  To elucidate the relationship between a crystal's structure, its thermal
conductivity, and its phonon dispersion characteristics, an analysis is
conducted on layered diatomic Lennard-Jones crystals with various mass ratios.
Lattice dynamics theory and molecular dynamics simulations are used to predict
the phonon dispersion curves and the thermal conductivity. The layered
structure generates directionally dependent thermal conductivities lower than
those predicted by density trends alone. The dispersion characteristics are
quantified using a set of novel band diagram metrics, which are used to assess
the contributions of acoustic phonons and optical phonons to the thermal
conductivity. The thermal conductivity increases as the extent of the acoustic
modes increases, and decreases as the extent of the stop bands increases. The
sensitivity of the thermal conductivity to the band diagram metrics is highest
at low temperatures, where there is less anharmonic scattering, indicating that
dispersion plays a more prominent role in thermal transport in that regime. We
propose that the dispersion metrics (i) provide an indirect measure of the
relative contributions of dispersion and anharmonic scattering to the thermal
transport, and (ii) uncouple the standard thermal conductivity
structure-property relation to that of structure-dispersion and
dispersion-property relations, providing opportunities for better understanding
of the underlying physical mechanisms and a potential tool for material design.
