Chemistry Reference
In-Depth Information
models can account for the unusual observations, which suggests that the wetting
layer most likely enters a novel state of very high mobility for
θ>θ
c
, similar to a
phase transition that needs to be better understood theoretically.
3.1 Diffusion Measurements with Externally Imposed
Concentration Gradients
A standard method to measure surface diffusion is based on monitoring the time evo-
lution of a non-equilibrium coverage profile when a coverage gradient is imposed
initially [
1
]. The gradient provides the driving force for atoms to diffuse from high to
low coverage regions, until a uniform equilibrium coverage distribution is attained
everywhere. The evolution of the coverage
θ
(
r
,
t
) at location
r
and time
t
obeys the
diffusion equation
∂θ
∂
t
=∇·
(
D
∇
θ)
(3.1)
where
D
c
(θ)
is the collective diffusion coefficient. For example, in 1-d step profile
evolution experiments along a direction
r
the coverage has one value
θ
1
in region
r
0. With time, atoms will move to equalize
the surface coverage as shown schematically in Fig.
3.1
. If there are no adatom
interactions (except site exclusion)
D
c
is coverage independent, the evolving profile
is described by
<
0 and a different value
θ
2
in region
r
>
1
erf
r
2
2
D
c
t
)
=
(θ
1
−
θ
2
)
2
θ(
r
,
t
−
/
(3.2)
Fig. 3.1
Schematic showing the spreading of 1-d profiles as in classical diffusion. The scaled
variable is
r
/
√
t
, the integrated shaded area and the slope are used to determine the
D
c
(θ)
coverage
dependence in the Boltzmann-Matano analysis
