Isotopic fractionation during diffusion

Van Orman J, Saal A, Bourdon B, Hauri E (2002a) A new model for U-series isotope fractionation during igneous proeesses with finite diffusion and multiple solid phases. EOS Trans, Am Geophys Union 83(47) Fall Meet Suppl Abstract V71C-02... 

Lundstrom CC, Chaussidon M, Hsui AT, Keleman P, Zimmermann M (2005) Observations of Li isotope variations in the Trinity ophiolite evidence for isotope fractionation by diffusion during mantle melting, Geochim Cosmochim Acta 69 735-751 Luz B, Barkan E (2000) Assessment of oceanic productivity with the triple-isotope composition of dissolved oxygen. Science 288 2028-2031... 

Earlier in this chapter, we discussed isotopic fractionation during evaporation. Under appropriate conditions, where the condensed phase remains isotopically well mixed and the gas phase is removed from the system to prevent back reaction, Rayleigh distillation will occur (Box 7.2), resulting in a condensed phase that is isotopically heavy relative to the starting composition (Fig. 7.9). Isotopic fractionation can occur during both condensation and evaporation, as demonstrated by experiments (Richter el al., 2002). But it is not necessary that isotopes fractionate during evaporation or condensation. It depends on the details of the process. If evaporation occurs into a gas phase that is sufficiently dense, back reactions between gas and liquid can reduce the isotopic fractionation to near the equilibrium value, which is very small. For example, sulfur in chondrules does not show the isotopic fractionation (Tachibana and Huss, 2005) expected during evaporation from a liquid. Also, evaporation from a solid does not produce isotopic fractionation in the solid because diffusion is much too slow to equilibrate the few layers of surface atoms that are fractionated with the bulk of the material. 

In subaerial C3 plants substrate and reactant (s and r, respectively, in Fig. 5.56) for photosynthesis are both gaseous (atmospheric) C02, which flows through the Calvin cycle (the dark reactions of photosynthesis see Box 1.10) to yield simple carbohydrates (p), which are in turn the source of various metabolic intermediates. The source of the intracellular (kinetic) isotopic fractionation during C fixation is the enzyme rubisco (D-ribulose 1,5-diphosphate carboxylase/oxygenase). There is also an isotopic fractionation resulting from the passage of C02 into the cell. Passive diffusion of C02, at a rate , favours 12C, but the fractionation is small... 

A good example of translational fractionation is one-way diffusion through an orifice that is smaller than the mean-free path of the gas. Related, but somewhat more complex velocity-dependent fractionations occur during diffusion through a host gas, liquid, or solid. In these fractionations the isotopic masses in the translational fractionation factor are often replaced by some kind of effective reduced mass. For instance, in diffusion of a trace gas JiR through a medium, Y, consisting of molecules with mass ttiy. 

Cygan RT, Wright K, Fisler DK, Gale JD, Slater B (2002) Atomistic models of carbonate minerals bulk and surface structures, defects, and diffusion. Mol Simul 28 475-495 Davis AM, Hashimoto A, Clayton RN, Mayeda TK (1990) Isotope mass fractionation during evaporation of Mg2Si04. Nature 347 655-658... 

If the cell is well supplied with nutrients, then the production of activated enzyme is great and this step is relatively fast. If the transport of sulfate into the cell cannot keep up with the reduction of sulfate, the concentration of sulfate within the cell becomes small, and very little of the isotopically fractionated sulfate inside the cell can leak back out of the cell. Thus, the effect of the internal isotopic fractionation on the outside world is minimal and the overall fractionation of the process is small. In a hypothetical extreme case, every sulfate anion entering the cell would be consumed by reduction. This would require a complete lack of isotopic fractionation, because when all S atoms entering are consumed, there can be no selection of light vs. heavy isotopes. The isotopic fractionation of the overall reduction reaction would be equal to that which occurs during the diffusion step only. 

Isotope effects of this kind are relevant for an understanding of the isotope composition of clay minerals and absorption of water on mineral surfaces. The tendency for clays and shales to act as semipermeable membranes is well known. This effect is also known as ultraliltration . Coplen and Hanshaw (1973) postulated that hydrogen isotope fractionations may occur during ultraliltration in such a way that the residual water is emiched in deuterium due to its preferential adsorption on the clay minerals and its lower diffusivity. 

The isotopic fractionation is easily seen in 8 N03 and 8 N2 distributions in the major open-ocean denitrification zones (Altabet et al., 1999 Brandes et al., 1998 Cline and Kaplan, 1975). Typical open ocean values ofsub-euphotic zone nitrate are about 5%o (Lehmann et al., 2005 Sigman et al., 2000 Wu et al., 1997) but within the ODZ they climb to upwards of 15%o. Concomitant with this increase is a decrease in the 8 N2 from about 0.6%o to 0.2%o (Fig. 6.15). The large enrichment of N-N03 and the mirror image decrease in N-N2 is undoubtedly due to fractionation during denitrification. It is also possible to derive a fraction factor, , from the isotope distributions in the ODZ if one makes some assumption about the amount of nitrate that has been removed by denitrification, i.e., the nitrate deficit. For the eastern tropical North Pacific Brandes et al. (1998) assumed a Raleigh fraction mechanism and both open (advection-reaction) and closed (diffusion-reaction) systems to derive fractionation factors from the data, in Fig. 6.15. (Raleigh fractionation 8 N03 = where 8 N03 is the isotopic composition... 

Most common is the process of mass-dependent fractionation, in which the stable isotope ratio is altered as the consequence of physical processes differentially affecting atoms or molecules of different mass. Isotopes are fractionated relative to one another according to thermodynamic, kinetic, and diffusion processes. A simple example is the way in which oxygen isotopes in water molecules are fractionated during the process of evaporation. Water molecules containing the lower mass isotope leO are more likely to become water vapor than those containing the higher mass isotope lsO. Hence the water vapor is enriched in isotope leO and the liquid water is enriched in isotope lsO. 

The FGB model calculates exchange by diffusion of all minerals in a rock during cooling or heating (Filer et al. 1992, 1993). This model considers any number of minerals and grain sizes in a rock, the diffusion characteristics of each mineral, the isotope fractionations, and various forms of 5T/5t. It can be calculated with the computer program FGB (Filer et al. 1994). 

Jahne et al. (1987) also investigated isotopic specific diffusion coefficients for He and the change in 5C (C02) during diffusive gas loss from water. The increase in He diffusivity for the He compared to Tie was in agreement with the ratio of the square-root of their masses. This result provides further supporting evidence that the diffusion coefficients for individual isotopic noble gas species can reasonably be determined as a function of mass from Table 5 for variable temperatures. This is in contrast with the results for the study of 5C (C02), which showed a fractionation factor far lower than the value predicted from the square root of the reduced mass. This discrepancy indicates that in the case of active gases the difference is not just an effect of mass but of the isotope specific interaction energy with the water molecules. 

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