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Thermodynamics and kinetics of the dehydration reaction of FePO4·2H2O
ARTICLE IN PRESS Physica B 405 (2010) 2350–2355
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Thermodynamics and kinetics of the dehydration reaction of FePO4 2H2O Banjong Boonchom a,, Spote Puttawong b a b
King Mongkut’s Institute of Technology Ladkrabang, Chumphon Campus, 17/1 M. 6 Pha Thiew District, Chumphon 86160, Thailand Department of Chemical Technology, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
a r t i c l e in f o
a b s t r a c t
Article history: Received 1 August 2009 Received in revised form 18 February 2010 Accepted 19 February 2010
The thermal decomposition kinetics of FePO4 2H2O in dynamical air atmosphere was studied by mean TG–DTG–DTA. The stage and product of the thermal decomposition were determined. A number of kinetic models and calculation procedures were used to determine the kinetic triplet and thermodynamic parameters characterizing the dehydration process. The obtained activation energy and most kinetic model indicate the single kinetic mechanism and three-dimension diffusion as ‘‘Ginstling–Brounstein equation (D4 model)’’, respectively. The thermodynamic functions (DH*, DG* and DS*) of the dehydration reaction are calculated by the activated complex theory and indicate that the process is non-spontaneous without connecting with the introduction of heat. The kinetic and thermodynamic results were satisfactory which present good correlation with a linear correlation coefficient close to unit a low standard deviation. & 2010 Elsevier B.V. All rights reserved.
Keywords: Inorganic compounds Thermogravimetric analysis (TGA) Non-isothermal kinetics Thermodynamic properties
1. Introduction Iron (III) phosphate, FePO4 has long been used in many fields such as catalysts, wastewater purification systems, ferroelectrics, lithium batteries and steel and glass industries [1]. It has recently been proposed as the cathode in lithium batteries and lithium metal phosphates can be used as cathode or anode electrodes in lithium batteries because it is the next generation of positive-electrode material for lithium batteries and offer additional advantages in practical applications due to its lower cost, safety, benign environmental properties, stability and low toxicity [2]. The existence of several crystalline iron phosphate phases was reported in the literatures: the orthorhombic heterosite FePO4, obtained from the delithiated LiFePO4, the monoclinic FePO4, and the orthorhombic FePO4, hydrated phases include the phosphosiderite (or metastrengite) FePO4 2H2O monoclinic and the FePO4 2H2O orthorhombic forms [3–6]. The successful application of the required material depends on the morphology and purity, which depend mainly on the conditions of synthesis. Different synthetic routes have so far been reported for synthesizing FePO4, LiFePO4 and some of the synthesis conditions reported in the literature [5–7]. It is well known that FePO4 was prepared by many phases of FePO4 2H2O and FePO4 3H2O precursors at high temperatures (4800 K) [5–7]. Consequently, the mechanisms, kinetic and thermodynamic studies of thermal decomposition reactions are needed in order to take advantage of this potential, which is a beneficial effect on the manufacturing cost [8,9]. The results obtained can be directly applied in materials science for Corresponding author. Tel.: + 66 7750 6422x4565; fax: + 66 7750 6411.
E-mail addresses: [email protected], [email protected] (B. Boonchom). 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.02.046
the preparation of various metals and alloys, cements, ceramics, glasses, enamels, glazes, polymer and composite materials because the great variety of factors with diverse effects such as reconstruction of solid state crystal lattices, formation and growth of new crystallization nuclei, diffusion of gaseous reagents or reaction products, materials heat conductance, static or dynamic character of the environment, physical state of the reagents—dispersity, layer thickness, specific area and porosity, type, amount and distribution of the active centers on solid state surface, etc [5–8]. The aim of the present work is to study the mechanisms, kinetics and thermodynamics of the decomposition of FePO4 2H2O using TG–DTG–DTA. Non-isothermal kinetic of the decomposition process of FePO4 2H2O was interpreted by the Flynm–Wall–Ozawa (FWO) [9] and the Kissinger–Akahira–Sunose (KAS) [10,11]. The possible conversion function has been estimated using the Coats and Redfern method which gives the best description of the studied decomposition process and allows the calculation of reliable values of kinetic triplet parameter [12]. The thermodynamic (DH*, DS*, DG*) and kinetic (E, A, mechanism and model) parameters of the decomposition reaction of FePO4 2H2O have attracted the interest of thermodynamic and kinetic scientists and are discussed for the first time.
2. Experimental 2.1. Synthesis and characterization FePO4 2H2O crystalline powder was synthesized by wet chemistry method [1,2]. In this study, FePO4 2H2O was prepared
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by precipitation from aqueous solution of FeCl3 6H2O and H3PO4 (86.4% w/w) at pH= 6.5 at the ‘‘precipitation end point’’, with ammonium hydroxide solution. During the synthesizing procedure, iron chloride was dissolved in distilled water followed by adding an equivalent amount of the phosphoric acid (86.4% w/w) with vigorous stirring at room temperature. Finally, the gel solution was obtained by adding 2 M ammonia solutions until pH 6.5. The white powder was isolated by filtration, then washed with deionized water and dried in air for 24 h. Thermal analysis measurements (thermogravimetry, TG; differential thermogravimetry, DTG; and differential thermal analysis, DTA) were carried out on a Pyris Diamond Perkin Elmer apparatus by increasing temperature from 323 to 1073 K with calcined a-Al2O3 powder as the standard reference. The experiments were carried out in air atmosphere at heating rates of 5, 10, 15, and 20 K min 1. The sample mass was added about 6.0– 10.0 mg in an aluminum crucible without pressing. The structures of FePO4 2H2O and its final decomposition products (FePO4) were studied by X-ray powder diffraction using X-ray diffractometer (Phillips PW3040, The Netherland) with Cu Ka radiation (l = 0.1546 nm). The morphology of the selected resulting samples was examined by scanning electron microscope (SEM) using LEO SEM VP1450 after gold coating. The room temperature FTIR spectra were recorded in the range of 4000–370 cm 1 with 8 scans on a Perkin-Elmer Spectrum GX FT-IR/FT-Raman spectrometer with the resolution of 4 cm 1 using KBr pellets (KBr, Merck, spectroscopy grade).
