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

Abstract

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