An algebraic method of paragenetic analysis is presented that may be applied to mineral assemblages containing any number of mineral solid-solutions and components. The method may be used to deduce the qualitative properties of chemical potential gradients in rocks and to obtain numerical estimates of the magnitude of the gradients. The method consists of solving a system of simultaneous equations that express analytically the relations between P, T, μi, and Xi,A for a given mineral assemblage. The system of equations includes (1) a Gibbs-Duhem equation for each mineral, (2) mass action equations between the chemical potentials of the components of the minerals, and (3) equations of the form (dμi−dμj) = −(Si,ASj,A)dT + (Vi,AVj,A)dP + Git,AdXi,A +… + Gi(j−1)AdX(j−1)A. Examples are given of applications of the method to igneous and metamorphic rocks.

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