| Sumari: | The properties of a material are unquestionably linked to its structure. Thus, in or- der to wholly understand, or even predict, a material’s properties we must establish a complete understanding of its structure. Developing this understanding becomes particularly challenging when a material comprises multiple components. Experi- mental measurements of complex materials are often complicated as they contain contributions from different components, and interpreting measurements of complex materials in terms of their individual components is a well established problem. This thesis concerns a newly developed multivariate analysis technique designed to break up experimental datasets and describe them in terms of a number of indi- vidual components. The algorithm at the heart of this is called Matrix Metropolis Factorisation (MMF)—it combines Metropolis Monte Carlo minimisation into a non- negative matrix factorisation algorithm to produce a robust and versatile method for decomposing experimental datasets. This thesis comprises applications of this methodology to the structural characterisation of complex materials. Active pharmaceutical ingredients (APIs) are often intentionally prepared in an amorphous form to improve drug solubility and bioavailability. Total scattering and PDF measurements have been used to study these disordered materials. I then show how MMF analysis of PDF data enables: (i) structural characterisation of the amorphous API in a complex preparation, (ii) determination of the maximum API loading level capable of inhibiting crystallisation, and (iii) identification of drug design strategies for improving stability of the amorphous form. Next, a number of mixed-metal framework materials are considered. Through MMF analysis of infrared spectroscopy data the distribution of neighbouring cations pairs is determined as a function of composition for three formate perovskite families, and Cd-doped ZIF-8. Atomistic pictures of domain formation are developed for each material which may, in principle, enable tuning of ferroelectric and sorption behaviour. Finally, I identify the existence of a locally ordered domain structure that persists above the magnetic ordering temperature of a simple cubic ferromagnet. MMF analysis of radial spin-correlation function data was used to determine regions of ferromagnetic order within a largely disordered paramagnetic phase. The systems considered each have complex structures that are governed by short- range interactions and can be described in terms of a small number of components. In each case, MMF analysis is used to identify these components, including those that cannot be measured in isolation. Fundamentally the same methodology is applied to data from different experimental techniques to probe the local structure of each system.
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