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• Abstract: found

Analytical prediction of logarithmic Rayleigh scattering in amorphous solids from tensorial heterogeneous elasticity with power-law disorder

1 , 2 , 3 , 4 , 1 , 2 , 3 , 4 , 5

Soft Matter

Royal Society of Chemistry (RSC)

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Abstract

A tensorial replica-field theory is developed to solve the elastic wave scattering problem in amorphous solids, which leads to the logarithmic correction to the Rayleigh scattering law.

Abstract

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.

Most cited references1

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Theory of Elasticity

(1986)
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Author and article information

Journal
SMOABF
Soft Matter
Soft Matter
Royal Society of Chemistry (RSC)
1744-683X
1744-6848
August 26 2020
2020
: 16
: 33
: 7797-7807
Affiliations
[1 ]Cavendish Laboratory
[2 ]University of Cambridge
[3 ]CB3 0HE Cambridge
[4 ]UK
[5 ]Department of Physics “A. Pontremoli”
Article
10.1039/D0SM00814A