INTRODUCTION

One of the main tasks of modern metallurgy regarding the achievement of the required properties of metal at minimum expenses for its production are discussed.

The required steel parameters can be provided by means of multi-stage production including the following [1]:

— preliminary refining (sulfur removal from cast iron);

— main refining (oxidation of impurities in steel making unit);

— additional refining (sulfur removal in ladle furnace unit (LFU) by its conversion into slag);

— degassing (removal of gases dissolved in metal).

Ladle metallurgy is one of the final stages. Its main task is finishing of liquid metal to preset and homogeneous chemical composition, required temperature, high purity in terms of non-metallic and harmful impurities [1–5].

One of the impurities that cause deterioration of service properties of steel is sulfur. Hence, the issue of its removal from metal is an urgent practical task [1, 2, 6–16].

The aim of this work is analysis of sulfur removal in LFU.

EXPERIMENTAL

The coefficient of sulfur distribution between metal and slag is determined as follows [17]:

$${{L}_{{\text{S}}}} = \frac{{({\text{S)}}}}{{[{\text{S}}]}} = {{C}_{{\text{S}}}}{{\gamma }_{{[{\text{S}}]}}}\frac{1}{{p_{{\{ {{{\text{O}}}_{2}}\} }}^{{\frac{1}{2}}}}}\frac{1}{{{{K}_{{[{\text{S}}]}}}}},$$
(1)

where CS is the sulfide capacity of slag; γ[S] is the coefficient of sulfur activity in metal; \(p_{{\{ {{{\text{O}}}_{2}}\} }}^{{0.5}}\) is the oxidation potential of medium; and K[S] is the equilibrium constant of sulfur distribution between metal and slag.

The coefficient of sulfur distribution in metal, the oxidation potential of medium, the equilibrium constant of sulfur distribution between metal and slag are sufficiently studied and available on publications [1, 18–21].

The sulfide capacity of slags CS is one of the most important properties of refining power of slags used upon extra furnace treatment of steel. This property is determined as a function F of temperature and composition of slag. Thus, it is determined experimentally and estimated thermodynamically [17].

One of the factors influencing in sulfide capacity is temperature.

It was studied in [22] how temperature influences the changes of sulfide capacity as a function of optical basicity (Fig. 1).

Fig. 1.
figure 1

Sulfide capacity log CS as a function of optical basicity at different temperatures.

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According to the data in [20], the sulfide capacity of slag at any temperature om the range of 1400–1700°C can be determined as follows:

$$\log {\kern 1pt} {{C}_{{\text{S}}}} = \frac{{22{\kern 1pt} 690{\kern 1pt} - {\kern 1pt} 54{\kern 1pt} 640\Lambda }}{T} + 43.6\Lambda - 25.2.$$
(2)

During estimation of sulfur coefficient, it was determined that the error of Eq. (2) with regard to the plots (Fig. 1) is more than 15%. Thus, this equation can hardly be applied for accurate theoretical estimations.

In mathematical terms, the plots (Fig. 1) can be described as follows [23]:

$${\text{log}}{\kern 1pt} {{C}_{{\text{S}}}} = 14.3\Lambda - 7.01 - \frac{{9908.1}}{T}.$$
(3)

The range of 1400–1650°C at the optical density Λ not higher than the error of the presented equation does not exceed 6%.

As the criterion of oxide melt basicity, the optical basicity is mostly used, which is characterized as the ability of oxygen anions in the slag to give their electrons to acceptor ions (probing ions) [24]. For the systems comprised of pure oxides, the optical basicity Λ is related with electronegativity of elements according to Pauling (Xi) as follows [24]:

$${{\Lambda }_{i}} = \frac{1}{{1.36({{X}_{i}} - 0.26)}}.$$
(4)

In previous works, it was determined that for the systems comprised of pure oxides, the optical basicity Λ is related with electronegativity of elements according to Pauling (Xi) as follows [22]:

$${{\Lambda }_{i}} = \frac{{0.75}}{{{{X}_{i}} - 0.25}}.$$
(5)

Application of Eqs. (4) and (5) allows to determine the optical basicity for any multicomponent systems comprised of non-transition (non-amphoteric) metals using the following equation [23, 24]:

$$\begin{gathered} \Lambda = \sum\limits_{i = 1}^n {({{X}_{i}}{{\Lambda }_{i}}) = {{X}_{{Me{{{\text{O}}}_{1}}}}}{{\Lambda }_{{Me{{{\text{O}}}_{1}}}}} + {{X}_{{Me{{{\text{O}}}_{2}}}}}{{\Lambda }_{{Me{{{\text{O}}}_{2}}}}}} \\ + \ldots + {{X}_{{Me{{{\text{O}}}_{n}}}}}{{\Lambda }_{{Me{{{\text{O}}}_{n}}}}}, \\ \end{gathered} $$
(6)

where Xi is the equivalent portion of ions introduced by this component; Λ is the optical basicity of the component.

