Part-crystalline part-liquid state and rattling-like thermal damping in materials with chemical-bond hierarchy

Understanding thermal and phonon transport in solids has been of great importance in many disciplines such as thermoelectric materials, which usually requires an extremely low lattice thermal conductivity (LTC). By analyzing the finite-temperature structural and vibrational characteristics of typical thermoelectric compounds such as filled skutterudites and Cu₃SbSe₃, we demonstrate a concept of part-crystalline part-liquid state in the compounds with chemical-bond hierarchy, in which certain constituent species weakly bond to other part of the crystal. Such a material could intrinsically manifest the coexistence of rigid crystalline sublattices and other fluctuating noncrystalline sublattices with thermally induced large-amplitude vibrations and even flow of the group of species atoms, leading to atomic-level heterogeneity, mixed part-crystalline part-liquid structure, and thus rattling-like thermal damping due to the collective soft-mode vibrations similar to the Boson peak in amorphous materials. The observed abnormal LTC close to the amorphous limit in these materials can only be described by an effective approach that approximately treats the rattling-like damping as a "resonant" phonon scattering.