Thermal properties in nanostructured materials are dominated by atomic scale and nanoscale inhomogeneities in crystal lattices. However, tools for studying nanoscale thermal properties have relied on theoretical frameworks and optical measurements of defect aggregates. Vibrational spectroscopy in a transmission electron microscope offers unprecedented access into nanoscale phonon physics. We have studied a SiGe quantum dot (QD) superlattice which is a strong candidate for high temperature thermoelectrics. These dome shaped, SiGe alloy QDs are bounded by a sharp and gradual interface due to its nonuniform alloy distribution. With a 6mev (~50 cm-1) energy resolution via a monochromated beam, we map Si optical phonons in a single SiGe QD. We find a composition-induced strain in the alloy matrix in the QD nanostructure that manifests as a redshift in the phonon energy that is exactly consistent with the nonuniform composition distribution. More notably, we find an accumulation of non-equilibrium phonons below the sharp interface. To investigate the dynamics of this further, I developed a new technique called differential momentum mapping (DPM) that allows for the mapping of propagating phonon modes. With this, we mapped phonon group velocity vectors showing unequivocally a drastically larger reflection of phonons from the sharp interface than the gradual one. For the first time, dynamical thermal processes at the nanoscale have been imaged.

This vibrational EELS capability is then applied to a ferroelectric-insulator system: BiFeO3/TbScO3 (BFO/TSO). Our goal for this study was to identify relationships between the phonon structure and ferroelectricity in BFO. Ferroelectric domain walls (DW) and the emergence of free charge gases at the interface offered us an excellent opportunity to also investigate nanoscale electron-phonon dynamics. We discovered that DW-localized shear strain due to alternating polarization, causes phonons to propagate anisotropically by utilizing the DPM technique developed in the previous work. Furthermore, the free charge gasses at the interface also break phonon symmetry but due to accumulated net charge rather than structural distortions. This work provides a nanoscale angle-resolved picture for the decrease in cross-DW and cross-interface thermal conductivity. Uncovering this physics is fundamental to the well-informed fabrication of ferroelectric-based materials and proper design of ferroelectric memories.

To enable trustable data analysis of EELS data, a data workflow stack has been developed with the following key aspects in mind: accuracy, efficiency, transparency, and useability. With the advent of advanced detectors and electron spectroscopy techniques, demand for intelligent, high throughput, processing has sky-rocketed, but the lack of programming and data analysis expertise has been a high barrier to entry. The developed modules serve to mitigate this problem by taking advantage of relatively low-level APIs that interface with data and provide scientific analysis tools and wrapping them in high-level modules designed for user-specific workflows. An example workflow for vibrational EELS includes aligning of the zero-loss peak (ZLP), background subtracting the vibrational signal, using PCA to reconstruct the data in a lower dimensional representation, fitting prominent peaks, and finally visualizing the data in the form of line plots or contour maps. This framework also includes tools for analyzing the fine structure of core-loss edges, bandgap measurements, and a general set of tools including deconvolution, clustering, and filtering. Because entire blocks in the workflow are condensed into single lines of code, these high-level modules can aid non-coders to process their data using innovative data analysis techniques