Chemistry Reference
In-Depth Information
Figure 6.10
Illustration of a Cu adatom hopping from a hollow site to an adjacent hollow site
on Cu(100). The diagram on the left shows the adatom (grey) before the hop, the middle shows
the transition state (TS), and the diagram on the right shows the adatom after the hop.
becoming an adatom. This process has the net effect of moving an adatom
between two sites on the surface. It was first detected on the (110) surfaces
of certain fcc metals, but has also been observed on the (100) surface of
metals including Al and Pt.
If we want to understand the diffusion of Cu adatoms on Cu(100), we
clearly should compare the rates of the two diffusion mechanisms shown in
Figs. 6.10 and 6.11. What do the NEB calculations described in the previous
section tell us about the possible occurrence of exchange hopping? The answer
is simple: nothing! Because we start our NEB calculations by supplying an
initial path that interpolates between the start and end states in Fig. 6.10, our
result cannot even give a hint that paths like the one in Fig. 6.11 exist, much
less give any detailed information about these paths. In more general terms:
NEB calculations are local not global optimization calculations, so an NEB
calculation can give accurate information about a particular transition
state, but it cannot indicate whether other transition states related to the
same initial state also exist.
Figure 6.11
Illustration of the exchange mechanism for self diffusion on the Cu(100) surface.
The diagram on the left shows the Cu adatom (dark grey) in a hollow site and highlights one of
the surface atoms in light grey. In the transition state, shown in the middle, both Cu atoms lie
above the plane of the surface. The diagram on the right shows the result after exchange,
where the original adatom has become part of the surface and the original surface atom has
become an adatom.
