Caroli Christiane, Lemaître Anaël
Sorbonne Universités, UPMC Université Paris 06, CNRS-UMR 7588, Institut des NanoSciences de Paris, 4 Place Jussieu, 75005 Paris, France.
NAVIER, UMR 8205, École des Ponts ParisTech, IFSTTAR, CNRS, UPE, Champs-sur-Marne, France.
J Chem Phys. 2020 Oct 14;153(14):144502. doi: 10.1063/5.0019964.
We investigate acoustic propagation in amorphous solids by constructing a projection formalism based on separating atomic vibrations into two, "phonon" (P) and "non-phonon" (NP), subspaces corresponding to large and small wavelengths. For a pairwise interaction model, we show the existence of a "natural" separation lengthscale, determined by structural disorder, for which the isolated P subspace presents the acoustic properties of a nearly homogenous (Debye-like) elastic continuum, while the NP one encapsulates all small scale non-affinity effects. The NP eigenstates then play the role of dynamical scatterers for the phonons. However, at variance with a conjecture of defect theories, their spectra present a finite low frequency gap, which turns out to lie around the Boson peak frequency, and only a small fraction of them are highly localized. We then show that small scale disorder effects can be rigorously reduced to the existence, in the Navier-like wave equation of the continuum, of a generalized elasticity tensor, which is not only retarded, since scatterers are dynamical, but also non-local. The full neglect of both retardation and non-locality suffices to account for most of the corrections to Born macroscopic moduli. However, these two features are responsible for sound speed dispersion and have quite a significant effect on the magnitude of sound attenuation. Although it remains open how they impact the asymptotic, large wavelength scaling of sound damping, our findings rule out the possibility of representing an amorphous solid by an inhomogeneous elastic continuum with the standard (i.e., local and static) elastic moduli.
我们通过构建一种投影形式理论来研究非晶态固体中的声学传播，该理论基于将原子振动分离为两个子空间，即对应于大波长的“声子”（P）子空间和对应于小波长的“非声子”（NP）子空间。对于一个成对相互作用模型，我们展示了存在一个由结构无序决定的“自然”分离长度尺度，对于该尺度，孤立的P子空间呈现出近乎均匀（类德拜）弹性连续体的声学特性，而NP子空间则包含了所有小尺度的非亲和效应。NP本征态随后充当声子的动态散射体。然而，与缺陷理论的一个猜想不同，它们的谱呈现出一个有限的低频间隙，结果发现该间隙位于玻色子峰频率附近，并且只有一小部分是高度局域化的。然后我们表明，小尺度无序效应可以严格地归结为在连续体的类纳维波动方程中存在一个广义弹性张量，该张量不仅是延迟的，因为散射体是动态的，而且是非局部的。完全忽略延迟和非局部性足以解释对玻恩宏观模量的大部分修正。然而，这两个特征导致了声速色散，并对声衰减的大小有相当显著的影响。尽管它们如何影响声衰减的渐近大波长标度仍然未知，但我们的发现排除了用具有标准（即局部和静态）弹性模量的非均匀弹性连续体来表示非晶态固体的可能性。
