Abstract
The quaternary reciprocal system Li,K‖Cl,Br,WO4 was partitioned into simplexes using graph theory by writing an adjacency matrix and solving a logical expression. A tree of phases of the system was constructed. The tree of phases has a linear structure and consists of two stable tetrahedra and a stable pentatope, which are divided by two partitioning triangles. In the quaternary reciprocal system Li,K‖Cl,Br,WO4, based on the constructed tree of phases, crystallizing phases were predicted. The partitioning triangles KCl-KBr-Li2WO4 and KCl-KBr-LiKWO4 were experimentally studied by differential thermal analysis. There are no invariant equilibrium points in the triangles. Continuous series of solid solutions are stable and do not decompose.
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