A heuristic method to uncover a possible unsoundness of a physical–chemical model

Abstract To ensure that a procedure tailored for thermodynamic optimization returns statistically optimal numerical values of the model’s parameters, the appropriateness of the model used to describe the Gibbs energy of the phase must be meticulously considered. In analyzing the suitability, one usually starts with the crystal structure of the phase and data on its homogeneity range. In addition to this minimum requirement, one tries to make good use of other (not necessarily thermodynamic) properties in the hope of obtaining a physically feasible phase model. Despite all the efforts, the model may demonstrate an unexpected behavior and result in artifacts on calculated phase boundaries and concentration and temperature dependencies of thermodynamic functions. It is extremely difficult if possible at all to formulate a criterion of correctness, which, if satisfied, guarantees that a corresponding model is physically sound. Instead of seeking such a condition of trustworthiness, it is suggested to use a criterion of erroneousness, which, if fulfilled, warns one against employing a model under examination. It is proposed to treat a fundamental constant (such as the gas constant R ) as an unknown model’s parameter and compare its estimation resulted from data treatment with its well-known value. If the latter does not fall into a confidence interval characterizing the former, then it might be advisable to revisit physical foundations the model rests on.