Examining the Validity of the Phonon Gas Model in Amorphous Materials

The idea of treating phonon transport as equivalent to transport through a gas of particles is termed the phonon gas model (PGM), and it has been used almost ubiquitously to try and understand heat conduction in all solids. However, most of the modes in disordered materials do not propagate and thus may contribute to heat conduction in a fundamentally different way than is described by the PGM. From a practical perspective, the problem with trying to apply the PGM to amorphous materials is the fact that one cannot rigorously define the phonon velocities for non-propagating modes, since there is no periodicity. Here, we tested the validity of the PGM for amorphous materials by assuming the PGM is applicable, and then, using a combination of lattice dynamics, molecular dynamics (MD) and experimental thermal conductivity data, we back-calculated the phonon velocities for the vibrational modes. The results of this approach show that if the PGM was valid, a large number of the mid and high frequency modes would have to have either imaginary or extremely high velocities to reproduce the experimental thermal conductivity data. Furthermore, the results of MD based relaxation time calculations suggest that in amorphous materials there is little, if any, connection between relaxation times and thermal conductivity. This then strongly suggests that the PGM is inapplicable to amorphous solids.