Dissolution Kinetics of Synthetic FeCr₂O₄ in CaO–MgO–Al₂O₃–SiO₂ Slag

Abstract

Cleaner production of alloys is of great significance to the protection of the ecological environment. At present, it has received widespread attention all over the world. Chromite smelting reduction direct alloying is an important production process in the production of stainless steel, which can make full use of chromite resources, thereby reducing production costs and preventing environmental damage caused by traditional processes. In order to reveal the dissolution mechanism of chromite ore, pure phase of synthetic FeCr₂O₄, the main component of chromite ore, was used to replace the real chromite with a complex composition and the dissolution process of it was investigated. The effects of basicity (w(CaO) + w(MgO)/w(SiO₂) + w(Al₂O₃)), Al₂O₃ content and temperature on the dissolution of FeCr₂O₄ in CaO–MgO–Al₂O₃–SiO₂ refining slag were studied under high purity argon atmosphere. The composition range of the slag sample is 35%–55%SiO₂, 15–35%CaO, 10–20%Al₂O₃ and 10%MgO. The results show that the solubility of FeCr₂O₄ increases with the decrease of basicity of slag from 1 to 0.54 and then the solubility of FeCr₂O₄ decreases with the decrease of slag basicity from 0.54 to 0.33. In the low basicity slag (B = 0.54), the solubility of FeCr₂O₄ will decrease with the increase of w(SiO₂)/w(Al₂O₃) from 2.25 to 5.50. The slag system with the best dissolution is 45% SiO₂, 25% CaO, 20% Al₂O₃ and 10% MgO. The solubility of FeCr₂O₄ increases with increasing temperature from 1500 to 1600°C. Meanwhile, distribution of elements in interface of FeCr₂O₄ and slag was analyzed by EDS. During the dissolution process, Fe, Mg and Al elements form a concentration gradient on the surface of the FeCr₂O₄. The width of the gradient interval is inversely proportional to the reaction time and solubility. The dissolution kinetic of FeCr₂O₄ was also investigated. The dissolution reaction on the surface of FeCr₂O₄ was the controlled step in the dissolution process. The activation energy of the dissolution reaction of FeCr₂O₄ in this slag is 266.05 kJ·mol⁻¹.

1. Introduction

Chromium is one of the most important alloying elements in the production process of iron and steel metallurgy, but in nature, chromium mainly exists in various ores, and these resources are difficult to directly use in the production process of stainless steel. The chromium, nickel and other alloys used in the stainless steel production process account for 70% of the production cost.¹⁾ At present, the production of chromium alloy raw materials is produced mainly through the method of carbothermal reduction, which reduces the chromium oxide in the chromium ore to obtain metallic chromium. This method requires a large amount of resources and generates a large amount of carbon monoxide and carbon dioxide gas, which causes the environment pollution.^2,3,4) In addition, for some specific chromium ore resources, it is necessary to convert the insoluble Cr³⁺ chromium salt into water-soluble Cr⁶⁺ chromate through alkali roasting, and then convert the chromate solution to chromium oxide by reduction or thermal decomposition. Finally, the chromium oxide is reduced to metallic chromium by the thermite method. The high-valance chromium element is toxic, and if the waste slag and liquid formed during the production process are treated improperly, it will also cause greater damage to the environment.^5,6,7) Therefore, if cheap chrome ore resources can be developed as raw materials for production, not only the resources can be used efficiently, but the damage to the environment can also be reduced.

Chromite smelting reduction direct alloying is an effective method for producing high-chromium molten iron, which can reduce production costs of stainless steel. C. S. Kucukkaragoz⁸⁾ studied the smelting reduction of chromite in the CaO–MgO–Al₂O₃–SiO₂ quaternary slag system, and proposed that the smelting reduction of chromium ore contains two steps of dissolution and reduction, which happen simultaneously, but the dissolution dominates in the early stage of the reaction. Since the main components of chromium ore are iron-chromium spinel and gangue components such as MgO and Al₂O₃, which are difficult to smelt. It is necessary to add low melting point compounds to turn these insoluble gangue components into molten slag, so as to better reduce chromium. Some researchers^{9,10,11,12,13,14,15,16,17,18,19)} have found that the addition of SiO₂ can promote the formation of low melting point compounds and slag, and promote the reduction of chromium. Dawson et al.²⁰⁾ found that at high temperatures, alkali metal fluorides form a eutectic mixture and act as a solvent for spinel components. These fluxes are usually part of the slag, so a suitable slag system will have a positive effect on the dissolution of chromium ore. Liu et al.^{21,22,23,24,25)} studied the influence of slag composition on the dissolution of chromium ore and found that in the range of high basicity (B = 0.8–1.6), the amount of chromium ore dissolved increases with the decrease of slag basicity, and the mass fraction of increasing Al₂O₃ and MgO will reduce the amount of chromium ore dissolved.

