Abstract:
The theory for the explanation of equilibrium morphologies of incommensurately
modulated one-dimensional
crystals, presented in a previous paper, is extended to the case of
incommensurately modulated
three-dimensional crystals. It is shown that, concerning the morphology,
there exists a one-to-one
correspondence between faces on the physical crystal and crystallographic
hyperplanes of the embedded
crystal in superspace. This holds for both main faces and satellite
faces. The occurrence of the latter, however,
is unique for incommensurately modulated crystals. It is shown that
the stability of satellite faces, as well as
main faces, can be attributed to a principle of selective cuts. The
superspace approach that is developed leads
to a calculation method for surface free energies that, in principle,
can be applied to incommensurately
modulated structures of arbitrary complexity. Equilibrium morphologies
are constructed from the calculated
surface free energies by means of; a standard Wulff plot. The dependence
of the equilibrium morphology on
several structural parameters is studied for an incommensurately modulated
simple cubic model crystal. This
study allows for a basic understanding of the differences in morphology
of AuTe2 crystals and
[(CH3)4N]2ZnCl4 crystals.