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An atomistic calculation of two-dimensional diffusion of a Pt adatom on a Pt(110) surface
Surface Science 0 North-Holland
79 (1979) L346-L348 Publishing Company
SURFACE SCIENCE LETTERS
AN ATOMISTIC CALCULATION
OF TWO-DIMENSIONAL
DIFFUSION OF A Pt
ADATOM ON A Pt( 110) SURFACE
Timur HALICIOGLU
*
Ames Research Center, NASA, Moffett Field, California 94035, USA Received
28 August
1978
Two-dimensional diffusion of a Pt adatom on a Pt (110) surface has been observed experimentally [l]. However, this type of diffusion is surprising, based on the channeled structure of this plane. Bassett and Webber [I] attributed this unexpected behavior to a number of factors which are believed to facilitate interchannel diffusion. One of the mechanisms they suggested is the replacement of a channelwall atom with the adatom by first creating a vacancy in the closed packed row adjacent to the adatom. In this paper, we report results of an atomistic calculation which supports twodimensional diffusion on a Pt atom on a Pt(ll0) surface. Our calculations for diffusion energies indicate that interchannel diffusion by the replacement of a channel-wall atom by the adatom is energetically favorable. It is associated, however, with a somewhat different mechanism than was suggested by Bassett and Webber. The activation energy, E,, for diffusion was calculated as:
where U, and ZJ, denote total energies of interaction of relaxed systems with the adatom located at the saddlepoint and the adatom located at the lattice site, respectively. Both Us and U, were calculated using Lennard-Jones pair interactions with parameters fitted to bulk properties [2]. Furthermore, Us and U, were minimized using a molecular statics method with respect to the positions of the adatom and 180 substrate atoms in the vicinity of the adatom. The rest of the substrate atoms (encompassing more than 2,000) were kept fixed in their lattice positions. In the minimization of U,, the adatom was permitted to relax only within a plane perpendicular to the [ 1 lo] direction [3]. The positions of surface atoms after relaxation given by our calculations indicate that the diffusion of the Pt adatom proceeds via an intermediate state (i.e., saddlepoint configuration) which’permits both channel and apparent interchannel diffusions to occur with the same energy of activation. For the intermediate state, relax* National
Research
Council
Research
Associate. L346
T. Halicioglu
/ Atomistic
calculation
of 20 diffusion
of Pt adatom
CHANNEL
(iii)
(iJ
L347
on Pt
DIFFUSION
I INTER CHANNEL DIFFUSION
LATTICE POINT CONFIGURATION
0X
rlNTERMEDIATE1 (id\ LSTATE: I SADDLE POINT CONFIGURATION
ADATOM WALL-ATOM
Fig. 1. Schematic
representation
of diffusion
mechanism
for a Pt adatom
on a Pt(l10)
surface.
ation causes one of the wall atoms - in proximity to the adatom at the saddlepoint - to be displaced (see fig. 1). For the minimum energy configuration, both the adatom and the displaced wall atom are found to be positioned 0.86 A above the surface plane. This intermediate structure can transform to a stable configuration in four different ways, shown schematically in fig. 1. These are: (i) the adatom can return to its original position, A; (ii) the adatom can move to position B - this would represent a channel diffusion; (iii) the displaced wall atom can go to location C; (iv) or it can go to D. The last two cases would represent the observed interchannel diffusion; in both cases, the wall atom is replaced by the adatom. Energetically, the intermediate state is found to be 1.07 eV higher than the lattice point position (for example, the adatom at position A). Even though this value is somewhat higher than the measured activation energy (0.84 f 0.1 eV), the present theoretical results clearly explain the two-dimensional diffusion mechanism of the Pt adatom on Pt (110) surface. A similar calculation with an Au adatom on Pt (110) surface did not produce
comparable results. The Au-Pt interaction is somewhat weaker than the Pt-Pt interaction, so that the displacement of a waif atom apparently does not take place during the relaxation process. A~~ord~l~g~y, for Au~Pt(~~~) ~ha~~ne~ diffusion is found to be more favorable energetically and this is concordant with experimental observations. The calculations carried out in this study are quite instructive in elucidating the two-dimensional diffusion of a Pt adatom on a Pt(l10) surface. Furthermore, the results indicate the importance of relaxation in studying the mechanism of selfdiffusion of an adatom.
References [I ] D.W. Bassett and P.R. Webber, Surface Sci. 70 (1978) 520. 121 T. I~aI~~~o~lu and C.M. Pound, Phys. Status Solidi A 30 (1975) 619. [3] For more details please see: T. Halicioglu and G.M. Pound, 3. Crystal Growth, to be published.