Since the dissolution and reduction of chromium ore are carried out at the same time during the smelting reduction process, it is very important to explore the interaction between dissolution and reduction. R. H. Eric et al.^26,27,28,29) conducted experiments on dissolution of chromium ore in crucibles of different materials and found that, the dissolution situation of chromite in the graphite crucible is obviously better than that in the molybdenum crucible. This proves that the reducing conditions promoted the dissolution process. In the CaO–MgO–Al₂O₃–SiO₂ system under reducing conditions, when the increase of MgO is compensated by the decrease of CaO, it will promote the dissolution of chromite. When the decrease of Al₂O₃ causes the increase of MgO, it will dissolve chromite. There are negative effects. In the process of dissolution, the three most important parameters are Al₂O₃ concentration, basicity and MgO/CaO.

According to the research of Morita et al.,^{5,30,31,32,33,34)} in the CaO–SiO₂–CrO_x–Al₂O₃ system at 1500–1600°C, the activity of CrO is greater than that of Cr₂O₃, which means that chromium divalent oxides are more likely to exist in the slag system. C. S. Kucukkaragoz⁸⁾ also proposed that in the early stage of smelting reduction of chromium ore, high-valent oxides of iron and chromium are reduced to FeO and CrO into the slag, and then further reduced to metal. The above studies indicate that the high-valent chromium oxides in chromium ore can form more soluble low-valent chromium oxides into the slag under reducing conditions, thereby promoting the dissolution of chromium ore.

The researches on the smelting reduction of chromite ore are more concentrated on the reduction part, and there is a lack of discussion on the dissolution part of chromite, especially the dissolution under the influence of non-reducing conditions. In addition, due to the complex composition of chromium ore, it will have a certain impact on the composition of the slag system, which will interfere with the study on the dissolution mechanism. The present work uses synthetic iron-chromium spinel instead of chromium ore, and explores the effects of basicity and Al₂O₃ concentration on the dissolution of chromium ore under non-reducing conditions. By studying the element distribution on the ore/slag interface, the controlling step of the dissolution reaction is determined. The dissolution kinetics model is also established.

2. Experiment

2.1. Materials

The chemical reagents Fe, Cr₂O₃, Fe₂O₃, CaCO₃, SiO₂, MgO, and Al₂O₃ (produced by Sinopharm) used in this work were analytically pure grade. The required reagent ratio was Cr₂O₃:Fe₂O₃:Fe = 3:1:1. The Cr₂O₃ and Fe₂O₃ were mixed in a ratio of 3:1. Cr₂O₃ and Fe₂O₃ were poured into a ball milling tank and then ball milled with alcohol for 20 hours, then dried at 200°C for 4 h. Then the analytical pure iron powder was ground for 15 minutes, mixed with the dried powder after ball milling. FeO, Fe₂O₃, and Fe were mixed and grounded in agate mortar for 20 minutes. The mixed powder was pressed into a cylinder in a steel mold under a pressure of 20 MPa with the diameter of 20 mm and height of 10 mm (mass is 10 g ± 0.2 g). The pressed cylinders were placed in an iron crucible and calcined for 24 hours at 1100°C, moreover synthetic at 1400°C for 4 hours under high purity argon (99.999%). to achieve the purpose of strengthening the hardness. The furnace was cooled slowly to room temperature. The synthetic samples were taken out the furnace and analyzed by X-ray diffraction (XRD).

The quaternary slag system CaO–MgO–Al₂O₃–SiO₂ was used to investigate dissolution of FeCr₂O₄. The specific experimental plan was shown in Table 1. The basicity of slag is defined as B = $\frac{w(\text{CaO})+w(\text{MgO})}{w({\text{SiO}}_2)+w(A{l}_2{O}_3)}$. The melting point of each slag is also calculated on the platform of Factsage 7.0.

Table 1. Experimental scheme (Calculated by Factsage 7.0).