2.2. Kinetics and thermodynamics Decomposition of crystal hydrates is a solid-state process of the type [13–16]: A (solid)-B (solid)+ C (gas). The kinetics of such reactions is described by various equations taking into account the special features of their mechanisms. The reaction can be expressed through the temperatures corresponding to fixed values of the extent of conversion (a = (mi ma)/(mi mf), where mi, ma and mf are the initial, actual and final sample mass at moment time, t) from experiments at different heating rates (b).
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The FWO [9] and the KAS [10,11] methods are two representative ones of model-free, which are convenient to calculate the activation energy. The activation energy (Ea) of the dehydration reaction of FePO4 2H2O can be calculated according to the FWO and the KAS equations. The FWO equation: AEa Ea ln b ¼ ln 5:33051:0516 ð1Þ RgðaÞ RT The KAS equation: b AEa Ea ln 2 ¼ ln RgðaÞ RT T
ð2Þ
where A (the pre-exponential factor) and E (the activation energy) are the Arrhenius parameters and R is the gas constant (8.314 Ra J mol 1 K 1). The gðaÞ ¼ 0 fdðaaÞ is the integral form of the f(a), which is the reaction model that depends on the reaction mechanism. For one dehydration reaction of FePO4 2H2O, the estimation of kinetic function model can be turned into a multiple linear regression problem through the Coats–Redfern method [12] as follows: gðaÞ AR 2RT Ea AR Ea ¼ ln 1 ffi ln ð3Þ ln bEa RT bEa RT Ea T2 Hence, ln(g(a)/T2) calculated for different a values at the single b value on 1000/T must give rise to a single master straight line, so the activation energy and the pre-exponential factor can be calculated from the slope and intercept through ordinary least square estimation. The activation energy and the pre-exponential factor can be calculated from the slope and intercept through ordinary least square estimation, which combined with nine conversion functions (Table 1) with the best equation [13]. Comparing the kinetic parameters from the Coats and Redfern equation, the probable kinetic model may be selected, where the values of Ea and A were calculated with the better linear correlation coefficient and the activation energies obtained from the Coats and Redfern equation above were showing good agreement to those obtained from the KAS and the Ozawa methods with a better correlation coefficient (r2). Hence, the
Table 1 Algebraic expressions of functions g(a) and f(a) and its corresponding mechanism [13,21]. f(a)
g(a)
Rate-determination mechanism
2(1 a)3/2
[1 (1 a) 1/2 1]
Chemical reaction
(1 a)
ln(1 a)
Avrami-Erofeev equation
(3/2) (1 a)[ ln(1 a)]1/3
[ ln(1 a)]2/3
Assumed random nucleation and its subsequent growth, n=1 Assumed random nucleation and its subsequent growth, n=1.5
3. Deceleratory rate equations 3.1. Phase boundary reaction (4) R3, F2/3
Power law
3(1 a)2/3
[1 ln(1 a)]1/3
Contracting volume (spherical symmetry) or two-thirds order
3.2. Based on the diffusion (5) D1 (6) D2 (7) D3
Parabola law (a = kt1/2) Valensi equation Jander equation
1/2a [ ln(1 a)] 1 (3/2)(1 a)2/3/[ln(1 a)1/ 3 ] (3/2)[(1 a) 1/3 1] 1
a2 a + (1 a)ln(1 a) [1 (1 a)1/3]2
One-dimension diffusion Two-dimension diffusion Three-dimension diffusion
[1 (2/3)a (1 a)2/3]
Three-dimension diffusion
No.
Symbol
Name of the function
1. Chemical process of mechanism non-invoking equations One and a haft order (1) F3/2 2. Sigmoid rate equations or random nucleation and subsequent growth Avrami-Erofeev equation (2) A1, F1
(3)
(8) (9)
A3/2
D4 D5
Ginstling–Brounstein Equation Zhuravlev Lesokhin Tempelman Equation
4/3
(3/2)(1 a) / [1 (1 a) 1/3]
[(1 a)
1/3
1]
2
Three-dimension diffusion
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pre-exponential factor A can be obtained by calculating the average value of A (s 1) from Eq. (3) for different heating rates. The other kinetics parameters of the process can be calculated using the fundamental theory of the activated complex theory (transition state) of Eyring [17–21], the following general equation may be written: ewkB Tp DS exp ð4Þ A¼ h R where A is the pre-exponential factor obtained from the Coats and Redfern method; e= 2.7183 is the Neper number; w is the transition factor, which is unity for monomolecular reactions; kB is the Boltzmann constant; h is the Plank constant, and Tp is the peak temperature of DTA curve. The change of the entropy may be calculated according to the formula Ah ð5Þ DS ¼ R ln ewkB Tp Since
DH ¼ E RTp
ð6Þ
where E* is the activation energy, Ea, obtained from the Coats– Redfern method. The changes of the enthalpy DH* and Gibbs free energy DG* for the activated complex formation from the reagent can be calculated using the well-known thermodynamic equation
DG ¼ DH Tp DS
ð7Þ
The heat of activation (DH*), entropy of activation (DS*), free energy of activation decomposition (DG*) were calculated at T= Tp (Tp is the DTA peak temperature at the corresponding stage), since this temperature characterizes the highest rate of the process, and therefore, is its important parameter.
