The Li,K,Ca,BaaEuro-F,WO4 quinary reciprocal system was differentiated on the basis of graph theory with account for already known inner secants. Possible exchange and complex-formation chemical reactions that occur throughout the composition polyhedron of the system were revealed. The results of the differentiation and thermal analysis of several samples in each Phase unit block (PUB) were used to build crystallization tree of the title system. It is for the first time that the set of physicochemical methods (differential thermal analysis, visual polythermal analysis, and X-ray powder diffraction in tandem with projective thermal analysis) was used to study the LiF-LiKWO4-Li2WO4-CaWO4-BaWO4 five-component system; this system is the stable pentatope of the Li,K,Ca,BaaEuro-F,WO4 quinary reciprocal system. The coordinates of invariant points were determined.
