Collaborative Research: Experimental and computational constraints on the isotope fractionation of Mossbauer-inactive elements in mantle minerals

深部矿物的同位素组成为地球内部结构和化学演化提供了重要的约束条件。深部矿物的同位素组成受同位素分馏控制，不同的同位素在不同的压力和温度下在不同的矿物之间重新分布。传统的深部矿物平衡同位素分馏约束方法有三种：理论计算、质谱分析和核共振散射。然而，每种方法都有其自身的挑战。理论计算受到模型中使用的物理近似的限制，必须以实验为基准；质谱法难以确定是否达到平衡，而且耗时；核共振散射只能应用于极少数Mössbauer-active元素。本提案描述了一项新的多学科研究，通过将最先进的x射线光谱学与理论计算相结合，通过协作和协同努力，对难以受传统实验方法约束的深地矿物的同位素分选进行研究。研究人员的方法是实验基准，时间效率高，直接反映平衡同位素分馏，可以应用于几乎所有元素。他们的目标是通过他们提出的研究来回答以下问题：1)深部矿物中的Mössbauer-inactive元素如何随着压力、温度和晶体结构重新分布？2)如何有效约束深部固溶体中Mössbauer-inactive元素的分馏？3)振动非调和性如何影响地幔硅酸盐的同位素分选？该项目将支持三名处于职业生涯早期到中期的研究人员在夏威夷大学茂纳分校（Zhang和B. Chen）和普渡大学（Chen M. Chen）继续他们的研究。通过这个项目，该团队将在国家用户设施中开发实验仪器和用于计算的开源代码，并且研究套件将供国内外地球科学及其他领域的研究人员使用。本项目将有本科生助理和博士后学者参与。该项目还致力于为参与的早期职业研究人员建立职业发展途径，推动地球科学领域的性别和种族平等，扩大传统上代表性不足的少数民族对STEM的参与。在高P-T条件下，地幔矿物组成元素的同位素分馏被认为是地球分异的分支，为地幔的组成和化学演化提供了重要线索。以前关于矿物间Mössbauer-inactive元素同位素分馏的研究要么是用质谱法测量的，达到平衡需要额外的谨慎，要么是在没有实验证实的情况下根据理论计算进行估计。研究人员已经证明，四配位Si的减配函数比（β-因子）可以通过理论计算校准的原位高t SXD实验来约束。在这个拟议的项目中，他们将首次扩展该方法，以确定非淬灭深地矿物中六配位Si的实验约束β因子。他们还将应对挑战，建立一种有效的方法，通过理论计算来确定固溶体中的β因子，这些计算将以SXD实验为基准，从而使他们能够研究深地矿物中六配位Ti的同位素分馏。他们提出的联合方法绕过了固体溶液的直接理论建模，这大大降低了计算成本。采用实验和理论模拟相结合的方法，研究了含水层状硅酸盐在振动非谐性作用下对Si β因子的修正。提出的实验基准机器学习框架，以建立一个高度准确而高效的模型，将使他们能够提供非调和矿物系统中Si β因子的可靠估计。虽然他们只建议研究Mössbauer-inactive元素（Si & Ti），但同样的方法可以扩展到其他元素，如C， O， Mg和Ca。所有这三个提议的任务将为地幔矿物中同位素分布的完整景观奠定基础，并将加强对地球同位素组成及其化学演化的理解。该项目由地球深层内部合作研究（CSEDI）和刺激竞争研究的既定计划（EPSCoR）共同资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Isotope compositions of deep-earth minerals provide crucial constraints on the earth’s internal structure and chemical evolution. The isotope compositions of deep-earth minerals are controlled by a process named isotope fractionation, in which different isotopes redistribute between different minerals under various pressures and temperatures. There are three conventional ways to constrain equilibrium isotope fractionation in deep-earth minerals, namely theoretical calculation, mass spectroscopy, and nuclear resonance scattering. However, each method has its own challenges. Theoretical calculation is limited by physical approximations used in the model and has to be benchmarked by experiments; mass spectroscopy has difficulty in determining the attainment of equilibrium and is time-consuming; and nuclear resonance scattering can only be applied to the few Mössbauer-active elements. This proposal describes a novel multidisciplinary study on the isotope fractionations of deep-earth minerals that are difficult to be constrained by conventional experimental approaches, through collaborative and synergetic efforts by combining state-of-the-art X-ray spectroscopy with theoretical calculations. The researcher's approach is experimentally benchmarked, time-efficient, directly reflects the equilibrium isotope fractionation, and can be applied to nearly all elements. They aim to answer the following questions with their proposed study: 1) How do the Mössbauer-inactive elements in deep-earth minerals redistribute with pressure, temperature, and crystal structure? 2) How to constrain the fractionation of Mössbauer-inactive elements in deep earth solid solutions efficiently? and 3) How does vibrational anharmonicity affect the isotope fractionation in mantle silicates? The project will support three early to mid-career researchers to continue their research at the University of Hawaii at Maona (Zhang and B. Chen) and Purdue University (M. Chen). Through this project, the team will develop both experimental instruments at a national user facility and open-source codes for computation, and the research suite will be available to domestic and international researchers in earth sciences and beyond. Undergraduate assistants and postdoc scholars will be involved in this project. This project is also committed to establishing the career development pathways for the involved early-career researchers, pushing for the gender and racial equality in geoscience, and broadening the participation in STEM of traditionally underrepresented minorities.The fractionation of the isotopes of constituent elements of mantle minerals at high P-T conditions are considered the ramifications of the differentiation of the Earth, offering crucial clues for the mantle’s composition and chemical evolution. Previous studies on the isotope fractionation of Mössbauer-inactive elements between minerals were either measured using mass spectroscopy in which the attainment of equilibrium requires additional caution, or estimated from theoretical calculations without corroboration from experiments. The researchers have demonstrated that the reduced partition function ratio (β-factor) of tetracoordinated Si can be constrained by theoretical-calculation-calibrated in-situ high-T SXD experiments. In this proposed project, they will extend the method to determine experimentally constrained β-factors of hexacoordinated Si in non-quenchable deep-earth minerals for the first time. They will also tackle challenges to establish an efficient approach to determine β-factors in solid solutions by theoretical calculations, which are to be benchmarked by SXD experiments and thus allows them to investigate the isotope fractionation of hexacoordinated Ti in deep-earth minerals. Their proposed combined approach circumvents direct theoretical modeling of solid solutions, which significantly reduces computational costs. Using the combined approaches of experiments and theoretical modeling, the correction to Si β-factor in hydrous phyllosilicates induced by the vibrational anharmonicity will be investigated. The proposed experimentally benchmarked machine learning framework to establish a highly accurate yet efficient model will allow them to provide reliable estimations of Si β-factor in anharmonic mineral systems. Though they only propose to study select Mössbauer-inactive elements (Si & Ti) in this proposal, the same approach can be extended to other elements such as C, O, Mg, and Ca. All the three proposed tasks will build the foundation for a complete landscape of isotope distribution in mantle minerals, and will enhance understanding of the Earth’s isotopic composition and in turn its chemical evolution. This project is jointly funded by Cooperative Studies of the Earth's Deep Interior (CSEDI) and the Established Program to Stimulate Competitive Research (EPSCoR).This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.