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need to cite (Ch 9 pg. 156 of textbook)

Distribution (Partition) Coefficient

A distribution constant $K_{D}$is used to define the relationship between the solid and liquid phase of a reaction. This equilibrium constant is often times referred to as $D$when dealing with trace elements, where

$K_{D}=C_{S}/C_{L}=X_{i}^{solid}/X_{i}^{liquid}$

$K_{D}=D$for trace elements

The equilibrium constant is an empirically determined value. These values depend on temperature, pressure, and composition of the mineral melt. $D$ values differ considerably between major elements and trace elements. By definition, incompatible trace elements have an equilibrium constant value of less than one because trace elements have higher concentrations in the melt than solids. Thus, this means that compatible elements have a value of $D>>1$.

Bulk Distribution Coefficient

The bulk distribution coefficient is used to calculate the elemental composition for any element $i$that makes up a mineral in a rock. The bulk distribution coefficient, ${\overline {D}}_{i}$, is defined as the distribution coefficient for the element $i$in mineral $A$.

${\overline {D}}_{i}=\Sigma W_{A}D_{i}^{A}$
where $i$ is the element of interest in the mineral, and $W_{A}$is the weight fraction of mineral $A$in the rock. $D_{i}^{A}$is the distribution coefficient