Partitioning ionic radius

Wood and Blundy (2001) developed an electrostatic model to describe this process. In essence this is a continuum approach, analogous to the lattice strain model, wherein the crystal lattice is viewed as an isotropic dielectric medium. For a series of ions with the optimum ionic radius at site M, (A(m))> partitioning is then controlled by the charge on the substituent (Z ) relative to the optimum charge at the site of interest, (Fig. 10) ... 

The approach taken here is to use the lattice strain model to derive the partition coefficient of a U-series element (such as Ra) from the partition coefficient of its proxy (such as Ba) under the appropriate conditions. Clearly the proxy needs to be an element that forms ions of the same charge and similar ionic radius to the U-series element of interest, so that the pair are not significantly fractionated from each other by changes in phase composition, pressure or temperature. Also the partitioning behavior of the proxy must be reasonably well constrained under the conditions of interest. Having established a suitable partition coefficient for the proxy, the partition coefficient for the U-series element can then be obtained via rearrangement of Equation (2) (Blundy and Wood 1994) ... 

Actinium is similarly easy to find a proxy for. It forms large trivalent cations with an ionic radius of 1.12 A in Vl-fold coordination. This is somewhat larger than La (1.032 A), which we will adopt as a proxy. The partitioning behavior of the lanthanides (denoted collectively Ln) is sufficiently well understood to make this a prudent choice. In some minerals, however, the larger size of Ac, may place it onto a larger lattice site than the lanthanides. This possibility should be considered for minerals with very large cation sites, such as amphiboles and micas. 

Bismuth forms both 3+ and 5+ cations, although the former are by far the more common in nature. The ionic radius of Bi is even closer to that of La, than Ac, so again La is taken as the proxy. As noted above, Bi has the same electronic configuration as Pb, with a lone pair. It is unlikely therefore that the Shannon (1976) radius for Bi is universally applicable. Unfortunately, there is too little known about the magmatic geochemistry of Bi, to use its partitioning behavior to validate the proxy relationship, or propose a revised effective radius for Bi. The values of DWD u derived here should be viewed in the light of this uncertainty. 

Partition coefficients for Po can be derived from those for Th using Equation (8) and the ionic radii in Table 2. We have not modified the ionic radius for Po" from the value... 

Perhaps the biggest challenge in estimating U-series partition coefficients is the case of protactinium partitioning into garnet. The difficulty arises because the ionic radius of... 

Schmidt et al. (1999) report Dpb of 0.034-0.045 for two experiments with leucite lamproite melt composition for a basanitic melt composition La Tourrette et al. (1995) give Z)pb = 0.10. In all three cases Z)pb consistently falls below, by a factor of 3, the parabola defined by the other 2+ cations, as previously noted for several other minerals. Here the implication is that the effective Xll-fold ionic radius of Pb is slightly smaller than the value given in Table 2, i.e., closer in size to rsr. Upb/Usr is between 0.6 and 1.2, in these experiments. In the PIXE partition study of Ewart and Griffin (1994) for acid volcanic rocks, Z)pb ranges from 0.21 to 2.1 (3 samples), with Upb/Usr of 0.29 to 2.9. Until there are further experimental determinations of Upb, or better constraints on its ionic radius, we suggest that Z)pb = E>sr-... 

One of the striking features about as constrained above, is that it is almost identical to the ionic radius of Pa in Vlll-fold coordination, suggesting that Pa will readily partition into zircon. However, until there are experimental data with which to... 

Figure 24. Lattice strain model applied to zircon-melt partition coefficients from Hinton et al. (written comm.) for a zircon phenocryst in peralkaline rhyolite SMN59 from Kenya. Ionic radii are for Vlll-fold coordination (Shannon 1976). The curves are fits to Equation (1) at an estimated eraption temperature of 700°C (Scaillet and Macdonald 2001). Note the excellent fit of the trivalent lanAanides, with the exception of Ce, whose elevated partition coefficient is due to the presence of both Ce and Ce" in the melt, with the latter having a much higher partition coefficient into zircon. The 4+ parabola cradely fits the data from Dj, and Dy, through Dzi to Dih, but does not reproduce the observed DuIDjh ratio. We speculate that this is due to melt compositional effects on Dzt and (Linnen and Keppler 2002), and possibly other 4+ cations, in very silicic melts. Because of its Vlll-fold ionic radius of 0.91 A (vertical line), Dpa is likely to be at least as high as Dwh, and probably considerably higher.

For uptake proceeding by isomorphous substitution, the partition coefficient D depends on thermodynamic parameters such as ionic radius of the impurity ions and the phases of the calcium sulfate as well as on kinetics. 

Figure 5.17. Relationship between the partition coefficient for inner aragonite shell and coexisting extrapallial fluid of the marine mollusc, Pinctada furcata, and ionic radius of the elements. (After Speer, 1983.)...

The ionic radius criterion for interpreting geochemical distributions of trace elements was given a boost in the early 1970 s when correlations were shown to exist between ionic radii and partition coefficients of some trace elements (Onuma et al., 1968 Higuchi and Nagasawa, 1969 Jensen, 1973). The influence of cation radius and charge on trace element distribution patterns was demonstrated by measurements of the distribution coefficient, >, defined by... 

The various rules that were enunciated to explain element distributions and partitioning in crystal/melt systems have had a profound influence in crystal chemistry and on interpretations of trace element geochemistry. They have served as useful guiding principles for predicting mineral occurrences and explaining the locations of trace elements in crystal structures. Thus, given the ionic radius and valence of a trace element, assessments can be made of the crystal structures most likely to accommodate that element. Well-known examples include... 

Although the rare-earth elements (REEs) have similar geochemical behavior, since they are all large-ion lithophile elements and most of them partition among melts and mineral phases as a smooth function of ionic radius (with the exception of europium, which, commonly being... 

Goldschmidt (1937, 1954) first recognized that the distribution of trace elements in minerals is strongly controlled by ionic radius and charge. The partition coefficient of a given trace element between solid and melt can be quantitatively described by the elastic strain this element causes by its presence in the crystal lattice. When this strain is large because of the magnimde of the misfit, the partition coefficient becomes small, and the element is partitioned into the liquid. This subject is treated in detail in Chapter 2.09. 

Trace Element Partitioning under Crustal and Uppermost Mantle Conditions The Influences of Ionic Radius, Cation Charge, Pressure, and Temperature... 

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