Cui Bingyu, Zaccone Alessio
Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB3 0HE Cambridge, UK.
Soft Matter. 2020 Aug 26;16(33):7797-7807. doi: 10.1039/d0sm00814a.
The damping or attenuation coefficient of sound waves in solids due to impurities scales with the wavevector to the fourth power, also known as Rayleigh scattering. In amorphous solids, Rayleigh scattering may be enhanced by a logarithmic factor although computer simulations offer conflicting conclusions regarding this enhancement and its microscopic origin. We present a tensorial replica field-theoretic derivation based on heterogeneous or fluctuating elasticity (HE), which shows that long-range (power-law) spatial correlations of the elastic constants, is the origin of the logarithmic enhancement to Rayleigh scattering of phonons in amorphous solids. We also consider the case of zero spatial fluctuations in the elastic constants, and of power-law decaying fluctuations in the internal stresses. Also in this case the logarithmic enhancement to the Rayleigh scattering law can be derived from the proposed tensorial HE framework.
由于杂质导致的固体中声波的阻尼或衰减系数与波矢的四次方成正比，这也被称为瑞利散射。在非晶态固体中，瑞利散射可能会因一个对数因子而增强，尽管计算机模拟对于这种增强及其微观起源给出了相互矛盾的结论。我们基于非均匀或波动弹性（HE）提出了一种张量复制场论推导，它表明弹性常数的长程（幂律）空间相关性是导致非晶态固体中声子瑞利散射对数增强的原因。我们还考虑了弹性常数零空间波动以及内应力幂律衰减波动的情况。在这种情况下，瑞利散射定律的对数增强也可以从所提出的张量HE框架中推导出来。
