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Raman and XRD study of polyhalite ore during calcinations
Vibrational Spectroscopy 102 (2019) 63–70
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Raman and XRD study of polyhalite ore during calcinations Huaide Cheng
a,b,⁎
a,b,c
, Jun Li
, Qingyu Hai
a,b
, Jianguo Song
a,b,c
, Xuehai Ma
a,b,c
T
a
Key Laboratory of Comprehensive and Highly Efficient Utilization of Salt Lake Resources, Qinghai Institute of Salt Lake, Chinese Academy of Sciences, Xining, 810008, China Key Laboratory of Salt Lake Geology and Environment of Qinghai Province, Xining, 810008, China c University of Chinese Academy of Sciences, Beijing, 100049, China b
ARTICLE INFO
ABSTRACT
Keywords: Phase transformation Polyhalite ore Calcinations Raman X ray Kinetics
In this paper, the thermal decomposition of polyhalite ore from Dayantan Playa in Qaidam Basin of China was investigated by X-ray powder diffractometry (XRD), Raman spectroscopy (Raman), and thermal analysis techniques (TG-DTG). The dehydration reaction of polyhalite ore takes place with the release of water and starts at about 510 K. The results of X-ray diffraction of roasting sample showed that polyhalite ore starts to decompose into anhydrite and langbeinite at 573 K. Raman spectroscopy, in conjunction with X-ray diffraction, was also used to follow the thermal decomposition of polyhalite ore. The changes of internal models of vibration of the SO4 ions in sulfates indicated the phase transformation polyhalite, langbeinite, and anhydrite. The reaction kinetics of thermal decomposition of polyhalite ore were successfully modeled by a Coats-Redfern equation () and the activation energy is found to be 208 kJ·mol−1. Additionally, the effect of roasting temperature on potassium extraction from polyhalite ore was studied.
1. Introduction
(K2SO4·2MgSO4), kieserite (MgSO4·H2O), epsomite (MgSO4·7H2O), etc. In China, potassium chloride and potassium sulfate are the main form of soluble potassium, and they have been produced from the Qarhan salt lake in Qinghai and the Lop Nor salt lake in Xinjiang, respectively. However, potash production is strongly dominated by Canada, Russia, Germany and Belarus, and the soluble hoevellite resource is scare in many parts of the world [9–11]. Globally, 31.9 million tones of potash fertilizer were demanded in 2014. This is expected to increase by 10.5% for potash fertilizer by 2019 [12,13]. Therefore, more efforts should be devoted to the development of the slightly soluble potassium resource in order to alleviate the shortage of soluble potassium, for example, polyhalite deposits of Qaidam Basin (Kunteyi Playa, 200 Mt.) and Sichuan Basin (Qu Xian, 1000 Mt.) in China [14,15]. Polyhalite ore is a suitable alternative potash source in support of sustainable agriculture. Herein, the dehydration mechanism and kinetics of the roasting and water leaching processes of the polyhalite ore from Dayantan Playa in Qaidam Basin of China are elucidated. The dehydration mechanism of polyhalite ore is proposed on the basis of X-ray diffraction (XRD), Raman spectroscopy (Raman), and thermal analysis techniques (TGDTG). The dehydration kinetics of the system is modeled using the Coats-Redferm equation. Knowledge about the dehydration properties and kinetics of polyhalite ore from Dayantan Playa in Qaidam Basin
Polyhalite, as one of the hydrous minerals coexisting with halite and anhydrite in marine evaporites, occurs widely in evaporites, especially rock salt formation, for example, deposits in Texas, New Mexico, Ukraine, and Germany [1]. The recent assessment by Kemp et al. [2] found that the world's largest highest grade deposits of polyhalite (2660 Mt. at 85.7% grade) is located in North Yorkshire, United Kingdom. Polyhalite has been reported to serve as a geological repository for storing used nuclear fuel and high level waste [3]. For example, the Waste Isolation Pilot Plant, located in Carlsbad, New Mexico, is a salt repository used for storing transuranic radioactive waste from nuclear weapon activities [4]. Commercially, polyhalite is mined as a potash source, because it contains important nutrient elements (K, Mg and S) for crop growth while being low in chlorine [5]. Polyhalite is soluble or leachable in aqueous solutions without calcinations, but dissolution is relatively slow. Most interests in extraction of potash from polyhalite have been on its calcinations and subsequent leaching with hot water, cold water, or other methods, which can convert the polyhalite ore particles to a water-soluble composition [6–8]. The resulting liquor may be subjected to various processes in order to yield products such as potassium sulfate (SOP or K2SO4), leonite (K2SO4·MgSO4·4H2O), schoenite (K2SO4·MgSO4·6H2O), langbeinite
⁎ Corresponding author at: Key Laboratory of Comprehensive and Highly Efficient Utilization of Salt Lake Resources, Qinghai Institute of Salt Lake, Chinese Academy of Sciences, Xining, 810008, China. E-mail address: [email protected] (H. Cheng).
https://doi.org/10.1016/j.vibspec.2019.04.007 Received 4 March 2019; Received in revised form 25 April 2019; Accepted 26 April 2019 Available online 26 April 2019 0924-2031/ © 2019 Elsevier B.V. All rights reserved.
Vibrational Spectroscopy 102 (2019) 63–70
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Table 1 The composition of polyhalite ore from Dayantan Playa using X-ray diffraction and chemical analysis. Substance components, wt.%
Mineral phases, wt.%
K2SO4
MgSO4
CaSO4
NaCl
Polyhalite
Halite
Quartz
Albite
Muscovite
10.29
8.66
15.06
30.49
34
25
14
21
6
may also help develop more effective strategies for its potassium extraction by calcinations and hot-leaching method.
quartz (SiO2), albite (NaAlSi3O8), halite (NaCl) and muscovite (KAl2(AlSi3O10)(OH)2). Thermal analysis techniques (TG-DTG) of polyhalite ore was used to track the reaction processes. The analysis was conducted in the temperature range of 300–820 K with a heating rate of 10 K/min., using a TG-DTG thermoanalyzer (STA449F3, NETZSCH, Germany). K+, Mg2+, Ca2+ and SO42− concentrations were determined at the Qinghai Institute of Salt Lakes, Chinese Academy of Science. The Mg2+、Ca2+ ion concentration was determined by complexometric titration with ethylenediaminetetraacetic acid standard solution. The K+ ion concentration was determined by gravimetric methods using sodium tetraphenylborate. The SO42− ion concentration was determined by using gravimetric methods with barium sulfate.