No.	w (CaO)	w (MgO)	w (Al2O3)	w (SiO2)	B	Melting point of slag (°C)
1	35	10	20	35	1	1424.34
2	25	10	20	45	0.54	1324.31
3	15	10	20	55	0.33	1334.69
4	25	10	15	50	0.54	1263.65
5	25	10	10	55	0.54	1282.2

2.2. Apparatus and Procedure

The experiment was carried out in a vertical MoSi₂ resistance furnace. 120 g of slag sample was charged into a molybdenum crucible with a size of φ60 mm × 62 mm × 60 mm. The molybdenum crucible was put into the furnace tube and heated to the target temperature 1550°C. During this experimental process, argon gas was introduced with the rate of 1 L/min. The slag was stirred by alumina rod with the speed of 150 rpm during the dissolution process. Initial stage of slag was sampled. Then, the FeCr₂O₄ cylinder was slowly put into the melt. Slag was sampled at 15, 30, 45, 60 and 90 minutes respectively and the position of each slag was kept as consistent as possible. The solubility is obtained by measuring the element content of the sample obtained from the molten slag at a predetermined time interval, and the solubility is characterized by the mass fraction of Cr₂O₃, w(Cr₂O₃), of the sample. The value of w(Cr₂O₃) is determined by Eq. (1):   

$$w(\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3)=\frac{{\text{c}}_{(\text{Cr})}\times {\text{V}}_{\text{Sample}}\times {\text{M}}_{{\text{Cr}}_2{\text{O}}_3}}{{\text{m}}_{\text{Sample}}\times 2\times {\text{M}}_{\text{Cr}}}\times 100\%$$(1)

where, c_(Cr) is the concentration of chromium in the sample measured by ICP; V_Sample is volume of sample solution; m_Sample is the quality of the slag sample; M_Cr and M_Cr2O3 are the molar mass values of Cr and Cr₂O₃, respectively.

2.3. Analytical Methods

After the reaction, the crucible was taken out and quickly cooled in water, and the slag interface was line-scanned by using SEM-EDS equipment (FEI Quanta, Netherland). Inductively coupled plasma optical emission spectrometer (Optima 7000DV, PerkinElmer, America) was used to detect the mass fraction of Cr in the slag sample.

3. Results and Discussions

3.1. Effect of Basicity on Dissolution of FeCr₂O₄

Figure 2 depicts the influence of different basicity on the solubility of synthetic FeCr₂O₄. The solubility of FeCr₂O₄ increases with the decrease of basicity from 1 to 0.54 and decreases with the further decrease of slag basicity, like from 0.54 to 0.33. It implies that solubility of FeCr₂O₄ can be enhanced by increasing SiO₂ amount, but it also gives opposite effect if further increasing SiO₂.

Fig. 1.

X-ray diffraction pattern for the synthetic FeCr₂O₄.

Fig. 2.

Effect of basicity on dissolution of FeCr₂O₄ at 1550°C. (Online version in color.)

For each slag sample, there is an increasing trend from the beginning, and then reaches a relative steady state at different time. In the case of B = 1, the dissolution amount of FeCr₂O₄ is 0.54%, the lowest among the three experiments, and it takes 30 min to get steady state. When the basicity is 0.54, the dissolution of FeCr₂O₄ in the slag is the highest, which can reach about 1% at 90 min. The dissolution of FeCr₂O₄ gradually increases with time, the dissolution rate is faster in the early stage, and then the dissolution rate slows down and gradually reaches equilibrium. Lower basicity is benefit to the dissolving FeCr₂O₄ in molten slag, but there is a critical point for this tendency.

3.2. Effect of SiO₂/Al₂O₃ on Dissolution of FeCr₂O₄

Figure 3 describes the influence of SiO₂/Al₂O₃ ratio on the solubility of synthetic FeCr₂O₄. The content of CaO and MgO is fixed, and the content of SiO₂ changes with the content of Al₂O₃. The content of Al₂O₃ decreases in the order of 20%, 15% and 10%, and the content of SiO₂ increases in the order of 45%, 50% and 55% in the slag. As the SiO₂/Al₂O₃ ratio decreases, the dissolution of FeCr₂O₄ gradually increases. Moreover, it was found that the dissolution rate trend of FeCr₂O₄ in the three groups of experiments basically coincided. The dissolution rate decreased significantly after 30 to 45 minutes and gradually tended to steady state.