3. Results and discussion 3.1. Characterization results TG–DTG–DTA curves of the thermal decomposition of FePO4 2H2O at heating rate of 10 K min 1 are shown in Fig. 1. The TG curve shows that the single well-defined decomposition step relates to the eliminations of water in range of 348–523 K. The corresponding observed mass loss is 20.27% by mass, which corresponds to 2.10 mol of water and is close to the theoretical value for FePO4 2H2O (19.27%, 2.00H2O). An endothermic effect
Fig. 1. TG–DTG–DTA curves of FePO4 2H2O in air at heating rate of 10 K min 1.
on DTA curves is observed at 398 K that agrees with the respective DTG peak. Further, four exothermic effects at 800, 849, 898 and 947 K without appreciable mass loss is observed on the DTA curve, which can be ascribed to a transition phase from amorphous to crystalline form of FePO4 [5–7]. A minor mass loss is observed, which corresponds to an exothermic peak on DTA with respective DTG peak at 849 K. The retained mass (89.73%) and water loss (20.27%) are compatible with the values expected for the formation of FePO4 and 2 moles water per mole of the synthesized FePO4, respectively. This indicates that the general formula should be FePO4 2H2O. The temperature at which theoretical mass loss is achieved can be also determined from the TG curve and considered to be the minimum temperatures needed for the calcinations process. Therefore, FePO4 2H2O sample was calcined at 673 K for 2 h in the furnace, which is the lower temperature as compared to those of the other hydrate precursors [1–5]. However, FePO4 in this work obtained by the calcined FePO4 2H2O at 623 K shows poor crystallization or amorphous phase, which is revealed by the observed broad peaks in XRD patterns (Fig. 2) and is in good agreement with the results reported in the literature [2,5,6]. Additionally, the crystallinity of FePO4 occurred at above 873 K of calcination supported a very stable inorganic framework system of the studied compound. This result is consistent with a transition phase from amorphous to crystalline, which is concluded in thermal analysis (DTA peak at over 947 K). The thermal stability, mechanism and phase transition temperature of the synthesized FePO4 2H2O reported in this work are different form those of our previous works (FePO4 3H2O [7] and AlPO4 2H2O [20]). Based on these results, we can conclude that the thermal results are caused by the nature of materials and synthesis conditions. The XRD patterns of iron phosphate dihydrate FePO4 2H2O and its dehydration product (FePO4) are shown in Fig. 2. As seen in Figs. 2a and b, the observed broad peaks in XRD patterns of the synthesized FePO4 2H2O and FePO4 indicate the predominance of the poor crystallization or amorphous phase as well as nanoparticles. This result is in good agreement with the results reported by Refs. [2,4–6], where the AlPO4 transforms from amorphous to a crystalline phase at about 873 K. It evidenced that this studied compound is a very stable inorganic framework system. Additionally, the result is consistent with a transition phase from amorphous to crystalline, which is concluded in thermal analysis.
Fig. 2. XRD patterns of FePO4 2H2O (a) and its dehydration product (FePO4) (b).
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FT-IR spectra of FePO4 2H2O and its dehydration product (FePO4) are shown in Fig. 3. Vibrational bands are identified in relation to the crystal structure in terms of the fundamental vibrating units namely PO34 , H2O, for FePO4 2H2O and PO34 for
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FePO4 [6,22]. FTIR spectra of PO34 in FePO4 2H2O and FePO4 show the antisymmetric stretching mode (n3) in 1000–1200 cm 1 region and the n4 mode in 400–560 cm 1 region. The observed bands in 1600–1700 cm 1 and 3000–3500 cm 1 region are attributed to the water bending and stretching vibrations. These water bands disappear in FT-IR spectra of its dehydration product (FePO4), which support a very good agreement with the thermal analysis results. The XRD data along with FTIR spectra confirm that the calcined FePO4 2H2O at 673 K transforms to FePO4. The SEM micrographs of FePO4 2H2O and its final decomposition product FePO4 are shown in Fig. 4. The particle shape and size are changed throughout the whole decomposition product. The SEM micrographs of FePO4 2H2O (Fig. 4a) and FePO4 (Fig. 4b) illustrate coalescence in aggregates of nanoparticles with sizes of o300 nm. The morphology of FePO4 shows smaller size than that of FePO4 H2O, which is the effect of the thermal dehydration process.
3.2. Kinetics and thermodynamics results
Fig. 3. FT-IR spectra of FePO4 2H2O (a) and its dehydration product (FePO4) (b).
According to isoconversional method, the basic data of a and T collected from the TG curves of the dehydration of FePO4 2H2O at various heating rates (5, 10, 15 and 20 K min 1) are illustrated in Table 2. According to Eqs. 1 and 2), the plots of ln b versus 1000/T (the FWO) and ln b/T2 versus 1000/T (the KAS) corresponding to different conversions a can be obtained by a linear regression of least-square method, respectively. The FWO and the KAS analysis results of four TG measurements below 573 K are presented in Fig. 5. The activation energies Ea can be calculated from the slopes of the straight lines with better linear correlation coefficient (r2 40.99). The slopes change depending on the degree of conversion (a) for the dehydration reaction of FePO4 2H2O. The activation energies are calculated at heating rates of 5, 10, 15, and 20 K min 1 via the FWO and the KAS methods in the a range of 0.2–0.8. The activation energies calculated by the FWO and the KAS methods are close to each other, which are shown in Table 3, so the results are credible. If Ea values are independent of a, the decomposition may be a simple reaction, while the dependence of Ea on a should be interpreted in terms of multi-step reaction mechanisms [13–16]. Neglecting the dependence of E versus a an average values of Ea =68.4870.93 kJ mol 1 (FWO) and 65.55 7 0.81 kJ mol 1 (KAS) are obtained. It was considered that the Ea values are independent of a if the relative error of the slope of the FWO and the KAS equations straight lines is lower than 10%. The activation energies change little with a, so we draw a conclusion that the dehydration reaction of FePO4 2H2O could be a single kinetic mechanism, which corresponds to an endothermic peak at 398 K in DTA curve. The single kinetic mechanism of the dehydration of the FePO4 2H2O reported in this work is different from a multi-step kinetic mechanism of its
Table 2 a T data at different heating rates, b (K min 1), for the dehydration reaction of FePO4 2H2O.
a
Fig. 4. SEM micrographs of FePO4 2H2O (a) and its dehydration product (FePO4) (b).
