Abstract: The first part of this dissertation is a study of martian mantle convection. The martian surface is roughly divided into southern highlands with thicker crust and northern lowlands with thinner crust. If the martian crust in enriched in heat-producing elements, the dichotomy in crustal thickness will cause the southern hemisphere to be more insulating than the northern hemisphere. This heterogeneous thermal boundary condition may affect the mantle dynamics. The martian mantle may be compositionally layered, which would also affect the pattern of convection. Here I explore the effects of compositional layering and the dichotomy. In transient laboratory experiments with both layering and a dichotomy, a single large upwelling forms early and persists for the equivalent of many Gyr. The steady-state calculations show only diffuse upwellings, which highlights the role of transience and initial conditions in mantle convection. The early formation of Tharsis may then constrain models of the differentiation and early thermal and chemical state of Mars. The second part of this dissertation is an analysis of the electronic structure of magnetite, the room-temperature and -pressure form of Fe ₃O₄. The structure of magnetite has three spaces for cations: one tetrahedral A site and two octahedral B sites. The B sites appear to be equivalent above a transition temperature T_V, and there is evidence that they are nonequivakent below it. I show that the nonequivalence may be present above T_V, but disguised by thermally activated electron hopping. I also show that this nonequivalence persists under compression, and that there is no evidence of charge transfer between the A and B sites as had been proposed by other authors.