Fig. 3.

Effect of SiO₂/Al₂O₃ on dissolution of FeCr₂O₄ at 1550°C. (Online version in color.)

It is interesting to note that the effect of Al₂O₃ on the dissolution of FeCr₂O₄ gives opposite results. In the work of Liu et al.,²¹⁾ the dissolution of FeCr₂O₄ in high-basicity slag (B = 1.2) and found that as the content of Al₂O₃ increases, replotted in Fig. 4. This is contrary to our experiment. In this experiment, the basicity of the fixed slag is 0.54 with a low basicity slag. It can be explained that basicity has a greater influence on the dissolution of FeCr₂O₄ than content of Al₂O₃. The increase of Al₂O₃ in high-basicity slag hinders the dissolution of FeCr₂O₄ more obviously. However, the decrease of Al₂O₃ content and increase of SiO₂ content in low-basicity slag has more obvious hindering effect on dissolution. This phenomenon may be related to the difference in the structure of high-basicity slag and low-basicity slag, which still needs to be concluded in future research.

Fig. 4.

Effect of Al₂O₃ on dissolution of chromite at 1580°C in Liu et al. reported. (Online version in color.)

3.3. Distribution of Elements at the Slag/FeCr₂O₄ Interface

In order to reveal the mechanism of FeCr₂O₄ dissolution in the slag, the distribution of elements at the slag/FeCr₂O₄ interface was observed carefully. which is detected by SEM-EDS.

Figure 5 shows the slag/FeCr₂O₄ interfaces of No. 3 at 90 s, 15 min, 30 min and 60 min, and line scanning results presented in Fig. 6. A distinct interface contacting slag with FeCr₂O₄ can be found. From the gradient of the color, it can be seen that a dense boundary layer is forming on the FeCr₂O₄. From the results of element distribution, it is obvious that the boundary layer exists, and the thickness gradually increases with time. It can be seen in the boundary layer that the content of elements Mg, Al and Fe exhibit obvious gradient changes in the boundary layer. The content of Mg and Al gradually increase from FeCr₂O₄ to boundary to slag phase, while the content of Fe gradually decreases. The content of Cr, Si, and Ca elements did not show significant change in the boundary layer, however, a sudden content change occurs at the position of the interface.

Fig. 5.

Slag/FeCr₂O₄ interface of Experiment No. 3 at (a) 90 s, (b) 15 min, (c) 30 min and (d) 60 min after reaction beginning. (Online version in color.)

Fig. 6.

Distribution of elements on slag/FeCr₂O₄ interface of Experiment No. 3 at (a) 90 s, (b) 15 min, (c) 30 min and (d) 60 min after reaction beginning. (Online version in color.)

In order to figure out the composition in boundary layer, the content of Mg, Fe, Al have been varied from Fig. 6. It may help us to know the mechanism of FeCr₂O₄ dissolution behavior.

Figure 7 gives the standard Gibbs free energy of the formation of several spinel phases that may be formed in the system at the experimental temperature. MgCr₂O₄ and MgAl₂O₄ is most stable spinel phase in the current temperature. According to thermodynamics, it can be inferred that the spinel solid solution formed is mainly MgAl₂O₄ and MgCr₂O₄. In addition, some studies have shown that,^{35,36,37,38,39)} FeO and MgO will form Mg_1−xFe_xO solid solution in the solid-liquid reaction at high temperature, and then dissolve from the solid solution into the slag. That explains why Mg, Al and Fe have a concentration gradient in the boundary layer. The thickness of the boundary layer increases with time, and the dissolution of FeCr₂O₄ gradually slows down with time. Therefore, it can be inferred that the boundary layer composed of mixed solid solution hinders the contact between FeCr₂O₄ and the slag, thereby inhibiting the progress of the dissolution reaction, and the cessation of the dissolution reaction is due to the thickening of the boundary layer.

Fig. 7.

Standard Gibbs free energy of the formation of several spinel phases. (Online version in color.)

The content of Cr, Si, and Ca elements remain relatively stable in the boundary layer, and only a sudden content change occurs at the interface. No concentration gradient can be found in the boundary layer. This indicates that Cr, Si, and Ca do not participate in the formation of solid solution at the boundary layer, and the process of mass transfer is completed at the interface rapidly.

