Bulk partition coefficient

Table 2. Experimentally determined mineral/melt partition coefficients (x 10 ) for U, Th, and Ba in clinopyroxene and garnet and calculated bulk partition coefficients (xlO ) for a garnet peridotite source.

Where /yand ps are the melt and solid densities, respectively, melt velocity. W is the solid upwelling velocity and A is the bulk partition coefficient. Note that if the partition coefficient A is 1, the effective velocity approaches the melt velocity, and also that the difference in effective velocity between elements with different Di decreases at larger porosities. In the following text, the subscripts 0, 1, and 2 are taken to refer to °Th, and Ra, respectively. 

At each step, a fraction of fluid f is added to the mantle wedge from the slab. The bulk partition coefficients used for fluid dehydration can be derived from published mineral/fluid partition coefficients (see Tables Al and A2). The composition of the residual slab is estimated as follows after At which is the time step between two melt extractions (similar equation for Th and Pa) ... 

Assumed source concentrations C0 for four arbitrary elements (column 2), mineral 1-liquid and mineral 2-liquid partition coefficients (columns 3 and 4), residual solid-liquid bulk partition coefficients calculated from mineral abundances listed in Table 9.2. Concentration units are arbitrary. 

The bulk partition coefficients are calculated from equation (9.2.3) as... 

In order to retrieve concentrations in the instantaneous solid, the instantaneous residual mineralogy and bulk partition coefficient must be calculated. 

Figure 9.9 AFC model for a bulk partition coefficient Dt = 2 and Ca /C0 = 5. Subscript a refers to the contaminant. Parameter r is defined in equation (9.4.12). The critical r value rc = 0.25, calculated from equation (9.4.18), separates the fractionation dominant field from the assimilation dominant field. The labels on the curves refer to the values of C,iq7Co. ...

This is the fundamental equation for batch melting. More complex batch melting models deal with the changes of the bulk partition coefficient D. Although this formula may also be expressed as... 

Fig. 1.3. Variation of Source-normalized concentrations with the degree of artial melting for trace elements with different bulk partition coefficients.

When K is a constant, the bulk partition coefficient becomes... 

Table 1.2. Summary of variations of mineral proportions and bulk partition coefficients during modal, eutectic and incongruent melting.

Melting modes Mineral proportions Bulk partition coefficients... 

Assuming constant bulk partition coefficient, from Eq. (1.7) for batch melting and Eq. (2.7) for fractional melting, we can make Figure 2.2 to show the behavior of a highly incompatible element with = 0.02... 

From section 1.4.2, the variation of the bulk partition coefficient is... 

Example. Calculate the concentration of an incompatible element normalized by the initial source concentration (C/Cq) with bulk partition coefficient D = 0.02 in the extracted dynamic melt and residual melt. Assuming 0 = 0.01. 

The concentration in the melt is related to the concentration in the solid by a bulk partition coefficient... 

We now need to find the variation of the bulk partition coefficient D as a function of the degree of melting. Mass balance of mineral i gives... 

This is the well-known Rayleigh fractionation law it is applicable to geological systems only when the bulk partition coefficients remain constant throughout fractional crystallization. 

If the bulk partition coefficient linearly varies with the percent of the remaining magma ( F) ... 

When the crystallized crystals always stay with the magma and reach chemical equilibrium, the compositions of the crystals are related to the composition of the melt by the bulk partition coefficient,... 

Problem. Demonstrate that low-degree/high-degree concentration ratio during dynamic melting is also inversely related to the bulk partition coefficients. 

For dynamic partial melting inversion, the highly incompatible element has bulk partition coefficient Dg about 0.001, and the ideal for the less-so-highly incompatible element would be between 0.01 and 0.1 so that Qb is different enough from Qa and from 1.0. Thus, La is suitable for Dg, and Nd, Sm, Eu, Gd, and Tb are suitable for Db- As can be seen from Table 7.2, the low-degree/high-degree Q values decrease... 

---