955 research outputs found
Elastic anomalies in glasses: the string theory understanding in the case of Glycerol and Silica
We present an implementation of the analytical string theory recently applied
to the description of glasses. These are modeled as continuum media with
embedded elastic string heterogeneities, randomly located and randomly
oriented, which oscillate around a straight equilibrium position with a
fundamental frequency depending on their length. The existence of a length
distribution reflects then in a distribution of oscillation frequencies which
is responsible for the Boson Peak in the glass density of states. Previously,
it has been shown that such a description can account for the elastic anomalies
reported at frequencies comparable with the Boson Peak. Here we start from the
generalized hydrodynamics to determine the dynamic correlation function
associated with the coherent, dispersive and attenuated, sound
waves resulting from a sound-string interference. Once the vibrational density
of states has been measured, we can use it for univocally fixing the string
length distribution inherent to a given glass. The density-density correlation
function obtained using such distribution is strongly constrained, and able to
account for the experimental data collected on two prototypical glasses:
glycerol and silica. The obtained string length distribution is compatible with
the typical size of elastic heterogeneities previously reported for silica and
supercooled liquids, and the atomic motion associated to the string dynamics is
consistent with the soft modes recently identified in large scale numerical
simulations as non-phonon modes responsible for the Boson Peak. The theory is
thus in agreement with the most recent advances in the understanding of the
glass specific dynamics and offers an appealing simple understanding of the
microscopic origin of the latter, while raising new questions on the
universality or material-specificity of the string distribution properties.Comment: 15 pages, 8 figure
Multiple scattering of elastic waves by pinned dislocation segments in a continuum
The coherent propagation of elastic waves in a solid filled with a random
distribution of pinned dislocation segments is studied to all orders in
perturbation theory. It is shown that, within the independent scattering
approximation, the perturbation series that generates the mass operator is a
geometric series that can thus be formally summed. A divergent quantity is
shown to be renormalizable to zero at low frequencies. At higher frequencies
said quantity can be expressed in terms of a cut-off with dimensions of length,
related to the dislocation length, and physical quantities can be computed in
terms of two parameters, to be determined by experiment. The approach used in
this problem is compared and contrasted with the scattering of de Broglie waves
by delta-function potentials as described by the Schr\"odinger equation
The scattering of phonons by infinitely long quantum dislocations segments and the generation of thermal transport anisotropy in a solid threaded by many parallel dislocations
A canonical quantization procedure is applied to the interaction of elastic
waves --phonons-- with infinitely long dislocations that can oscillate about an
equilibrium, straight line, configuration. The interaction is implemented
through the well-known Peach-Koehler force. For small dislocation excursions
away from the equilibrium position, the quantum theory can be solved to all
orders in the coupling constant. We study in detail the quantum excitations of
the dislocation line, and its interactions with phonons. The consequences for
the drag on a dislocation caused by the phonon wind are pointed out. We compute
the cross-section for phonons incident on the dislocation lines for an
arbitrary angle of incidence. The consequences for thermal transport are
explored, and we compare our results, involving a dynamic dislocation, with
those of Klemens and Carruthers, involving a static dislocation. In our case,
the relaxation time is inversely proportional to frequency, rather than
directly proportional to frequency. As a consequence, the thermal transport
anisotropy generated on a material by the presence of a highly-oriented array
of dislocations is considerably more sensitive to the frequency of each
propagating mode, and therefore, to the temperature of the material.Comment: 21 pages, 8 figure
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