J. Phys. Chem. C 2009, 113, 16031–16035
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Self-Adsorption on a Pt (111) Surface Yu Shu,† Jian-Min Zhang,*,† Ke-Wei Xu,‡ and Vincent Ji§ College of Physics and Information Technology, Shaanxi Normal UniVersity, Xian 710062, Shaanxi, PR China, State-Key Laboratory for Mechanical BehaVior of Materials, Xian Jiaotong UniVersity, Xian 710049, Shaanxi, PR China, and ICMMO/LEMHE UMR CNRS 8182, UniVersite´ Paris-Sud 11, 91405 Orsay Cedex, France ReceiVed: May 20, 2009; ReVised Manuscript ReceiVed: June 25, 2009
The energy and force of a Pt adatom on a Pt (111) surface have been calculated by the modified analytical embedded atom method (MAEAM). With increasing the distance of the adatom from the surface, maps of energy and perpendicular force can be classified into four regions: repulsive, transformed, strongly attractive, and weakly attractive. In the repulsive and transformed regions, the maximum (minimum) values of energy and force appear above the top (hollow) of the first layer of atoms of the Pt (111) surface due to a stronger pair-potential interaction. In strongly attractive regions, energy and force maps are more complicated than those in other regions because of the effects of the many body interactions and nonspherical distribution of the electrons of the atoms in the crystal. For the Pt adatom on the Pt (111) surface, the stable position is 0.19 nm above the fcc hollow of the first layer atoms, and the corresponding lowest energy is -4.5545 eV. The favorable migration path for the Pt adatom should be jumping between the two nearest hollow positions due to the very low migration energy needed of about 0.1 eV. Introduction A detailed knowledge of the energy, force, and configuration of the gas and metal adatoms on a metal surface is very important for understanding many surface phenomena, including chemical reactions, catalysis, and crystal growth. Many modern experimental techniques, field ion microscopy (FIM)1,2 and atomic force microscopy (AFM),3,4 for example, have been used to observe the configuration of adatoms on a metal surface or to measure the force acting on adatoms from a metal surface. In addition to these experimental methods, a simulation method has also been used by Komiyama et al. to study the force acting on an Fe adatom from a Cu (100) surface using pair-potential theory.5 It is well-known that the local environment of the surface is substantially different from the uniform bulk in metallic systems, and the many body interactions that depend upon the environment should be taken into account. In contrast to the pair-potential theory that considers only the potential energy of a system of particles, the embedded atom method (EAM)6,7 presents the energy of atom in a system as a sum of electrostatic interactions with each of its near neighbors and an energy to embed the atom in the local electron density created by its neighbor atoms. Considering directional bonding of atoms in crystal, Baskes and Zhang et al. developed the modified EAM (MEAM)8 and modified analytical EAM (MAEAM).9-12 MAEAM has successfully calculated many characteristics of pure metals and alloys, which compared well with experimental results and other theories.13-16 In our previous papers, MEAM and MAEAM have been used to calculate surface energy,17-19 grain boundary energy,20-22 and interface energy.23-25 Many experimental results related to these face defects have been explained satisfactory. In this paper, the energies and perpendicular forces of the Pt adatom on the Pt (111) surface have been calculated by * Corresponding author. E-mail:
[email protected]. Telephone: +86 29 85308456. † Shaanxi Normal University. ‡ Xian Jiaotong University. § Universite´ Paris-Sud 11.
