Equilibrium Fractionation of Non-traditional Isotopes: a Molecular Modeling Perspective

1区 地球科学 Q1 Earth and Planetary Sciences
M. Blanchard, E. Balan, E. Schauble
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引用次数: 72

Abstract

The isotopic compositions of natural materials are determined by their parent reservoirs, on the one hand, and by fractionation mechanisms, on the other hand. Under the right conditions, fractionation represents isotope partitioning at thermodynamic equilibrium. In this case, the isotopic equilibrium constant depends on temperature, and reflects the slight change of free energy between two phases when they contain different isotopes of the same chemical element. The practical foundation of the theory of mass-dependent stable isotope fractionation dates back to the mid-twentieth century, when Bigeleisen and Mayer (1947) and Urey (1947) proposed a formalism that takes advantage of the Teller–Redlich product rule (Redlich 1935) to simplify the estimation of equilibrium isotope fractionations. In this chapter, we first give a brief introduction to this isotope fractionation theory. We see in particular how the various expressions of the fractionation factors are derived from the thermodynamic properties of harmonically vibrating molecules, a surprisingly effective mathematical approximation to real molecular behavior. The central input data of these expressions are vibrational frequencies, but an approximate formula that requires only force constants acting on the element of interest can be applied to many non-traditional isotopic systems, especially at elevated temperatures. This force-constant based approach can be particularly convenient to use in concert with first-principles electronic structure models of vibrating crystal structures and aqueous solutions. Collectively, these expressions allow us to discuss the crystal chemical parameters governing the equilibrium stable isotope fractionation. Since the previous volume of Reviews in Mineralogy and Geochemistry dedicated to non-traditional stable isotopes, the number of first-principles molecular modeling studies applied to geosciences in general and to isotopic fractionation in particular, has significantly increased. After a concise introduction to computational methods based on quantum mechanics, we will focus on the modeling of isotopic properties in liquids, which represents a bigger methodological challenge than …
非传统同位素的平衡分馏:分子模拟的视角
天然物质的同位素组成一方面由其母储层决定,另一方面由分馏机制决定。在适当的条件下,分馏表现为热力学平衡下的同位素分配。在这种情况下,同位素平衡常数取决于温度,反映了当两相含有同一化学元素的不同同位素时,两相之间自由能的微小变化。质量依赖稳定同位素分馏理论的实践基础可以追溯到20世纪中叶,当时Bigeleisen和Mayer(1947)和Urey(1947)提出了一种利用Teller-Redlich积规则(Redlich 1935)简化平衡同位素分馏估计的形式主义。在本章中,我们首先简要介绍了同位素分馏理论。我们特别看到了分馏因子的各种表达式是如何从谐波振动分子的热力学性质中推导出来的,这是对真实分子行为的一种令人惊讶的有效数学近似。这些表达式的中心输入数据是振动频率,但一个近似公式只需要作用于感兴趣元素的力常数,可以应用于许多非传统的同位素系统,特别是在高温下。这种基于力常数的方法可以特别方便地与振动晶体结构和水溶液的第一性原理电子结构模型一起使用。总的来说,这些表达式使我们能够讨论控制平衡稳定同位素分馏的晶体化学参数。自从《矿物学和地球化学评论》上一卷专门讨论非传统稳定同位素以来,应用于一般地球科学,特别是同位素分馏的第一性原理分子模型研究的数量显著增加。在简要介绍了基于量子力学的计算方法之后,我们将重点介绍液体中同位素性质的建模,这是一个比……
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来源期刊
Reviews in Mineralogy & Geochemistry
Reviews in Mineralogy & Geochemistry 地学-地球化学与地球物理
CiteScore
8.30
自引率
0.00%
发文量
39
期刊介绍: RiMG is a series of multi-authored, soft-bound volumes containing concise reviews of the literature and advances in theoretical and/or applied mineralogy, crystallography, petrology, and geochemistry. The content of each volume consists of fully developed text which can be used for self-study, research, or as a text-book for graduate-level courses. RiMG volumes are typically produced in conjunction with a short course but can also be published without a short course. The series is jointly published by the Mineralogical Society of America (MSA) and the Geochemical Society.
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