A new equation for the temperature dependence of the excess Gibbs energy of solution phases

During CALPHAD optimization procedures, the excess Gibbs energy of solution phases is usually described by the Redlich–Kister (RK) polynomial. The RK polynomial includes interaction parameters ( L i ), usually described as linear functions of temperature ( L i = a i − b i T ), with semi-empirical parameters a i and b i usually having the same signs. Consequently, the excess Gibbs energy will change its sign at a certain high temperature and will have an infinite value at infinitely high temperature. This is in conflict with thermodynamic constraints and can also lead to artificial phase stabilization in some of the calculated phase diagrams, such as the appearance of an artificial miscibility gap having no maximum critical temperature. Such artifacts can usually be avoided, if the following new semi-empirical equation is used for the interaction energy of solution phases: L i = h 0 i ⋅ exp ( − T τ 0 i ) . Parameter h 0 i (J/mol) is the enthalpy part of L i at T = 0  K, while parameter τ 0 i (K) is the temperature at which L i would change its sign if it were extrapolated linearly from T = 0  K. Parameter h 0 i can have any sign, but parameter τ 0 i must be always positive. The new equation can be extended to describe more complex behavior in certain systems as: L i = h 0 i ⋅ exp ( − T τ 0 i ) ⋅ [ 1 + ∑ j = 1 m a i j ⋅ ( T τ 0 i ) j ] , with a i j being adjustable semi-empirical parameters for the given L i .