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Mechanism and kinetic study of hydrogen reduction of ultra-fine spherical MoO3 to MoO2
Int. Journal of Refractory Metals and Hard Materials 54 (2016) 342–350
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Mechanism and kinetic study of hydrogen reduction of ultra-fine spherical MoO3 to MoO2 Lu Wang, Guo-Hua Zhang ⁎, Kuo-Chih Chou State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 8 July 2015 Received in revised form 5 September 2015 Accepted 10 September 2015 Available online 14 September 2015 Keywords: Mechanism Kinetics Reduction Morphology Molybdenum trioxide
a b s t r a c t The mechanism and kinetics of hydrogen reduction of ultra-fine spherical MoO3 to MoO2 have been investigated in the present work. The results show that the reduction of MoO3 to MoO2 obeys the two-step reduction mechanism with the generation of intermediate product Mo4O11. The final product MoO2 always keeps the same morphology as Mo4O11. The experimental data can be well described by using the dual interface reaction model. It was found that the rate controlling steps for the first (from MoO3 to Mo4O11) and second reactions (from Mo4O11 to MoO2) were interface chemical reaction and diffusion, respectively, with the activation energies extracted to be 122 kJ/mol and 114 kJ/mol. When the reaction extent (defined as the ratio of weight loss of MoO3 at time t to the theoretical maximum weight loss from MoO3 to MoO2 due to the removal of oxygen during the reduction process) is in the range of 0 to 0.7, both the reduction of MoO3 to Mo4O11 and Mo4O11 to MoO2 occurred simultaneously; when the reaction extent is in the range of 0.7 to 1, only the reduction of Mo4O11 to MoO2 occurred in the reduction process. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Molybdenum metal powders with suitable morphology, size and purity are of immense importance for alloy preparation by powder metallurgy (PW) [1,2]. The industrial production of metallic molybdenum powders is a stepwise process that begins with the reduction of MoO3 to MoO2 by hydrogen [3–5]. This step is an important stage in producing metallic molybdenum, since it has a great influence on the purity and morphology of produced metal molybdenum products [3]. Therefore, it is a prerequisite to have a high quality of MoO3 and MoO2 in order to produce high-performance metal molybdenum powders. Many investigators [6–13] have investigated the mechanism and kinetics of hydrogen reduction of MoO3 to MoO2 in recent years. Kennedy and Bevan [8] conducted the reduction reaction in the temperature range of 753 K to 873 K and reported that the reduction rate is controlled by the diffusion of oxygen ions from the bulk to surface with the activation energy extracted to be 113 kJ/mol. Sloczynski [10] carried out the investigation on the reduction of MoO3 by H2, whose experimental findings confirmed the validity of the autocatalytic reaction model (CAR), according to which the reduction of MoO3 to MoO2 is a consecutive reaction and Mo4O11 is the intermediate product. In addition, it was also concluded that the dissociative adsorption of the reductant H2 was the rate-determining step. Ressler et al. [11] reported that the reduction of MoO3 was a one-step process (MoO3 → MoO2) at the temperature below 698 K, while at the temperature above 698 K, the ⁎ Corresponding author. E-mail address: [email protected] (G.-H. Zhang).
http://dx.doi.org/10.1016/j.ijrmhm.2015.09.003 0263-4368/© 2015 Elsevier Ltd. All rights reserved.
formation of Mo4O11 could be observed. Schulmeyer and Ortner [12] studied the mechanisms of hydrogen reduction of molybdenum oxides and reported that it showed a reaction path of MoO3 → Mo4O11 → MoO2 via chemical vapor transport (CVT), and the formed Mo4O11 and MoO2 exhibited different size distributions and shapes depending on the local partial pressure of H2O. Dang et al. [13] postulated a twointerface reaction model to analyze the reduction processes of MoO3 to MoO2 and concluded that the rate controlling step for the reduction reaction of MoO3 to Mo4O11 was the interface chemical reaction, while that for the reaction of Mo4O11 to MoO2 was changed with the temperature. As stated above, although many related studies have been carried out, the mechanism and kinetic behaviors of hydrogen reduction of MoO3 to MoO2 is a long debated question. In the present work, ultrafine spherical MoO3 particles, which had never been used before, were used for the experimental work to study the reduction kinetics and its influence on the morphology of product MoO2, as a preliminary work to prepare the ultra-fine Mo powder. 2. Materials and experimental procedures 2.1. Materials Ultra-fine MoO3 powders from Jinduicheng Molybdenum Co., Ltd. were used for the experimental purposes. Fig. 1 shows the X-ray diffraction patterns of the studied MoO3 powders. As can be seen from it, most of the studied MoO3 grains belong to monoclinic crystal system (βMoO3), but some belong to orthorhombic crystal system (α-MoO3),
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respectively. It can be seen from Fig. 3 that the sizes of MoO3 particles are less than 1 μm. In addition, most of the particles are spherical except very few orthorhombic (α-MoO3) and hexagonal (h-MoO3) particles. 2.2. Experimental procedures
Fig. 1. X-ray diffraction patterns of studied ultra-fine MoO3 powders.
which is a thermodynamically stable phase below the melting point of MoO3 [14–16]. In order to identify the transition temperature between β-MoO3 and α-MoO3, the non-isothermal Differential Thermal Analysis (DTA) curve of the ultra-fine MoO3 powders was measured and shown in Fig. 2 from room temperature to 850 K with the heating rate of 10 K/min under high purity Ar atmosphere. The DTA curve from 850 K to room temperature was also done to check whether α-MoO 3 can transform back to β-MoO3 again at the transition temperature found in the heating process. If the transition was taken place, the β-MoO3 is a thermodynamically stable phase at the temperature below the characteristic temperature; if not, the β-MoO3 is only a metastable phase. From Fig. 2, it can be seen that there is an exothermic peak with the peak temperature of 708 K in the heating process, but there is no peak in the cooling process. Therefore, it can be concluded that β-MoO3 is a metastable phase and could be transformed to αMoO3 at 708 K, which is in agreement with the transformation temperature of 723 K obtained by McCarron [15]. Since all the reduction temperatures in the present study are higher than 708 K, all the MoO3 are transferred to one phase α-MoO3. The field-emission scanning electron microscope (FE-SEM) and scanning electron microscope (SEM) were used to analyze the morphology of MoO3 samples, with the results shown in Fig. 3(a) and (b),
In order to monitor the weight loss continuously during the reduction process, a thermal analysis system (HTC-2, Beijing Hengjiu Instrument Ltd. China), which includes a thermogravimetry (TG) microbalance with a precision of ±0.1 μg, was used. The schematic diagram of the experimental apparatus is shown in Fig. 4. In each experiment run, MoO3 samples of about 40 mg were used and filled into the alumina crucible “3”, which has a dimension of 7 mm in inner diameter and 7 mm in height. A “dead-burnt” identical alumina crucible “2” was used as the standard reference material. After the crucible “3” with samples was positioned on the supported holder “4”, Ar gas was introduced into the system to drive the air out. Then the furnace was heated from room temperature to the desired reduction temperature with the heating rate of 10 K/min. When the temperature was in stable state and the air was driven out completely, Ar gas was switched to the reducing gas H2 to start the reduction reaction. After the experiment was finished, H2 was switched to Ar again and the samples were cooled to the room temperature. The isothermal kinetic experiments were conducted at 763 K, 773 K, 793 K, 813 K and 833 K. The samples for XRD and morphology analyses were obtained after reacting for different times at 713 K (180 min, 420 min), 753 K (120 min, 180 min), 793 K (15 min, 35 min and 60 min), 813 K (5 min, 15 min, 20 min, 30 min and 40 min) and 833 K (30 min) respectively. In all the experimental runs, a constant gas flow rate of 60 ml/min of H2 (b5 ppm O2) was kept during the reduction process, this level was found to be sufficient for diminishing the diffusion resistance in the gas-boundary layer around the particle. The gas flow rate was controlled by gas flow controllers “1” (Allicant, Model MC-500SCCM-D). XRD technology (Model TTRIII, Japan) was used to identify the phase composition. FE-SEM (ZEISS SUPRA 55) and SEM (Model S250MK3, Cambridge) were used to observe the evolution processes of morphologies. 3. Results 3.1. Isothermal reduction kinetics of ultra-fine MoO3 powders The kinetic curves of reduction extent (defined as the ratio of weight loss of MoO3 to the maximum weight loss from MoO3 to MoO2 due to the remove of oxygen) versus time at 763 K, 773 K, 793 K, 813 K and 833 K are shown in Fig. 5. It can be easily seen that there are linear relationships between the reacted extent and time in all cases except 763 K, which has a retard at the initial stage. The phenomenon indicates that the reduction mechanism is influenced by the reduction temperature. 3.2. X-ray diffraction analyses
Fig. 2. DTA curves of the studied ultra-fine MoO3 powders under high purity Ar atmosphere (heating rate: 10 K/min).
