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Anharmonic Phonon Behavior Using Hamiltonian Constructed via Irreducible Derivatives.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Anharmonic Phonon Behavior Using Hamiltonian Constructed via Irreducible Derivatives./
Author:	Xiao, Enda.
Description:	1 online resource (138 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-01, Section: B.
Contained By:	Dissertations Abstracts International85-01B.
Subject:	Condensed matter physics. -
Online resource:	click for full text (PQDT)
ISBN:	9798379780494

Anharmonic Phonon Behavior Using Hamiltonian Constructed via Irreducible Derivatives.
Xiao, Enda.

Anharmonic Phonon Behavior Using Hamiltonian Constructed via Irreducible Derivatives. - 1 online resource (138 pages)

Source: Dissertations Abstracts International, Volume: 85-01, Section: B.

Thesis (Ph.D.)--Columbia University, 2023.

Includes bibliographical references

Phonon anharmonicity is critical for describing various phenomena in crystals, including lattice thermal conductivity, thermal expansion, structural phase transitions, and many others. Including anharmonicity in the calculation of condensed matter observables developed rapidly in the past decade. First-principles computation of cubic phonon interactions have been performed in many systems, and the quartic interactions have begun to receive more attention. In this study, reliable Hamiltonians are constructed purely in terms of quadratic, cubic, and quartic irreducible derivatives, which are calculated efficiently and precisely using the lone and bundled irreducible derivative approaches (LID and BID). The resulting Hamiltonians give rise to a nontrivial many-phonon problem which requires some approximation in order to compute observables. We implemented self-consistent diagrammatic approaches to evaluate the phonon self-energy, including the Hartree-Fock approximation for phonons and quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Additionally, we implemented molecular dynamics in order to yield the numerically exact solution in the classical limit. The molecular dynamics solution is robust for directly comparing to experimental results at sufficiently high temperatures, and for assessing our diagrammatic approaches in the classical limit.Anharmonic vibrational Hamiltonians were constructed for CaF2, ThO2, and UO2. Diagrammatic approaches were used to evaluate the phonon self-energy, yielding the phonon lineshifts and linewidths and the thermal conductivity within the relaxation time approximation. Our systematic results allowed us to resolve the paradox of why first-principles phonon linewidths strongly disagree with results extracted from inelastic neutron scattering (INS). We demonstrated that the finite region in reciprocal space required in INS data analysis, the q-voxel, must be explicitly accounted for within the calculation in order to draw a meaningful comparison. We also demonstrated that the q-voxel is important to properly compare the spectrum measured in inelastic X-ray scattering (IXS), despite the fact that the q-voxel is much smaller. Accounting for the q-voxel, we obtained good agreement for the scattering function linewidths up to intermediate temperatures. Additionally, good agreement was obtained for the thermal conductivity. Another topic we addressed is translation symmetry breaking caused by factors such as defects, chemical disorder, and magnetic order. These phenomena will lead to shifts and broadening of the phonon spectrum, and formally the single particle Green's function encodes these effects. However, it is often desirable to obtain an approximate non-interacting spectrum which contains the effective shifts of the phonon frequencies, allowing straightforward comparison with experimentally measured scattering peak locations. Such an effective phonon dispersion can be obtained using a band unfolding technique, and in this study we formulated unfolding in the context of irreducible derivatives. We showcased the unfolding of phonons in UZr2, where chemical disorder is present, and compared the results with experimental IXS data. Additionally, we extended the unfolding technique to anharmonic terms and demonstrated this using 3rd and 4th order terms in the antiferromagnetic phase of UO2.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798379780494Subjects--Topical Terms:

1148471
Condensed matter physics.
Subjects--Index Terms:

AnharmonicityIndex Terms--Genre/Form:

554714
Electronic books.

Anharmonic Phonon Behavior Using Hamiltonian Constructed via Irreducible Derivatives.
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502 $a Thesis (Ph.D.)--Columbia University, 2023.
504 $a Includes bibliographical references
520 $a Phonon anharmonicity is critical for describing various phenomena in crystals, including lattice thermal conductivity, thermal expansion, structural phase transitions, and many others. Including anharmonicity in the calculation of condensed matter observables developed rapidly in the past decade. First-principles computation of cubic phonon interactions have been performed in many systems, and the quartic interactions have begun to receive more attention. In this study, reliable Hamiltonians are constructed purely in terms of quadratic, cubic, and quartic irreducible derivatives, which are calculated efficiently and precisely using the lone and bundled irreducible derivative approaches (LID and BID). The resulting Hamiltonians give rise to a nontrivial many-phonon problem which requires some approximation in order to compute observables. We implemented self-consistent diagrammatic approaches to evaluate the phonon self-energy, including the Hartree-Fock approximation for phonons and quasiparticle perturbation theory, where both the 4-phonon loop and the real part of the 3-phonon bubble are employed during self-consistency. Additionally, we implemented molecular dynamics in order to yield the numerically exact solution in the classical limit. The molecular dynamics solution is robust for directly comparing to experimental results at sufficiently high temperatures, and for assessing our diagrammatic approaches in the classical limit.Anharmonic vibrational Hamiltonians were constructed for CaF2, ThO2, and UO2. Diagrammatic approaches were used to evaluate the phonon self-energy, yielding the phonon lineshifts and linewidths and the thermal conductivity within the relaxation time approximation. Our systematic results allowed us to resolve the paradox of why first-principles phonon linewidths strongly disagree with results extracted from inelastic neutron scattering (INS). We demonstrated that the finite region in reciprocal space required in INS data analysis, the q-voxel, must be explicitly accounted for within the calculation in order to draw a meaningful comparison. We also demonstrated that the q-voxel is important to properly compare the spectrum measured in inelastic X-ray scattering (IXS), despite the fact that the q-voxel is much smaller. Accounting for the q-voxel, we obtained good agreement for the scattering function linewidths up to intermediate temperatures. Additionally, good agreement was obtained for the thermal conductivity. Another topic we addressed is translation symmetry breaking caused by factors such as defects, chemical disorder, and magnetic order. These phenomena will lead to shifts and broadening of the phonon spectrum, and formally the single particle Green's function encodes these effects. However, it is often desirable to obtain an approximate non-interacting spectrum which contains the effective shifts of the phonon frequencies, allowing straightforward comparison with experimentally measured scattering peak locations. Such an effective phonon dispersion can be obtained using a band unfolding technique, and in this study we formulated unfolding in the context of irreducible derivatives. We showcased the unfolding of phonons in UZr2, where chemical disorder is present, and compared the results with experimental IXS data. Additionally, we extended the unfolding technique to anharmonic terms and demonstrated this using 3rd and 4th order terms in the antiferromagnetic phase of UO2.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Condensed matter physics. $3 1148471
650 4 $a Applied physics. $3 1181953
650 4 $a Thermodynamics. $3 596513
653 $a Anharmonicity
653 $a Green's function
653 $a Phonon
653 $a Thermal conductivity
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710 2 $a Columbia University. $b Chemical Physics. $3 1186670
773 0 $t Dissertations Abstracts International $g 85-01B.
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