Mass-dependent isotope fractionation

Variations in isotopic compositions that are generated by isotope fractionation associated with chemical, physical, or (on Earth) biological processes are generally of mass-dependent nature. This implies that the magnitude of an isotope effect is proportional to the mass difference of the respective isotopes. Such mass-dependent isotope effects are hence generally most prevalent for lighter elements, which feature the largest relative differences in isotopic masses, and classic stable isotope studies were therefore focused on the elements H, C, N, O, and S. However, more recent studies, often conducted by MC-ICP-MS, have shown that natural isotope fractionation is also common for many heavier elements in both terrestrial rocks and meteorites [26, 27]. 

Many common processes and reactions generate isotope effects, hence there are also many possible applications. For example, isotope ratio data can be applied to obtain constraints on environmental conditions (e.g., temperatures, gas pressures) and reaction pathways. In addition, they are commonly used both as a material tracer and for the quantification of the mass fluxes [26]. 

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Young ED, Galy A, Nagahara H (2002) Kinetic and equilibrium mass-dependent isotope fractionation laws in nature and their geochemical and cosmochemical significance. Geochim Cosmochim Acta 66 1095-1104... 

Early studies of Mg isotope ratios in geological materials used the notation A Mg to mean per mil deviations from a standard as expressed in Equation (1) above, a convention that persists today (e.g., Elsu et al. 2000). The values assigned to A "Mg in those studies represent the level of mass-dependent isotopic fractionation relative to the standard. The same convention defined fi Mg as the per mil deviation from the standard after correction for the mass fractionation evidenced by A "Mg. In this system of nomenclature, A values refer to mass dependentfractionations while 5 values refer to deviations from mass-dependent fractionation (i.e., the S Mg defines excesses in Mg relative to mass fractionation attributable to decay of the extinct nuclide Al). In some cases A "Mg has been replaced by the symbol Fn,g (Kennedy et al. 1997) where the F refers to fractionation. ... 

Figure 16. Schematic illustration of envelopes of gas species i, in this case Mg, surrounding a volatilizing molten chondrule in space. The size of the gas envelope is a function of ambient background pressure P by virtue of the effect that pressure has on the gas molecule diffusivity D,. The diffusion coefficient can be calculated from the kinetic theory of gases, as shown. The level of isotopic fractionation associated with volatilization of the molten chondrule depends upon the balance between the evaporative flux J vap and the condensation flux Tom When the fluxes are equal (i.e., when = 0), there is no mass-dependent isotope fractionation associated with volatilization. This will be the case when the local partial pressure P, approaches the saturation partial pressure P,...

Figure 1. Schematic representation of the calcium mass spectrum in (a) natural materials, (b) a Ca- Ca tracer solution used for separating natural mass dependent isotopic fractionation from mass discrimination caused by thermal ionization, and (c) a typical mixture of natiwal calcium and tocer calcium used for analysis. The tracer solution has roughly equal amounts of Ca and Ca. In (c) the relative isotopic abundances are shown with an expanded scale. Note that in the mixed sample, masses 42 and 48 are predominantly from the tracer solution, and masses 40 and 44 are almost entirely from natural calcium. This situation enables the instrumental fractionation to be gauged from the Ca/ Ca ratio, and the natural fractionation to be gauged from the sample Ca/ Ca ratio.

We have known for many years that large isotopic fractionations of heavy elements like Pb develop in the source regions of TIMS machines. Nonetheless, most of us held fast to the conventional wisdom that no significant mass-dependent isotopic fractionations were likely to occur in natural or laboratory systems for elements that are either heavy or engaged in bonds with a dominant ionic character. With the relatively recent appearance of new instrumentation like MC-ICP-MS and heroic methods development in TIMS analyses, it became possible to make very precise measurements of the isotopic ratios of some of these non-traditional elements, particularly if they comprise three or more isotopes. It was eminently reasonable to reexamine these systems in this new light. Perhaps atomic weights could be refined, or maybe there were some unexpected isotopic variations to discover. There were. 

