Einstein oscillators that impede thermal transport

The Einstein model of a solid usually lacks a clear illustration in introductory solid-state physics courses because most solids are much better described by the Debye model. Filled antimony skutterudites, materials that have recently attracted much attention because of their potential for thermoelectric applications, provide a canonical illustration of the Einstein model. The filling atoms are loosely bound in the atomic cage formed by their neighbors, and hence their description as independent harmonic oscillators is adequate. Simple models for the heat capacity and thermal conductivity of a solid are introduced, with emphasis on the density of vibrational states. These models are used in conjunction with experimental results obtained from heat capacity and inelastic neutron scattering measurements to demonstrate the applicability of the concept of the Einstein oscillator to the filling guests in antimony skutterudites. The importance of these Einstein oscillators for impeding thermal transport is discussed and some simple problems involving the heat capacity, thermal conductivity, and inelastic neutron scattering are proposed.