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Temperature (K)
b=5
b = 10
b = 20
b = 30
365.76 372.81 379.91 387.44 395.73 405.80 419.88
372.86 381.69 390.11 398.21 407.65 418.91 434.60
380.66 390.03 398.17 406.64 417.09 428.54 444.47
388.30 396.05 404.08 412.42 422.12 433.24 449.16
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Table 4 Kinetics parameters obtained from the differential method and the integral method at different heating rates (b = 5, 10, 15 and 20 K min 1). Model
Coats–Redfern method Ea/kJ mol 1
F3/2 A1, F1 A3/2 F2/3 D1 D2 D3 D4 D5
Fig. 5. FWO analysis (a) and KAS analysis (b) for the dehydration of FePO4 2H2O.
Table 3 Activation energies (Ea) vs. correlation coefficient (r2) calculated by FWO and KAS methods for the dehydration of FePO4 2H2O.
a
FWO method
KAS method
Ea/kJ mol 1
r2
Ea/kJ mol 1
r2
0.2 0.3 0.4 0.5 0.6 0.7 0.8
67.93 68.90 69.42 69.73 68.18 68.77 69.02
0.9801 0.9937 0.9976 0.9983 0.9986 0.9987 0.9984
65.17 66.07 66.49 66.69 64.91 65.35 65.37
0.9760 0.9923 0.9971 0.9979 0.9983 0.9984 0.9980
Average
68.48 70.93
0.9948
65.55 7 0.81
0.9937
isostructural (AlPO4 2H2O) reported in our previous work [21]. However, the average activation energy of dehydration process of FePO4 2H2O reported in this work is close to those of its isostructural AlPO4 2H2O reported in our previous work (69.6877 kJ mol 1 for the Kissinger method) [21]. Moreover, these activation energy values obtained from this work are lower
ln A/s 1
r2
Ea
7 Error
ln A
7 Error
17.07 37.82 22.96 32.77 55.15 62.81 72.28 65.94 14.47
1.03 1.78 1.20 1.57 2.39 2.71 3.11 2.84 0.93
3.91 2.79 2.39 0.22 5.72 8.36 10.47 8.32 4.58
0.46 0.56 0.52 0.66 0.97 1.09 1.23 1.14 0.43
0.99535 0.98176 0.97773 0.97232 0.95653 0.96721 0.97747 0.97108 0.98573
than those of the dehydration reaction of FePO4 3H2O for the FWO method and (130.18718 kJ mol 1 130.33719 kJ mol 1 for the KAS method) reported in our previous work [7]. In this respect, these data will be important for further studies of the studied compound, which include studies under carefully controlled reaction conditions. For kinetic function model analysis from the Coat–Redfern equation (Eq. 3), we can draw a conclusion that the possible conversion function is the based on the three-dimension diffusion mechanism (D4 model), Ginstling–Brounstein Eq. [f(a)= (3/2)(1 a) 1/3 1] 1 and g(a) =[1 (2/3)a (1 a)2/3], which are shown in Table 4. The correlated kinetic parameters are Ea = 65.9472.83 kJ mol 1 and ln A= 8.3271.14 s 1. Additionally, the strengths of molecular binding in the crystal lattice are different. Consequently, the dehydration temperatures and kinetic parameters are different. The activation energy for the losing of crystal water lie in the range of 60–80 kJ mol–1, while the value for coordinately bounded one are within the range of 130– 160 kJ mol–1 [20]. The energy of activation found in D4 model for the dehydration reaction suggests that the water molecules are water of crystallization. This result is different from the most kinetic model of the dehydration reaction of FePO4 3H2O (F2.5 model from the Coats–Rendfern method) reported in our pervious work [7]. The calculated values of DH*, DS* and DG* were calculated by Tp (418 K) in the highest heating rate and found to be 130.65 kJ mol 1, 30.32 J K 1 mol 1 and 117.98 kJ mol 1, respectively. The entropy of activation (DS*) value for the dehydration step is positive. It means that the corresponding activated complexes were with lower degree of arrangement than the initial state. Since the dehydration of FePO4 2H2O proceeds as a single reaction, the formation of the activated complex passed in situ. In terms of the activated complex theory (transition theory) [15,22–26], a positive value of DS* indicates a malleable activated complex that leads to a large number of degrees of freedom of rotation and vibration. A result may be interpreted as a ‘‘fast’’ stage. On the other hand, a negative value of DS* indicates a highly ordered activated complex and the degrees of freedom of rotation as well as of vibration are less than those in the nonactivated complex. This results may indicate a ‘‘slow’’ stage. Therefore, the dehydration reaction of FePO4 2H2O may be interpreted as ‘‘fast’’ stage [15,22–26]. The positive value of the enthalpy DH* indicates the endothermic reaction, which is consistent with an endothermic effects in DTA data (Fig. 1). Additionally, the positive value of DG* for the dehydration stage shows that it is non-spontaneous process and is necessary to connect with the introduction of heat. These thermodynamic
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functions are consistent with kinetic parameters and thermal analysis data.
4. Conclusions FePO4 2H2O decomposes in one step by starting after 300 K and the final product is FePO4, playing a more and more important role in the development of advanced rechargeable lithium ion batteries. A single value of E for different a can be assigned to a single reaction process, which relates to the elimination of water of crystallization in the structure. On the basis of correctly established values of the apparent activation energy, pre-exponential factor and the changes of entropy, enthalpy and Gibbs free energy, certain conclusions can be made concerning the mechanisms and characteristics of the processes. The data of kinetics and thermodynamics play an important role in theoretical study, application development and industrial production of a compound as a basis of theoretical. Consequently, these data will be important for further studies of the studied compound and are applied to solve various scientific and practical problems involving the participation of solid phases.
Acknowledgement This work is financially supported by the Thailand Research Fund (TRF), the Commission on Higher Education (CHE) and Research Grant for New Scholar, Ministry of Education, Thailand.
