Representation of thermodynamic properties of quaternary systems using interaction parameters

Integral excess free energy of a quaternary system has been expressed in terms of the MacLaurin infinite series. The series is subjected to appropriate boundary conditions and each of the derivatives correlated to the corresponding interaction coefficients. The derivation of the partial functions involves extensive summation of various infinite series pertaining to the first order and quaternary parameters to remove any truncational error. The thermodynamic consistency of the derived partials has been established based on the Gibbs-Duhem relations. The equations are used to interpret the thermodynamic properties of the Fe-Cr-Ni-N system.