Abstract
We present first principles calculations of the phonon dispersions of \BiTe and discuss these in relation to the acoustic phonon
interface scattering in ceramics. The phonon dispersions show agreement with what is known from neutron scattering for the optic modes.
We find a difference between the generalized gradient approximation and local density results for the acoustic branches. This is a
consequence of an artificial compression of the van der Waals bonded gaps in the \BiTe structure when using the generalized gradient approximation.
As a result local density approximation calculations provide a better description of the phonon dispersions in Bi$_{2}$Te$_{3}$. A key characteristic
of the acoustic dispersions is the existence of a strong anisotropy in the velocities. We develop a model for interface
scattering in ceramics with acoustic wave anisotropy and apply this to \BiTe and compare with PbTe and diamond.
