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Thermodynamic Evaluation of Reaction Abilities of Structural Units in Fe-O Binary Melts Based on the Atom–Molecule Coexistence Theory

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Abstract

A thermodynamic model for calculating the mass action concentrations \( N_{i} \) of structural units in Fe-O binary melts based on the atom–molecule coexistence theory, i.e., AMCT-\( N_{i} \) model, has been developed and verified to be valid through comparing with the calculated activities \( a_{{{\text{R,}}i}} \) of both O and Fe over a temperature range from 1833 K to 1973 K (1560 °C to 1700 °C). Moreover, activity coefficients \( \gamma_{\text{O}}^{{}} \) or \( f_{{{\%,{\text O}}}} \) or \( f_{\text{H,O}} \) of O coupled with activity \( a_{\text{R,O}} \) or \( a_{{{\% , \text{O}}}} \) or \( a_{\text{H,O}} \) of O and the corresponding first-order activity interaction coefficient \( \varepsilon_{\text{O}}^{\text{O}} \) or \( e_{\text{O}}^{\text{O}} \) or \( h_{\text{O}}^{\text{O}} \) of O to O have also been determined by the developed AMCT-\( N_{i} \) model and verified to be credible. In addition, the molar mixing thermodynamic properties of Fe-O binary melts have been determined to be accurate. Values of the calculated mass action concentration \( N_{\text{Fe}} \) of free Fe are in good agreement with results of the calculated activity \( a_{\text{R,Fe}} \) of Fe relative to pure liquid Fe(l) as standard state in Fe-O binary melts. The calculated mass action concentration \( N_{\text{O}} \) of free O has a closely corresponding relationship with the calculated activity \( a_{\text{R,O}} \) of O relative to ideal O2 at 101,325 Pa as standard state in Fe-O binary melts. However, values of the calculated mass action concentration \( N_{\text{O}} \) of free O are much greater than results of the calculated activity \( a_{\text{R,O}} \) of O in Fe-O binary melts. The converted mass action concentration \( N_{\text{O}}^{\prime} \) of total O relative to ideal O2 at 101,325 Pa as standard state can be obtained through transferring standard state of the calculated mass action concentration \( N_{\text{O}} \) of free O. The converted mass action concentration \( N_{\text{O}}^{\prime} \) of total O or the converted activity \( a_{\text{R,O}}^{\text{AMCT}} \) of O can well be matched with the calculated activity \( a_{\text{R,O}} \) of O in Fe-O binary melts. Although the obtained expression of first-order activity interaction coefficient \( \varepsilon_{\text{O}}^{\text{O}} \) or \( e_{\text{O}}^{\text{O}} \) or \( h_{\text{O}}^{\text{O}} \) by the developed AMCT-\( N_{i} \) model for Fe-O binary melts is different with that based on the calculated activity \( a_{\text{R,O}} \) or \( a_{{{{\%,{ \text O}}}}} \) or \( a_{\text{H,O}} \) of O, they can be applied to accurately predict activity \( a_{\text{R,O}} \) or \( a_{{{{\%, {\text O}}}}} \) or \( a_{\text{H,O}} \) of O in Fe-O binary melts. The molar mixing thermodynamic properties such as molar mixing enthalpy change/entropy change/Gibbs energy change of Fe-O binary melts can reliably be determined from the converted mass action concentration \( N_{\text{O}}^{\prime} \) of O or the converted activity \( a_{\text{R,O}}^{\text{AMCT}} \) of O as well as the calculated mass action concentration \( N_{\text{Fe}} \) of [Fe] by the developed AMCT-\( N_{i} \) model for Fe-O binary melts.

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Abbreviations

\( a_{i} \) :

Activity of element i or compound i (–)

\( a_{{{\text{R,}}i}} \) :

Activity of element i or compound i relative to pure matter i (l or s or g) as standard state with mole fraction \( x_{i} \) as concentration unit and following Raoult’s law under the condition of taking ideal solution as reference state, i.e., \( a_{{{\text{R,}}i}} = \gamma_{i} x_{i} \) (–)

\( a_{\text{R,O}}^{\text{AMCT}} \) :

Converted activity \( a_{\text{R,O}} \) of O in Fe-O binary melts by developed AMCT-\( N_{i} \) model (–)

\( a_{{{\%,}i}} \) :

Activity of element i referred to 1 mass pct of element i as standard state with mass percentage [pct i] as concentration unit and obeying Henry’s law under the condition of taking infinitely dilute ideal solution as reference state, i.e., \( a_{{{\%,}i}} = f_{{{\%,}i}} [{\text{pct}} i] \) (–)

\( a_{{{\%, \text{O}}}}^{\text{AMCT}} \) :

Calculated \( a_{{{\%,\text{O}}}} \) of O in Fe-O binary melts by developed AMCT-\( N_{i} \) model (–)

\( a_{{{\text{H,}}i}} \) :

Activity of element i relative to hypothetical pure matter i (l or s or g) as standard state with mole fraction \( x_{i} \) as concentration unit and conforming to Henry’s law under the condition of taking infinitely dilute ideal solution as reference state, i.e., \( a_{{{\text{H,}}i}} = f_{{{\text{H,}}i}} x_{i} \) (–)

\( a_{\text{H,O}}^{\text{AMCT}} \) :

Calculated \( a_{\text{H,O}} \) of O in Fe-O binary melts by developed AMCT-\( N_{i} \) model (–)

\( b_{i} \) :

Mole number of element i in 100 g metallic melts before reaction equilibrium for forming associated molecules or compounds, having the same meaning with \( n_{i}^{0} \) (mol)

\( e_{i}^{i} \) :

First-order activity interaction coefficient of element i to i in metallic melts related with activity coefficient \( f_{{{\%,}i}} \) (–)

\( f_{{{\%,}i}} \) :

Activity coefficient of element i in metallic melts related with activity \( a_{{{\%,}i}} \) (–)

\( f_{{{\text{\%,O}}}}^{0} \) :

Henrian activity coefficient of O in infinitely dilute Fe-O binary melts coupled with activity coefficient \( f_{{{\text{\%,O}}}} \) (–)

\( f_{{{\text{H,}}i}} \) :

Activity coefficient of element i in metallic melts related with activity \( a_{{{\text{H,}}i}} \) (–)

\( f_{\text{H,O}}^{0} \) :

Henrian activity coefficient of O in infinitely dilute Fe-O binary melts coupled with activity coefficient \( f_{\text{H,O}} \) (–)

\( \Delta_{\text{r}} G_{{{\text{m,}}i}}^{{\Theta , {\text{R}}}} \) :

Standard molar Gibbs free energy change of reaction for forming compound i based on activity \( a_{{{\text{R,}}i}} \) for reactants and products (J/mol)

\( \Delta_{\text{sol}} G_{{{\text{m,0}} . 5 {\text{O}}_{ 2} \to [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}} }}^{{\Theta , {\%}}} \) :

Standard molar Gibbs free energy change of dissolved O2 for forming [pct O] as 1.0 in Fe-O binary melts referred to 1 mass pct of [O] as reference state (J/mol)

\( \Delta_{\text{sol}} G_{{{\text{m,0}} . 5 {\text{O}}_{ 2} \to [ {\text{O]}}_{{{\text{ [at.\%O] = 1}} . 0}} }}^{{\Theta , {\text{at.\% }}}} \) :

Standard molar Gibbs free energy change of dissolved O2 for forming [at. pct O] as 1.0 in Fe-O binary melts referred to 1 atomic percentage of [O] as reference state (J/mol)

\( h_{i}^{i} \) :

First-order activity interaction coefficient of element i in metallic melts related with activity coefficient \( f_{{{\text{H,}}i}} \) (–)

\( K_{i}^{{\Theta , {\text{R}}}} \) :

Standard equilibrium constant of chemical reaction for forming compound i based on activity \( a_{{{\text{R,}}i}} \) for reactants or products (–)

\( K_{i}^{{\Theta , {\%}}} \) :

Standard equilibrium constant of chemical reaction for forming compound i based on activity \( a_{{{\% ,}i}} \) for reactants or products (–)

\( L_{{{\text{O,}}N_{\text{O}} \to a_{\text{R,O}} }}^{\prime} \) :

Transformation coefficient from the calculated \( N_{\text{O}} \) of free O to activity \( a_{\text{R,O}} \) of O (–)

\( \overline{{L^{\prime} }}_{{{\text{O,}}N_{\text{O}} \to a_{\text{R,O}} }} \) :

Average of transformation coefficient from the calculated \( N_{\text{O}} \) of free O to activity \( a_{\text{R,O}} \) of O (–)

\( M_{i} \) :

Relative atomic mass of element i (–)

\( n_{i}^{0} \) :

Mole number of element i in 100 g metallic melts before reaction equilibrium for forming associated molecule or compound, having the same meaning of \( b_{i} \) (mol)

\( n_{i} \) :

Equilibrium mole number of structural unit i in 100 g metallic melts based on the AMCT (mol)

\( \Sigma n_{i} \) :

Total equilibrium mole number of all structural units in 100 g metallic melts based on the AMCT (mol)

\( N_{i} \) :

Mass action concentrations of structural unit i in metallic melts based on the AMCT (–)

\( p_{i} \) :

Partial pressure of species i in gaseous phase (Pa)

\( p^{\Theta } \) :

Standard pressure of gas at sea level and 273 K (0 °C) as 101,325 Pa (Pa)

\( R \) :

Gas constant [8.314 J/(mol K)]

\( T \) :

Absolute temperature (K)

\( x_{i} \) :

Mole fraction of element i or compound i in metallic melts (–)

[at. pct i]:

Atomic percentage of element i in metallic melts, having the same meaning with 100\( x_{i} \) (–)

[pct i]:

Mass percentage of element i or compound i in metallic melts (–)

\( \gamma_{i} \) :

Activity coefficient of element i related with activity \( a_{{{\text{R,}}i}} \) (–)

\( \gamma_{i}^{0} \) :

Raoultian activity coefficient of element i in infinitely dilute metallic melts relative to pure matter i (l or s or g) as standard state and taking infinitely dilute ideal solution as reference state, i.e., equal to value of \( \gamma_{{i ,x_{i} \to 0.0}} \) (–)

\( \varepsilon_{i}^{i} \) :

First-order activity interaction coefficient of element i in metallic melts related with activity coefficient \( \gamma_{i} \) (–)

\( \mu_{{i_{2} ( {\text{g}})}}^{*} \) :

Chemical potential of diatomic gas i 2 as ideal gas at 101,325 Pa (J/mol)

\( \mu_{{i_{2} ( {\text{g}})}}^{*} (T) \) :

Chemical potential of diatomic gas i 2 as ideal gas at 101,325 Pa at temperature T (J/mol)

\( \mu_{{[i]_{{0.5i_{2}}}}} \) :

Chemical potential of dissolved element i relative to ideal diatomic gas i 2 gas at 101,325 Pa as standard state (J/mol)

\( \mu_{{\%[i]_{[\%i] = 1.0}}} \) :

Chemical potential of dissolved element i relative to [% i] as 1.0 as reference state, (J/mol)

\( \mu_{{\%[i]_{[\%i] = 1.0} }}^{\Theta } \) :

Standard chemical potential of dissolved element i relative to [pct i] as 1.0 as standard state (J/mol)

ci :

Molecule i or compound i (–)

References

  1. [1] L. S. Darken and R. W. Gurry: The System Iron-Oxygen. I. The Wüstite Field and Related Equilibria. J. Am. Chem. Soc., 1945, vol. 67 (8), pp 1398–1412.

    Article  Google Scholar 

  2. [2] L. S. Darken and R. W. Gurry: The System Iron-Oxygen. II. Equilibrium and Thermodynamics of Liquid Oxide and Other Phases. J. Am. Chem. Soc., 1946, vol. 68(5), pp. 798–816.

    Article  Google Scholar 

  3. [3] P. J. Spencer and O. Kubaschewski: A Thermodynamic Assessment of the Iron–oxygen System. Calphad, 1978, vol. 2(2), pp. 147–167.

    Article  Google Scholar 

  4. [4] R. P. Goel, H. H. Kellogg, and J. Larrain: Mathematical Description of the Thermodynamic Properties of the Systems Fe-O and Fe-O-SiO2. Metall. Trans. B, 1980, vol. 11B(1), pp. 107–117.

    Article  Google Scholar 

  5. [5] B. Björkman: An assessment of the system Fe-O–SiO2 using a structure based model for the liquid silicate. Calphad, 1985, vol. 9(3), pp. 271–282.

    Article  Google Scholar 

  6. [6] B. Sundman: An Assessment of the Fe-O System. J Phase Equilib., 1991, vol. 12(1), pp. 127–40.

    Article  Google Scholar 

  7. [7] H. A. Wriedt: The Fe-O (iron–oxygen) system. J Phase Equilib., 1991, vol. 12(2), pp. 170–200.

    Article  Google Scholar 

  8. [8] M. Kowalski and P. J. Spencer: Thermodynamic Reevaluation of the Cr–O, Fe-O and Ni–O Systems: Remodeling of the Liquid, BCC and FCC Phases. Calphad, 1995, vol. 19(3), pp. 229–243.

    Article  Google Scholar 

  9. [9] M. Selleby and B. Sundman: A Reassessment of the Ca-Fe-O System. Calphad, 1996, vol. 20(3), pp. 381–392.

    Article  Google Scholar 

  10. [10] S. A. Decterov, E. Jak, P. C. Hayes, and A. D. Pelton: Experimental Study of Phase Equilibria and Thermodynamic Optimization of the Fe-Zn-O System. Metall. Mater. Trans. B, 2001, vol. 32B(4), pp. 643–657.

    Article  Google Scholar 

  11. [11] A. V. Khvan, O. B. Fabrichnaya, G. Savinykh, R. Adam, and H. J. Seifert: Thermodynamic Assessment of the Cu–Fe-O System. J Phase Equilib. Dif., 2011, vol. 32(6), pp. 498–511.

    Article  Google Scholar 

  12. [12] D. Shishin and S. A. Decterov: Critical Assessment and Thermodynamic Modeling of the Cu–O and Cu–O–S Systems. Calphad, 2012, vol. 38, pp. 59–70.

    Article  Google Scholar 

  13. [13] D. Shishin, T. Hidayat, E. Jak, and S. A. Decterov: Critical Assessment and Thermodynamic Modeling of the Cu–Fe-O System. Calphad, 2013, vol. 41, pp. 160–179.

    Article  Google Scholar 

  14. [14] T. Hidayat, D. Shishin, E. Jak, and S. A. Decterov: Thermodynamic Reevaluation of the Fe-O System. Calphad, 2015, vol. 48, pp. 131–44.

    Article  Google Scholar 

  15. [15] J. Chipman: Equilibrium in the Oxidation of Liquid Iron by Steam and the Free Energy of Ferrous Oxide in Liquid Steel. J. Am. Chem. Soc., 1933, vol. 55(8), pp. 3131–3139.

    Article  Google Scholar 

  16. J. Chipman and M.G. Fontana: Ind. Eng. Chem., 1935, vol. 7(6), pp. 391–95.

  17. [17] M. G. Fontana and J. Chipman: Trans. Amer. Soc. Metals, 1936, vol.24, pp. 313–333.

    Google Scholar 

  18. A.M. Samarin and J. Chipman: Trans. Am. Inst. Min. Met. Eng., 1937, vol. 125, pp. 331–45.

  19. [19] C. R. Taylor and J. Chipman: Equilibria of Liquid Iron and Simple Basic and Acid Slags in a Rotating Induction Furnace. Trans. AIME, 1943, vol. 154(6), pp. 228–247.

    Google Scholar 

  20. M.N. Dastur and J. Chipman: Trans. Am. Inst. Min. Met. Eng., 1949, vol.185, pp.441–445.

    Google Scholar 

  21. W. A. Fischer and H. vom Ende: . Arch. Eisenhüttenwes, 1950, vol. 21(9+10), pp. 297–304.

    Google Scholar 

  22. W. A. Fischer and H. vom Ende: Arch. Eisenhüttenwes, 1952, vol. 23(1+2), pp. 21–33.

    Google Scholar 

  23. V. V. Averin, A. Y. Polyakov, and A. M. Samarin: Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk., 1955, No. 3, pp. 90.

  24. [24] H. A. Wriedt and J. Chipman: Oxygen in Liquid Iron–Nickel Alloys. Trans. AIME, 1956, vol. 206(September), pp. 1195–1199.

    Google Scholar 

  25. [25] N. A. Gokcen: Equilibria in Reactions of Hydrogen, and Carbon Monoxide with Dissolved Oxygen in Liquid Iron;Equilibrium in Reduction of Ferrous Oxide with Hydrogen, and Solubility of Oxygen in Liquid Iron. Trans. AIME, 1956, vol. 206(November), pp. 1558–1567.

    Google Scholar 

  26. V. V. Averin, A. Y. Polyakov, and A. M. Samarin: Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk, 1957, No. 8, pp. 120.

  27. [27] Y. H. Chou: Physical Chemistry of Deoxidation of Steel. Acta Metall. Sin., 1958, vol. 3(3), pp. 238-252.

    Google Scholar 

  28. [28] T. P. Floridis and J. Chipman: Activity of Oxygen in Liquid Iron Alloys. Trans. Metall. Soc. AIME, 1958, vol. 212(4), pp. 549–553.

    Google Scholar 

  29. K. Gunji and S. Matoba: On the Equilibrium between Mn and O in Molten Iron. Tetsu–to–Hagané, 1959, vol. 45(9), pp. 926–928.

    Google Scholar 

  30. S. Matoba, K. Gunji, and T. Kuwana: Tetsu–to–Hagané, 1959, vol. 45(12), pp. 1328–1334.

    Google Scholar 

  31. [31] H. Sakao and K. Sano: Investigation on the Best Experimental Condition for Equilibrating Hydrogen with Oxygen in Liquid Iron. J. Japan Inst. Met. Mater., 1959, vol. 23(11), pp. 667–70.

    Google Scholar 

  32. H. Schenck and K. H. Gerdom: Arch. Eisenhüttenwes, 1959, vol. 30(8), pp. 451–460.

    Google Scholar 

  33. [33] H. Sakao and K. Sano: Determination of the Equilibrium Constant of the Reaction of Hydrogen with Oxygen in Liquid Iron. J. Japan Inst. Met. Mater., 1959, vol. 23(11), pp. 671–674.

    Google Scholar 

  34. [34] H. Sakao and K. Sano: Equilibrium between Dissolved Oxygen in Liquid Iron and H2-H2O Gas Mixtures. Trans. Japan. Inst. Metals, 1960, vol. 1(1), pp.38–42.

    Article  Google Scholar 

  35. [35] H. Sakao and K. Sano: Activity of Oxygen in Liquid Fe–Ni, Fe-Co and Ni–Co Alloys. J. Japan Inst. Met. Mater., 1962, vol. 26(1), pp. 30–34.

