Theoretical Investigations of Mantle and Core Materials

这项研究的目的是更好地了解铁对地球矿物性质的影响，以及地球核心的性质，地球核心由金属铁与镍和轻元素合金组成。使用基于基础物理学的理论方法，不需要任何实验输入。性质是从基础物理学计算的，使用原子核的位置及其电荷作为基本输入。 新技术将通过将理论预测与实验进行比较来开发和测试。这项研究的结果将是重要的地球物理数据的解释和地球化学和地球动力学建模。这项工作的目标是（1）使预测有用的固体地球的建模（2）更好地了解矿物的行为，并帮助解释实验数据和（3）提供指导的实验设计。本研究的结果将包括电子结构、状态方程、弹性、声子色散和晶格动力学、热性质、X射线和光学光谱。含有铁和其他过渡金属的材料对于目前基于密度泛函理论的方法是有问题的。例如，作为重要的下地幔相镁钨铁矿（（Mg，Fe）O）的端元的钨铁矿（FeO），被传统能带理论预测为金属，但却是绝缘体。传统方法的失败被理解为是由于平均场或自洽场近似。 以前的工作也使用LDA+U模型，它确实给出了反铁磁（AFM）有序菱面体方铁矿和镁方铁矿的间隙。然而，LDA+U不能给出室温或高温顺磁立方结构的间隙，因此不能说它解决了电子物理学的问题。也有迹象表明铁金属本身存在问题。地球的内核被广泛认为是由六方密堆积（hcp）铁和百分之几的轻元素组成。然而，理论状态方程与实验存在着很大的差异。理论预测AFM铁的基态低于50 GPa，这在一定程度上改善了状态方程，但迄今为止还没有实验证实hcp-Fe的磁性。对于铁镍合金，理论和实验存在明显的差异，理论预测了可观测到的超精细场，但同步穆斯堡尔实验没有观察到磁性的迹象。研究人员将使用动态平均场（DMFT）来解决矿物和铁金属中的铁问题。这是一个发展中的方法，他们也将有助于其测试和发展。与标准能带理论和LDA+U不同，DMFT包括动态量子涨落，这被认为是正确描述过渡金属氧化物的关键。量子涨落也可能是Fe-Ni中观察到的差异的原因。对于FeO，量子涨落可以理解为电子在铁离子上跳跃和跳跃。自旋也会波动，正是自旋方向的波动引起顺磁行为。DMFT包括所有这些波动通过时间（频率）依赖绿色？对于嵌入晶体其余部分的离子、原子或团簇的量子杂质模型（通过精确对角化求解）获得的“函数”。过渡金属及其氧化物的物性预测是准确预测地球物质物性的关键问题。 直到现在，才发展出包含成功理论基本要素的技术。这是一个深层次的问题，30多年来，理解这些材料的实验和理论一直是研究的活跃领域。

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.