Study on the mechanochemical oxidation of ilmenite

Study on the mechanochemical oxidation of ilmenite

Journal of Alloys and Compounds 459 (2008) 354–361 Study on the mechanochemical oxidation of ilmenite Chun Li ∗ , Bin Liang College of Chemical Engin...

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Journal of Alloys and Compounds 459 (2008) 354–361

Study on the mechanochemical oxidation of ilmenite Chun Li ∗ , Bin Liang College of Chemical Engineering, Sichuan University, Chengdu 610065, PR China Received 6 December 2006; received in revised form 19 April 2007; accepted 21 April 2007 Available online 4 May 2007

Abstract The oxidation kinetics and mechanism of ilmenite milled in air and oxygen atmospheres were investigated. Effects of mill spin rate, milling ball/ore mass ratio and oxygen pressure on the oxidation were examined. The results showed that the former two parameters significantly affected the oxidation process while the influence of oxygen pressure was demonstrated only in a low initial O2 pressure range. An evident O2 adsorption (macroadsorption) was observed at high O2 pressures (≥50 kPa) but it disappeared with decreasing of O2 pressure. The oxidation was mechanochemically limited at the initial O2 pressures from 152.0 to 33.4 kPa. With further decreasing of the O2 pressure to ≤27.4 kPa, the oxidation changed to be controlled by the O2 adsorption on the active sites of ilmenite particles surface (micro-adsorption). The mechanochemical oxidation occurred mainly at those active sites with the c-axis lattice strain. The mechanism of the oxidation was suggested, upon which a rate equation in kinetic regime was built and derived as follows: d(1 − a) = 2.1 × 10−5 R2.044 ac2.616 (1 − α)2 dt when t > 0.5 h and FeTiO3 oxidation extent α ≤ 85%. Beyond the extent, the oxidation was limited by O2 diffusion through the solid products layer. © 2007 Elsevier B.V. All rights reserved. −

Keywords: Ilmenite; Mechanochemistry; Oxidation kinetics; Mechanism

1. Introduction A wide range of mechanochemical or mechanically activated reactions involving gaseous reactants (e.g. gas mediums) have been reported [1–10]. Mechanical treatments considerably affect the physical/chemical properties of pulverized materials, such as calcination temperature, melting point, dissolution rate, etc., and therefore they received extensive investigations [11–14]. Most of the researchers tried to distinguish the difference between mechanochemical and thermochemical reactions of solid substances [6,7,15]. Unfortunately, mechanochemical reaction kinetics was rarely reported, especially the kinetics associated with a gaseous reactant. In this work, ilmenite was milled in a ball mill device. The kinetics of the mechanochemical reaction between ilmenite and oxygen was examined. Based on studying the adsorption of O2 ,



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the reaction mechanism was discussed. The investigation also has strong industrial links. In industry, ilmenite is primarily used to produce titanium dioxide pigment. Sulfate process, one of widely employed routes [16], in which ilmenite is dissolved in a concentrated sulfuric acid (≥85 wt.%) at an elevated temperature, brings with many environmental problems due to its off-gas pollution. Its explosively emission of sulfur-contained off-gas is very difficult to deal with. Using a mechanochemical technique, the ilmenite can be dissolved under a moderate temperature and acid concentration. As a result, the emission of off-gas is controllable. Some literature reported the effects of mechanical activation on the dissolution of ilmenites [11,17–20]. Our previous work showed that mechanical pretreatment remarkably improved the dissolution of Panzhihua ilmenite [18,19]. However, the oxidation of ilmenite during the mechanical milling significantly influenced the dissolution rate [11,21]. To well understand the mechanochemical oxidation and control the mechanical treatment parameters, in this work, the kinetics of the mechanochemical oxidation of ilmenite was investigated.

C. Li, B. Liang / Journal of Alloys and Compounds 459 (2008) 354–361 Table 1 Chemical composition of testing Panzhihua ilmenite (wt.%) TiO2 FeO Fe2 O3 MgO SiO2 Al2 O3 MnO2

47.25 34.21 5.56 6.23 2.75 1.49 0.61

2. Experimental 2.1. Material Ilmenite powder, provided by Titanium Company of Panzhihua Steel & Iron (Group) Corporation, Sichuan, China, was used in the experiments. It had a size fraction of −150 + 100 ␮m. Its chemical composition was analyzed in our previous work [18,19], as shown in Table 1. XRD analysis showed that the major mineral phase was a hexagonal structure FeTiO3 .

