Thermodynamic assessment of conditions for co-reduction of zinc and iron by carbon from oxides of concentrates and waste from metallurgical enterprises

Reaction (3) is achieved at 550 °C when the carbon monoxide content (in the gas phase composed of CO and СО₂) is approximately 50 %. At 640 °C, the equilibrium P_CO is roughly 0.4. At higher temperatures, reaction (3) can occur at low concentrations of carbon monoxide (CO): at 1000 °С 1000 °С P_CO ≈ 0.2 atm; at 1200 °С P_CO ≈ 0.1 atm [7].

At the third stage, reduction of iron from wustite with carbon monoxide CO occurs through the reaction

this reduction process takes place at elevated concentrations of carbon monoxide CO in the gas phase. Specifically, at 700 °С P_CO ≥ 0.6 atm, СО:СО₂ ≈ 1.5; at 400 °С P_CO ≥ 0.68 atm, СО:СО₂ ≈ 2; at 1300 °С P_CO ≥ 0.76 atm, СО:СО₂ ≈ 2.7 [8]).

The reduction of zinc from oxide occurs through the reaction

however, this process is intricate due to intense zinc evaporation and the formation of α-Fe – Zn solid solutions and Fe – Zn melts.

In the presence of solid carbon or the potential for its formation during the decomposition of carbon monoxide (CO), the reduction of oxides at all stages can be achieved through direct contact interaction with solid carbon, known as direct reduction. Thermodynamically, this process is more favorable; however, its efficient implementation requires fine grinding and thorough mixing of the reagents to maximize the interaction surface. The composition of the equilibrium gas phase in this case is constrained by the equilibrium of the Boudoir reaction

For the practical implementation of carbon-thermal reduction technologies, it is crucial to determine the parameters of phase-chemical interactions occurring at the third and final stage of the process.

The thermodynamic analysis was based on the following initial data: one of the latest versions of the state diagram of the iron–zinc system [9], which notably differs from those previously presented in reference literature (refer to Fig. 1 in [10]); the phase chemical equilibrium diagram of the Fe – С – О system (see Fig. 4 in [11]); and reference data concerning the thermodynamic properties of iron, zinc, and carbon oxides [12 – 14].

According to the state diagram of Fe – Zn alloys [9], zinc undergoes melting at a temperature of 419.6 °C (forming a eutectic with less than 0.1 % Fe at 419.4 °C). As the temperature increases to 531 °C, the solubility of iron in the zinc melt rises, reaching approximately 2.5 %. Upon exceeding the equilibrium iron concentrations, a solid solution, known as the ζ phase (Zn ≈ 94 ÷ 97 %), precipitates from the melt. At 531 °C, the ζ phase undergoes decomposition through a peritectic reaction, giving rise to the δ₁ phase (solid solution Zn ≈ 88 ÷ 92 %). The δ₁ phase coexists with the “Г₁” phase (81 – 86 % Zn), until 550 °C, at which point it decomposes, forming the “Г” phase. The “Г” phase coexists with the δ and α-iron phases up to 667 – 780 °С. In the temperature range of 667 – 780 °C, it coexists with α-ferrite and a liquid melt containing iron ranging from 2.5 to 8.5 %. At 780 °C, the “Г” phase undergoes decomposition through a peritectic reaction into a liquid melt containing approximately 8 % iron and a solid solution based on α ferrite with a zinc content of 46 %. At temperatures lower (300 °C) and higher (up to 1535 °C), the zinc content in the ferrite solution decreases nearly to zero. Consequently, the region of Fe – Zn solid solutions extends within the range of zinc concentrations of 0 – 46 % in the solution and temperatures of 0 – 1535 °C. Additionally, there exists a broader two-phase region, encompassing iron-based solid solutions containing 0 – 46 % Zn and liquid Fe – Zn melts with a zinc content ranging from 0 (at 153 °C) to 92 % (at 780 °С).

