  Computationally efficient modeling of the thermal conductivity of materials
is crucial to thorough experimental planning and theoretical understanding of
thermal properties. We present a modeling approach in this work that utilizes
frequency-dependent effective medium to calculate lattice thermal conductivity
of nanostructured solids. The method accurately predicts a significant
reduction in the thermal conductivity of nanostructured Si80Ge20 systems, along
with previous reported thermal conductivities in nanowires and
nanoparticles-in-matrix materials. We use our model to gain insight into the
role of long wavelength phonons on the thermal conductivity of nanograined
silicon-germanium alloys. Through thermal conductivity accumulation
calculations with our modified effective medium model, we show that phonons
with wavelengths much greater than the average grain size will not be impacted
by grain boundary scattering, counter to the traditionally assumed notion that
grain boundaries in solids will act as diffusive interfaces that will limit
long wavelength phonon transport. This is further supported through a
modulation frequency dependent thermal conductivity as measured with
time-domain thermoreflectance.
