Difficulties arise however when visualizing and analyzing three-dimensional objects quantitatively, such as determining the range of ∆µ A i values for which a material is stable against competing compounds. To mitigate such difficulties, VTAnDeM projects the stability region of a given ternary/quaternary material onto Colors correspond to the element/compound that introduces the bound to the phase stability region. For a quaternary material, a four-phase equilibrium appears as a vertex of the stability region with well-defined chemical potentials. A three-phase equilibrium appears as an edge, and a two-phase equilibrium appears as a facet.