Examining the Validity of the Phonon Gas Model in Amorphous Materials

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.

Propagating elastic vibrations dominate thermal conduction in amorphous silicon

“…Specifically, by calculating the density of states of the propagating vibrations with a Debye model, we estimate that about 24% of all modes are propagating waves. Our observation is consistent with prior calculations of dynamical structure factor [6,19] but is inconsistent with prior conclusions that propagons have frequencies less than 2-3 THz in amorphous silicon [3,[5][6][7]17,20].…”

Thermal Conductivity of Amorphous Materials

“…Conceptually, propagons largely resemble the usual definition of phonons and can carry energy with a speed governed by the group velocity. Thus, propagons can usually be treated as long wavelength phonons with the PGM, but this model is not applicable to diffusons based on a detailed study using normal mode lifetime analysis . Using nonequilibrium MD simulations, He et al reported that propagons with an MFP on the order of micrometer contribute roughly half the total thermal conductivity in amorphous silicon .…”

“…Various simulation and experimental methodologies have been developed in the study of the physical characteristics of thermal transport in amorphous materials. Molecular dynamics (MD) simulation is a commonly used computational tool . In MD simulation, the positions and velocities of all atoms evolve following Newton's laws of motion.…”

Rethinking phonons: The issue of disorder

“…We then used a cubic supercell of a 2 × 2 × 2 conventional unit cell, which consists of 64 atoms in total, to compute the various terms in Eq. (9).…”

“…[1][2][3] Each step in vibrational mode energy is then thought of as a quasi-particle termed a phonon, and the theory describing their transport is known as the phonon gas model (PGM). [1][2][3][4][5][6][7][8][9] The PGM was largely born out of the types of vibrations that would exist in an infinitely large, pure, homogeneous crystal (IPHC). In such a system, one can solve the equations of motion in the harmonic limit and find that all solutions correspond to plane wave modulated vibrations, as a result of the periodicity.…”