Phonon free energy in silicon carbide polytypism.
MJ Rutter, V Heine.
Abstract
Silicon carbide is a much-studied polytypic substance. It is formed
from layers stacking on top of each other, each layer taking one of
two possible orientations. The electronic free energies of many of
these stacking sequences, or polytypes, are almost identical,
Thus the phonon free energy, usually insignificant compared with
electronic energies, can become important in favouring one polytype
over another. It is known from experiment that SiC transforms from the
4H to 6H phase as temperature increases, and there is some evidence
for other intermediate phases. A simplified model of SiC's structure
is presented, in which the phonon free energy could indeed drive
the observed transition. This model shows that the phonon free energy
can cause an interaction between reversals in the stacking direction
which is long-ranged, decaying as the inverse square of the separation
of the reversals. The authors would argue that such a result is
probably of a general nature. The stability of long-period
intermediate phases and the possibility of a "devil's staircase" (an
infinite sequence of intermediate phases) occuring are then
investigated. For the family of interactions studied no staircase is
found, but rather just a single step. This conclusion is quite
consistent with experimental evidence in the case of silicon carbide.
This preprint is available as gzipped postscript
here.
The paper will be presented at Aperiodic97 in Alpe d'Huez, France.