The polynomial representation of thermodynamic properties in dilute solutions

Attempts to extend the interaction parameter formalism to higher-order polynomials and to render it thermodynamically consistent at finite solute concentrations have resulted in much confusion. The literature is reviewed with a view to clarifying the issues. The problem is best and most simply resolved through extension of the quadratic formalism, which has a sound theoretical foundation. A new and general set of equations for estimating higher-order parameters from binary parameters is derived. The applicability of using molar ratios rather than mole fractions in the polynomial expansions is discussed. The formation of associate species (such as the formation of “AlO” associates in molten Fe) is treated. In such cases of strong solute-solute interactions, the usual practice of expressing the interaction parameters as linear functions of (1/T) is invalid. Finally, for more concentrated solutions, the advantage of using the Kohler or Toop interpolation models rather than the commonly used Muggianu model is shown.