The calculation of phase diagrams from first principles constitutes a critical test of accuracy of both quantum and statistical mechanical models. The slightest variation of calculated energies can result in drastic changes in the topology of phase diagrams: the location of phase boundaries and even the nature of the phases in mutual equilibrium is determined by the common tangent construction so that small alterations in the shape or relative positions of free energy curves can cause common tangents to connect completely different sets of phases, structures, and concentrations. In other words, phase diagrams result from ''non-local minimization:'' all possible free energy curves of all possible phases must be considered, at all concentrations, and compared to one another. Only ''prototype'' systems were considered. The tight binding CPA was used as basic quantum mechanical framework, and the CVM was used for the statistical mechanical calculations.