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coverage falls below
θ<θ
c
. Preliminary fits
to account for the increase of the refilling time by four orders of magnitude as
θ
c
,
E
G
=
E
g
(θ
c
)
+
ε(θ
c
−
θ)
with
θ
decreases by 0.1ML below
6eV/0.1ML[
3
].
The adatom-vacancy model is based on numerous assumptions that indepen-
dently are added to account for the unusual observations. It is not clear how these
assumptions are physically justified: the very low diffusion barrier, the absolute val-
ues of
E
θ
c
require
ε
=
0
.
2 eV in preliminary fits [
3
] (for such a soft metal
as Pb), and the most unintuitive assumption being the increasing cost to generate a
vacancy by 0.6 eV/0.1ML as the layer is diluted minutely. These assumptions have
not yet been justified by DFT or even heuristic arguments. In addition, if the model is
matched at one temperature then the fit will not be as good at a different temperature
since all rates
R
R
,
R
G
are a strong function of temperature and they will change
their value. The (7
=
0
.
35 eV,
E
G
=
0
.
7) wetting layer is amorphous so it is even harder to envision
how vacancies are generated and how the energy cost increases dramatically with
decreasing
×
θ
.
3.5 Comparison with Other Pb Diffusion Experiments
How do the magnitudes of these unusual mobilities of the different wetting layers
on Si(111) compare with the diffusion of Pb on Pb macroscopic crystals? As can
be seen from Fig.
3.7
, which compares the refilling time for different hole radii
on the two interfaces within the temperature range
285 K, one can
conclude that the refilling speeds are in the range 20-1000 nm/s on the (7
∼
262 K
<
T
<
×
7) and
α(
√
3
×
√
3
150-5800 nm/s on the
m.
The coverages of the two phases in Fig.
3.7
were (approximately) 1.6ML on the
(7
)
for comparable hole radii in the range 5-20
μ
α(
√
3
×
√
3
. The quoted values are not meant for direct
comparison because the refilling times as discussed previously are sensitive func-
tions of
×
7) and 1.22ML on the
)
θ<θ
c
but they set up the scale of the speed (to be compared
with the STM and other results in the literature). From the STM experiments on the
(7
θ
especially for
7) and at the much lower temperature of 190 K, the speed of the ring growth
around the top of islands is 0.05 nm/s as seen in Fig.
3.2
; but, at higher temperature
of 242 K [
31
], the speed is at least 20 nm/s, which is comparable to the refilling
speed shown in Fig.
3.7
b, although direct coverage comparison is not easy. In mak-
ing this comparison, the ring speed on top of an island might be expected to be lower
than the wetting layer hole filling speed because there is the additional barrier [
38
]
to overcome at the island edge during transport of atoms to the island top.
In [
49
], Pb “neck” formation was studied of the top layer on Pb crystals at higher
temperature 318 K (so the top layer is in a “liquid” state due to surface “melting”).
The neck forms as a result of the tip-surface interaction and the high electric field.
Pb is mobile, moving toward the area under the tip making a “neck” and bridging
the tip surface gap with a speed which depends on temperature. This shorts the
gap and leads to a higher current for the same tip-surface voltage. By retracting
the tip over a certain distance
×
t
, the connection can be
broken which increases the gap resistance as sensed from the abrupt decrease of
z
within a time interval