The XRD patterns of reduction products at 713 K and 753 K are presented in Fig. 6, it can be known that Mo4O11 as an intermediate product is formed during the reduction process. From Fig. 6(b), MoO3 is disappeared when the reaction extent is achieved 0.78 (α = 0.78), with the main peaks of intermediate oxide Mo4O11 and final product MoO2. The XRD patterns of reduction products at higher temperatures (793 K and 813 K) are shown in Fig. 7. Both Fig. 7(a) and (b) show that Mo4O11 as an intermediate product is indeed formed in the reduction process; the peaks for Mo4O11 increase at first and go down gradually until disappearance. MoO3 is vanished when the reduction extent is 0.764 at 793 K. Combining with Fig. 6(b), it may indicate that the onestage reduction (MoO3 → Mo4O11) is completed when the reduction extent is around 0.7. It was worth noting that the used MoO3 in all cases
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Fig. 3. Morphologies of studied ultra-fine MoO3 powders: (a) obtained by FE-SEM technology and (b) obtained by SEM technology.
has transformed from β-MoO3 into α-MoO3 during the heating processes at about 708 K, as shown in Fig. 2.
and at both uncompleted and completed reduction states, as shown in Fig. 9(e) and (f). The reasons for the phenomenon will be discussed in the following sections.
3.3. Morphological characteristics of reduction products 3.3.1. Morphologies—effect of reaction temperature Fig. 8 shows the FE-SEM photographs of the final product MoO2 at five different temperatures (713 K, 753 K, 793 K, 813 K and 833 K). Fig. 8(a) represents the morphology of the sample reduced at 713 K, which obviously shows that the final product MoO2 were spherical and the size of MoO2 were fairly small, which almost had the same sizes as the raw MoO3 powders, as shown in Fig. 3. However, as shown in Fig. 8(b), when reduced at 753 K, the morphology of final product MoO2 included spherical particles, but also some platelet-shaped crystals. Furthermore, it is clearly seen that there are some cracks and some small particles at the surface. While with the temperature increasing to 793 K, as shown in Fig. 8(c), most of the product MoO2 presented platelet shape or skeleton structure. At the much higher temperatures, as shown in Fig. 8(d) and (e), the products were all platelet-shaped. 3.3.2. Morphology—effect of reaction extent Fig. 9 shows the morphology evolutions of reduction products at 813 K at different reaction extents, which show that the morphologies of reduction products have remarkable changes with increasing the reaction extent. When the reaction extent was 0.166 as shown in Fig. 9(a), the spherical grains were gradually decreased and disappeared. When the reaction extent was above 0.642, all of the products presented platelet-shaped, as shown in Fig. 9(b), (c) and (d). One of the facts that can't be ignored is that it has an obvious agglomeration phenomenon occurring in all the reducing temperatures
3.3.3. Morphology—obtained at special conditions Fig. 10 shows the morphologies of products obtained at different experimental conditions, which are easier to analyze the reduction mechanism and the morphologies of Mo4O11. When the sample was reduced at 713 K and had a reduction extent of 0.331, as shown in Fig. 10(a) and (b), it can be obviously seen that an amount of small nucleus were formed on the surface, and the spherical nonporous raw MoO3 (Fig. 3) changed to be porous products, which indicates that the transformation to next oxide phase is oriented from the surface to the center of the grain [12]. The products appeared to be a cauliflower morphology or multilayer structure. Combining with the XRD analysis results, as shown in Fig. 6(a), the main phase was Mo4O11, thus the small nucleus may be the intermediate product Mo4O11. That is to say, the morphologies of Mo4O11 are spherical and the same as these of the raw MoO3 and the final product MoO2 at the temperature of 713 K. When the sample was reduced at 753 K and had a reduction extent of 0.780, as shown in Fig. 10(c), the products were spherical or oval shaped. While when the temperature reached 793 K with the reduction extent of 0.764, as shown in Fig. 10(d), all of the products were plateletshaped or skeleton structure. Combining with the results of XRD patterns (Figs. 6(b) and 7(a)), the products were mainly composed of Mo4O11 and MoO2 at these reaction extents, and thus it may indicate that Mo4O11 and MoO2 have the same morphology. Therefore, it can be concluded that the morphology of produced MoO2 depends on the morphology of intermediate product Mo4O11. MoO2 keeps the same morphology as Mo4O11.
Fig. 4. Schematic diagram of the experimental apparatus for the TG analysis. 1, Gas flow meter. 2, Calibrated alumina crucible. 3, Experimental alumina crucible, 4, Sample holder and thermo-couple. 5, HCT-2 TG analyzer. 6, Data collector. 7, Beaker flask A. 8, Beaker flash B. 9, Exhaust gases.
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Fig. 5. Isothermal reduction curves of ultra-fine MoO3 to MoO2 by pure hydrogen.
Fig. 7. XRD patterns of ultra-fine MoO3 reduced by pure hydrogen at (a) 793 K and (b) 813 K. (α represents the reaction extent).
4. Discussion 4.1. Reaction mechanism
Fig. 6. XRD patterns of ultra-fine MoO3 reduced by pure hydrogen at (a) 713 K and (b) 753 K. (α represents the reaction extent).
4MoO3 þ H2 ¼ Mo4 O11 þ H2 O
ð1Þ
Mo4 O11 þ 3H2 ¼ 4MoO2 þ3H2 O
ð2Þ
MoO3 →TP1ðgÞ →Mo4 O11 →TP2ðgÞ →MoO2
ð3Þ
In the present study, MoO3 is first transformed to Mo4O11, and then Mo4O11 is further reduced to the final product MoO2, as expressed in Eqs. (1) and (2), which is easily seen in Figs. 6 and 7. However, the morphologies of final product MoO2 are different at different reduction temperatures, which may be resulted from the different reaction mechanisms. Schulmeyer and Ortner [12] and Dang et al. [13] studied the reduction mechanism of molybdenum oxides and proposed two different reaction paths: pseudomorphic transformation and transformation via chemical vapor transport (CVT) route as shown in Eq. (3). It has been found that during the reduction process of MoO3 by H2, the morphology of final product MoO2 reduced at the temperature of 713 K keeps the same spherical shape as the raw MoO3, as can be seen in Fig. 8(a),
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Fig. 8. FE-SEM photographs of ultra-fine MoO3 samples completely reduced by pure hydrogen at (a) 713 K, (b) 753 K, (c) 793 K, (d) 813 K, and (e) 833 K.