Fe – Zn solid solutions based on α ferrite undergo a magnetic transformation within the temperature range of 769 °C (0 % Zn) to 623 °C (20 % Zn).

Zinc exhibits high vapor elasticity, and its vapor pressure above pure zinc follows the equation

according to this equation \(P_{\rm{Zn}}^{\rm{o}} \) = 0.1 atm at 720 °С, \(P_{\rm{Zn}}^{\rm{o}} \) = 1 atm at 907 °С, \(P_{\rm{Zn}}^{\rm{o}} \) = 10 atm at 1183 °С, \(P_{\rm{Zn}}^{\rm{o}} \) = 57 atm at 1500 °С. Equilibrium zinc vapor pressures above solid solutions of α-Fe – Zn and melts vary in accordance with changes in the activity of zinc in them and temperature, described by the equation a_ZnO = f (x_Zn, T).

Due to the lack of data on the activities of components in the Fe – Zn system, the Fe – Cu system was employed as a prototype. In the Fe – Cu system, a broad range of solid solutions based on α-Fe – Cu ferrite (Cu ≈ 0 ÷ 8 %) exists, bordering in the temperature range of 1094 – 1484 °C with an even wider two-phase region: solid solution (α-Fe) – melt (Cu = 8_{(1484 °С)} ÷ 97_(1094 °) %) [10]. Substantial positive deviations from Raoult’s law are observed in Fe – Cu melts. At 1550 °C in Fe – Cu melts with a copper content of 0 – 4 % γ_Cu = 10.1. With an increase in the concentration of copper in the melt, the activity of copper decreases: at x_Cu = 0.1 (10 %) – γ_Cu = 5.4, a_Cu = 0.56; at x_Cu = 0.2 (18 %) – γ_Cu = 13.8, a_Cu = 0.71; at x_Cu = 0.4 (37 %) – γ_Cu = 2.0, a_Cu = 0.8; at x_Cu = 0.8 (70 %) – γ_Cu = 1.2, a_Cu = 0.89 [15]. It is noteworthy that in homogeneous melts with positive deviations from Raoult’s law, these positive deviations increase as the temperature decreases. When the concentration dependence lines reach a_i = f (x_i, T) = const for compositions corresponding to x_i of the liquidus at a given temperature, the values of a_i within the two-phase region remain constant until the x_i of the solidus is reached. Simultaneously, positive deviations from Raoult’s law increase even more. Furthermore, the activity of components in a homogeneous solid solution decreases as their concentration in the solution decreases.

The values of activities and activity coefficients of zinc in Fe – Zn solid solutions and melts, as per these assumptions, are depicted in Fig. 2.

In melts with high zinc content (more than 50 %), zinc activity coefficients exhibit minimal deviation from unity, and zinc activities demonstrate slight positive deviations from Raoult’s law. In solid solutions with a zinc content ranging from 5 to 25 % and temperatures between 1000 and 1400 °C, the activity of zinc varies from 0.5 to 0.9, and the activity coefficients are γ_Zn = 5 ÷ 9, indicating substantial positive deviations from Raoult’s law.

Consequently, even above solid solutions (α-Fe, Zn) containing relatively small amounts of zinc (5 – 10 %), the vapor pressure of zinc is substantial. The equilibrium values of zinc activities in solid solutions and melts, along with the vapor pressure of zinc above solid solutions, are plotted on the state diagram of the Fe – Zn system (Fig. 1). Based on the provided data, it can be inferred that at a zinc content in the α-iron solid solution of 5 – 10 %, the vapor pressure of zinc at t ≈ 1050 °C reaches 0.5 atm, and at 1300 °C, it surpasses 1 atm. As the zinc concentration in the solid solution increases, the vapor pressure of zinc also increases. For instance, t ≈ 1050 °C, it attains 0.1 atm and 0.5 atm at 5 and 20 % zinc content, respectively.

