Understanding phonon scattering and vibrational localization in nanoparticle-in-alloy composites
Date
2024
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Publisher
University of Delaware
Abstract
Embedding nanostructures in semiconductors is known to enhance phonon scattering and reduce thermal conductivity. While there are well developed processes to model these effects at low volume fractions in the independent scattering approximation, knowledge of how to most efficiently engineer these interactions in dense random nanostructures is lacking. For example, random interference patterns in highly disordered materials may lead to Anderson localized vibrational modes, which offer the promise of zero heat transfer. This dissertation explores scattering and localization phenomena in dense nanostructures through application and extension of the Frequency Domain Perfectly Matched Layer (FDPML) computational approach as well as modal analysis. The structure is as follows. ☐ In Chapter 1, I discuss background concepts and tools related to phonons, phonon scattering, and theoretical tools we and others have used to study phonon transport. The most important to this dissertation is the FDPML method developed by our group and used extensively in Chapter 2, 3, and 4. ☐ In Chapter 2, I investigate phonon transport in large 2D domains with randomly embedded nanoparticles over a wide range of nanoparticle loadings and wavelengths. I use two numerical tools: (1) the FDPML method to implement a Landauer transmission coefficient study, from which mean free path and localization length can be extracted and (2) modal decomposition, which calculates the eigenmodes of a large but finite random nanocomposite, and analyze the modes to determine which is localized and if so, what their localization length and displacement patterns look like. ☐ One focus of the Chapter 2 study is how well the independent scattering approximation holds as volume fraction is increased. Using the Landauer approach I identify regions where the mean free path scales as ℓ ∝ (V_f)^-1 , a tell-tale sign of the independent scattering approximation. I find that the approximation remains valid up to relatively high volume fractions exceeding 10% and often higher, depending on scattering parameter. In the Mie regime, the approximations continues to be valid up to at least 30% volume fraction. In regimes where the approximation holds, it is possible to estimate transport properties by calculating mean free paths using the scattering cross section of a single scatterer, which is significantly easier to calculate. The FDPML method can directly calculate the scattering cross section for a singe particles, so we have done this and compared the mean free paths obtained directly via FDPML for the nanocomposite against calculated mean free paths based on a single scatterer. It is found that the directly calculated mean free paths for the composite are often higher, despite the ℓ ∝ (V _f)^-1 in the direct calculation. I develop a new technique that exploits the calculated spatial distribution of scattered energy in a variant of the FDPML method in order to calculate the scattering phase function, from which I conclude that nanoparticle scattering is often biased strongly in the forward direction, so that even if the scattering cross section is large it does not necessarily lead to low mean free path. ☐ The other focus of the Chapter 2 study is the fundamental science behind localized phonons and what features of a nanocomposite determine their existence and associated localization length. In particular, this is the first study ever of a nanocomposite with truly 2D disorder. The Landauer approach in this study was unable to detect localized phonon transmission except at very small wavelengths (near the Brillouin zone edge) and for very high volume fractions (exceeding 30%). Modal analysis on the other hand was able to identify a large number of localized modes at frequencies above the maximum phonon frequency of the denser phase. The displacement patterns of these modes indicate that these low participation-ratio (PR) modes exist as delocalized modes in gaps of light material surrounded by the denser phase. From this, which it is concluded that localization is caused by energetic confinement, rather than Anderson Localization. An example of how to use this information to engineer localization is given, in which we create a high volume fraction of lighter phase particles embedded in a heavy matrix, where it is observed that every nanoparticle then supports localized modes. ☐ Chapter 3 develops a new multimode extension to FDPML method with the aim to enhance efficiency when computing transport properties. The basic concept is to compute transport properties in FDPML by exploiting linearity to superpose all phonons with the same frequency (or at least within a narrow range) and obtain an average transmission coefficient via a single calculation. A process for mesh generation, frequency binning, superposition, and post processing is described. In particular, using a judicious choice of superposition coefficients, it is shown possible to easily interpret the average transmission coefficients obtained. In addition, for the first time, we identify the mathematical connection between the transmission function, commonly reported for atomistic Green’s function (AGF) approaches, and transmission coefficient from multimode FDPML, allowing these techniques to be compared in the future. We verify/validate the multimode algorithm by comparing its solutions to both exact calculations and mode-by-mode FDPML calculation, using both simple domains and in random nanocomposite systems. ☐ In Chapter 4, the multimode FDPML method is applied to analyze the variation of phonon localization length across the frequency spectrum with much finer resolution than that possible in our Chapter 2 study. This study largely confirms the findings in Chapter 2. A significant decrease for modes inaccessible to the heavier material within nanoparticle-embedded composites is observed. In addition, we do observe some lower frequency modes with much longer localization length modes that are not strictly subject to energetic confinement.
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Keywords
Phonon scattering, Vibrational localization, Nanoparticles, Nanostructures, Atomistic Green's function