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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. Mössbauer 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 …