  Crystals and glasses exhibit fundamentally different heat conduction
mechanisms: the periodicity of crystals allows for the excitation of
propagating vibrational waves that carry heat, as first discussed by Peierls;
in glasses, the lack of periodicity breaks Peierls' picture and heat is mainly
carried by the coupling of vibrational modes, often described by a harmonic
theory introduced by Allen and Feldman. Anharmonicity or disorder are thus the
limiting factors for thermal conductivity in crystals or glasses; hitherto, no
transport equation has been able to account for both. Here, we derive such
equation, resulting in a thermal conductivity that reduces to the Peierls and
Allen-Feldman limits, respectively, in anharmonic-and-ordered or
harmonic-and-disordered solids, while also covering the intermediate regimes
where both effects are relevant. This approach also solves the long-standing
problem of accurately predicting the thermal properties of crystals with
ultralow or glass-like thermal conductivity, as we show with an application to
a thermoelectric material representative of this class.

Materials Science