| Summary: | Transition metal oxides are a family of materials where the physical properties are determined by the strong interplay between orbitals, spins, and electron charge. This thesis aims to understand the local orbital ordering and its relation to the physical properties. Both neutron and X-ray total scattering data have been collected and analysed using a small box approach to obtain specific information about the orbital ordering and its relation to the physical properties within three canonical systems: the spin-glass material Y<sub>2</sub>Mo<sub>2</sub>O<sub>7</sub>; the parent endmember compound, LaMnO<sub>3</sub>, of the doped manganites showing colossal magneto resistance (CMR); and a related series of different compositions, namely La<sub>1-x</sub>Ca<sub>x</sub>MnO<sub>3</sub>. Y<sub>2</sub>Mo<sub>2</sub>O<sub>7</sub> consist of Jahn-Teller active Mo<sup>4+</sup> ions which occupy corner-sharing tetrahedra in a frustrated pyrochlore lattice. In most pyrochlore oxides both frustration and positional disorder must be present to show spin-glass behaviour. In this thesis I present how the Mo<sup>4+</sup> ions on each frustrated tetrahedron dimerise, leading to structural disorder on the Mo site large enough to drive the spin-glass state in Y<sub>2</sub>Mo<sub>2</sub>O<sub>7</sub>. LaMnO<sub>3</sub> undergoes a canonical orbital order/disorder transition at ~750K which is the same as the transition that precedes CMR itself in doped manganites. Here I find a discontinuity in local structure that indicates a fundamental change in the type of orbital arrangement at the transition. In the analysis of the transition I realise the difficulty of discriminating between local structure models when static and dynamic disorder are strongly coupled. Nevertheless, my data show a subtle but consistent preference for the anisotropic Potts model. La<sub>1-x</sub>Ca<sub>x</sub>MnO<sub>3</sub> is of high interest because of its ability to show CMR. Here, I synthesised nine different sample compositions, using the citric gel method. I present a discontinuity in local structure as a function of composition similar to the observed orbital order/disorder transition in LaMnO<sub>3</sub>. An extended study of the local structure of La<sub>0.5</sub>Ca<sub>0.5</sub>MnO<sub>3</sub> composition as a function of temperature is presented. This study indicates that there is a difference in the sample composition depending on which synthesis method used. However, the study shows that Goodenoughâs CO/OO model for the ground state of La<sub>0.5</sub>Ca<sub>0.5</sub>MnO<sub>3</sub> is too simplified and suggests that a different model may represent the low temperature state better.
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