“…The present model for ternary SiO 2 -AO-BO systems plus sulphur, where sulphide ions (S 2− ) can again substitute for free oxygen ions (O 2− ), has been recently proposed [14]. In the present work, this model was applied to ternary SiO 2 -Na 2 O-MO (M = Ca, Mn, Mg, Fe) systems plus sulphur, which can be represented as a square pyramid with SiO 2 at the apex level, and as shown in Figure 1, the base represents a reciprocal ternary subsystem Na 2 , M // O, S. The mixing Gibbs free energy of this system includes seven terms that can be used to estimate the activities of each component (SiO 2 , Na 2 O, MO, Na 2 S, MS):…”