It is well established that oxygen fugacity, fO₂ , is one of the key parameters that needs to be quantified in order to understand igneous processes, model the geophysical behaviour of the core and mantle, to understand the exchange of C-O-H-S gases between the atmosphere and the interior of the Earth, and to further our understanding of other terrestrial planets. Despite this it remains one of the most poorly constrained geochemical variables, limiting our understanding of terrestrial systems. Recent work has focused on using accessory minerals for determining magmatic fO₂ , as a probe to constraining conditions in planetary interiors. Accessory minerals are already important petrological tools for providing insight into magmatic conditions. These minerals may concentrate a variety of trace elements, and hence are crucial in understanding the elemental budget of magmas. Accessory minerals such as zircon and apatite are also some of the hardier minerals found in igneous rocks and are, therefore, less likely to be altered by processes such as chemical weathering, metasomatism or crustal anatexis. Furthermore, study of detrital accessory minerals in ancient sedimentary rocks could provide much needed insight into the evolution of the oxidation state of the early Earth. This work aims to assess how the compositions and structures of two accessory minerals, spinel and apatite, respond to variations in magmatic fO₂ and to determine whether these minerals could act as probes of fO₂ in planetary interiors. Focus has been concentrated on the element manganese, as (1) it is a relatively abundant trace element, (2) it can exist in valence states from Mn²⁺ to Mn⁵⁺ in nature, and (3) recent work has suggested that Mn may become preferentially concentrated in apatite under reduced conditions. In an initial investigation, large single crystals of Mn-rich spinel were synthesised under a variety of fO₂ conditions. X-ray absorption near edge structure (XANES) spectroscopy and structural refinements of single crystal X-ray diffraction data were used to determine Mn valence state and coordination. Results show that Mn is present in spinel as both Mn²⁺ and Mn³⁺, distributed over both octahedral and tetrahedral cation sites. However, in contrast to the Fe⁺²/Fe³⁺ ratio, little variation in Mn valence as a function of fO₂ was observed. Results were, however, useful in testing and refining protocols for modelling Mn XANES data in a simple, model system. In contrast to results from spinel, previous studies have indicated that Mn valence may change significantly in the accessory mineral apatite due to variations in magmatic fO₂ . To test this, crystals of apatite in equilibrium with different silicate melt compositions were synthesised at high pressure/temperature. Mn partitioning between apatite and melt was determined by electron probe microanalysis (EPMA), and Mn valence state determined by XANES spectroscopy. Although EPMA data revealed that there is no dependence of Mn partitioning on fO₂ , it was noted that partitioning is dependent on melt composition. In more silica-rich melts, a reduction in proportion of non-bridging oxygen reduces the ability of melts to incorporate Mn. As such, apatite crystallising in more evolved melts is expected to be enriched in Mn. These results are confirmed by XANES data, which indicate that Mn is present in coexisting apatite and silicate melt as Mn⁺⁻¹²³⁴⁵⁺², with no observed variation in Mn valence state with fO₂ . In a final, preliminary investigation, attention was turned to Eu and Ce. Inferred variations in the valence state of these rare earth elements, i.e. En²⁺/En³⁺ and Ce³⁺/Ce⁴⁺, are already of use in petrological modelling. Two series of experiments were conducted to synthesise Eu and Ce-bearing silicate glasses (both Fe-bearing and Fe-free) over a range of fO₂ conditions, and apatite in equilibrium with various silicate melt compositions at high pressure/temperature, again over a range of fO₂ conditions. XANES characterisation of glasses demonstrates systematic variations in En²⁺/En³⁺ ratio with fO₂ . In contrast, Ce is dominantly present in quenched glasses as Ce³⁺ under all fO₂ conditions. In apatite, there is little variation in En²⁺/En³⁺, with Eu dominantly incorporated as En³⁺. Ce in apatite is dominantly incorporated as Ce³⁺. These results indicate that apatite-melt partitioning of Eu should be dependent on fO₂ , potentially providing a probe of magmatic fO₂ once the effects of melt compositions are constrained. Results presented here highlight the potential use of apatite as a petrological indicator. However, in contrast to previous work, I show that apatite-melt partitioning of Mn is largely independent of fO₂ . In fact, observed trends in apatite chemistry previously suggested to indicate variations in magmatic fO₂ can instead be fully explained by the observed influence of melt structure/composition on Mn partitioning. In contrast, En contents of apatite (for example apatite/whole rock ratios) may provide insight into oxidation state in the deep Earth. However, more work is required to constrain the influence of fO₂ on En (and other element) partitioning. Importantly, results here highlight the important influence which melt structure has on element partitioning. This control indicates that it is unlikely that fO₂ in the early Earth can be inferred from the chemistry of detrital minerals in sedimentary rocks, or inherited minerals in igneous/metamorphic rocks, as the composition of magmas from which these minerals crystallised cannot easily be constrained.