Optical basicity is characterized by the ability of oxygen anions to give their electrons to acceptor ions [24]. In terms of ionic structure of slags, the basicity is the existence of free oxygen anions. In both cases, the slag basicity is determined by the existence of free oxygen anions or their activity in molten oxides [24–26].

According to the data in [18, 24, 26], molten oxide can be presented as a packing of oxygen anions (O2–), between which other components of the melt are located: cations Ca2+, Mg2+, SiO4+, Al3+, and others. The cations are characterized by a significantly different force of electrostatic field in comparison with each other.

The cations of acidic oxides (Si4+, P5+, B3+) are characterized by the highest force of electric field (the lowest radius at higher charge). Thus, they attract more intensively negatively charged oxygen ions O2–, forming complex anions of \({\text{SiO}}_{4}^{{4 - }}\) type. The oxygen anions in the considered complexes do not participate in chemical reaction. Thus, the refining power of slag decreases [26].

Metal cations Ca2+, Mg2+, not possessing high electrostatic force (higher radius at lower charge), are not capable to form stable complex anions. Thus, the addition of basic oxides into slag leads to an increase in the content of free oxygen anions and an increase in the refining power of slag.

Cations Al3+, possessing electrostatic field of medium force, can exhibit both basic and acidic properties depending on the slag composition.

Considering the structure of metallurgical slags, let us estimate the optical basicity as follows:

$$\Lambda = \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{\Lambda }_{i}})}}_{{{\text{bas}}}}}} - \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{\Lambda }_{i}})}}_{{{\text{acid}}}}}} + {{X}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}{{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}},$$
(7)

where Xi is the equivalent portion of ions added by this component; Yi is the interaction parameter of the considered oxide related with electronegativity of elements according to Pauling; and \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) is the interaction parameter of Al2O3.

The proposed equation accounts for the influence of basic and acidic oxides as well as the existence of Al2O3.

For basic and acidic oxides, the optical basicity has been determined. Also, it is known for amphoteric oxides. However, as shown in [25], Al2O3 can exhibit both basic and acidic properties. Thus, the optical basicity will change respectively depending on the slag composition.

In order to calculate the rational composition of slag induced in LFU, it is required to analyze the changes of properties of Al2O3.

In steel-making ladle upon treatment in LFU, the free running highly basic slags are induced of the following chemical composition [25]: 45.0–61.9 (54.0)% CaO; 10.0–30.2 (22.1)% SiO2; 1.8–29.6 (13.5)% Al2O3; 2.1–9.8 (7.3)% MgO; less than 1.0% FeO; and less than 1.0% MnO (average value in brackets).

In order to determine the interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\), the heats in LFU were analyzed. For each selected heat, the following estimations were made:

— \({{L}_{{{{{\text{S}}}_{{{\text{act}}}}}}}}\)—the actual coefficient of sulfur distribution in metal;

— γ[S]—the coefficient of sulfur activity in metal;

— \(p_{{\{ {{{\text{O}}}_{2}}\} }}^{{0.5}}\)—the oxidation potential of medium;

— K[S]—the equilibrium constant of sulfur distribution between metal and slag;

— CS—the sulfide capacity of slag (calculated so that \({{L}_{{{{{\text{S}}}_{{{\text{act}}}}}}}}\) = \({{L}_{{{{{\text{S}}}_{{{\text{theor}}}}}}}}\) due to the change in the interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\)).

The estimated and actual indices are summarized in Table 1.

Table 1.   Estimated and real indices of selected heats
Full size table

RESULTS AND DISCUSSION

Following data in Fig. 2, the interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) is high in the slags comprised completely only of the homogeneous phase. In the heterogeneous slags, the interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) is lower than in the homogeneous slags. This can be attributed to the fact that a deficit of basic oxide CaO (the main source of free oxygen anions) exists in the homogenous slags. Under the considered conditions, Al2O3 starts to exhibit more basic properties rather than acidic ones. Therefore, in the homogeneous slags, the interaction parameter of aluminum oxide is higher.