MAEAM. When the adatom is very close to the surface, the maximum (minimum) values of the energy and repulsive force appear above the top (hollow) of the first layer atoms of the Pt (111) surface. With increasing the distance of the adatom from the surface, energy and force become negative, and their maps are more complicated than those obtained by using pair-potential because of dominant effects of the many body interaction and nonspherical distribution of the electrons of the atoms in the crystal. The stable position of the Pt adatom is found to be 0.19 nm above the hollow of the first layer atoms of the Pt (111) surface, but the energy corresponding fcc hollow is a little smaller than the hcp hollow. There are no relevant available experimental and calculational data about the energy and force of a Pt adatom on a Pt (111) surface for comparison. Our calculational results could give some guidance for experimental study. MAEAM In MAEAM, the total energy of a system Etotal is expressed as12
Etotal )
∑ F(Fi) + 21 ∑ ∑ φ(rij) + ∑ M(Pi) i
i
Fi )
j(*i)
(1)
i
∑ f(rij)
(2)
∑ f 2(rij)
(3)
j(*i)
Pi )
j(*i)
where F(Fi) is the energy to embed an atom in site i with electron density Fi, which is given by a linear superposition of spherical averaged atomic electron density of other atoms f(rij), rij is the separation distance of atom j from atom i, φ(rij) is the pair-potential between atoms i and j, and M(Pi) is the modified term, which describes the energy change due to nonspherical distribution of atomic electronic density and deviation from the linear superposi-
10.1021/jp904709g CCC: $40.75 2009 American Chemical Society Published on Web 08/13/2009
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tion. Embedding function F(Fi), pair-potential φ(rij), modified term M(Pi), and atomic electron density f(rij) take the following forms11,12
[
( )]( ) F Fe
F(Fi) ) -F0 1 - n ln
F Fe
n
(4)
(
M(Pi) ) R
2
rij + k2 r1e
4
rij + k3 r1e
) [(
)]
2 Pi Pi - 1 exp -1 Pe Pe
r1e rij
-12
(5)
R)
k0 ) -
C44 (eV nm-3)
0.39239
5.84
1.20
2120
1720
520
F0 (eV)
n
R
k0 (eV)
k1 (eV)
k2 (eV)
k3 (eV)
4.64
0.4992
0.4219
-0.7167
0.4857
-0.0646
0.0966
(7)
∑ φ(rj) + M(P)
(14)
∑ f(rj)
(15)
∑ f 2(rj)
(16)
1 2
j
Ω(C11 + 2C12)(C11-C12) 216E1fC44 Ω(C12 - C44) n2F0 32 8
F)
j
P)
j
The R () x, y, z) component of the force acting on the Pt adatom from the Pt (111) surface can be calculated by
fR)-
(8)
∂E ) -F′(F) ∂rjR
∑ j
f′(rj)rjR 1 rj 2
∑ j
φ′(rj)rjR rj
2M′(P)
∑
f(rj)f′(rj)rjR rj
j
(9)
(11)
Ω(-33C44 - 32C12 + 32C11) 1020
(12)
8Ω(9C44 + C12 - C11) 5355
(13)
k3 )
C12 (eV nm-3)
6
Ω(1311C44 + 939C12 - 939C11) 9520
k2 )
C11 (eV nm-3)
E ) F(F) +
E1f Ω(5481C44 + 2989C12 - 2989C11) 9 42840 (10)
k1 )
Ef1v (eV)
(6)
where subscript e indicates equilibrium, F0 ) Ec - E1f, and fe and r1e are the electron density and the first nearest neighbor distance at equilibrium. Six parameters, n, R, k0, k1, k2, and k3, in eqs 4-6 can be determined by fitting lattice constant a, cohesion energy Ec, f , and elastic constants C11, monovacancy formation energy E1v C12, and C44 in the metals considered
n)
Ec (eV)
(111) surface, the energy of the Pt adatom can be expressed explicitly as
2
( )
f(rij) ) fe
a (nm)
TABLE 2: Calculated Parameters of Platinum for MAEAM
() ( ) ( )
rij φ(rij) ) k0 + k1 r1e
TABLE 1: Input Physical Parameters of Platinum
(17)
where rRj represents the R component of the surface atom j separated a distance rj from the adatom. Considering two-dimensional periodicity of a Pt (111) surface along [11j0] and [112j] directions (here we define the x-, y-, and z-axis as along the [11j0], [112j], and [111] direction, respectively), a calculation unit cell with cell lengths of Lx ) 4a × 21/2, Ly ) 2a × 61/2, and Lz ) 20a/31/2, (containing 20 layers from the bottom of the cell along the z- axis) are used for the Pt (111) surface (Figure 1). The total number of atoms is 1280, and for every layer atoms is 64. From surface energy calculation of fcc metals, we found that the surface energy as a function of the number of layers converges around 10 layers.17 So a 20 layer system is large enough to model the surface effects. As is shown in Figure 1 for a top view of the Pt adatom on the Pt (111) surface, the areas closed by real and broken lines are the calculation unit cell of the Pt (111) surface and scan region of
where Ω ) a3/4 is the atomic volume in fcc metals. By substituting physical parameters, the lattice constant a,26 f cohesion energy Ec, monovacancy formation energy E1v , and 27 elastic constants C11, C12, and C44 of platinum (listed in Table 1) into eqs 8-13, the parameters needed for energy calculation with MAEAM can be obtained (listed in Table 2). Calculated Method and Model For the Pt adatom (taken as atom i here and neglected subscript i in following equations for convenience) on the Pt
Figure 1. Top view of the Pt adatom on the Pt (111) surface. Areas closed by real and broken lines are the calculation unit cell of the Pt (111) surface and scan region of the Pt adatom, respectively. Right panel represents the high-symmetry adsorption sites on the Pt (111) surface.
