Thermodynamic Calculation among Cerium, Oxygen, and Sulfur in Liquid Iron

Thermodynamic calculation has been applied to predict the inclusion formation in molten SS400 steel. When the Cerium addition in liquid iron is 70 ppm and the initial Oxygen and Sulphur are both 110 ppm, the formation of oxides containing Cerium would experience the transformation from Ce2O3 to CeO2 and also the formation of sulfides containing Cerium would experience the transformation from CeS to Ce2S3 and then to Ce3S4. Below 2000 K the most thermodynamic stable matter is CeO2 and the less thermodynamic stable inclusion is CeS. Only when the amount of [O] is extremely low and the amount of [S] and [Ce] is relatively high, Ce2S3 has the possibility to form.

Scientific RepoRts | 6:35843 | DOI: 10.1038/srep35843 cerium is optimal. To determine the separation sequence for various oxides and sulfides of cerium, the amount of cerium in the calculations was set as 1 mol to compare the Gibbs free energy of formation for various inclusions, which can be derived as: (2) where J denotes the reaction quotient (unitless), ∆ G is the Gibbs free energy change of reaction (J/mol), ∆ G θ denotes the Gibbs free energy change of reaction for unmixed reactants and products at standard conditions (J/mol), R is the gas constant (J·mol −1 ·K −1 ), T is temperature (K), and K is the equilibrium constant (unitless). The Gibbs free energy of oxides, sulfides and oxysulfides of cerium are shown in Table 2 14,[21][22][23][24][25][26] . Below 2000 K, the most thermodynamically stable inclusion was CeO 2 , as shown in Fig. 1. Therefore, CeO 2 likely formed in the molten iron when the temperature reached the simulated steelmaking temperature of 1873 K. In Fig. 1, it could be read that the least thermodynamic stable inclusion is CeS and the thermodynamic stale sequence of the possible inclusion formed in liquid steel is CeO 2 > Ce 2 O 3 > Ce 2 O 2 S > Ce 2 S 3 > Ce 3 S 4 > CeS. However, the most thermodynamically stable matter does not guarantee the formation of CeO 2 , because the formation of oxides containing cerium are controlled not only by the equilibrium constant but also by the concentrations of cerium and oxygen in the molten iron. That is to say, the formation of CeO 2 at 1873 K is also determined by the solubility product of CeO 2 and the concentration of cerium and oxygen, even though the Gibbs Free Energy of CeO 2 is the lowest at 1873 K.
The activities and activity coefficient of Ce, O and S can be written as Eqs (9) and (10) from Wagner's relation 7 and Lupis' relation 20 as follow, [Ce] [Ce] [Ce] where f i is the Henrian activity coefficient of component i relative to the dilute solution and e i j is the first-order interaction parameter of i on j in molten iron; w[i] and w[ j] are the mass percentages of elements i and j, respectively (Table 3); α i i s the activity of element i.
By using data 22,23 from Tables 2 and 3, the following curves for Ce-S and Ce-O in Fig. 2 can be calculated. The key to derive every line in Fig. 2 is the relation of equilibrium constant, Gibbs free energy and the amount of the chemical compositions for every possible inclusion according to Wagner's relation 19 and Lupis' relation 20 . When the equilibrium constant is linked to the amount of the chemical compositions for every possible inclusion, equations for Fig. 2 can be obtained. When the weight percentage of cerium, oxygen and sulphur are known in the molten iron at 1873 K, the main inclusion formed would be found in Fig. 2. As shown in Fig. 2, if the cerium addition in liquid iron is 70 ppm and the initial oxygen and sulphur are both 110 ppm, the formation of oxides containing cerium would experience the transformation from Ce 2 O 3 to CeO 2 and also the formation of sulfides containing cerium would experience the transformation from CeS to Ce 2 S 3 and then to Ce 3 S 4 . From Fig. 2, when the temperature of molten iron reached 1873 K, Ce 3 S 4 is the main product, as the amount of cerium in molten iron is high and the amount of sulphur is relatively lower compared to the formation of CeS and Ce 2 S 3 .
In order to investigate the formation conditions of Ce 2 O 3 , Ce 2 S 3 and Ce 2 O 2 S, the doubly saturated curve with Ce 2 O 3 /Ce 2 O 2 S and Ce 2 S 3 /Ce 2 O 2 S are calculated, using the thermodynamic data derived in Tables 2 and  Equation 1-2. In molten iron, it is assumed that  Figure 3 was derived from the above calculations. In Fig. 3

