All available thermodynamic and phase diagram data for the condensed phases of the (Al2O3 + Na2O), (Al2O3 + Na2O + SiO2), and (Al2O3 + Na2O + AlF3 + NaF) systems have been critically assessed. Model parameters for solid solutions and a single set of parameters for the liquid solution in the binary, ternary, and ternary reciprocal systems have been optimized and permit to reproduce most of the critically reviewed experimental data. The Modified Quasichemical Model in the Quadruplet Approximation was used for the oxyfluoride (mixture of molten oxides and salts) liquid solution, which exhibits strong first-nearest-neighbor and second-nearest-neighbor short-range order. This thermodynamic model takes into account both types of short-range order as well as the coupling between them. The charge compensation effect present in the (Al2O3 + Na2O + SiO2) system was taken into account by adding a (NaAl)(4+) species in the liquid solution. (C) 2012 Elsevier Ltd. All rights reserved.