2. Experimental 2.1. Materials The polyhalite ore containing silicates and halite was collected from Dayantan Playa in Qaidam Basin of Qinghai, China. Semi-quantitative analysis of the ore was carried out by X-ray powder diffraction (XRD), and its composition of soluble materials was determined using a chemical analytical method. The results are shown in Table 1. The ore was crushed and milled, and the ore powder was sieved with mesh screens to give a particle size of ～0.2 mm. Doubly-distilled water was used in all experiments, as well as for the analytical measurements. Standard glassware was used in all experiments.
3. Results and discussion 3.1. Thermal analysis of polyhalite
2.2. Laboratory experiment
Polyhalite is stable up to a temperature ranging from 508 to 578 K in a "dry" environment, at which it starts to undergo dehydration [16–18]. The relatively large range of dehydration temperature is likely due to differences in experimental conditions (e.g., partial water vapor pressure, grain size, heating rate and the flowing gas used) and sample characteristics (e.g., crystallinity) [16]. Thermal behavior of polyhalite [4] by a high-temperature synchrotron X-ray diffraction study indicated that: (1) at about 506 K, polyhalite starts to decompose into water vapor, anhydrite (CaSO4) and two langbeinite-type phases, K2CaxMg2-x(SO4)3, with different Ca/Mg ratios; (2) on further heating to 919 K, the two langbeinite phases are combined into a single-phase triple salt, K2CaMg(SO4)3. The relevant reactions are listed as follows:
The study of the roasting process was conducted by placing the polyhalite ore in a muffle furnace (JZ-5-1200, Shang Hai Jing Zhao Machinery Equipment Co., Ltd., China) at temperature ranging from 558 to 773 K for 2 h. The roasted samples were then transferred to a 50 ml glass and leached with water at 363 K for 20 min. The ratio of solid and liquid was 1:1 (g: ml) and the agitation speed was 60 rpm. The liquid and solid phases were separated by filtration (SHZ-3 circulating water vacuum pump, Shanghai Yarong Biochemistry Factory, China). 2.3. Characterization X-ray powder diffraction (XRD) patterns of polyhalite ore and the roasted mixtures were recorded with Cu Kα radiation (λ = 1.54 Å) at a tube voltage of 40 kV and a tube current of 30 mA (X’ Pert Pro, PANalytical, Netherlands). As can be seen in Fig. 1, the main crystalline phases in the sample are polyhalite (K2SO4·2CaSO4·MgSO4·2H2O),
K2Ca2Mg(SO4)4·2H2O→CaSO4+(A)K2CaxMg2-x(SO4)3+(1-A) K2CayMg2-y(SO4)3+2H2O
(1)
(A)K2CaxMg2-x(SO4)3+(1-A)K2CayMg2-y(SO4)3→K2CaMg(SO4)3
(2)
Fig. 1. X-ray diffraction pattern of the polyhalite ore sample. 64
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Thermal decomposition of polyhalite [18] by a DSC/TG and X-ray diffraction investigation indicated that: (1) at 558 K, polyhalite starts to release the crystal water; (2) anhydrite and two solid solutions of the compositions K2SO4·1.76MgSO4·0.24CaSO4 and K2SO4·0.64MgSO4· 1.36CaSO4 is taking place; (3) the mechanism of decomposition runs through triple salt K2SO4·MgSO4·CaSO4. The relevant reactions are listed as follows: K2Ca2Mg(SO4)4·2H2O→K2SO4·MgSO4·CaSO4+CaSO4+2H2O
(3)
2(K2SO4·MgSO4·CaSO4)→0.64(K2SO4·1.76MgSO4·0.24CaSO4) +1.36(K2SO4·0.64MgSO4·1.36CaSO4)
(4)
3.3. Characteristic of the roasted sample To clarify the phase composition after the water release and consequential reactions, samples of polyhalite ore were roasted over the temperature range of 558–773 K, roasting time for 2 h. The X-ray diffraction patterns of the roasted samples are shown in Fig. 3. At 558 K, polyhalite ore remained stable up. When the temperature reached 573 K, it started to decompose into anhydrite, langbeinite and water vapor. Synchronously, diffraction peaks from anhydrite and langbeinite were discerned, respectively (Fig. 3). When the temperature was increased to 623 K, no diffraction peaks from polyhalite were discerned, suggesting completion of the polyhalite ore decomposition. Fig. 3 shows the fitted X-ray diffraction patterns of langbeinite and anhydrite at 623, 673, 723, and 773 K. Moreover, the contents of anhydrite and langbeinite in roasting sample increases with roasting temperature increases, from 623 K to 773 K, as reflected by the sharper peaks of the earlier. This behavior suggested that the degree of structure destruction of polyhalite is controlled by the roasting temperature. As can be seen in Fig. 3, the X-ray diffraction intensity of halite, quartz, muscovite and albite in roasting products is invariably, indicating its invalid for thermal decomposition of polyhalite ore.
Although in present paper the dehydration and the decomposition of polyhalite have been investigated, there is disagreement regarding the nature of the intermediates formed during the decomposition and in decomposition temperatures. Moreover, kinetic parameters for the decomposition stages have also not been reported so far. 3.2. TG-DTG analysis of polyhalite ore In Fig. 2 the decomposition curves (DSC, TG and DTG) obtained by heating the polyhalite ore sample to 820 K are shown. There are two stages of weight loss accompanied by two endothermic peaks at 357.4 K and 618.3 K, respectively, as can be seen in Fig. 2. A first weight loss occurred between 300 and 400k, which has to be associated with the release of the free-water in polyhalite ore. A second weight loss occurred between 510 and 650 K, corresponding to a broad endothermic peak in the DTG curve. This implies that the dehydration reaction of polyhalite ore took place with the release of water and started at about 510 K. Although the DSC peak is at 618.3 K, the dehydration process occurs over the temperature range 510–650 K. Thus, the onset temperature of dehydration lies within the reported range of 508–578 K [18].
3.4. K recovery of the roasted sample The effect of roasting temperature on the recovery of potassium was studied by leaching roasted sample with water at 363 K, leaching time for 20 min. Fig. 4 shows variations of potassium extraction efficiency for polyhalite ore as a function of roasting temperature. It showed that the recovery of potassium increases when the roasting temperature increases from 623 to 773 K, whereas the concentration of potassium progressively increases. Moreover, it can be observed that K recovery is more than 95%, and K concentration exceed for 43 g/l. The cure changes of potassium recovery and concentration agree with the results
Fig. 2. TG-DTG/DSC curves of polyhalite ore from room temperature to 820 K. 65
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H. Cheng, et al.