Similarly, the slag/FeCr₂O₄ interface and boundary layer of different slag series at 90 s are compared, as shown in Figs. 8 and 9. It can be seen that the change trend of the content of each element is consistent with the trend described above, and the thickness of the boundary layer is inversely proportional to the solubility of the FeCr₂O₄ in the slag system. The difference in the thickness of the boundary layer in the three groups of slag is not obvious. In addition, it can be found that the concentration gradient of Mg in No. 2 slag (Fig. 8(a)) is the most obvious, followed by No. 5 slag (Fig. 8(c), and finally No. 3 slag (Fig. 8(b)). The solubility of FeCr₂O₄ in the three groups of slags decreased in this order.

Fig. 8.

Slag/FeCr₂O₄ interface of Experiment (a) No. 2, (b) No. 3 and (c) No. 5 at 90 s after reaction beginning. (Online version in color.)

Fig. 9.

Elements’ distribution on slag/FeCr₂O₄ interface of Experiment (a) No. 3, (b) No. 2 and (c) No. 5 at 90 s after reaction beginning. (Online version in color.)

Some thermodynamic data of three groups of slags in experiment are listed in Table 2. It can be found that among the three groups of slags, MgO in No. 2 has a higher activity, followed by No. 5, and MgO in No. 3 has the smallest activity. In addition, the viscosity of these three groups of slags gradually increases in the order above. This indicates that MgO in No. 2 slag has a greater limit to participate in the reaction through the interface, and it is easier to react with FeO to form solid solution, thereby accelerating the dissolution process at initial stage. Furthermore, the viscosity of No. 2 slag is smaller and the fluidity of the slag phase is stronger, which also promotes the dissolution process from the perspective of kinetics as well. Therefore, the solubility of chromium ore in No. 2 slag is highest one among these slag compositions.

Table 2. Some thermodynamic data of Slag 2, 3 and 5 (Calculated by Factsage 7.0).

No.	α (MgO)	Viscosity (Pa·S)
2	9.84 × 10−3	0.709
3	5.41 × 10−3	3.084
5	7.99 × 10−3	0.859

3.4. Effect of Temperature on Dissolution of FeCr₂O₄

The slag system of No. 2 was selected to investigate the effect of temperature on the solubility. as shown in Fig. 10. The dissolution rate is relatively fast in the early stage, and the reaction gradually slows down after 45 minutes, and then gradually stabilizes. As the temperature gradually increased, the solubility at each time point increased significantly.

Fig. 10.

Effect of temperature on dissolution of FeCr₂O₄ in Slag 2. (Online version in color.)

The reasons for the increase in temperature to promote the dissolution of FeCr₂O₄ can be attributed to the following: First, the dissolution of FeCr₂O₄ is an endothermic process, and the higher the temperature, it is more beneficial to promote the dissolution. Secondly, the increase in temperature increases the superheat of the slag, promotes heat transfer, and makes the chromium ore easier to melt. In addition, the viscosity of the slag decreases with the increase of temperature, and the fluidity of the slag liquid is improved, which makes the diffusion easier.

3.5. Dissolution Kinetics of FeCr₂O₄

This experiment uses synthetic FeCr₂O₄ instead of chromite, so the dissolution reaction can be expressed as:   

$$\mathrm{F}\mathrm{e}\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_4=(\mathrm{F}\mathrm{e}\mathrm{O})+(\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3)$$(2)

The entire dissolution process can be divided into two steps: the dissolution reaction of FeCr₂O₄ at the interface and the diffusion of liquid products from the surface of unreacted FeCr₂O₄ into the slag. Therefore, the unreacted nucleus model can be used to describe the macro kinetics of the dissolution process.

According to the element distribution and thermodynamic analysis on the interface, it can be seen that the concentration of chromium in the unreacted nucleus and the boundary layer does not change significantly, and there is a sudden change in the interface position between the boundary layer and the slag phase. This can be understood as: After the surface dissolution reaction, FeO and Cr₂O₃ diffuse outwards, and at the same time combine with MgO and Al₂O₃ in the slag phase to form an insoluble mixed solid solution, and then the mixed solid solution is re-dissolved so that FeO and Cr₂O₃ enter the slag phase. Therefore, in the initial stage of the reaction, the dissolution rate is faster, but as time goes by, the thickness of the mixed solid solution gradually increases, hindering the contact between the unreacted nucleus and the slag. This process can be regarded as the direct dissolution of the chromite containing gangue components. The response can be expressed as:   