which may be due to the slow reaction rate and low saturation vapor pressures of gaseous species TP1 and TP2. Therefore, the pseudomorphic transformation mechanism should be dominant, and the morphology of produced MoO2 can keep the same as that of the raw MoO3. When the reduction temperatures were in the range of 793 K to 833 K, the reaction rate was much faster than that at 713 K, which will form many molecules of gaseous phases TP1 and TP2, meanwhile their transport rates can be much faster and more Mo4O11 and MoO2 nuclei can be formed. These nuclei grown into platelet shape, as showed in Fig. 8(c), (d) and (e). Therefore, the reduction reaction obeyed chemical vapor transport (CVT) mechanism. However, when the reduction temperature was 753 K, the reaction rate and saturation vapor pressures of gaseous phases TP1 and TP2 were larger than that at 713 K but slower than that above 793 K, which lead to the coexistences of spherical and platelet shape product MoO2, as showed in Fig. 8(b). Therefore, both the pseudomorphic transformation and chemical vapor transport (CVT) mechanisms worked at the temperature of 753 K. On the other hand, the reduction of MoO3 to MoO2 by hydrogen is an exothermic reaction, which will release amounts of heat and increase the local temperature. The higher the reaction temperature is, the larger the released heat will be. When the local temperature approaches the melting point of MoO3 (1068 K) [17,18], the raw MoO3 will be melted which leads to the sticking of particles. It may be the reason for the phenomenon that the particles became larger as increasing the temperature. Furthermore, the agglomeration may be also resulted from the formation of eutectic between MoO3 and Mo4O11, which has a much lower melting point (823 K to 873 K) [4]. Therefore, the agglomeration and sticking of products are due to the combination of the local
temperature increase and the formation of eutectic, which are in well agreement with the results of Enneti and Wolfe [4]. 4.2. Reaction kinetics It can be obviously seen from the isothermal reduction kinetic curves shown in Fig. 5, the curve of 763 K is different from the others, which may be resulted from the different reaction mechanisms. It was concluded that in the temperature range of 735 K to 773 K, the reduction of MoO3 to MoO2 by H2 obeyed the nucleation and growth mechanism [13]. By adding the MoO2 nuclei, it was found that the reduction rate was significantly promoted, while at high temperatures, the effect was much weaker. So the following analyses were done only in the temperature range of 773 K to 833 K. According to the dual interface reaction model [13], the overall reaction extent can be expressed as a linear relationship with α1 and α2 with the corresponding weighting factors (α1 and α2 represent the reaction extents of the first and second reactions, respectively). So, the overall reaction extent can be expressed as α ¼ ε1 α1 þ ε2 α2
ð4Þ
where ε1 and ε2 are the constants depending on the complete removal of oxygen of the first (from MoO3 to Mo4O11) and second (from Mo4O11 to MoO2) reactions. So, it is easy to obtain that ε1 and ε2 are equal to 0.25 and 0.75, respectively. Table 1 lists the algebraic expressions of integral functions g (α) and the explicit forms α [19–21]. These expressions are generally applied for
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Fig. 9. Morphologies of ultra-fine MoO3 samples reduced by hydrogen at 813 K. (a) α = 0.166, (b) α = 0.642, (c) α = 0.915, (d) α = 1, (e) α = 0.642, (f) α = 1. (a, b, c, d, obtained by the FE-SEM; e, f, obtained by the SEM. α represents the reaction extent).
Fig. 10. Morphologies of products obtained at different experimental conditions. (a) T = 713 K, α = 0.331, amplified by 30,000 times, (b) T = 713 K, α = 0.331, amplified by 80,000 times, (c) T = 753 K, α = 0.78, (d) T = 793 K, α = 0.764.
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Table 1 List of the rate expressions of different gas–solid reaction models. Models
Integral form g(α) = kt
Explicit form
Geometrical contraction models 1. Contracting area (R2) 2. Contracting volume (R3)
1 − (1 − α)1/2 1 − (1 − α)1/3
α = 1 − (1 − kt)2 α = 1 − (1 − kt)3
Diffusion models 3. Jander equation (2D, n = 1/2) 4. Jander equation (2D, n = 2) 5. Jander equation (3D, n = 1/2) 6. Jander equation (3D, n = 2)
[1 − (1 − α)1/2]1/2 [1 − (1 − α)1/2]2 [1 − (1 − α)1/3]1/2 [1 − (1 − α)1/3]2
α = 1 − [1 − (kt)2]2 α = 1 − [1 − (kt)1/2]2 α = 1 − [1 − (kt)2]3 α = 1 − [1 − (kt)1/2]3
Nucleation and growth models 7. Power law (P2) 8. Power law (P3) 9. Avrami-Erofe'ev (A1.5) 10. Avrami-Erofe'ev (A2) 11. Avrami-Erofe'ev (A3) 12. Avrami-Erofe'ev (A4)
α1/2 α1/3 [−ln(1 − α)]2/3 [−ln(1 − α)]1/2 [−ln(1-α)]1/3 [−ln(1-α)]1/4
α = (kt)2 α = (kt)3 α = 1 − exp[−(kt)3/2] α = 1 − exp[−(kt)2] α = 1 − exp[−(kt)3] α = 1 − exp[−(kt)4]
the kinetic analysis of gas–solid reactions and encompass most common mechanisms. In Table 1, k is the rate constant as a function of temperature, and the temperature dependence of the rate constant is described by the Arrhenius equation, ΔE k ¼ A exp − RT
ð5Þ
where A is the pre-exponential factor (frequency factor), ΔE is the activation energy, R is the gas constant and T is the absolute temperature. Substituting Eq. (5) and the different models in Table 1 into Eq. (4), and the corresponding reaction models will be obtained. According to the best fit of the experimental data, it is found that model 2 and model 5 can well describe the reduction processes of MoO3 to Mo4O11 and Mo4O11 to MoO2 in the temperature range of 773 K to 833 K, respectively. Thus the total reaction extent α can be written as ( 3 ) ΔE1 t α ¼ ε1 1− 1−A1 exp − RT 9 8 " 2 #3 = < ΔE2 t þ ε2 1− 1− A2 exp − ; : RT
Fig. 11. Comparisons of calculated and measured reaction extent vs reaction time curves for the reduction of MoO3 to MoO2 by pure hydrogen. (R is the correlation coefficient).
