  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.
