Trace elements kinetic fractionation

Figure 9.16 Kinetic fractionation during crystal growth. Steady-state distribution of melt concentrations in the vicinity of a solid growing at the rate v for trace elements with different solid-liquid fractionation coefficients [equation (9.6.5), Tiller et al. (1953)]. The stippled area indicates the steady-state chemical boundary-layer with thickness <5 = <5>/v.

For kinetic disequilibrium partitioning of trace elements, equation (9.6.6) after Burton et al. (1953) is commonly presented as an alternative to equation (9.6.5) due to Tiller et al. (1953) (e.g., Magaritz and Hofmann, 1978 Lasaga, 1981 Walker and Agee, 1989 Shimizu, 1981). However, the relative values of viscosity and chemical diffusivity in common liquids and silicate melts make the momentum boundary-layer (i.e., the liquid film which sticks to the solid) orders of magnitude thicker than the chemical boundary layer. It is therefore quite unlikely that, except for rare cases of transient state, liquid from outside the momentum boundary-layer may encroach on the chemical boundary-layer, i.e., <5 may actually be taken as infinite. As a simple description of steady-state disequilibrium fractionation, the model of Tiller et al. (1953) has a much better physical rationale. A more elaborate discussion of these processes may be found in Tiller (1991a, b). 

Bermond, A., and Varrault, G. (2004). Application of a kinetic fractionation of trace elements (Cd, Cu Pb) in unpolluted soil samples. Environ. Technol. 25, 293-300. 

Ghestem, J. P., and Bermond, A. (1999). Feasibility study of a fractionation of trace elements in soil samples based on kinetics. Environ. Technol. 20, 1119-1128. 

Among the benefits from using isotopic analysis to study trace element movement across the geosphere and biosphere is the realization that Hg shows mass-independent fractionation that enhances our ability to define the sources of this toxic element [13]. Isotopes of Ca and Mg in biogenic carbonates indicate that there are both equilibrium mineralogical controls and kinetic controls on how these elements are incorporated by organisms from the geosphere and... 

When stable isotopes are used, for example, as tracers for in vivo metabolic studies, typically the tracer flux is being measured and inferences are made about the flux of the material being traced ( tracee ). When there is no isotope fractionation, the flux of the heavy tracer is equal to the flux of the lighter major isotope and hence the tracee flux. However, when there is isotope fractionation the fluxes of the heavy tracer and tracee are not equal and thus the flux derived from the kinetic analysis of the tracer is not equal to that of the tracee. For example, is fractionated between water and carbon dioxide (a = 1.041 at 25°C) thus the rate of removal of by CO2 is 4.1% greater than the rate of removal. Because comprises 99.8% of the oxygen pool, the rate of CO2 production is essentially equal to the rate of removal by CO2, which will be less by 4.1% than that measured from 0. Without taking this correction into account, the calculated tracee flux will be in error. On the other hand, the isotope effect becomes negligible in the distribution of the isotopes of heavier elements therefore, no corrections are necessary in the tracer experiments. 

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