  Infrared carbon stars without visible counterparts are generally known as
extreme carbon stars. We have selected a subset of these stars with absorption
features in the 10-13 $\mu$m range, which has been tentatively attributed to
silicon carbide (SiC). We add three new objects meeting these criterion to the
seven previously known, bringing our total sample to ten sources. We also
present the result of radiative transfer modeling for these stars, comparing
these results to those of previous studies. In order to constrain model
parameters, we use published mass-loss rates, expansion velocities and
theoretical dust condensation models to determine the dust condensation
temperature. These show that the inner dust temperatures of the dust shells for
these sources are significantly higher than previously assumed. This also
implies that the dominant dust species should be graphite instead of amorphous
carbon. In combination with the higher condensation temperature we show that
this results in a much higher acceleration of the dust grains than would be
expected from previous work. Our model results suggest that the very optically
thick stage of evolution does not coincide with the timescales for the
superwind, but rather, that this is a very short-lived phase. Additionally, we
compare model and observational parameters in an attempt to find any
correlations. Finally, we show that the spectrum of one source, IRAS
17534$-$3030, strongly implies that the 10-13 $\mu$m feature is due to a solid
state rather than a molecular species.