The outcomes of thermodynamic analysis of the reduction of iron and zinc from oxides are depicted in Fig. 3 as dependences of the functions ΔG° = f (T), reduced to 1 mole of oxygen in the initial gas phase for oxide formation reactions, and the corresponding number of moles of the initial oxide for reduction reactions.

The reduction of iron from wustite by carbon monoxide CO through reaction (4)

initiates at 580 °C in the absence of solid carbon (point F in Fig. 3, where the lines ΔG° = f (T) for reactions (6) and (7) intersect):

For reaction (4) at t = 580 °С \(\Delta G_{\rm{(4)}}^{\rm{o}} \) = 0 (point F′), P_CO:P_CO2 = 1, P_O2 ≈ 10\(^-\)²⁵ atm; at t = 1200 °С \(\Delta G_{\rm{(4)}}^{\rm{o}} \) = –25 kJ; at t = 1500 °С \(\Delta G_{\rm{(4)}}^{\rm{o}} \) = –55 kJ.

The reduction of zinc from zincite by carbon monoxide CO through reaction (5)

commences at higher temperatures. For the point L′ in Fig. 3 t_start ≈ 1320 °С, \(\Delta G_{\rm{(5)}}^{\rm{o}} \) = 0, P_O2 ≈ 10\(^-\)¹⁰ atm; at t = 1500 °С \(\Delta G_{\rm{(5)}}^{\rm{o}} \) = –55 kJ. At t = 1500 °С the lines ΔG° = f (T) for reactions (4) and (5) at intersect at \(\Delta G_{\rm{(4)}}^{\rm{o}} \) = \(\Delta G_{\rm{(5)}}^{\rm{o}} \) = –55 kJ (point D in Fig. 3).

At temperatures lower than 1500 °С \(\Delta G_{\rm{(4)}}^{\rm{o}} \) < \(\Delta G_{\rm{(5)}}^{\rm{o}} \), at t ˃ 1500 °С \(\Delta G_{\rm{(5)}}^{\rm{o}} \) < \(\Delta G_{\rm{(4)}}^{\rm{o}} \). It can be assumed that in the temperature range of 1320 – 1500 °С, under the conditions of a reducing atmosphere required for the production of iron metal by reaction (1) – (P_CO:P_CO2 > 1, P_O2 < 10\(^-\)⁸ atm), reduced iron can act as a zinc-reducing agent from zincite. At higher temperatures, zinc vapor can reduce iron from wustite:

(8)

Thus, the reduction of zinc from zincite by carbon monoxide CO is possible only at temperatures above 1320 °C (400 °C above the boiling point of zinc), with zinc obtained only in the vapor state. In practice, reactions (4), (5), and (8) proceed in parallel, and the reduced iron acts as a catalyst for reaction (5). The practical realization of the indirect reduction process is not realistic due to the low values of ΔG° for reactions (4), (5), (8).

The processes of iron and zinc reduction from oxides by solid carbon are governed by reactions (9) and (10):

The initiation of reduction for reaction (9) is characterized in Fig. 3 by point A: the intersection of lines ΔG° = f (T) for reactions (6) and (11):

for reaction (10), it is marked by point K: the intersection of lines ΔG° = f (T) for reactions (11) and (12):

Parameters of point А: t_start ≈ 650 °С, P_CO:P_CO2 ≈ 1.1, P_O2 ≈ 10\(^-\)²¹ atm; \(\Delta G_{\rm{(9)start}}^{\rm{o}} \) = 0 (point А′); for point K: t_start ≈ 960 °С (approximately 330 °С lower than for reaction (5)), P_CO:P_CO2 ≈ 10², P_O2 ≈ 10\(^-\)¹⁹ atm; \(\Delta G_{\rm{(10)start}}^{\rm{o}}\) = 0 (point K′).

