9.8 Summary

• A distribution coefficient, Di, also called a 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 iin a magma (L) at equilibrium as given in equation (1).
• 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.
• If Di ≫ 1, the trace element (i) is said to be compatible with the mineral.
• If Di ≪ 1, the trace element (i) is said to be 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 Di 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.
• The effects on trace element concentrations in magmas due to partial melting can be modeled by the Shaw batch melting equation, equation (4).
• Rare Earth Elements, 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.

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