Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amorphous solids. DeGiuli, E.; Laversanne-Finot, A.; Duering, G.; Lerner, E.; and Wyart, M. SOFT MATTER, 10(30):5628-5644, ROYAL SOC CHEMISTRY, 2014.
abstract   bibtex   
Connectedness and applied stress strongly affect elasticity in solids. In various amorphous materials, mechanical stability can be lost either by reducing connectedness or by increasing pressure. We present an effective medium theory of elasticity that extends previous approaches by incorporating the effect of compression, of amplitude e, allowing one to describe quantitative features of sound propagation, transport, the boson peak, and elastic moduli near the elastic instability occurring at a compression e(c). The theory disentangles several frequencies characterizing the vibrational spectrum: the onset frequency omega(0) similar to root e(c) - e where strongly-scattered modes appear in the vibrational spectrum, the pressure-independent frequency omega(*) where the density of states displays a plateau, the boson peak frequency omega(BP) found to scale as omega(BP) similar to root omega(0)omega(*), and the Ioffe-Regel frequency omega(IR) where scattering length and wavelength become equal. We predict that sound attenuation crosses over from omega(4) to omega(2) behaviour at omega(0), consistent with observations in glasses. We predict that a frequency-dependent length scale l(s)(omega) and speed of sound v(omega) characterize vibrational modes, and could be extracted from scattering data. One key result is the prediction of a flat diffusivity above omega(0), in agreement with previously unexplained observations. We find that the shear modulus does not vanish at the elastic instability, but drops by a factor of 2. We check our predictions in packings of soft particles and study the case of covalent networks and silica, for which we predict omega(IR) approximate to omega(BP). Overall, our approach unifies sound attenuation, transport and length scales entering elasticity in a single framework where disorder is not the main parameter controlling the boson peak, in agreement with observations. This framework leads to a phase diagram where various glasses can be placed, connecting microscopic structure to vibrational properties.
@article{
 title = {Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amorphous solids},
 type = {article},
 year = {2014},
 identifiers = {[object Object]},
 pages = {5628-5644},
 volume = {10},
 publisher = {ROYAL SOC CHEMISTRY},
 city = {THOMAS GRAHAM HOUSE, SCIENCE PARK, MILTON RD, CAMBRIDGE CB4 0WF, CAMBS, ENGLAND},
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 last_modified = {2017-03-14T13:46:52.169Z},
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 abstract = {Connectedness and applied stress strongly affect elasticity in solids.
In various amorphous materials, mechanical stability can be lost either
by reducing connectedness or by increasing pressure. We present an
effective medium theory of elasticity that extends previous approaches
by incorporating the effect of compression, of amplitude e, allowing one
to describe quantitative features of sound propagation, transport, the
boson peak, and elastic moduli near the elastic instability occurring at
a compression e(c). The theory disentangles several frequencies
characterizing the vibrational spectrum: the onset frequency omega(0)
similar to root e(c) - e where strongly-scattered modes appear in the
vibrational spectrum, the pressure-independent frequency omega(*)
where the density of states displays a plateau, the boson peak frequency
omega(BP) found to scale as omega(BP) similar to root
omega(0)omega(*), and the Ioffe-Regel frequency omega(IR) where
scattering length and wavelength become equal. We predict that sound
attenuation crosses over from omega(4) to omega(2) behaviour at
omega(0), consistent with observations in glasses. We predict that a
frequency-dependent length scale l(s)(omega) and speed of sound v(omega)
characterize vibrational modes, and could be extracted from scattering
data. One key result is the prediction of a flat diffusivity above
omega(0), in agreement with previously unexplained observations. We find
that the shear modulus does not vanish at the elastic instability, but
drops by a factor of 2. We check our predictions in packings of soft
particles and study the case of covalent networks and silica, for which
we predict omega(IR) approximate to omega(BP). Overall, our approach
unifies sound attenuation, transport and length scales entering
elasticity in a single framework where disorder is not the main
parameter controlling the boson peak, in agreement with observations.
This framework leads to a phase diagram where various glasses can be
placed, connecting microscopic structure to vibrational properties.},
 bibtype = {article},
 author = {DeGiuli, Eric and Laversanne-Finot, Adrien and Duering, Gustavo and Lerner, Edan and Wyart, Matthieu},
 journal = {SOFT MATTER},
 number = {30}
}
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