A solid conducts heat through both transverse and longitudinal acoustic phonons, but a liquid employs only longitudinal vibrations. Here, we report that the crystalline solid AgCrSe2 has liquid-like thermal conduction. In this compound, Ag atoms exhibit a dynamic duality that they are exclusively involved in intense low-lying transverse acoustic phonons while they also undergo local fluctuations inherent in an order-to-disorder transition occurring at 450 K. As a consequence of this extreme disorder-phonon coupling, transverse acoustic phonons become damped as approaching the transition temperature, above which they are not defined anymore because their lifetime is shorter than the relaxation time of local fluctuations. Nevertheless, the damped longitudinal acoustic phonon survives for thermal transport. This microscopic insight might reshape the fundamental idea on thermal transport properties of matter and facilitates the optimization of thermoelectrics.
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