries, and the interaction of an oxygen atom and a hydrogen atom with these lithium microclusters for the on-top, open and bridge sites. Calculations have been performed with Molecular Dynamics Simulation Methods (MDSM) at 1 K temperature. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: Molecular dynamics simulation methods
1. Introduction
energy of the pure lithium system was defined as follows:
Knowledge of the defects and electronic and thermodynamic features of a metal are of importance for its use in technology. Lithium is the simplest metal, with three electrons. Data on lithium microclusters and quantum mechanics calculations including the interaction between an oxygen atom, a hydrogen atom and lithium microclusters are available in the literature [1–3]. In addition, some calculation methods such as energy minimization, which require less computer calculation time and are simpler compared with quantum mechanics calculations, are also available [4,5]. The interaction of atoms and molecules with metal surfaces is a subject of great interest for both fundamental physics and technology [6,7]. As applications, we mention such fields as catalysis, corrosion of metals and nuclear reactor and hot fusion technologies. In this study, we have selected an empirical many-body potential energies function (PEF) which comprises two- and three-body atomic interactions [8]. The total interaction
Ftot BLi–Li
n X
n X
Uij rij 1 BLi–Li–Li
i,j
Wijk rij ; rik ; rjk 1
i,j,k
where Uij and Wijk express the two- and three-body interactions. rij is the interatomic distance between atoms i and j. BLi–Li and BLi–Li–Li are the two-body parameter for the lithium–lithium atom pairs and the three-body parameter for the lithium–lithium–lithium atom triplets, respectively. The total interaction energy of the M–Lin (M is O or H) system, and the chemisorption energy (or binding energy) of the M atom, respectively, were defined as follows:
Ftot BM–Li
n X
Uij rij 1 BLi–Li
i,j
1 BM–Li–Li
n X
Uij rij
i,j n X
Wijk rij ; rik ; rjk
i,j,k
1 BLi–Li–Li
n X
Wijk rij ; rik ; rjk
2
i,j,k
* Corresponding author. Tel.: 190-248-234-6000; fax: 190-248234-6005. E-mail address: [email protected] (I. Kara).
Fchem BM–Li
0022-3697/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(99)00311-X
n X i,j
Uij rij 1 BM–Li–Li
n X
Wijk rij ; rik ; rjk
i,j,k
3
690
I. Kara, N. Kolsuz / Journal of Physics and Chemistry of Solids 61 (2000) 689–694
Table 1 Parameters used in the calculations [3,4] (M is Li, O and H) Parameters
Li–Li
O–Li
H–Li
˚) ro (A 2e0 (eV) ˚) k (eV/A A (eV) n BM–Li BM–Li–Li
2.6729 1.040 1.593 4.16 0.953009759 0.47164059 20.86610413
1.6950 3.490 13.003 13.96 0.927167969 0.79981804 21.16009521
1.5927 2.4287 6.4029 9.7148 0.445763443 0.59337425 21.02554893
where BM–Li is the two-body parameter for the M(O or H)– lithium atom pair, and BM – Li – Li is the three-body parameter for the M(O or H)–lithium–lithium atom triplets. By using this PEF, the microclusters containing 3–7 atoms of various elements in different crystalline structures were studied and reasonable results were obtained [9–12]. Here, we have investigated the Lin, O–Lin and H–Lin n 3–10 interactions by means of Molecular Dynamics Simulation Methods (MDSM) at 1 K temperature. During the simulation the system was thermally equilibrated at a given temperature. The behaviour of the system (microclusters) has been investigated for 3000 time-steps (each
time step is 1:0 × 10214 s: In the first 1500 time-steps velocities of the particles were rescaled to the velocity with respect to the desired temperature, and in the last 1500 time-steps, the particles were set free completely for the system to be the most stable. First, we calculated the lattice constant and the average interaction energy per atom of lithium microclusters containing 3–10 atoms in bcc(100) and bcc(110) surface symmetries. Second, we calculated the chemisorption energy and the equilibrium-distance (oxygen or hydrogen atom–surface distance) of the M (O and H) atom. The potential parameters used in the calculations are given in Table 1. Each lithium microcluster is denoted by Lin(n1, n2, n3), where n is the total number of atoms in the microcluster and n1, n2, n3 are the number of atoms in the first, second and third layer, respectively. These systems have recently been studied by means of the unrestricted Hartree–Fock (UHF) method, many-body perturbation theory (MBPT) and energy minimization (EM).
2. Lin microclusters In this section we report the structures and energies of lithium microclusters containing 3–10 atoms in bcc(100)
Table 2 Calculated interatomic distance amin (in a.u.), average interaction energy per atom Eb (in kcal/mol) with the corresponding literature values of ˚) amin and Eb for the microclusters in bcc surface models. (1 a.u. 0.529177 A Microcluster
aminMDSM
bcc(100) surface model 5.56 Li3 (3, 0, 0) Li4 (4, 0, 0) 5.43 Li4 (2, 2, 0) 6.07 Li5 (5, 0, 0) 5.16 5.71 Li5 (4, 1, 0) Li6 (6, 0, 0) 5.21 Li6 (2, 2, 2) 6.18 Li8 (6, 2, 0) 5.60 Li9 (9, 0, 0) 5.77 5.85 Li9 (5, 4, 0) Li9 (4, 1, 4) 6.55 Li10 (5, 4, 1) 5.82 bcc(110) surface model Li3 (2, 1, 0) 5.56 6.68 Li4 (4, 0, 0) Li5 (5, 0, 0) 6.25 Li5 (4, 1, 0) 6.15 Li6 (6, 0, 0) 6.37 Li7 (7, 0, 0) 5.77 6.69 Li8 (6, 2, 0) Li9 (9, 0, 0) 6.90 Li9 (5, 4, 0) 6.53 Li10 (5, 4, 1) 6.69 a b
Ref. [4]. Ref. [3].
