Thermal Conductivity Measurements Across a Pressure-Induced Phase Transition: Application to Heat Flow in Earth's Interior

The thermal conductivity of minerals in Earth's lowermost mantle is important for the thermal and chemical evolution of Earth. In the thermal boundary layer separating the core and mantle, the bulk thermal conductivity helps determine the heat flux out of the core. The core heat flux is an important unknown, which has implications for the energy available to power the core geodynamo, the age of the solid inner core, and the style of mantle convection. Measurements of thermal conductivity at high pressure and temperature conditions do not agree on the value at CMB conditions, and estimates range from about 5 W/mK to 15 W/mK. Recent experiments have helped constrain the pressure dependence of thermal conductivity at constant temperature. However, phase transitions in mantle minerals, such as the spin transition in ferropericlase, could complicate the extrapolation of lower pressure and temperature measurements to the conditions at the core-mantle boundary (CMB).In this dissertation, I build on a new method to measure thermal conductivity at high pressures and temperatures using continuous wave laser heating in the diamond anvil cell and apply it to pressure induced phase transitions. I test the method using the face-centered-cubic (B1) to body-centered-cubic (B2) phase transition in NaCl. This study produced thefirst measurement of NaCl thermal conductivity across the B1-B2 phase transition.I use the method developed for ionic salts and apply it to the mantle mineral, ferroper- iclase, (Mg,Fe)O, over the pressure range of 22 GPa to 61 GPa. This range of pressure includes the reported spin transition of octahedrally coordinated iron, from the high spin state to the mixed spin state. Material properties such as the bulk modulus and sound velocity decrease sharply with pressure in the mixed spin state. I measure a correlative reduction of thermal conductivity with pressure. This measurement is consistent with independent thermo-reflectance measurements of ferropericlase thermal diffusivity.Combining new ferropericlase thermal conductivity measurements with those of bridgmanite, and accounting for the spin transition, an updated thermal conductivity profile for the mantle can be calculated. The spin transition reduction has only a minor effect on the depth dependence of mantle thermal conductivity. This is due to the dominant modal percentage of bridgmanite, which is about 80% of the mantle by volume. Including the spin transition effect, I find an increase in thermal conductivity of the mantle by a factor of about 2 from the top of the lower mantle to the core-mantle boundary. These results are consistent with other recent studies, which use different measurement techniques.The thermal conductivity depth dependence of ferropericlase and bridgmanite using the methods in this dissertation result in a CMB bulk thermal conductivity of 5.2 W/mK. Ac- counting for uncertainty in the thickness and temperature change across the CMB, this thermal conductivity maps to a total heat flux of 5.1 to 9.3 TW. This range is consistent with an old inner core, the crystallization of which has has been integral to powering the geodynamo for a significant portion of Earth's history. Future work to bring existing measurements of thermal conductivity at CMB pressures into agreement will need to resolve questions about the temperature dependence at the extreme conditions of the lowermost mantle.In a separate study, I use an analogous application of the heat equation to model the mass transport of sediment on hillslopes. Hillslope processes are important for understand- ing how surface landforms evolve over time. The application of linear diffusion to describe the transport of grains down slope is used to date geomorphic surfaces. However, several lines of evidence, from theoretical considerations, to laboratory experiments and field observations suggest that the linear diffusion equation has limited predictive power for modelling of scarp degradation. Here we use high resolution elevation data and optically stimulated luminescence dates of sediment from a set of terrace risers in New Zealand and show that those degraded terrace risers are better explained by nonlinear diffusion