Bridging glass-like and crystal-like thermal transport: A unified model for disordered and complex solids

Thermal transport in disordered crystals, mixed systems, and structurally complex solids displays a continuous evolution between glass-like and crystal-like behavior that is not captured by conventional phonon-based models. We develop a unified phenomenological framework that combines a Peierls-type phonon contribution with a coherence term describing wave-like tunneling of vibrational excitations. The model quantitatively reproduces experimental measurements of κ(T) for more than 75 systems, including clathrates, mixed crystals, perovskites, orientationally disordered solids, organic semiconductors, and amorphous polymers, over temperatures from 0.1 to 300 K. Systematic trends in the phonon-phonon scattering amplitude A, the plateau conductivity κpl, and the coherence energy E reflect underlying structural order and enable predictive modelling of κ(T) for arbitrary compositions. Comparison with molecular-dynamics simulations of solid amorphous Si and nanostructured composites, confirms the accuracy of the dual-component approach across diffusive and wave-like regimes. The physically interpretable parameters and broad applicability of the framework make it suitable for machine-learning integration and data-driven discovery of low-thermal-conductivity and thermoelectric materials.