Fig. 3. X-ray diffraction patterns of the polyhalite ore sample roasted at.558–773 K.
of the X-ray diffraction analysis on the different roasting temperature (Figs. 3 and 4). Therefore, the degree of structure destruction of polyhalite increases when the roasting temperature increases from 623 to 773 K, which accelerates the potassium extraction efficiency greatly.
has a space group T4, the primitive unit cell containing two formula units, [SO4] tetrahedra and [MgO6] octahedra. In order to understand the formation of the anhydrite and langbeinite after roasting polyhalite ore, the Raman spectroscopy of polyhalite ore and its roasted products has to be studied, since the characteristic signals observed in these spectra are the basis of the Raman spectroscopic analysis. The most intense bands expected in the Raman spectra of sulfate salts are related with vibrations of the sulfate ion. Some interesting effects have been attributed to the coupling of sulphate group vibration modes and external crystal modes predominantly. The correlation of modes, ν1、ν2、ν3、ν4 of a free ion SO42− with its vibrations in langbeinite, anhydrite and polyhalite is given in Table 2. The correlation splitting of the totally symmetrical
3.5. Raman spectroscopy of the roasted sample Polyhalite crystallize in a triclinic symmetry with the space group Fī [19] or Pī [20]. The structure consists of [SO4] tetrahedra, [MgO6] octahedra and triangular dodecahedra with K situating in 11-oxygencoordinated position. Each H2O oxygen is bonded to one Mg2+ and one K+. Anhydrite has a space group D2h, the primitive unit cell containing two formula units, [SO4] tetrahedra and [CaO8] polyhedra. Langbeinite
Fig. 4. Effect of roasting temperature on potassium recovery and concentration (with roasting time of 2 h, leaching temperature of 363 K and leaching time of 20 min.). 66
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good agreement with the values reported in Raman spectra study of langbeinite. When the roasting temperature is to be 673 K, the Raman spectrum of the roasted mixtures shows that: (1) the emergence of bands at 1158, 1128, 676, 500 and 418 cm−1, which are in good agreement with the values reported in Raman spectra study of anhydrite; (2) the emergence of bands at 1052 and 610 cm−1, which are in good agreement with the values reported in Raman spectra study of langbeinite. In summary, from the Raman spectroscopic data of the polyhalite ore and the roasted mixtures, it is easy to note the difference of bands observed for each SO42− mode exits in these sulfates. Apparently the Raman spectra of these sulfates also reveal the structural relationship among them.
Table 2 Correlation of modes of a free SO4 ion and internal vibrations of sulfate ions in langbeinite, anhydrite and polyhalite (Spectra frequencies are given in cm−1). Polyhalite [22,23]
Langbeinite [24]
Anhydrite [25]
Assignment
1014 (1017) 987 (991)
1030 1029 1027 447 449 463 462 1103 1104 1111 1136 1139 1155 1120 1146 1122 1223 1225 604 607 610 612 622 625 629 632 643 648 649 650
1016
ν1 symmetry stretching
415 497
ν2 symmetry bending
1128 1110 1160
ν3 anti-symmetry stretching
477 464 448 436 1181 1165 1144 1130 1094 1069
652 641 626 620
674 608 625
3.6. Dissociation mechanism and kinetic parameters of polyhalite ore The use of thermogravimetric data to evaluate kinetic parameters of solid-state reactions involving weight loss has been investigated by number of workers [27–31]. In the present work, the kinetic parameters of thermal decomposition of polyhalite ore were calculated using a model free approach of Coats and Redfern (CR) from TG-DTG data (Fig. 2) in the following way. For a solid state reaction involving weight loss, it can be expressed as follows:
ν4 anti-symmetry bending
xA (s)
(5)
yB(s) + zC(g )
For the reaction Eq. (5), the rate of disappearance of A under nonisothermal condition can be expressed by the following relation [32]:
d A E = exp f( ) dT RT
(6)
where A is the pre-exponential factor, E is the activation energy, R is the gas constant, is the fraction reacted at temperature T , f ( ) the conversion function which is dependent on the mechanism of the reaction and the rate of heating employed in the experiment. Usually the change of reaction ( ) is used to study the solid state reactions kinetics:
mode ν1 is insignificant and is within the limits of experimental error. It should be noted that the crystal field splits the degenerate modes rather vigorously. Thus, the magnitudes of the splitting △ν/ν for the mode frequencies ν2 and ν4 of a free ion are 6–7%, while for ν3 it reaches 10–11%. Such static splitting may be associated with the distortion of sulfate tetrahedral by a crystal field [21]. Considering the free ion symmetry of SO42− (Td), there are four normal modes of vibration: ν1 symmetric stretching, ν2 symmetry bending, ν3 anti-symmetric stretching, and ν4 anti-symmetry bending, all of them are Raman active. The stretching modes usually occur in the 950-1200 cm-1 region, and the bending modes appears in the 400650 cm-1 [26]. For free SO42− ion vibration in polyhalite ore and its roasted products, it can be seen from Fig. 5 that symmetric stretching mode (ν1) at 1018 cm-1, symmetry bending mode (ν2) at 464 cm-1 and anti-symmetry bending mode (ν4) at 630 cm-1, respectively. Fig. 5 shows the Raman spectra of the polyhalite ore and the roasted mixtures. The Raman spectrum recorded of polyhalite ore at room temperature shows two strong bands at 1018 and 992 cm−1, which clearly belong to the SO42- ν1. In addition, there are signals in the region of SO42- ν3 (1165, 1135, and 1074 cm−1), SO42- ν4 (630, and 622 cm−1), and SO42- ν2 (468, 440, and 455 cm−1). These values are in good agreement with the values reported in Raman spectra study of polyhalite (See Table 2). When the roasting temperature is to be 773 K, the Raman spectrum of the roasted mixtures shows that: (1) the emergence of bands at 1160, 1129, 676, 500 and 419 cm−1, which are in good agreement with the values reported in Raman spectra study of anhydrite; (2) the emergence of bands at 1055 and 611 cm−1, which are in good agreement with the values reported in Raman spectra study of langbeinite. When the roasting temperature is to be 723 K, the Raman spectrum of the roasted mixtures shows that: (1) the emergence of bands at 1159, 1128, 676, 500 and 418 cm−1, which are in good agreement with the values reported in Raman spectra study of anhydrite; (2) the emergence of bands at 1053 and 610 cm−1, which are in
mo mt
=
mt m
(7)
Where m 0 , mt , and m are initial sample mass, sample mass at time t and sample mass at the end of reaction, respectively. Eq. (6) can be represented by its integral form as follows:
g( )
0
d = f( )
T
A
exp
0
E dT RT
(8)
The algebraic expressions of the integral functions that are tested in this work are listed in Table 3. These expressions are applied for the kinetic analysis of solid reactions and encompass most common mechanism. TG-DTG experimental data were used to evaluate kinetic parameters and arrive at the mechanism of the reaction. The kinetic of thermal decomposition of polyhalite ore was followed by employing the Coats and Redfern approximation [27] which gives the expression
ln
g( ) T2
= ln
A plot of ln
AR 1 E
g( ) T2
2RT E
versus
1 T
E RT
(9)
gives a straight line when the correct
function is used in the equation. The g ( ) function describes the mechanism of reaction. Straight lines with high-correlation coefficient and low standard deviation were selected to represent the possible cong( )
trolling mechanism. Plots of ln T2 versus 1 for the thermal decomT position of polyhalite ore are shown in Fig. 6. The corresponding kinetic parameters were then calculated from Fig. 6 using CR method and shown in Table 4. As can be seen that a high-correlation coefficient exists in diffusion model, it reaches 0.9839−0.9904. It is seen that the
67
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Fig. 5. Raman spectra of the polyhalite ore and the roasted mixtures.
