We will use new electronic structure methods to better understand the effects of iron in minerals in Earth's mantle and core. We will constrain physical properties important for our understanding of the Earth, including phase transitions that are responsible for changes in density, sound speeds, and electrical and thermal conductivity. Predicting properties of transition metals and transition metal oxides is a remaining key problem in accurate prediction of properties of Earth materials. Only now have the techniques been developed that include the basic ingredients of a successful theory. This is a deep problem, and experiments and theory to understand these materials have been active areas of research for over 30 years. The goal of this work is to (1) make predictions useful for modeling of the solid Earth (2) better understand mineral behavior and help in interpreting experimental data, (3) develop and test methods for highly correlated materials such as transition metal oxides and transition metal bearing perovskites, and (4) 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.
Materials containing iron and other transition metals are problematic for density functional theory, the standard for first-principles studies of materials. For example, wüstite (FeO), end-member of the important lower mantle phase magnesiowüstite ((Mg,Fe)O), is predicted to be a metal by conventional band theory, but is an insulator. The LDA+U model, with which much progress has been made, gives a gap for antiferromagnetically (AFM) ordered rhombohedral wüstite and magnesiowüstite, but cannot give a gap for the room temperature or high temperature paramagnetic cubic structure, nor does it correctly predict insulator to metal transitions. There are also indications of problems for iron metal itself. Earth's inner core is widely believed to consist of hexagonal close-packed (hcp) iron with a few percent light elements. Theory predicts an AFM ground state of iron below 50 GPa, but to date there is no experimental confirmation of magnetic order in hcp-Fe. There is a clear discrepancy in theory and experiment for Fe-Ni, where theory predicts observable hyperfine fields, but synchrotron Mössbauer experiments observe no sign of magnetism. Our most recent work shows that the elasticity of hcp iron at inner core conditions does not, after all, explain the observed seismic anisotropy. The inner core thus cannot be pure hcp iron alloy. Ni and other minor elements stabilize the fcc structure, so that the inner core may consist of two major phases, thus explaining the seismically observed heterogeneity. We will address the problem of Fe in minerals and iron metal using dynamical mean field theory (DMFT) integrated with density functional theory (DFT). Unlike standard band theory and LDA+U, DMFT includes dynamical quantum and thermal fluctuations, which are believed to be crucial in correctly describing transition metal oxides.
