Hygromagmatophile and Incompatible Elements

Assuming ideal solution behavior by AP+, U, and MU in the melt, equation 10.129 reduces to 

Based on equation 10.130 (figure 10.18), Treuil et al. (1979) suggested that hygromagmato-phile behavior is restricted to the field 1, where K, whereas for values 

According to Treuil, the constant concentration ratio of two hygromagmatophile elements is indicative of fractional crystallization. From the Doerner-Hoskins equation  

Error A associated with equation 10.132 can be expressed as a function of F (Allegre et al., 1977)  

However, equation 10.133 is not sufficient to ascribe magmatic evolution to fractional crystallization if it is not supported by petrologic evidence. Adopting the formalism of Shaw (1970), it may be shown that the distribution of hygromagmatophile elements in fractionally accumulated liquids leads to the same sort of linear array. The equation 

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