Polyhalite is a suitable alternative potash source in support of sustainable agriculture. Many of the processes suggested for the utilization of polyhalite ore depend upon calcinations of this complex salt. Thus, studying the thermal decomposition process of polyhalite ore is important. In this work, the thermal decomposition of polyhalite ore from Dayantan Playa in Qaidam Basin of China was investigated by the X-ray diffraction, Raman spectroscopy, and thermal analysis techniques (TGDTG). It has been found that the dehydration reaction of polyhalite ore takes place with the release of water and starts at about 510 K according to TG-DTG/DSC analysis. The dehydration was governed by D3 Janders diffusion mechanism. The results of X-ray diffraction and Raman spectra of roasting sample showed that (1) polyhalite ore starts to decompose into anhydrite, langbeinite, at 573 K; (2) the component of CaSO4 in polyhalite is in the form of anhydrite, the components of K2SO4 and MgSO4 in polyhalite are in the form of langbeinite, (3) a tendency for X-ray diffraction intensity of anhydrite and langbeinite to weaken increases visibly with roasting temperature; (4) the Raman spectra of sulfates reveals the structural relationship among them; (5) the X-ray diffraction intensity of halite, quartz, muscovite and albite in roasting products is invariably, indicating its invalid for thermal decomposition of polyhalite ore. A sharp increase of potassium recovery and concentration can be observed for roasting mixtures from 623 to 773 K by leaching with 363 K hot water. K yield exceeded 95%, and K concentration surpassed 43 g/l. The reaction kinetics of thermal decomposition of polyhalite ore were successfully modeled by a CoatsRedfern equation and the activation energy is found to be 208 kJ·mol−1. It has been demonstrated that the structural damage of polyhalite ore is very important to extract its values elements of K, Mg and SO4.
Table 3 Solid state rate equations. Reaction Model Nucleation Models 1 Power Law (P2) 2 Power Law (P3) 3 Power Law (P4) 4 Avrami-Erofeev (A2) 5 Avrami-Erofeev(A3) 6 Avrami-Erofeev (A4) Diffusion Models 7 One dimensional Diffusion (D1) 8 Two dimensional Diffusion (D2) 9 Three dimensional Diffusion, Jander's (D3) 10 Three dimensional Diffusion, Ginstling Brounshtein (D4) Reaction order Models 11 First order (F1) 12 Second order (F2) 13 Third order (F3) Geometrical contraction Models 14 Contracting cylinder (R2) 15 Contracting Sphere (R3)
g(α) α1/2 α1/3 α1/4 [-ln(1-α)]1/2 [-ln(1-α)]1/3 [-ln(1-α)]1/4 α2 (1-α)ln(1-α)+ α [1-(1-α)1/3]2 1-(2/3) α-(1-a)2/3 -ln(1-α) 1/(1-α) [1/(1-α)]2 1-(1-α)1/2 1-(1-α)1/3
results best fit D3, Janders diffusion model, and the calculated activation energy becomes 208 kJ·mol−1 which is in close agreement with advanced work [33] (50.2 kcal mol−1). 4. Conclusions The development of the slightly soluble potassium resource has recently attracted to alleviate the shortage of soluble potassium.
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Fig. 6. Plots of ln
g( ) T2
versus
Table 4 Kinetic parameters extracted from Fig. 6 using CR method. Reaction Model
Ea/kJ·mol−1
A/min−1
｜r｜
P2 P3 P4 A2 A3 A4 D1 D2 D3 D4 F1 F2 F3 R2 R3
28.74 12.66 4.64 41.52 21.16 11.12 173.44 188.8 206.28 194.60 102.46 36.64 92.76 89.08 93.42
5.56 × 108 1.05 × 109 7.98 × 108 1.95 × 108 6.84 × 108 4.66 × 108 1.61 × 106 4.81 × 106 8.14 × 106 2.11 × 106 1.48 × 106 1.12 × 108 5.68 × 105 1.14 × 107 1.11 × 107
0.9805 0.9594 0.8636 0.9663 0.9460 0.8993 0.9904 0.9875 0.9839 0.9863 0.9768 0.8272 0.8798 0.9828 0.9808
1 T
for different models.
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Acknowledgments We are grateful to editors and an anonymous reviewer for their helpful comments. This work was supported by the applied Basic Research Project of Qinghai Province (Grant No. 2016-ZJ-781). References [1] J.K. Warren, Evaporites: Sediments, Resources and Hydrocarbons, (2006), https:// doi.org/10.1007/3-540-32344-9. [2] S.J. Kemp, F.W. Smith, D. Wagner, I. Mounteney, C.P. Bell, C.J. Milne, C.J.B. Gowing, T.L. Pottas, An improved approach to characterize potash-bearing evaporite deposits, evidenced in North Yorkshire, United Kingdom, Econ. Geol. 111 (2016) 719–742, https://doi.org/10.2113/econgeo.111.3.719. [3] F.D. Hansen, C.D. Leigh, Salt Disposal of Heat-Generating Nuclear Waste, (2011). [4] H. Xu, X. Guo, J. Bai, Thermal behavior of polyhalite: a high-temperature synchrotron X-ray diffraction study, Phys. Chem. Miner. 44 (2017) 125–135, https:// doi.org/10.1007/s00269-016-0842-5.
