The phonon gas model (PGM) is the idea that the quantized collective vibrations of atoms, termed phonons, can be treated as a gas of particles that exchange energy through scattering events. The PGM is originated from the behaviors observed and rationalized in homogenous crystalline solids. It has exhibited remarkable success in describing the behavior of a wide variety of solids, microstructures, nanostructures and molecules. Given its success, it has become the primary lens with which phonon transport is viewed. However, for amorphous materials, or other structurally/compositionally-disordered systems, due to the lack of periodicity, one cannot clearly define the phonon velocity. Since the PGM hinges on knowledge of the phonon velocities, the application of the PGM to amorphous materials has been highly questionable. Here, we developed a new method for direct calculation of the modal contributions to thermal conductivity, which is termed the Green-Kubo modal analysis (GKMA). The GKMA method combines the lattice dynamics formalism with the Green-Kubo formula for thermal conductivity, such that the thermal conductivity becomes a direct summation of modal contributions, where one does not need to define a phonon velocity. The predicted temperature dependent thermal conductivity of several amorphous materials shows the best agreement with experiments to date. Furthermore, we demonstate a few cases that the PGM fails. We first exhibit the violations of the PGM in case studies of the amorphous materials and single polymer chains. PGM based methods fail to explain the experimental results of the thermal conductivity of the amorphous solids. Then we utilize GKMA to calculate and explain the results. It further proves the deficiency of the PGM based methods on predicting the thermal properties on non-crystaline solids.
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