2EbMDSM
aminEM a
2EbEM a
aminMBPT b
2EbMBPT b
2EbUHF b
9.04 11.42 11.52 11.67 13.60 13.79 15.48 17.88 16.13 19.29 17.58 20.17
5.12 5.44 6.63 5.17 6.42 5.44 6.93 5.94 5.45 6.71 6.56 6.90
8.53 11.43 11.49 11.67 12.92 13.68 15.09 15.58 16.04 17.02 17.52 18.34
5.31 5.50 6.45 5.25 6.20 5.50 6.40 6.30 5.60 6.54 6.20 6.61
8.32 4.79 11.02 9.54 11.59 5.60 15.89 15.50 11.85 15.43 16.88 18.32
3.30 21.81 4.75 3.50 4.69 25.24 5.04 4.12 6.46 6.56 6.13 7.10
9.04 11.42 11.68 13.60 13.77 14.93 18.10 16.12 19.28 20.17
6.16 6.40 6.10 6.79 6.41 6.41 6.87 6.43 6.96 6.97
8.93 11.30 11.69 13.37 13.54 14.81 16.54 15.91 17.94 18.70
6.13 6.72 6.33 6.36 6.68 6.65 6.75 6.65 6.54 6.61
3.38 12.07 11.70 12.23 8.87 12.90 13.67 12.99 15.88 16.61
22.73 2.17 5.22 3.30 2.96 7.09 7.08 7.13 8.39 7.92
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Table 3 Calculated oxygen–surface distance, R (in a.u.), and oxygen chemisorption energy, Ec (in kcal/mol) in O–Lin microclusters with bcc surface models Microcluster
Rmin MDSM
bcc(100) surface model on-top O–Li5 (1,4,0) 3.32 3.31 O–Li5 (5,0,0) O–Li9 (5,4,0) 3.37 O–Li10 (5,4,1) 3.38 O–Li10 (1,4,5) 3.36 open-site O–Li4 (4,0,0) 0.10 O–Li5 (4,1,0) 0.51 O–Li9 (4,5,0) 0.24 0.31 O–Li9 (4,1,4) bridge O–Li2 (2,0,0) 2.08 O–Li4 (2,2,0) 22.18 22.03 O–Li8 (2,6,0) O–Li8 (6,2,0) 21.52 O–Li6 (2,2,2) 20.86 bcc(110) surface model on-top O–Li3 (1,2,0) 3.34 O–Li5 (1,4,0) 3.28 3.37 O–Li5 (5,0,0) O–Li7 (7,0,0) 3.30 O–Li9 (5,4,0) 3.41 O–Li10 (5,4,1) 3.40 3.31 O–Li10 (1,4,5) open-site O–Li3 (2,1,0) 21.78 O–Li4 (4,0,0) 0.80 O–Li5 (4,1,0) 21.08 21.70 O–Li9 (4,5,0) bridge O–Li2 (2,0,0) 1.10 O–Li8 (2,6,0) 22.70 O–Li8 (6,2,0) 21.09 a b
2Ec MDSM
Rmin EM a
2Ec EM a
Rmin MBPT b
2Ec MBPT b
63.22 63.19 63.03 62.95 62.78
3.20 3.09 3.19 3.20 3.21
63.90 85.80 66.70 65.80 63.40
3.21 3.07 3.34 2.90 3.44
58.70 57.50 19.20 25.90 47.90
167.70 164.52 151.95 163.28
0.00 0.14 0.01 0.11
169.80 158.30 144.30 149.40
0.00 0.12 0.00 0.22
181.70 156.00 126.50 144.20
113.90 174.65 170.50 161.15 160.41
2.10 21.65 21.67 21.61 22.18
111.00 175.90 171.50 171.50 174.00
1.31 21.60 21.41 21.74 21.35
131.50 194.00 169.50 169.50 160.10
63.91 64.13 63.54 64.02 63.10 63.19 63.99
3.20 3.21 3.10 3.12 3.17 3.17 3.21
63.80 63.30 83.50 79.90 71.90 71.80 63.40
3.95 3.21 3.50 3.34 3.37 3.45 3.28
31.80 58.70 42.60 49.40 75.90 80.40 62.50
153.67 158.59 177.52 159.77
21.05 0.01 21.11 21.20
149.20 154.50 174.00 166.40
21.10 0.00 20.96 20.50
190.70 132.70 173.20 152.90
112.12 189.54 194.51
2.48 22.52 22.46
107.90 172.10 172.20
1.31 22.14 22.64
131.50 174.90 174.90
Ref. [4]. Ref. [3].
and bcc(110) surface symmetries. We have considered the Lin systems that are the most stable systems studied with MBPT. The model microclusters were selected from Refs. [1–3]. Therefore, figures related to the microclusters considered are not shown here. In the application, we have calculated the interatomic distance, amin, and the average interaction energy per atom (or binding energy per atom), Eb Eb ET =n; for microcluster models in both bcc(100) and bcc(110) surface symmetries. We have considered a total of 22 different geometries from bcc(100) and bcc(110). For Lin microclusters in bcc surface symmetries, the present results and literature values are given in Table 2. For Lin(3–10) microclusters in bcc(100), the calculated
average interaction energies per atom vary between 9.04 and 20.17 kcal/mol. However, a variation between 5.56 and 6.55 a.u. in the lattice constant is observed. For the same surface symmetries, the average interaction energy per atom is determined to be between 4.79 and 18.32 kcal/mol, and the lattice constant as between 5.25 and 6.61 a.u. by MBPT. On the other hand, the corresponding values obtained by EM are 8.53–18.34 kcal/mol, and 5.12–6.93 a.u. In these surface symmetries, both the average interaction energies per atom and the lattice constant are in agreement with literature values. For the bcc structure, the lattice constant of lithium obtained by using the linear-combinations-ofGaussian-type-orbitals (LCGTO) method was 6.32 a.u. from the Rajagopar–Singhal–Kimball (RSK) model,
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Table 4 Calculated hydrogen–surface distance, R (in a.u.), and hydrogen chemisorption energy, Ec (in kcal/mol) in H–Lin microclusters with bcc surface models Microcluster
Rmin MDSM
bcc(100) surface model on-top H–Li5(1,4,0) 3.15 3.15 H–Li5(5,0,0) H–Li9(5,4,0) 3.20 H–Li10(5,4,1) 3.22 H–Li10(1,4,5) 3.22 open-site H–Li4(4,0,0) 0.05 H–Li5(4,1,0) 0.01 H–Li9(4,5,0) 0.07 20.27 H–Li9(4,1,4) bridge H–Li2(2,0,0) 1.74 H–Li4(2,2,0) 2.05 0.54 H–Li8(2,6,0) H–Li8(6,2,0) 1.18 bcc(110) surface model on-top H–Li3(1,2,0) 3.21 H–Li5(1,4,0) 3.26 H–Li5(5,0,0) 3.23 3.34 H–Li7(7,0,0) H–Li9(5,4,0) 3.39 H–Li10(5,4,1) 3.23 H–Li10(1,4,5) 3.23 open-site H–Li3(2,1,0) 2.50 H–Li4(4,0,0) 0.01 H–Li5(4,1,0) 1.92 H–Li9(4,5,0) 21.61 bridge 0.80 H–Li2(2,0,0) H–Li8(2,6,0) 20.99 H–Li8(6,2,0) 20.42 a b
2Ec MDSM
Rmin EM a
2Ec EM a
Rmin MBPT b
2EcMBPT b
2Ec UHF b
32.03 32.03 31.43 31.25 31.29
3.10 2.99 3.16 3.16 3.10
29.7 36.0 28.1 28.4 30.1
3.15 3.25 3.30 3.50 3.50
33.6 26.7 45.2 5.4 14.2
25.6 15.3 31.4 31.6 30.8
47.72 46.77 44.67 44.78
0.01 0.19 0.30 0.16
69.5 61.6 54.8 51.3
0.45 0.30 0.20 0.50
45.5 40.3 33.7 69.9
44.2 31.4 46.8 51.7
55.87 47.74 45.73 45.54
1.94 21.65 21.57 21.69
52.5 70.1 61.2 61.2
2.05 1.60 20.55 22.60
44.9 42.4 48.2 48.2
48.3 35.8 84.7 84.7
31.93 31.41 31.52 30.55 29.72 31.18 31.23
3.06 3.08 3.00 3.06 3.11 3.11 3.07
31.6 31.3 35.2 31.4 30.5 30.5 31.5
3.15 3.20 3.30 3.20 3.25 3.20 3.35
56.8 40.7 24.6 6.1 51.8 40.6 35.1
29.7 33.1 7.2 210.4 11.5 24.5 19.6
48.25 47.72 46.67 45.24
21.03 0.01 21.09 20.83