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a fixed rotation rate of 200 rev/min in different gas atmospheres (O2 , N2 or air). Under air atmosphere, the two gas valves (5 and 5 ) were opened to laboratory air. Different spin rates (450, 500, 540 or 580 rpm) and ball/ore mass ratios (20, 40, 80) were used. After allotted times the containers were unloaded and the milled sample was scraped out. To investigate the influence of gas atmosphere, the milling operation was conducted at a spin rate of 580 rpm with 2 g of ilmenite sample and a fixed ball/ore mass ratio of 40. The gas volume inside the container was measured by water mass method, being 143 ml. Before a milling operation the two valves were opened. One of them was connected to a gas gauge to measure pressure, the other was used to evacuate out the air inside up to a residual pressure of 100 Pa and then backfill given gases to desired pressures. The pressure was calibrated from ambient temperature (20–30 ◦ C) to 23 ◦ C. After the valves were closed, the container was installed on the rotation platform. Turned on the rotation motor, after a given time, stopped milling and removed the container off the rotation plat, cooled with a electric fan to room temperature, and then connected to the pressure gauge. The residual gas pressure was measured and calibrated to 23 ◦ C. At last, the container was opened and the milled sample was discharged. The as-prepared samples were immediately chemically analyzed and characterized with various techniques.

2.2. Ball milling experiments 2.3. Analysis and characterization Ball milling experiments were conducted in a vertical planetary ball mill (QM-1SP2, Nanjing, China). The mill has a rotation platform, over which four stainless steel milling containers are fixed. The rotation radium of the containers is 100 mm. The containers are designed as a jacket structure (see Fig. 1). The inner cell is about 100 ml with a radius of 26.4 mm, on its cover a 3 mm diameter hole is opened in order to connect inside and outside voids. The closed outside container was installed with two gas valves. About 80 g of stainless steel milling balls (Ø6 mm) and several grams of the ilmenite powder were placed inside the inner cell. The milling operation was conducted at

Fig. 1. Schematic diagram of the milling body. (1) Container; (2) cover; (3) milling balls; (4) cell; (5 and 5 ) valve; (6) pressure gauge; (7) valve.

Ferrous iron content of the milled samples was determined by redox titration method, in which the samples were dissolved by a hydrochloric and hydrofluoric acid solution under an oxygen-free atmosphere and then the ferrous ion was oxidized by a K2 Cr2 O7 standard solution. Based on variation of the Fe2+ content before and after the milling, the ilmenite oxidation extent was calculated. Total iron contents of the milled samples were also determined using redox titration technique, in which the samples were molten using potassium pyrosulfate and then leached with deionized water. The ferric ion in the solution was reduced to Fe2+ using stannous chloride. After the excess stannous chloride being oxidized by mercury chloride, the ferrous ion was titrated using a K2 Cr2 O7 standard solution. A precision pressure gauge and a precision vacuum gauge (ZB-150A, Zhejiang, PR China) were employed to measure the gas pressures inside the containers. Their measurement ranges are 0–0.25 MPa and −0.1 to 0 Mpa, respectively. The allowable error of the gauges is less than 0.4% at the temperature of 23 ◦ C. The error increases with deviation of working temperature t of the gauge from the temperature. In the range of 5–40 ◦ C the error can be expressed as ≤[0.4% + |t − 23|0.04%]. During measurement of the residual O2 pressure, the small amount of air inside the connecting pipe L and L (see Fig. 1) may affect the accuracy. The measurement error was eliminated by a pressure balance method. Before measurement, a balance pressure was introduced through S opening by evacuating or back filling O2 into connector L–L . The balance pressure was adjusted to the objective value of the residual O2 pressures (P0) estimated according to the measured Fe3+ /Fe2+ ratio. Closing the valve 7 and opening the valve 5, a somewhat more accurate pressure datum P1 was obtained. In the next measurement the balance pressure in the connector L–L was further adjusted to P1, and a more accurate pressure value P2 was obtained. Repeated the operation above until the relative error between two neighboring measured pressures for the same milling condition was less than 2.0%. The as-obtained pressure data were all converted from the room temperature to 23 ◦ C. X-ray diffraction (XRD) experiments were performed using XRD (X’Pert Pro MPD, Philips, the Netherlands). The voltage and anode current used were 40 kV and 40 mA, respectively. The Cu K␣ = 0.15405 nm and continuously scanning mode with 0.02 interval and 0.25 s of set time were used to collect the XRD patterns of samples. Parallel X-ray incident beams of hybrid mirror with divergence slit of 1/8◦ and diffracted beam of the parallel plate collimator with Soller slit 0.04 Rad and prepositional detector were used in all XRD experiments. The structure refinement of FeTiO3 was performed on Cerius2 platform (MSI company, USA). The Rietveld method was embedded in DWBS90 software package in Cerius2 [22]. The original crystal model was constructed based on the data with Cerius2 . The principle of Rietveld is refining the parameters of original crystal model to meet the XRD experimental data with Netwon–Raphson algo-

