Lattice thermal conductivity of deformed crystals

Kumar, Anil; Ansari, M. Afzal

doi:10.1016/0378-4363(88)90285-9

Cited by 4 publications

(2 citation statements)

References 20 publications

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“…Nevertheless, the motion of atoms in crystalline materials turns out to be most readily described not in terms of the individual atoms, but in terms of traveling waves, which are named lattice vibrations by Born [47]. In a lattice dynamics (LD) system with a harmonic approximation, the displacement of atoms can be decomposed into a linear combination of normal modes [48], permitting only a discrete set of wavevectors. The number of allowed wavevectors is equal to the number of primitive unit cells.…”

Section: The Lattice Dynamics Formulationmentioning

confidence: 99%

Passing waves from atomistic to continuum

Chen

Díaz

Xiong

et al. 2018

Journal of Computational Physics

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Progress in the development of coupled atomistic-continuum methods for simulations of critical dynamic material behavior has been hampered by a spurious wave reflection problem at the atomistic-continuum interface. This problem is mainly caused by the difference in material descriptions between the atomistic and continuum models, which results in a mismatch in phonon dispersion relations. In this work, we introduce a new method based on atomistic dynamics of lattice coupled with a concurrent atomistic-continuum method to enable a full phonon representation in the continuum description. This then permits the passage of short-wavelength, high-frequency phonon waves from the atomistic to continuum regions. The benchmark examples presented in this work demonstrate that the new scheme enables the passage of all allowable phonons through the atomistic-continuum interface; it also preserves the wave coherency and energy conservation after phonons transport across multiple atomistic-continuum interfaces. This work is the first step towards developing a concurrent atomistic-continuum simulation tool for non-equilibrium phononmediated thermal transport in materials with microstructural complexity.

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Section: The Lattice Dynamics Formulationmentioning

confidence: 99%

Passing waves from atomistic to continuum

Chen

Díaz

Xiong

et al. 2018

Journal of Computational Physics

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show abstract

“…For a harmonic approximation, atomic displacements can be decomposed into a linear combination of normal modes with a discrete set of wavevectors where the number of wavevectors equals the number of unit cells [37,38]. If we only consider the contributions from short-wavelength phonons with k > k C , then the displacement of the α th particle in a unit cell at undeformed position x is given as follows:…”

Section: Lattice Dynamics Methodsmentioning

confidence: 99%

Transmitting multiple high-frequency waves across length scales using the concurrent atomistic-continuum method

Davis,

Agrawal

2022

Preprint

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Coupled atomistic-continuum methods can describe large domains and model dynamic material behavior for a much lower computational cost than traditional atomistic techniques. However, these multiscale frameworks suffer from wave reflections at the atomistic-continuum interfaces due to the numerical discrepancy between the fine-scaled and coarse-scaled models. Such reflections are non-physical and may lead to unfavorable outcomes such as artificial heating in the atomistic region. In this work, we develop a technique to allow the full spectrum of phonons to be incorporated into the coarse-scaled regions of a periodic concurrent atomistic-continuum (CAC) framework. This scheme tracks phonons generated at various time steps and thus allows multiple high-frequency wave packets to travel between the atomistic and continuum regions. Simulations performed with this method demonstrate the ability of the technique to preserve the coherency of waves with a range of wavevectors as they propagate through the domain. This work has applications for systems with defined boundary conditions and may be extended to more complex problems involving waves randomly nucleated from an impact within a multiscale framework.

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Transmitting multiple high-frequency phonons across length scales using the concurrent atomistic–continuum method

Davis

Agrawal

2022

Computational Materials Science

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Lattice thermal conductivity of deformed crystals

Cited by 4 publications

References 20 publications

Passing waves from atomistic to continuum

Passing waves from atomistic to continuum

Transmitting multiple high-frequency waves across length scales using the concurrent atomistic-continuum method

Transmitting multiple high-frequency phonons across length scales using the concurrent atomistic–continuum method

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