The Earth, like any other warm object, cools with time by shedding its heat to the surroundings. The rate limiting step is transfer of heat from inside the hotter interior to the surface, where heat release is manifest in volcanoes and motions of the crustal and lithospheric plates, which in turn generate earthquakes. These near-surface phenomena impact the biosphere and human endeavors and thus understanding the interior heat source that drives them is important. Cooling of the interior is governed by physical properties of minerals and rocks, foremost of which are thermal diffusivity and conductivity. Recent technology transfer of laser-flash analysis (LFA) from materials science now permits accurate measurement of thermal transport properties of geologic materials. However, studies of the Earth's interior require data at conditions not accessible by experiment, e.g., T > 2300 K and P > 100 GPa. Therefore, a robust theoretical model is needed to extrapolate the trends seen in the laboratory data to conditions in the Earth. Models are available, but have serious flaws, including being benchmarked against old data that contain significant and systematic errors. This proposal concerns development of a much improved robust theoretical model and providing accurate, state-of-the-art measurements of thermal diffusivity against which this model can be benchmarked. The proposed research is important to understand conduction in the outermost lithosphere layers and in the interior boundary between metal core and rock mantle, mantle circulations in the interior, and thermal evolution of planetary bodies due to nonlinear feedback in conservation equations. This work will further our understanding of not only planetary scale processes, but also probes the microscopic origin of heat transport. Specifically, older methods, involving physical contact with thermocouples, underestimate thermal diffusivity (D) by ~25% near 298 K, and provide incorrect signs and magnitude for D/T. Many models are based on the erroneous notion that thermal conductivity (* =*CPD, where is density and CP is heat capacity) can be obtained entirely from thermodynamic properties, which are static and depict equilibrium behavior, whereas transport by it nature is dynamic, involving interactions of vibrating atoms, and occurs under non-equilibrium conditions. We therefore propose construction of a new type of model based on a computational method that combines the quantitative, first-principles calculation of the dynamic interactions of vibrations in the mineral and microscopic Boltzmann transport theory to predict steady-state non-equilibrium distribution and changes in vibrational energy, and to benchmark this model against laser-flash measurements of simple, but relevant, systems. The mineral physics group and the solid-state theory group will work in parallel to establish reliable experimental and theoretical data, respectively. Initially, the study will focus on simple systems for which calculations are clearly feasible: Si, NaCl, and MgO, subsequently expanding to Al2O3 and Mg2SiO4. Experimental efforts will concentrate on interfacing a diamond anvil cell with the LFA to improve accuracy in measuring *D/*P. Theoretical efforts include developing a database of vibrational interactions (anharmonicity), and implementing efficient algorithms. In addition, the two groups will work closely to better interpret the experimental data with the newly calculated detailed thermal transport properties of each phonon. Dominant heat transport mechanisms will be summarized, and the insights will be utilized to construct new transport models providing uniform agreement among the mineral systems studied. Finally, thermal diffusivity data at T-P conditions that not yet accessible by experiment will be predicted. Multiple models will be explored to estimate possible theoretical uncertainty. Re the greater impact and infrastructure components of the proposal: Thermal diffusivity data are central to any problem in planetary science that involves thermal gradients, e.g., accretion, magma production, contact aureoles, planetary differentiation. Because the results shed light on microscopic behavior, this study is relevant to mineral physics, petrology, and geophysics. The current project directs efforts towards the only accurate method for measuring D and a new type of theoretical modeling with a sound basis. Synergy will be in part accomplished by students participating in research at both facilities. Training of graduate students in state-of-the-art techniques will be a focus, and exposure to both theory and experiment will provide a well-rounded education. The project will improve diversity in science by involving both minority and women students.
