Introduction

Titanium carbide (TiC), as the main ingredient of cemented carbide, is widely used in the machine manufacturing, metallurgy, and aerospace fields, due to its high melting point, high hardness, and high chemical resistance. Carbothermal reduction of TiO2 is currently the main method to produce TiC powder.1 However, this process has the disadvantages of high cost and heavy pollution.1,2,–3

Titanium-bearing blast furnace (BF) slag, containing about 23–29% TiO2, is a byproduct of the iron-making process in the Panzhihua–Xichang area of China.2,4 More than 70 million tons of titanium-bearing BF slag has been accumulated, increasing at the rate of about 3.5 million tons per year.5 Such an enormous amount of stored titanium-bearing BF slag may cause significant environmental pollution and represents resource waste. However, there are currently no energy-efficient, cheap ways to use the titanium in such slag. Therefore, many researchers have focused on utilization of titanium-bearing BF slag,3,5,6,7,8,–9 particularly secondary utilization of titanium. In recent years, some researchers have proposed a method to prepare TiC from titanium-bearing BF slag. Hu et al.3 proposed preparation of TiC in vacuum using a method based on carbothermal reduction and acid leaching. The influence of the carbon content, reduction time, and vacuum degree on such formation of TiC was investigated. Zhen et al.10 studied synthesis of TiC by carbothermal reduction of titanium-bearing BF slag in a tube furnace,11 and subsequently investigated the effect of the reduction time and carbon particle size on such preparation of TiC. The proposed process offers lower-cost preparation of TiC with increased utilization efficiency of titanium-bearing BF slag.

To complete the process and improve the efficiency of preparation of TiC by carbothermal reduction of titanium-bearing BF slag, thermogravimetric analysis (TGA) and quadrupole mass spectrometry (QMS) were used in this work to investigate the reduction kinetics of titanium-bearing BF slag.

Experimental Procedures

Materials

The chemical composition of the Ti-bearing slag used in these experiments is presented in Supplementary Table SI. Before the experiments, milled slag (~ 74 μm) was homogeneously mixed with carbon powder (~ 50 μm, 99.9% commercial purity) at mass ratio of 1:0.38.3

Thermogravimetric Analysis

TGA experiments were carried out using a Setsys Evo 1750 TGA apparatus (Setaram, France). Slag–carbon mixture was heated from ambient temperature to 1450°C in the furnace at predetermined heating rate of 4°C/min, 6°C/min or 8°C/min. The flow rate of argon was determined to be 20 mL/min. When the temperature reached 1450°C, the samples were held for several hours to complete the reduction process. The final mass of samples was recorded. During reduction, the quantitative composition of the off-gas was simultaneously monitored by connecting the TGA apparatus to a QMS with LC-D200 (Tilon, UK) apparatus, previously calibrated, until the temperature reached 1450°C. The phase transformations during reduction were investigated by x-ray diffraction (XRD) analysis using a D/Max2500/PC apparatus (Rigaku Corporation, Japan).

Rate Law and Kinetic Analysis12,13,14, – 15

For details, see the Supplementary Material section “Rate law and kinetic analysis.”

Results and Discussion

Carbothermal Reduction Behavior

Titanium-bearing BF slag, considered to be a mixture of the main oxides TiO2, Al2O3, CaO, SiO2, Fe2O3, and FeO, was investigated using thermodynamics calculations with FactSage6.2 (Thermfact and GTT-Technologies, Germany). The relationship between the Gibbs free energy of reduction of oxides and temperature was obtained and is shown in Fig. 1a. The results indicated that iron oxide can be reduced to Fe at 700°C, whereas the titanium oxide can be reduced at temperatures > 1050°C. The other oxides (Al2O3, CaO, and SiO2) cannot be reduced below 1450°C. It is inferred that iron oxide is easier to reduce than titanium oxide. The iron oxide is first reduced to low-valence-state oxides then to Fe (Fe2O3 → Fe3O4 → FeO → Fe).16,17,–18 Similarly, TiO2 is first reduced to a low-valence-state oxide then to TiC at higher temperature (TiO2 → TinO2n–1 → TiC).19,20,–21 It is worth noting that several low-valence-state titanium oxides will be produced during the reduction.

