The crystal-melt equilibria in complex fifteen component melts are modeled based on quasicrystalline concepts. A pseudobinary phase diagram between acmite (which melts incongruently to a transition metal ferrite spinel) and nepheline is defined. The pseudobinary lies within the Al{sub 2}O{sub 3}-Fe{sub 2}O{sub 3}-Na{sub 2}O-SiO{sub 2} quaternary system that defines the crystallization of basalt glass melts. The pseudobinary provides the partitioning of species between the melt and the primary liquidus phases. The medium range order of the melt and the melt-crystal exchange equilibria are defined based on a constrained mathematical treatment that considers the crystallochemical coordination of the elemental species in acmite and nepheline. The liquidus phases that form are shown to be governed by the melt polymerization and the octahedral site preference energies. This quasicrystalline liquidus model has been used to prevent unwanted crystallization in the world's largest high level waste (HLW) melter for the past three years while allowing >10 wt% higher waste loadings to be processed
