Non-isothermal kinetics study on synthesis of LiFePO4 via carbothermal reduction method

Thermochimica Acta 566 (2013) 298–304

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Non-isothermal kinetics study on synthesis of LiFePO4 via carbothermal reduction method Lihua He, Xuheng Liu, Zhongwei Zhao ∗ School of Metallurgical Science and Engineering, Central South University, Changsha, Hunan 410083, PR China

a r t i c l e

i n f o

Article history: Received 21 March 2013 Received in revised form 19 May 2013 Accepted 11 June 2013 Available online 18 June 2013 Keywords: Lithium iron phosphate Thermal kinetics Avrami Carbothermal reduction

a b s t r a c t Non-isothermal kinetics of lithium ion phosphate synthesis via carbothermal reduction method with raw materials Li2 CO3 , FePO4 ·2H2 O and C6 H12 O6 ·2H2 O is studied by thermogravimetry-differential scanning calorimetry (TG–DSC) technology. The results indicate the synthesis process can be divided into two stages: dehydration and LiFePO4 formation. The apparent activation energy and natural logarithm frequency factor (ln A-value) for dehydration reaction is respectively 83.4 ± 4.7 kJ mol−1 and 22.1 ± 1.5 s−1 , and that for LiFePO4 formation reaction is in turn 184.2 ± 10.4 kJ mol−1 and 28.3 ± 1.9 s−1 . Additionally, the mechanism for dehydration and LiFePO4 formation stages is Avrami’s A1.5 and A4 , respectively. Furthermore, the dehydration process is diffusion controlled, and the crystallization of LiFePO4 formation is controlled by nuclei being formed randomly and growing in three-dimensions, and the kinetic equations for each stage are shown as follows:



Dehydration stage :

2/3

[− ln(1 − a)]

= 3.96 × 109 exp

−

8.34 × 104 RT



LiFePO4 formation stage :

1/4

[− ln(1 − a)]

= 1.95 × 1012 exp

−



t;

1.84 × 105 RT

 t;

where ˛ is the fractional conversion, T the calcination temperature (K), t the calcination time (s), R the gas constant (8.314 J mol−1 K−1 ). © 2013 Elsevier B.V. All rights reserved.

1. Introduction Since lithium iron phosphate, LiFePO4 , was first reported as a positive electrode for rechargeable lithium-ion batteries in 1997 by John Goodenough et al. [1], it is being actively investigated and has been considered as one of the most promising cathode materials for lithium ion batteries due to its low cost, nontoxic, high lithium intercalation voltage, high theoretical specific capacity and greater thermal stability [2,3]. Compared with other lithium ion batteries cathode materials, such as LiCoO2 , LiNiO2 , LiMn2 O4 and LiNi1/3 Co1/3 Mn1/3 O2 , it shows lower cost and higher safety performance. For example, using lithium iron phosphate as a cathode material to replace expensive LiCoO2 could reduce the cathode cost from 10% to 50% of the battery cost [4]. Based on these superiorities, LiFePO4 is used as one of the main cathode materials in the electric and hybrid electric vehicles [5].

∗ Corresponding author. Tel.: +86 731 88830476; fax: +86 731 88710171. E-mail address: [email protected] (Z. Zhao). 0040-6031/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tca.2013.06.014

Conventionally, LiFePO4 powders were synthesized through solid-state chemistry method, such as solid-state reaction, mechanochemical activation and carbothermal reduction methods. Generally, in the case of LiFePO4 , the starting mixture consists of a stoichiometric amount of iron salt, lithium salt, phosphate salt and a proportion of polymer as a carbon source in the LiFePO4 /C composite formation. The starting mixture firstly was decomposed at the temperature of 300–400 ◦ C to expel the gases, and after being reground, calcined at a temperatures ranging from 400 ◦ C to 800 ◦ C for 10–24 h [6]. Noteworthily, the calcination temperature and heating time have a direct influence on the purity, morphology and electromechanical performance of the materials. On the one hand, excessively high temperature may bring about a large lithium volatilization. Meanwhile, the ferrous iron will be oxidized to ferric iron, which could cause the formation of impurities, corresponding with a deviation from the stoichiometry. On the other hand, too long a heating time not only results in an increase in manufacturing cost but also forms a bigger particle size of the LiFePO4 powders, which in turn, leads to serious electrochemical performance deterioration. Actually, the foremost of the LiFePO4 solid-phase synthesis processes is the control of particle nucleation and growth, and it has