ð6Þ
where numbers 1 and 2 represent the 1st and 2nd reactions, respectively. Fig. 11 shows the comparisons of the results of measured and calculated reaction extents with Eq. (6), it can be easily seen that the model calculated results are well in agreement with the experimental data. Also, it can be found from Fig. 11(b) that the calculated curve of 763 K by the parameter optimized with the data of 773 K, 793 K, 813 K and 833 K has a large deviation with the experimental data at the initial stage, which may be influenced by the nucleation effect which always occurred at the low temperature. So, the corresponding kinetic equation can be given as shown in Eq. (7). In Eq. (7), R is the gas constant, 8.314 J/(mol⋅K); T is the absolute temperature, K; 122084 and 114769 are the activation energies, J/mol. ( 3 ) 122:084 α ¼ 0:25 1− 1−2:549 106 exp − t RT 8 9 " 2 #3 = < 114:769 þ 0:75 1− 1− 5:759 105 exp − t : ; RT ð7Þ 3 122:084 t −0:75 ¼ 1−0:25 1−2:549 106 exp − RT (
2 )3 114:769 1− 5:759 105 exp − : t RT
The activation energies for the reduction reaction of MoO 3 to Mo4 O 11 and Mo 4O 11 to MoO 2 are extracted to be 122.084 kJ/mol and 114.769 kJ/mol, respectively, which are close to the values of 143.6 kJ/mol and 132.3 kJ/mol obtained by Dang et al. [13] in the temperature range of 793 K to 829 K. One difference is that the rate controlling step for the reduction reaction of MoO3 to Mo4O11 is contracting area (model 1) obtained by Dang et al. [13], while in the present work, the rate controlling step for that is contracting volume (model 2), which is supported by the spherical shaped raw MoO3 materials used in the present study as shown in Fig. 3. 4.3. Applications of the model According to the above kinetic analyses, it is found that the reduction of MoO3 to MoO2 belongs to the two-step reduction mechanism with the intermediate product Mo4O11. α1
α2
MoO3 → Mo4 O11 → MoO2
ð8Þ
The expression forms of α1 and α2 are obtained as follows, 3 122:084 t α1 ¼ 1− 1−2:549 106 exp − RT
ð9Þ
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"
2 #3 114:769 5 α2 ¼ 1− 1− 5:759 10 exp − t RT
ð10Þ
where α1 and α2 are in the range of 0 to 1. If assuming the initial raw materials of MoO3 were 1 g, because α1 and α2 represent the reaction extents of the reactions from MoO3 to Mo4O11 and from Mo4O11 to MoO2, respectively, then after time t, the masses of reacted and unreacted MoO3 are α1 g and (1-α1) g, respectively. Therefore, the produced Mo4O11 will be α1
MMo4 O11 4MMoO3
reacted and unreacted Mo4O11 will be α 1
α 2 g and α1
ð1−α2 Þ g, and the produced MoO2 will be α1
MMo4 O11 4MMoO3
α2
MMo4 O11 4MMoO3
4MMoO2 MMo4 O11
g.
According to the above analyses, the masses of MoO3, Mo4O11 and MoO2 can be calculated as follows, mMoO3 ;t ¼ 1−α1 mMo4 O11 ;t ¼ α1
mMoO2 ;t ¼ α1
ð11Þ
M Mo4 O11 MMo4 O11 ð1−α2 Þ ¼ α1 ð1−α2 Þ 4MMoO3 4MMoO3
M Mo4 O11 4MMoO2 MMoO2 α2 ¼ α1 α2 4MMoO3 MMo4 O11 MMoO3
ð12Þ
ð13Þ
where m is the mass after time t, and M is the relative molecule weight. Substituting Eqs. (9) and (10) into Eqs. (11), (12) and (13), yield 3 122:084 t mMoO3 ;t ¼ 1−2:549 106 exp − RT
" 2 #3 α 1 MMo4 O11 114:769 5 ¼ 1− 5:759 10 exp − ð15Þ t 4M MoO3 RT
mMoO2 ;t ¼
( 3 ) M MoO2 122:084 1− 1−2:549 106 exp − t M MoO3 RT 9 8 " 2 #3 = < 114:769 5 1− 1− 5:759 10 exp − t ; : RT
ð16Þ
g. Due to
the transformation of Mo4O11 to MoO2, after time t, the masses of MMo4 O11 4MMoO3
mMo4 O11 ;t
349
ð14Þ
So, the relationship between the mass of different components and reaction time t can be obtained. Fig. 12 shows the weights of different oxides with time plotted according to Eqs. (14), (15) and (16) at different temperatures. It can be easily seen that MoO3 and MoO2 are monotonously decreased and increased, respectively. Whereas for Mo4O11, it first increases to a maximum value and then decreases until it is completely disappeared. The phenomenon can be proved by the results of the XRD patterns in Figs. 6 and 7. If approximately assuming mMoO3 ;t ¼ 0:01 g
ð17Þ
as the critical disappearing point of MoO3 (the remaining mass is 1% relative to the initial mass), the corresponding critical time t and critical reaction extent α are listed in Table 2. It can be seen that even though the critical time of MoO3 decreases when increasing the reaction temperature, the critical reaction extent is almost kept constant, which is around 0.7. According to the XRD analysis shown in Fig. 7, it can be known that the raw MoO3 was already exhausted when the reaction extent is 0.764, which is well coincided with the predicted value of 0.7. Therefore, it can be known that the three oxide phases can coexist only when reaction
Fig. 12. Predicted mass values of different oxides at different temperatures.
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References
Table 2 Lists of critical time and critical reaction extent. Temperature/(K)
773
793
813
833
Critical time/min Critical reaction extent α
54.7 0.7001
33.4 0.7228
21.5 0.6974
13.9 0.7050
extent is below 0.7. While the reaction extent is above 0.7 (not equal to 1), only Mo4O11 and MoO2 existed in the system, and there is only the reduction reaction from Mo4O11 to MoO2. 5. Conclusions In the present study, the hydrogen reduction of MoO3 to MoO2 in the temperature range of 763 K to 833 K was investigated. The following conclusions can be drawn. 1. The morphology of intermediate product Mo4O11 has a great influence on that of the final product MoO2. MoO2 always keeps the same morphology as Mo4O11. 2. Reduction of MoO3 to MoO2 obeys the two-stage reaction mechanism with the intermediate oxide Mo4O11. The rate controlling steps for the reduction of MoO3 to Mo4O11 and Mo4O11 to MoO2 are interface chemical reaction and diffusion model, respectively. The extracted activation energies are 122 kJ/mol and 114 kJ/mol, respectively. 3. When the reaction extent is in the range of 0 to 0.7, both the reductions of MoO3 to Mo4O11 and Mo4O11 to MoO2 occur simultaneously; when the reaction extent is in the range of 0.7 to 1, only the reduction of Mo4O11 to MoO2 occur in the reduction process.
Acknowledgments The authors gratefully acknowledge the support by Jinduicheng Molybdenum Co., Ltd. in raw material and the financial support from the National Natural Science Foundation of China (51304018 and 51474141).
[1] S. Majumdar, I. Sharma, I. Samajdar, P. Bhargava, Kinetic studies on hydrogen reduction of MoO3 and morphological analysis of reduced Mo powder, Metall. Mater. Trans. B Process Metall. Mater. Process. Sci. 39 (2008) 431–438. [2] J. Dang, G.H. Zhang, K.C. Chou, A morphological study of the reduction of MoO2 by hydrogen, High Temp. Mater. Processes (2014)http://dx.doi.org/10.1515/htmp2014-0064. [3] J. Dang, G.H. Zhang, K.C. Chou, Phase transitions and morphology evolutions during hydrogen reduction of MoO3 to MoO2, High Temp. Mater. Processes (2014) 1–8. [4] R.K. Enneti, T.A. Wolfe, Agglomeration during reduction of MoO3, Int. J. Refract. Met. Hard Mater. 31 (2012) 47–50. [5] E. Lalik, Kinetic analysis of reduction of MoO3 to MoO2, Catal. Today 169 (2011) 85–92. [6] J. Von Destinon-Forstmann, The hydrogen reduction kinetics of molybdenum oxides, Can. Metall. Q. 4 (1965) 1–12. [7] D.T. Hawkins, W.L. Worrell, Hydrogen reduction of MoO3 at temperatures between 300° and 450 °C, Metall. Trans. 1 (1970) 271–273. [8] M. Kennedy, S. Bevan, A kinetic study of the reduction of molybdenum trioxide by hydrogen, J. Less Common Met. 36 (1974) 23–30. [9] W. Thöni, P. Hirsch, The reduction of MoO3 at low temperatures, Philos. Mag. 33 (1976) 639–662. [10] J. Słoczyński, Kinetics and mechanism of molybdenum (VI) oxide reduction, J. Solid State Chem. 118 (1995) 84–92. [11] T. Ressler, R. Jentoft, J. Wienold, M. Günter, O. Timpe, In situ XAS and XRD studies on the formation of Mo suboxides during reduction of MoO3, J. Phys. Chem. B 104 (2000) 6360–6370. [12] W.V. Schulmeyer, H.M. Ortner, Mechanisms of the hydrogen reduction of molybdenum oxides, Int. J. Refract. Met. Hard Mater. 20 (2002) 261–269. [13] J. Dang, G.H. Zhang, K.C. Chou, R.G. Reddy, Y. He, Y. Sun, Kinetics and mechanism of hydrogen reduction of MoO3 to MoO2, Int. J. Refract. Met. Hard Mater. 41 (2013) 216–223. [14] S. Balakumar, H. Zeng, Growth modes in vapour-phase prepared orthorhombic molybdenum trioxide crystals, J. Cryst. Growth 197 (1999) 186–194. [15] E. McCarron, β-MoO3: a metastable analogue of WO3, J. Chem. Soc. Chem. Commun. (1986) 336–338. [16] T. Mizushima, Y. Moriya, N.H.H. Phuc, H. Ohkita, N. Kakuta, Soft chemical transformation of α-MoO3 to β-MoO3 as a catalyst for vapor-phase oxidation of methanol, Catal. Commun. 13 (2011) 10–13. [17] A. Chychko, L. Teng, S. Seetharaman, MoO3 evaporation studies from binary systems towards choice of Mo precursors in EAF, Steel Res. Int. 81 (2010) 784–791. [18] E. Gulbransen, K. Andrew, F. Brassart, Vapor pressure of molybdenum trioxide, J. Electrochem. Soc. 110 (1963) 242–243. [19] R. Ebrahimi Kahrizsangi, M.H. Abbasi, A. Saidi, Model-fitting approach to kinetic analysis of non-isothermal oxidation of molybdenite, J. Chem. Eng. Res. 26 (2007) 119–123. [20] S. Vyazovkin, C.A. Wight, Model-free and model-fitting approaches to kinetic analysis of isothermal and nonisothermal data, Thermochim. Acta 340 (1999) 53–68. [21] B.S. Kim, E.Y. Kim, H.S. Jeon, H.I. Lee, J.C. Lee, Study on the reduction of molybdenum dioxide by hydrogen, Mater. Trans. 49 (2008) 2147.
