Diffusion stable isotopes

A number of special processes have been developed for difficult separations, such as the separation of the stable isotopes of uranium and those of other elements (see Nuclear reactors Uraniumand uranium compounds). Two of these processes, gaseous diffusion and gas centrifugation, are used by several nations on a multibillion doUar scale to separate partially the uranium isotopes and to produce a much more valuable fuel for nuclear power reactors. Because separation in these special processes depends upon the different rates of diffusion of the components, the processes are often referred to collectively as diffusion separation methods. There is also a thermal diffusion process used on a modest scale for the separation of heflum-group gases (qv) and on a laboratory scale for the separation of various other materials. Thermal diffusion is not discussed herein. 

Irreversible processes are mainly appHed for the separation of heavy stable isotopes, where the separation factors of the more reversible methods, eg, distillation, absorption, or chemical exchange, are so low that the diffusion separation methods become economically more attractive. Although appHcation of these processes is presented in terms of isotope separation, the results are equally vaUd for the description of separation processes for any ideal mixture of very similar constituents such as close-cut petroleum fractions, members of a homologous series of organic compounds, isomeric chemical compounds, or biological materials. 

Eiler JM, Baumgartner LP, Valley JW (1992) Intercrystalline stable isotope diffusion a fast grain boundary model. Contrib Mineral Petrol 112 543-557... 

Graham CM (1981) Experimental hydrogen isotope studies. Diffusion of hydrogen in hydrous minerals, and stable isotope exchange in metamorphic rocks. Contrib Mineral Petrol 76 216-228 Hoefs J (2004) Stable isotope geochemistry. S" Edition. Springer, Berlin... 

Hervig RL, Moore G (2003) Fractionation of boron (and lithium) between hydrous fluid and silicate melt diffusion, contamination, and orphaned experiments. EOS Trans, Am Geophys Union 84 F163 Hoefs J (1997) Stable Isotope Geochemistry, 4 ed. Springer-Verlag, Berlin... 

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... 

Because the above equation is identical to the diffusion equation of a stable component, it can be solved the same way. After solving for w, then C can be found as we . For diffusion of two isotopes, one stable and one radioactive, because they have the same diffusivity, the concentration profile for the radioactive nuclide is simply the concentration profile of the stable isotope multiplied by either (i) Toe , where Fq is the initial isotopic ratio, or (ii) F, where F is the isotopic ratio at the time of measurement of the profiles. 

Chemical processes such as evaporation and condensation, precipitation of a mineral from a fluid phase, or diffusion can cause small changes in the relative abundances of the isotopes of the elements involved. These small isotopic shifts, which are typically a few parts in a thousand, are the basis for stable isotope geochemistry and cosmochemistry. 

UF6 is a solid (mp 64 °C) but has a high vapor pressure (15.3 kPa at 25 °C). Since 19F is the only stable isotope of fluorine, the only molecular species by mass in UF6 are 235UF6 and 238UF6. Repeated diffusion of UF6 (g) through porous plugs (or centrifugation of the vapor) concentrates 235 UF6 relative to 238 UF6, since the speed of diffusion varies inversely as the square root of the molecular mass. This enrichment is not needed for... 

Radioactive or stable isotopes of noble gases are also used to determine vertical turbulent diffusion in natural water bodies. For instance, the decay of tritium (3H)— either produced by cosmic rays in the atmosphere or introduced into the hydrosphere by anthropogenic sources—causes the natural stable isotope ratio of helium, 3He/ 4He, to increase. Only if water contacts the atmosphere can the helium ratio be set back to its atmospheric equilibrium value. Thus the combined measurement of the 3H-concentration and the 3He/4He ratio yields information on the so-called water age, that is, the time since the analyzed water was last exposed to the atmosphere (Aeschbach-Hertig et al., 1996). The vertical distribution of water age in lakes and oceans allows us to quantify vertical mixing. 

During self-diffusion in a pure material, whether a gas, liquid, or solid, the components diffuse in a chemically homogeneous medium. The diffusion can be measured using radioactive tracer isotopes or marker atoms that have chemistry identical to that of their stable isotope. The tracer concentration is measured and the tracer diffusivity (self-diffusivity) is inferred from the evolution of the concentration profile. 

Leaf gas exchange rates are highly dependent on local climatic factors influencing C02 diffusion and evaporation rates, especially temperature lapse rates. The dependency of gas-exchange parameters on local climatic factors and leaf anatomy may account for the wide variability in leaf stomatal responses and stable isotope composition over elevation transects found in different species and different regions. 

These questions can be answered by using diffusion markers. Atoms of one element (or both) can be marked by a radioactive or stable isotope. Radioactive Si (half... 

This phenomenon forms the basis for the formulations of Urey (1947) and Bigeleisen and Mayer (1947) for the temperature dependence of isotopic exchange between two molecules. With the nearly simultaneous development of the isotope-ratio mass spectrometer by Nier et al. (1947), the potential for application of stable isotopes was created. Other isotopic fractionation processes are observed in kinetics, diffusion, evaporation-condensation, crystallization, and biology (e.g., photosynthesis, respiration, nitrogen fixation, sulfate reduction, and transpiration). The concomitant isotopic fractionations can also be used to provide details of the relevant process. 

Natural waters formed of —99.7% of H2 0 are also constituted of other stable isotopic molecules, mainly H2 0 (—2%o), H2 0 ( 0.5%o), and HD 0 (—0.3%c), where H and D (deuterium) correspond to and H, respectively. Owing to slight differences in physical properties of these molecules, essentially their saturation vapor pressure, and their molecular diffusivity in air, fractionation processes occur at each phase change of the water except sublimation and melting of compact ice. As a result, the distribution of these water isotopes varies both spatially and temporally in the atmosphere, in the... 

The same physical principles are utilized to develop isotopic models which better account for the transport of air masses at a regional scale, such as done by Fisher (1992) using a regional stable isotope model coupled to a zonally averaged global model. Other authors such as Eriksson (1965) and more recently Hendricks et al. (2000) considered the transport of water both by advective and eddy diffusive processes, the latter inducing less fractionation. 

Highly saline water of distinctive isotopic composition is often found in environments of such depth and low permeability that flow rates must be extremely low or zero. These waters are often characterized by Ca " -Cl compositions and stable isotope composition above the meteoric waterline (see Chapter 5.17). They apparently result from water-rock equihbration over very long periods of time. Geochemically, they have little influence on waters in active circulation systems, but mobile isotopes of the noble gases diffusing upward from this environment can be a powerful tool for understanding the flow systems into which they move. The noble-gas isotopes can also provide clues to the histories of these nearly static waters. 

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