Diffusion isotopic fractionation

Another consequence of the diffusion controlled fractionation process is that significant isotopic fractionations should occur. Peeters et al. (2002) suggested the use of Ne/ Ne ratios to test the validity of PR-model to describe gas partitioning in ground waters. In the few aquifers where Ne isotopes have been analyzed, no significant diffusive isotopic fractionation has been found so far (Peeters et al. 2002). 

However, as the MR-model proaches the PR-model, it also predicts diffusive isotopic fractionation, i.e., the e/ Ne should be significantly lower than the atmospheric ratio (Peeters et al. 2002). Since such a depletion of air-derived light noble... 

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... 

Rameback H, Berglund M, Kessel R, Wellum R (2002) Modeling isotope fractionation in thermal ionization mass spectrometry filaments having diffusion controlled emission. Int J Mass Spectrom 216 203-208 Roe JE, Anhar AD, Barling J (2003) Nonhiological fractionation of Fe isotopes evidence of an equilibrium isotope effect. Chem Geol 195 69-85... 

Layne GD (2003) Advantages of secondary ion mass spectrometry (SIMS) for stable isotope microanalysis of the trace light elements. EOS Trans, Am Geophys Union 84 F1635 Lundstrom CC, Chaussidon M, Kelemen P (2001) A Li isotope profile in a dunite to Iherzolite transed within the Trinity Ophiolite evidence for isotopic fractionation by diffusion. EOS Trans, Am Geophys Union 82 991... 

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,...

Richter FM, Davis AM, Ehel DS, Hashimoto A (2002) Elemental and isotopic fractionation of Type B calcium-, aluminum-rich inclusions Experiments, theoretical considerations, and constraints on their thermal evolution. Geochim Cosmochim Acta 66 521-540 Richter FM, Davis AM, DePaolo DJ, Watson EB (2003) Isotope fractionation by chemical diffusion between molten basalt and rhyolite. Geochim Cosmochim Acta 67 3905-3923 Rudnick RL, Fountain DM (1995) Nature and composition of the continental crust—a lower crustal perspective. Rev Geophys 33 267-309... 

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. 

Because this reaction must involve two steps, diffusion of selenate into the interlayer spaces of the green rust followed by electron transfer from Fe(ll) green rust, Johnson and Bullen (2003) interpreted this result using a two-step model similar to that discussed above. The diffusion step presumably has very little isotopic fractionation associated with it. Step 2 might be expected to involve a kinetic isotope effect similar to that observed in the HCl reduction experiments. As is discussed above, if the diffusion step is partially rate-limiting, the isotopic fractionation for the overall process should be less than the kinetic isotope effect occurring at the reduction step. This appears to be the case, as the ese(vi)-se(iv) value of 7.4%o is somewhat smaller than that observed for reduction by strong HCl (12%o). 

The meehanism of Mo removal in suboxie systems is unelear, and so the fundamental nature of this fraetionation requires further study. However, the effeet may be rmderstood in terms of a two layer diffusion-reaetion model in whieh a reaetion zone in the sediment (where Mo is ehemieally removed) is separated from seawater by a purely diffusive zone in which there is no chemical reaction (Braudes and Devol 1997). The presence of a diffusive zone is likely because Mo removal presumably occurs in suMdic porewaters that lie a finite distance L below the sediment-water interface (Wang and van Cappellen 1996 Zheng et al. 2000a). If HjS is present in the reactive zone such that Mo is removed below this depth, then Mo isotope fractionation in the diffusive zone may be driven by isotope effects in the reactive zone. 

Some aspects of this phenomenon are still controversial, because diffusion-induced isotopic fractionation effects may be erroneously ascribed to differential reaction kinetics (see section 11.6.2), and vice versa. 

Basically, whenever isotopic exchanges occur between different phases (i.e., heterogeneous equilibria), isotopic fractionations are more appropriately described in terms of differential reaction rates. Simple diffusion laws are nevertheless appropriate in discussions of compositional gradients within a single phase— induced, for instance, by vacancy migration mechanisms, such as those treated in section 4.10—or whenever the isotopic exchange process does not affect the extrinsic stability of the phase. 

Ordinary diffusion can cause significant isotope fractionations. In general, light isotopes are more mobile and hence diffusion can lead to a separation of light from heavy isotopes. For gases, the ratio of diffusion coefficients is equivalent to the inverse square root of their masses. Consider the isotopic molecules of carbon in CO2 with masses and C 0 0 having molecular weights of 44 and 45. 

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. 

From this simplified scheme, it follows that the diffusional process is reversible, whereas the enzymatic carbon fixation is irreversible. The two-step model of carbon fixation clearly suggests that isotope fractionation is dependent on the partial pressure of CO2, i.e. PCO2 of the system. With an unlimited amount of CO2 available to a plant, the enzymatic fractionation will determine the isotopic difference between the inorganic carbon source and the final bioproduct. Under these conditions, C fractionations may vary from -17 to —40%o (O Leary 1981). When the concentration of CO2 is the limiting factor, the diffusion of CO2 into the plant is the slow step in the reaction and carbon isotope fractionation of the plant decreases. 

Relatively large isotopic differences have been found in slow flowing groundwater, where Cl-isotope fractionation is attributed to a diffusion process (Kaufmann et al. 1984,1986 Desaulniers et al. 1986). Cl depletions detected in some pore waters have been attributed to processes such as ion filtration, alteration and dehydration... 

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... 

Parkinson IJ, Hammond SJ, James RH, Rogers NW (2007) High-temperature lithium isotope fractionation insights from lithium isotope diffusion in magmatic systems. Earth Planet Sci Lett 257 609-621... 

Richter R, Hoernes S (1988) The application of the increment method in comparison with experi-mentaUy derived and calculated O-isotope fractionations. Chemie derErde 48 1-18 Richter FM, Liang Y, Davis AM (1999) Isotope fractionation by diffusion in molten oxides. Geochim Cosmochim Acta 63 2853-2861... 

---