The pair distribution function (PDF) is a powerful tool for structure analysis. It maps atom-pair correlations of an entire observed region into real space.  Contributed by the strong interaction between electrons and matter, and the tuneable electron beam size in transmission electron microscope (TEM), this concept can be adapted to TEM to produce an electron‑based PDF (ePDF), which enables local structure analysis at the nanoscale. Moreover, by extending one‑dimensional powder PDF into two and three dimensions, multi‑dimensional ePDF provides in‑lab tools for probing 3D atom-atom pair correlation within nanocrystals. In this thesis, I present the development and application of multi‑dimensional ePDF methods across a variety of nanomaterials.

In the initial study, powder ePDF was applied to Eu‑doped ZnO nanosponges. High‑resolution scanning transmission electron microscopy (STEM) imaging revealed Eu incorporation both doped within the hexagonal ZnO lattice, and as Eu‑rich amorphous phase at grain boundaries. Subsequent ePDF analysis quantified different Eu-O coordination environments, establishing a theoretical and practical foundation to understand the structure of Eu-doped ZnO nanosponges.

To obtain angular‑resolved atom-pair correlations in single crystal specimens, this thesis adapts both the three‑dimensional PDF (3D‑PDF) and its difference counterpart (3D-ΔPDF) to TEM. A customized data processing pipeline then enables in‑lab computation of full 3D-ePDFs. To demonstrate the method’s versatility, we first applied 3D-ePDF to piezoceramic perovskites, where it cleanly resolved both in‑phase and antiphase octahedral tilts and quantitatively measured A‑site cation displacements. Next, we turned to a novel structural material, high‑entropy alloys (HEAs). STEM imaging initially revealed an uneven distribution of heavy elements, and subsequent 3D-ΔPDF analysis uncovered local chemical ordering networks within structure. In particular, we showed that Hf atoms preferentially occupy specific lattice sites. Such finding correlates directly with the alloy’s enhanced ductility and strength.

Finally, the beam‑sensitive Prussian blue analogues (PBAs) were studied. Considering the PBAs degraded fast under electron beam illumination, the serial electron diffraction (SerialED) with 2D ePDF was applied. We successfully identifying correlated vacancy networks and local disorder that conventional TEM could not capture due to radiation damage.

Overall, our work establishes a suite of complementary ePDF methodologies, 1D, 2D, and 3D, tailored to sample stability and complexity. By harnessing the strong electron-matter interaction and accessible in‑lab instrumentation, these approaches deliver unprecedented local‑structure insights across crystalline, amorphous, and composite materials, paving the way for rational design of next‑generation functional materials.