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Thermodynamics and kinetics of the dehydration reaction of FePO4 2H2O Banjong Boonchom a,, Spote Puttawong b a b
King Mongkut’s Institute of Technology Ladkrabang, Chumphon Campus, 17/1 M. 6 Pha Thiew District, Chumphon 86160, Thailand Department of Chemical Technology, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand
a r t i c l e in f o
a b s t r a c t
Article history: Received 1 August 2009 Received in revised form 18 February 2010 Accepted 19 February 2010
The thermal decomposition kinetics of FePO4 2H2O in dynamical air atmosphere was studied by mean TG–DTG–DTA. The stage and product of the thermal decomposition were determined. A number of kinetic models and calculation procedures were used to determine the kinetic triplet and thermodynamic parameters characterizing the dehydration process. The obtained activation energy and most kinetic model indicate the single kinetic mechanism and three-dimension diffusion as ‘‘Ginstling–Brounstein equation (D4 model)’’, respectively. The thermodynamic functions (DH*, DG* and DS*) of the dehydration reaction are calculated by the activated complex theory and indicate that the process is non-spontaneous without connecting with the introduction of heat. The kinetic and thermodynamic results were satisfactory which present good correlation with a linear correlation coefficient close to unit a low standard deviation. & 2010 Elsevier B.V. All rights reserved.
Keywords: Inorganic compounds Thermogravimetric analysis (TGA) Non-isothermal kinetics Thermodynamic properties
1. Introduction Iron (III) phosphate, FePO4 has long been used in many fields such as catalysts, wastewater purification systems, ferroelectrics, lithium batteries and steel and glass industries [1]. It has recently been proposed as the cathode in lithium batteries and lithium metal phosphates can be used as cathode or anode electrodes in lithium batteries because it is the next generation of positive-electrode material for lithium batteries and offer additional advantages in practical applications due to its lower cost, safety, benign environmental properties, stability and low toxicity [2]. The existence of several crystalline iron phosphate phases was reported in the literatures: the orthorhombic heterosite FePO4, obtained from the delithiated LiFePO4, the monoclinic FePO4, and the orthorhombic FePO4, hydrated phases include the phosphosiderite (or metastrengite) FePO4 2H2O monoclinic and the FePO4 2H2O orthorhombic forms [3–6]. The successful application of the required material depends on the morphology and purity, which depend mainly on the conditions of synthesis. Different synthetic routes have so far been reported for synthesizing FePO4, LiFePO4 and some of the synthesis conditions reported in the literature [5–7]. It is well known that FePO4 was prepared by many phases of FePO4 2H2O and FePO4 3H2O precursors at high temperatures (4800 K) [5–7]. Consequently, the mechanisms, kinetic and thermodynamic studies of thermal decomposition reactions are needed in order to take advantage of this potential, which is a beneficial effect on the manufacturing cost [8,9]. The results obtained can be directly applied in materials science for Corresponding author. Tel.: + 66 7750 6422x4565; fax: + 66 7750 6411.
E-mail addresses: [email protected], [email protected] (B. Boonchom). 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.02.046
the preparation of various metals and alloys, cements, ceramics, glasses, enamels, glazes, polymer and composite materials because the great variety of factors with diverse effects such as reconstruction of solid state crystal lattices, formation and growth of new crystallization nuclei, diffusion of gaseous reagents or reaction products, materials heat conductance, static or dynamic character of the environment, physical state of the reagents—dispersity, layer thickness, specific area and porosity, type, amount and distribution of the active centers on solid state surface, etc [5–8]. The aim of the present work is to study the mechanisms, kinetics and thermodynamics of the decomposition of FePO4 2H2O using TG–DTG–DTA. Non-isothermal kinetic of the decomposition process of FePO4 2H2O was interpreted by the Flynm–Wall–Ozawa (FWO) [9] and the Kissinger–Akahira–Sunose (KAS) [10,11]. The possible conversion function has been estimated using the Coats and Redfern method which gives the best description of the studied decomposition process and allows the calculation of reliable values of kinetic triplet parameter [12]. The thermodynamic (DH*, DS*, DG*) and kinetic (E, A, mechanism and model) parameters of the decomposition reaction of FePO4 2H2O have attracted the interest of thermodynamic and kinetic scientists and are discussed for the first time.
2. Experimental 2.1. Synthesis and characterization FePO4 2H2O crystalline powder was synthesized by wet chemistry method [1,2]. In this study, FePO4 2H2O was prepared
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by precipitation from aqueous solution of FeCl3 6H2O and H3PO4 (86.4% w/w) at pH= 6.5 at the ‘‘precipitation end point’’, with ammonium hydroxide solution. During the synthesizing procedure, iron chloride was dissolved in distilled water followed by adding an equivalent amount of the phosphoric acid (86.4% w/w) with vigorous stirring at room temperature. Finally, the gel solution was obtained by adding 2 M ammonia solutions until pH 6.5. The white powder was isolated by filtration, then washed with deionized water and dried in air for 24 h. Thermal analysis measurements (thermogravimetry, TG; differential thermogravimetry, DTG; and differential thermal analysis, DTA) were carried out on a Pyris Diamond Perkin Elmer apparatus by increasing temperature from 323 to 1073 K with calcined a-Al2O3 powder as the standard reference. The experiments were carried out in air atmosphere at heating rates of 5, 10, 15, and 20 K min 1. The sample mass was added about 6.0– 10.0 mg in an aluminum crucible without pressing. The structures of FePO4 2H2O and its final decomposition products (FePO4) were studied by X-ray powder diffraction using X-ray diffractometer (Phillips PW3040, The Netherland) with Cu Ka radiation (l = 0.1546 nm). The morphology of the selected resulting samples was examined by scanning electron microscope (SEM) using LEO SEM VP1450 after gold coating. The room temperature FTIR spectra were recorded in the range of 4000–370 cm 1 with 8 scans on a Perkin-Elmer Spectrum GX FT-IR/FT-Raman spectrometer with the resolution of 4 cm 1 using KBr pellets (KBr, Merck, spectroscopy grade).