J. Phys. Chem. C, Vol. 113, No. 36, 2009 16033
Figure 2. Maps of the energy (left) and perpendicular force (right) for the Pt adatom at zad ) 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, and 0.40 nm above the first layer of the Pt (111) surface. The view direction is with azimuth angle φ ) 15° and pole angle ψ ) 60°.
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TABLE 3: Distance from the Surface (zad), Maximum and Minimum Values of Energies (Emax and Emin), and Perpendicular Forces (fmax and fmin) Acting on the Pt Adatom from the Pt (111) Surface zad (nm) Emax (eV)
0.10
0.15
10070 73.377 (top) (top) Emin (eV) 9.706 -3.026 (hollow) (hollow) fmax (eV/nm) 1207300 6291.680 (top) (top) 516.381 87.618 fmin (eV/nm) (hollow) (hollow) Maximum and minimum values correspond to the upper and of the first layer atoms in Fig. 1.
0.20
0.25
0.30
0.35
0.40
-2.740 -3.966 -3.218 -2.677 -2.250 (top) (hollow) (top) (bridge) (hollow) -4.547 -4.010 -3.307 -2.714 -2.275 (hollow) (bridge) (hollow) (top) (top) 134.869 -12.943 -12.651 -8.705 -5.972 (top) (bridge) (hollow) (top) (hollow) -5.698 -14.493 -14.309 -11.712 -7.685 (hollow) (top) (bridge) (hollow) (top) lower limits in Fig. 2, the words in parenthesis indicate the corresponding positions
the Pt adatom, respectively. The right panel of Figure 1 represents four high-symmetry adsorption sites on the Pt (111) surface: top, fcc hollow, hcp hollow, and bridge with enlarged Pt atoms. In order to obtain a panorama of the energy and force for the Pt adatom on the Pt (111) surface, the Pt adatom is initially placed at zad ) 0.10 nm above the first layer of the Pt (111) surface, and the scanning process is performed on a (5a × 21/2/4) × (2a × 61/2/3) area (at the center of the calculation unit cell surface) by moving the x and y coordinates of the adatom at intervals of 0.01 nm along the x- and y-direction, respectively. Then, the Pt adatom is moved up at intervals of 0.05 nm per step until zad ) 0.4 nm, and at each step the same scanning process is repeated again. Energy and Force for the Pt Adatom on the Pt (111) Surface Figure 2 shows the energy (left) and perpendicular force (right) maps for the Pt adatom at zad ) 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, and 0.40 nm above the first layer of the Pt (111) surface. The view direction is with azimuth angle φ ) 15° and pole angle ψ ) 60°. Table 3 lists the maximum and minimum values of the energy and force and corresponding positions (in parenthesis) related to the first layer atoms (Figure 1). According to the force acting on the adatom from the surface, we can classify the energy and force maps into four regions: (1) Repulsive region, where the adatom is very close to the surface (zad ) 0.10 and 0.15 nm), the energy decreases with increasing distance of the Pt adatom from the surface, and the force acting on the Pt adatom is positive (means repulsive) and also decreases with increasing distance. As is summarized in the second and third columns of Table 3, the maximum values of the energy and repulsive force appear on the top of the first layer atoms of the Pt (111) surface, and the minimum values correspond to the hollow positions. In other words, the contour maps of energy and force could be seen simply as a duplicate of the Pt (111) surface. (2) Transformed region, where the adatom is close to the surface (zad ) 0.20 nm), the value of the energy in the top region, and the value of the force in the hollow region go from from positive to negative (means attractive). Although a few enhance contours appear around the top of the first layer atoms, the maximum repulsive force is still on the top of the first layer atoms. (3) Strongly attractive region, when the adatom is near the surface (zad ) 0.25 and 0.30 nm), the energy is negative, and the force is strongly attractive. Maps of the energy and force become more complicated. (4) Weakly attractive region, when the adatom is far from the surface (zad ) 0.35 and 0.40 nm) and the absolute values of the energy and attractive force decrease and tend toward zero. Energy and force maps tend to become smooth and simple again.
