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Research Summary. The research of the group can be categorised into the following topics: Strongly Correlated Materials: Correlated electronic materials are those which the interaction between the valence electrons can strongly influence the materials properties. They are interesting as their unique properties are of considerable utility for device physics, functional materials and the study of fundamental condensed matter physics. Recently, there has been renewed interest in materials that exhibit a solid-solid structural phase transition at a critical temperature. An example is vanadium dioxide (VO2), where spontaneous (non-diffusion limited) atomic rearrangement occurs due to external excitation. Switching speeds on the femto-second timescale have been observed. To study this system we utilise the SACLA X-FEL facility. Here we combine CXD imaging with a cross-correlated femto-second pump-probe scheme that allows us to image structural changes with a time resolution of the order of a few femto-seconds. Our findings will likely aid in the development of a dynamical theory that can fully describe this structural change. Strong Phase Structures: Strain engineering plays an important role in the development of devices in the semiconductor industry today. It is also utilised directly in a number of device applications including piezoelectric actuators and sensors. When the amount of strain exceeds a certain limit (unique to each material), the accompanying strong phase structure makes strain mapping challenging. This research topic aims to investigate the origin of strong phase structures in nanometre scale materials and how they impact the CXD imaging process. We do so by systematically studying the transition into the strong phase structure regime. Results obtained here are also of value in developing advanced numerical optimisation techniques for phase recovery. Non-linear Optimisation: Correlated electronic materials that undergo a spontaneous crystalline deformation can experience a significant strain. This can pose a challenge when reconstructing and interpreting information obtained from CXD imaging. We have previously shown that materials exhibiting strong phase structure require special optimisation methods to reconstruct the real-space object. Our group has developed the first algorithm to reconstruct data known to have strong phase structure. There are however still significant developments necessary to discover robust algorithms that are universally effective. Nanomaterials and Devices: The increasing need to make smaller device structures with enhanced functionality has led the move away from conventional top-down lithographic approaches toward the utilisation of self-assembled nanoscale structures. The unique morphologies exhibited by many nanocrystals make them ideal for various applications including biochemical sensors, photodetectors, light emitters, transistors, high frequency oscillators, and waveguides. Our research into nanomterials and devices is centred on self-assembled metal-oxide nanocrystals which have the advantage of high chemical resistance and low thermal degradance. This includes group II-VI semiconductor materials such as zinc oxide (ZnO).