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H. Cheng, et al. [22] G. Wollmann, D. Freyer, W. Voigt, Polyhalite and its analogous triple salts, Monatsh. Chem. 139 (2008) 739–745, https://doi.org/10.1007/s00706-0070835-7. [23] P. Vargas Jentzsch, R.M. Bolanz, V. Ciobota, B. Kampe, P. Rösch, J. Majzlan, J. Popp, Raman spectroscopic study of calcium mixed salts of atmospheric importance, Vib. Spectrosc. 61 (2012) 206–213, https://doi.org/10.1016/j.vibspec. 2012.03.007. [24] B. Brezina, L.M. Rabkin, V.I. Torgashev, Raman spectra and phase transitions in some langbeinites, Ferroelectrics 48 (1983) 247–258, https://doi.org/10.1080/ 00150198308227860. [25] B.J. Berenblut, P. Dawson, G.R. Wilkinson, A comparison of the Raman spectra of anhydrite (CaSO4) and gypsum (CaSO4·2H2O), Spectrochim. Acta Part A Mol. Spectrosc. 29 (1973) 29–36, https://doi.org/10.1016/0584-8539(73)80005-4. [26] V. Ramakrishnan, V.U. Nayar, G. Aruldhas, Vibrational spectra of LiRbSO4, Infrared Phys. 25 (1985) 607–610, https://doi.org/10.1016/0020-0891(85)90013-2. [27] A.W. Coats, J.P. Redfern, Kinetic parameters from thermogravimetric data, Nature 201 (1964) 464–466, https://doi.org/10.1038/201464a0. [28] E.S. Freeman, B. Carroll, The application of thermoanalytical techniques to reaction kinetics: the thermogravimetric evaluation of the kinetics of the decomposition of
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Raman and XRD study of polyhalite ore during calcinations Huaide Cheng
a,b,⁎
a,b,c
, Jun Li
, Qingyu Hai
a,b
, Jianguo Song
a,b,c
, Xuehai Ma
a,b,c
T
a
Key Laboratory of Comprehensive and Highly Efficient Utilization of Salt Lake Resources, Qinghai Institute of Salt Lake, Chinese Academy of Sciences, Xining, 810008, China Key Laboratory of Salt Lake Geology and Environment of Qinghai Province, Xining, 810008, China c University of Chinese Academy of Sciences, Beijing, 100049, China b
ARTICLE INFO
ABSTRACT
Keywords: Phase transformation Polyhalite ore Calcinations Raman X ray Kinetics
In this paper, the thermal decomposition of polyhalite ore from Dayantan Playa in Qaidam Basin of China was investigated by X-ray powder diffractometry (XRD), Raman spectroscopy (Raman), and thermal analysis techniques (TG-DTG). The dehydration reaction of polyhalite ore takes place with the release of water and starts at about 510 K. The results of X-ray diffraction of roasting sample showed that polyhalite ore starts to decompose into anhydrite and langbeinite at 573 K. Raman spectroscopy, in conjunction with X-ray diffraction, was also used to follow the thermal decomposition of polyhalite ore. The changes of internal models of vibration of the SO4 ions in sulfates indicated the phase transformation polyhalite, langbeinite, and anhydrite. The reaction kinetics of thermal decomposition of polyhalite ore were successfully modeled by a Coats-Redfern equation () and the activation energy is found to be 208 kJ·mol−1. Additionally, the effect of roasting temperature on potassium extraction from polyhalite ore was studied.
1. Introduction
(K2SO4·2MgSO4), kieserite (MgSO4·H2O), epsomite (MgSO4·7H2O), etc. In China, potassium chloride and potassium sulfate are the main form of soluble potassium, and they have been produced from the Qarhan salt lake in Qinghai and the Lop Nor salt lake in Xinjiang, respectively. However, potash production is strongly dominated by Canada, Russia, Germany and Belarus, and the soluble hoevellite resource is scare in many parts of the world [9–11]. Globally, 31.9 million tones of potash fertilizer were demanded in 2014. This is expected to increase by 10.5% for potash fertilizer by 2019 [12,13]. Therefore, more efforts should be devoted to the development of the slightly soluble potassium resource in order to alleviate the shortage of soluble potassium, for example, polyhalite deposits of Qaidam Basin (Kunteyi Playa, 200 Mt.) and Sichuan Basin (Qu Xian, 1000 Mt.) in China [14,15]. Polyhalite ore is a suitable alternative potash source in support of sustainable agriculture. Herein, the dehydration mechanism and kinetics of the roasting and water leaching processes of the polyhalite ore from Dayantan Playa in Qaidam Basin of China are elucidated. The dehydration mechanism of polyhalite ore is proposed on the basis of X-ray diffraction (XRD), Raman spectroscopy (Raman), and thermal analysis techniques (TGDTG). The dehydration kinetics of the system is modeled using the Coats-Redferm equation. Knowledge about the dehydration properties and kinetics of polyhalite ore from Dayantan Playa in Qaidam Basin
Polyhalite, as one of the hydrous minerals coexisting with halite and anhydrite in marine evaporites, occurs widely in evaporites, especially rock salt formation, for example, deposits in Texas, New Mexico, Ukraine, and Germany [1]. The recent assessment by Kemp et al. [2] found that the world's largest highest grade deposits of polyhalite (2660 Mt. at 85.7% grade) is located in North Yorkshire, United Kingdom. Polyhalite has been reported to serve as a geological repository for storing used nuclear fuel and high level waste [3]. For example, the Waste Isolation Pilot Plant, located in Carlsbad, New Mexico, is a salt repository used for storing transuranic radioactive waste from nuclear weapon activities [4]. Commercially, polyhalite is mined as a potash source, because it contains important nutrient elements (K, Mg and S) for crop growth while being low in chlorine [5]. Polyhalite is soluble or leachable in aqueous solutions without calcinations, but dissolution is relatively slow. Most interests in extraction of potash from polyhalite have been on its calcinations and subsequent leaching with hot water, cold water, or other methods, which can convert the polyhalite ore particles to a water-soluble composition [6–8]. The resulting liquor may be subjected to various processes in order to yield products such as potassium sulfate (SOP or K2SO4), leonite (K2SO4·MgSO4·4H2O), schoenite (K2SO4·MgSO4·6H2O), langbeinite
⁎ Corresponding author at: Key Laboratory of Comprehensive and Highly Efficient Utilization of Salt Lake Resources, Qinghai Institute of Salt Lake, Chinese Academy of Sciences, Xining, 810008, China. E-mail address: [email protected] (H. Cheng).
https://doi.org/10.1016/j.vibspec.2019.04.007 Received 4 March 2019; Received in revised form 25 April 2019; Accepted 26 April 2019 Available online 26 April 2019 0924-2031/ © 2019 Elsevier B.V. All rights reserved.