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rithm. The parameters to be refined in present study were more than 40, but only lattice strain was selected to characterize the oxidation process. Thermal analysis experiments were carried out on a simultaneous thermogravimetric and differential thermal analyser (TG/DTA) (Seiko, Japan, EXSTAR6000), with a heating rate of 15 K/min and an nitrogen (N2 purity over 99.999%) flow rate of 300 ml/min. Surface area measurement was conducted using a multipoint BET technique (Quantachrome, America, NOVA-3000).

3. Results and discussion 3.1. Mechanochemical oxidation of ilmenite Chen systematically investigated the thermochemical and mechanochemical oxidation reaction of ilmenite in air [6] and a pure oxygen gas [7]. Unlike the thermal reaction, in which thermal oxidation reactions consist of a low-temperature (<1000 ◦ C) reaction with the formation of intermediate phases (Fe2 Ti3 O9 and Fe2 O3 ) and high-temperature (>1000 ◦ C) reactions with the formation of final thermally stable phases (Fe2 TiO5 and TiO2 ), only the following low-temperature reaction occurred during ball milling both in atmospheres of air and pure oxygen gas: 6FeTiO3 + (3/2)O2 = 2Fe2 Ti3 O9 + Fe2 O3

(1)

Therefore, all the following stoichiometric calculations were based on the oxidation reaction. In addition, Fe contamination due to abrasion from mill and balls during ball milling is a common phenomenon [23,24]. To avoid effect of the contamination on the calculation of ilmenite oxidation extent, a preliminary experiment was performed. The result was presented in Table 2. The total iron content increased slightly ab initio with milling time. Upon milling over 10 h, the content significantly increased. Therefore, in the following experiments the milling time was limited to 10 h unless it was noted. 3.1.1. Effect of spin rate For a planetary ball mill a spin rate corresponds to a centrifugal acceleration, which considerably influences mechanochemical processes [25]. The oxidation extents of Fe2+ in ilmenite under different spin rates are illustrated in Fig. 2. The milling operation was conducted under air atmosphere. The results show that the spin rate significantly enhanced the oxidation. The oxidation degree for 10 h milling samples reached ∼53% at 450 rev/min and 80% at 580 rev/min, respectively. A s-shape oxidation curve was observed, which indicated that the oxidation reaction existed an induction period.

Fig. 2. Effect of spin rate on oxidation of ilmenite (milling ball/ore mass ratio of 40:1).

3.1.2. Effect of milling ball/ore mass ratio In ball mills, more balls increase the milling intensity. High ball/mass ratio means more impact opportunities upon unit mass of solid powder and the milled powder obtains more mechanical energy. The influence of ball/mass ratio on the oxidation of Fe2+ in ilmenite was investigated under a spin rate of 580 rev/min and air atmosphere. The results show that ball/ore mass ratio significantly affected oxidation conversion (Fig. 3). The induction period was also observed. In addition, the oxidation reaction leveled off after the oxidation extent was in excess of 85%. 3.1.3. Effect of oxygen pressure In the air, oxygen partial pressure is about 21.3 kPa. Milling under air atmosphere was considered to conduct under the constant oxygen pressure. Because the milling container is open to air, the air was soaked through the opened valves 5 and 5 when

Table 2 Variation of total iron in the ilmenite samples milled at a spin of 580 rpm with milling time Milling time (h)

Total iron content (wt.%)

4 6 8 10 14

30.52 30.55 30.60 30.70 32.55

Fig. 3. Effect of milling ball/ore mass ratio on oxidation of ilmenite (spin rate of 580 rpm).