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Int. Journal of Refractory Metals and Hard Materials journal homepage: www.elsevier.com/locate/IJRMHM
Mechanism and kinetic study of hydrogen reduction of ultra-fine spherical MoO3 to MoO2 Lu Wang, Guo-Hua Zhang ⁎, Kuo-Chih Chou State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083, China
a r t i c l e
i n f o
Article history: Received 8 July 2015 Received in revised form 5 September 2015 Accepted 10 September 2015 Available online 14 September 2015 Keywords: Mechanism Kinetics Reduction Morphology Molybdenum trioxide
a b s t r a c t The mechanism and kinetics of hydrogen reduction of ultra-fine spherical MoO3 to MoO2 have been investigated in the present work. The results show that the reduction of MoO3 to MoO2 obeys the two-step reduction mechanism with the generation of intermediate product Mo4O11. The final product MoO2 always keeps the same morphology as Mo4O11. The experimental data can be well described by using the dual interface reaction model. It was found that the rate controlling steps for the first (from MoO3 to Mo4O11) and second reactions (from Mo4O11 to MoO2) were interface chemical reaction and diffusion, respectively, with the activation energies extracted to be 122 kJ/mol and 114 kJ/mol. When the reaction extent (defined as the ratio of weight loss of MoO3 at time t to the theoretical maximum weight loss from MoO3 to MoO2 due to the removal of oxygen during the reduction process) is in the range of 0 to 0.7, both the reduction of MoO3 to Mo4O11 and Mo4O11 to MoO2 occurred simultaneously; when the reaction extent is in the range of 0.7 to 1, only the reduction of Mo4O11 to MoO2 occurred in the reduction process. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Molybdenum metal powders with suitable morphology, size and purity are of immense importance for alloy preparation by powder metallurgy (PW) [1,2]. The industrial production of metallic molybdenum powders is a stepwise process that begins with the reduction of MoO3 to MoO2 by hydrogen [3–5]. This step is an important stage in producing metallic molybdenum, since it has a great influence on the purity and morphology of produced metal molybdenum products [3]. Therefore, it is a prerequisite to have a high quality of MoO3 and MoO2 in order to produce high-performance metal molybdenum powders. Many investigators [6–13] have investigated the mechanism and kinetics of hydrogen reduction of MoO3 to MoO2 in recent years. Kennedy and Bevan [8] conducted the reduction reaction in the temperature range of 753 K to 873 K and reported that the reduction rate is controlled by the diffusion of oxygen ions from the bulk to surface with the activation energy extracted to be 113 kJ/mol. Sloczynski [10] carried out the investigation on the reduction of MoO3 by H2, whose experimental findings confirmed the validity of the autocatalytic reaction model (CAR), according to which the reduction of MoO3 to MoO2 is a consecutive reaction and Mo4O11 is the intermediate product. In addition, it was also concluded that the dissociative adsorption of the reductant H2 was the rate-determining step. Ressler et al. [11] reported that the reduction of MoO3 was a one-step process (MoO3 → MoO2) at the temperature below 698 K, while at the temperature above 698 K, the ⁎ Corresponding author. E-mail address: [email protected] (G.-H. Zhang).
http://dx.doi.org/10.1016/j.ijrmhm.2015.09.003 0263-4368/© 2015 Elsevier Ltd. All rights reserved.
formation of Mo4O11 could be observed. Schulmeyer and Ortner [12] studied the mechanisms of hydrogen reduction of molybdenum oxides and reported that it showed a reaction path of MoO3 → Mo4O11 → MoO2 via chemical vapor transport (CVT), and the formed Mo4O11 and MoO2 exhibited different size distributions and shapes depending on the local partial pressure of H2O. Dang et al. [13] postulated a twointerface reaction model to analyze the reduction processes of MoO3 to MoO2 and concluded that the rate controlling step for the reduction reaction of MoO3 to Mo4O11 was the interface chemical reaction, while that for the reaction of Mo4O11 to MoO2 was changed with the temperature. As stated above, although many related studies have been carried out, the mechanism and kinetic behaviors of hydrogen reduction of MoO3 to MoO2 is a long debated question. In the present work, ultrafine spherical MoO3 particles, which had never been used before, were used for the experimental work to study the reduction kinetics and its influence on the morphology of product MoO2, as a preliminary work to prepare the ultra-fine Mo powder. 2. Materials and experimental procedures 2.1. Materials Ultra-fine MoO3 powders from Jinduicheng Molybdenum Co., Ltd. were used for the experimental purposes. Fig. 1 shows the X-ray diffraction patterns of the studied MoO3 powders. As can be seen from it, most of the studied MoO3 grains belong to monoclinic crystal system (βMoO3), but some belong to orthorhombic crystal system (α-MoO3),
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respectively. It can be seen from Fig. 3 that the sizes of MoO3 particles are less than 1 μm. In addition, most of the particles are spherical except very few orthorhombic (α-MoO3) and hexagonal (h-MoO3) particles. 2.2. Experimental procedures
Fig. 1. X-ray diffraction patterns of studied ultra-fine MoO3 powders.
