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This thesis used a range of simulation techniques to investigate the various effects rareearth element doping has on barium titanate with a focus on their ability to increase the lifetime of such ceramics. Finite element simulation was used to look for a relationship between user generated regional input permittivities, conductivities and microstructures based on experimental core-shell microstructures formed in rare-earth element doped barium titanate and the simulated bulk output properties. No simple analytical relationship was found. Input properties for more local regions are needed for accurate simulations. These cannot easily be obtained from experiment. Experimental spectra (XRD and TEM) of perovskites were simulated from molecular dynamics simulations. The simulated spectra include dynamical information. The spectra along with the in-house analytical PALAMEDES code were used to interpret tilt features in the simulated systems. The code gives quantitative values for tilt and volumes for A and B sites in the system and identifies tilt phase. Static simulations of doped barium titanate demonstrate the affinity of rare-earth dopants to form specific compensation schemes. The simulation results agree with experiment. Lifetime improvements due to rare-earth dopants have been theorised to be due to oxygen vacancy trapping. Further simulations show that all mid-size trivalent rare-earth elements can strongly trap oxygen vacancies. The differences seen in lifetime improvements between rare-earths is due to their distribution and compensation schemes they adopt. Advanced sampling techniques were used to look at self-diffusion and rare-earth diffusion in barium titanate. The applicability of Mean Squared Displacement, Steered MD, Umbrella sampling and Metadynamics to solid-state systems is discussed. The selfdiffusion results agreed with available experimental values. Dysprosium was found to be the most mobile rare-earth of those investigated in barium titanate lattice suggesting that a combination of its mobility and preference to dope in a self-compensatory manner is the reason for its superior lifetime improvements.

The interactions between organic molecules and minerals is fundamental to the under- standing of processes such as biomineralisation, the attachment of bacteria to surfaces and the design of synthetic materials within biomimetics. This thesis shows how molec- ular dynamics simulations can be employed to study the organic - inorganic interactions and give new insights into the molecular binding at mineral surfaces that play a role in these processes. The incorporation of amino acids within calcium carbonate crystals was simulated and show a high energy associated with the incorporation of these molecules. The amino acids get incorporated in-between the lattice planes of the crystal, causing small anisotropic distortions to the crystal. The inclusion of these molecules occurs via a goodness-of-fit principle, where disruptions to the crystal lattice should be kept to a minimum. These simulations show good agreement with experimental X-ray data. Simulations of multiple tripeptides show a different conformational behaviour of the peptides in solution than on the surface of calcium carbonate. Whereas the pep- tides exhibit a flexible behaviour in solution, binding to the mineral surface induces a disorder-to-order transition and the peptides become rigid. These changes in con- formational behaviour offer insight into the structure and behaviour of intrinsically disordered proteins. The polymer poly acrylic acid was simulated to analyse its conformational behaviour. In the presence of counter ions the polymer exhibits a flexible, extended conformation, whereas a coiled conformation is found in the absence of counter ions. The simulations in this work agree well with experimental spectroscopy studies. The binding of the polymer to a mineral surface is not only governed by the number of functional groups, but also the flexibility of the polymer. These results give an insight in how such molecules can aid the attachment of bacteria to surfaces.