- A
**distribution coefficient**,**D**, also called a_{i}**partition coefficient**, for a trace element**i**is the ratio of the concentration of the element**i**in a mineral (S) and the concentration of the element**i**in a magma (L) at equilibrium as given in equation (1). - The value of
**D**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 H_{i}_{2}O. - If
**D**, the trace element (i) is said to be_{i}≫ 1**compatible**with the mineral. - If
**D**, the trace element (i) is said to be_{i}≪ 1**incompatible**with the mineral. - For compatible elements, removal of even a relatively small portion of a magma by fractional crystallization of the mineral, can have a large effect on the concentration of the incompatible element in the magma.
- The effects on trace element concentrations in magmas due to fractional crystallization can be modeled by the Raleigh fractiontion equation, equation (2).
- For any element with
**D**much different than one, removal of even a small portion of a magma from a rock by partial melting, can have a large effect on the weight percent of the element in the magma relative to its weight percent in the rock._{i} - The effects on trace element concentrations in magmas due to partial melting can be modeled by the Shaw batch melting equation, equation (4).
**R**are**E**arth**E**lements, the lanthanide elements (atomic numbers 57-71), are trace elements of particular interest to petrologists because their distribution coefficients can be different by orders of magnitude in different minerals.- Because REE occur in concentrations that differ by orders of magnitude from one another, REE data are typically normalized by the REE values for a standard rock, such as a C1 carbonaceous chrondite (meteorite).
- Normalized REE patterns are used to characterize igneous rocks and to constrain the mineralogy of source rocks for magmas.
- A series of simple criteria proposed by Victor Goldschmidt in 1937 (Goldschmidt's Rules) serve as a guide to which elements might be preferentially concentrated in a particular mineral.

9.8 Summary