Fig. 1
figure 1

(a) Changes of Gibbs free energy with temperature at 1 atm and (b) XRD patterns of samples in the experiments

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Ti-bearing BF slag was reduced using carbon powder at three different heating rates. As a result of the limitations of the experimental equipment, in this study, only the experimental TGA data obtained from room temperature to 1450°C were used to calculate the nonisothermal reduction kinetics of the titanium-bearing BF slag.

The XRD patterns of the original sample, and samples obtained at 1100°C and after the complete reduction experiments are shown in Fig. 1b. The results indicate that phases containing iron were reduced to Fe at 1100°C, whereas phases containing titanium were reduced to TiC after the complete reduction experiments.

The weight loss, reduction degree, and reduction rate are shown as functions of temperature in Fig. 2a, b, and c, respectively, revealing that the heating rate clearly affected all three. The slag was reduced until the temperature reached 595°C. When the temperature exceeded 670°C, the mass loss from the sample slowed due to a lower reduction rate. However, the weight loss changed again when the temperature reached 800°C. For the different heating rates, the weight loss, reduction degree, and reduction rate clearly increased with increase of the temperature > 800°C. The reduction degree in this study reached 0.93, 0.88, and 0.81 for heating rate of 4°C/min, 6°C/min, and 8°C/min.

Fig. 2
figure 2

(a) Weight loss, (b) reduction degree, (c) reduction rate, and (d) off-gas content recorded by QMS for titanium-bearing BF slag versus temperature at different heating rates

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Figure 2d shows the results of analysis of the off-gas from the reduction experiments carried out at different heating rates. Three obvious CO2 peaks are observed at temperatures ranging from 530°C to 700°C for the different heating rates, whereas CO was not detected. This may be due to reduction of phases containing iron in the slag (Fe2O3 → Fe3O4). When the temperature exceeded 900°C, CO and CO2 appeared simultaneously. The contents of CO and CO2 increased with increasing temperature, and the CO concentration was much higher than that of CO2. It is worth noting that two distinct dips can be observed from 800°C to 1095°C, consistent with the results for \( \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} \). This may reflect the reaction of Fe3O4 → FeO and FeO → Fe. When the temperature exceeded 1095°C, based on the results of the thermodynamics calculations, phases containing titanium should start to be reduced. With increase of the temperature, the content of CO first increased then decreased, and then again, particularly for the rate of 4°C/min. It can be inferred that the reduction reactions TiO2 → TinO2n−1 and TinO2n−1 → TiC occurred at this stage. When the temperature exceeded 900°C, the CO content increased greatly. Meanwhile, the reduction degree significantly increased, indicating the main reduction stage of the slag.

Therefore, combining the results in Figs. 1 and 2, the reduction process of titanium-bearing BF slag can be divided into two stages. The first stage mainly corresponds to reduction of phases containing iron (from iron oxide to Fe) and gasification reaction of carbon (CO2 + C = 2CO) at temperatures < 1095°C. In the second stage, the reaction is mainly reduction of phases containing titanium at temperatures > 1095°C.

Calculation of Activation Energy Using Flynn–Wall–Ozawa Method

Reduction of iron oxide mainly occurs at lower temperature and lower reduction degree. Figure 2b indicates that the reduction degree was less than 0.10 at 1100°C. Therefore, to completely exclude the influence of reduction of iron oxide, the reduction degree values from 0.15 to 0.80 in steps of 0.05 were used to calculate the activation energy using Eq. 7 (see supplementary material). The relationships between lg β and 1/T corresponding to the selected reduction degrees are plotted in Supplementary Fig. S1, showing a linear relationship. The activation energy for reduction of titanium-bearing BF slag was calculated from the slopes using the Flynn–Wall–Ozawa method. The activation energy values are presented in Supplementary Table SIII. Note that the activation energy at different reduction degrees first increased, then decreased to 194.8 kJ/mol, then increased to 253.45 kJ/mol when the reduction degree reached 0.80, indicating that the samples were more difficult to reduce in the latter stage. The activation energy value for the entire reduction process was s 221.2 kJ/mol. This TGA–QMS method provides an alternative approach to calculate the reduction kinetics of titanium-bearing BF slag.