It is a common practice to describe mass dependent isotope fractionation processes by a single linear curve on a three-isotope-plot (Matsuhisa et al. 1978). The resulting straight lines are referred to as terrestrial mass fractionation lines and deviations from it are used as indicating nonmass-dependent isotope effects. The three-isotope-plot is based on the approximation of a power law function to linear format. To describe how far a sample plots off the mass-dependent fractionation line, a new term has been introduced A 0, A Mg, A S, etc. Several definitions of A have been introduced in the literature, which have been discussed by Assonov and Bren-ninkmeijer (2005). The simplest definition is given by ... 

A nice property of isotopes is that when minerals form from a common source such as a magma, all minerals will have identical isotopic ratios (the same as that in the magma) if all isotopes are corrected for mass-dependent isotopic fractionation. That is, if several minerals in a volcanic rock crystallized at roughly the same time (within a day, a month, a year, or 1000 years, depending on the resolution of age determination), they would all have the same " Nd/ " " Nd ratio. Hence, in the above equation, ( " Nd/ " " Nd)o is a constant. Furthermore, for rocks formed at the same time, — 1) is also a constant. Because Sm and Nd have different chemical properties, their concentrations and hence the Sm/ Nd ratio vary from one mineral to another. With different Sm/Nd ratios in different minerals, after some time (such as one billion years), the Nd/ Nd ratio would vary from one mineral to another. Hence, when we measure Nd/ " " Nd... 

Besides the problem of accounting for the chemical abundances of planetary noble gases, there are characteristic differences in isotopic composition between planetary noble gases in meteorites and the solar gases that presumably represent the nebula from which meteorites formed. For Ar and Kr the differences are modest or perhaps nonexistent or can ultimately be explained in terms of a reasonable degree of mass-dependent isotopic fractionation. For Ne (Figure 3.3) and Xe (Figure 7.6), the... 

Unlike elemental concentrations, isotopic compositions are only affected a little by chemical differentiation processes. Mass-dependent isotopic fractionations can arise in chemical partitioning (cf. Section 2.9), of course, but on the scale of interest in the present context, plausible fractionation effects are small, especially at the high temperatures prevalent in the mantle. We can thus be much more confident that a noble gas isotopic composition measured in a mantle-derived sample is indeed characteristic of its mantle source. Representative mantle ranges for selected isotopic ratios are presented in Table 6.2. 

Apart from fission and radiogenic components, it appears that the principal underlying relationship between terrestrial Xe and solar Xe is a strong (about 3.5%/amu) mass-dependent isotopic fractionation. This is shown in Figure 7.6. To a good approximation, atmospheric Xe is related to SUCOR Xe, a solar Xe composition calculated to be surface-correlated Xe in a lunar mare soil. However, it is also clear that slight deviation from a linear trend indicates that atmospheric Xe and solar Xe cannot be related solely by fractionation. 

A hallmark of the two prototypical FUN inclusions (whose individual names are Cl and EK-1-4-1) is that their only distinguishing characteristics are their isotopic compositions. In all other properties they are identical to normal type B CAIs. To this day it remains tme that there is no certain way to recognize a FUN CAI except by isotopic analysis. For example, the FUN inclusion AXCAI-2271 from Axtell (Srinivasan et al, 2000), shown in Figure 15, is a compact type A (melilite-rich) CAI whose ordinary appearance gives no hint of its peculiar isotopic properties. Nevertheless, certain kinds of CAIs do have a statistical propensity toward unusual isotopic properties. FoBs are relatively rare, yet four of them possess large degrees of mass-dependent isotopic fractionation (Clayton et al., 1984 Davis et al, 1991 MacPherson and Davis, 1992)... 

The origin of mass-dependent isotopic fractionation in FUN CAIs is commonly (and somewhat casually) assumed to be the result of Rayleigh-type distillation, while the inclusions were molten. It is true that a strong case for distillation has been made in the case of the so-called HAL-type hibonites (see Section 1.08.7), based on trace element and isotopic properties (Lee et al, 1979, 1980 Davis et al, 1982 Ireland et al, 1992 Floss et al, 1996). Such an origin is problematic for other FUN CAIs, however, especially those that are otherwise identical in bulk composition to non-FUN CAIs. Most notably this is true of the FoBs that also happen to have F or FUN properties (Clayton et al, 1984 Davis et al, 1991). These objects are magnesium-rich relative to other CAIs, yet distillation experiments conducted on chondritic starting materials consistently show that... 

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