Jump processes in surface diffusion - Bilkent University - Faculty of ...

48 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) 39–61
Fig. 24. Replacement of Pt adatom on Ni(100) by Ni atom [49]. (a) Pt atom
deposited on Ni(100) at 77 K. (b) After heating to 250 K for one minute, Pt
adatom disappears. (c) After partial field evaporation. (d) On complete field
evaporation of one layer of nickel, Pt atom reappears.
as a possible mechanism [17,23,25,52–59], and roughly half
favored atom exchange during diffusion. For Ni(100) [17,59–
71], out of a total of nineteen estimates, only eight considered
exchange as an option, and fewer than half of these indicated
an exchange of atoms as primary in the diffusion process.
Here it is important to note the observation of Perkins and
DePristo [65] as well as of Chang and Wei [60] that the
activation energy for exchange depends strongly on the size of
the cell used in the calculations, while the hopping energy is
not sensitive to this factor. Much more work has been done to
understand diffusion on Cu(100) [17,29,53,58–68,70–90,110–
112]. Half the investigations considered exchange as an option,
but only three studies gave an indication of atom exchange
taking place. For Pd(100) [17,27,59–62,64,66,69–71,92,93],
three estimates favored hopping as the principal mechanism,
but after increasing the size of the cell in the calculations
three favoured exchange [17,60,65]. Only one out of six studies
considered exchange in diffusion on Ag(100) [17,27,59–62,64–
71,76,91,94–97,109–112] possibly indicating a rate of atom
exchange comparable to atom hopping; the remainder gave
hopping as the mode of diffusion. Not too much calculational
work has been done to evaluate diffusion characteristics on
Ir(100) [37,92], Pt(100) [17,92,98], and Au(100) [17,66,99],
but all of them indicate that the preferred path for diffusion was
by atom exchange.
Although the outcome of some of the theoretical estimates
is not that certain, the evidence is firm that exchange between
an adatom and a lattice atom occurs in diffusion on (100)
planes of Ir [45], Pt [44], and Ni [49], and probably also on
Au [17,66,99]. There have been attempts to rationalize the
conditions under which exchange will dominate in diffusion.
For Al(100), Feibelman [100] pointed out that the transition
state for atom exchange was stabilized by the covalent nature
of aluminum. Kellogg et al. [47] correlated exchange diffusion
with the relaxation of surface atoms around the binding site of
the adatom. Yu and Scheffler [94] argued that “tensile surface
stress plays the key role for the exchange diffusion on fcc(100)
surfaces”, and is important not only for Au(100), but also for
Fig. 25. Multiple atom exchange process in molecular dynamics simulation of
adatom on Cu(100) at 900 K [75]. Adatom (black) moves into substrate, causing
eventual emergence of a substrate atom at some distance from the original entry.
Al(100) and 5d metals. However, Feibelman and Stumpf [92]
have done detailed density functional calculations for the (100)
surfaces of Rh, Ir, Pd, and Pt, and found no clear relation
between surface stress and the diffusion barrier. Instead, they
concluded that exchange diffusion was favored, as proposed
by Kellogg et al. [47], when the relaxation of the substrate
around an adatom was largest. Right now, however, it appears
that predicting from experimental information which systems
will undergo atom exchange in surface diffusion is an uncertain
matter.
2.3. Via multiple events
The results for exchange processes in diffusion described
so far have been obtained at reasonably low temperatures,
and have revealed a single event. Experiments at higher
temperatures, to explore the possibility of multiple processes,
are difficult and have not yet been explored. However, these
conditions are accessible to molecular dynamics simulations,
and have been probed starting in 1993 with the work of Black
and Tian [75], who studied copper on Cu(100) relying on
embedded atom potentials [101]. At 900 K, a high temperature
for copper, they found that an atom adsorbed on the surface
entered into the surface layer, straining the adjacent surface
atoms as indicated in Fig. 25. The strain caused a surface atom
to leave, popping out, not adjacent to the original entry point,
but farther away.
This peculiar event was again found in the work of
Cohen [76], who did similar simulations on Ag, Al, Au, Cu, Pd,
Pt, and Ni. On the (100) plane of aluminum she found that an
atom entered the surface and travelled two sites and then over
one before emerging again. The barrier for this novel diffusion
was much higher than for ordinary hopping, and for all the
metals above except for nickel would only become important
above half the melting point. For nickel, the temperature for this
diffusion process was expected to be even higher. An Arrhenius
plot of the different diffusion processes is given in Fig. 26,
and shows clearly that at elevated temperatures the new type
of diffusion event makes significant contributions.