Most Probable Mechanism Function

To determine the most probable mechanism function for nonisothermal reduction of titanium-bearing BF slag, the Šatava–Šesták method was applied. According to previous works,13,18,19,21 the Avrami–Erofeev model, diffusion model, and chemical reaction model are the most probable mechanism functions for the carbothermal reduction experiments. The Šatava–Šesták method can be used to obtain the differential and integral expressions for the common reaction mechanisms.

For different heating rates, linear fit results for lg β versus 1/T are shown in Fig. 3. The calculated results for the activation energy, preexponential factor, and correlation coefficients are presented in Table I. Note that the linearity of g(α) for D2, D3, D4, and D8 is excellent, with the activation energies of the D4 reaction model at different heating rates being closer than the others. Moreover, the activation energies of the D4 reaction model calculated using the Flynn–Wall–Ozawa method (Table SII) and Flynn–Wall–Ozawa method (221.2 kJ/mol) agree well with each other. Therefore, the D4 reaction model, namely, g(α) = [(1 + α)1/3 − 1]2 and f(α) = 3/2(1 + α)2/3[(1 + α)1/3 − 1]−1, is the most probable mechanism function for nonisothermal reduction of titanium-bearing BF slag. The reaction mechanism identified in this study is in agreement with the reaction mechanisms proposed for TiO2 in previous studies.22 Meanwhile, according to the results in Table I, the activation energy (Es) and preexponential factor (lg A) increased from 223.1 kJ/mol to 234.8 kJ/mol and 2.26/min to 2.81/min as the heating rate was increased from 4°C/min to 8°C/min.

Fig. 3
figure 3

Relationship between g(α) and 1/T at (a) 4°C/min, (b) 6°C/min, and (c) 8°C/min

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Table I Selected possible reaction models based on Šatava–Šesták method
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Kinetics Model

The kinetics model for nonisothermal reduction of titanium-bearing BF slag can be obtained by substituting the activation energy and preexponential factor into the D4 reaction model. The nonisothermal kinetic models at different heating rates are presented in Table II.

Table II Kinetic model of reduction of titanium-bearing slag in slag–carbon mixture
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Conclusions

The reduction kinetics of titanium-bearing BF slag was studied by TGA–QMS method. The following conclusions can be obtained:

  1. 1.

    Carbothermal reduction of titanium-bearing BF slag can be divided into two stages. The first stage is reduction of phases containing iron and gasification of carbon at temperatures < 1095°C, and the second stage is reduction of phases containing titanium at temperatures > 1095°C. The reduction degree increased with increase of temperature, and CO2 was the main off-gas at temperatures < 700°C whereas CO became the main off-gas at temperatures > 900°C. With increasing heating rate, the weight loss and reduction degree decreased, especially when the temperature was higher than 800°C.

  2. 2.

    The activation energy estimated by the Flynn–Wall–Ozawa method was 221.2 kJ/mol, and the activation energies estimated using the Šatava–Šesták method were 223.1 kJ/mol, 227.9 kJ/mol, and 234.8 kJ/mol at heating rate of 4°C/min, 6°C/min, and 8°C/min, respectively.

  3. 3.

    The most probable mechanism function for the nonisothermal reduction of titanium-bearing BF slag is the D4 reaction model with integral and differential forms of g(α) = [(1 + α)1/3 − 1]2 and f(α) = 3/2(1 + α)2/3[(1 + α)1/3 − 1]−1, respectively. Kinetic models for nonisothermal carbothermal reduction of titanium-bearing BF slag were obtained.