The phase equilibria relationships in the Li₃A1F₆-A1₂0₃ binary system, the Li₃A1F₆-Na₃AlF₆-A1₂0₃ ternary system and the LiF-A1F₃-Na₃A1F₆-Al₂0₃ quaternary system have been investigated using a combination of X-ray powder diffraction, DTA, quenching and optical microscopy techniques. The compatibility relations at 500°C for the ternary and quaternary systems, the Li₃A1F₆-A1₂0₃ binary system and the ternary liquidus surface were determined. The binary system was found to have a eutectic at 754°C and 1 mole % Al₂0₃. The liquidus surface was found to contain the following three invariant points: 1. eutectic - 66 mole % Li₃A1F₆, 29% Na₃A1F₆, 5% A1₂0₃ and 670°C 2. peritectic - 51 mole % Li₃A1F₆, 42.5% Na₃A1F₆, 65% A1₂0₃ and 683°C 3. reaction point - 65 mole % Li₃A1F₆, 33% Na₃A1F₆, 2% A1₂0₃ and 693°C. The 500°C isothermal section contains three 3-phase regions and one 2-phase region. The quaternary system contains 7 compatibility tetrahedra at 500°C. / Master of Science