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Long jumps in surface diffusion: theory and simulation

Francesco Montalenti and  Riccardo Ferrando
 INFM and CFSBT/CNR, Dipartimento di Fisica, Università di Genova, Genova, I 16146, Italy

a) Long-jumps in Cu, Ag and Au self diffusion on (110)(1 X 1) surfaces

As it is well known, a single-jump model is not appropriate to describe adatoms surface diffusion. Indeed, diffusion does not proceed only by jumps but also through the exchange
mechanism. More, in jump-diffusion long jumps must be takem into account, as demonstrated by theory and experiments on different systems. From the available results, it is hard to extract a general trend: why, for example, no long jumps are observed in Mo/W(211), few in Rh/W(211)  (< 3 % on the total jumps number), while they are common in Pd/W(211) (~20 %) [1] ?
In order to investigate if at least on similar systems an universal behavior can be extracted, we study, by MD simulations, Cu, Ag and Au self-diffusion on their (110) (1 X 1) surfaces.
The metals are modeled by tight-binding semi-empirical potentials. When the occurence of long jumps is investigated in details, it arises that, even for three somewhat similar metals self-diffusing in the same geometry, different scenario are found. Indeed, double jumps are practically absent in Au, and frequent in Cu, Ag showing an intermediate behavior.
As it is well known, the long-jump probability is expected to be inversely proportional
to  the dissipation D on the lattice cell [2,3]. In order to calculate D, we use the diffusion path approximation, i.e. we assume one-dimensional diffusion among the most probable diffusion path. Results are unsatisfactory, since the relative values of D do not justify the stong difference between Cu, Ag and Au. So, we carry out a different kind of analysis. Our idea is that the detailed topology of the adatom-surface potential can influence the long-jump probability:
a large saddle point between two adsorption minima  will encourage long-jumps ! This idea can be quantified by calculating the ratio r between the transverse vibration frequencies on the minimum and on the saddle point respectively: the larger is such ratio, the easier is a long jump. Indeed, we found [4] r to be much larger in Cu than in Au, with an intermediate value for Ag, in qualitative agreement with the long-jump statistics found with our MD simulations.

b) Effective long jumps

Since Au and Pt(110) surfaces are more stable in the (1 X 2) reconstructed missing-row geometry, we analyzed self-diffusion on such surfaces too. As explained in [5], a new
diffusion mechanism occurs, the Metastable Walk (MW), which can give raise to effective long jumps. Indeed, MWs can not be experimentally distinguished [6] from double jumps, but they do give their contribution at the  distant-cells  moves statistics.  If for Au we found that double MWs are about the 25% of double jumps, their influence in Pt/Pt(110)(1 X 2) diffusion could be remarkable.
We found another system where effective long jumps occur [7]. Again with effective
long jump, we indicate a diffusion mechanism which, though is not a real long jump, gives raise to an experimental output which can not be distinguished from a real long-jump event.
Indeed, if we consider a weakly-bound dimer diffusing on a surface, characterized by a dissociation energy much larger than the single adatom jump barrier, the Dissociation-Reassociation mechanism can cause effective long jumps in the dimer difffusion. We analitically calculated the corresponding long-jump probability distribution P(l), finding that asymptotically (but such result is already a good approximation for l > 3)
P(l)~ l-2 . This law is universal, for it is found under very general hypothesis, and foresees an interesting result, since P(l) slowly decays with l. We recall that in adatom diffusion, P(l) decays much faster, roughly as an exponential [2,8], as demonstrated by the fact that no systems where a significant statistics of long jumps for l > 2 could be collected, have been yet found.

1) G. Ehrlich, Surf. Sci. 246 (1991) 1.
2) R. Ferrando, R. Spadacini and G. Tommei, Phys. Rev. E 48 (1993) 2437; Surf. Sci. 311 (1994) 411.
3) Yu Georgievskii and E. Pollak, Phys. Rev. E 49 (1994) 5098.
4) F. Montalenti and R. Ferrando, submitted
5) F. Montalenti and R. Ferrando, Phys. Rev. B 58 (1998) 3617.
6) F. Montalenti and R. Ferrando, submitted
7) F. Montalenti and R. Ferrando, under preparation
8) K.D. Dobbs and D.J. Doren, J. Chem. Phys. 97 (1992) 3722.

Reprint of Ref. 5 , and Preprint of Ref. 4 (Jumps and concerted moves in Cu, Ag and Au(110) adatom self-diffusion),6 (Leap-frog diffusion mechanism for one-dimensional chains on missing-row reconstructed surfaces) and 7 (An universal law for dimers diffusion) are available: please e-mail us !


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