Figure 3. Variation of the energy with distance zad of the Pt adatom from the first layer of the Pt (111) surface for four high-symmetry adsorption sites: top, bridge, fcc hollow, and hcp hollow.
In repulsive and transformed regions, all of the energy and force maps are similar and simple, and the positions corresponding to the maximum (minimum) values of energy and force are on the top (hollow) of the first layer atoms. In fact, at each position of the Pt adatom, the energies and forces corresponding to the many body effect, pair-potential, and modified term, i.e, first, second, and third terms in eqs 14 and 17, are calculated, and the total energies and forces are the sum. After comparing these results, we found that in the repulsive and transformed regions these pictures result mainly from relatively larger effects of the pair-potential (second term in eqs 14 and 17) and are similar to the results obtained by Komiyama et al. with the pair-potential theory.5 The complicated contours of the energy and force in the strongly attractive region result mainly from the many body effects (first term in eqs 14 and 17) and nonspherical distribution of electrons of the atoms in the crystal (third term in eqs 14 and 17). In weakly attractive regions, the contributions to the total energy and force from the three terms in eqs 14 and 17 become small. Variations in the energy and force with distance zad between the Pt adatom and first layer of the Pt (111) surface are shown in Figures 3 and 4, respectively, for four high-symmetry adsorption sites: top, fcc hollow, hcp hollow, and bridge. From Figures 3and 4, it is interesting to note the following. (1) The lowest energies just correspond where the force is zero. (2) When distance zad is less than about 0.23 nm (0.24 nm), three divarications are observed distinctly for the positions top, bridge, and hollow for the energy (force). For the same distance zad, the energy (force) corresponding to these three positions decreases, successively. (3) When the distance zad is larger than about 0.23 nm (0.24 nm), however, all of the curves become closer to each other and will tend to their zero asymptote terminally. (4) The energy (force) curves corresponding to two positions, hcp hollow and fcc hollow, almost superpose each other because the most energy (force) is contributed from the
J. Phys. Chem. C, Vol. 113, No. 36, 2009 16035 These mainly result from the many body effects and nonspherical distribution of the electrons of the atoms in the crystal. (3) With continued increasing distance, the effects acting on the Pt adatom from the surface become weaker, and the energy and force maps become smooth (weakly attractive region). (4) The stable position for the Pt adatom on the Pt (111) surface is 0.19 nm above the hollow of the first layer atoms, and the corresponding lowest energy is -4.55 eV. (5) The favorable migration path is from a hollow crossing a bridge to a neighbor hollow because very low migration energy of about 0.1 eV is needed. Figure 4. Variation of the force with distance zad of the Pt adatom from the first layer of the Pt (111) surface for four high-symmetry adsorption sites: top, bridge, fcc hollow, and hcp hollow.
TABLE 4: Lowest Energies (Emin) and Corresponding Distances (zad) for the Pt Adatom above the First Layer of the Pt (111) Surface for Four High-Symmetry Adsorption Sites position
top
bridge
hcp hollow
fcc hollow
Emin (eV) zad (nm)
–4.2122 0.23
–4.4577 0.20
–4.5503 0.19
–4.5545 0.19
nearest atoms, and the array of the first layer atoms is similar for these two positions. (5) The stable position for the Pt adatom on the Pt (111) surface is 0.19 nm above the hollow of the first layer atoms. However, the energy corresponding to the fcc hollow is a little smaller than that of the hcp hollow, and the lowest energy is -4.5545 eV. This means that the adatom will diffuse from the other positions to these stable positions. Comparing various migration paths and from energy minimization, we know that the favorable migration path is from a hollow crossing a bridge to a neighbor hollow. The potential barrier, that is migration energy, is about 0.1 eV. Conclusions With MAEAM, the energy and force perpendicular to the surface have been calculated for different distances of the Pt adatom from the Pt (111) surface. The results show that (1) when the adatom is very close to the surface (repulsive region), the energy is positive, and the force is repulsive. The maximum values of the energy and repulsive force appear on the top of the first layer atoms of the Pt (111) surface, and the minimum values correspond to about the hollow of the first layer. The pair-potential interaction dominates the other interactions. (2) With increasing the distance of the Pt adatom from the surface, the energy changes from positive to negative, and the repulsive force changes to an attractive force (transformed region), and then a strongly attractive region follows, where the energy and force maps are more complicated than those in other regions.
