Nuclide coefficients

Both dynamic melting and equilibrium transport melting require that the porosity when two nuclides are fractionated from one another is similar to the size of the larger of the partition coefficients for the two nuclides. Given the low values of the experimental determinations of Du and Dxh, the porosities required to explain the observational data in these models are generally less than 0.5% and often times closer to 0.1%. Such low porosity estimates have been criticized based on physical grounds given the low estimated mantle permeability derived from the extent of melt connection observed in experiments (Paul 2001). 

Figure 24. Drawing of the continuous leaching model used by Vigier et al. (2001) to estimate the residence time of particles in the soils of the Mackenzie Basin, and the related equations. This model assumes that particles are continuously leached in the soil before leaving to the river. Dissolved load of the river integrates the present leaching of the whole soil profile. 238, 234, 230 and 226 are the leaching coefficients of h and Tla nuclides, respectively, and x is the duration of the chentical...

These equations converge towards those of the fractional melting model for tp Dh and, contrary to McKenzie (1985) equation (29), CUq tends to C0 when porosity partition coefficient are of the same order of magnitude, large variability is achieved in both the solid and the residue, a point which will be returned below. Considerable attention has been recently focussed on this model which may explain the fractionation of some strongly incompatible nuclides in the U decay series (McKenzie, 1985 Williams and Gill, 1989 Beattie, 1993). 

Figure 11,8 Composite decay curves for (A) mixtures of independently decaying species, (B) transient equilibrium, (C) secular equilibrium, and (D) nonequilibrium, a composite decay curve b decay curve of longer-lived component (A) and parent radio nuclide (B, C, D) c decay curve of short-lived radionuclide (A) and daughter radionuclide (B, C, D) d daughter radioativity in a pure parent fraction (B, C, D) e total daughter radioactivity in a parent-plus-daughter fraction (B). In all cases, the detection coefficients of the various species are assumed to be identical. From Nuclear and Radiochemistry, G. Friedlander and J. W. Kennedy, Copyright 1956 by John Wiley and Sons. Reprinted by permission of John Wiley and Sons Ltd.

Diffusion coefficient (often interdiffusivity or chemical diffusivity) daughter nuclide... 

The distribution coefficients of the parent and daughter nuclides are important in U-series disequilibria. If the parent has a higher distribution coefficient than the daughter, its extraction from the matrix is retarded and the daughter/parent activity ratio in the melt can be greater than 1. Experiments have shown that Dy > Dj for garnet peridotites but Du spinel peridotites at low pressures. Due to experimental difficulties, Dro and Dpa are not directly known but are inferred to be very small. Therefore, it is reasonable to assume Dj, >Di and Du > Dp for both garnet peridotites and spinel peridotites. 

Therefore, the preliminary investigation described herein examined several aspects of the behavior of the equilibrium distribution coefficients for the sorption of rubidium, cesium, strontium, barium, silver, cadmium, cerium, promethium, europium, and gadolinium from aqueous sodium chloride solutions. These solutions initially contained one and only one of the nuclides of interest. For the nuclides selected, values of Kp were then... 

Therefore, based on available literature, the following sorption results were expected (l) as a result of the smectite minerals, the sorption capacity of the red clay would be primarily due to ion exchange associated with the smectites and would be on the order of 0.8 to I.5 mi Hi equivalents per gram (2) also as a result of the smectite minerals, the distribution coefficients for nuclides such as cesium, strontium, barium, and cerium would be between 10 and 100 ml/gm for solution-phase concentrations on the order of 10"3 mg-atom/ml (3) as a result of the hydrous oxides, the distribution coefficients for nuclides such as strontium, barium, and some transition metals would be on the order of 10 ml/gm or greater for solution-phase concentrations on the order of 10 7 mg-atom/ml and less (U) also as a result of the hydrous oxides, the solution-phase pH would strongly influence the distribution coefficients for most nuclides except the alkali metals (5) as a result of both smectites and hydrous oxides being present, the sorption equilibrium data would probably reflect the influence of multiple sorption mechanisms. As discussed below, the experimental results were indeed similar to those which were expected. 

For the nuclides studied (rubidium, cesium, strontium, bariun silver, cadmium, cerium, promethium, europium, and gadolinium) the distribution coefficients generally vary from about 10 ml/gm at solution-phase concentrations on the order of 10 mg-atom/ml to 10 and greater at concentrations on the order of 10 and less. These results are encouraging with regard to the sediment being able to provide a barrier to migration of nuclides away from a waste form and also appear to be reasonably consistent with related data for similar oceanic sediments and related clay minerals found within the continental United States. 

For each nuclide studied, the sorption distribution coefficients appeared to result from a minimum of two separate mechanisms. In all cases, one mechanism appears to be an ion-exchange phenomena associated with the silicate phases and appears to have a relatively much larger sorption capacity than the other mechanism. In the case of cesium (and probably rubidium) the second mechanism appears to also be related to the silicate phases and may or may not be an ion-exchange phenomena. However, for the other elements studied, the second mechanism appears to be related to the hydrous iron and manganese oxides and again may or may not be an ion-exchange process. 

The results of this preliminary investigation (particularly the general behavior of the distribution coefficients and the Identification of multiple sorption mechanisms) will provide a basis from which plans can be developed for studying the sorption and complex chemistry of the actinides. The results will also provide a basis from which plans can be developed for studying sorption equilibria involving several competing nuclides. 

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