2.2. Kinetics and thermodynamics Decomposition of crystal hydrates is a solid-state process of the type [13–16]: A (solid)-B (solid)+ C (gas). The kinetics of such reactions is described by various equations taking into account the special features of their mechanisms. The reaction can be expressed through the temperatures corresponding to fixed values of the extent of conversion (a = (mi ma)/(mi mf), where mi, ma and mf are the initial, actual and final sample mass at moment time, t) from experiments at different heating rates (b).
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The FWO [9] and the KAS [10,11] methods are two representative ones of model-free, which are convenient to calculate the activation energy. The activation energy (Ea) of the dehydration reaction of FePO4 2H2O can be calculated according to the FWO and the KAS equations. The FWO equation: AEa Ea ln b ¼ ln 5:33051:0516 ð1Þ RgðaÞ RT The KAS equation: b AEa Ea ln 2 ¼ ln RgðaÞ RT T
ð2Þ
where A (the pre-exponential factor) and E (the activation energy) are the Arrhenius parameters and R is the gas constant (8.314 Ra J mol 1 K 1). The gðaÞ ¼ 0 fdðaaÞ is the integral form of the f(a), which is the reaction model that depends on the reaction mechanism. For one dehydration reaction of FePO4 2H2O, the estimation of kinetic function model can be turned into a multiple linear regression problem through the Coats–Redfern method [12] as follows: gðaÞ AR 2RT Ea AR Ea ¼ ln 1 ffi ln ð3Þ ln bEa RT bEa RT Ea T2 Hence, ln(g(a)/T2) calculated for different a values at the single b value on 1000/T must give rise to a single master straight line, so the activation energy and the pre-exponential factor can be calculated from the slope and intercept through ordinary least square estimation. The activation energy and the pre-exponential factor can be calculated from the slope and intercept through ordinary least square estimation, which combined with nine conversion functions (Table 1) with the best equation [13]. Comparing the kinetic parameters from the Coats and Redfern equation, the probable kinetic model may be selected, where the values of Ea and A were calculated with the better linear correlation coefficient and the activation energies obtained from the Coats and Redfern equation above were showing good agreement to those obtained from the KAS and the Ozawa methods with a better correlation coefficient (r2). Hence, the
Table 1 Algebraic expressions of functions g(a) and f(a) and its corresponding mechanism [13,21]. f(a)
g(a)
Rate-determination mechanism
2(1 a)3/2
[1 (1 a) 1/2 1]
Chemical reaction
(1 a)
ln(1 a)
Avrami-Erofeev equation
(3/2) (1 a)[ ln(1 a)]1/3
[ ln(1 a)]2/3
Assumed random nucleation and its subsequent growth, n=1 Assumed random nucleation and its subsequent growth, n=1.5
3. Deceleratory rate equations 3.1. Phase boundary reaction (4) R3, F2/3
Power law
3(1 a)2/3
[1 ln(1 a)]1/3
Contracting volume (spherical symmetry) or two-thirds order
3.2. Based on the diffusion (5) D1 (6) D2 (7) D3
Parabola law (a = kt1/2) Valensi equation Jander equation
1/2a [ ln(1 a)] 1 (3/2)(1 a)2/3/[ln(1 a)1/ 3 ] (3/2)[(1 a) 1/3 1] 1
a2 a + (1 a)ln(1 a) [1 (1 a)1/3]2
One-dimension diffusion Two-dimension diffusion Three-dimension diffusion
[1 (2/3)a (1 a)2/3]
Three-dimension diffusion
No.
Symbol
Name of the function
1. Chemical process of mechanism non-invoking equations One and a haft order (1) F3/2 2. Sigmoid rate equations or random nucleation and subsequent growth Avrami-Erofeev equation (2) A1, F1
(3)
(8) (9)
A3/2
D4 D5
Ginstling–Brounstein Equation Zhuravlev Lesokhin Tempelman Equation
4/3
(3/2)(1 a) / [1 (1 a) 1/3]
[(1 a)
1/3
1]
2
Three-dimension diffusion
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pre-exponential factor A can be obtained by calculating the average value of A (s 1) from Eq. (3) for different heating rates. The other kinetics parameters of the process can be calculated using the fundamental theory of the activated complex theory (transition state) of Eyring [17–21], the following general equation may be written: ewkB Tp DS exp ð4Þ A¼ h R where A is the pre-exponential factor obtained from the Coats and Redfern method; e= 2.7183 is the Neper number; w is the transition factor, which is unity for monomolecular reactions; kB is the Boltzmann constant; h is the Plank constant, and Tp is the peak temperature of DTA curve. The change of the entropy may be calculated according to the formula Ah ð5Þ DS ¼ R ln ewkB Tp Since
DH ¼ E RTp
ð6Þ
where E* is the activation energy, Ea, obtained from the Coats– Redfern method. The changes of the enthalpy DH* and Gibbs free energy DG* for the activated complex formation from the reagent can be calculated using the well-known thermodynamic equation
DG ¼ DH Tp DS
ð7Þ
The heat of activation (DH*), entropy of activation (DS*), free energy of activation decomposition (DG*) were calculated at T= Tp (Tp is the DTA peak temperature at the corresponding stage), since this temperature characterizes the highest rate of the process, and therefore, is its important parameter.
