Universal Relation between Guest Free Space and Lattice Thermal Conductivity Reduction by Anharmonic Rattling in Type-I Clathrates

Since the early days of studies on thermoelectric clathrates it has been evidenced that the lowering of thermal conductivity in these compounds is related to the guest ion's rattling characteristics. Here we report on the relation between the guest vibration and lattice thermal conductivity κ L in single crystalline samples of type-I clathrates Ba 8 In 16 Ge 30- x M x (M = Si, Sn) with n-type carriers. On going from M x = Si 1.6 to M x = Sn 2.2 , the lattice parameter increases by 1% from 11.20 to 11.30 A. This is accompanied by a decrease from 39 to 35 K in the local vibration energy of the Ba guest ions in the tetrakaidecahedron cages, and a strong suppression of κ L , which shows glasslike temperature dependence for M x = Sn 2.2 . We further demonstrate that the lowering of κ L at 150 K shows universality behavior and scales very well with the guest free space for vibration in all type-I clathrates, largely independent of the guest or framework ions.