Chemistry Reference
In-Depth Information
Fig. 1.12
Strain patterns of a system at
k
B
T
/ε
=
0
.
1for(
a
)
n
y
=
108,
n
x
=
30 and (
b
)
n
y
=
108,
n
x
20. The calibration bars are shown on the right-hand side of the graphs, and the orientation
of the coordinate axes is indicated at the right side
=
[
28
]
n
x
→
1 one finds that defects need to be nucleated one by one, and hence
a time-consuming equilibration process is needed to generate an (approximately)
periodic arrangement of the defects (solitons) along the
y
-direction (note that at
nonzero temperature anyway we must expect large thermal fluctuations of these
defects around their average positions). In fact, sometimes states are formed where
the number of defects
n
d
deviates from the theoretical value as estimated above.
Presumably these are metastable configurations, separated by (large) barriers from
the equilibrium behavior.
Therefore, we have artificially prepared [
12
] other initial states, where for a given
misfit
n
x
−
3 inner rows, with the
n
d
excess particles
in each of these rows initially at random positions. Indeed we find that this way of
preparation of the system leads to a much more regular pattern of the resulting strain
density waves (Fig.
1.12
).
The periodicity of the soliton staircase shows up very nicely when one studies
the Lindemann parameter
we put
n
y
+
n
d
particles in the
n
x
−
u
x
(
R
n
)
−
u
x
(
R
n
)
2
[
12
] but this shall
not be further elaborated here. However, we emphasize that by such confinement
of crystals with boundaries that create misfit we can create a superstructure (via the
wavelength of the strain density wave pattern) which is of the same order as the
thickness of the strip.
(
n
)
defined as
1.6 Conclusions
In this brief review, confinement of two-dimensional crystals in strip geometry was
considered, based on Monte Carlo simulations of a generic model and pertinent the-
oretical considerations. It was argued that the confinement has particularly dramatic
