This proposal is to use first-principles theoretical methods to study and simulate the minerals of the Earth's mantle. The goal of this work is to (1) make predictions useful for modeling of the solid Earth and interpretation of seismic data where data are not yet available (2) better understand mineral behavior and help in interpreting experimental data and (3) provide guidance for the design of experiments. The term "first-principles" means that no experimental data are directly used; properties are computed from fundamental physics using as basic input the positions of the atomic nuclei and their charges. Even the positions of the nuclei can be optimized, or allowed to move dynamically at finite temperatures. Nevertheless, the basic problems and starting configurations generally come from experimental data or observations. This research is not instead of experiments, but rather works together with experimental studies. The advantages of first-principles methods include the possibility of detecting problems with experiments or discovering new physics, where theory and data disagree, and providing provisional data outside the currently accessible experimental regime or when data are not yet available due to the difficulty of such experiments. The following are proposed: (1) To study the thermal equations of state, thermoelasticity, and phase stability of the important solid solutions between periclase and wustite (Mg, Fe1-x)O, silicate perovskite (Ca,Mg,Al,Si,Fe)2O3, and transition zone garnets (Ca,Mg,Al)3(Al,Fe,Mg)2 (Si,Al)3O12 (2) To study the behavior of iron-bearing oxides and silicates at high pressures using state-of-the-art electronic structure methods such as LDA+U and dynamical mean field theory (DMFT) and (3) To study diffusion in silicate perovskite.
A variety of methods will be used. Potential models will be fit to density functional theory computations allowing molecular dynamics (MD) simulations at the temperature and pressures of the deep Earth. Solid solutions will be studied using supercells and quasi-random structures as well as effective Hamiltonians and cluster expansions with Monte Carlo. Iron-bearing systems will be studied using methods that go beyond conventional band theory; in particular the PI will study Fe1-xO wustite, hematite Fe2O3, and magnetite Fe3O4 and their high-pressure polymorphs in order to better understand the behavior of ferrous and ferric iron at high pressures and temperatures. Special attention will be paid to the behavior of Fe, Al, and vacancies in silicate perovskite, which have been shown to have major effects on the elasticity of perovskite. Diffusion and finite temperature elasticity will be studied using free-energy integrations within MD.
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