Fig. 2.
figure 2

Interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) as a function of slag type and content of Al2O3 in it: () homogenous slag; () heterogeneous slag.

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With an increase in the Al2O3 content in the slags, its interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) decreases. When its content in the slag is in excess of 30%, this oxide exhibits acidic properties, which agrees well with the laboratory results [25].

Considering significant discrepancy in the refining properties of the considered slags, it is required to analyze separately the changes of interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) for homogeneous and heterogeneous slags.

The estimated optical basicity \({{\Lambda }_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) of heterogeneous slags is illustrated in Fig. 3.

Fig. 3.
figure 3

Interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) as a function of content of Al2O3 in homogeneous constituent of heterogeneous slag.

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With an increase in the Al2O3 content in slag, its interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) decreases, which can be determined as follows:

$$Y_{{{\text{A}}{{{\text{l}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{3}}}}}}^{{{\text{hetero*}}}} = - 0.0365({\text{A}}{{{\text{l}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{3}}}}) + 1.013,$$
(8)

where (Al2O3) is the oxide content in homogeneous constituent of metallurgical slag.

The optical basicity of heterogeneous slags induced in LFU can be determined as follows:

$$\begin{gathered} \Lambda = \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{Y}_{i}})}}_{{{\text{bas}}}}}} - \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{Y}_{i}})}}_{{{\text{acid}}}}}} \\ + {{X}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\left( { - 0.0365\left( {{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}} \right) + 1.013} \right). \\ \end{gathered} $$
(9)

The estimations of the interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) of homogeneous slags are illustrated in Fig. 4.

Fig. 4.
figure 4

Interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) as a function of alumina content in homogeneous slag.

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According to the data in [25], it is known that it exhibits basic properties at the Al2O3 content up to 16% in the slag. Hence, for the considered conditions, we assume maximum (0.8) values of the interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) (Fig. 4). Then, the total optical basicity of the molten slag under these conditions will be determined for homogeneous slags by the following equations:

$$\Lambda _{{{\text{homo}}}}^{{*0 - 16}} = \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{Y}_{i}})}}_{{{\text{bas}}}}}} - \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{Y}_{i}})}}_{{{\text{acid}}}}}} + {{0.8}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}},$$
(10)
$$\begin{gathered} \Lambda _{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}^{{{\text{homo}}}} = - 0.0069{{({\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}})}^{2}} \\ + \,\,0.2175({\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}) - 0.9338, \\ \end{gathered} $$
(11)
$$\begin{gathered} \Lambda _{{{\text{homo}}}}^{{*16 - 36}} = \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{Y}_{i}})}}_{{{\text{bas}}}}}} - \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{Y}_{i}})}}_{{{\text{acid}}}}}} + {{X}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}} \\ \times \,\,\left( { - 0.0069{{{({\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}})}}^{2}} + 0.2175({\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}) - 0.9338} \right), \\ \end{gathered} $$
(12)
$$\Lambda _{{{\text{homo}}}}^{{*36}} = \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{Y}_{i}})}}_{{{\text{bas}}}}}} - \sum\limits_{i = 1}^n {{{{({{X}_{i}}{{Y}_{i}})}}_{{{\text{acid}}}}}} - {{X}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}.$$
(13)

Equation (10): at Al2O3 content up to 16%; Eqs. (11), (12): at Al2O3 content in the range of 16–36%; Eq. (13): at Al2O3 content higher than 36%.

If the Al2O3 content in the slag is higher than 16%, then it starts to decrease basic properties. At the Al2O3 content in the range from 16 to 36%, the interaction parameter \({{Y}_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) of the considered oxide will vary according to Eq. (11) and total optical basicity of the molten slag will be determined by Eq. (10).

At the Al2O3 content in the slag higher than 36%, this oxide will exhibit only acidic properties and total optical basicity will be determined by Eq. (13). However, for more accurate estimations, the equation should be refined.

Equations (9)–(13) allow to determine optical basicity of the slag in LFU and to estimate its rational composition required for refining processes.

CONCLUSIONS

Theoretical estimations carried out for actual heats demonstrate that the sulfide capacity can be reasonably determined by the ionic theory of slags. The changes of optical basicity \({{\Lambda }_{{{\text{A}}{{{\text{l}}}_{2}}{{{\text{O}}}_{3}}}}}\) have been determined at various slag composition. A known value of optical basicity allows to determine sulfide capacity of slag, distribution coefficient of sulfur between metal and slag, and, respectively, final content of sulfur in metal.