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Fig. 5. Oxygen pressure variation as a function of milling time under different initial oxygen pressures. (—) calculated value; (- - -) experimental value.

Fig. 4. Effect of initial oxygen pressure on oxidation of ilmenite.

oxygen was consumed. However, to observe oxygen influence, in the experiments the container was sealed, vacuumed and back filled with pure oxygen. The initial oxygen pressures were 152.0, 101.3, 70.9, 53.7, 33.4 and 27.4 kPa, respectively. To check the leakage of milling cell at high pressures and operating temperature, a blank experiment without ilmenite was carried out at a N2 pressure of 202.6 kPa for up to 10 h. The results indicated that the containers were pressure tight. Using ideal gas equation, the initial amounts of oxygen were estimated on void volume of the containers (143 ml each). The stoichiometric amount of oxygen for completely oxidation of ferrous ion is about 0.076 g. The initial amounts of oxygen inside the containers were about 3.70, 2.47, 1.73, 1.30, 0.82 or 0.67 times of the stoichiometric value. The experimental results of the Fe2+ oxidation are demonstrated in Fig. 4, and therefore, the residual oxygen pressures at 296 K were calculated from the experimental data by stoichiometric coefficient. The calculation data are presented in Fig. 5 (the solid lines). The results show that oxidation was fast under high O2 pressure, the reaction rate was almost same as the rate under the air atmosphere when the O2 initial pressure ≥33.4 kPa. The oxidation rate is independent of the initial oxygen pressure in the range of 152.0–33.4 kPa, indicating that reaction is the zero order to oxygen. Further investigation exhibited that both the milling rotation rate and the ball/ore mass ratio could significantly affect the oxidation process under the same O2 pressure range. As a conclusion, the reaction is mechanochemically limited. For a lower initial O2 pressure, such as 27.4 kPa, the limitation of oxygen became not negligible and the oxidation rate considerably slowed down after 2 h. In the test with sealed air atmosphere, the container was filled with air and the initial oxygen partial pressure was 21.3 kPa. Having milled for 4 h, the

Fe2+ oxidation percentage was only ∼33%, at the same time, the O2 partial pressure inside the container dropped to ∼6 kPa. A same oxidation trend was also observed when milling in pure oxygen atmosphere with initial pressure of 21.3 kPa. Clearly, the reason is the reaction either having neared equilibrium or being too slow at the O2 pressures of ∼6 kPa. Due to lack of the thermodynamic data of Fe2 Ti3 O9 species we cannot calculate the equilibrium pressure of O2 gas for the above oxidation reaction (1). Therefore, an extended milling test was conducted in pure oxygen atmosphere with initial pressure of 21.3 kPa. The results are presented in Table 3. The oxidation continued but with a rather slow speed after 4 h of milling, indicating that the leveling off at an O2 pressures ≤∼6 kPa was due to the kinetic rate. A further investigation showed that the milling parameters (rotation rate and ball/ore mass ratio) influenced this oxidation little in the O2 pressure range. Therefore, the process is not mechanochemical reaction limited. 3.2. Oxygen adsorption during ball milling Gas adsorption by solids during their grinding is well known [8,9,26]. Oxygen pressure change during ball milling is an effective indication for absorption and oxidation reaction, which was first, reported by Puttaswamy et al. [9]. Similarly, more compliTable 3 Variation of FeTiO3 oxidation extent with milling time at an initial O2 pressure of 21.3 kPa Milling time (h)

Fe2+ oxidation extent (%)

0.5 1 2 4 6 10 14

4.4 19.6 28.3 32.6 33.8 35.2 36.3

Note: Effect of the iron contamination due to extended milling has been removed during calculation of the Fe2+ oxidation extents listed above.

