Hypothetical systems are useful to enhance the rigor of computerized algorithms and to enhance the applicability of the developed software to physically realistic systems. This paper deals with the calculation of miscibility gaps using the method of the addition of linear contributions. We derived a formalism, which underlies the method, for a multicomponent system. We applied the method to hypothetical miscibility gaps in a single ternary solution form for which the Gibbs energy is characterized by more than two minima. We show that specific Gibbs energy expressions at constant pressure and temperature result in the formation of multiple three-phase fields and multiple critical points. We present an algorithm for the calculation of miscibility gaps in ternary systems, which are characterized by these properties. We applied our method to the system KBr–LiBr–NaBr, having the characteristic that the solid form may separate into three phases with the same crystal structure at low temperatures
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