  The lattice thermal conductivities of silicon clathrate frameworks II and
VIII are investigated by using ab initio lattice dynamics and iterative
solution of the linearized Boltzmann transport equation(BTE) for phonons.
Within the temperature range 100-350 K, the clathrate structures II and VIII
were found to have lower lattice thermal conductivity values than silicon
diamond structure (d-Si) by factors of 1/2 and 1/5, respectively. The main
reason for the lower lattice thermal conductivity of the clathrate structure II
in comparison to d-Si was found to be the harmonic phonon spectra, while in the
case of the clathrate structure VIII, the difference is mainly due to the
harmonic phonon spectra and partly due to shorter relaxation times of phonons.
In the studied clathrate frameworks, the anharmonic effects have larger impact
on the lattice thermal conductivity than the size of the unit cell. For the
structure II, the predicted lattice thermal conductivity differs approximately
by factor of 20 from the previous experimental results obtained for a
polycrystalline sample at room temperature.
