Theoretical Investigations of Mantle and Core Materials

我们将使用新的电子结构方法来更好地了解铁在地球地幔和地核矿物中的作用。我们将限制对我们了解地球很重要的物理性质，包括导致密度变化的相变，声速，电导率和热导率。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。这项工作的目标是（1）做出对固体地球建模有用的预测（2）更好地理解矿物行为并帮助解释实验数据，（3）开发和测试高度相关的材料（如过渡金属氧化物和过渡金属钙钛矿）的方法，以及（4）为实验设计提供指导。第一性原理是指不直接使用实验数据，而是以原子核的位置及其电荷作为基本输入，从基础物理学中计算出性质。含有铁和其他过渡金属的材料对于密度泛函理论来说是有问题的，密度泛函理论是材料第一性原理研究的标准。例如，在下地幔相镁钨铁矿（（Mg，Fe）O）的端元中，钨铁矿（FeO）被传统能带理论预测为金属，但它是绝缘体。LDA+U模型已经取得了很大的进展，它给出了反铁磁（AFM）有序菱面体方铁矿和镁方铁矿的能隙，但不能给出室温或高温顺磁立方结构的能隙，也不能正确预测绝缘体到金属的转变。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。理论预测AFM基态铁低于50 GPa，但到目前为止，还没有实验证实hcp-Fe中的磁序。铁镍合金的理论和实验有明显的差异，理论预测可观测到超精细场，但同步加速器穆斯堡尔实验没有观察到磁性的迹象。我们最近的工作表明，hcp铁在内核条件下的弹性毕竟不能解释观测到的地震各向异性。因此，内芯不能是纯hcp铁合金。镍和其他微量元素稳定了面心立方结构，因此内核可能由两个主要相组成，从而解释了地震观测到的不均匀性。我们将利用动力学平均场理论（DMFT）结合密度泛函理论（DFT）来解决矿物和铁金属中的铁问题。与标准能带理论和LDA+U不同，DMFT包括动态量子和热涨落，这被认为是正确描述过渡金属氧化物的关键。

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.