64.2 63.5 66.2 56.3
1.35 1.00 1.90 21.00
46.6 26.9 50.6 49.0
49.4 30.1 40.3 48.7
56.23 45.70 45.50
1.95 1.36 1.44
52.4 48.7 46.6
2.05 1.50 1.65
44.9 63.6 59.2
48.3 57.4 37.7
Ref. [5]. Ref. [15].
6.35 a.u. from the Hedin–Lundqvist (HL) model and 6.59 a.u. from the Kohn–Sham–Gaspar (KSG) model [13]. The experimental value for the bcc structure has been determined to be 6.58 a.u. by Anderson and Swenson [14]. The general trend is that the agreement between the present results and the experimental results increase as the number of atoms in the microcluster increases. For n $ 4; Lin nonplanar structures are usually more stable than planar structures. However, this state is n . 4 with respect to MBPT results. In general, the presence of the second-layer atoms enhances the microcluster stability. For Lin microclusters in bcc(110), the calculated average interaction energy per atom varied between 9.04 and 20.17 kcal/mol. However, the calculated lattice constant is between 5.56 and 6.9 a.u. For the same surface symmetries,
values between 3.38 and 16.61 kcal/mol for the average interaction energy per atom and between 6.13 and 6.75 a.u. for the lattice constant were obtained by Ray and Hira [15] with MBPT. Calculated average values of between 8.93 and 18.70 kcal/mol, and between 6.16 and 6.96 a.u. were obtained for the interaction energy per atom and the lattice constant, respectively, by Kolsuz et al. [4] by EM. In the bcc(110) surface symmetries, we have obtained the average lattice constant as 6.35 a.u. The calculated average interaction energies per atom and lattice constants are in agreement with literature values. In the bcc(110) surface symmetries, Lin nonplanar structures are usually more stable than planar structures. In the bcc(100) and bcc(110) surface symmetries, the values of the lithium microclusters support one another
I. Kara, N. Kolsuz / Journal of Physics and Chemistry of Solids 61 (2000) 689–694
with MDSM. The overall trend in our average interaction energies per atom showed an increase in stability with increase of microcluster size, until at n 10 we recovered 53.5% (20.17 kcal/mol) of the cohesive energy of bulk lithium. The experimental value is known to be 37.7 kcal/ mol [16]. The Li10 microcluster is the most stable in the bcc(100) and bcc(110) surface symmetries. The calculated lattice constants of microclusters are in agreement with experimental and theoretical results. The crystallographic structure of lithium metal, in real situations, is bcc(110) surface symmetries [16].
3. Interaction of an oxygen atom with Lin microclusters In this section, we have investigated the interaction between an oxygen atom and Lin microclusters at bcc(100) and bcc(110) surface symmetries. The O–Lin systems can be classified into three categories based on the position of approach of the oxygen atom: the on-top position, the open-site position, and the bridge position. The idea here is to model the peaks, valleys and ridges in the irregularities on the metal surface by the on-top, opensite and bridge positions, respectively. For O–Lin microclusters, the equilibrium distance (oxygen–surface distance), R, the chemisorption energy of the oxygen atom, Ec, and the literature values for bcc(100) and bcc(110) surface models are given in Table 3. We have calculated the average equilibrium distance, R, of the oxygen atom from the closest lithium microcluster plane to be 3.33, 0.29 and 20.90 a.u. on the bcc(100) surface for the on-top, open-site and bridge positions, respectively. However, the corresponding average chemisorption energy of the oxygen atom is calculated as 63.24, 161.86 and 156.12 kcal/mol, respectively, for the on-top, open-site and bridge positions. For the on-top, open-site and bridge positions, Kolsuz et al. [4] reported the average equilibrium distance as 3.18, 0.07 and 21.0 a.u.; and the chemisorption energy as 68.33, 155.45 and 160.77 kcal/ mol of an oxygen atom on bcc(100) surface symmetries. Hira and Ray [3] reported the average equilibrium distance as 3.15, 0.08 and 20.96 a.u.; and the average chemisorption energy as 38.60, 152.09 and 164.94 kcal/mol for an oxygen atom on a bcc(100) surface on these positions. Hermann and Bagus [1] reported values of 3.22, 20.02 and 21.52 a.u., for the average equilibrium distance and 33.9, 62.3 and 99.4 kcal/mol for the average chemisorption energy of an oxygen atom on a bcc(100) surface for the same positions. We have calculated the average equilibrium distance, R, of an oxygen atom from the closest lithium microcluster plane as 3.33, 20.76 and 20.89 a.u. on the bcc(110) surface, respectively for the on-top, open-site and bridge sites. However, the average chemisorption energy of the oxygen atom is calculated as 63.76, 162.38 and 165.39 kcal/mol, for the same positions. For the on-top, open-site and bridge positions, Kolsuz et al. [4] reported
693
the average equilibrium distance as 3.17, 20.83 and 20.83 a.u., and the average chemisorption energy as 70.25, 161.02 and 150.73 kcal/mol on bcc(100) surface symmetries. Hira and Ray [3] reported the average equilibrium distance as 3.38, 20.64 and 21.15 a.u.; and the average chemisorption energy as 59.93, 161.37 and 160.43 kcal/mol for an oxygen atom on a bcc(100) surface at these positions. Negative values of R denote penetration of the oxygen atom into the microcluster. The general trend is that agreement between the present MDSM results and the EM and MBPT results is not bad. The agreement for distances is better than that for energies. The agreement in energy between the present MDSM results and EM results is better than that of MBPT and EM.
