The purpose of this work was to determine the liquidus surface of the cryolite-rich portion of the ternary system Na₃AlF₆-CaF₂-AlF₃ and to establish the effect of Al₂O₃ on the operation of the Hall cell electrolysis. A series of isotherm of the cryolite-rich portion were graphed. It was shown that pseudo-binary phase diagrams of Al₂O₃ and bulk composition in the cryolite-rich portion of the Na₃AlF₆-CaF₂-AlF₃ system were found to be simple eutectic. The temperatures and the alumina contents of the double solubility limit, two important parameters for the Hall cell, of the joins 95 Na₃AlF₆/5 AlF₃-Na₃AlF₆, 90 Na₃AlF₆/ 10 NaCaAlF₆ and 85 Na₃AlF₃/15 AlF₃-NaCaAlF₆ were determined. The cryolite liquidus temperature of the quaternary system Na₃AlF₆-CaF₂-AlF₃-Al₂O₃ was found to be expressed by: T_Liq.. (C) = 1009.4 + 4.059(CaF₂) - 1.167(CaF₂)² + 0.968 x (CaF₂)(AlF₃) - 0.105(CaF₂)(AlF₃)² + 0.073 x (CaF₂)²(AlF₃) + 0.002(CaF₂)² (AlF₃)² - 4.165 x (AlF₃) - 0.054(AlF₃)² - 5.33(Al₂O₃) for CaF₂ 3.8~11.25%, AlF₃ 5~20%. / M.S.