which is a thermodynamically stable phase below the melting point of MoO3 [14–16]. In order to identify the transition temperature between β-MoO3 and α-MoO3, the non-isothermal Differential Thermal Analysis (DTA) curve of the ultra-fine MoO3 powders was measured and shown in Fig. 2 from room temperature to 850 K with the heating rate of 10 K/min under high purity Ar atmosphere. The DTA curve from 850 K to room temperature was also done to check whether α-MoO 3 can transform back to β-MoO3 again at the transition temperature found in the heating process. If the transition was taken place, the β-MoO3 is a thermodynamically stable phase at the temperature below the characteristic temperature; if not, the β-MoO3 is only a metastable phase. From Fig. 2, it can be seen that there is an exothermic peak with the peak temperature of 708 K in the heating process, but there is no peak in the cooling process. Therefore, it can be concluded that β-MoO3 is a metastable phase and could be transformed to αMoO3 at 708 K, which is in agreement with the transformation temperature of 723 K obtained by McCarron [15]. Since all the reduction temperatures in the present study are higher than 708 K, all the MoO3 are transferred to one phase α-MoO3. The field-emission scanning electron microscope (FE-SEM) and scanning electron microscope (SEM) were used to analyze the morphology of MoO3 samples, with the results shown in Fig. 3(a) and (b),
In order to monitor the weight loss continuously during the reduction process, a thermal analysis system (HTC-2, Beijing Hengjiu Instrument Ltd. China), which includes a thermogravimetry (TG) microbalance with a precision of ±0.1 μg, was used. The schematic diagram of the experimental apparatus is shown in Fig. 4. In each experiment run, MoO3 samples of about 40 mg were used and filled into the alumina crucible “3”, which has a dimension of 7 mm in inner diameter and 7 mm in height. A “dead-burnt” identical alumina crucible “2” was used as the standard reference material. After the crucible “3” with samples was positioned on the supported holder “4”, Ar gas was introduced into the system to drive the air out. Then the furnace was heated from room temperature to the desired reduction temperature with the heating rate of 10 K/min. When the temperature was in stable state and the air was driven out completely, Ar gas was switched to the reducing gas H2 to start the reduction reaction. After the experiment was finished, H2 was switched to Ar again and the samples were cooled to the room temperature. The isothermal kinetic experiments were conducted at 763 K, 773 K, 793 K, 813 K and 833 K. The samples for XRD and morphology analyses were obtained after reacting for different times at 713 K (180 min, 420 min), 753 K (120 min, 180 min), 793 K (15 min, 35 min and 60 min), 813 K (5 min, 15 min, 20 min, 30 min and 40 min) and 833 K (30 min) respectively. In all the experimental runs, a constant gas flow rate of 60 ml/min of H2 (b5 ppm O2) was kept during the reduction process, this level was found to be sufficient for diminishing the diffusion resistance in the gas-boundary layer around the particle. The gas flow rate was controlled by gas flow controllers “1” (Allicant, Model MC-500SCCM-D). XRD technology (Model TTRIII, Japan) was used to identify the phase composition. FE-SEM (ZEISS SUPRA 55) and SEM (Model S250MK3, Cambridge) were used to observe the evolution processes of morphologies. 3. Results 3.1. Isothermal reduction kinetics of ultra-fine MoO3 powders The kinetic curves of reduction extent (defined as the ratio of weight loss of MoO3 to the maximum weight loss from MoO3 to MoO2 due to the remove of oxygen) versus time at 763 K, 773 K, 793 K, 813 K and 833 K are shown in Fig. 5. It can be easily seen that there are linear relationships between the reacted extent and time in all cases except 763 K, which has a retard at the initial stage. The phenomenon indicates that the reduction mechanism is influenced by the reduction temperature. 3.2. X-ray diffraction analyses
Fig. 2. DTA curves of the studied ultra-fine MoO3 powders under high purity Ar atmosphere (heating rate: 10 K/min).
The XRD patterns of reduction products at 713 K and 753 K are presented in Fig. 6, it can be known that Mo4O11 as an intermediate product is formed during the reduction process. From Fig. 6(b), MoO3 is disappeared when the reaction extent is achieved 0.78 (α = 0.78), with the main peaks of intermediate oxide Mo4O11 and final product MoO2. The XRD patterns of reduction products at higher temperatures (793 K and 813 K) are shown in Fig. 7. Both Fig. 7(a) and (b) show that Mo4O11 as an intermediate product is indeed formed in the reduction process; the peaks for Mo4O11 increase at first and go down gradually until disappearance. MoO3 is vanished when the reduction extent is 0.764 at 793 K. Combining with Fig. 6(b), it may indicate that the onestage reduction (MoO3 → Mo4O11) is completed when the reduction extent is around 0.7. It was worth noting that the used MoO3 in all cases
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Fig. 3. Morphologies of studied ultra-fine MoO3 powders: (a) obtained by FE-SEM technology and (b) obtained by SEM technology.
has transformed from β-MoO3 into α-MoO3 during the heating processes at about 708 K, as shown in Fig. 2.
and at both uncompleted and completed reduction states, as shown in Fig. 9(e) and (f). The reasons for the phenomenon will be discussed in the following sections.
3.3. Morphological characteristics of reduction products 3.3.1. Morphologies—effect of reaction temperature Fig. 8 shows the FE-SEM photographs of the final product MoO2 at five different temperatures (713 K, 753 K, 793 K, 813 K and 833 K). Fig. 8(a) represents the morphology of the sample reduced at 713 K, which obviously shows that the final product MoO2 were spherical and the size of MoO2 were fairly small, which almost had the same sizes as the raw MoO3 powders, as shown in Fig. 3. However, as shown in Fig. 8(b), when reduced at 753 K, the morphology of final product MoO2 included spherical particles, but also some platelet-shaped crystals. Furthermore, it is clearly seen that there are some cracks and some small particles at the surface. While with the temperature increasing to 793 K, as shown in Fig. 8(c), most of the product MoO2 presented platelet shape or skeleton structure. At the much higher temperatures, as shown in Fig. 8(d) and (e), the products were all platelet-shaped. 3.3.2. Morphology—effect of reaction extent Fig. 9 shows the morphology evolutions of reduction products at 813 K at different reaction extents, which show that the morphologies of reduction products have remarkable changes with increasing the reaction extent. When the reaction extent was 0.166 as shown in Fig. 9(a), the spherical grains were gradually decreased and disappeared. When the reaction extent was above 0.642, all of the products presented platelet-shaped, as shown in Fig. 9(b), (c) and (d). One of the facts that can't be ignored is that it has an obvious agglomeration phenomenon occurring in all the reducing temperatures
3.3.3. Morphology—obtained at special conditions Fig. 10 shows the morphologies of products obtained at different experimental conditions, which are easier to analyze the reduction mechanism and the morphologies of Mo4O11. When the sample was reduced at 713 K and had a reduction extent of 0.331, as shown in Fig. 10(a) and (b), it can be obviously seen that an amount of small nucleus were formed on the surface, and the spherical nonporous raw MoO3 (Fig. 3) changed to be porous products, which indicates that the transformation to next oxide phase is oriented from the surface to the center of the grain [12]. The products appeared to be a cauliflower morphology or multilayer structure. Combining with the XRD analysis results, as shown in Fig. 6(a), the main phase was Mo4O11, thus the small nucleus may be the intermediate product Mo4O11. That is to say, the morphologies of Mo4O11 are spherical and the same as these of the raw MoO3 and the final product MoO2 at the temperature of 713 K. When the sample was reduced at 753 K and had a reduction extent of 0.780, as shown in Fig. 10(c), the products were spherical or oval shaped. While when the temperature reached 793 K with the reduction extent of 0.764, as shown in Fig. 10(d), all of the products were plateletshaped or skeleton structure. Combining with the results of XRD patterns (Figs. 6(b) and 7(a)), the products were mainly composed of Mo4O11 and MoO2 at these reaction extents, and thus it may indicate that Mo4O11 and MoO2 have the same morphology. Therefore, it can be concluded that the morphology of produced MoO2 depends on the morphology of intermediate product Mo4O11. MoO2 keeps the same morphology as Mo4O11.
Fig. 4. Schematic diagram of the experimental apparatus for the TG analysis. 1, Gas flow meter. 2, Calibrated alumina crucible. 3, Experimental alumina crucible, 4, Sample holder and thermo-couple. 5, HCT-2 TG analyzer. 6, Data collector. 7, Beaker flask A. 8, Beaker flash B. 9, Exhaust gases.
