When a mineral and a magma are at equilibrium, the ratio of the weight percent concentration of a trace element (i) in the solid (CiS) relative to its weight percent concentration in the liquid (CiL) is observed to be nearly independent of the value of CiL. In other words, the ratio is constant. This ratio is called a distribution coefficient Di defined as:
(1) Di = CiS /CiL
The distribution coefficient, Di, has also been called a partition coefficient in the geologic literature, so read carefully and write clearly when using distribution coefficients. Follow the nomenclature recommendations of Beattie and others (1993).
The value of Di for a particular trace element depends principally on the the mineral (e.g. olivine) and on the liquid composition (e.g. basalt), and to a lesser extent on other variables such as temperature, pressure, and the activity of H2O. Because the concentrations of trace elements are so small, Di is analogus to a Henry's Law constant and does not vary greatly if the physical conditions and magma composition do not vary greatly.
The distribution coefficients Di can be very different for different minerals. For example, the distribution coefficients for yttrium (DY) for various minerals in equilibrium with basalt are:
| Olivine | Opx | Cpx | Plag | Spinel | Garnet | Amph |
|---|---|---|---|---|---|---|
| 0.005 | 0.01 | 0.4 | 0.008 | 0.05 | 3.1 | 0.4 |
(data from White, 2013, Table 7.5). During melting or crystallization some trace elements are likely to be more concentrated in a particular mineral (Di > 1), whereas other trace elements are likely to be more concentrated in the magma (Di < 1). If Di ≫ 1, the trace element (i) is said to be compatible with the mineral (e.g. Y & Garnet 👍). If Di ≪ 1, the trace element (i) is said to be incompatible with the mineral (e.g. Y & Olivine 👎 ).
