Theoretical Investigations of Mantle Materials

该提案是利用第一性原理理论方法来研究和模拟地球地幔的矿物。这项工作的目标是（1）在数据尚不可用的情况下，为固体地球的建模和地震数据的解释做出有用的预测（2）更好地理解矿物行为并帮助解释实验数据和（3）为实验设计提供指导。术语“第一性原理”意味着不直接使用实验数据;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。甚至原子核的位置也可以被优化，或者允许在有限的温度下动态移动。尽管如此，基本问题和起始构型通常来自实验数据或观察。本研究不是以实验代替研究，而是与实验研究相结合。第一性原理方法的优点包括在理论和数据不一致的情况下发现实验问题或发现新物理的可能性，以及在目前可获得的实验制度之外或由于这些实验的困难而无法获得数据时提供临时数据。建议如下：（1）研究方镁石和方石英之间重要固溶体的热状态方程、热弹性和相稳定性（Mg，Fe 1-x）O，硅酸盐钙钛矿（Ca，Mg，Al，Si，Fe）2 O3和过渡区石榴石（Ca，Mg，Al）3（Al，Fe，Mg）2（Si，（2）利用最先进的电子结构方法，如LDA+，研究含铁氧化物和硅酸盐在高压下的行为。U和动力学平均场理论（DMFT）;（3）研究硅酸盐钙钛矿中的扩散。潜在的模型将适合密度泛函理论计算，允许在地球深部的温度和压力下进行分子动力学模拟。固体解决方案将研究使用超细胞和准随机结构，以及有效的哈密顿量和簇展开与蒙特卡洛。将使用超越传统能带理论的方法研究含铁系统;特别是PI将研究Fe 1-xO方铁矿，赤铁矿Fe 2 O3和磁铁矿Fe 3 O 4及其高压多晶型物，以更好地了解亚铁和三价铁在高压和高温下的行为。特别注意的是，在硅酸盐钙钛矿中的Fe，Al和空位的行为，已被证明对钙钛矿的弹性有重大影响。扩散和有限温度弹性将使用MD内的自由能积分进行研究。

EAR-0310139This 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.--