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Table 1 The composition of polyhalite ore from Dayantan Playa using X-ray diffraction and chemical analysis. Substance components, wt.%
Mineral phases, wt.%
K2SO4
MgSO4
CaSO4
NaCl
Polyhalite
Halite
Quartz
Albite
Muscovite
10.29
8.66
15.06
30.49
34
25
14
21
6
may also help develop more effective strategies for its potassium extraction by calcinations and hot-leaching method.
quartz (SiO2), albite (NaAlSi3O8), halite (NaCl) and muscovite (KAl2(AlSi3O10)(OH)2). Thermal analysis techniques (TG-DTG) of polyhalite ore was used to track the reaction processes. The analysis was conducted in the temperature range of 300–820 K with a heating rate of 10 K/min., using a TG-DTG thermoanalyzer (STA449F3, NETZSCH, Germany). K+, Mg2+, Ca2+ and SO42− concentrations were determined at the Qinghai Institute of Salt Lakes, Chinese Academy of Science. The Mg2+、Ca2+ ion concentration was determined by complexometric titration with ethylenediaminetetraacetic acid standard solution. The K+ ion concentration was determined by gravimetric methods using sodium tetraphenylborate. The SO42− ion concentration was determined by using gravimetric methods with barium sulfate.
2. Experimental 2.1. Materials The polyhalite ore containing silicates and halite was collected from Dayantan Playa in Qaidam Basin of Qinghai, China. Semi-quantitative analysis of the ore was carried out by X-ray powder diffraction (XRD), and its composition of soluble materials was determined using a chemical analytical method. The results are shown in Table 1. The ore was crushed and milled, and the ore powder was sieved with mesh screens to give a particle size of ～0.2 mm. Doubly-distilled water was used in all experiments, as well as for the analytical measurements. Standard glassware was used in all experiments.
3. Results and discussion 3.1. Thermal analysis of polyhalite
2.2. Laboratory experiment
Polyhalite is stable up to a temperature ranging from 508 to 578 K in a "dry" environment, at which it starts to undergo dehydration [16–18]. The relatively large range of dehydration temperature is likely due to differences in experimental conditions (e.g., partial water vapor pressure, grain size, heating rate and the flowing gas used) and sample characteristics (e.g., crystallinity) [16]. Thermal behavior of polyhalite [4] by a high-temperature synchrotron X-ray diffraction study indicated that: (1) at about 506 K, polyhalite starts to decompose into water vapor, anhydrite (CaSO4) and two langbeinite-type phases, K2CaxMg2-x(SO4)3, with different Ca/Mg ratios; (2) on further heating to 919 K, the two langbeinite phases are combined into a single-phase triple salt, K2CaMg(SO4)3. The relevant reactions are listed as follows:
The study of the roasting process was conducted by placing the polyhalite ore in a muffle furnace (JZ-5-1200, Shang Hai Jing Zhao Machinery Equipment Co., Ltd., China) at temperature ranging from 558 to 773 K for 2 h. The roasted samples were then transferred to a 50 ml glass and leached with water at 363 K for 20 min. The ratio of solid and liquid was 1:1 (g: ml) and the agitation speed was 60 rpm. The liquid and solid phases were separated by filtration (SHZ-3 circulating water vacuum pump, Shanghai Yarong Biochemistry Factory, China). 2.3. Characterization X-ray powder diffraction (XRD) patterns of polyhalite ore and the roasted mixtures were recorded with Cu Kα radiation (λ = 1.54 Å) at a tube voltage of 40 kV and a tube current of 30 mA (X’ Pert Pro, PANalytical, Netherlands). As can be seen in Fig. 1, the main crystalline phases in the sample are polyhalite (K2SO4·2CaSO4·MgSO4·2H2O),
K2Ca2Mg(SO4)4·2H2O→CaSO4+(A)K2CaxMg2-x(SO4)3+(1-A) K2CayMg2-y(SO4)3+2H2O
(1)
(A)K2CaxMg2-x(SO4)3+(1-A)K2CayMg2-y(SO4)3→K2CaMg(SO4)3
(2)
Fig. 1. X-ray diffraction pattern of the polyhalite ore sample. 64
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Thermal decomposition of polyhalite [18] by a DSC/TG and X-ray diffraction investigation indicated that: (1) at 558 K, polyhalite starts to release the crystal water; (2) anhydrite and two solid solutions of the compositions K2SO4·1.76MgSO4·0.24CaSO4 and K2SO4·0.64MgSO4· 1.36CaSO4 is taking place; (3) the mechanism of decomposition runs through triple salt K2SO4·MgSO4·CaSO4. The relevant reactions are listed as follows: K2Ca2Mg(SO4)4·2H2O→K2SO4·MgSO4·CaSO4+CaSO4+2H2O
(3)
2(K2SO4·MgSO4·CaSO4)→0.64(K2SO4·1.76MgSO4·0.24CaSO4) +1.36(K2SO4·0.64MgSO4·1.36CaSO4)
(4)
3.3. Characteristic of the roasted sample To clarify the phase composition after the water release and consequential reactions, samples of polyhalite ore were roasted over the temperature range of 558–773 K, roasting time for 2 h. The X-ray diffraction patterns of the roasted samples are shown in Fig. 3. At 558 K, polyhalite ore remained stable up. When the temperature reached 573 K, it started to decompose into anhydrite, langbeinite and water vapor. Synchronously, diffraction peaks from anhydrite and langbeinite were discerned, respectively (Fig. 3). When the temperature was increased to 623 K, no diffraction peaks from polyhalite were discerned, suggesting completion of the polyhalite ore decomposition. Fig. 3 shows the fitted X-ray diffraction patterns of langbeinite and anhydrite at 623, 673, 723, and 773 K. Moreover, the contents of anhydrite and langbeinite in roasting sample increases with roasting temperature increases, from 623 K to 773 K, as reflected by the sharper peaks of the earlier. This behavior suggested that the degree of structure destruction of polyhalite is controlled by the roasting temperature. As can be seen in Fig. 3, the X-ray diffraction intensity of halite, quartz, muscovite and albite in roasting products is invariably, indicating its invalid for thermal decomposition of polyhalite ore.
