| Summary: | The use of ab initio Density Functional Theory (DFT) to calculate key Nuclear Magnetic Resonance (NMR) parameters has been shown to be very successful in a variety of cases. These calculations allow one to extract meaningful data from NMR measurements by providing a foundation for spectral peak assignment. However, first principle calculations for disordered systems, typically based on a single realisation of the disorder, are inadequate if the NMR parameters depend sensitively on the location of the disordered species. In this thesis, a number of different approaches for characterising disorder in solids are presented. The aim of which is to overcome current challenges regarding the computational cost of conventional supercell approaches that make it difficult to perform a direct study of the complete configurational ensemble for any supercell with a sufficient simulation cell. A case study is presented for the Ge-based apatite La7.5Ca2.5Ge6O25.75 that shows that the number of configurations one needs to consider can be vastly reduced by exploiting the symmetry of the system over a wholly enumerative approach, although exhaustive statistical averaging of the atomic positions required to reproduce the atomic resolution afforded by the solid-state NMR (ssNMR) measurement makes this problem intractable via this methodology. The sodium potassium niobate system (NaxK1-xNbO3) is studied across a series of compositions between the ordered KNbO3 and NaNbO3 end-members. This novel material exhibits purely atomic position / permutation disorder that is reflected in initial 23Na and 93Nb MAS NMR studies, but the true explanation of the disorder described by this data is not well understood. The Special Quasi-random Structure (SQS) approach to studying this disorder is presented as a computationally cheaper alternative to the supercell approach. It is noted that further studies are required to assess whether this is an adequate description of the NaxK1-xNbO3 system due the complications of modelling the complex tilting patterns exhibited by these structures. A combined ssNMR and GIPAW-DFT approach is reported to resolve the complex disorder within the vaterite polymorph of calcium carbonate. The computational data for the various structural candidates in the literature is utilised to simulate the highly sensitive DOR data, thereby elevating the predictive capability of this complementary approach to substantiate the stacking model of vaterite that views the material as a dynamic system under ambient conditions.
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