Isotopes, stable equilibrium

Isotopic Exchange/Equilibrium. Chemical steps are required at the outset of the procedure to insure isotopic exchange between the radionuclide to be analyzed (the radioanalyte) and the tracer or carrier that has been added. The carrier or tracer and the radioanalyte must be in the same oxidation state and chemical species in solution. This effort is not required for radionuclides that exist in only a single form, such as Group 1A (Li, Na, K, Rb) elements that are consistently in their +1 state in solution. Other elements (such as I or Ru) that have multiple oxidation states, and also can form stable complexes, will require steps to insure that the added carrier or tracer and the radioanalyte exchange before the analysis is started. 

A phenol-degrading community was examined using phenol followed by analysis of the stable-isotope-labeled RNA by equilibrium density centrifugation, and complemented... 

A useful analogy for understanding secular equilibrium is visualizing a decay chain as a series of pools of water (Fig. 2). These pools eventually lead to a continuously filling pool representing a stable isotope of lead (either ° Pb, ° Pb or ° Pb). Over the timescale... 

For the study of mixed oxides, one should characterize the various sites. In this case, the first step is to characterize the CO adsorption at various equilibrium pressures at low temperature, followed by evacuation at increasing temperatures to obtain information about the stabilities of the various species. Although the C—O stretching frequency is the most informative parameter, the data determining the stabilities of the various species can be decisive for the assignment of the bands. Multiple carbonyls adsorbed on the same metal cation are possible, and in order to identify them isotopic mixtures should be used. Sometimes the polycarbonyls are very stable and in this case, if 12CO is adsorbed first and then 13CO introduced, mixed species may not form at ambient temperature. 

Fig. 25.4. Oxygen and carbon stable isotopic compositions of calcite ( ) and dolomite ( ) cements from Lyons sandstone (Levandowski et al., 1973), and isotopic trends (bold arrows) predicted for dolomite cements produced by the mixing reaction shown in Figure 25.3, assuming differing CO2 fugacities (25, 50, and 100) for the Fountain brine. Fine arrows, for comparison, show isotopic trends predicted in calculations which assume (improperly) that fluid and minerals maintain isotopic equilibrium over the course of the simulation. Figure after Lee and Bethke (1996).

Isotope Dilution Condition that occurs when a stable isotope of the analyzed metal is added to the seawater. After equilibrium with the sample,... 

Equations (8) and (10) are applicable to stable isotope systems where isotopic fractionation occurs through mass-dependent processes which comprise the majority of cases described in this volume. These relations may also be used to identify mass-independent fractionation processes, as discussed in Chapter 2 (Birck 2004). Mass-dependent fractionation laws other than those given above distinguish equilibrium from kinetic fractionation effects, and these are discussed in detail in Chapters 3 and 6 (Schauble 2004 Yormg and Galy 2004). Note that distinction between different mass-dependent fractionation laws will generally require very... 

We briefly review processes in which isotopic fractionations may be recorded in isotopically distinct reservoirs that are preserved in nature. These concepts have been extensively covered in the H, C, O, and S isotope literature, and we illustrate several examples for the non-traditional stable isotope systems discussed in this volume. One of the simplest processes that produces isotopically distinct reservoirs would be slow reaction of substance A to B, where A and B remain open to complete isotopic exchange during the process. This is commonly referred to as closed system equilibrium, and the changes in isotopic compositions that occur may be defined by the exact relation ... 

Fortier SM, Cole DR, Wesolowski DJ, Riciputi LR, Paterson BA, Valley JW, Horita J (1995) Determination of the magnetite-water equilibrium oxygen isotope fractionation factor at 350°C a comparison of ion microprobe and laser fluorination techniques. Geochim Cosmochim Acta 59 3871-3875 Friedman I, O Neil JR (1977) Compilation of Stable Isotope Fractionation Factors of Geochemical Interest. US Geol Surv Prof Paper 440-KK... 

Skulan JL, Beard BL, Johnson CM (2002) Kinetic and equilibrium Fe isotope fractionation between aqueous Fe(III) and hematite. Geochim Cosmochim Acta 66 2995-3015 Stewart MA, Spivack AJ (2004) The stable-chlorine isotope compositions of natural and anthropogenic materials. Rev Mineral Geochem 55 231-254... 

This review will introduce basic techniques for calculating equilibrium and kinetic stable isotope fractionations in molecules, aqueous complexes, and solid phases, with a particular focus on the thermodynamic approach that has been most commonly applied to studies of equilibrium fractionations of well-studied elements (H, C, N, O, and S) (Urey 1947). Less direct methods for calculating equilibrium fractionations will be discussed briefly, including techniques based on Mossbauer spectroscopy (Polyakov 1997 Polyakov and Mineev 2000). 

General rules governing equilibrium stable isotope fractionations... 

Fractionations are typically very small, on the order of parts per thousand or parts per ten thousand, so it is common to see expressions like 1000 ln(a) or 1000 (a-l) that magnify the difference between a and 1. a =1.001(1000 [a-l] = 1) is equivalent to a 1 per mil (%o) fractionation. Readers of the primary theoretical literature on stable isotope fractionations will frequently encounter results tabulated in terms of P-factors or equilibrium constants. For present purposes, we can think of Pjjh as simply a theoretical fractionation calculated between some substance JiR containing the elementX, and dissociated, non-interacting atoms ofX. In the present review the synonymous term Uxr-x is used. This type of fractionation factor is a convenient way to tabulate theoretical fractionations relative to a common exchange partner (dissociated, isolated atoms), and can easily be converted into fractionation factors for any exchange reaction ... 

Equilibrium stable isotope fractionation is a quantum-mechanical phenomenon, driven mainly by differences in the vibrational energies of molecules and crystals containing atoms of differing masses (Urey 1947). In fact, a list of vibrational frequencies for two isotopic forms of each substance of interest—along with a few fundamental constants—is sufficient to calculate an equilibrium isotope fractionation with reasonable accuracy. A succinct derivation of Urey s formulation follows. This theory has been reviewed many times in the geochemical... 

Figure 1. Translation, rotation, and vibration of a diatomic molecule. Every molecule has three translational degrees of freedom corresponding to motion of the center of mass of the molecule in the three Cartesian directions (left side). Diatomic and linear molecules also have two rotational degrees of freedom, about rotational axes perpendicular to the bond (center). Non-linear molecules have three rotational degrees of freedom. Vibrations involve no net momentum or angular momentum, instead corresponding to distortions of the internal structure of the molecule (right side). Diatomic molecules have one vibration, polyatomic linear molecules have 3V-5 vibrations, and nonlinear molecules have 3V-6 vibrations. Equilibrium stable isotope fractionations are driven mainly by the effects of isotopic substitution on vibrational frequencies.

This relation correctly predicts that most equilibrium stable isotope fractionations are inversely proportional to the square of absolute temperature, and is the basis of equilibrium fractionation rule (1). A detailed derivation of the Bigeleisen and Mayer model has been presented in an earlier review (Criss 1991). 

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