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distribution coefficient - This is the ratio between the concentration of an element in one phase divided by the concentration in another phase. It is also known as a partition coefficient. For igneous systems, the partition coefficient of interest is the solid/liquid partition coefficient (D, sometimes also abbreviated KD) given by:
D = (conc. in solid)/(conc. in melt)
Partition coefficients can be determined by experiment and they allow magmatic processes to be modelled. They represent equilibrium partitioning, but they apply to various types of magmatic processes, such as equilibrium crystallization, fractional crystallization, equilibrium melting, etc. They can be a function of melt composition, mineral composition, temperature, pressure, fO2, etc. For siderophile elements in iron meteorites, the relevant partition coefficients are those between solid metal and liquid metal.
incompatible element - This is an element that tends to prefer a liquid to a solid. It is defined by D < 1. According to the author, Ni has a solid metal/liquid metal partition coefficient (or D-value) of ~0.85, indicating that it is an incompatible element. An incompatible element such as Ni would tend to become progressively enriched in metallic liquid as crystallization proceeded, or it would be enriched in the first-formed metallic partial melts.
compatible element - This is an element that
tends to prefer a solid to a liquid. It is defined by D > 1.
During crystallization, elements with D > 1 are removed from residual liquids.
During melting, compatible elements tend to be depleted in partial melts
and concentrated in residual solids. Ir has a solid metal/liquid
metal D-value ~ 4.