Phase Tree of the Quinary Reciprocal System Li+,K+||F–,Cl–,Br–,\({\text{CrO}}_{4}^{{2 - }}\) and Investigation of the LiF–Li2CrO4–KCl–KBr Stable Tetrahedron

The quinary reciprocal system Li⁺,K⁺||F^–,Cl^–,Br^–,\({\text{CrO}}_{4}^{{2 - }}\) has been divided into simplexes using graph theory: by making up an adjacency matrix and solving a logical expression. The results have been used to construct the phase tree of the system, which has a linear structure and consists of four stable secant tetrahedra, four stable pentatopes, and one stable hexatope. The number and composition of phases crystallizing in the system have been predicted. The LiF–KCl–KBr–Li₂CrO₄ stable tetrahedron has been studied using differential thermal analysis and X-ray diffraction. The tetrahedron has no invariant equilibrium points. The continuous series of solid solutions between potassium chloride and potassium bromide has been shown to be stable, without decomposition. Three solid phases have been shown to crystallize in the tetrahedron: LiF, Li₂CrO₄, and KCl_xBr_1–x.