PROFESSIONAL TECHNICAL AND SCIENTIFIC PAPERS

 

Evaluation of surface tension of mold fluxes containing fluoride

 

 

J.F. Xu^I; PW. Gu^I; L.J. Su^I; J.Y. Zhang^II

^ISchool of Iron and Steel, Soochow University. Suzhou, China. ORCiD: J.F. Xu: http://orcid.org/0000-0002-5753-4041; P.W. Gu: http://orcid.org/0009-0002-6394-1062; L.J. Su: http://orcid.org/0009-0009-1226-2642
^IIState Key Laboratory of Advanced Special Steel. Shanghai University. Shanghai. China. ORCiD: http://orcid.org/0009-0007-5393-1983

Correspondence

 

 

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ABSTRACT

Surface tension of mold flux is a key factor affecting optimum casting conditions. A thermodynamic model was developed to determine the surface tension of mold flux containing fluoride based on the ion and molecule coexistence theory of slag structure and Butler's equation. The relationship between composition and surface tension was investigated by this model. Results indicated that the calculated values showed good agreement with literature data, and the average error was 8.19%. The surface tension value of the CaO-Al2O3-based mold flux was larger than that of the CaO-SiO2-based mold flux. The surface tension in a multi-component system decreased with increasing contents of SiO₂, CaF₂, and Na₂O, which are considered surface-active components. This trend was more significant in the CaO-Al₂O₃-based mold flux.

Keywords: surface tension, mold flux, fluoride, coexistence theory, model

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Introduction

During the continuous casting of steel, the mold flux plays an important role in process performance and product defects, which directly determine the final slab quality (Mills et al., 2005). Typical mold fluxes belong to the conventional CaO-SiO2-based system and the newly developed CaO-Al2O3-based system. CaF₂, MgO, and Na₂O are added to mold flux to modify its properties (Wang et al., 2016). Although the presence of fluoride in mold flux has been identified as a health hazard and correlated to incidences of cancer, it is still widely used because of its remarkable effect on increasing melting point, viscosity, and surface tension. Knowledge of the surface tension of molten slag is useful for understanding various surface or interfacial phenomena in high-temperature processes. Many metallurgical phenomena are closely related to surface tension (Wang et al., 2016). The surface tension of mold flux is a key factor in achieving optimum casting conditions in a continuous casting process, because it affects the interfacial reaction between the mold flux and steel, the absorption of inclusions, and corrosion of the mold nozzle.

The main interest of this work concerns the surface tension of mold flux containing fluoride. Several prior experimental studies were carried out to determine surface tension data for mold fluxes (Mills et al., 2011; Slag Atlas, 1995); however, due to inherent problems and difficulties associated with measurements at high temperature, calculated results have become increasingly important for acquiring such data. It is necessary to have access to reliable models for estimating surface tension. There are many models for estimating surface tension of molten slag (Aune et al., 2002; Cheng and Liao, 1999; Chou and Zhang, 2009; Dong et al., 2014; Mills et al., 2011; Qiao et al., 2001; Xu et al., 2016; Zhang et al., 2003), most of which are proposed based on the structure of atoms and molecules with a physical picture of the practical solution, or combine theoretical considerations with practical thermodynamics. In the present work, based on the ion and molecule coexistence theory of slag structure and Butler's equation, a new thermodynamic model was developed for determining the surface tension of mold flux containing fluoride. The relationship between the composition and surface tension was also investigated, which helps to understand its performance and provide candidates for the design of new mold fluxes.