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The estimation shows that milling at an oxygen pressure ≥50 kPa for over 30 min the ilmenite adsorbed oxygen more than 0.23 g/100 g ore (abbreviated as macro-adsorption). The adsorption amount increased with increasing O2 pressure. In all operations under same initial oxygen pressure, the adsorbed amount lowered along with the milling time. With an oxygen pressure lower than 50 kPa the adsorbed O2 dropped to near zero and the macro-sorption phenomena disappeared. When the sample was milled for 1 h at initial O2 pressure of 152.0 kPa, the oxygen adsorption amount was about 1.78 g/100 g ore. It is obviously larger than its weight loss (∼1%) during the thermal analysis (in Fig. 5) due to the reaction of part of the adsorbed O2 with ilmenite. 3.3. Mechanochemical oxidation mechanism Fig. 6. TG/DTA trace of sample milled in 152.0 kPa O2 for 1 h.

cated pressure changes of ammonia gas was observed during ball milling of pure B and Zr powders, which are found to be caused by a series of absorption, hydridation and nitridation reactions [8,10]. In present investigation, after milling operation, the residual oxygen pressure inside milling cell was measured with the connected pressure gauge. The measured pressures are compared in Fig. 5 with the values calculated from Fe2+ oxidation extents. In the low initial pressure range, the two values are comparable, however, the oxygen consumed in Fe2+ oxidation reaction is considerably less than the reduction in gas phase when the initial oxygen pressure was ≥101.3 kPa. This difference is possibly due to the oxygen adsorption under high oxygen pressure atmosphere. To further verify the occurrence of oxygen adsorption, the ilmenite sample, milled for 1 h at an initial oxygen pressure of 152.0 kPa, was subjected to a combined thermogravimetric and differential thermal analysis in N2 atmosphere (see Fig. 6). In the range of 25–500 ◦ C the sample lost ∼1% of its initial weight and an evident exothermic peak, in the meantime, was observed. The weight loss is mainly associated with the O2 desorption, and, at the same time, part of the ilmenite oxidized by the adsorbed O2 according to the exothermal peak. The wide desorption temperature indicates that the adsorbed oxygen was mainly in chemical adsorption. From the difference between the calculated and experimentally measured residual oxygen pressures, we estimated the amount of the adsorbed oxygen. The results are presented in Table 4.

The mechanochemical oxidation of ilmenite is a typical gas–solid heterogeneous reaction, the reaction includes four major steps: (1) transfer of O2 through gas boundary layer onto the surface of ilmenite particles; (2) diffusion of O2 through the solid products layer; (3) adsorption of O2 on the un-reacted particle surface; (4) reaction of the adsorbed oxygen with Fe2+ . From the O2 adsorption amount (Table 4) and the crosssection area of a single oxygen molecule (∼6.78 × 10−20 m2 [27]), the areas of monolayer coverage of the adsorbed O2 for each gram ore were estimated (see Fig. 7). In comparison the BET areas of the milled samples were measured. To avoid effect of O2 adsorption the samples were annealed in a flowing N2 gas at 550 ◦ C for 0.5 h prior to the measurement. The results are also shown in Fig. 7. At high oxygen pressures (e.g. ≥101.33 kPa), the area estimated from adsorbed O2 is higher than the BET area. The result means that multilayer O2 adsorption exists and part of the adsorbed oxygen is in physical adsorption. Under a low initial O2 pressures, the estimated area is smaller than the BET area. However, the results (in Fig. 4) show that the decreasing adsorption did not affect the mechanochemical oxidation, indicating that the oxidation only took place on highly active sites. These active sites might preferably adsorb oxygen molecules due to higher surface energy. Low oxygen pressures could prevent oxygen macro-adsorption from occurrence, but a local adsorption with adsorption amounts ≤0.05 g O2 /100 g ore (abbreviated as micro-adsorption), especially on these highly active sites might be possible. It is why the oxidation significantly happened even under low initial O2 pressures from 53.7 to 33.4 kPa.

Table 4 Variation of adsorbed oxygen amount (g) per 100 g ore with milling time at different initial O2 pressures Initial O2 pressure (kPa)

152.0 101.3 70.9 53.7

Milling time (h) 0.5

1

2

4

6

2.40 (123.9) 1.11(87.2) 0.60(62.4) 0.23(50.5)

1.78 (123.6) 0.84(83.1) 0.41 (57.5) 0.05 (44.1)

1.58 (119.7) 0.82 (77.3) 0.26 (52.9) ∼0 (38.5)

1.43 (113.2) 0.67 (70.5) 0.05 (47.1) ∼0 (30.4)

1.20 (111.9) 0.56 (66.6) ∼0 (42.6) ∼0 (25.3)

Note: Corresponding oxygen pressures (kPa) measured are given in the parentheses.

