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

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Abstract

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.

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Abbreviations

\( \Delta g_{ij} \) :

Gibbs energy change for the formation of two moles of (i–j) 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 (–)

K :

The equilibrium constant (–)

\( n_{i} \) :

Number of moles of i (mol)

\( n_{ij} \) :

Number of moles of (i–j) pairs (mol)

R:

Gas constant (8.314 J/mol K)

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

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

T :

Absolute temperature (K)

\( X_{i} \) :

Mole fraction of i (–)

\( X_{ij} \) :

Pair fraction of (i–j) pairs (–)

\( Y_{i} \) :

Coordination-equivalent fraction of i (–)

\( Z_{i} \) :

Coordination number of i (–)

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

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

\( \kappa \) :

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

MQM:

Modified Quasichemical Model

SRO:

Short-Range Ordering

CALPHAD:

CALculation of PHAse Diagram

WIPF:

Wagner’s Interaction Parameter Formalism

JSPS:

Japan Society for the Promotion of Science

UIPF:

Unified Interaction Parameter Formalism

FNN:

First-Nearest Neighbor

EMF:

Electro Motive Force

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Acknowledgment

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

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Author notes

  1. Min-Kyu Paek (Graduate Student, Post-Doc.)

    Present address: Department of Mining and Materials Engineering, McGill University, Montreal, QC, H3A 2B2, Canada

Authors and Affiliations

  1. Department of Materials Engineering, Hanyang University, ERICA, Ansan, 426-791, Republic of Korea

    Min-Kyu Paek (Graduate Student, Post-Doc.) & Jong-Jin Pak (Professor)

  2. Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Pohang, Kyungbuk, 790-784, Republic of Korea

    Youn-Bae Kang (Associate Professor)

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  1. Min-Kyu Paek
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Correspondence to Youn-Bae Kang.

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Manuscript submitted November 20, 2014.

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Paek, MK., Pak, JJ. & Kang, YB. Aluminum Deoxidation Equilibria in Liquid Iron: Part II. Thermodynamic Modeling. Metall Mater Trans B 46, 2224–2233 (2015). https://doi.org/10.1007/s11663-015-0369-z

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