3. Results and discussion 3.1. Characterization results TG–DTG–DTA curves of the thermal decomposition of FePO4 2H2O at heating rate of 10 K min 1 are shown in Fig. 1. The TG curve shows that the single well-defined decomposition step relates to the eliminations of water in range of 348–523 K. The corresponding observed mass loss is 20.27% by mass, which corresponds to 2.10 mol of water and is close to the theoretical value for FePO4 2H2O (19.27%, 2.00H2O). An endothermic effect
Fig. 1. TG–DTG–DTA curves of FePO4 2H2O in air at heating rate of 10 K min 1.
on DTA curves is observed at 398 K that agrees with the respective DTG peak. Further, four exothermic effects at 800, 849, 898 and 947 K without appreciable mass loss is observed on the DTA curve, which can be ascribed to a transition phase from amorphous to crystalline form of FePO4 [5–7]. A minor mass loss is observed, which corresponds to an exothermic peak on DTA with respective DTG peak at 849 K. The retained mass (89.73%) and water loss (20.27%) are compatible with the values expected for the formation of FePO4 and 2 moles water per mole of the synthesized FePO4, respectively. This indicates that the general formula should be FePO4 2H2O. The temperature at which theoretical mass loss is achieved can be also determined from the TG curve and considered to be the minimum temperatures needed for the calcinations process. Therefore, FePO4 2H2O sample was calcined at 673 K for 2 h in the furnace, which is the lower temperature as compared to those of the other hydrate precursors [1–5]. However, FePO4 in this work obtained by the calcined FePO4 2H2O at 623 K shows poor crystallization or amorphous phase, which is revealed by the observed broad peaks in XRD patterns (Fig. 2) and is in good agreement with the results reported in the literature [2,5,6]. Additionally, the crystallinity of FePO4 occurred at above 873 K of calcination supported a very stable inorganic framework system of the studied compound. This result is consistent with a transition phase from amorphous to crystalline, which is concluded in thermal analysis (DTA peak at over 947 K). The thermal stability, mechanism and phase transition temperature of the synthesized FePO4 2H2O reported in this work are different form those of our previous works (FePO4 3H2O [7] and AlPO4 2H2O [20]). Based on these results, we can conclude that the thermal results are caused by the nature of materials and synthesis conditions. The XRD patterns of iron phosphate dihydrate FePO4 2H2O and its dehydration product (FePO4) are shown in Fig. 2. As seen in Figs. 2a and b, the observed broad peaks in XRD patterns of the synthesized FePO4 2H2O and FePO4 indicate the predominance of the poor crystallization or amorphous phase as well as nanoparticles. This result is in good agreement with the results reported by Refs. [2,4–6], where the AlPO4 transforms from amorphous to a crystalline phase at about 873 K. It evidenced that this studied compound is a very stable inorganic framework system. Additionally, the result is consistent with a transition phase from amorphous to crystalline, which is concluded in thermal analysis.
Fig. 2. XRD patterns of FePO4 2H2O (a) and its dehydration product (FePO4) (b).
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FT-IR spectra of FePO4 2H2O and its dehydration product (FePO4) are shown in Fig. 3. Vibrational bands are identified in relation to the crystal structure in terms of the fundamental vibrating units namely PO34 , H2O, for FePO4 2H2O and PO34 for
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FePO4 [6,22]. FTIR spectra of PO34 in FePO4 2H2O and FePO4 show the antisymmetric stretching mode (n3) in 1000–1200 cm 1 region and the n4 mode in 400–560 cm 1 region. The observed bands in 1600–1700 cm 1 and 3000–3500 cm 1 region are attributed to the water bending and stretching vibrations. These water bands disappear in FT-IR spectra of its dehydration product (FePO4), which support a very good agreement with the thermal analysis results. The XRD data along with FTIR spectra confirm that the calcined FePO4 2H2O at 673 K transforms to FePO4. The SEM micrographs of FePO4 2H2O and its final decomposition product FePO4 are shown in Fig. 4. The particle shape and size are changed throughout the whole decomposition product. The SEM micrographs of FePO4 2H2O (Fig. 4a) and FePO4 (Fig. 4b) illustrate coalescence in aggregates of nanoparticles with sizes of o300 nm. The morphology of FePO4 shows smaller size than that of FePO4 H2O, which is the effect of the thermal dehydration process.
3.2. Kinetics and thermodynamics results
Fig. 3. FT-IR spectra of FePO4 2H2O (a) and its dehydration product (FePO4) (b).
According to isoconversional method, the basic data of a and T collected from the TG curves of the dehydration of FePO4 2H2O at various heating rates (5, 10, 15 and 20 K min 1) are illustrated in Table 2. According to Eqs. 1 and 2), the plots of ln b versus 1000/T (the FWO) and ln b/T2 versus 1000/T (the KAS) corresponding to different conversions a can be obtained by a linear regression of least-square method, respectively. The FWO and the KAS analysis results of four TG measurements below 573 K are presented in Fig. 5. The activation energies Ea can be calculated from the slopes of the straight lines with better linear correlation coefficient (r2 40.99). The slopes change depending on the degree of conversion (a) for the dehydration reaction of FePO4 2H2O. The activation energies are calculated at heating rates of 5, 10, 15, and 20 K min 1 via the FWO and the KAS methods in the a range of 0.2–0.8. The activation energies calculated by the FWO and the KAS methods are close to each other, which are shown in Table 3, so the results are credible. If Ea values are independent of a, the decomposition may be a simple reaction, while the dependence of Ea on a should be interpreted in terms of multi-step reaction mechanisms [13–16]. Neglecting the dependence of E versus a an average values of Ea =68.4870.93 kJ mol 1 (FWO) and 65.55 7 0.81 kJ mol 1 (KAS) are obtained. It was considered that the Ea values are independent of a if the relative error of the slope of the FWO and the KAS equations straight lines is lower than 10%. The activation energies change little with a, so we draw a conclusion that the dehydration reaction of FePO4 2H2O could be a single kinetic mechanism, which corresponds to an endothermic peak at 398 K in DTA curve. The single kinetic mechanism of the dehydration of the FePO4 2H2O reported in this work is different from a multi-step kinetic mechanism of its
Table 2 a T data at different heating rates, b (K min 1), for the dehydration reaction of FePO4 2H2O.
a
Fig. 4. SEM micrographs of FePO4 2H2O (a) and its dehydration product (FePO4) (b).
