An extension of Wagner's analysis of competing scale formation

Wagner's criterion to predict the minimum concentration of solute (N_B(min)⁰)necessary for the exclusive formation of its scale has been modified to incorporate both thermodynamic and kinetics requirements. The analysis presented here involves a receding alloy/scale interface for which the composition of the alloy at this interface is governed by thermodynamic equilibrium between the two competing scale phases and the base alloy. This is a more rigorous analysis than that of Wagner's, who assumed the alloy/scale interface to be immobile and the solute composition at the interface to be zero. A comparison is made between values of N_B(min)⁰found experimentally and those predicted by Wagner's and the present criterion for a number of alloy-gas systems. It is shown that the criterion developed in the present analysis can often provide a better approximation of the actual N_B(min)⁰.The expressions derived from the present analysis have been extended also in a semiquantitative manner to provide a criterion for the minimum amount of solute in the alloy required for the transition from internal to external scale formation.