4. Interaction of a hydrogen atom with Lin microclusters In this section, we investigate the interaction between a hydrogen atom and Lin microclusters at bcc(100) and bcc(110) surface symmetries. For the H–Lin microcluster, the equilibrium distance (hydrogen–surface distance), R, the chemisorption energy of the hydrogen atom, Ec, and the literature values for bcc(100) and bcc(110) surface models are given in Table 4. We have calculated the average equilibrium distance, R, of a hydrogen atom from the closest lithium microcluster plane on a bcc(100) surface to be 3.16, 0.11 and 1.37 a.u., respectively, for the on-top, open-site and bridge positions. However, the average chemisorption energy of hydrogen atom is calculated to be 31.87, 45.98 and 48.72 kcal/mol, for the same positions. For these positions, Kolsuz and Erkoc¸ [5] reported the average equilibrium distance as 3.08, 0.17 and 20.74 a.u., and the average chemisorption energy as 30.91, 59.32 and 61.25 kcal/mol. Hira and Ray [15] reported the average equilibrium distance as 3.30, 0.36 and 0.12 a.u.; and the chemisorption energy as 28.08, 47.35 and 45.92 kcal/mol for a hydrogen atom on a bcc(100) surface at these positions. Pacchioni and Koutecky [17] reported the average chemisorption energy as 56.6 kcal/ mol for a hydrogen atom on a bcc(100) surface for the on-top sites. The experimental distance in the H–Li system has been determined as the equilibrium distance with value 6.58 a.u., and the chemisorption energy as 57.7 kcal/mol [18]. We have calculated the average equilibrium distance, R, of a hydrogen atom from the closest lithium microcluster plane on a bcc(110) surface to be 3.24, 0.71 and 20.20 a.u., respectively, for the on-top, open-site and bridge sites. However, the corresponding average chemisorption energies are calculated as 31.34, 46.97 and 49.14 kcal/ mol, for the on-top, open-site and bridge positions. Kolsuz and Erkoc¸ [5] reported the average equilibrium distance to be 3.07, 20.74 and 1.58 a.u.; and the average chemisorption energy to be 31.90, 62.54 and 49.23 kcal/mol for the
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hydrogen atom on bcc(110) surface symmetries. Hira and Ray [3] reported values of 3.22, 0.81 and 1.73 a.u. for the average equilibrium distance and 37.38, 43.27 and 55.90 kcal/mol for the average chemisorption energy of hydrogen atom on a bcc(110) surface for the on-top, open-site and bridge sites, respectively. In both surfaces, the hydrogen on-top position is energetically least favourable. In the bcc(100) and bcc(110) surface, the order of value of the chemisorption energy in the three positions is as Eon-top , Eopen , Ebridge : Clearly, the on-top approach is the least suitable for chemisorption, while the open and the bridge positions are the most suited. We conclude that the ridges in the surface irregularities on the metallic surface of lithium are the best sites for adsorption, while adsorption is weakest at the peaks. When the M(O or H)–Lin interactions were examined with EM the M atoms were placed in three different positions on the Lin microclusters which had bcc symmetry, and the atoms of the Lin microcluster were held stable in the interaction, only the M atom being allowed to get close to the cluster surface. This approach was performed during the study. In fact, from a study of the interaction of the M atom and atoms of the Lin microcluster, the stable structure of Lin is disturbed and the interaction continues until the M–Lin system comes to a decisive structure. This kind of a study in literature has been performed with the unrestricted Hartree–Fock (UHF) method, many-body perturbation theory (MBPT) and energy minimisation (EM). The UHF method and the MBPT depend on quantum mechanic calculations. The results of these methods are time consuming and difficult as well as being valid. In the EM has been performed a energy minimisation with an empirical many-body potential energies function (PEF) which comprises two- and three-body atomic interactions. In this study, the Lin microclusters have been held stable in the interaction and only the M atom was allowed to get close to the cluster surface. This is an approach performed during
the study. As for MDSM, the same potential energies function was used, and the system was completely set free and nothing was applied as limit condition during the study. In the MDSM the M atom and Lin microcluster were released, allowing the M–Lin system to reach a stable structure and thereafter the distance of the M atom to be tied to the surface and the chemisorption energies of the M atom were calculated. We are in the belief that this model is more physical. General trends are of our results are in agreement with the results of literature.
References [1] K. Hermann, P.S. Bagus, Phys. Rev. B 17 (10) (1977) 4082– 4099. [2] A.S. Hira, A.K. Ray, Surf. Sci. 234 (1990) 397–411. [3] A.S. Hira, A.K. Ray, J. Phys. B: At. Mol. Opt. Phys. 24 (1991) 881–896. [4] N. Kolsuz, M. C ¸ ivi, S. Erkoc¸, Mod. Phys. Lett. A 10 (2) (1995) 125. [5] N. Kolsuz, S. Erkoc¸, J. Sci. Engng (University of Firat) 5 (1) (1993) 89. [6] R. Gomer, Chemisorption on Metals, Solid State Phys. Ser., , 1975, pp. 30. [7] N.H. March, Chemical Bounds Outside Metal Surfaces, Plenum, New York, 1986. [8] S. Erkoc¸, Phys. Status. Solidi B 152 (1989) 447. [9] S. Erkoc¸, Chem. Phys. Lett. 173 (1) (1990) 57. [10] Y. Tahtamoni, S. Erkoc¸, Phys. Stat. Sol. (b) 156 (K5) (1990) 162. [11] S. Erkoc¸, Phys. Status. Solid B 161 (1990) 211. [12] S. Erkoc¸, Atom Molecules and Microclusters 19 (1991) 423. [13] J.C. Boettger, S.B. Trickey, Phys. Rev. B 32 (6) (1985) 3391. [14] M.S. Anderson, C.A. Swenson, Phys. Rev. 159 (1) (1985) 98. [15] A.K. Ray, A.S. Hira, Phys. Rev. B 37 (17) (1988) 9943. [16] H.-O. Beckmann, J. Koutecky, Surf. Sci. 120 (1982) 127. [17] J. Pacchioni, Koutecky, Surf. Sci. 144 (1984) 602. [18] C. Kittel, Introduction to Solid State Physics, 8, Wiley, New York, 1984.
