Structural metrics of high-temperature lattice conductivity

An atomic structure-based model for high-temperature lattice conductivity is developed for both compact crystals and cage-bridge crystals. For compact crystals, where long-range acoustic phonons dominate, the Debye temperature TD and Grüneisen parameter γ are estimated using interatomic potentials to arrive at the lattice conductivity relation. Under the assumption of homogeneous deformation, TD is estimated according to a simplified force constant matrix and a phenomenological combinative rule for force constants, which is applicable to an arbitrary pair of interacting atoms. Also, γ is estimated from a general Lennard-Jones potential form and the combination of the bonds. The results predicted by the model are in close agreement with the experimental results. For cage-bridge crystals, where both short-range acoustic phonons and optical phonons may be important, a simple mean-free path model is proposed: The phonon mean-free path of such a crystal at high temperatures is essentially limited by its structure and is equal to the cage size. This model also shows good agreement with the results of experiments and molecular dynamics simulations. Based on this atomic-level model, the structural metrics of crystals with low or high lattice conductivity are discussed, and some strategies for thermal design and management are suggested.