The origin of sound damping in amorphous solids: Defects and beyond

Comprehending sound damping is integral to understanding the anomalous low temperature properties of glasses. After decades of theoretical and experimental studies, Rayleigh scattering scaling of the sound attenuation coefficient with frequency Γ∼ωd+1, became generally accepted when quantum and finite temperature effects can be neglected. Rayleigh scaling invokes a picture of scattering from defects. However, it is unclear how to define glass defects, or even if defects are necessary for Rayleigh scaling. Here we determine a particle level contribution to sound damping in the Rayleigh scaling regime. We find that there are areas in the glass that contribute more to sound damping than other areas over a range of frequencies, which allows us to define defects. We show that over a range of glass stability, sound damping scales linearly with the fraction of particles in the defects. However, sound is still attenuated in ultra-stable glasses where no defects are identified. We show that sound damping in these glasses is due to nearly uniformly distributed non-affine microscopic forces that arise after macroscopic deformations of non-centrosymetric structures. To fully understand sound attenuation in glasses, one has to consider contributions from defects and a defect-free background, which represents a new paradigm of sound damping in glasses.

Methods
These data were computed from simulations of a model glass forming liquid. The simulated systems were quenched to their nearest potential energy minimum, an inherent structure. We calculated the eigenvalues and eigenvectors of the Hessian matrix that was calculated at the inherent structure. These eigenvalues and eigenvectors were used to calculate sound attenuation using a microscopic theory. The theory was compared to sound attenuation calculated using harmonic simulations of the same glasses. 

The inherent structures were found using LAMMPS simulation code. The eigenvalues and eigenvectors were determined using ARPACK. The calculation of the Hessian matrix and sound attenuation from the microscopic theory was determined from in in-house code. The simulations used to determine sound attenuation were performed using in-house code.

理解声阻尼是解析玻璃态材料反常低温特性的核心环节。历经数十年理论与实验研究，当可忽略量子效应与有限温度效应时，声衰减系数随频率的瑞利散射标度关系Γ~ω^{d+1}已被广泛接受。瑞利标度基于缺陷散射的物理图像，但目前尚不清楚如何明确定义玻璃态缺陷，甚至无法确定缺陷是否是瑞利标度成立的必要条件。
本文探究了瑞利标度区间内声阻尼的粒子级贡献。我们发现，在一定频率范围内，玻璃中存在部分区域的声阻尼贡献显著高于其他区域，借此可对缺陷进行明确定义。研究证实，在一定的玻璃态稳定性区间内，声阻尼与缺陷内粒子占比呈线性标度关系。但在未检测到缺陷的超稳定玻璃中，声衰减依然存在。我们表明，这类玻璃的声阻尼源于非中心对称结构经宏观变形后产生的近似均匀分布的非仿射微观作用力。若要全面理解玻璃态材料的声衰减机制，必须同时考虑缺陷与无缺陷背景的贡献，这为玻璃态声阻尼研究提供了全新范式。

方法
本数据集基于模型玻璃形成液体的模拟结果计算得到。模拟体系被淬冷至其最邻近势能极小点，即固有结构（inherent structure）。我们计算了固有结构处的海森矩阵（Hessian matrix）的本征值与本征向量，并借助微观理论利用这些本征量计算声衰减，将该理论计算结果与同一玻璃体系的简谐模拟所得声衰减结果进行了对比。
固有结构的求解采用LAMMPS模拟软件包完成。本征值与本征向量的计算使用ARPACK工具库实现。海森矩阵计算与基于微观理论的声衰减计算均通过自研代码完成。用于声衰减计算的模拟实验同样通过自研代码执行。