 

Model for estimating surface tension

A model derived for the estimation of surface tension of ionic mixtures was applied to a six-component molten slag in the CaO-MgO-Al2O3-SiO2-CaF2-Na2O system, which is a typical mold flux containing fluoride for continuous casting. Based on Butler's equation, the surface tension (a) of a mold flux containing fluoride is calculated as follows (Butler, 1932):

where subscript i refers to CaO, MgO, Al₂O₃, SiO₂, CaF_2, or Na₂O in the present work. R is the gas constant, T is the absolute temperature, and Ai = N₀^1/3-V_i^2/3 corresponds to the molar surface area in a monolayer of pure molten component i (N₀ is Avogadro's number, Vi is the molar volume of the pure molten component i). Ni^Surf and N_i^Bulk are the mass action concentrations (activities) of component i in the surface and bulk, respectively.

For surface tension of the CaO-MgO-Al₂O₃-SiO₂-CaF₂-Na₂O system, Equation [1] can be expressed as Equations [2]-[7]:

where the molar volumes of the pure molten components ( Vi) recommended by Mills et al. (2011) are used in the present model, as listed in Table I The surface tension of pure component i is given by σ_i^Pure, and the equations for determining the temperature dependences of surface tension are listed in Table II(Mills et al., 2011; National Institute of Standards and Technology, 1987).

 

 

 

 

Based on the above description, the key points of the model for surface tension calculation are established from the mass action concentrations in the surface (N_i^Surf) and bulk (N_i^Bulk) for the CaO-MgO-Al₂O₃-SiO₂-CaF₂-Na₂O system. The mass action concentrations of the structures in the surface and bulk were calculated by the ion and molecule coexistence theory of slag structure and related diagrams (Slag Atlas, 1995; Zhang, 2001; Zhang, 2003) as follows:

> The structural units of the surface phase of the CaO-MgO-Al2O3-SiO2-CaF2-Na2O system are the same as in the bulk phase of the molten slag, and composed of simple ions (Ca²+, Mg²+, Na²+, O^2-, F^-), simple molecules (Al2O3, SiO2), and complex molecules. At metallurgical temperatures, components such as CaO, MgO, CaF2, and Na2O in molten slag can dissociate to form simple ions. Components such as SiO2 and Al2O3 in molten slag cannot be dissociated due to the predominance of covalent bonds, and thus exist in a molecular state or in the form of complex compounds. The structural units of this system are listed in Table III.

> There are dynamic equilibrium chemical reactions between simple ions, simple molecules, and complex molecules both in the surface and bulk layers.

Taking calcium silicate formation as an example:

> There are dynamic equilibria between ions and molecules both in the surface and bulk layers. The chemical reactions and their thermodynamic parameters are given in Table III (Bale et al., 2002; Turkdogan, 1980; Wu et al., 2014).

> Chemical reactions in molten slags obey the Law of Mass Action in both the surface and bulk layers. Equation [9] can be applied:

where K^θ _2CaO-SiO2 is the chemical reaction equilibrium constant of Equation [9], and can be calculated from AG^θ. The surface mass action concentrations depicted by N_2CaO-SiO2^Sulf,N^Sulf_CaO and N^Sulf_SiO2 are those of 2CaO-SiO₂, ion couples (Ca²++ O^2-), and sio2, respectively; the respective corresponding bulk mass action concentrations are given by N'^Bulk _2CaO-SiO2, N^Bulk_CaO , and N^Bulk_SiO2

The mass action concentrations of the structural unit are defined as the ratio of the equilibrium mole number of structural unit i to the total equilibrium mole numbers of all structural units, calculated by Ni = ni/ Σn_i. The mole numbers of CaO, MgO, Al₂O₃, SiO₂, CaF₂, and Na₂O in 100 g of total slag mass are defined as b₁ = n_CaO, b2 = nMgO, b₃ = n_CaF2, b₄ = n_Na2O, a₁ = n_Al2O3, and a₂ = n_sío2, respectively. The symbols of the mass action concentrations for all structural units are listed as follows: N1 = NCaO, N2 = NMgO, N3 = NAl2O3, N4 = N_siO2, N₅ = N_CaF2, N₆ = N_Na2O. Mass equilibria formulae for the CaO-MgO-Al2O3-SiO2-CaF2-Na2O system are given by Equations [10]-[16]:

Therefore, Equations [10]-[16] are the governing equations of the developed thermodynamic model for calculating mass action concentrations Ni of structural units or ion couples in the CaO-MgO-Al₂O₃-SiO₂-CaF₂-Na₂O system for a certain temperature and components, where N7-N53 can be represented by N1-N6.

