A general algorithm for the computation of chemical equilibria in complex systems containing non-ideal solutions has been developed. The method is a G-minimization based on repeated linear and nonlinear programming steps. A computer program (THERIAK) based on this algorithm has been written and was used to solve a great variety of problems, ranging from a simple blast furnace calculation to liquid-liquid unmixing in a four component silicate melt. The computing times are in the magnitude of 1/2 to 2 seconds for each calculation. The method can also be used to test the consequences of thermodynamic models and data in systems of interest to many fields, including chemistry, geochemistry and metallurgy. Integrated powder diffraction intensities can be used to measure Mn-Mg and Fe-Mg site occupancies in olivines because of the difference in scattering factors between Mg and Mn or Fe. Theoretically calculated intensity ratios are subject to uncertainties from positional parameters (less than 3.5 % for peaks with a relative intensity greater than 25 %) and unknown charge distribution (up to 30 %). Several peak ratios are less subject to this last uncertainty and may be used to measure the site occupancies in olivines. 27 synthetic Fe-Mn-Mg olivines (800 °C, vacuum, with graphite) were investigated with Mossbauer spectroscopy and XRD intensity evaluation, producing occupancies accurate to approximately 0.03 per site. A thermodynamic speciation model represents the data very well. Preliminary Fe-Mn-Mg exchange experiments involving olivine and garnet place some limits on element distributions between these two minerals. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate