Metallurgical and Materials Transactions B

, Volume 46, Issue 5, pp 2224–2233 | Cite as

Aluminum Deoxidation Equilibria in Liquid Iron: Part II. Thermodynamic Modeling

  • Min-Kyu Paek
  • Jong-Jin Pak
  • Youn-Bae KangEmail author


Al deoxidation equilibria in liquid iron over the whole composition range from very low Al ([pct Al] = 0.0027) to almost pure liquid Al were thermodynamically modeled for the first time using the Modified Quasichemical Model in the pair approximation for the liquid phase. The present modeling is distinguished from previous approaches in many ways. First, very strong attractions between metallic components, Fe and Al, and non-metallic component, O, were taken into account explicitly in terms of Short-Range Ordering. Second, the present thermodynamic modeling does not distinguish solvent and solutes among metallic components, and the model calculation can be applied from pure liquid Fe to pure liquid Al. Therefore, this approach is thermodynamically self-consistent, contrary to the previous approaches using interaction parameter formalism. Third, the present thermodynamic modeling describes an integral Gibbs energy of the liquid alloy in the framework of CALPHAD; therefore, it can be further used to develop a multicomponent thermodynamic database for liquid steel. Fourth, only a small temperature-independent parameter for ternary liquid was enough to account for the Al deoxidation over wide concentration (0.0027 < [pct Al] < 100) and wide temperature range [1823 K to 2139 K (1550 °C to 1866 °C)]. Gibbs energies of Fe-O and Al-O binary liquid solutions at metal-rich region (up to oxide saturation) were modeled, and relevant model parameters were optimized. By merging these Gibbs energy descriptions with that of Fe-Al binary liquid modeled by the same modeling approach, the Gibbs energy of ternary Fe-Al-O solution at metal-rich region was obtained along with one small ternary parameter. It was shown that the present model successfully reproduced all available experimental data for the Al deoxidation equilibria. Limit of previously used interaction parameter formalism at high Al concentration is discussed.


Liquid Alloy Liquid Iron Optimize Model Parameter Ternary Parameter Pair Fraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


\( \Delta g_{ij} \)

Gibbs energy change for the formation of two moles of (ij) pairs (J/mol)

\( \Delta S^{\text{config}} \)

Configurational entropy of mixing (J/mol K)

[pct i]

Mass percent of i (–)

\( a_{i} \)

Raoultian activity of i (–)

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

Wagner’s first-order interaction parameter of j on i (–)

\( f_{i} \)

Henrian activity coefficient of i in mass pct scale (–)

\( g_{i}^{^\circ } \)

Molar Gibbs energy of pure component i (J/mol)

\( h_{i} \)

Henrian activity of i in mass pct scale (–)


The equilibrium constant (–)

\( n_{i} \)

Number of moles of i (mol)

\( n_{ij} \)

Number of moles of (ij) pairs (mol)


Gas constant (8.314 J/mol K)

\( r_{i}^{j} \)

Wagner’s second-order interaction parameter of j on i (–)


Absolute temperature (K)

\( X_{i} \)

Mole fraction of i (–)

\( X_{ij} \)

Pair fraction of (ij) pairs (–)

\( Y_{i} \)

Coordination-equivalent fraction of i (–)

\( Z_{i} \)

Coordination number of i (–)

\( Z_{ij}^{i} \)

Coordination number of i in ij binary solution when all nearest neighbors of an i are j’s

\( \kappa \)

Holcomb and Pierre’s model parameter for the exponential function,[63] (–)


Modified Quasichemical Model


Short-Range Ordering


CALculation of PHAse Diagram


Wagner’s Interaction Parameter Formalism


Japan Society for the Promotion of Science


Unified Interaction Parameter Formalism


First-Nearest Neighbor


Electro Motive Force



This study was supported by a Grant (NRF-2013K2A2A2000634) funded by the National Research Foundation of Korea, Republic of Korea.


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2015

Authors and Affiliations

  1. 1.Department of Materials EngineeringHanyang UniversityAnsanRepublic of Korea
  2. 2.Graduate Institute of Ferrous TechnologyPohang University of Science and TechnologyPohangRepublic of Korea
  3. 3.Department of Mining and Materials EngineeringMcGill UniversityMontrealCanada

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