Although in present paper the dehydration and the decomposition of polyhalite have been investigated, there is disagreement regarding the nature of the intermediates formed during the decomposition and in decomposition temperatures. Moreover, kinetic parameters for the decomposition stages have also not been reported so far. 3.2. TG-DTG analysis of polyhalite ore In Fig. 2 the decomposition curves (DSC, TG and DTG) obtained by heating the polyhalite ore sample to 820 K are shown. There are two stages of weight loss accompanied by two endothermic peaks at 357.4 K and 618.3 K, respectively, as can be seen in Fig. 2. A first weight loss occurred between 300 and 400k, which has to be associated with the release of the free-water in polyhalite ore. A second weight loss occurred between 510 and 650 K, corresponding to a broad endothermic peak in the DTG curve. This implies that the dehydration reaction of polyhalite ore took place with the release of water and started at about 510 K. Although the DSC peak is at 618.3 K, the dehydration process occurs over the temperature range 510–650 K. Thus, the onset temperature of dehydration lies within the reported range of 508–578 K [18].
3.4. K recovery of the roasted sample The effect of roasting temperature on the recovery of potassium was studied by leaching roasted sample with water at 363 K, leaching time for 20 min. Fig. 4 shows variations of potassium extraction efficiency for polyhalite ore as a function of roasting temperature. It showed that the recovery of potassium increases when the roasting temperature increases from 623 to 773 K, whereas the concentration of potassium progressively increases. Moreover, it can be observed that K recovery is more than 95%, and K concentration exceed for 43 g/l. The cure changes of potassium recovery and concentration agree with the results
Fig. 2. TG-DTG/DSC curves of polyhalite ore from room temperature to 820 K. 65
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H. Cheng, et al.
Fig. 3. X-ray diffraction patterns of the polyhalite ore sample roasted at.558–773 K.
of the X-ray diffraction analysis on the different roasting temperature (Figs. 3 and 4). Therefore, the degree of structure destruction of polyhalite increases when the roasting temperature increases from 623 to 773 K, which accelerates the potassium extraction efficiency greatly.
has a space group T4, the primitive unit cell containing two formula units, [SO4] tetrahedra and [MgO6] octahedra. In order to understand the formation of the anhydrite and langbeinite after roasting polyhalite ore, the Raman spectroscopy of polyhalite ore and its roasted products has to be studied, since the characteristic signals observed in these spectra are the basis of the Raman spectroscopic analysis. The most intense bands expected in the Raman spectra of sulfate salts are related with vibrations of the sulfate ion. Some interesting effects have been attributed to the coupling of sulphate group vibration modes and external crystal modes predominantly. The correlation of modes, ν1、ν2、ν3、ν4 of a free ion SO42− with its vibrations in langbeinite, anhydrite and polyhalite is given in Table 2. The correlation splitting of the totally symmetrical
3.5. Raman spectroscopy of the roasted sample Polyhalite crystallize in a triclinic symmetry with the space group Fī [19] or Pī [20]. The structure consists of [SO4] tetrahedra, [MgO6] octahedra and triangular dodecahedra with K situating in 11-oxygencoordinated position. Each H2O oxygen is bonded to one Mg2+ and one K+. Anhydrite has a space group D2h, the primitive unit cell containing two formula units, [SO4] tetrahedra and [CaO8] polyhedra. Langbeinite
Fig. 4. Effect of roasting temperature on potassium recovery and concentration (with roasting time of 2 h, leaching temperature of 363 K and leaching time of 20 min.). 66
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good agreement with the values reported in Raman spectra study of langbeinite. When the roasting temperature is to be 673 K, the Raman spectrum of the roasted mixtures shows that: (1) the emergence of bands at 1158, 1128, 676, 500 and 418 cm−1, which are in good agreement with the values reported in Raman spectra study of anhydrite; (2) the emergence of bands at 1052 and 610 cm−1, which are in good agreement with the values reported in Raman spectra study of langbeinite. In summary, from the Raman spectroscopic data of the polyhalite ore and the roasted mixtures, it is easy to note the difference of bands observed for each SO42− mode exits in these sulfates. Apparently the Raman spectra of these sulfates also reveal the structural relationship among them.
Table 2 Correlation of modes of a free SO4 ion and internal vibrations of sulfate ions in langbeinite, anhydrite and polyhalite (Spectra frequencies are given in cm−1). Polyhalite [22,23]
Langbeinite [24]
Anhydrite [25]
Assignment
1014 (1017) 987 (991)
1030 1029 1027 447 449 463 462 1103 1104 1111 1136 1139 1155 1120 1146 1122 1223 1225 604 607 610 612 622 625 629 632 643 648 649 650
1016
ν1 symmetry stretching
415 497
ν2 symmetry bending
1128 1110 1160
ν3 anti-symmetry stretching
477 464 448 436 1181 1165 1144 1130 1094 1069
652 641 626 620
674 608 625
3.6. Dissociation mechanism and kinetic parameters of polyhalite ore The use of thermogravimetric data to evaluate kinetic parameters of solid-state reactions involving weight loss has been investigated by number of workers [27–31]. In the present work, the kinetic parameters of thermal decomposition of polyhalite ore were calculated using a model free approach of Coats and Redfern (CR) from TG-DTG data (Fig. 2) in the following way. For a solid state reaction involving weight loss, it can be expressed as follows:
ν4 anti-symmetry bending
xA (s)
(5)
yB(s) + zC(g )
For the reaction Eq. (5), the rate of disappearance of A under nonisothermal condition can be expressed by the following relation [32]:
d A E = exp f( ) dT RT
(6)
where A is the pre-exponential factor, E is the activation energy, R is the gas constant, is the fraction reacted at temperature T , f ( ) the conversion function which is dependent on the mechanism of the reaction and the rate of heating employed in the experiment. Usually the change of reaction ( ) is used to study the solid state reactions kinetics:
