Assimilation-fractional crystallization AFC

The symbols used in Section 1.5 to describe the evolution of element i concentration in the solid and the liquid during fractional crystallization will be kept. Other parameters used in the present derivation are almost identical to those of DePaolo (1981) although reference to time, which is immaterial to the mass balance and equilibrium conditions, has been omitted. Let a be the subscript representing the assimilated material, and assume that country-rocks concentration Cj is constant. Mass balance requires 

Inserting the logarithmic differential of concentration into equation (9.4.14) gives 

Defining the residual melt fraction F relative to the initial amount of magma M0 as 

No assumption on constant parameters has been made so far. If the amount of mineral precipitated is proportional to the amount of assimilated material, e.g., if latent heat is conserved, then r is constant. For the initial liquid state F = 1, C iq = C0 as in Section 9.3.1 

Making a=(l— r) 1, the equation of Allegre and Minster (1978) for wall-rock dissolution during fractional crystallization is obtained, which is therefore equivalent to the AFC equation (9.4.17) derived by DePaolo (1981). 

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During fractional crystallization, the country rocks may assimilate the crystallizing magmas (DePaolo, 1981 O Hara, 1998). This process is called assimilation-fractional crystallization (AFC) (DePaolo, 1981). The conservation of mass for a trace element requires... 

Spera, F.J. and Bohrson, W.A., 2001. Energy-constrained open-system magmatic processes I general model and energy-constrained assimilation and fractional crystallization (EC-AFC) formulation. J. Petrol., 42 999-1018. 

If phenocryst compositions cannot explain trends in a rock series and a fractional and/racttonal crystallization model does not. appear to worlt, it is instructive to consider the crystallization possibility of simultaneous assimilation, of the country rock and fractional crystallization. This process, often abreviated to AFC, was first proposed by Bowen... 

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