Iron and Steel Division - Thermodynamic Interaction Parameters of Elements in Liquid Iron

Thermodynamic intevaction pararnetevs of elements E2(2), for dilute binary solutions of a component "2" in liquid iron, i.e., E(22) = 9 In f2/?N2 where f2 is the activity coefficient and N2 the mole fraction, and E(3) 2 = In f2/ N3 dilute ternary solutions of "2" and "3," and the carbon saturation parameter sc(3) (In f c/ N3) N c/N Fe for N3 - 0, are critically examined and correlated. It has been found that the interaction parameters and the atomic numbers of alloying elements follow regular periodic putterns. PHYSICO-chemical behavior of alloying elements in molten iron have become the subject of numerous investigations during the past 25 years. Consequently, the mutual effects of elements in the iron-rich solutions Fe-C-X, Fe-N-X, Fe-H-X, Fe-O-X, and Fe-S-X where X represents an alloying element, have gradually become better understood. These effects for a given temperature and pressure may be expressed by the interaction parameter of Wagner1, 2 derived briefly in the following manner. The complete differential of the Gibbs free-energy equation at constant temperature and pressure is dF = Fl dn, + F2 dn, + F3 dn3+ . . . [ 1] where F is the free energy; F 1, the partial molar free energy of "I"; and n,, the number of moles of "i." Cross-differentiation of this expression* *Cross-differentials are obtained as follows: Since the order of differentiation of F with n2 and n3 is immaterial, the left sides of the second differentials are equal, hence the derivation of Eq. [2] is obtained. For a dilute solution of components 2 and 3 in solvent 1, with the substitution of RT In f i = Fi xs for Fi where fi is the activity coefficient, and Fixs is the excess partial molar free energy, Eq. [2] becomes O) [3] where N2 and N, are the mole fractions. The interaction parameters are defined by