C. Li, B. Liang / Journal of Alloys and Compounds 459 (2008) 354–361

Fig. 7. Variation of specific surface area with milling time. (1, 2, 3, 4) Calculated oxygen coverage area on a solid surface under initial O2 pressure 152.0, 101.3, 70.9 and 53.7 kPa, respectively. (5) BET area of the ilmenite milled at initial O2 pressure of 152.0 kPa.

With further lowering of O2 pressure, however, even the micro-adsorption became difficult. This can explain the decreasing of oxidation rate after 2 h of milling with the initial O2 pressure of 27.4 kPa. Since the oxygen gas in the cells was in severe turbulence generated by movement of milling balls, the transfer of O2 through gas boundary layer should not be a question. And at low oxidation extents the solid products coated on the un-reacted ilmenite particles surface could be easily removed by milling, and would not affect the inner diffusion of O2 . Therefore, the oxidation was probably limited by O2 adsorption on the ilmenite powder surfaces. When the oxygen pressure dropped to ∼6 kPa, the oxidation nearly stopped, indicating that only very weak micro-adsorption occurred. Parallel experiments were conducted to observe the influence of oxidation on solid structure. The ilmenite samples were milled at oxygen and nitrogen atmospheres, respectively. The initial pressures were 101.3 kPa and the spin rate was 580 rev/min. Fig. 8 illustrates the XRD results of the milled samples. From the XRD data, we estimated the lattice strains (ε) for the milled samples using the method of Rietveld structure refinement, and the calculation results are shown in Fig. 9. The lattice strains in a-axis of the ilmenite unit cell when milled in N2 gas were only slightly larger than those in O2 gas. The c-axis lattice strains, however, were three- to four-fold larger. It indicates that oxidation mainly occurred on the surface perpendicular to the c-axis, which maintained the strain in a relatively low level. Therefore, the surface active sites mentioned above are probably the ones with the c-axis strain. During the milling the fraction and the level of the c-axis strain in ilmenite particles increased with milling time. This can partially explain the presence of the “induction period” evident in initial stages in Figs. 2–4. Another reason for the “induc-

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Fig. 8. XRD patterns of samples milled, respectively, in O2 and N2 for 1, 2, 4, and 6 h.

tion period” may be due to the particle size reduction occurring mainly in the initial 30 min (in Fig. 10). In this period, d50 of the milled samples decreased from ∼140 to 1.22 ␮m. In contrary, d50 slowly increased to 1.43 and 1.92 ␮m for 1 and 6 h, respectively. The change trend is well in agreement with the results observed when milling with porcelain cells and balls [18], and also the results of BET measurements (shown in Fig. 7). Increasing milling strength resulted in more active sites and higher strains in c-axial direction. As the result, high ball/ore mass ratio or mill spin rate can enhance the mechanochemical oxidation reaction.

Fig. 9. Variation of lattice strain with milling time under different atmospheres.

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Fig. 10. Particle size distributions of the unmilled ore and samples milled for different times. (1) Unmilled; (2) 30 min; (3) 60 min; (4) 360 min.

where n is a constant, >0; k2 is a parameter associated with the ball milling system. Substituting Eqs. (3) and (4) into Eq. (2):

3.4. Kinetics of mechanochemical oxidation for ilmenite 3.4.1. Kinetic modeling Based on the above analysis, the oxidation rate equation (with an initial oxygen pressure ≥33.4 kPa) can be expressed as follows: −

dw = kFSPOm2 dt

(2)

where w is the un-reacted mass of ilmenite (FeTiO3 ) at time t, k is rate constant, F is the frequency of the valid impact between the sample particles and milling balls, S is the surface area with the c-axis strain among the valid impact area (Sc ) between a particle and a milling ball, PO2 is the oxygen pressure at time t, m = 0, is the reaction order of oxygen. In Eq. (2): w = w0 (1 − α),

S = Sc (1 − α)[εc ]

where w0 is the initial ilmenite (FeTiO3 ) mass, α is the oxidation extent of FeTiO3 at time t, [εc ] is percentage of the area with the c-axis strain on the un-reacted ilmenite surface. Since [εc ] increases with milling time, let [εc ] = k1 (1 − α)l where l is a constant, <0; k1 depends on the ball milling system (including spin rate, ball/ore mass ratio, etc.). Therefore S = Sc k1 (1 − α)1+l

(3)

Because the BET area of the samples milled over 0.5 h gradually reduced (see the line 5 in Fig. 7), the particle number decreased, and so did the F, which can be expressed: F = k2 (1 − α)n

Fig. 11. Fit of the model to the data shown in Fig. 2 (for the data with milling time over 1 h).

