Distribution (Partition) coefficient

Abundance of elements in the Earth's crust. The x-axis displays the atomic number, plotted against the abundance measured per million silicon atoms.

In a mineral, nearly all elements distribute unevenly between the solid and liquid phase. This phenomenon known as chemical fractionation and can be described by an equilibrium constant, ${\displaystyle K}$ which sets a fixed distribution of an element between any two phases at equilibrium.^[1] A distribution constant ${\displaystyle K_{D}}$ is used to define the relationship between the solid and liquid phase of a reaction. This value is essentially a ratio of the concentration of an element between two phases, typically between the solid and liquid phase in this context. This constant is often referred to as ${\displaystyle D}$ when dealing with trace elements, where

${\displaystyle K_{D}={\frac {C_{S}}{C_{L}}}={\frac {X_{i}^{solid}}{X_{i}^{liquid}}}}$

${\displaystyle K_{D}=D}$ for trace elements

The equilibrium constant is an empirically determined value. These values depend on temperature, pressure, and composition of the mineral melt. ${\displaystyle D}$ 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.^[1] This means that compatible elements have a value of ${\displaystyle D>1}$. Thus, incompatible elements are concentrated in the melt, whereas compatible elements tend to be concentrated in the solid. Compatible elements with ${\displaystyle D\gg 1}$ are strongly fractionated and have very low concentrations in the liquid phase.

Bulk distribution coefficient

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

${\displaystyle {\overline {D}}_{i}=\Sigma W_{A}D_{i}^{A}}$

where ${\displaystyle i}$ is the element of interest in the mineral, and ${\displaystyle W_{A}}$ is the weight fraction of mineral ${\displaystyle A}$ in the rock. ${\displaystyle D_{i}^{A}}$ is the distribution coefficient for the element in mineral ${\displaystyle A}$.^[1] This constant can be used to describe how individual elements in a mineral is concentrated in two different phases. During chemical fractionation, certain elements may become more or less concentrated, which can allow geochemists to quantify the different stages of magma differentiation.^[4] Ultimately, these measurements can be used to provide further understanding of elemental behavior in different geologic settings.

Understanding the Earth's interior

Previous studies have used compatibility of trace elements to see the effect it would have on the melt structure of the peridotite solidus.^[7] In such studies, partition coefficients of specific elements were examined and the magnitude of these values gave researchers some indication about the degree of polymerization of the melt. A study conducted in East China in 1998 looked at the chemical composition of various elements found in the crust in China. One of the parameters used to characterize and describe the crustal structure in this region was compatibility of various element pairs.^[8] Essentially, studies like this showed how compatibility of certain elements can change and be affected by the chemical compositions and conditions of Earth's interior.

Oceanic volcanism is another topic that commonly incorporates the use of compatibility. Since the 1960s, the structure of Earth's mantle started being studied by geochemists. The oceanic crust, which is rich in basalts from volcanic activity, show distinct components that provides information about the evolution of the Earth's interior over the geologic timescale. Incompatible trace elements become depleted when mantle melts and become enriched in oceanic or continental crust through volcanic activity. Other times, volcanism can produce enriched mantle melt onto the crust. These phenomena can be quantified by looking at radioactive decay records of isotopes in these basalts, which is a valuable tool for mantle geochemists.^[2] More specifically, the geochemistry of serpentinites along the ocean floor, specifically subduction zones, can be examined using compatibility of specific trace elements.^[9] The compatibility of lead (Pb) into zircons under different environments can also be an indication of zircons in rocks. When observing levels of non-radiogenic lead in zircons, this can be a useful tool for radiometric dating of zircons.^[10]