From phonons to the thermal properties of complex thermoelectric crystals: The case of type-I clathrates

Abstract

Exploiting the structural complexity of crystals at the scale of their unit cell is a well-established strategy in the search for efficient materials for energy conversion, which aims at disentangling and separately engineering heat and charge transport. This route has resulted in the discovery of clathrates with exceptionally low lattice thermal conductivity but essentially unaffected and tunable electronic properties. Although their thermal conductivity behaves similarly to the one of glasses, its origin is fundamentally different. Indeed, phonons with long lifetime were observed over the whole Brillouin zone, thus excluding an interpretation in terms of a reduced mean free path. However, the energy–momentum phase space which contains these heat carrying phonons is capped by a dense spectrum of diffusive modes. The thermal properties of clathrates can therefore be split in two parts: a narrow low energy regime that contains propagative modes which dominate the thermal transport, and a broad high energy range consisting of diffusive modes that dominate the heat capacity. Based on this understanding, a simple phenomenological model, based on a basic description in terms of Debye and Einstein modes, is derived that allows for a meaningful interpretation of experimental data, by providing a connection to the underlying microscopic origin. Finally, the criteria for determining the minimum lattice thermal conductivity are redefined and strategies for decreasing the lattice conductivity are proposed.