Investigation of Lin, O–Lin and H–Lin interactions by molecular dynamics simulation methods I. Kara a,*, N. Kolsuz b a
Department of Physics, Burdur Education Faculty of S.D.U., 15100 Burdur, Turkey b Department of Physics, Pamukkale University, 20017 Denizli, Turkey Received 11 December 1998; accepted 15 September 1999
Abstract We have investigated the structures and energies of lithium microclusters containing 3–10 atoms in the bcc(100) and bcc(110) surface symmetries, and the interaction of an oxygen atom and a hydrogen atom with these lithium microclusters for the on-top, open and bridge sites. Calculations have been performed with Molecular Dynamics Simulation Methods (MDSM) at 1 K temperature. q 2000 Elsevier Science Ltd. All rights reserved. Keywords: Molecular dynamics simulation methods
1. Introduction
energy of the pure lithium system was defined as follows:
Knowledge of the defects and electronic and thermodynamic features of a metal are of importance for its use in technology. Lithium is the simplest metal, with three electrons. Data on lithium microclusters and quantum mechanics calculations including the interaction between an oxygen atom, a hydrogen atom and lithium microclusters are available in the literature [1–3]. In addition, some calculation methods such as energy minimization, which require less computer calculation time and are simpler compared with quantum mechanics calculations, are also available [4,5]. The interaction of atoms and molecules with metal surfaces is a subject of great interest for both fundamental physics and technology [6,7]. As applications, we mention such fields as catalysis, corrosion of metals and nuclear reactor and hot fusion technologies. In this study, we have selected an empirical many-body potential energies function (PEF) which comprises two- and three-body atomic interactions [8]. The total interaction
Ftot BLi–Li
n X
n X
Uij rij 1 BLi–Li–Li
i,j
Wijk rij ; rik ; rjk 1
i,j,k
where Uij and Wijk express the two- and three-body interactions. rij is the interatomic distance between atoms i and j. BLi–Li and BLi–Li–Li are the two-body parameter for the lithium–lithium atom pairs and the three-body parameter for the lithium–lithium–lithium atom triplets, respectively. The total interaction energy of the M–Lin (M is O or H) system, and the chemisorption energy (or binding energy) of the M atom, respectively, were defined as follows:
Ftot BM–Li
n X
Uij rij 1 BLi–Li
i,j
1 BM–Li–Li
n X
Uij rij
i,j n X
Wijk rij ; rik ; rjk
i,j,k
1 BLi–Li–Li
n X
Wijk rij ; rik ; rjk
2
i,j,k
* Corresponding author. Tel.: 190-248-234-6000; fax: 190-248234-6005. E-mail address: [email protected] (I. Kara).
Fchem BM–Li
0022-3697/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved. PII: S0022-369 7(99)00311-X
n X i,j
Uij rij 1 BM–Li–Li
n X
Wijk rij ; rik ; rjk
i,j,k
3
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I. Kara, N. Kolsuz / Journal of Physics and Chemistry of Solids 61 (2000) 689–694
Table 1 Parameters used in the calculations [3,4] (M is Li, O and H) Parameters
Li–Li
O–Li
H–Li
˚) ro (A 2e0 (eV) ˚) k (eV/A A (eV) n BM–Li BM–Li–Li
2.6729 1.040 1.593 4.16 0.953009759 0.47164059 20.86610413
1.6950 3.490 13.003 13.96 0.927167969 0.79981804 21.16009521
1.5927 2.4287 6.4029 9.7148 0.445763443 0.59337425 21.02554893
where BM–Li is the two-body parameter for the M(O or H)– lithium atom pair, and BM – Li – Li is the three-body parameter for the M(O or H)–lithium–lithium atom triplets. By using this PEF, the microclusters containing 3–7 atoms of various elements in different crystalline structures were studied and reasonable results were obtained [9–12]. Here, we have investigated the Lin, O–Lin and H–Lin n 3–10 interactions by means of Molecular Dynamics Simulation Methods (MDSM) at 1 K temperature. During the simulation the system was thermally equilibrated at a given temperature. The behaviour of the system (microclusters) has been investigated for 3000 time-steps (each
time step is 1:0 × 10214 s: In the first 1500 time-steps velocities of the particles were rescaled to the velocity with respect to the desired temperature, and in the last 1500 time-steps, the particles were set free completely for the system to be the most stable. First, we calculated the lattice constant and the average interaction energy per atom of lithium microclusters containing 3–10 atoms in bcc(100) and bcc(110) surface symmetries. Second, we calculated the chemisorption energy and the equilibrium-distance (oxygen or hydrogen atom–surface distance) of the M (O and H) atom. The potential parameters used in the calculations are given in Table 1. Each lithium microcluster is denoted by Lin(n1, n2, n3), where n is the total number of atoms in the microcluster and n1, n2, n3 are the number of atoms in the first, second and third layer, respectively. These systems have recently been studied by means of the unrestricted Hartree–Fock (UHF) method, many-body perturbation theory (MBPT) and energy minimization (EM).
2. Lin microclusters In this section we report the structures and energies of lithium microclusters containing 3–10 atoms in bcc(100)
Table 2 Calculated interatomic distance amin (in a.u.), average interaction energy per atom Eb (in kcal/mol) with the corresponding literature values of ˚) amin and Eb for the microclusters in bcc surface models. (1 a.u. 0.529177 A Microcluster
aminMDSM
bcc(100) surface model 5.56 Li3 (3, 0, 0) Li4 (4, 0, 0) 5.43 Li4 (2, 2, 0) 6.07 Li5 (5, 0, 0) 5.16 5.71 Li5 (4, 1, 0) Li6 (6, 0, 0) 5.21 Li6 (2, 2, 2) 6.18 Li8 (6, 2, 0) 5.60 Li9 (9, 0, 0) 5.77 5.85 Li9 (5, 4, 0) Li9 (4, 1, 4) 6.55 Li10 (5, 4, 1) 5.82 bcc(110) surface model Li3 (2, 1, 0) 5.56 6.68 Li4 (4, 0, 0) Li5 (5, 0, 0) 6.25 Li5 (4, 1, 0) 6.15 Li6 (6, 0, 0) 6.37 Li7 (7, 0, 0) 5.77 6.69 Li8 (6, 2, 0) Li9 (9, 0, 0) 6.90 Li9 (5, 4, 0) 6.53 Li10 (5, 4, 1) 6.69 a b
Ref. [4]. Ref. [3].