    Google Scholar 

  36. [36] H. Sakao and K. Sano: Activity of Oxygen in Liquid Fe–Ni–Co Alloys. J. Japan Inst. Met. Mater., 1962, vol. 26(1), pp. 34–38.

    Google Scholar 

  37. [37] H. Sakao and K. Sano: Activity and Solubility of Oxygen in Liquid Iron–Chromium Alloy. J. Japan Inst. Met. Mater., 1962, vol. 26(4), pp. 236–240.

    Google Scholar 

  38. [38] H. Sakao and K. Sano: Activity of Oxygen in Liquid Fe–Ni–Cr Alloys. J. Japan Inst. Met. Mater., 1962, vol. 26(9), pp. 596–600.

    Google Scholar 

  39. [39] H. Sakao and K. Sano: Activity of Oxygen in Liquid Fe–Co–Cr and Ni–Co–Cr Alloys. J. Japan Inst. Met. Mater., 1963, vol. 27(4), pp. 147–151.

    Google Scholar 

  40. K. Gunji and S. Matoba: On the Equilibrium between Manganese and Oxygen in Liquid Iron. Tetsu–to–Hagané, 1963, vol. 49(5), pp. 758–764.

    Google Scholar 

  41. [41] E. S. Tankins, N. A. Gokcen, and G. R. Belton: The Activity and Solubility of Oxygen in Liquid Iron, Nickel, and Cobalt. Trans. Metall. Soc. AIME. 1964, vol. 230, pp. 820–827.

    Google Scholar 

  42. S. Matoba and T. Kuwana: Effects of Nickel, Cobalt, Tungsten, Molybdenum, Chromium and Tin on the Activity Coefficient of Oxygen in Liquid Iron: Activity of oxygen in liquid steel–I. Tetsu–to–Hagané, 1965, vol. 51(2), pp. 163–169

    Google Scholar 

  43. S. Matoba and T. Kuwana: Activity of Oxygen in Liquid Iron Alloys Containing Several Kinds of Elements Simultaneously Activity of oxygen in liquid steel–II. Tetsu–to–Hagané, 1965, vol. 51(6), pp. 1114–21

    Google Scholar 

  44. [44] M. T. Hepworth, R. P. Smith, and E. T. Turkdogan: Permeability, Solubility, and Diffusivity of Oxygen in BCC Iron. Trans. Metall. Soc. AIME, 1966, vol. 236, pp. 1278–1283.

    Google Scholar 

  45. [45] K. Schwerdtfeger: Measurements of Oxygen Activity in Iron, Iron-Silicon, Manganese and Iron-Manganese Melts Using Solid Electrolyte Galvanic Cells. Trans. Metall. Soc. AIME, 1967, vol. 239, pp. 1276–1281.

    Google Scholar 

  46. [46] W. A. Fischer and W. Ackermann: Direct electrochemical determination of the oxygen content of metal I-Investigation in iron, cobalt, nickel, and copper melts. Arch. Eisenhüttenwes, 1966, vol. 37(1), pp. 43–47.

    Google Scholar 

  47. J. Chipman: Activity of Interstitial and Nonmetallic Solutes in Dilute Metallic Solution: Lattice Ratio as a Concentration Variable. Trans. Metall. Soc. AIME, (Trans. Metallurgical Society of AIME,) 1967, vol. 239(9), pp. 1332–36.

    Google Scholar 

  48. [48] K. Schwerdtfeger: Measurement of Oxygen Activity in Iron, Iron-Silicon, Manganese and Iron-Manganese Melts Using Solid Electrolyte Galvanic Cells. Trans. Met. Soc. AIME, 1967, vol. 239, pp. 1276-1281.

    Google Scholar 

  49. [49] B. F. Belov, I. A. Novochatskij and Y. A. Lobanov: RUSS Met., 1967,(3), pp. 53-62.

    Google Scholar 

  50. [50] W. A. Fischer and D. Janke: Electrochemical Determination of the Oxygen Partial Pressure in Steam-hydrogen Mixtures and Iron melts Containing Oxygen. Arch. Eisenhüttenwes, 1968, vol. 39(2), pp. 89–99.

    Google Scholar 

  51. [51] H. Schenck, E. Steinmetz, and P. Ch. H. Rhee: Oxygen Activity in the System Iron-oxygen and Possibility of Acting upon It by Means of Added Elements at Steelmaking Temperatures III Action upon the Oxygen Activity by Means of Nickel. Arch. Eisenhüttenwes, 1969, vol. 40(8), pp. 619–620.

    Google Scholar 

  52. [52] W. A. Fischer, D. Janke, and W. Ackermann: Thermodynamics of the Dissolution of Oxygen in Fe-Co, Fe-Ni, Fe-Cu and Co-Ni Melts. Arch. Eisenhüttenwes, 1970, vol. 41(4), pp. 361–367.

    Google Scholar 

  53. [53] W. A. Fischer and G. Pateisky: The Suitability of Solid Metal /Metallic Oxide Mixtures as Reference Potentials in Oxygen Measuring Cell. Arch. Eisenhüttenwes, 1970, vol. 41(7), pp. 661–673.

    Google Scholar 

  54. [54] P. A. Distin, S. G. Whiteway, and C. R. Masson: Solubility of Oxygen in Liquid Iron from 1785 °C to 1960°C. A New Technique for the Study of Slag-Metal Equilibria. Can. Metall. Q., 1971, vol. 10(1), pp. 13–18.

    Article  Google Scholar 

  55. [55] G. K. Sigworth and J. F. Elliott: The Thermodynamics of Liquid Dilute Iron Alloys. Metal Science, 1974, vol. 8(1), pp. 298–310.

    Article  Google Scholar 

  56. [56] D. Janke and W. A. Fischer: Thermochemical Data for the Reactions 2Cr + 3/2O2 = Cr2O3, Mo + O2 = MoO2 and 1/2O2 =[O] in Liquid Iron. Arch. Eisenhüttenwes, 1975, vol. 46(12), pp. 755–60.

    Google Scholar 

  57. [57] N. H. Santander and O. Kubaschewski: The Thermodynamics of the Copper–oxygen System. High Temp-High Press., 1975, vol. 7, pp. 573–582.

    Google Scholar 

  58. [58] W. A. Fischer and J. F. Schumacher: The Solubility of Oxygen in Pure Iron from the Melting Point to 2046 °C, Determined Using the Levitation Melting Method. Arch. Eisenhüttenwes., 1978, vol. 49(9), pp. 431–433.

