First principles lattice thermal conductivity of Li$_{\mathrm{2}}$Se, Li$_{\mathrm{2}}$Te and alloys: phase space guidelines for thermal transport

The lattice thermal conductivities ($k)$ of Li$_{\mathrm{2}}$Se, Li$_{\mathrm{2}}$Te and alloys are examined using a first-principles Peierls-Boltzmann transport methodology. The dominant resistance to heat-carrying acoustic phonons in Li$_{\mathrm{2}}$Se and Li$_{\mathrm{2}}$Te comes from the interactions of these modes with two optic phonons, aoo scattering. In typical cubic and hexagonal materials ($e.g.$, Si, GaAs, AlN) aoo scattering does not play a considerable role in determining $k$, as it requires significant bandwidth and dispersion of the optic phonon branches, both present in Li$_{\mathrm{2}}$Se and Li$_{\mathrm{2}}$Te. We discuss how these properties and other features of the phonon dispersion ($e.g.$, bunching of the acoustic branches and an acoustic-optic frequency gap) combine to determine the overall conductivity of a material. Thus, microscopic scattering phase space arguments are generalized to give a more comprehensive view of intrinsic thermal transport in crystalline solids. We note that these general considerations are important for the discovery and design of new `high$ k$' and `low $k$' materials for thermal management applications.