0.2 0.3 0.4 0.5 0.6 0.7 0.8
Temperature (K)
b=5
b = 10
b = 20
b = 30
365.76 372.81 379.91 387.44 395.73 405.80 419.88
372.86 381.69 390.11 398.21 407.65 418.91 434.60
380.66 390.03 398.17 406.64 417.09 428.54 444.47
388.30 396.05 404.08 412.42 422.12 433.24 449.16
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Table 4 Kinetics parameters obtained from the differential method and the integral method at different heating rates (b = 5, 10, 15 and 20 K min 1). Model
Coats–Redfern method Ea/kJ mol 1
F3/2 A1, F1 A3/2 F2/3 D1 D2 D3 D4 D5
Fig. 5. FWO analysis (a) and KAS analysis (b) for the dehydration of FePO4 2H2O.
Table 3 Activation energies (Ea) vs. correlation coefficient (r2) calculated by FWO and KAS methods for the dehydration of FePO4 2H2O.
a
FWO method
KAS method
Ea/kJ mol 1
r2
Ea/kJ mol 1
r2
0.2 0.3 0.4 0.5 0.6 0.7 0.8
67.93 68.90 69.42 69.73 68.18 68.77 69.02
0.9801 0.9937 0.9976 0.9983 0.9986 0.9987 0.9984
65.17 66.07 66.49 66.69 64.91 65.35 65.37
0.9760 0.9923 0.9971 0.9979 0.9983 0.9984 0.9980
Average
68.48 70.93
0.9948
65.55 7 0.81
0.9937
isostructural (AlPO4 2H2O) reported in our previous work [21]. However, the average activation energy of dehydration process of FePO4 2H2O reported in this work is close to those of its isostructural AlPO4 2H2O reported in our previous work (69.6877 kJ mol 1 for the Kissinger method) [21]. Moreover, these activation energy values obtained from this work are lower
ln A/s 1
r2
Ea
7 Error
ln A
7 Error
17.07 37.82 22.96 32.77 55.15 62.81 72.28 65.94 14.47
1.03 1.78 1.20 1.57 2.39 2.71 3.11 2.84 0.93
3.91 2.79 2.39 0.22 5.72 8.36 10.47 8.32 4.58
0.46 0.56 0.52 0.66 0.97 1.09 1.23 1.14 0.43
0.99535 0.98176 0.97773 0.97232 0.95653 0.96721 0.97747 0.97108 0.98573
than those of the dehydration reaction of FePO4 3H2O for the FWO method and (130.18718 kJ mol 1 130.33719 kJ mol 1 for the KAS method) reported in our previous work [7]. In this respect, these data will be important for further studies of the studied compound, which include studies under carefully controlled reaction conditions. For kinetic function model analysis from the Coat–Redfern equation (Eq. 3), we can draw a conclusion that the possible conversion function is the based on the three-dimension diffusion mechanism (D4 model), Ginstling–Brounstein Eq. [f(a)= (3/2)(1 a) 1/3 1] 1 and g(a) =[1 (2/3)a (1 a)2/3], which are shown in Table 4. The correlated kinetic parameters are Ea = 65.9472.83 kJ mol 1 and ln A= 8.3271.14 s 1. Additionally, the strengths of molecular binding in the crystal lattice are different. Consequently, the dehydration temperatures and kinetic parameters are different. The activation energy for the losing of crystal water lie in the range of 60–80 kJ mol–1, while the value for coordinately bounded one are within the range of 130– 160 kJ mol–1 [20]. The energy of activation found in D4 model for the dehydration reaction suggests that the water molecules are water of crystallization. This result is different from the most kinetic model of the dehydration reaction of FePO4 3H2O (F2.5 model from the Coats–Rendfern method) reported in our pervious work [7]. The calculated values of DH*, DS* and DG* were calculated by Tp (418 K) in the highest heating rate and found to be 130.65 kJ mol 1, 30.32 J K 1 mol 1 and 117.98 kJ mol 1, respectively. The entropy of activation (DS*) value for the dehydration step is positive. It means that the corresponding activated complexes were with lower degree of arrangement than the initial state. Since the dehydration of FePO4 2H2O proceeds as a single reaction, the formation of the activated complex passed in situ. In terms of the activated complex theory (transition theory) [15,22–26], a positive value of DS* indicates a malleable activated complex that leads to a large number of degrees of freedom of rotation and vibration. A result may be interpreted as a ‘‘fast’’ stage. On the other hand, a negative value of DS* indicates a highly ordered activated complex and the degrees of freedom of rotation as well as of vibration are less than those in the nonactivated complex. This results may indicate a ‘‘slow’’ stage. Therefore, the dehydration reaction of FePO4 2H2O may be interpreted as ‘‘fast’’ stage [15,22–26]. The positive value of the enthalpy DH* indicates the endothermic reaction, which is consistent with an endothermic effects in DTA data (Fig. 1). Additionally, the positive value of DG* for the dehydration stage shows that it is non-spontaneous process and is necessary to connect with the introduction of heat. These thermodynamic
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functions are consistent with kinetic parameters and thermal analysis data.
4. Conclusions FePO4 2H2O decomposes in one step by starting after 300 K and the final product is FePO4, playing a more and more important role in the development of advanced rechargeable lithium ion batteries. A single value of E for different a can be assigned to a single reaction process, which relates to the elimination of water of crystallization in the structure. On the basis of correctly established values of the apparent activation energy, pre-exponential factor and the changes of entropy, enthalpy and Gibbs free energy, certain conclusions can be made concerning the mechanisms and characteristics of the processes. The data of kinetics and thermodynamics play an important role in theoretical study, application development and industrial production of a compound as a basis of theoretical. Consequently, these data will be important for further studies of the studied compound and are applied to solve various scientific and practical problems involving the participation of solid phases.
Acknowledgement This work is financially supported by the Thailand Research Fund (TRF), the Commission on Higher Education (CHE) and Research Grant for New Scholar, Ministry of Education, Thailand.
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