79 (1979) L346-L348 Publishing Company
SURFACE SCIENCE LETTERS
AN ATOMISTIC CALCULATION
OF TWO-DIMENSIONAL
DIFFUSION OF A Pt
ADATOM ON A Pt( 110) SURFACE
Timur HALICIOGLU
*
Ames Research Center, NASA, Moffett Field, California 94035, USA Received
28 August
1978
Two-dimensional diffusion of a Pt adatom on a Pt (110) surface has been observed experimentally [l]. However, this type of diffusion is surprising, based on the channeled structure of this plane. Bassett and Webber [I] attributed this unexpected behavior to a number of factors which are believed to facilitate interchannel diffusion. One of the mechanisms they suggested is the replacement of a channelwall atom with the adatom by first creating a vacancy in the closed packed row adjacent to the adatom. In this paper, we report results of an atomistic calculation which supports twodimensional diffusion on a Pt atom on a Pt(ll0) surface. Our calculations for diffusion energies indicate that interchannel diffusion by the replacement of a channel-wall atom by the adatom is energetically favorable. It is associated, however, with a somewhat different mechanism than was suggested by Bassett and Webber. The activation energy, E,, for diffusion was calculated as:
where U, and ZJ, denote total energies of interaction of relaxed systems with the adatom located at the saddlepoint and the adatom located at the lattice site, respectively. Both Us and U, were calculated using Lennard-Jones pair interactions with parameters fitted to bulk properties [2]. Furthermore, Us and U, were minimized using a molecular statics method with respect to the positions of the adatom and 180 substrate atoms in the vicinity of the adatom. The rest of the substrate atoms (encompassing more than 2,000) were kept fixed in their lattice positions. In the minimization of U,, the adatom was permitted to relax only within a plane perpendicular to the [ 1 lo] direction [3]. The positions of surface atoms after relaxation given by our calculations indicate that the diffusion of the Pt adatom proceeds via an intermediate state (i.e., saddlepoint configuration) which’permits both channel and apparent interchannel diffusions to occur with the same energy of activation. For the intermediate state, relax* National
Research
Council
Research
Associate. L346
T. Halicioglu
/ Atomistic
calculation
of 20 diffusion
of Pt adatom
CHANNEL
(iii)
(iJ
L347
on Pt
DIFFUSION
I INTER CHANNEL DIFFUSION
LATTICE POINT CONFIGURATION
0X
rlNTERMEDIATE1 (id\ LSTATE: I SADDLE POINT CONFIGURATION
ADATOM WALL-ATOM
Fig. 1. Schematic
representation
of diffusion
mechanism
for a Pt adatom
on a Pt(l10)
surface.
ation causes one of the wall atoms - in proximity to the adatom at the saddlepoint - to be displaced (see fig. 1). For the minimum energy configuration, both the adatom and the displaced wall atom are found to be positioned 0.86 A above the surface plane. This intermediate structure can transform to a stable configuration in four different ways, shown schematically in fig. 1. These are: (i) the adatom can return to its original position, A; (ii) the adatom can move to position B - this would represent a channel diffusion; (iii) the displaced wall atom can go to location C; (iv) or it can go to D. The last two cases would represent the observed interchannel diffusion; in both cases, the wall atom is replaced by the adatom. Energetically, the intermediate state is found to be 1.07 eV higher than the lattice point position (for example, the adatom at position A). Even though this value is somewhat higher than the measured activation energy (0.84 f 0.1 eV), the present theoretical results clearly explain the two-dimensional diffusion mechanism of the Pt adatom on Pt (110) surface. A similar calculation with an Au adatom on Pt (110) surface did not produce
comparable results. The Au-Pt interaction is somewhat weaker than the Pt-Pt interaction, so that the displacement of a waif atom apparently does not take place during the relaxation process. A~~ord~l~g~y, for Au~Pt(~~~) ~ha~~ne~ diffusion is found to be more favorable energetically and this is concordant with experimental observations. The calculations carried out in this study are quite instructive in elucidating the two-dimensional diffusion of a Pt adatom on a Pt(l10) surface. Furthermore, the results indicate the importance of relaxation in studying the mechanism of selfdiffusion of an adatom.
References [I ] D.W. Bassett and P.R. Webber, Surface Sci. 70 (1978) 520. 121 T. I~aI~~~o~lu and C.M. Pound, Phys. Status Solidi A 30 (1975) 619. [3] For more details please see: T. Halicioglu and G.M. Pound, 3. Crystal Growth, to be published.