Chemistry Reference
In-Depth Information
effects on the ordering, given the fact that a two-dimensional crystal is a “criti-
cal system” (lack of positional long-range order, possibility that melting happens
according to the KTHNY scenario).
Assuming a confinement that is commensurate with the crystal structure, it was
shown that confinement enhances the positional order in the direction perpendicu-
lar to the boundary (“layering”) and that orientational order parallel to the bound-
ary always gets enhanced. However, positional order parallel to the flat boundary
(“planar wall”) gets weakened or even destroyed. Both the crossover to quasi-one-
dimensional behavior of strips of finite width and surface critical behavior con-
tribute to these effects, and the shear elastic constant of the strip was found to be
(almost) zero.
Particularly interesting are compressed strips, where transitions occur from
n
to
n
1 rows parallel to the walls. The “structured wall” boundary condition then
implies incommensurability with the periodicity of the film, leading to the formation
of “soliton staircases” along the boundaries, and the solitons act as cores of standing
strain waves in the system.
While the original motivation of this research stems from colloidal crystals [
17
-
20
], we emphasize that related phenomena could occur in very different systems,
e.g., various semiconductor devices such as quantum dot superlattices [
29
], lattice-
mismatched fused GaAs/In P wafers [
30
], Ge
x
S
i
1
−
x
/
−
Si heterostructures [
31
], and
rotationally misaligned Si wafers covalently bonded together [
32
]. In all such sys-
tems boundary-induced strain fields can occur. A particularly nice example where
the misfit between a crystal and a frozen boundary can be controlled by external
magnetic field is superconducting vortex lattices [
33
]. A very interesting aspect,
closely related to the work reviewed here but out of scope of this chapter, is uncon-
ventional nonlinear mechanical response properties of confined solids [
34
,
35
].
Thus, we feel that the phenomena described in the present brief review should have
widespread applications in the physics of condensed matter.
Acknowledgments
This research was partially supported by the Deutsche Forschungsgemein-
schaft (DFG), Project TR 6/C4.
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