> The relationship between surface tension of a melt system and mass action concentrations of surface and bulk components conforms to Butler's equation. The process to estimate the surface tension model is shown in Figure 1; detailed discussions of this method are given by Cheng and Liao (1999) and Xu et al. (2017). For a given slag chemical composition xi and temperature T, the K_i^θ reaction equilibrium constant can be calculated, and then the mass action concentrations in the bulk (N_i^Bulk) can be calculated from the mole fractions of the components and the chemical reaction equilibria constants of complex molecules based on the ion and molecule coexistence theory. Surface tension (σ) and the mass action concentrations in the surface (N_i^Sur ) can be calculated from N_i^Bulk, σ_i^Pure, and A_i based on this theory and Butler's equation.

 

 

Results and discussion

Comparison between estimated values and experimental data

Comparison between the estimated surface tension values and those measured, as reported from the literature, for the CaO-MgO- Al₂O₃-SiO₂-CaF₂-Na₂O related system is shown in Figure 2 The average error (Δ) of all calculated values can be assessed using Equation [17], where the Δ(%) value is calculated by taking the summation of the percentage differences of the calculated and measured values and dividing by the number of data points:

 

 

 

The estimated values using this model were compared with experimental data to verify the model. The result indicated that the estimated values agree with the experimental data (Dou et al., 2009; Slag Atlas, 1995). For all calculated values, the average error A(%) is 8.19%. The detailed average errors for related experimental systems are also shown in Table IV The average error A(%) for the MgO-Al₂O₃-SiO₂-CaF₂ system is about 12.67%, which could be related to the slag composition, which has high CaF2 content and no CaO. The deviation of individual points is also relatively large in the CaO-Al₂O₃-SiO₂-CaF₂-Na₂O system. The larger experimental measurements may be related to the fact that the slag may be in a non-homogeneous region due to its lower basicity (~ 0.45) owing to low CaF₂ and Al₂O₃ contents. The model prediction achieved reasonable accuracy of surface tension variation in the fully liquid phase of the CaO-MgO-Al₂O₃-SiO₂-CaF₂-Na₂O system and its sub-systems.

Surface tension of CaO-SiO₂-based mold flux

Traditional mold flux is based on the CaO-SiO2 system, which has low basicity (CaO/SiO2 mass ratio) and low viscosity, to which fluxing agents such as CaF₂, Na₂O, and B2O3 are added to optimize

the properties. The surface tension of the CaO-SiO2-CaF2 system was evaluated, and the calculated results are shown in Figure 3 The four lines in this figure indicate the calculated results for the iso-surface tensions at 330, 360, 390, and 420 mN/m. Figure 3also shows the boundary of the homogeneous region at 1773 K, calculated using the thermodynamic software FACTSAGE. The result indicates that both CaF₂ content and basicity influence the surface tension. When the CaF2 content was lower than 20%, the effects of basicity and CaF₂ addition on the surface tension were similar; when the CaF2 content was higher than 20%, the basicity had a more significant effect. Figure 4(a) shows the effect of basicity with different Al₂O₃ contents on the surface tension at 1773 K. The results indicate that the surface tension increased with increase of basicity. The trends of surface tension effected by the Al₂O₃ content and basicity were the same. Figure 4(b) shows the effect of the CaF₂ content with different Na₂O contents on the surface tension at 1773 K. The surface tension decreased with increase of CaF₂ content. The trends of surface tension effected by Na₂O content and CaF2 content were also the same, although Na2O had a more significant effect.

