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 the

first 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.

The thermal conductivity of the Earth's lowermost mantle controls the rate of heat flow across the core-mantle boundary, and is thus a critical parameter for determining the core and mantle thermal state and evolution. This parameter and its dependence on pressure, temperature, and composition are poorly known, in part due to the inherent difficulties in determining thermal conductivities at the high pressures and temperatures (135 GPa and 3800 K) that occur at the base of the mantle. In this dissertation I estimate the thermal conductivity of the lower mantle using measurements of the thermal conductivity of MgO and (Mg,Fe)SiO3 perovskite made at high pressure and high temperature in the laser-heated diamond anvil cell. Using three-dimensional heat flow modeling, I demonstrate that the steady-state temperature distributions that form during laser heating experiments in the diamond anvil cell depend on the sample thermal conductivity as well as the experimental geometry. Relative thermal conductivity can be determined by comparing measured temperature vs. laser power curves with a numerical model. I use this technique to determine the pressure-dependence of thermal conductivity of MgO and (Mg,Fe)SiO3 perovskite, and then I extrapolate absolute measurements of thermal conductivity taken near ambient pressure to lower mantle conditions. I also estimate the contribution of radiation to heat transfer in the lower mantle. My resulting value for the thermal conductivity of the lowermost mantle is approximately 6 W/m*K, lower than the commonly assumed value of 10 W/m*K. When combined with estimates for the lower mantle boundary layer temperature gradient, the total core-mantle boundary heat flow is roughly 7 TW. This heat flow implies a slow growth rate for the Earth's inner core.

Carbon is an essential component to life on Earth, and plays a role in the carbon cycle at the surface of the Earth. Beyond these surface interactions lies the deep carbon cycle. This cycle controls the flux of carbon subducting into the earth and provides clues as a possible carbon reservoir in the deep earth. The studies included in this dissertation examine various forms of carbonate under high pressure, high temperature conditions found in the deep earth. Carbon is subducted as carbonate in calcite, aragonite and dolomite, as elemental carbon or as CO2. To achieve these the high pressures experienced by subducting material, diamond anvil cells are used to expose milligrams of material to extremem conditions. The experiments detailed here were conducted using a wide range of diamond anvil cell techniques and the data was collected at numerous synchrotron and neutron diffraction facilities across the globe including the Advanced Light Source, Lawrence Berekely National Laboratory, the Spallation Neutron Source, Oak Ridge National Laboratory and the European Synchrotron Radiation Facility, Grenoble France. These experiments are the result of fruitful collaborations that brought scientist from around the globe together to study the thermoelastic properties of carbonate and CO2. I found important thermoelastic properties for the following minerals: hanksite, tychite, kutnohorite, aragonite and carbon dioxide. Each study yields isothermal bulk modulus data and the studies on aragonite and carbon dioxide also yield thermal expansion data. The equation of state, phase stability and thermoelastic data derived from these experiments will inform models of planetary interiors while giving insight into the evolution of carbon at the high pressures and temperatures of the Earth’s interior.

High pressure and temperature equations of state are powerful tools for probing the behavior of matter at extreme conditions. The recent deployment of third generation synchrotron light sources combined with stable, reproducible laser heating has allowed the measurement of high pressure and temperature equations of state in the diamond anvil cell. In this document I leverage this new capability to address several types of questions in the Earth sciences. Measurements of osmium metal are used to investigate different formulations of the equation of state and the measurement of very incompressible materials. Measurements of iron ringwoodite are used to examine trade-offs in seismic observables with thermal and compositional anomalies. Finally, the equation of state of cobalt oxide is used to make predictions about redox relations in the early Earth during core formation.

The deep Earth volatile cycle has far-reaching impacts on the atmosphere, climate, hydrologic cycle, and biosphere of our planet. Volatile species in minerals are exchanged between Earth’s surface and interior. Earth’s interior contains the largest reservoir of volatiles on the planet. However, our understanding of this reservoir is limited. The deep Earth cannot be directly sampled, so we rely on models and laboratory experiments to simulate analogous conditions. Prior experiments have determined equations of state and the phase stabilities of many abundant mineral species at deep Earth conditions, however less work has been done on volatile-bearing minerals. Determining the behavior of volatile-bearing minerals using high pressure and temperature experiments can resolve which mineral phases store volatiles in the deep Earth. These experiments give additional insight into chemical processes in the deep Earth, and will help to shed light on the formation and chemical evolution of our planet. In this dissertation, I use Raman and infrared spectroscopy to investigate the high-pressure behavior of the lead sulfate, anglesite (PbSO4), in the diamond anvil cell. This work gives insights into the behavior of sulfates, commonly subducted sulfur-bearing minerals, at mantle pressures. I produce the first high-pressure infrared spectroscopy measurements on anglesite, extend the pressure range studied with Raman spectroscopy, and discover a previously unknown phase transition. I make measurements of the bulk modulus and its pressure derivative for anglesite using X-ray diffraction and the Birch-Murnaghan equation of state. This study confirms previous observations of a phase transition in anglesite and produces a thorough X-ray diffraction dataset to 50 GPa. Using X-ray diffraction and Raman spectroscopy, I measure the bulk modulus and Gr�neisen parameters of the nickel carbonate, gasp�ite (NiCO3). These experiments produce the first high-pressure Raman measurements on gasp�ite and greatly extend the pressure range studied with X-ray diffraction. This work reveals systematic trends among the transition metal carbonates: gasp�ite, having the smallest cation radius, is the most stable at high pressures. To aid our understanding of the relative phase stability of mantle minerals, I perform a pioneering set of experiments to determine the reaction products of CO2 and manganese metal. The results of these experiments inform us of the relative stabilities between carbonates and oxides and give insights into minerals that could store carbon in the deep Earth.