This goal of this research is to understand better the effects of iron on the properties of minerals in the Earth, and the properties of Earth's core, which consists of metallic iron alloyed with nickel and light elements. Theoretical methods based on fundamental physics are used which do not require any experimental input. Properties are computed from fundamental physics using as basic input the positions of the atomic nuclei and their charges. New techniques will be developed and tested by comparing the theoretical predictions with experiment. The results of this study will be important in interpreting geophysical data and in geochemical and geodynamic modeling of the Earth. 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 and (3) provide guidance for the design of experiments. Results of this study will include electronic structure, equations of state, elasticity, phonon dispersion and lattice dynamics, thermal properties, and X-ray and optical spectra. Materials containing iron and other transition metals are problematic for current methods based on density functional theory. For example, wüstite (FeO), endmember 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 failure of conventional methods is understood to be due to the mean field or self-consistent field approximation. Previous work has also used the LDA+U model, which does give a gap for antiferromagnetically (AFM) ordered rhombohedral wüstite and magnesiowüstite. However, LDA+U cannot give a gap for the room temperature or high temperature paramagnetic cubic structure, so it cannot be said to solve the problem for geophysics. 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. However, there are significant discrepancies in the theoretical equation of state with experiment. Theory predicts an AFM ground state of iron below 50 GPa, which improves the equation of state somewhat, but to date there is no experimental confirmation of magnetism 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. The investigators will address the problem of Fe in minerals and iron metal using dynamical mean field (DMFT). This is a developing method, and they will also contribute to its testing and development. Unlike the standard band theory and LDA+U, DMFT includes dynamical quantum fluctuations, which are believed to be crucial in correctly describing transition metal oxides. Quantum fluctuations may also be responsible for the observed discrepancies in Fe-Ni. For FeO, quantum fluctuations can be understood as electrons hopping on and off of iron ions. The spin also fluctuations, and it is the fluctuation in spin direction that gives rise to paramagnetic behavior. DMFT includes all of these fluctuations via a time (frequency) dependent Green?' function obtained for the quantum impurity model of an ion, atom, or cluster (solved via exact diagonalization) embedded in the rest of the crystal. 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.
