The phase equilibria relationships in the Na₃AlF₆-AlF₃-LiF ternary system have been investigated using a combination of quenching, optical microscopy, DTA, and x-ray powder diffraction techniques. The compatibility relations at 500°C, the binary system Na₃AlF₆-Li₃AlF₆, and the ternary liquidus surface were determined. The liquidus surface was found to contain the following five important invariant points: 1) eutectic - 81% LiF, 9.5% Na₃AlF₆, 9.5% AlF₃ and 685°C 2) eutectic - 56% LiF, 6% Na₃AlF₆, 38% AlF₃ and 585°C 3) eutectic - 37% LiF, 17% Na₃AlF₆, 46% AlF₃ and 620°C 4) peritectic - 30% LiF, 37% Na₃AlF₆, 33% AlF₃ and 660°C 5) reaction point - 65% LiF, 9% Na₃AlF₆, 26% AlF₃ and 675°C The 500°C isothermal section contains 7 three-phase regions and 2 large two-phase regions. The binary system Na₃AlF₆-Li₃AlF₆ contained 2 incongruently melting compounds, many polymorphic transformations, and a eutectic at 690°C and 67 mole % Li₃AlF₆. / Master of Science