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Nanostructure describes the network of defective and distorted atomic structure existing on the nanoscale within materials. This nanostructure bridges the gap between idealised crys- talline structure and real materials, playing a deterministic role in tailoring physico-chemical properties, as well as providing a basis for mechanistic understanding of complex processes such as mechanical deformation and phase transformation. Characterising nanostructure, to develop understanding of materials, requires experimental techniques capable of probing the structure with spatial resolution on the order of nanometres and across regions of interest up to micrometres. Recent developments in electron microscopy, enabling the acquisition of numerous diffraction patterns in a spatially resolved manner, combined with modern computational power, provides a route to meet this need as developed in this work. Scanning electron diffraction (SED) involves the acquisition of a two-dimensional elec- tron diffraction pattern at each probe position in a two-dimensional scan of a specimen. An information rich 4-dimensional (4D-SED) dataset is obtained that can be analysed extensively post-facto using a wide-range of computational methods. The acquisition of such 4D-SED data from the specimen at numerous orientations may also enable the reconstruction of nanostructure in three-dimensions via tomographic methods. In this work, methods for the acquisition and analysis of 4D-SED data are developed and applied to reveal nanostructure in two and three-dimensions. These methods are applied to various prototypical characterisation challenges in materials science, particularly: strain mapping in two and three dimensions, revealing inter-phase crystallographic relationships, mapping grains in two-dimensional materials, and probing nanostructure in polyethylene.

This thesis discusses various large multi-dimensional dataset analysis methods and their applications. Particular attention is paid to non-linear optimization analyses and general processing algorithms and frameworks when the datasets are significantly larger than the available computer memory. All new presented algorithms and frameworks were implemented in the HyperSpy analysis toolbox. A novel Smart Adaptive Multi-dimensional Fitting (SAMFire) algorithm is presented and applied across a range of scanning transmission electron microscope (STEM) experiments. As a result, the Stark effect in quantum disks was mapped in a cathodoluminescence STEM experiment, and fully quantifiable 3D atomic distributions of a complex boron nitride core-shell nanoparticle were reconstructed from an electron energy loss spectrum (EELS) tilt-series. The EELS analysis also led to the development of two new algorithms to extract EELS near-edge structure fingerprints from the original dataset. Both approaches do not rely on standards, are not limited to thin or constant thickness particles and do not require atomic resolution. A combination of the aforementioned fingerprinting techniques and SAMFire allows robust quantifiable EELS analysis of very large regions of interest. A very large dataset loading and processing framework, “LazySignal”, was developed and tested on scanning precession electron diffraction (SPED) data. A combination of SAMFire and LazySignal allowed efficient analysis of large diffraction datasets, successfully mapping strain across an extended (ca. 1 μm × 1 μm) region and classifying the strain fields around precipitate needles in an aluminium alloy.