L. He et al. / Thermochimica Acta 566 (2013) 298–304

been reported that smaller grain/particle size of LiFePO4 has a beneficial effect on high-rate capacity [7]. In order to obtain high purity, small size, uniform distribution and good performance powders, an effective measure is to have a deeper understanding of the kinetic behaviors, i.e. the reaction mechanism of the LiFePO4 synthesis processes, which is helpful to find the optimum conditions for LiFePO4 synthesis so as to optimize the performance of LiFePO4 products. During the methods of solid-state kinetics study, simultaneou thermogravimetry (TG) and differential scanning calorimetry (DSC) are the most common techniques for researching the characteristics of solid-state reaction, such as the beginning temperature of reaction, phase transformation temperature, degree and state of the reaction, and control process of the reaction [8–10]. Thus, it may be a useful technology for us to have a deep research on the mechanism of LiFePO4 synthesis reaction. In recent years, much research work had focused on the atomic-scale investigation of defects, dopants, and lithium transport in the LiFePO4 [11–15], but neglected the research on macroscale synthesis mechanism. Up to now, the thermal kinetics of LiFePO4 precipitation with raw materials Li2 CO3 , FePO4 ·2H2 O and C6 H12 O6 ·2H2 O via carbothermal reduction method has not been reported in detail. In this paper, the kinetics of LiFePO4 precipitation was studied by means of a differential thermal analysis (DSC) under different heating rates. Based on that, the apparent activation energy and frequency factor will be calculated via Ozawa–Flynn–Wall and/or Kissinger methods. Furthermore, the most probable mechanism function for the LiFePO4 synthesis process will also be determined via Coats–Redfern method, corresponding with the final-deduced kinetic equations being obtained.

299

n the reaction order number, and f(˛) depends on the particular decomposition mechanism. For a certain reaction, A and n are constant values, when ˛ is certain value, the function f(˛) is a constant. So, the plot of lg ˇ ∼ 1/T is a straight line with its slope (−0.4567E/R). Under different heating rates ˇ and the same fractional conversion, we can plot the relation curve of the lg ˇ ∼ 1/T, then the apparent activation energy of the reaction can be calculated from the slope of the straight line. Apart from the above integral method, another differential method, Kissinger’s method, has been used in the work to determine the activation energy of solid state reactions from plots of the logarithm of the heating rate versus the inverse of the temperature at the maximum reaction rate in constant heating rate experiments [21]. And its principle just as shown in Eq. (5): Kissinger’s formula

ln

ˇ TP2

= ln

AR E 1 − E R TP

(5)

where TP is the peak temperature, and ˇ, A, E, R have the known meanings. For a certain reaction, the frequency factor A is constant, and ln(AR/E) is also a constant. The plot of ln(ˇ/TP2 )∼(1/TP ) is a line, with its slope (−E/R) and intercept ln(AR/E). Using the slope and intercept values of the line, the apparent activation energy E and frequency factor A can be calculated out, respectively. Compared to other methods, these two methods present the advantage that they do not require previous knowledge of the reaction mechanism for determining the activation energy, and therefore researchers usually used the activation energies obtained via these two methods to check their thermo-degradation mechanism models [22]. 2.2. Determination of reaction mechanism