, it can be concluded that Ce 2 O 3 and Ce 2 O 2 S can exist in molten iron in a wide amount range of [Ce], [O] and [S]. More importantly, only when the amount of [O] is extremely low and the amount of [S] and [Ce] is relatively high, Ce 2 S 3 has the possibility to form.
Cerium is a perfect deoxidizer and desulfurizer for steel purification. Compared with other elements, for example Aluminum, Titanium, Magnesium and Calcium 27,28 , which can also deoxidize and desulfurize, cerium can formed a complex compound Ce 2 O 2 S which contains Oxygen and Sulphur together. The formation possibility of Ce 2 O 2 S has been verified by Hu's research 29 when they studied the effect of Ce addition on the C-Mn steel microstructure. It is reproted by Wang 26 that Ce 2 O 3 is easier to form in molten iron when the iron molten temperature is 1873 K. However, the thermodynamic conditions were changed when the temperature decreases from 1873 K to solidus temperature. On the other hand, when the temperature of molten iron decreases to that at which solid steel starts to form, the cerium and oxygen in the molten iron begin to segregate. Their amounts are respectively:  Table 3. First-order interaction parameter e i j of cerium, oxygen, and sulfur at 1873 K 30 .

Figure 2. Deoxidation and Desulphurization with Cerium in liquid iron at 1873 K.
Scientific RepoRts | 6:35843 | DOI: 10.1038/srep35843 The solidus temperature of SS400 is 1777 K. The solubility product of the Ce 2 O 3 formed in molten iron can be expressed as:   The solubility product of the Ce 2 O 3 formed in molten iron at equilibrium can be expressed as: 3 ( 74695 18 75) 2 3 From Eqs (11) to (14), the solubility products versus solidification ratio (f s ) are plotted in Fig. 4. In Fig. 4(a), where the simulated oxygen concentration in liquid steel is 10 ppm and the cerium concentration varies from 0.1% to 0.5%, the solubility products versus solidification ratio (f s ) are plotted with the varying cerium concentration (shown in the colorful lines of Fig. 4(a)) and the equilibrium constant of Ce 2 O 3 (K Ce2O3 ) versus solidification ratio f s is curved as the black solid line in Fig. 4(a). It is read in Fig. 4(a) that the colorful lines are all in the above of the black solid line, which means Ce 2 O 3 prefers to segregate in liquid phase with the 10 ppm Oxygen concentration in liquid iron. Moreover, the same conclusion can be drawn from the similar Fig. 4(b-d) with 50 ppm, 100 pmm, 200 ppm oxygen concentration in liquid iron. The inset red diagrams in Fig. 4(a-d) are the detailed solid black curves appeared in Fig. 4(a-d). Figure 4 shows that when the oxygen concentration in molten iron was increased from 10 to 200 ppm and the cerium concentration was in the range of 0.1% to 0.5%, Ce 2 O 3 preferred to segregate in the liquid phase.

Conclusion
By the addition of cerium in molten SS400 steel, when the temperature of molten iron reached 1873 K, at the same time that the Cerium addition in liquid iron is 70 ppm and the initial Oxygen and Sulphur are both 110 ppm, the formation of oxides containing Cerium would experience the transformation from Ce 2 O 3 to CeO 2 and also the formation of sulfides containing Cerium would experience the transformation from CeS to Ce 2 S 3 and then to Ce 3 S 4 . Below 2000 K the most thermodynamic stable matter CeO 2 and the least thermodynamic stable inclusion is CeS. And the thermodynamic stable sequence of the possible inclusions formed in liquid steel is CeO 2 > Ce 2 O 3 > Ce 2 O 2 S > Ce 2 S 3 > Ce 3 S 4 > CeS. Only when the amount of [O] is extremely low and the amount of [S] and [Ce] is relatively high, Ce 2 S 3 has the possibility to form. With the amount of oxygen in molten iron increasing from 10 ppm to 200 ppm and the amount range of cerium increasing from 0.1% to 0.5%, Ce 2 O 3 prefers to segregate in liquid phase all the time.