Abstract
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.
Highlights
There is a gap in the theoretical understanding of heat conduction through amorphous solids and a lack of numerical methodologies for predicting the associated mode level thermal conductivity contributions
If one were to try and rationalize the results in terms of the phonon gas model (PGM), one would expect that the corresponding thermal diffusivity contributions must follow the same temperature dependence as the relaxation times determined from molecular dynamics (MD)
For amorphous silicon (a-Si), on the other hand (see Fig. 3(c)), the modes exhibit positive σ when comparing 100–300 K, which implies the relaxation time could be a suitable descriptor in that temperature regime, but Fig. 3(d) shows that between 300–800 K there is a marked change in the behavior and σ becomes negative for most modes
Summary
Materials received: 07 April 2016 accepted: 01 November 2016 Published: 05 December 2016. From the PGM perspective, thermal conductivity depends on the individual mode heat capacities (c), phonon group velocities (vg), and relaxation times (τ) as, κ. Imaginary velocities have no sensible interpretation in the PGM and velocities that are orders of magnitude greater than the speed of sound are nonsensical, even if one assumes the real quantum relaxation times are an order of magnitude larger These two observations lead us to conclude that one cannot self-consistently rationalize the usage of the PGM in a-SiO2 and it is likely that the lack of applicability may extend to many, if not all, amorphous materials.
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