The good use of compatible and incompatible elements

Taking the differential form of the fractional crystallization equation leads to 

For small extents of crystallization, the maximum change, and thereby the most valuable information on F, will be obtained from elements with high Dt (compatible elements) such as Ni in basaltic olivine. Elements with ), 1 (incompatible elements), such as Th, Ba or rare-earth elements in basaltic systems, will provide basically no clue to F variations. In addition, information carried by incompatible elements, which do not fractionate with respect to each other, is entirely redundant. This is better shown by taking the relative change in the ratio of two elements il and i2 per increment of crystallization 

Taking the log-derivative of the partial melting equation (9.2.2) relative to F leads to 

We will assume small degrees of melting, i.e., F 1. Two extreme cases will be considered. For compatible elements (D, F) 

Elements have therefore to be used for what they are good at. In a suite of rocks, 

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