    Google Scholar 

  59. [59] T. Chiang and Y. A. Chang: The Activity Coefficient of Oxygen in Binary Liquid Metal Alloys. Metall. Trans. B, 1976, vol. 7B(3), pp. 453–467.

    Article  Google Scholar 

  60. [60] R. Y. Lin and Y. A. Chang: The Activity Coefficient of Nitrogen in Binary Liquid Metal Alloys. Metall. Trans. B, 1977, vol. 8B(1), pp. 293–300.

    Article  Google Scholar 

  61. [61] S. H. Kuo and Y. A. Chang: On the Relationships Between the Activity Coefficient of Nonmetallic Solutes in Liquid Metals and Binary Alloys. Metall. Trans. B, 1978, vol. 9B(1), pp. 154–156.

    Article  Google Scholar 

  62. [62] Y.A. Chang and D. C. Hu: On the Gibbs Energy Interaction Parameters of Oxygen and Nitrogen in Liquid Alloys. Metall. Trans. B, 1979, vol. 10B(1), pp. 43–48.

    Article  Google Scholar 

  63. [63] K. T. Jacob: Solubility and Activity of Oxygen in Liquid Manganese. Metall. Mater. Trans. B, 1981, vol. 12B(4), pp. 675–678.

    Article  Google Scholar 

  64. [64] H. S. C. O’Neill: Systems Fe-O and Cu–O: Thermodynamic Data for the Equilibria Fe–’FeO’, Fe–Fe3O4, ‘FeO’– Fe3O4, Fe3O4–Fe2O3, Cu–Cu2O, and Cu2O–CuO from EMF Measurements. Amer. Mineral. (American Mineralogist), 1988, vol. 73(5–6), pp. 470–86.

    Google Scholar 

  65. [65] S. S. Shibaev, P. V. Krasovskii, K. V. Grigorovitch: Solubility of Oxygen in Iron-Silicon Melts in Equilibrium with Silica at 1873 K. ISIJ Int., 2005, vol. 45(9), pp. 1243–47.

    Article  Google Scholar 

  66. S.S. Shibaev and K.V. Grigorovich: J. Phys., 2008, vol. 98, p. 032012. DOI:10.1088/1742-6596/98/3/032012.

    Google Scholar 

  67. C. Wagner: Thermodynamics of Alloys, Addison-Wesley, London, England, 1952, pp. 51-53.

    Google Scholar 

  68. [68] B. Sundman: Modification of the Two-sublattice Model for Liquids. Calphad, 1991, vol. 15(2), pp. 109–119.

    Article  Google Scholar 

  69. [69] J. X. Chen: Handbook of Common Figures, Tables and Data for Steelmaking, 2nd ed., Metallurgical Industry Press. Beijing, 2010.

    Google Scholar 

  70. [70] J. Y. Zhang, Metallurgical Physicochemistry. Metallurgical Industry Press, Beijing, 2004.

    Google Scholar 

  71. [71] X. H. Huang, Principles of Ironmaking and Steelmaking (3rd edition), Metallurgical Industry Press, Beijing, 2005.

    Google Scholar 

  72. [72] S. K. Wei, Thermodynamics of Metallurgical Processes, Science Press, Beijing, 2010.

    Google Scholar 

  73. [73] X. M. Yang, J. S. Jiao, R. C. Ding, C. B. Shi, and H. J. Guo: A Thermodynamic Model for Calculating Sulphur Distribution Ratio between CaO–SiO2–MgO–Al2O3 Ironmaking Slags and Carbon Saturated Hot Metal Based on the Ion and Molecule Coexistence Theory. ISIJ Int., 2009, vol. 49(12), pp. 1828–37.

    Article  Google Scholar 

  74. [74] C. B. Shi, X. M. Yang, J. S. Jiao, C. Li, and H. J. Guo: A Sulphide Capacity Prediction Model of CaO–SiO2–MgO–Al2O3 Ironmaking Slags Based on the Ion and Molecule Coexistence Theory. ISIJ Int., 2010, vol. 50(10), pp. 1362–72.

    Article  Google Scholar 

  75. [75] X. M. Yang, C. B. Shi, M. Zhang, G. M. Chai, and F. Wang: A Thermodynamic Model of Sulfur Distribution Ratio between CaO–SiO2–MgO–FeO–MnO–Al2O3 Slags and Molten Steel during LF Refining Process Based on the Ion and Molecule Coexistence Theory. Metall. Mater. Trans. B, 2011, vol. 42B(6), pp. 1150–80.

    Article  Google Scholar 

  76. [76] X. M. Yang, C. B. Shi, M. Zhang, G. M. Chai, and J. Zhang: A Sulfide Capacity Prediction Model of CaO–SiO2–MgO–FeO–MnO–Al2O3 Slags during LF Refining Process Based on the Ion and Molecule Coexistence Theory. Metall. Mater. Trans. B, 2012, vol. 43B(2), pp. 241–66.

    Article  Google Scholar 

  77. [77] X. M. Yang, J. P. Duan, C. B. Shi, M. Zhang, Y. L Zhang, and J. C. Wang: A Thermodynamic Model of Phosphorus Distribution Ratio between CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 Slags and Molten Steel during Top–Bottom Combined Blown Converter Steelmaking Process Based on the Ion and Molecule Coexistence Theory. Metall. Mater. Trans. B, 2011, vol. 42B(4), pp. 738–70.

    Article  Google Scholar 

  78. [78] X. M. Yang, C. B. Shi, M. Zhang, J. P. Duan, and J. Zhang: A Thermodynamic Model of Phosphate Capacity for CaO–SiO2–MgO–FeO–Fe2O3–MnO–Al2O3–P2O5 Slags Equilibrated with Molten Steel during a Top–Bottom Combined Blown Converter Steelmaking Process Based on the Ion and Molecule Coexistence Theory. Metall. Mater. Trans. B, 2011, vol. 42B(5), pp. 951–76.

    Article  Google Scholar 

  79. [79] X. M. Yang, C. B. Shi, M. Zhang and J. Zhang: A Thermodynamic Model for Prediction of Iron Oxide Activity in Some FeO–Containing Slag Systems. Steel Res. Int., 2012, vol. 83(3), pp. 244–58.

