The crystal-melt equilibria in complex 15 component simulated high-level waste (HLW) glass melts are modeled on the basis of quasicrystalline concepts. A pseudobinary phase diagram between a transition metal ferrite spinel (an incongruent melt product of transition metal iron-rich acmite) and nepheline is defined in Part II on the basis of these concepts. The pseudobinary lies within the Al2O3-Fe2O3-Na2O-SiO2 quaternary system that defines the crystallization of basalt glass melts. Part I defines the complex transition metal species that crystallize in waste glasses, the role of the octahedral site preference energies, the evidence for quasicrystalline clustering in waste glasses, and the potential quasicrystalline exchange reactions at the liquidus. The liquidus model developed on the basis of these concepts has been used to prevent unwanted crystallization in the world's largest HLW melter for the past 4 years while allowing > 10 wt% higher waste loadings to be processed.