$$\begin{array}{l}(\mathrm{M}\mathrm{g},\mathrm{\hspace{0.17em} }\mathrm{F}\mathrm{e})\mathrm{O}\cdot (\mathrm{C}\mathrm{r},\mathrm{\hspace{0.17em} }\mathrm{A}\mathrm{l},\mathrm{\hspace{0.17em} }\mathrm{F}\mathrm{e}){}_2{\mathrm{O}}_3=\\ (\mathrm{M}\mathrm{g}\mathrm{O})+(\mathrm{F}\mathrm{e}\mathrm{O})+(\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3)+(\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3)+(\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3)\end{array}$$(3)

Therefore, when describing the reaction process by changing the content of chromium, the reaction model can be further simplified to an unreacted nucleus model without product layer. The unreacted nucleus and the boundary layer on its surface can be regarded as same species, and the content of chromium remains unchanged in the two layers.

The mass transfer rate of FeCr₂O₄ to molten slag through the slag/FeCr₂O₄ interface is:   

$${\text{v}}_{\text{D}}={\text{k}}_{\text{D}}{\text{A(C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}}\text{)}$$(4)

where, k_D is the mass transfer rate coefficient of Cr₂O₃; A is the contact area between FeCr₂O₄ and slag, m²; ${\text{C}}_{\text{Cr}2\text{O}3}^{\text{S}}$ and ${\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}}$ are the molar concentrations of Cr₂O₃ at the slag/FeCr₂O₄ interface and slag, mol·m⁻³.

The chemical reaction rate of FeCr₂O₄ dissolution at the interface is:   

$${\text{v}}_{\text{r}}={\text{k}}_{\text{r}}{\text{Af(C}}_{\text{Cr}2\text{O}3}^{\text{S}}\text{)}$$(5)

where, k_r is the chemical reaction rate constant; ${\text{f(C}}_{\text{Cr}2\text{O}3}^{\text{S}}\text{)}$ is a function of ${\text{C}}_{\text{Cr}2\text{O}3}^{\text{S}}$. The dissolution reaction can be regarded as a first-order irreversible reaction, so that ${\text{f(C}}_{\text{Cr}2\text{O}3}^{\text{S}}\text{)}$ = ${\text{C}}_{\text{Cr}2\text{O}3}^{\text{S}}$.

Since the whole process is in a quasi-steady state, it can be considered that the dissolution reaction rate of FeCr₂O₄ is equal to the mass transfer rate of the liquid product at the interface, that is, v_r = v_D = v. Equations (4) and (5) are combined to get:   

$$\text{v}=\frac{{\text{A(C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}}\text{)}}{\frac{1}{{\text{k}}_{\text{D}}}+\frac{1}{{\text{k}}_{\text{r}}}}$$(6)

$\frac{1}{\text{k}}=\left(\frac{1}{{\text{k}}_{\text{r}}}+\frac{1}{{\text{k}}_{\text{D}}}\right)$ is assumed to represent the total resistance of the reaction process, so that Eq. (6) can be simplified as:   

$$\text{v}={\text{kA(C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}}\text{)}$$(7)

The consumption rate of FeCr₂O₄ can be expressed by the decrease of its volume per unit time:   

$${\text{R}}_{\text{S}}=-\frac{\rho \text{dV}}{\text{Mdt}}$$(8)

where, ρ is the density of FeCr₂O₄, kg·m⁻³; M is the molar mass of FeCr₂O₄, kg·mol⁻³; V is the volume of FeCr₂O₄, and t is the reaction time.

The consumption rate of FeCr₂O₄ is equal to the total rate of the reaction process, so v = R_S:   

$$-\frac{\rho \text{dV}}{\text{Mdt}}={\text{kA(C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}}\text{)}$$(9)

Because the mass transfer process is very fast, the resistance during the mass transfer process is negligible. Therefore, it can be considered that the dissolution reaction on the surface of the FeCr₂O₄ is the controlling step in the entire dissolution process. So k ≈ k_r, and the reaction can be expressed as:   

$$-\frac{\rho \text{dV}}{\text{Mdt}}={\text{k}}_{\text{r}}{\text{A(C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}}\text{)}$$(10)

