Energy transport in glasses

Abstract

The temperature dependence of the thermal conductivity is linked to the nature of the energy transport at a frequency ω, which is quantified by thermal diffusivity d(ω). Here we study d(ω) for a poorly annealed glass and a highly stable glass prepared using the swap Monte Carlo algorithm. To calculate d(ω), we excite wave packets and find that the energy moves diffusively for high frequencies up to a maximum frequency, beyond which the energy stays localized. At intermediate frequencies, we find a linear increase of the square of the width of the wave packet with time, which allows for a robust calculation of d(ω), but the wave packet is no longer well described by a Gaussian as for high frequencies.In this intermediate regime, there is a transition from a nearly frequency independent thermal diffusivity at high frequencies to d(ω) ∼ ω −4 at low frequencies. For low frequencies the sound waves are responsible for energy transport and the energy moves ballistically. The low frequency behavior can be predicted using sound attenuation coefficients.The thermal conductivity of amorphous solids is vastly different than that of their crystalline counterparts. The existence of several common features in the temperature dependence of the thermal conductivity of amorphous solids indicates a common origin 1-8 . At temperatures below ∼ 1K the thermal conductivity grows as T 2 compared to T 3 growth for crystalline solids. This quadratic growth of the thermal conductivity with temperature is generally attributed to two-level tunneling states 3,5,7,9-11 , although alternative explanations exist 12-14 . Around T ≈ 10K a plateau develops in the thermal conductivity and there is a nearly linear rise in the thermal conductivity after the plateau.The temperature dependence of the thermal conductivity κ can be analyzed in terms of frequency dependent thermal diffusivity d(ω), which quantifies how fast a wave packet, narrowly peaked around a frequency ω, propagates [15][16][17][18] . At low temperatures, only the low frequency modes are excited, and only the low frequency thermal diffusivity significantly contributes to the thermal conductivity. The most prevalent theories attribute the low frequency thermal diffusivity to two-level states, which provide the dominant contribution below 1K, and to thermal transport due to sound waves 19,20 . By considering the sound waves as a phonon gas, Debye argued that there is a contribution to d(ω) given by v(ω) (ω)/3 where v(ω) is the speed of sound and (ω) is the mean free path 21 . It is often assumed, and confirmed in recent simulations, that sound attenuation obeys Rayleigh scaling, and thus the contribution due to sound waves behaves as d s (ω) ∼ ω −422-24 . Several researchers demonstrated that the thermal conductivity can be accurately described for temperatures at and below the low temperature plateau by combining the contributions to d(ω) due to two level systems and due to sound waves 19,20,25,26 .At room temperature, where all vibrational modes are excited, the average mean free path...

Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses

“…For glasses, there are additional low-frequency modes that result in a peak in the reduced total density of states D(ω)/ω d−1 , which is referred to as the boson peak [8][9][10][11]. Understanding the nature of the additional modes provides insight into the physics behind the anomalous properties of glasses [12][13][14][15][16][17][18][19][20].…”

Density of States below the First Sound Mode in 3D Glasses

“…Due to the need of a very large amount of computation, it is now impossible for us to determine precisely how D(ω) scales with ω at very low frequencies below the first sound mode, but future work may be able to resolve this. In addition, it would be also necessary to check whether increasing the glass stability spectacularly may change our major conclusion since the glass stability matters a lot in modulating various properties of glasses [6,15,18,39,48,[55][56][57][58][59][60].…”

“…These excess modes, termed usually nonphononic or quasilocalized modes [9], could be observed in a broad class of glasses, and hence has become one universal hallmark of glasses. Importantly, it has been suggested explicitly that these excess modes could also give some insight into the understanding of glasses' other elusive properties [9][10][11][12][13][14][15][16][17][18], e.g., the mechanical and thermal properties of glasses, and the dynamics of supercooled liquids.…”

Low-frequency hybridized excess vibrations of two-dimensional glasses

“…For instance, at temperatures near 3 K-10 K in 3D glasses, the reduced specific heat C(T )/T 3 exhibits a peak that is suggested to originate from the boson peak referring to the maximum in the reduced density of states D(ω)/ω 2 . Additionally, numerous studies [9][10][11][12][13][14][15][16][17][18][19][20] over the past few decades have already established compelling connections between properties of excess modes and those of glasses and even glass-forming liquids.…”