Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects

Abstract

Sound attenuation in low temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here we analyze sound attenuation starting directly from the microscopic equations of motion. We derive an exact expression for the zero-temperature sound damping coefficient and verify that it agrees with results of earlier sound attenuation simulations. The small wavevector analysis of this expression shows that sound attenuation is primarily determined by the non-affine displacements' contribution to the wave propagation coefficient coming from the frequency shell of the sound wave.

Theory of sound attenuation in amorphous solids from nonaffine motions

“…and therefore, expanding at small wave-vector, we get Σ ∼ k 2 /β > 0 which indeed gives a constant, and importantly a negative correction to the speed of sound and the static shear modulus, in agreement with previous numerical calculations [17,18,21] and theoretical analysis [13][14][15].…”

“…( 18) are valid only in the region where Re ω = vk. Equation ( 18) is in perfect agreement with the discussion in [18]. By taking the imaginary part of the autocorrelation function in Eq.…”

“…It predicts also the crossover from diffusive to Rayleigh damping at larger wavevector and the Rayleigh damping itself and unveils its microscopic origin from nonaffine motions, thus superseding all previous models that start from the continuum macroscopic level. The analytical prediction of Rayleigh damping from nonaffinity is fully supported by recent numerical data [18]. Importantly, our main result in Eq.…”

“…The theory is first-principles and fully microscopic, and, unlike all previous approaches, it starts at the level of microscopic particle motions. This fully analytical theoretical structure thus provides a microscopic prediction of the damping Γ(k) as a function of k. Not only it is able to predict the diffusive damping at low k, including the prefactor which is, for the first time, related to important physical parameters (the Debye frequency, the nonaffine correction to the shear modulus, and the microscopic friction due to anharmonicity); it also predicts the experimentally observed [9] crossover from diffusive damping to Rayleigh damping at higher k. Also, it is fully supported by recent numerical results which also suggested the dominant role of nonaffine motions in the Rayleigh damping based on simulations [18].…”

“…Sound attenuation -Now that we have found the stress-stress auto-correlation function, we can use it to obtain the transverse displacement auto-correlation function χ u T u T (ω, k) which in the rest of the manuscript will be indicated as C(ω, k), and that can be written as [18,19,22,23]:…”