    Article  Google Scholar 

  80. [80] X. M. Yang, M. Zhang, J. L. Zhang, P. C. Li, J. Y. Li, and J. Zhang: Representation of Oxidation Ability for Metallurgical Slags Based on the Ion and Molecule Coexistence Theory. Steel Res. Int., 2014, vol. 85(3), pp. 347–75.

    Article  Google Scholar 

  81. [81] J. Y. Li, M. Zhang, M. Guo, and X. M. Yang: Enrichment Mechanism of Phosphate in CaO–SiO2–FeO–Fe2O3–P2O5 Steelmaking Slags. Metall. Mater. Trans. B, 2014, vol. 45B(5), pp. 1666–82.

    Article  Google Scholar 

  82. [82] X. M. Yang, J. Y. Li, G. M. Chai, M. Zhang, and J. Zhang: Prediction Model of Sulfide Capacity for CaO–FeO–Fe2O3–Al2O3–P2O5 Slags in a Large Variation Range of Oxygen Potential Based on the Ion and Molecule Coexistence Theory. Metall. Mater. Trans. B, 2014, vol. 45B(6), pp. 2118–37.

    Article  Google Scholar 

  83. [83] J. Zhang: Computational Thermodynamics of Metallurgical Melts and Solutions, Metallurgical Industry Press, Beijing, China, 2007, pp. 40–70.

    Google Scholar 

  84. [84] X. M. Yang, M. Zhang, P. C. Li, J. Y. Li, J. L. Zhang, and J. Zhang: A Thermodynamic Model for Representation Reaction Abilities of Structural Units in Fe–S Binary Melts Based on the Atom–Molecule Coexistence Theory. Metall. Mater. Trans. B, 2012, vol. 43B(6), pp. 1358–87.

    Article  Google Scholar 

  85. [85] X. M. Yang, M. Zhang, P. C. Li, J. Y. Li, and J. Zhang: A Thermodynamic Model for Representation Reaction Abilities of Structural Units in Full Composition Range of Fe–Si Binary Melts Based on the Atom–Molecule Coexistence Theory. Steel Res. Int., 2013, vol. 84(8), pp. 784–811.

    Article  Google Scholar 

  86. [86] X. M. Yang, J. Y. Li, P. C. Li, M. Zhang, and J. Zhang: Determination of Activity Coefficients of Elements and Related Thermodynamic Properties of Fe–Si Binary Melts Based on the Atom–Molecule Coexistence Theory. Steel Res. Int., 2014, vol. 85(2), pp. 164–206.

    Article  Google Scholar 

  87. [87] X. M. Yang, P. C. Li, J. Y. Li, J. L. Zhang, M. Zhang, and J. Zhang: Representation Reaction Abilities of Structural Units and Related Thermodynamic Properties in Fe–P Binary Melts Based on the Atom–Molecule Coexistence Theory, Steel Res. Int., 2014, vol. 85(3), pp. 426–460.

    Article  Google Scholar 

  88. X.M. Yang, J.Y. Li, M.F. Wei, and J. Zhang: A Thermodynamic Model for Representation Reaction Abilities of Structural Units in Fe–C Binary Melts Based on the Atom–Molecule Coexistence Theory. (unpublished 2015).

  89. X.M. Yang, J.Y. Li, M.F. Wei, and J. Zhang: Determination and Evaluation of Three Kinds of Activity Coefficients of Carbon and Related Mixing Thermodynamic Properties of Fe–C Binary Melts Based on the Atom–Molecule Coexistence Theory. (unpublished 2015).

  90. [90] The Japan Society for the Promotion of Science, The 19th Committee on Steelmaking: Steelmaking Data Sourcebook, Gordon and Breach Science Publishers, New York, NY, 1988.

    Google Scholar 

  91. [91] R. Zhu, Y. Q. Qiu, and J. Zhang: Calculation Model of Mass Action Concentrations for Fe-C-O Metallic Melts. J. Univ. Sci. Tech. Beijing, 1996, vol. 18(5), pp. 414-418.

    Google Scholar 

  92. [92] S. K. Wei: Application of Activity in Metallurgical Physicochemistry. China Industry Press, Beijing, China, 1964.

    Google Scholar 

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Acknowledgement

This work is supported from the National Natural Science Foundation of China (NSFC) by a Grant of No. 51174186.

Conflict of interest

The authors declare no competing financial interest.

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Authors and Affiliations

  1. State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Xue-min Yang, Jin-yan Li & Meng-fang Wei

  2. School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, 100083, P.R. China

    Jin-yan Li & Jian Zhang

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  1. Xue-min Yang
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Manuscript submitted March 11, 2015.

Appendix

Appendix

The Raoultian activity coefficient \( \gamma_{\text{O}}^{0} \) of O in infinitely dilute Fe-O binary melts can correlate relationship with activity coefficient \( \gamma_{\text{O}} \) and \( f_{{{\% , \text{O}}}} \) of O by Eq. [1a] as[70,71,87,89]

$$ \gamma_{\text{O}}^{0} = \frac{{\gamma_{\text{O}} }}{{f_{{{\% , \text{O}}}} }} \times \frac{{(M_{\text{Fe}} - M_{\text{O}} ) + 100M_{\text{O}} }}{{[{\text{pct O}}](M_{\text{Fe}} - M_{\text{O}} ) + 100M_{\text{O}} }} \quad ( - )$$
(1a)

The dissolving process of ideal O2 into Fe-O binary melts for formation of Fe-O binary melts with [pct O] as 1.0 referred to 1 mass pct as reference state can be represented using chemical potential \( \mu_{{ [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}} }} \) of the dissolved [O] by

$$ \frac{1}{2}{\text{O}}_{2} \left( {\text{g}} \right) = \left[ {\text{O}} \right]_{{\left[ {\%{\text{O}}} \right] = 1.0}};\,\mu_{{ [ {\text{O]}}_{{ [\% {\text{O] = 1}} . 0}} }} = \mu_{{ [ {\text{O]}}}} - 0.5\mu_{{{\text{O}}_{ 2} ( {\text{g)}}}}^{*} (T) = \mu_{{\% , [ {\text{O]}}_{{ [\% {\text{O] = 1}} . 0}} }}^{\Theta } - 0.5\mu_{{{\text{O}}_{ 2} ( {\text{g)}}}}^{*} (T)\;\left( {\text{J/mol}} \right) $$
(A1)