2EbMDSM
aminEM a
2EbEM a
aminMBPT b
2EbMBPT b
2EbUHF b
9.04 11.42 11.52 11.67 13.60 13.79 15.48 17.88 16.13 19.29 17.58 20.17
5.12 5.44 6.63 5.17 6.42 5.44 6.93 5.94 5.45 6.71 6.56 6.90
8.53 11.43 11.49 11.67 12.92 13.68 15.09 15.58 16.04 17.02 17.52 18.34
5.31 5.50 6.45 5.25 6.20 5.50 6.40 6.30 5.60 6.54 6.20 6.61
8.32 4.79 11.02 9.54 11.59 5.60 15.89 15.50 11.85 15.43 16.88 18.32
3.30 21.81 4.75 3.50 4.69 25.24 5.04 4.12 6.46 6.56 6.13 7.10
9.04 11.42 11.68 13.60 13.77 14.93 18.10 16.12 19.28 20.17
6.16 6.40 6.10 6.79 6.41 6.41 6.87 6.43 6.96 6.97
8.93 11.30 11.69 13.37 13.54 14.81 16.54 15.91 17.94 18.70
6.13 6.72 6.33 6.36 6.68 6.65 6.75 6.65 6.54 6.61
3.38 12.07 11.70 12.23 8.87 12.90 13.67 12.99 15.88 16.61
22.73 2.17 5.22 3.30 2.96 7.09 7.08 7.13 8.39 7.92
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Table 3 Calculated oxygen–surface distance, R (in a.u.), and oxygen chemisorption energy, Ec (in kcal/mol) in O–Lin microclusters with bcc surface models Microcluster
Rmin MDSM
bcc(100) surface model on-top O–Li5 (1,4,0) 3.32 3.31 O–Li5 (5,0,0) O–Li9 (5,4,0) 3.37 O–Li10 (5,4,1) 3.38 O–Li10 (1,4,5) 3.36 open-site O–Li4 (4,0,0) 0.10 O–Li5 (4,1,0) 0.51 O–Li9 (4,5,0) 0.24 0.31 O–Li9 (4,1,4) bridge O–Li2 (2,0,0) 2.08 O–Li4 (2,2,0) 22.18 22.03 O–Li8 (2,6,0) O–Li8 (6,2,0) 21.52 O–Li6 (2,2,2) 20.86 bcc(110) surface model on-top O–Li3 (1,2,0) 3.34 O–Li5 (1,4,0) 3.28 3.37 O–Li5 (5,0,0) O–Li7 (7,0,0) 3.30 O–Li9 (5,4,0) 3.41 O–Li10 (5,4,1) 3.40 3.31 O–Li10 (1,4,5) open-site O–Li3 (2,1,0) 21.78 O–Li4 (4,0,0) 0.80 O–Li5 (4,1,0) 21.08 21.70 O–Li9 (4,5,0) bridge O–Li2 (2,0,0) 1.10 O–Li8 (2,6,0) 22.70 O–Li8 (6,2,0) 21.09 a b
2Ec MDSM
Rmin EM a
2Ec EM a
Rmin MBPT b
2Ec MBPT b
63.22 63.19 63.03 62.95 62.78
3.20 3.09 3.19 3.20 3.21
63.90 85.80 66.70 65.80 63.40
3.21 3.07 3.34 2.90 3.44
58.70 57.50 19.20 25.90 47.90
167.70 164.52 151.95 163.28
0.00 0.14 0.01 0.11
169.80 158.30 144.30 149.40
0.00 0.12 0.00 0.22
181.70 156.00 126.50 144.20
113.90 174.65 170.50 161.15 160.41
2.10 21.65 21.67 21.61 22.18
111.00 175.90 171.50 171.50 174.00
1.31 21.60 21.41 21.74 21.35
131.50 194.00 169.50 169.50 160.10
63.91 64.13 63.54 64.02 63.10 63.19 63.99
3.20 3.21 3.10 3.12 3.17 3.17 3.21
63.80 63.30 83.50 79.90 71.90 71.80 63.40
3.95 3.21 3.50 3.34 3.37 3.45 3.28
31.80 58.70 42.60 49.40 75.90 80.40 62.50
153.67 158.59 177.52 159.77
21.05 0.01 21.11 21.20
149.20 154.50 174.00 166.40
21.10 0.00 20.96 20.50
190.70 132.70 173.20 152.90
112.12 189.54 194.51
2.48 22.52 22.46
107.90 172.10 172.20
1.31 22.14 22.64
131.50 174.90 174.90
Ref. [4]. Ref. [3].