Acknowledgment. The authors acknowledge the State Key Development for Basic Research of China (Grant 2004CB619302) for providing financial support for this research. References and Notes (1) Schwoebel, P. R.; Foiles, S. M.; Bisson, C. L.; Kellogg., G. L. Phys. ReV. B 1989, 40, 10639. (2) Leiva, E. P. M.; Del Po´Polo, M. G.; Schmickler., W. Chem. Phys. Let. 2000, 320, 393. (3) Binnig., G. Ultramicroscopy 1992, 42-44, 7. (4) Ohnesorge, F.; Binnig., G. Science 1993, 260, 1451. (5) Komiyama, M.; Tsujimichi, K.; Ohkubo, S.; Tazawa, K.; Kubo, M.; Miyamoto., A. Jpn. J. Appl. Phys. 1995, 34, 789. (6) Daw, M. S.; Baskes., M. I. Phys. ReV. Lett. 1983, 50, 1285. (7) Daw, M. S.; Baskes., M. I. Phys. ReV. B 1984, 29, 6443. (8) Baskes., M. I. Phys. ReV. B 1992, 46, 2727. (9) Zhang, B. W.; Ouyang., Y. F. Phys. ReV. B 1993, 48, 3022. (10) Zhang, B. W.; Ouyang, Y. F.; Liao, S. Z.; Jin., Z. P. Phys. B 1999, 26, 218. (11) Zhang, B. W.; Ouyang., Y. F. Phys. B 1993, 92, 431. (12) Hu, W. Y.; Shu, X. L.; Zhang, B. W.; et al. J. Phys. D. 2000, 33, 711. (13) Zhang, B. W.; Ouyang, Y. F.; Liao, S. Z.; Jin., Z. P. Phys. B 1996, 101, 161. (14) Hu, W. Y.; Zhang, B. W.; Huang, B. Y.; Gao, F.; Bacon., D. J. J. Phys.: Condens. Matter 2001, 13, 1193. (15) Hu, W. Y.; Zhang, B. W.; Shu, X. L.; Huang., B. Y. J. Alloys. Comp. 1999, 287, 159. (16) Ackland, G. J. Non-Pairwise Potentials and Defect Modelling for Transition Metals. Ph.D Thesis, University of Oxford, Oxford, U.K., 1987. (17) Zhang, J. M.; Ma, F.; Xu., K. W. Appl. Surf. Sci. 2004, 229, 34. (18) Zhang, J. M.; Ma, F.; Xu., K. W. Surf. Interface Anal. 2003, 35, 662. (19) Zhang, J. M.; Ma, F.; Xu, K. W.; Xin., X. T. Surf. Interf. Anal. 2003, 35, 805. (20) Zhang, J. M.; Wei, X. M.; Xin., H. Surf. Interface Anal. 2004, 36, 1500. (21) Zhang, J. M.; Wei, X. M.; Xin., H. Appl. Surf. Sci. 2005, 243, 1. (22) Zhang, J. M.; Wei, X. M.; Xin, H.; Xu., K. W. Chin. Phys. 2005, 14, 1015. (23) Ma, F.; Zhang, J. M.; Xu., K. W. Surf. Interface Anal. 2003, 36, 355. (24) Zhang, J. M.; Xin, H.; Wei., X. M. Appl. Surf. Sci. 2005, 246, 14. (25) Xin, H.; Zhang, J. M.; Wei, X. M.; Xu., K. W. Surf. Interface Anal. 2005, 37, 608. (26) Barrett, C. S. Massalski., T. B. Structure of Metals, 3rd ed.; Pergamon Press: Oxford, U.K., 1980. (27) Gray., D. E. American Institute of Physics Handbook, 3rd ed.; McGraw-Hill: New York, 1972.
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