9.7 Goldschmidt's Rules

V.M. Goldschmidt was one of the first geochemists to measure and study trace element concentrations in minerals. In his 1937 paper, he proposed some simple criteria as a guide to which elements might be preferentially concentrated in a particular mineral. They are:
  1. Two ions with the same radius and the same charge are equally likely to be found in a given mineral. For example, Sr (r=0.118 nm (VI), +2) is likely to be found in the same minerals as Ca (r=0.100 nm (VI), +2). DSr for plagioclase in basalt is 2.7. DCa for plagioclase in basalt is 1.1.
  2. If two ions have a similar radius and the same charge, the smaller ion will be more abundant in a mineral grown from the same magma. For example, Sr (r=0.118 nm (VI), +2) is more likely to be found in plagioclase than is Ba (r=0.135 nm (VI), +2). DSr for plagioclase in basalt is 2.7. DBa for plagioclase in basalt is 0.33.
  3. If two ions have a similar radius but different charges, the ion with the higher charge will be more abundant in a mineral grown from the same magma. For example, Ti (r=0.061 nm (VI), +4) is more likely to be found in plagioclase than is Cr (r=0.062 nm (VI), +3). DTi for plagioclase in basalt is 0.04. DCr for plagioclase in basalt is 0.02. Many counter examples can be found for this rule.
The scientific literature is rich with papers about trace element distribution coefficients, their measurement, calculation, and their applications in igneous petrology. There is a good online database of distribution coefficients, the Geochemical Earth Reference Model (GERM) Partition Coefficient (Kd) Database. A theoretical background can be found in W.M. White's writings on trace elements and some history of the field in J.H. Jones Geochemical Perspectives issue.