(4)



kk1 k2 Sc d(1 − α) (1 − α)1+l+n = wo dt

(5)

Let kt = kk1 k2 Sc /wo , p = 1 + l + n, we obtain −

d(1 − α) = kt (1 − α)p dt

(6)

3.4.2. Determination of kinetic equation Using trial and error method, fitting the data in Fig. 2 to Eq. (6) shows that when P = 2 the integration equation of Eq. (6) can well describe the experimental results (see Fig. 11): 1 = kt t + const. 1−α

(7)

The apparent rate constants at various centrifugal acceleration velocities with a ball/ore ratio of 40:1 were estimated and listed in Table 5. Fitting the data in Fig. 3 to Eq. (7) (see Fig. 12), the model gives a good representation to the oxidation process at low oxidation extent range. Beyond an extent of 85%, however, there is an obvious discrepancy. It is probably due to influence of the solid products (Fe2 Ti3 O9 and Fe2 O3 ) on O2 diffusion, which were not easily removed by milling due to high products/reactants mass ratio. In this stage, the oxidation was limited by O2 diffusion through the solid products layer. Table 5 The apparent rate constants under various centrifugal accelerations Spin rate (min)

Centrifugal acceleration (m/s2 )

Rate constant

580 540 500 450

2.47 2.15 1.84 1.49

0.43 0.25 0.17 0.11

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pressure ≥50 kPa. Below the pressure, the adsorption disappeared. However, the local adsorption (micro-adsorption) on the active sites with the c-axis strain still existed. (4) The mechanochemical oxidation of ilmenite occurred primarily at the surface sites with the c-axis lattice strain. There are four major steps in the reaction: transport of O2 through gas boundary layer onto the surface of solid particles; diffusion of O2 through the solid products layer; O2 molecule adsorption on the active sites with the c-axis strain; and interaction of the adsorbed O2 with the ilmenite. (5) When milling in air atmosphere, the following mechanochemical rate equation in kinetic regime was obtained: d(1 − α) = 2.1 × 10−5 R2.044 ac2.616 (1 − α)2 dt where t > 0.5 h and α ≤ 85%. Beyond the oxidation extent, the reaction was limited by O2 diffusion through the solid products layer. −

Fig. 12. Fit of the model to the data in Fig. 3 (for the data with milling time over 1 h).

Table 6 The apparent rate constants under various milling ball/ore mass ratios Milling ball/ore mass ratio

Rate constant

20:1 40:1 80:1

0.10 0.43 1.72

From Fig. 12 the apparent rate constants in kinetic regime were estimated and presented in Table 6. Assume kt = f(ac )g(R), where f(ac ) is a function of centrifugal acceleration velocity ac , g(R) is a function of milling ball/ore mass ratio R. From the data in Tables 5 and 6 an equation of the apparent rate constant is regressed as kt = 2.1 × 10−5 R2.044 ac2.616 Therefore, the rate equation of mechanochemical oxidation of ilmenite by O2 in kinetic regime can be expressed as d(1 − α) = 2.1 × 10−5 R2.044 ac2.616 (1 − α)2 dt when t > 0.5 h.



References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

4. Conclusion [21]

(1) The mill spin rate and milling ball/ore mass ratio significantly influenced the mechanochemical oxidation of ilmenite. (2) At a initial oxygen pressure ≥33.4 kPa, the oxidation was independent of O2 pressure, and mechanochemical reaction is in kinetic limit. When the initial oxygen pressure ≤27.4 kPa, the oxidation was limited by O2 adsorption. (3) There was an oxygen macro-adsorption accompanying the mechanochemical oxidation of ilmenite at a oxygen

[22] [23] [24] [25] [26] [27]

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