Many low-thermal-conductivity (κL) crystals show intriguing temperature (T) dependence of κL: κL ∝ T−1 (crystal-like) at intermediate temperatures whereas weak T-dependence (glass-like) at high temperatures. It has been in debate whether thermal transport can still be described by phonons at the Ioffe-Regel limit. In this work, we propose that most phonons are still well defined for thermal transport, whereas they carry heat via dual channels: normal phonons described by the Boltzmann transport equation theory, and diffuson-like phonons described by the diffusion theory. Three physics-based criteria are incorporated into first-principles calculations to judge mode-by-mode between the two phonon channels. Case studies on La2Zr2O7 and Tl3VSe4 show that normal phonons dominate low temperatures while diffuson-like phonons dominate high temperatures. Our present dual-phonon theory enlightens the physics of hierarchical phonon transport as approaching the Ioffe-Regel limit and provides a numerical method that should be practically applicable to many materials with vibrational hierarchy.

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Lu 1/6) 2 Si 2 O 7 has been designed and successfully synthesized following the strategy of high entropy engineering. The asprepared single-phase 6RE-disilicate possesses a new γ-type crystal structure (monoclinic, P2 1 /c) beyond the α-, βand δ-type parent structures of six single RE disilicates. Six-species RE cations are homogeneously distributed on RE lattice sites and our multicomponent disilicate demonstrates outstanding thermal stability from room temperature up to around 1900°C. This work extends the knowledge of strategic multicomponent modification of complex ceramics with extremely high phase stability.