and bcc(110) surface symmetries. We have considered the Lin systems that are the most stable systems studied with MBPT. The model microclusters were selected from Refs. [1–3]. Therefore, figures related to the microclusters considered are not shown here. In the application, we have calculated the interatomic distance, amin, and the average interaction energy per atom (or binding energy per atom), Eb Eb ET =n; for microcluster models in both bcc(100) and bcc(110) surface symmetries. We have considered a total of 22 different geometries from bcc(100) and bcc(110). For Lin microclusters in bcc surface symmetries, the present results and literature values are given in Table 2. For Lin(3–10) microclusters in bcc(100), the calculated
average interaction energies per atom vary between 9.04 and 20.17 kcal/mol. However, a variation between 5.56 and 6.55 a.u. in the lattice constant is observed. For the same surface symmetries, the average interaction energy per atom is determined to be between 4.79 and 18.32 kcal/mol, and the lattice constant as between 5.25 and 6.61 a.u. by MBPT. On the other hand, the corresponding values obtained by EM are 8.53–18.34 kcal/mol, and 5.12–6.93 a.u. In these surface symmetries, both the average interaction energies per atom and the lattice constant are in agreement with literature values. For the bcc structure, the lattice constant of lithium obtained by using the linear-combinations-ofGaussian-type-orbitals (LCGTO) method was 6.32 a.u. from the Rajagopar–Singhal–Kimball (RSK) model,
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Table 4 Calculated hydrogen–surface distance, R (in a.u.), and hydrogen chemisorption energy, Ec (in kcal/mol) in H–Lin microclusters with bcc surface models Microcluster
Rmin MDSM
bcc(100) surface model on-top H–Li5(1,4,0) 3.15 3.15 H–Li5(5,0,0) H–Li9(5,4,0) 3.20 H–Li10(5,4,1) 3.22 H–Li10(1,4,5) 3.22 open-site H–Li4(4,0,0) 0.05 H–Li5(4,1,0) 0.01 H–Li9(4,5,0) 0.07 20.27 H–Li9(4,1,4) bridge H–Li2(2,0,0) 1.74 H–Li4(2,2,0) 2.05 0.54 H–Li8(2,6,0) H–Li8(6,2,0) 1.18 bcc(110) surface model on-top H–Li3(1,2,0) 3.21 H–Li5(1,4,0) 3.26 H–Li5(5,0,0) 3.23 3.34 H–Li7(7,0,0) H–Li9(5,4,0) 3.39 H–Li10(5,4,1) 3.23 H–Li10(1,4,5) 3.23 open-site H–Li3(2,1,0) 2.50 H–Li4(4,0,0) 0.01 H–Li5(4,1,0) 1.92 H–Li9(4,5,0) 21.61 bridge 0.80 H–Li2(2,0,0) H–Li8(2,6,0) 20.99 H–Li8(6,2,0) 20.42 a b
2Ec MDSM
Rmin EM a
2Ec EM a
Rmin MBPT b
2EcMBPT b
2Ec UHF b
32.03 32.03 31.43 31.25 31.29
3.10 2.99 3.16 3.16 3.10
29.7 36.0 28.1 28.4 30.1
3.15 3.25 3.30 3.50 3.50
33.6 26.7 45.2 5.4 14.2
25.6 15.3 31.4 31.6 30.8
47.72 46.77 44.67 44.78
0.01 0.19 0.30 0.16
69.5 61.6 54.8 51.3
0.45 0.30 0.20 0.50
45.5 40.3 33.7 69.9
44.2 31.4 46.8 51.7
55.87 47.74 45.73 45.54
1.94 21.65 21.57 21.69
52.5 70.1 61.2 61.2
2.05 1.60 20.55 22.60
44.9 42.4 48.2 48.2
48.3 35.8 84.7 84.7
31.93 31.41 31.52 30.55 29.72 31.18 31.23
3.06 3.08 3.00 3.06 3.11 3.11 3.07
31.6 31.3 35.2 31.4 30.5 30.5 31.5
3.15 3.20 3.30 3.20 3.25 3.20 3.35
56.8 40.7 24.6 6.1 51.8 40.6 35.1
29.7 33.1 7.2 210.4 11.5 24.5 19.6
48.25 47.72 46.67 45.24
21.03 0.01 21.09 20.83
64.2 63.5 66.2 56.3
1.35 1.00 1.90 21.00
46.6 26.9 50.6 49.0
49.4 30.1 40.3 48.7
56.23 45.70 45.50
1.95 1.36 1.44
52.4 48.7 46.6
2.05 1.50 1.65
44.9 63.6 59.2
48.3 57.4 37.7
Ref. [5]. Ref. [15].
6.35 a.u. from the Hedin–Lundqvist (HL) model and 6.59 a.u. from the Kohn–Sham–Gaspar (KSG) model [13]. The experimental value for the bcc structure has been determined to be 6.58 a.u. by Anderson and Swenson [14]. The general trend is that the agreement between the present results and the experimental results increase as the number of atoms in the microcluster increases. For n $ 4; Lin nonplanar structures are usually more stable than planar structures. However, this state is n . 4 with respect to MBPT results. In general, the presence of the second-layer atoms enhances the microcluster stability. For Lin microclusters in bcc(110), the calculated average interaction energy per atom varied between 9.04 and 20.17 kcal/mol. However, the calculated lattice constant is between 5.56 and 6.9 a.u. For the same surface symmetries,
values between 3.38 and 16.61 kcal/mol for the average interaction energy per atom and between 6.13 and 6.75 a.u. for the lattice constant were obtained by Ray and Hira [15] with MBPT. Calculated average values of between 8.93 and 18.70 kcal/mol, and between 6.16 and 6.96 a.u. were obtained for the interaction energy per atom and the lattice constant, respectively, by Kolsuz et al. [4] by EM. In the bcc(110) surface symmetries, we have obtained the average lattice constant as 6.35 a.u. The calculated average interaction energies per atom and lattice constants are in agreement with literature values. In the bcc(110) surface symmetries, Lin nonplanar structures are usually more stable than planar structures. In the bcc(100) and bcc(110) surface symmetries, the values of the lithium microclusters support one another
I. Kara, N. Kolsuz / Journal of Physics and Chemistry of Solids 61 (2000) 689–694
with MDSM. The overall trend in our average interaction energies per atom showed an increase in stability with increase of microcluster size, until at n 10 we recovered 53.5% (20.17 kcal/mol) of the cohesive energy of bulk lithium. The experimental value is known to be 37.7 kcal/ mol [16]. The Li10 microcluster is the most stable in the bcc(100) and bcc(110) surface symmetries. The calculated lattice constants of microclusters are in agreement with experimental and theoretical results. The crystallographic structure of lithium metal, in real situations, is bcc(110) surface symmetries [16].
