
Francesco
Montalenti and
Riccardo
Ferrando
INFM and CFSBT/CNR, Dipartimento di Fisica, Università
di Genova, Genova, I 16146, Italy
a) Longjumps in Cu, Ag and Au self diffusion on (110)(1 X 1) surfaces
As it is well known, a singlejump 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 jumpdiffusion 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 selfdiffusion on their (110) (1 X 1) surfaces.
The metals are modeled by tightbinding semiempirical
potentials. When the occurence of long jumps is investigated in details,
it arises that, even for three somewhat similar metals selfdiffusing 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 longjump
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 onedimensional
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 adatomsurface potential can influence the longjump probability:
a large
saddle point between two adsorption minima will encourage longjumps
! 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 longjump 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 missingrow geometry,
we analyzed selfdiffusion 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 distantcells 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 longjump event.
Indeed, if
we consider a weaklybound dimer diffusing on a surface, characterized
by a dissociation energy much larger than the single adatom jump barrier,
the DissociationReassociation mechanism can
cause effective long jumps in the dimer difffusion.
We analitically calculated the corresponding longjump 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.
References:
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 selfdiffusion),6 (Leapfrog diffusion mechanism for onedimensional chains on missingrow reconstructed surfaces) and 7 (An universal law for dimers diffusion) are available: please email us !