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Energy Transport in Low Dimensional ...

Raj, Anant.

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Energy Transport in Low Dimensional Systems: Phonons and Beyond Phonon Descriptors.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Energy Transport in Low Dimensional Systems: Phonons and Beyond Phonon Descriptors./
作者:	Raj, Anant.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
面頁冊數:	241 p.
附註:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
標題:	Nuclear engineering. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10610804
ISBN:	9781369856873

Energy Transport in Low Dimensional Systems: Phonons and Beyond Phonon Descriptors.
Raj, Anant.

Energy Transport in Low Dimensional Systems: Phonons and Beyond Phonon Descriptors. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 241 p.

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)--North Carolina State University, 2017.

Thermal conduction in solid state electrical insulators has long been associated with the normal mode of the vibrating atoms known as phonons. In the quantum framework, phonons are treated as bosons, which can be described by the Boltzmann kinetic theory. While the concept of phonons is critical to explaining several thermal properties, recent developments are challenging the notion of phonons as the true carriers of heat. In an alternate framework, which is more fundamental, thermal conduction can be described by the linear response or equivalently, the Green-Kubo (GK) theory. The GK theory, however, does not lend itself naturally to identify the modes of vibrations in a crystalline state. In the past two decades, several attempts have been made to merge these two disparate theories though with limited success. The primary objective of this dissertation is to develop a theoretical framework that can accommodate the GK and phonon theories while maintaining mathematical and physical consistency.

ISBN: 9781369856873Subjects--Topical Terms:

595435
Nuclear engineering.

Energy Transport in Low Dimensional Systems: Phonons and Beyond Phonon Descriptors.
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245 1 0 $a Energy Transport in Low Dimensional Systems: Phonons and Beyond Phonon Descriptors.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2017
300 $a 241 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
500 $a Advisers: Jacob Eapen; Korukonda Murty.
502 $a Thesis (Ph.D.)--North Carolina State University, 2017.
520 $a Thermal conduction in solid state electrical insulators has long been associated with the normal mode of the vibrating atoms known as phonons. In the quantum framework, phonons are treated as bosons, which can be described by the Boltzmann kinetic theory. While the concept of phonons is critical to explaining several thermal properties, recent developments are challenging the notion of phonons as the true carriers of heat. In an alternate framework, which is more fundamental, thermal conduction can be described by the linear response or equivalently, the Green-Kubo (GK) theory. The GK theory, however, does not lend itself naturally to identify the modes of vibrations in a crystalline state. In the past two decades, several attempts have been made to merge these two disparate theories though with limited success. The primary objective of this dissertation is to develop a theoretical framework that can accommodate the GK and phonon theories while maintaining mathematical and physical consistency.
520 $a Following a brief description of the phonon theory in Chapter 2, a mathematically consistent general solution to the phonon equation of motion is presented in Chapter 3. It is shown that the displacements necessarily should include a left moving and a right moving wave train to satisfy all the internal degrees of freedom. The identification of the amplitudes in +q and -- q wave vector directions provides a fundamental breakthrough for describing the correct form of energy and heat current modes expressed in normal mode coordinates.
520 $a In Chapter 4, a numerically efficient method based on the ratio of normal mode coordinates of velocity to those of displacements is presented for determining the phonon dispersion curve. While the theory is known before, the method has never been employed for computing phonon dispersion using atomistic simulations. Case studies on a monoatomic chain, a diatomic chain, and graphene demonstrate that the ratio method outperforms in accuracy and speed over the conventional method of using a fast Fourier transform (FFT).
520 $a The most impactful results of the dissertation are presented in Chapters 5 and 6. First, the mathematical and physical consistency conditions for heat carrier modes are derived in Chapter 5. It is shown that a real microscopic heat flux in normal mode coordinates can be consistently defined, and the net phonon population can be expressed as a difference in amplitudes along +q and --q wave vector directions. It is further demonstrated that phonon-phonon cross-correlations, which emerge naturally, can play a dominant role in the thermal transport process, especially for low-dimension systems; the derivation also identifies a correction term for phonon self-correlations. Interestingly, the correction from energy correlations leads to phonon lifetimes that are noticeably lower than those estimated using the existing approaches.
520 $a For low dimensional systems, it is more appropriate to investigate the local heat current and energy fluctuations in appropriate normal coordinates than to probe an ill-defined thermal conductivity. In Chapter 6, the theoretical framework for analyzing local energy and heat current fluctuations in corresponding (energy/flux) normal coordinates is presented. These energy/current modes are then connected to the phonon normal modes that allows the exciting possibility of analyzing energy/heat modes in the more familiar framework of displacement (phonon) normal modes. First, the energy/current modes are derived exactly for a harmonic one-dimensional monoatomic chain; the theoretical prediction is verified subsequently using atomistic simulations. The theoretical derivation reveals a rather intriguing denouement on the possible combinations of phonon modes. Even with harmonic interaction, pairs of phonon modes combine to produce energy/heat modes if and only if they satisfy the three-phonon scattering law. It is known that three-phonon processes are required for thermal dissipation, and the appearance of the three-phonon scattering condition, from the energy/current modes, indicates the distinct possibility of predicting the phonon interaction types directly from the pertinent microscopic variables (energy/current) -- a long sought after goal in recent theoretical studies. The three-phonon synergy has the lowest order of interaction, and this condition arises naturally with the interference of energy/heat waves. It is anticipated that if anharmonicity and higher dimensionality are included, higher order processes will evolve naturally without the need to specify or postulate the nature of phonon interactions in thermal transport.
590 $a School code: 0155.
650 4 $a Nuclear engineering. $3 595435
650 4 $a Nanoscience. $3 587832
650 4 $a Physics. $3 516296
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710 2 $a North Carolina State University. $b Nuclear Engineering. $3 2099591
773 0 $t Dissertation Abstracts International $g 78-10B(E).
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