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Fig. 5. Isothermal reduction curves of ultra-fine MoO3 to MoO2 by pure hydrogen.
Fig. 7. XRD patterns of ultra-fine MoO3 reduced by pure hydrogen at (a) 793 K and (b) 813 K. (α represents the reaction extent).
4. Discussion 4.1. Reaction mechanism
Fig. 6. XRD patterns of ultra-fine MoO3 reduced by pure hydrogen at (a) 713 K and (b) 753 K. (α represents the reaction extent).
4MoO3 þ H2 ¼ Mo4 O11 þ H2 O
ð1Þ
Mo4 O11 þ 3H2 ¼ 4MoO2 þ3H2 O
ð2Þ
MoO3 →TP1ðgÞ →Mo4 O11 →TP2ðgÞ →MoO2
ð3Þ
In the present study, MoO3 is first transformed to Mo4O11, and then Mo4O11 is further reduced to the final product MoO2, as expressed in Eqs. (1) and (2), which is easily seen in Figs. 6 and 7. However, the morphologies of final product MoO2 are different at different reduction temperatures, which may be resulted from the different reaction mechanisms. Schulmeyer and Ortner [12] and Dang et al. [13] studied the reduction mechanism of molybdenum oxides and proposed two different reaction paths: pseudomorphic transformation and transformation via chemical vapor transport (CVT) route as shown in Eq. (3). It has been found that during the reduction process of MoO3 by H2, the morphology of final product MoO2 reduced at the temperature of 713 K keeps the same spherical shape as the raw MoO3, as can be seen in Fig. 8(a),
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Fig. 8. FE-SEM photographs of ultra-fine MoO3 samples completely reduced by pure hydrogen at (a) 713 K, (b) 753 K, (c) 793 K, (d) 813 K, and (e) 833 K.
which may be due to the slow reaction rate and low saturation vapor pressures of gaseous species TP1 and TP2. Therefore, the pseudomorphic transformation mechanism should be dominant, and the morphology of produced MoO2 can keep the same as that of the raw MoO3. When the reduction temperatures were in the range of 793 K to 833 K, the reaction rate was much faster than that at 713 K, which will form many molecules of gaseous phases TP1 and TP2, meanwhile their transport rates can be much faster and more Mo4O11 and MoO2 nuclei can be formed. These nuclei grown into platelet shape, as showed in Fig. 8(c), (d) and (e). Therefore, the reduction reaction obeyed chemical vapor transport (CVT) mechanism. However, when the reduction temperature was 753 K, the reaction rate and saturation vapor pressures of gaseous phases TP1 and TP2 were larger than that at 713 K but slower than that above 793 K, which lead to the coexistences of spherical and platelet shape product MoO2, as showed in Fig. 8(b). Therefore, both the pseudomorphic transformation and chemical vapor transport (CVT) mechanisms worked at the temperature of 753 K. On the other hand, the reduction of MoO3 to MoO2 by hydrogen is an exothermic reaction, which will release amounts of heat and increase the local temperature. The higher the reaction temperature is, the larger the released heat will be. When the local temperature approaches the melting point of MoO3 (1068 K) [17,18], the raw MoO3 will be melted which leads to the sticking of particles. It may be the reason for the phenomenon that the particles became larger as increasing the temperature. Furthermore, the agglomeration may be also resulted from the formation of eutectic between MoO3 and Mo4O11, which has a much lower melting point (823 K to 873 K) [4]. Therefore, the agglomeration and sticking of products are due to the combination of the local
temperature increase and the formation of eutectic, which are in well agreement with the results of Enneti and Wolfe [4]. 4.2. Reaction kinetics It can be obviously seen from the isothermal reduction kinetic curves shown in Fig. 5, the curve of 763 K is different from the others, which may be resulted from the different reaction mechanisms. It was concluded that in the temperature range of 735 K to 773 K, the reduction of MoO3 to MoO2 by H2 obeyed the nucleation and growth mechanism [13]. By adding the MoO2 nuclei, it was found that the reduction rate was significantly promoted, while at high temperatures, the effect was much weaker. So the following analyses were done only in the temperature range of 773 K to 833 K. According to the dual interface reaction model [13], the overall reaction extent can be expressed as a linear relationship with α1 and α2 with the corresponding weighting factors (α1 and α2 represent the reaction extents of the first and second reactions, respectively). So, the overall reaction extent can be expressed as α ¼ ε1 α1 þ ε2 α2
ð4Þ
where ε1 and ε2 are the constants depending on the complete removal of oxygen of the first (from MoO3 to Mo4O11) and second (from Mo4O11 to MoO2) reactions. So, it is easy to obtain that ε1 and ε2 are equal to 0.25 and 0.75, respectively. Table 1 lists the algebraic expressions of integral functions g (α) and the explicit forms α [19–21]. These expressions are generally applied for
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Fig. 9. Morphologies of ultra-fine MoO3 samples reduced by hydrogen at 813 K. (a) α = 0.166, (b) α = 0.642, (c) α = 0.915, (d) α = 1, (e) α = 0.642, (f) α = 1. (a, b, c, d, obtained by the FE-SEM; e, f, obtained by the SEM. α represents the reaction extent).
Fig. 10. Morphologies of products obtained at different experimental conditions. (a) T = 713 K, α = 0.331, amplified by 30,000 times, (b) T = 713 K, α = 0.331, amplified by 80,000 times, (c) T = 753 K, α = 0.78, (d) T = 793 K, α = 0.764.
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Table 1 List of the rate expressions of different gas–solid reaction models. Models
Integral form g(α) = kt
Explicit form
Geometrical contraction models 1. Contracting area (R2) 2. Contracting volume (R3)
1 − (1 − α)1/2 1 − (1 − α)1/3
α = 1 − (1 − kt)2 α = 1 − (1 − kt)3
Diffusion models 3. Jander equation (2D, n = 1/2) 4. Jander equation (2D, n = 2) 5. Jander equation (3D, n = 1/2) 6. Jander equation (3D, n = 2)
[1 − (1 − α)1/2]1/2 [1 − (1 − α)1/2]2 [1 − (1 − α)1/3]1/2 [1 − (1 − α)1/3]2
α = 1 − [1 − (kt)2]2 α = 1 − [1 − (kt)1/2]2 α = 1 − [1 − (kt)2]3 α = 1 − [1 − (kt)1/2]3
Nucleation and growth models 7. Power law (P2) 8. Power law (P3) 9. Avrami-Erofe'ev (A1.5) 10. Avrami-Erofe'ev (A2) 11. Avrami-Erofe'ev (A3) 12. Avrami-Erofe'ev (A4)
α1/2 α1/3 [−ln(1 − α)]2/3 [−ln(1 − α)]1/2 [−ln(1-α)]1/3 [−ln(1-α)]1/4
α = (kt)2 α = (kt)3 α = 1 − exp[−(kt)3/2] α = 1 − exp[−(kt)2] α = 1 − exp[−(kt)3] α = 1 − exp[−(kt)4]
the kinetic analysis of gas–solid reactions and encompass most common mechanisms. In Table 1, k is the rate constant as a function of temperature, and the temperature dependence of the rate constant is described by the Arrhenius equation, ΔE k ¼ A exp − RT
ð5Þ
where A is the pre-exponential factor (frequency factor), ΔE is the activation energy, R is the gas constant and T is the absolute temperature. Substituting Eq. (5) and the different models in Table 1 into Eq. (4), and the corresponding reaction models will be obtained. According to the best fit of the experimental data, it is found that model 2 and model 5 can well describe the reduction processes of MoO3 to Mo4O11 and Mo4O11 to MoO2 in the temperature range of 773 K to 833 K, respectively. Thus the total reaction extent α can be written as ( 3 ) ΔE1 t α ¼ ε1 1− 1−A1 exp − RT 9 8 " 2 #3 = < ΔE2 t þ ε2 1− 1− A2 exp − ; : RT
Fig. 11. Comparisons of calculated and measured reaction extent vs reaction time curves for the reduction of MoO3 to MoO2 by pure hydrogen. (R is the correlation coefficient).
