  We investigate the role of rattling guest atoms on the lattice
thermal-conductivity of a type-I clathrate Ba$_{8}$Ga$_{16}$Ge$_{30}$ by
first-principles lattice dynamics. Comparing phonon properties of filled and
empty clathrates, we show that rattlers cause 10-fold reductions in the
relaxation time of phonons by increasing the phonon-phonon scattering
probability. Contrary to the resonant scattering scenario, the reduction in the
relaxation time occurs in a wide frequency range, which is crucial for
explaining unusually low thermal-conductivities of clathrates. We also find
that the impact of rattlers on the group velocity of phonons is secondary
because the flattening of phonon dispersion occurs only in a limited phase
space in the Brillouin zone.