3. Interaction of an oxygen atom with Lin microclusters In this section, we have investigated the interaction between an oxygen atom and Lin microclusters at bcc(100) and bcc(110) surface symmetries. The O–Lin systems can be classified into three categories based on the position of approach of the oxygen atom: the on-top position, the open-site position, and the bridge position. The idea here is to model the peaks, valleys and ridges in the irregularities on the metal surface by the on-top, opensite and bridge positions, respectively. For O–Lin microclusters, the equilibrium distance (oxygen–surface distance), R, the chemisorption energy of the oxygen atom, Ec, and the literature values for bcc(100) and bcc(110) surface models are given in Table 3. We have calculated the average equilibrium distance, R, of the oxygen atom from the closest lithium microcluster plane to be 3.33, 0.29 and 20.90 a.u. on the bcc(100) surface for the on-top, open-site and bridge positions, respectively. However, the corresponding average chemisorption energy of the oxygen atom is calculated as 63.24, 161.86 and 156.12 kcal/mol, respectively, for the on-top, open-site and bridge positions. For the on-top, open-site and bridge positions, Kolsuz et al. [4] reported the average equilibrium distance as 3.18, 0.07 and 21.0 a.u.; and the chemisorption energy as 68.33, 155.45 and 160.77 kcal/ mol of an oxygen atom on bcc(100) surface symmetries. Hira and Ray [3] reported the average equilibrium distance as 3.15, 0.08 and 20.96 a.u.; and the average chemisorption energy as 38.60, 152.09 and 164.94 kcal/mol for an oxygen atom on a bcc(100) surface on these positions. Hermann and Bagus [1] reported values of 3.22, 20.02 and 21.52 a.u., for the average equilibrium distance and 33.9, 62.3 and 99.4 kcal/mol for the average chemisorption energy of an oxygen atom on a bcc(100) surface for the same positions. We have calculated the average equilibrium distance, R, of an oxygen atom from the closest lithium microcluster plane as 3.33, 20.76 and 20.89 a.u. on the bcc(110) surface, respectively for the on-top, open-site and bridge sites. However, the average chemisorption energy of the oxygen atom is calculated as 63.76, 162.38 and 165.39 kcal/mol, for the same positions. For the on-top, open-site and bridge positions, Kolsuz et al. [4] reported
693
the average equilibrium distance as 3.17, 20.83 and 20.83 a.u., and the average chemisorption energy as 70.25, 161.02 and 150.73 kcal/mol on bcc(100) surface symmetries. Hira and Ray [3] reported the average equilibrium distance as 3.38, 20.64 and 21.15 a.u.; and the average chemisorption energy as 59.93, 161.37 and 160.43 kcal/mol for an oxygen atom on a bcc(100) surface at these positions. Negative values of R denote penetration of the oxygen atom into the microcluster. The general trend is that agreement between the present MDSM results and the EM and MBPT results is not bad. The agreement for distances is better than that for energies. The agreement in energy between the present MDSM results and EM results is better than that of MBPT and EM.
4. Interaction of a hydrogen atom with Lin microclusters In this section, we investigate the interaction between a hydrogen atom and Lin microclusters at bcc(100) and bcc(110) surface symmetries. For the H–Lin microcluster, the equilibrium distance (hydrogen–surface distance), R, the chemisorption energy of the hydrogen atom, Ec, and the literature values for bcc(100) and bcc(110) surface models are given in Table 4. We have calculated the average equilibrium distance, R, of a hydrogen atom from the closest lithium microcluster plane on a bcc(100) surface to be 3.16, 0.11 and 1.37 a.u., respectively, for the on-top, open-site and bridge positions. However, the average chemisorption energy of hydrogen atom is calculated to be 31.87, 45.98 and 48.72 kcal/mol, for the same positions. For these positions, Kolsuz and Erkoc¸ [5] reported the average equilibrium distance as 3.08, 0.17 and 20.74 a.u., and the average chemisorption energy as 30.91, 59.32 and 61.25 kcal/mol. Hira and Ray [15] reported the average equilibrium distance as 3.30, 0.36 and 0.12 a.u.; and the chemisorption energy as 28.08, 47.35 and 45.92 kcal/mol for a hydrogen atom on a bcc(100) surface at these positions. Pacchioni and Koutecky [17] reported the average chemisorption energy as 56.6 kcal/ mol for a hydrogen atom on a bcc(100) surface for the on-top sites. The experimental distance in the H–Li system has been determined as the equilibrium distance with value 6.58 a.u., and the chemisorption energy as 57.7 kcal/mol [18]. We have calculated the average equilibrium distance, R, of a hydrogen atom from the closest lithium microcluster plane on a bcc(110) surface to be 3.24, 0.71 and 20.20 a.u., respectively, for the on-top, open-site and bridge sites. However, the corresponding average chemisorption energies are calculated as 31.34, 46.97 and 49.14 kcal/ mol, for the on-top, open-site and bridge positions. Kolsuz and Erkoc¸ [5] reported the average equilibrium distance to be 3.07, 20.74 and 1.58 a.u.; and the average chemisorption energy to be 31.90, 62.54 and 49.23 kcal/mol for the
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hydrogen atom on bcc(110) surface symmetries. Hira and Ray [3] reported values of 3.22, 0.81 and 1.73 a.u. for the average equilibrium distance and 37.38, 43.27 and 55.90 kcal/mol for the average chemisorption energy of hydrogen atom on a bcc(110) surface for the on-top, open-site and bridge sites, respectively. In both surfaces, the hydrogen on-top position is energetically least favourable. In the bcc(100) and bcc(110) surface, the order of value of the chemisorption energy in the three positions is as Eon-top , Eopen , Ebridge : Clearly, the on-top approach is the least suitable for chemisorption, while the open and the bridge positions are the most suited. We conclude that the ridges in the surface irregularities on the metallic surface of lithium are the best sites for adsorption, while adsorption is weakest at the peaks. When the M(O or H)–Lin interactions were examined with EM the M atoms were placed in three different positions on the Lin microclusters which had bcc symmetry, and the atoms of the Lin microcluster were held stable in the interaction, only the M atom being allowed to get close to the cluster surface. This approach was performed during the study. In fact, from a study of the interaction of the M atom and atoms of the Lin microcluster, the stable structure of Lin is disturbed and the interaction continues until the M–Lin system comes to a decisive structure. This kind of a study in literature has been performed with the unrestricted Hartree–Fock (UHF) method, many-body perturbation theory (MBPT) and energy minimisation (EM). The UHF method and the MBPT depend on quantum mechanic calculations. The results of these methods are time consuming and difficult as well as being valid. In the EM has been performed a energy minimisation with an empirical many-body potential energies function (PEF) which comprises two- and three-body atomic interactions. In this study, the Lin microclusters have been held stable in the interaction and only the M atom was allowed to get close to the cluster surface. This is an approach performed during
the study. As for MDSM, the same potential energies function was used, and the system was completely set free and nothing was applied as limit condition during the study. In the MDSM the M atom and Lin microcluster were released, allowing the M–Lin system to reach a stable structure and thereafter the distance of the M atom to be tied to the surface and the chemisorption energies of the M atom were calculated. We are in the belief that this model is more physical. General trends are of our results are in agreement with the results of literature.
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