ð6Þ
where numbers 1 and 2 represent the 1st and 2nd reactions, respectively. Fig. 11 shows the comparisons of the results of measured and calculated reaction extents with Eq. (6), it can be easily seen that the model calculated results are well in agreement with the experimental data. Also, it can be found from Fig. 11(b) that the calculated curve of 763 K by the parameter optimized with the data of 773 K, 793 K, 813 K and 833 K has a large deviation with the experimental data at the initial stage, which may be influenced by the nucleation effect which always occurred at the low temperature. So, the corresponding kinetic equation can be given as shown in Eq. (7). In Eq. (7), R is the gas constant, 8.314 J/(mol⋅K); T is the absolute temperature, K; 122084 and 114769 are the activation energies, J/mol. ( 3 ) 122:084 α ¼ 0:25 1− 1−2:549 106 exp − t RT 8 9 " 2 #3 = < 114:769 þ 0:75 1− 1− 5:759 105 exp − t : ; RT ð7Þ 3 122:084 t −0:75 ¼ 1−0:25 1−2:549 106 exp − RT (
2 )3 114:769 1− 5:759 105 exp − : t RT
The activation energies for the reduction reaction of MoO 3 to Mo4 O 11 and Mo 4O 11 to MoO 2 are extracted to be 122.084 kJ/mol and 114.769 kJ/mol, respectively, which are close to the values of 143.6 kJ/mol and 132.3 kJ/mol obtained by Dang et al. [13] in the temperature range of 793 K to 829 K. One difference is that the rate controlling step for the reduction reaction of MoO3 to Mo4O11 is contracting area (model 1) obtained by Dang et al. [13], while in the present work, the rate controlling step for that is contracting volume (model 2), which is supported by the spherical shaped raw MoO3 materials used in the present study as shown in Fig. 3. 4.3. Applications of the model According to the above kinetic analyses, it is found that the reduction of MoO3 to MoO2 belongs to the two-step reduction mechanism with the intermediate product Mo4O11. α1
α2
MoO3 → Mo4 O11 → MoO2
ð8Þ
The expression forms of α1 and α2 are obtained as follows, 3 122:084 t α1 ¼ 1− 1−2:549 106 exp − RT
ð9Þ
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"
2 #3 114:769 5 α2 ¼ 1− 1− 5:759 10 exp − t RT
ð10Þ
where α1 and α2 are in the range of 0 to 1. If assuming the initial raw materials of MoO3 were 1 g, because α1 and α2 represent the reaction extents of the reactions from MoO3 to Mo4O11 and from Mo4O11 to MoO2, respectively, then after time t, the masses of reacted and unreacted MoO3 are α1 g and (1-α1) g, respectively. Therefore, the produced Mo4O11 will be α1
MMo4 O11 4MMoO3
reacted and unreacted Mo4O11 will be α 1
α 2 g and α1
ð1−α2 Þ g, and the produced MoO2 will be α1
MMo4 O11 4MMoO3
α2
MMo4 O11 4MMoO3
4MMoO2 MMo4 O11
g.
According to the above analyses, the masses of MoO3, Mo4O11 and MoO2 can be calculated as follows, mMoO3 ;t ¼ 1−α1 mMo4 O11 ;t ¼ α1
mMoO2 ;t ¼ α1
ð11Þ
M Mo4 O11 MMo4 O11 ð1−α2 Þ ¼ α1 ð1−α2 Þ 4MMoO3 4MMoO3
M Mo4 O11 4MMoO2 MMoO2 α2 ¼ α1 α2 4MMoO3 MMo4 O11 MMoO3
ð12Þ
ð13Þ
where m is the mass after time t, and M is the relative molecule weight. Substituting Eqs. (9) and (10) into Eqs. (11), (12) and (13), yield 3 122:084 t mMoO3 ;t ¼ 1−2:549 106 exp − RT
" 2 #3 α 1 MMo4 O11 114:769 5 ¼ 1− 5:759 10 exp − ð15Þ t 4M MoO3 RT
mMoO2 ;t ¼
( 3 ) M MoO2 122:084 1− 1−2:549 106 exp − t M MoO3 RT 9 8 " 2 #3 = < 114:769 5 1− 1− 5:759 10 exp − t ; : RT
ð16Þ
g. Due to
the transformation of Mo4O11 to MoO2, after time t, the masses of MMo4 O11 4MMoO3
mMo4 O11 ;t
349
ð14Þ
So, the relationship between the mass of different components and reaction time t can be obtained. Fig. 12 shows the weights of different oxides with time plotted according to Eqs. (14), (15) and (16) at different temperatures. It can be easily seen that MoO3 and MoO2 are monotonously decreased and increased, respectively. Whereas for Mo4O11, it first increases to a maximum value and then decreases until it is completely disappeared. The phenomenon can be proved by the results of the XRD patterns in Figs. 6 and 7. If approximately assuming mMoO3 ;t ¼ 0:01 g
ð17Þ
as the critical disappearing point of MoO3 (the remaining mass is 1% relative to the initial mass), the corresponding critical time t and critical reaction extent α are listed in Table 2. It can be seen that even though the critical time of MoO3 decreases when increasing the reaction temperature, the critical reaction extent is almost kept constant, which is around 0.7. According to the XRD analysis shown in Fig. 7, it can be known that the raw MoO3 was already exhausted when the reaction extent is 0.764, which is well coincided with the predicted value of 0.7. Therefore, it can be known that the three oxide phases can coexist only when reaction
Fig. 12. Predicted mass values of different oxides at different temperatures.
350
L. Wang et al. / Int. Journal of Refractory Metals and Hard Materials 54 (2016) 342–350
References
Table 2 Lists of critical time and critical reaction extent. Temperature/(K)
773
793
813
833
Critical time/min Critical reaction extent α
54.7 0.7001
33.4 0.7228
21.5 0.6974
13.9 0.7050
extent is below 0.7. While the reaction extent is above 0.7 (not equal to 1), only Mo4O11 and MoO2 existed in the system, and there is only the reduction reaction from Mo4O11 to MoO2. 5. Conclusions In the present study, the hydrogen reduction of MoO3 to MoO2 in the temperature range of 763 K to 833 K was investigated. The following conclusions can be drawn. 1. The morphology of intermediate product Mo4O11 has a great influence on that of the final product MoO2. MoO2 always keeps the same morphology as Mo4O11. 2. Reduction of MoO3 to MoO2 obeys the two-stage reaction mechanism with the intermediate oxide Mo4O11. The rate controlling steps for the reduction of MoO3 to Mo4O11 and Mo4O11 to MoO2 are interface chemical reaction and diffusion model, respectively. The extracted activation energies are 122 kJ/mol and 114 kJ/mol, respectively. 3. When the reaction extent is in the range of 0 to 0.7, both the reductions of MoO3 to Mo4O11 and Mo4O11 to MoO2 occur simultaneously; when the reaction extent is in the range of 0.7 to 1, only the reduction of Mo4O11 to MoO2 occur in the reduction process.
Acknowledgments The authors gratefully acknowledge the support by Jinduicheng Molybdenum Co., Ltd. in raw material and the financial support from the National Natural Science Foundation of China (51304018 and 51474141).
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