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

Lund, Fernando; Scheihing-Hitschfeld, Bruno

doi:10.3390/nano10091711

Cited by 7 publications

(2 citation statements)

References 48 publications

(130 reference statements)

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“…However, current simulation tools appear to be still insufficient to gauge the impact of defects, particularly extended, resonant defects such as dislocations, on phonon transport 21 . Molecular dynamics methods have also been used 22,23 , but shortcomings have recently been pointed out by Bedoya-Martínez et al 24 Quite recently, and after decades of the formulation of the traditionally used theoretical models for the phonon-dislocation interaction 25,26 , dislocation dynamics such as it is used in the present work has been incorporated into the understanding of thermal transport 27,28 .…”

Section: Introductionmentioning

confidence: 99%

Diffusion of elastic waves in a continuum solid with a random array of pinned dislocations

Churochkin,

Lund

2022

Preprint

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The propagation of incoherent elastic energy in a three-dimensional solid due to the scattering by many, randomly placed and oriented, pinned dislocation segments, is considered in a continuum mechanics framework. The scattering mechanism is that of an elastic string of length L that reradiates as a response to an incoming wave. The scatterers are thus not static but have their own dynamics. A Bethe-Salpeter (BS) equation is established, and a Ward-Takahashi Identity (WTI) is demonstrated. The BS equation is written as a spectral problem that, using the WTI, is solved in the diffusive limit. To leading order a diffusion behavior indeed results, and an explicit formula for the diffusion coefficient is obtained. It can be evaluated in an Independent Scattering Approximation (ISA) in the absence of intrinsic damping. It depends not only on the bare longitudinal and transverse wave velocities but also on the renormalized velocities, as well as attenuation coefficients, of the coherent waves. The influence of the length scale given by L, and of the resonant behavior for frequencies near the resonance frequency of the strings, can be explicitly identified. A Kubo representation for the diffusion constant can be identified. Previous generic results, obtained with an energy transfer formalism, are recovered when the number of dislocations per unit volume is small. This includes the equipartition of diffusive energy density which, however, does not hold in general. The formalism bears a number of similarities with the behavior of electromagnetic waves in a medium with a random distribution of dielectric scatterers; the elastic interaction, however, is momentum dependent.

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Section: Introductionmentioning

confidence: 99%

Diffusion of elastic waves in a continuum solid with a random array of pinned dislocations

Churochkin,

Lund

2022

Preprint

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“…The quantum theory has also been studied in some detail, leading to new insights into the role played by dislocations in thermal transport [25,26]. A rather unexpected application of these results is to the understanding of the acoustic properties of glasses in the THz range [27,28], where the continuum approach is helpful in getting around the fact that glasses have no crystal structure.…”

Section: Introductionmentioning

confidence: 99%

Coherent propagation and incoherent diffusion of elastic waves in a two dimensional continuum with a random distribution of edge dislocations

Churochkin¹,

Lund²

2020

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We study the coherent propagation and incoherent diffusion of in-plane elastic waves in a two dimensional continuum populated by many, randomly placed and oriented, edge dislocations. Because of the Peierls-Nabarro force the dislocations can oscillate around an equilibrium position with frequency ω 0 . The coupling between waves and dislocations is given by the Peach-Koehler force.This leads to a wave equation with an inhomogeneous term that involves a differential operator.In the coherent case, a Dyson equation for a mass operator is set up and solved to all orders in perturbation theory in independent scattering approximation (ISA). As a result, a complex index of refraction is obtained, from which an effectve wave velocity and attenuation can be read off, for both longitudinal and transverse waves. In the incoherent case a Bethe-Salpeter equation is set up, and solved to leading order in perturbation theory in the limit of low frequency and wave number.A diffusion equation is obtained and the (frequency-dependent) diffusion coefficient is explicitly calculated. It reduces to the value obtained with energy transfer arguments at low frequency.An important intermediate step is the obtention of a Ward-Takahashi identity (WTI) for a wave equation that involves a differential operator, which is shown to be compatible with the ISA.

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A combined theoretical-experimental investigation of thermal transport in low-dose irradiated thorium dioxide

et al. 2022

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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

Cited by 7 publications

References 48 publications

Diffusion of elastic waves in a continuum solid with a random array of pinned dislocations

Diffusion of elastic waves in a continuum solid with a random array of pinned dislocations

Coherent propagation and incoherent diffusion of elastic waves in a two dimensional continuum with a random distribution of edge dislocations

A combined theoretical-experimental investigation of thermal transport in low-dose irradiated thorium dioxide

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