mode ν1 is insignificant and is within the limits of experimental error. It should be noted that the crystal field splits the degenerate modes rather vigorously. Thus, the magnitudes of the splitting △ν/ν for the mode frequencies ν2 and ν4 of a free ion are 6–7%, while for ν3 it reaches 10–11%. Such static splitting may be associated with the distortion of sulfate tetrahedral by a crystal field [21]. Considering the free ion symmetry of SO42− (Td), there are four normal modes of vibration: ν1 symmetric stretching, ν2 symmetry bending, ν3 anti-symmetric stretching, and ν4 anti-symmetry bending, all of them are Raman active. The stretching modes usually occur in the 950-1200 cm-1 region, and the bending modes appears in the 400650 cm-1 [26]. For free SO42− ion vibration in polyhalite ore and its roasted products, it can be seen from Fig. 5 that symmetric stretching mode (ν1) at 1018 cm-1, symmetry bending mode (ν2) at 464 cm-1 and anti-symmetry bending mode (ν4) at 630 cm-1, respectively. Fig. 5 shows the Raman spectra of the polyhalite ore and the roasted mixtures. The Raman spectrum recorded of polyhalite ore at room temperature shows two strong bands at 1018 and 992 cm−1, which clearly belong to the SO42- ν1. In addition, there are signals in the region of SO42- ν3 (1165, 1135, and 1074 cm−1), SO42- ν4 (630, and 622 cm−1), and SO42- ν2 (468, 440, and 455 cm−1). These values are in good agreement with the values reported in Raman spectra study of polyhalite (See Table 2). When the roasting temperature is to be 773 K, the Raman spectrum of the roasted mixtures shows that: (1) the emergence of bands at 1160, 1129, 676, 500 and 419 cm−1, which are in good agreement with the values reported in Raman spectra study of anhydrite; (2) the emergence of bands at 1055 and 611 cm−1, which are in good agreement with the values reported in Raman spectra study of langbeinite. When the roasting temperature is to be 723 K, the Raman spectrum of the roasted mixtures shows that: (1) the emergence of bands at 1159, 1128, 676, 500 and 418 cm−1, which are in good agreement with the values reported in Raman spectra study of anhydrite; (2) the emergence of bands at 1053 and 610 cm−1, which are in
mo mt
=
mt m
(7)
Where m 0 , mt , and m are initial sample mass, sample mass at time t and sample mass at the end of reaction, respectively. Eq. (6) can be represented by its integral form as follows:
g( )
0
d = f( )
T
A
exp
0
E dT RT
(8)
The algebraic expressions of the integral functions that are tested in this work are listed in Table 3. These expressions are applied for the kinetic analysis of solid reactions and encompass most common mechanism. TG-DTG experimental data were used to evaluate kinetic parameters and arrive at the mechanism of the reaction. The kinetic of thermal decomposition of polyhalite ore was followed by employing the Coats and Redfern approximation [27] which gives the expression
ln
g( ) T2
= ln
A plot of ln
AR 1 E
g( ) T2
2RT E
versus
1 T
E RT
(9)
gives a straight line when the correct
function is used in the equation. The g ( ) function describes the mechanism of reaction. Straight lines with high-correlation coefficient and low standard deviation were selected to represent the possible cong( )
trolling mechanism. Plots of ln T2 versus 1 for the thermal decomT position of polyhalite ore are shown in Fig. 6. The corresponding kinetic parameters were then calculated from Fig. 6 using CR method and shown in Table 4. As can be seen that a high-correlation coefficient exists in diffusion model, it reaches 0.9839−0.9904. It is seen that the
67
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H. Cheng, et al.
Fig. 5. Raman spectra of the polyhalite ore and the roasted mixtures.
Polyhalite is a suitable alternative potash source in support of sustainable agriculture. Many of the processes suggested for the utilization of polyhalite ore depend upon calcinations of this complex salt. Thus, studying the thermal decomposition process of polyhalite ore is important. In this work, the thermal decomposition of polyhalite ore from Dayantan Playa in Qaidam Basin of China was investigated by the X-ray diffraction, Raman spectroscopy, and thermal analysis techniques (TGDTG). It has been found that the dehydration reaction of polyhalite ore takes place with the release of water and starts at about 510 K according to TG-DTG/DSC analysis. The dehydration was governed by D3 Janders diffusion mechanism. The results of X-ray diffraction and Raman spectra of roasting sample showed that (1) polyhalite ore starts to decompose into anhydrite, langbeinite, at 573 K; (2) the component of CaSO4 in polyhalite is in the form of anhydrite, the components of K2SO4 and MgSO4 in polyhalite are in the form of langbeinite, (3) a tendency for X-ray diffraction intensity of anhydrite and langbeinite to weaken increases visibly with roasting temperature; (4) the Raman spectra of sulfates reveals the structural relationship among them; (5) the X-ray diffraction intensity of halite, quartz, muscovite and albite in roasting products is invariably, indicating its invalid for thermal decomposition of polyhalite ore. A sharp increase of potassium recovery and concentration can be observed for roasting mixtures from 623 to 773 K by leaching with 363 K hot water. K yield exceeded 95%, and K concentration surpassed 43 g/l. The reaction kinetics of thermal decomposition of polyhalite ore were successfully modeled by a CoatsRedfern equation and the activation energy is found to be 208 kJ·mol−1. It has been demonstrated that the structural damage of polyhalite ore is very important to extract its values elements of K, Mg and SO4.
Table 3 Solid state rate equations. Reaction Model Nucleation Models 1 Power Law (P2) 2 Power Law (P3) 3 Power Law (P4) 4 Avrami-Erofeev (A2) 5 Avrami-Erofeev(A3) 6 Avrami-Erofeev (A4) Diffusion Models 7 One dimensional Diffusion (D1) 8 Two dimensional Diffusion (D2) 9 Three dimensional Diffusion, Jander's (D3) 10 Three dimensional Diffusion, Ginstling Brounshtein (D4) Reaction order Models 11 First order (F1) 12 Second order (F2) 13 Third order (F3) Geometrical contraction Models 14 Contracting cylinder (R2) 15 Contracting Sphere (R3)
g(α) α1/2 α1/3 α1/4 [-ln(1-α)]1/2 [-ln(1-α)]1/3 [-ln(1-α)]1/4 α2 (1-α)ln(1-α)+ α [1-(1-α)1/3]2 1-(2/3) α-(1-a)2/3 -ln(1-α) 1/(1-α) [1/(1-α)]2 1-(1-α)1/2 1-(1-α)1/3
results best fit D3, Janders diffusion model, and the calculated activation energy becomes 208 kJ·mol−1 which is in close agreement with advanced work [33] (50.2 kcal mol−1). 4. Conclusions The development of the slightly soluble potassium resource has recently attracted to alleviate the shortage of soluble potassium.
68
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Fig. 6. Plots of ln
g( ) T2
versus
Table 4 Kinetic parameters extracted from Fig. 6 using CR method. Reaction Model
Ea/kJ·mol−1
A/min−1
｜r｜
P2 P3 P4 A2 A3 A4 D1 D2 D3 D4 F1 F2 F3 R2 R3
28.74 12.66 4.64 41.52 21.16 11.12 173.44 188.8 206.28 194.60 102.46 36.64 92.76 89.08 93.42
5.56 × 108 1.05 × 109 7.98 × 108 1.95 × 108 6.84 × 108 4.66 × 108 1.61 × 106 4.81 × 106 8.14 × 106 2.11 × 106 1.48 × 106 1.12 × 108 5.68 × 105 1.14 × 107 1.11 × 107
0.9805 0.9594 0.8636 0.9663 0.9460 0.8993 0.9904 0.9875 0.9839 0.9863 0.9768 0.8272 0.8798 0.9828 0.9808
1 T
for different models.
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