The shape of FeCr₂O₄ is cylinder. The dissolution model of a cylindrical solid immersed in a liquid is simplified as the solid shrinks along the radius, and the volume and area data are substituted:   

$$2\pi \text{r(r}+{\text{h)k}}_{\text{r}}({\text{C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}})=-\frac{\rho }{\text{M}}2\pi \text{rh}\frac{\text{dr}}{\text{dt}}$$(11)

The Eq. (11) is integrated to get:   

$$\mathrm{t}=\frac{\rho \text{h}}{{\text{k}}_{\text{r}}{\text{M(C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}}\text{)}}ln\left(\frac{{\text{r}}_0+\text{h}}{{\text{r}}_{\text{i}}+\text{h}}\right)$$(12)

where, r₀ and r_i are the initial radius of the FeCr₂O₄ and the radius of the FeCr₂O₄ at reaction time t_i, respectively, and h is the height of the FeCr₂O₄. The experimental data is substituted into Eq. (11) and the relationship between t and $ln\left(\frac{{\text{r}}_0+\text{h}}{{\text{r}}_{\text{i}}+\text{h}}\right)/({\text{C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}})$ could be found. The result is shown in Fig. 11. It can be seen that there is a linear relationship between t and $ln\left(\frac{{\text{r}}_0+\text{h}}{{\text{r}}_{\text{i}}+\text{h}}\right)/({\text{C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}})$.

Fig. 11.

The plot of time versus $ln\left(\frac{{\text{r}}_0+\text{h}}{{\text{r}}_{\text{i}}+\text{h}}\right)/({\text{C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}})$ ((a). different slags, (b). different temperatures). (Online version in color.)

According to the relationship between t and $ln\left(\frac{{\text{r}}_0+\text{h}}{{\text{r}}_{\text{i}}+\text{h}}\right)/({\text{C}}_{\text{Cr}2\text{O}3}^{\text{S}}-{\text{C}}_{\text{Cr}2\text{O}3}^{\text{i}})$, k_r under different temperatures can be obtained, and the relationship between k_r and reaction temperature T can also be obtained, as shown in Fig. 12. It can be seen that there is a linear relationship between k_r and temperature, which conforms to the Arrhenius law:   

$${\text{k}}_{\text{r}}={\text{Ae}}^{-\text{E}/\text{RT}}$$(13)

Fig. 12.

Arrhenius plot of dissolution rate of FeCr₂O₄ in Slag 2.

From this, the activation energy of the dissolution reaction can be worked out. The result is E = 266.05 kJ·mol⁻¹. In Liu’s work, the activation energy of dissolution process of chromite is 524.34 kJ·mol⁻¹.²²⁾ It can be concluded that the pure FeCr₂O₄ phase requires less activation energy than the dissolution of chromite, and the controlling step of this process is the dissolution reaction on the interface.

4. Conclusions

In this experiment, we studied the dissolution behavior of synthetic FeCr₂O₄ under non-reducing conditions, discussed the effects of basicity, Al₂O₃ content and temperature on the dissolution of FeCr₂O₄, and established a kinetic model for the dissolution of chromium in the slag. Some conclusions have been drawn as follows:

(a) When the slag basicity decreases from 1 to 0.54, the solubility of FeCr₂O₄ increases with the decrease of slag basicity; when the slag basicity decreases from 0.54 to 0.33, the solubility of FeCr₂O₄ decreases with the decrease of slag basicity. When the basicity of the slag is 0.54, the dissolution of chromite gradually increases with increasing SiO₂/Al₂O₃ ratio. The slag system with the best dissolution is 45% SiO₂, 25% CaO, 20% Al₂O₃ and 10% MgO.

(b) During the reaction process, Fe, Mg, Al elements react when they pass through the interface, and mainly produce MgAl₂O₄ and Mg_1−xFe_xO solid solutions, which adhere to the surface of unreacted FeCr₂O₄ to form a boundary layer. The width of the boundary layer is inversely proportional to the reaction time and solubility. The content of Cr, Si, and Ca elements only changes at the interface, and there is no obvious concentration gradient.

(c) The solubility of FeCr₂O₄ increases with increasing temperature. The dissolution reaction on the surface of the FeCr₂O₄ ore is the controlling step during the dissolution process. The activation energy of the dissolution reaction of FeCr₂O₄ in this slag is 266.05 kJ·mol⁻¹.

Acknowledge

The authors are grateful for the financial support of this work from the National Natural Science Foundation of China (No. 51922003, 51904286, 51774027, 51734002).

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