Generic energy formalism for reciprocal quadruplets within the two-sublattice quasichemical model

Ever-increasing interests to more accurate thermodynamic predictions of phase diagrams motivate more reliable thermodynamic models to be developed. The Modified Quasichemical Model within the two-sublattice Quadruplet Approximation (MQMQA) was thus established in well response to these interests and motivations. However, the model still needs to be further improved in order to have better thermodynamic predictions of arbitrary reciprocal solutions. The present paper proposes a new and generic formalism to characterize the Gibbs energy of the ternary reciprocal quadruplet within the framework of the MQMQA. The new formalism circumvents the problem spawned from solving the singular matrix of mass equations. Resultantly, energy landscapes of reciprocal solutions can be better defined everywhere in reciprocal composition spaces. With the current improvement, the MQMQA is believed to be one of the most reliable thermodynamic models for various types of solutions with or without short-range ordering.