A basic theoretical understanding of stable isotope fractionations can help researczzzhers plan and interpret both laboratory experiments and measurements on natural samples. The goal of this chapter is to provide an introduction to stable isotope fractionation theory, particularly as it applies to mass-dependent fractionations of non-traditional elements and materials. Concepts are illustrated using a number of worked examples. For most elements, and typical terrestrial temperature and pressure conditions, equilibrium isotopic fractionations are caused by the sensitivities of molecular and condensed-phase vibrational frequencies to isotopic substitution. This is explained using the concepts of vibrational zero-point energy and the partition function, leading to Urey’s (1947) simplified equation for calculating isotopic partition function ratios for molecules, and Kieffer’s (1982) extension to condensed phases. Discussion will focus on methods of obtaining the necessary input data (vibrational frequencies) for partition function calculations. Vibrational spectra have not been measured or are incomplete for most of the substances that Earth scientists are interested in studying, making it necessary to estimate unknown frequencies, or to measure them directly. Techniques for estimating unknown frequencies range from simple analogies to well-studied materials to more complex empirical force-field calculations and ab initio quantum chemistry. Mossbauer spectroscopy has also been used to obtain the vibrational properties of some elements, particularly iron, in a variety of compounds. Some kinetic isotopic fractionations are controlled by molecular or atomic translational velocities; this class includes many diffusive and evaporative fractionations. These fractionations can be modeled using classical statistical mechanics. Other kinetic fractionations may result from the isotopic sensitivity of the activation energy required to achieve a transition state, a process that (in its simplest form) can be modeled using a modification of Urey’s equation (Bigeleisen 1949).

Theoretical estimates of isotopic fractionations are particularly powerful in systems that are difficult to characterize experimentally, or when empirical …

Applying Stable Isotope Fractionation Theory to New Systems

Application of Fe isotopes to tracing the geochemical and biological cycling of Fe

A critical look at iron paleoredox proxies: New insights from modern euxinic marine basins

Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(II) and Fe(III)

As demonstrated by the chapters in this short course, stable isotope techniques are an important tool in almost every branch of the earth sciences. Central to many of these applications is a quantitative understanding of equilibrium isotope partitioning between substances. Indeed, it was Harold Urey’s (1947) thermodynamically based estimate of the temperature-dependence of 18O/16O fractionation between calcium carbonate and water, and a recognition of how this information might be used to determine the temperatures of ancient oceans, that launched the science of stable isotope geochemistry. The approach pioneered by Urey has since been used to estimate temperatures for a wide range of geological processes (e.g. Emiliani 1955; Anderson et al. 1971; Clayton 1986; Valley, this volume). In addition to their geothermometric applications, equilibrium fractionation data are also important in the study of fluid-rock interactions, including those associated with diagenetic, hydrothermal, and metamorphic processes (Baumgartner and Valley, this volume; Shanks, this volume). Finally, a knowledge of equilibrium fractionation is a necessary first step in evaluating isotopic disequilibrium, a widespread phenomenon that is increasingly being used to study temporal relationships in geological systems (Cole and Chakraborty, this volume).

In the fifty-four years since the publication of Urey’s paper, equilibrium fractionation data have been reported for many minerals and fluids of geological interest. These data were derived from: (1) theoretical calculations following the methods developed by Urey (1947) and Bigeleisen and Mayer (1947); (2) direct laboratory experiments; (3) semi-empirical bond-strength models; and (4) measurement of fractionations in natural samples. Each of these methods has its advantages and disadvantages. However, the availability of a variety of methods for calibrating fractionation factors has led to a plethora of calibrations, not all of which are in agreement. In this chapter, we evaluate the major methods for determining fractionation factors. …

Equilibrium Oxygen, Hydrogen and Carbon Isotope Fractionation Factors Applicable to Geologic Systems

The use of Mössbauer spectroscopy in stable isotope geochemistry

Equilibrium Iron Isotope Fractionation Factors of Minerals: Reevaluation from the Data of Nuclear Inelastic Resonant X-ray Scattering and Mossbauer Spectroscopy

Determination of tin equilibrium isotope fractionation factors from synchrotron radiation experiments

Oxygen isotope fractionation factors involving cassiterite (SnO2): I. calculation of reduced partition function ratios from heat capacity and X-ray resonant studies

Low-temperature heat capacity of tin dioxide: new standard data on thermodynamic functions

S. D. Mineev

Papers

The use of Mössbauer spectroscopy in stable isotope geochemistry

Equilibrium Iron Isotope Fractionation Factors of Minerals: Reevaluation from the Data of Nuclear Inelastic Resonant X-ray Scattering and Mossbauer Spectroscopy

Determination of tin equilibrium isotope fractionation factors from synchrotron radiation experiments

Oxygen isotope fractionation factors involving cassiterite (SnO2): I. calculation of reduced partition function ratios from heat capacity and X-ray resonant studies

Low-temperature heat capacity of tin dioxide: new standard data on thermodynamic functions