In the literature, no detailed description is reported about how to detect if a miscibility gap exists in terms of interaction parameters analytically. In this work, a method to determine the likelihood of the presence of a miscibility gap in a binary substitutional solution phase is proposed in terms of interaction parameters. The range of the last interaction parameter along with the former parameters is analyzed for a set of self-consistent parameters associated with the miscibility gap in assessment process. Furthermore, we deduce the first and second derivatives of Gibbs energy with respect to composition for a phase described with a sublattice model in a binary system. The Al-Zn and Al-In phase diagrams are computed by using a home-made code to verify the efficiency of these techniques. The method to detect the miscibility gap in terms of interaction parameters can be generalized to sublattice models. At last, a system of equations is developed to efficiently compute the Gibbs energy curve of a phase described with a sublattice model.