 

 

Surface tension of CaO-Al₂O₃-based mold flux

The newly developed CaO-Al₂O₃-based mold flux has a high Al₂O₃ content and relatively low SiO₂ content. This flux shows strong potential for application to continuous casting (Wang et al., 2016). Surface tension of the CaO-Al₂O₃-CaF₂ system was also evaluated, and the calculated results are shown in Figure 5 The five lines in this figure indicate the calculated results for the iso-surface tensions at 360, 390, 420, 450, and 480 mN/m. The boundary of the homogenous phase region at 1773 K, calculated using the thermodynamic software FACTSAGE, is also shown. The surface tension value of the CaO-Al₂O₃-based mold flux is larger than that of the CaO-SiO2-based mold flux. The result also indicates that the surface tension significantly decreased with increase of CaF₂ content. The effects of CaO and Al₂O₃ contents on surface tension are not significant for a given CaF₂ content. CaF₂ addition has a more significant effect on surface tension than the mass ratio of CaO/Al₂O₃. Figure 6(a) shows the effect of the CaO/Al₂O₃ mass ratio for different SiO2 contents on the surface tension at 1773 K. With increase of the CaO/Al₂O₃ mass ratio, the surface tension decreased with increase of SiO₂ content. For the same SiO₂ content, the surface tension slowly increased with increase in the CaO/Al2O3 mass ratio. Figure 6(b) shows the effect of CaF₂ content for different Na₂O contents on the surface tension at 1773 K. The surface tension significantly decreased with CaF2 content, more strongly than that in the CaO-SiO2-based mold flux. The trend of change of surface tension with Na₂O content was the same as that of CaF2 content, but CaF₂ had a more significant effect.

 

 

These results confirm other reports (Mills et al., 2011) that the surface-active components (SiO₂, CaF₂, and Na₂O) preferentially migrate to the surface and cause a sharp decrease in surface tension. In general, on the basis of the additive method widely used for alloys and slags, surface tension of slag depends on the surface tension of the oxides (Mills, 1993). The surface tensions of CaO, MgO, Al2O₃, SiO₂, CaF₂, and Na₂O pure components are 625, 642, 710, 298, 32,8 and 232 mN/m at 1773 K, respectively (Hanao et al., 2007). Because the surface tensions of pure SiO₂, CaF₂, and Na₂O are much lower than those of CaO, MgO, and Al2O3, surface tension of mold flux will decrease with small increases in SiO₂, CaF₂, and

Na₂O contents. For instance, with increasing basicity of the CaO-SiO2-based mold flux, the SiO₂ content will reduce, which could lead to an increase in the slag surface tension. With increasing CaO/ Al₂O₃ mass ratio in the CaO-Al₂O₃-based mold flux, the content of surface-active components is only slightly reduced and surface tension slowly increases.

 

Conclusions

> A thermodynamic model for determining the surface tension of mold flux slag containing fluoride was developed based on the ion and molecule coexistence theory of slag structure and Butler's equation. The results indicated that the surface tension model could fit the experimental data well.

> Surface tension of the CaO-Al2O3-based mold flux is larger than that of the CaO-SiO2-based mold flux. The surface tension in a multi-component system decreased with increasing content of surface-active components: SiO₂, CaF₂, and Na₂O. This effect was more significant in the CaO-Al₂O₃-based mold flux.

>In the CaO-SiO2-based system, the surface tension increased with increasing basicity and Al2O3 content. In the CaO-Al₂O₃-based system, the surface tension slowly increased with increasing CaO/Al2O3 mass ratio and decreased with increasing SiO2 content.

 

Acknowledgements

This work was supported by Project no. 51704201, sponsored by the National Natural Science Foundation of China. English editing of this manuscript was carried by Kathryn C. Sole (PhD).

 

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Correspondence:
J.F. Xu
Email: xujifangsuda@163.com

Received: 5 Aug. 2020
Revised: 10 Feb. 2024
Accepted: 15 May 2024
Published: December 2024