Possible mechanism for glass-like thermal conductivities in crystals with off-center atoms

In the filled $\mathrm{Ga}∕\mathrm{Ge}$ clathrate, $\mathrm{Eu}$ and $\mathrm{Sr}$ are off center in site 2 but $\mathrm{Ba}$ is on center. All three filler atoms $(\mathrm{Ba},\mathrm{Eu},\mathrm{Sr})$ have low-temperature Einstein modes; yet only for the $\mathrm{Eu}$ and $\mathrm{Sr}$ systems is there a large dip in the thermal conductivity, attributed to the Einstein modes. No dip is observed for $\mathrm{Ba}$. Here we argue that it is the off-center displacement that is crucial for understanding this unexplained difference in behavior. It enhances the coupling between the “rattler” motion and the lattice phonons for the $\mathrm{Eu}$ and $\mathrm{Sr}$ systems, and turns on/off another scattering mechanism (for $1\mathrm{K}<T<20\mathrm{K}$) produced by the presence/absence of off-center sites. The random occupation of different off-center sites produces a high density of symmetry-breaking defects which scatter phonons. It may also be important for improving our understanding of other glassy systems.