Distribution coefficients trace elements

Model Studies. In model studies of adsorption, one deals with simple, well-defined systems, where usually a single well-characterized solid phase is used and the composition of the ionic medium is known, so that reactions competing with the adsorption may be predicted. It is not a trivial problem to compare the results from such model studies with those from field studies, or to use model results for the interpretation of field data. In field studies, a complex mixture of solid phases and dissolved components, whose composition is only poorly known, has to be considered competitive reactions of major ions and trace metal ions for adsorption may take place, and the speciation of the trace metal ions is often poorly understood. In order to relate field studies to model studies, distribution coefficients of elements between the dissolved and solid phases are useful. These distribution coefficients are of the following form ... 

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... 

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. 

The distribution of trace elements between phases may be described by a distribution coefficient or partition coefficient (Mclntire, 1963). The Nemst distribution coefficient is used extensively in trace element geochemistry and describes the equilibrium distribution of a trace element between a mineral and a melt. The Nemst distribution coefficient is defined by ... 

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.

In qualitative terms, microscopic interactions are caused by differences in crystal chemical properties of trace element and carrier, such as ionic radius, formal charge, or polarizability. This type of reasoning led Onuma et al. (1968) to construct semilogarithmic plots of conventional mass distribution coefficients K of various trace elements in mineral/melt pairs against the ionic radius of the trace element in the appropriate coordination state with the ligands. An example of such diagrams is shown in figure 10.6. 

The formulation of this coefficient derives from the consideration that solid/liquid trace element distribution can be ascribed to the existence of simple exchange equilibria of the type... 

In this case, trace element and carrier occupy the same structural position both in the solid phase and in the melt and are subject to the same compositional effects in both phases (i.e., extension of the cation matrix in the melt and amount of anorthite component in the solid). Figure 10.9A shows the effect of normalization the conventional partition coefficient of Sr between plagioclase and liquid varies by about one order of magnitude under equal P-T conditions, with increasing anorthite component in solid solution, whereas normalized distribution coefficient D is virtually unaffected. Figure 10.9B shows the same effect for the Ba-Ca couple. 

The fractionation factor a represents the relative distribution of heavy and light isotopes in the two phases at equihbrium (somewhat similar to the normalized distribution coefficient adopted in trace element geochemistry cf section 10.8) ... 

Zou, H.B., 2000. Modeling of trace element fractionation during non-modal dynamic melting with linear variations in mineral/melt distribution coefficients. Geochim. Cosmochim. Acta, 64 1095-1102. 

Partition (Distribution) Coefficients In describing the partitioning of a trace element among coexisting phases, we frequently use a partition (distribution) coefficient for a given element, defined as a concentration ratio C2/Cj. Here C is concentration, and the subscripts identify the phases often the normalizing phase is some convenient reservoir, such as a silicate melt, with which several other phases may equilibrate. For noble gases, it is often most convenient to normalize to a gas phase. If the concentrations are expressed in the same units, the distribution coefficient is dimensionless. It is conventional to cite noble gas concentrations in condensed phases in cm3 STP/g, however, and to describe the gas phase by partial... 

Ionic radius. The wide variation of metal-oxygen distances within individual coordination sites and between different sites in crystal structures of silicate minerals warns against too literal use of the radius of a cation, derived from interatomic distances in simple structures. Relationships between cation radius and phenocryst/glass distribution coefficients for trace elements are often anomalous for transition metal ions (Cr3+, V3+, Ni2+), which may be attributed to the influence of crystal field stabilization energies. 

Banno, S. Matsui, Y. (1973) On the formation of partition coefficients for trace element distribution between minerals and magma. Chem. Geol., 11,1-15. 

Data Representation. Transformations can be applied to the data so that they will more closely follow the normal distribution that is required for certain procedures or for removing (or lessening) unwanted influences. Certainly for data analysis in which major, minor, and trace elemental concentrations are used, some form of scaling is necessary to keep the variables with larger concentrations from having excessive weight in the calculation of many coefficients of similarity. 

A common application of this equation to trace element modeling is to examine the variations in trace element abundances and ratios for elements with different bulk distribution coefficients (Figure 7). In this plot, F is the fraction of melt for equilibrium crystallization, F proceeds from... 

Figure 7 Illustration of the effects of equilibrium (batch) crystallization or melting on trace element abundances, (a) Variation in liquid concentration (Cl) (normalized to unit source concentration Cq= 1) as a function of melt fraction (F) for six elements with different bulk distribution coefficients (D). (b) Change in the ratios of incompatible elements with different Ds as a function of F. Each curve is for a different pair of elements that have the Z)s indicated. Note that when D < 0.1, incompatible element ratios can be changed only at very low extents of melting (or high extents of crystallization) (Langmuir et al., 1992) (reproduced by permission of American Geophysical...

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