Taking ideal O2 at 101,325 Pa as standard state or 1 mass pct of O as standard state cannot change chemical potential \( \mu_{{ [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}} }} \) of the dissolved [O] in Fe-O binary melts with [pct O] as 1.0 as reference state in Eq. [A1]. Hence, chemical potential \( \mu_{{ [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}} }} \) of the dissolved [O] in Fe-O binary melts with [pct O] as 1.0 as reference state in Eq. [A1] can also be expressed as

$$ \mu_{{ [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}} }} = 0.5\mu_{{{\text{O}}_{ 2} ( {\text{g)}}}}^{ * } (T) + RT\ln a_{\text{R,O}}{{_{{{[\%\text{O] = 1}} . 0}} }} = \mu_{{{\% , [ \text{O]}}_{{{[\%\text{O] = 1}} . 0}} }}^{\Theta } + RT\ln a_{{{\% , \text{O}}_{{{[\%\text{O] = 1}} . 0}} }} \quad {\rm {(J/mol)}} $$
(A2)

The standard molar Gibbs free energy change \( \Delta_{\text{sol}} G_{{{\text{m,0}} . 5 {\text{O}}_{ 2} \to [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}} }}^{{\Theta , {\%}}} \) of dissolving O2 for forming [pct O] as 1.0 as reference state in Fe-O binary melts referred to 1 mass pct as reference state can be formulated through combining Eqs. [A1] and [A2] as

$$ \Delta_{\text{sol}} G_{{{\text{m,0}} . 5 {\text{O}}_{ 2} \to [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}} }}^{\Theta ,\%} \equiv \mu_{{ [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}} }} = \mu_{{{\% , [ \text{O]}}_{{{[\%\text{O] = 1}} . 0}} }}^{\Theta } - 0.5\mu_{{{\text{O}}_{ 2} ( {\text{g)}}}}^{ * } = RT\ln \left( {\frac{{a_{{{\text{R,O}}_{{{[\%\text{O] = 1}} . 0}} }} }}{{a_{{{\% , \text{O}}_{{{[\%\text{O] = 1}} . 0}} }} }}} \right)\quad \left( {{\text{J}}/{\text{mol}}} \right) $$
(A3)

The mole fraction \( x_{\text{O}} \) of O in Fe-O binary melts can be expressed as

$$ x_{\text{O}} = \frac{{{{[{\text{pct O}}]} \mathord{\left/ {\vphantom {{[{\text{pct O}}]} {M_{\text{O}} }}} \right. \kern-0pt} {M_{\text{O}} }}}}{{\frac{{[{\text{pct O}}]}}{{M_{\text{O}} }} + \frac{{100\, - \,[{\text{pct O}}]}}{{M_{\text{Fe}} }}}} = \frac{{[{\text{pct O}}]M_{\text{Fe}} }}{{[{\text{pct O}}](M_{\text{Fe}} - M_{\text{O}} ) + 100M_{\text{O}} }} \quad ( - ) $$
(A4)

Thus, the term \( {{a_{\text{R,O}} } \mathord{\left/ {\vphantom {{a_{\text{R,O}} } {a_{{{\% , \text{O}}}} }}} \right. \kern-0pt} {a_{{{\% , \text{O}}}} }} \) can be expressed by combining Eqs. [1a] and [A4] as[70,71,86]

$$ \frac{{a_{\text{R,O}} }}{{a_{{{\% , \text{O}}}} }} = \frac{{x_{\text{O}} \gamma_{\text{O}} }}{{[{\text{pct O}}]f_{{{\% , \text{O}}}} }} = \frac{{M_{\text{Fe}} }}{{(M_{\text{Fe}} - M_{\text{O}} ) + 100M_{\text{O}} }}\gamma_{\text{O}}^{0} \quad ( - ) $$
(A5)

Equation [A5] means that the term \( {{a_{\text{R,O}} } \mathord{\left/ {\vphantom {{a_{\text{R,O}} } {a_{{{\% , \text{O}}}} }}} \right. \kern-0pt} {a_{{{\% , \text{O}}}} }} \) is independent of oxygen content as mass pct [pct O] or mole fraction \( x_{\text{O}} \) of O in Fe-O binary melts. Therefore, the term \( {{a_{{{\text{R,O}}_{{{[\%\text{O] = 1}} . 0}} }} } \mathord{\left/ {\vphantom {{a_{{{\text{R,O}}_{{{[\%\text{O] = 1}} . 0}} }} } {a_{{{\% , \text{O}}_{{{[\%\text{O] = 1}} . 0}} }} }}} \right. \kern-0pt} {a_{{{\% , \text{O}}_{{{\text{ [\% O] = 1}} . 0}} }} }} \) under the condition of [% O]=1.0 is identical to the term \( {{a_{\text{R,O}} } \mathord{\left/ {\vphantom {{a_{\text{R,O}} } {a_{{{\% , \text{O}}}} }}} \right. \kern-0pt} {a_{{{\% , \text{O}}}} }} \) by

$$ \frac{{a_{{{\text{R,O}}_{{[\% {\text{O}}] = 1.0}} }} }}{{a_{{\% ,{\text{O}}_{{[\% {\text{O}}] = 1.0}} }} }} \equiv \frac{{a_{\text{R,O}} }}{{a_{{\%,{\text{O}}}} }} = \frac{{M_{\text{Fe}} }}{{(M_{\text{Fe}} - M_{\text{O}} ) + 100M_{\text{O}} }}\gamma_{\text{O}}^{0} $$
(A6)

The standard molar Gibbs free energy change \( \Delta_{\text{sol}} G_{{{\text{m,0}} . 5 {\text{O}}_{ 2} \to [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}} }}^{{\Theta , {\%}}} \) of dissolving O2 for forming [pct O] as 1.0 in Fe-O binary melts with [pct O] as 1.0 as reference state in Eq. [A3] can be represented by inserting Eq. [A6] into Eq. [A3] as[70,71,86,89]

$$ \Delta_{\text{sol}} G_{{{\text{m, 0}} . 5 {\text{O}}_{ 2} \to [ {\text{O]}}_{{{\text{ [\% O] = 1}} . 0}} }}^{{\Theta , {\text{ \% }}}} = RT\ln \left( {\frac{{M_{\text{Fe}} }}{{(M_{\text{Fe}} - M_{\text{O}} ) + 100M_{\text{O}} }}\gamma_{\text{O}}^{0} } \right) \quad {\rm {(J/mol)}} $$
(A7)

