Determination of defect equilibria in minerals

We have developed a general computation procedure DEFEQ that enables equilibrium defect concentrations in minerals to be quantitatively determined over the range of thermodynamic conditions that encompasses both laboratory experiments and Earth conditions. The governing equations are the quasichemical reactions between defects, conservation of lattice site ratios, and conservation of charge. The input parameters are the enthalpies and entropies for the defect reactions and the thermodynamic conditions which include temperature, gaseous fugacity, and chemical activities. A modified Newton-Raphson algorithm is used to simultaneously solve the nonlinear set of equations without a priori simplifications on charge balance or lattice site conservation. Our method is general and can be applied to materials other than minerals such as oxide superconductors, semiconductors, and ceramics. The method is illustrated with results from the study of (Mg,Fe)O.