Above 960 °C, in the entire temperature range, reaction (9) has a significant advantage over reaction (10) (\(\Delta G_{\rm{(9)}}^{\rm{o}} \) – \(\Delta G_{\rm{(10)}}^{\rm{o}} \) = –80 kJ).

During the co-reduction of iron and zinc, the presence of carbon facilitates the formation of the ternary carbide Fe₃ZnC [12]. This carbide coexists at temperatures of at least 780 °C with α-iron (with a zinc content in a solid solution based on α-iron lower than 46 % and carbon higher than 4 %) and the “Г” phase with a zinc content of 71 – 74 %. The “Г” phase decomposes at 780 °C through a peritectic reaction (13) with the formation of α-iron and a liquid phase containing approximately 7 % Fe, 89 % Zn, 4 % C:

The presence of carbon restricts the reduction processes by limiting the composition of the gas phase (CO:CO₂ ratio) in accordance with the equilibrium constant of the Boudoir reaction (6).

The presented volumetric diagram (Fig. 4, face A) indicates that in the presence of solid carbon, the reduction temperature of iron from wustite corresponds to t_start ≈ 690 °С (for the formation of cementite Fe₃C t_start ≈ 680 °С) with the CO:CO₂ ratio in the gas phase approximately 1.5. In the presence of excess carbon, the concentration of carbon monoxide CO in the gas phase aligns with the equilibrium for reaction (6). The CO:CO₂ ratio at 690 °C is approximately 1.5; at 900 °C, it is approximately 19; at higher temperatures, the content of carbon monoxide CO is almost 100 % (CO:CO₂ ≥ 10²) (Fig. 4).

Similarly, during the reduction of zinc by carbon according to reaction (10) at the start temperature of the reduction t_start ≈ 960 °С and higher CO:CO₂ ≥ 10².

It is worth noting that at low temperatures (below 1200 °C), the activities of iron and carbon show slight deviations from their molar concentrations [14], and their variations in Fe – Zn solid solutions and melts do not significantly affect the equilibrium of reactions (9) and (10).

During the carbothermal co-reduction of a mixture of zinc and iron oxides, the primary reduction product consists of crystalline iron nuclei formed by reactions (1) (in the temperature range 580 – 1535 °C) and (5) (above 700 °C until the formation of the iron-carbon melt). The reduction of zinc with its transition into iron nuclei, along with the formation of solid solutions based on α-iron, begins almost simultaneously with the emergence of a new phase (α-iron). This process is similar to what occurs during the co-reduction of manganese and silicon, where primary small drops of metal (MnC_x) with 5 – 8 % silicon are present [16]. In the melting of calcium carbide, in the primary drops of metal formed in the low-temperature levels of the ore smelting furnace bath, up to 8 % silicon in the ferrous alloy is also detected. It is noteworthy that in Mn – Si and Fe – Si alloys, there are strong negative deviations from Raoult’s law (γ_Si ≈ 10\(^-\)³), and in Fe – Zn alloys with low zinc concentrations (x_Zn < 0.2), there are positive deviations γ_Zn[Fe] = 4 ÷ 10 (Fig. 2). Considering the high vapor elasticity of zinc and the potential formation of low-melting films of melts on the surface of α-iron nuclei, along with the intense evaporation of zinc from their surfaces, and the kinetic challenges associated with zinc diffusion inside solid-phase nuclei, it can be assumed that most of the zinc transitions into the vapor-gas phase. Consequently, the equilibrium states of solid metal – slag – gas are practically unattainable due to these factors.

The calculated thermodynamic parameters of the Fe – Zn – O – C system are illustrated in Fig. 4. The analysis reveals that achieving a concentration of 5 ÷ 10 % Zn in the α-Fe solid solution is possible at temperatures between 700 – 800 °C, with a_Zn = 0.9, and an equilibrium vapor pressure of zinc at approximately 0.01 atm (Fig. 1). In surface films that are supersaturated with zinc P_Zn > 0.1 atm, reaching 1 atm at 1300 – 1200 °С.