Theoretical Phonon Spectroscopy Using Predictive Atomistic Simulations

Tianli Feng, Purdue University

Abstract

In this thesis, two atomic level simulation methods, i.e., first principles perturbation theory and molecular dynamics (MD), are advanced to address the fundamental as well as emerging questions of thermal transport in a broad range of materials, and to manipulate the thermal transport in nanomaterials by nanoengineering. First of all, the perturbation theory has been improved and applied to predicting the phonon dispersion and relaxation time spectra of solids. In the past ten years, the perturbation theory has achieved great success in predicting thermal properties, whereas the prediction was limited to the lowest order of perturbation, i.e., three-phonon scattering, and thus the results could not match well with experiment in many cases. The calculation of higher-order phonon scattering, i.e., four-phonon scattering, yet has been a longstanding challenge. We have developed the formalism for four-phonon scattering rate by explicitly determining quantum mechanical scattering probability matrices for the full Brillouin zone. κ of Lennard-Jones argon is reduced by more than 60% at 80 K when four-phonon scattering is included. Including four-phonon scattering resistance gives ∼20-30% reduction in thermal conductivity at temperatures ∼1000 K for diamond and Si than when including only three-phonon processes, as is typically done, bringing agreement between experiment and simulations at the entire temperature range. Surprisingly, four-phonon scattering is crucial in determining κ for zincblende boron arsenide, a material with predicted highest natural thermal conductivity previously. Four-phonon scattering is found to reduce its κ substantially, by 37% at room temperature and 60% at 1000 K. The relatively strong four-phonon scattering in BAs originates from weak three-phonon scattering that arises from properties of its phonon dispersion coupled with fundamental conservation conditions. These conditions do not as strictly restrict the available scatterings for four-phonon process. We expect that four-phonon scattering will play similarly important roles in materials for which three-phonon processes are weak and high κ is dominated by large phonon lifetimes rather than large acoustic velocities. We have developed a method for the first time based on the perturbation theory to calculate the temperature-dependent phonon dispersion. The frequency shifts at finite temperatures including the effects of thermal expansion, three-phonon scattering, and four-phonon scattering are obtained. We find that the frequency shift increases linearly with temperature at high temperature and is dominated by the four-phonon term in the whole temperature range. The thermal expansion effect plays an important role at high temperatures. At a given temperature, generally the frequency shift is proportional to the frequency, except for the transverse acoustic mode, the shift of which increases more than linearly with frequency. The calculated results agree reasonably well with existing data from inelastic neutron scattering measurement. Since current perturbation theory has limitations in the study of the thermal transport in large scale or the structures with defects, to study them we turn to the MD simulations together with phonon modal analysis methods. We have proved both analytically and numerically that the phonon eigenvector is not necessary in the frequency-domain Normal mode analysis (NMA). Then, we have adopted it to investigate mode-wise phonon properties of defected graphene, and studied the impacts of three popular types of defects, Stone-Thrower-Wales (STW) defect, double vacancy (DV), and mono vacancy (MV). Phonon-STW defect scattering rate is found to have no significant frequency dependence, while the phonon scattering by DVs or MVs exhibits a frequency dependence of ∼ω 1.1-1.3, providing a critical revisit to the traditionally used ∼ω 4 dependence. We note that MV-defected graphene has a portion of phonons with even longer mean free path (MFP) than the other two defected graphene samples, at the same defect concentration, although MV-defected graphene has the lowest effective MFP and thermal conductivity. More importantly, a new modal analysis method based on nonequilibrium MD has been developed to probe the spectral phonon temperature (SPT), which has never been resolved by atomistic simulations before. Taking silicon thin film and graphene as examples, we directly obtained the SPT and observed the local thermal nonequilibrium between the ballistic and diffusive phonons. Such nonequilibrium also generally exists across interfaces and is surprisingly large, and it provides a significant additional thermal interfacial resistance mechanism besides phonon reflection. Our SPT results directly show that the vertical thermal transport across the dimensionally mismatched graphene/substrate interface is through the coupling between flexural acoustic phonons of graphene and the longitudinal phonons in the substrate with mode conversion. In the dimensionally matched interfaces, e.g. graphene/graphene junction and graphene/boron nitride planar interfaces, strong coupling occurs between the acoustic phonon modes on both sides, and the coupling decreases with interfacial mixing. The SPT method together with the spectral heat flux can eliminate the size effect of the thermal conductivity prediction induced from ballistic transport. (Abstract shortened by ProQuest.)

Degree

Ph.D.

Advisors

Ruan, Purdue University.

Subject Area

Mechanical engineering

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