Size Effect on the Thermal Conductivity of a Type-I Clathrate

Clathrates are a materials class with an extremely low phonon thermal conductivity, which is key ingredient for high thermoelectric conversion efficiency. Here, we present study on the type-I clathrate La$_{1.2}$Ba$_{6.8}$Au$_{5.8}$Si$_{38.8}\square_{1.4}$ directed at lowering conductivity even further by forming mesoscopic wires out of it. Our hypothesis that interaction low-energy rattling modes guest atoms (La and Ba) acoustic modes, originate mainly from framework (formed Au Si atoms, some vacancies $\square$), cuts off their dispersion thereby tilts balance phonons relevant transport to long-wavelength ones. Thus, size effects expected set in relatively long length scales. The structuring was carried using top-down approach, where wires, ranging 1260 nm 630 diameter, were cut piece single crystal focused ion beam technique. Measurements performed self-heating $3\omega$ technique down 80 K. Indeed, they reveal reduction room-temperature sizable fraction $\sim$40 % our thinnest wire, confirming hypothesis.