Consequently, the standard molar Gibbs free energy change \( \Delta_{\text{r}} G_{{{\text{m,O,gas}} - {\text{metal}}}}^{\Theta } \) of dissolving O2 in Fe-O binary melts with [pct O] as 1.0 as standard state in Eq. [5] can be presented under the condition of \( a_{{{\text{R}},{\text{O}}}} \equiv \left( {{{p_{{{\text{O}}_{2} }} } \mathord{\left/ {\vphantom {{p_{{{\text{O}}_{2} }} } {p^{\theta } }}} \right. \kern-0pt} {p^{\theta } }}} \right)^{0.5} \) as

$$ \frac{1}{2}{\text{O}}_{2} \left( {\text{g}} \right) = \left[ {\text{O}} \right]_{{\left[ {\% {\text{O}}} \right] = 1.0}} ;\;\Delta_{\text{r}} G_{{{\text{m,O,gas}} - {\text{metal}}}}^{\Theta } = - RT\ln \left( {K_{\text{O}}^{\Theta ,\% } } \right) = - RT\ln \left( {\frac{{a_{{\% , {\text{O}}}} }}{{\left( {{{p_{{\text{O}_{2} }} } \mathord{\left/ {\vphantom {{p_{{O_{2} }} } {p^{\theta } }}} \right. \kern-0pt} {p^{\theta } }}} \right)^{0.5} }}} \right) = RT\ln \left( {\frac{{a_{\text{R,O}} }}{{a_{{{\% , \text{O}}}} }}} \right)({\text{J/mol}}) $$
(A8)

Thus, \( \Delta_{\text{r}} G_{{{\text{m,O,gas}} - {\text{metal}}}}^{\Theta } \) is identical to \( \Delta_{\text{sol}} G_{{{\text{m,0}} . 5 {\text{O}}_{ 2} \to [ {\text{O]}}_{{{[\%\text{O] = 1}} . 0}}}}^{{\Theta , {\%}}} \) as described in Section II–B–2–(a).

However, atomic percentage of O as [at. pct O] is also applied in numerous literature such as by Chang et al.[59–62] for describing the standard molar Gibbs free energy change \( \Delta_{\text{sol}} G_{{{\text{m,0}} . 5 {\text{O}}_{ 2} \to [ {\text{O]}}_{{{[\text{at}.\%\text{O] = 1}} . 0}} }}^{{\Theta , {\text{at.\%}}}} \) of dissolving O2 for forming [at. pct O] as 1.0 in Fe-O binary melts with [at. pct O] as 1.0 as reference state. Because [at. pct i] is equal to one hundred times of mole fraction \( x_{i} \) of i, i.e., [at. pct i] = \( 100x_{i} \), the term \( {{a_{\text{R,O}} } \mathord{\left/ {\vphantom {{a_{\text{R,O}} } {a_{\text{at.pct,O}} }}} \right. \kern-0pt} {a_{\text{at.\%,O}} }} \) can be described as

$$ \frac{{a_{\text{R,O}} }}{{a_{\text{at.\%,O}} }} = \frac{{x_{\text{O}} \gamma_{\text{O}}^{{}} }}{{[{\text{at. \% O}}]f_{\text{at.\%,O}} }} = \frac{{x_{\text{O}} \gamma_{\text{O}}^{{}} }}{{100x_{\text{O}} f_{\text{at.\%,O}} }} = \frac{ 1}{100} \times \frac{{\gamma_{\text{O}}^{{}} }}{{f_{\text{at.\%,O}}}} \quad ( - ) $$
(A9)

Activity coefficient \( f_{\text{at.\%,O}} \) of O is assumed to be equal to \( f_{{{\% , \text{O}}}} \), the term \( {{\gamma_{\text{O}} } \mathord{\left/ {\vphantom {{\gamma_{\text{O}} } {f_{\text{at.pct,O}} }}} \right. \kern-0pt} {f_{\text{at.\%,O}} }} \) can be derived through Eq. [1a] by

$$ \frac{{\gamma_{\text{O}} }}{{f_{\text{at.\%,O}} }} = \frac{{\gamma_{\text{O}} }}{{f_{{{\% , \text{O}}}} }} = \frac{{[{\text{at. pct O}}](M_{\text{Fe}} - M_{\text{O}} ) + 100M_{\text{O}} }}{{(M_{\text{Fe}} - M_{\text{O}} ) + 100M_{\text{O}} }} \times \gamma_{\text{O}}^{0} \quad ( - ) $$
(A10)

Under the condition of [at. pct O] = 1.0, combining Eqs. [A10] and [A9] produces

$$ \frac{{a_{{{\text{R,O}}_{{ [ {\text{at.\%O] = 1}} . 0}} }} }}{{a_{{{\text{at.\%,O}}_{{ [ {\text{at.\%O] = 1}} . 0}} }} }} = \frac{1}{100} \times \frac{{\gamma_{\text{O}}}}{{f_{\text{at.\%,O}} }} = \frac{{\gamma_{\text{O}}^{0}}}{100}\quad ( - ) $$
(A11)

Consequently, the standard molar Gibbs free energy change \( \Delta_{\text{sol}} G_{{{\text{m,0}} . 5 {\text{O}}_{ 2} \to [ {\text{O]}}_{{{\% [ \text{at.\%O] = 1}} . 0}} }}^{{\Theta , {\text{at.\% }}}} \) of dissolving O2 for forming [at. pct O] as 1.0 in Fe-O binary melts with [at. pct O] as 1.0 as reference state can be derived through inserting Eq. [A11] into Eq. [A3] as[13,14]

$$ \frac{1}{2}{\text{O}}_{2} \left( {\text{g}} \right) = \left[ {\text{O}} \right]_{{\left[{{\text{at}} .\%{\text{O}}} \right] = 1.0}}; \;\Delta_{\text{sol}} G_{{{\text{m}},0.5{\text{O}}_{2} \to [{\text{O}}]_{{ [ {\text{at}} . {\text{\%O] = 1}} . 0}} }}^{{\Theta , {\text{at}} . {\text{\%}}}} = RT\ln \left( {\frac{{\gamma_{\text{O}}^{0} }}{100}} \right)\;\left( {\text{J/mol}} \right) $$
(A12)

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Yang, Xm., Li, Jy., Wei, Mf. et al. Thermodynamic Evaluation of Reaction Abilities of Structural Units in Fe-O Binary Melts Based on the Atom–Molecule Coexistence Theory. Metall Mater Trans B 47, 174–206 (2016). https://doi.org/10.1007/s11663-015-0482-z

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