2. Kinetic principle 2.1. Calculation of kinetic triplets Generally, from the viewpoints of chemistry reaction dynamics, two principal objectives are common to the vast majority of kinetic studies. One of these is the determination of the rate equation that satisfactorily describes the extent of conversion of reactant(s) or formation of product(s) with time as reaction proceeds, usually, but not necessarily, at constant temperature. The second purpose of kinetic analysis is to determine the influence of temperature on the rate of reaction [16–19]. Therefore, it was necessary for us to estimate the traditional kinetic triplets, i.e. activation energy, frequency factor and kinetic equation. Here, Ozawa–Flynn–Wall and Kissinger methods were used to calculate the activation energy of the reaction of LiFePO4 preparation. For Ozawa–Flynn–Wall method, based on Eqs. (1)–(3), the Ozawa–Flynn–Wall formula can be deduced and expressed quantitatively by Eq. (4) [20,21]: Mass action raw :

d˛ = kf (˛) dt

(1)



Arrhenius formula :

Heating rate formula :

Ozawa–Flynn–Wall :

k = A exp −

ˇ=

E RT



dT dt

(2)

According to the above introductions, we know that the apparent activation energy, E, and frequency factor, A, can be estimated via Ozawa–Flynn–Wall and/or Kissinger’s method. Nevertheless, the reaction mechanisms of the processes still mystify us. In order to get understanding the nature of the synthesis, the key was to obtain the mechanism for the LiFePO4 synthesis processes. The purpose of specific thermal decomposition process is to obtain the most probable mechanism function. Here, Coats–Redfern method [23,24] was used to achieve this aim, and it can be described as Eq. (6). Coats–Redfern method

ln

 G(˛)  T2

= ln

 AR  ˇE

−

E RT

(6)

where G(˛) is an integral expression for the mechanisms of solid state processes listed in Table 1, and ˇ, A, E, R have the known meanings. By using the reaction models [25] shown in Table 1 and Coats–Redfern methods, the activation energy and frequency factor can be determined from the plot of ln(G(˛)/T2 ) vs. 1/T. To determine the most probable mechanism function of the reaction, two preconditions should be satisfied simultaneously: firstly the value of E and A estimated by Coats–Redfern method must be comparable with that obtained via Doyle–Ozawa and Kissinger methods; secondly the linear correlation coefficient of the fitting curve must greater than 0.98.

(3) 3. Experimental procedure

AE E − 2.315 − 0.4567 log ˇ = log RT Rf (˛) (4)

where ˛ is the fractional conversion, t the reaction time, k the reaction rate constant, A the frequency factor, E the apparent active energy, R the gas constant, T the temperature, ˇ the heating rate,

LiFePO4 precursors preparation: The LiFePO4 precursors were synthesized by using Li2 CO3 , FePO4 ·2H2 O and C6 H12 O6 ·2H2 O (A.R., XILONG Chemical Co., Ltd., China) as starting materials. Stoichiometric amounts of Li2 CO3 and FePO4 ·2H2 O were ground thoroughly along with C6 H12 O6 ·2H2 O (55.9 g/mol LiFePO4 ) by ball-milling in alcohol environment for 5 h, and then the mixed slurry was dried

300

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Table 1 Traditional reaction models for the mechanisms of solid state processes. Symbol

Model

G(˛)

f(˛)

D1 D2 D3 An R1 R2 R3 P2 P3 P4

One-dimensional diffusion Two-dimensional diffusion Three-dimensional diffusion Avrami–Erofeev (n = 1.5, 2, 3, 4) Phase boundary reaction Phase boundary reaction Phase boundary reaction Power law Power law Power law

˛2 ˛ + (1 − ˛)ln(1 − ˛) [1 − (1 − ˛)1/3 ]2 [−ln(1 − ˛)](1 /n) ˛ 1 − (1 − ˛)1/2 1 − (1 − ˛)1/3 ˛1/2 ˛1/3 ˛1/4

˛−1 /2 [−ln(1 − ˛)]−1 1.5(1 − ˛)2/3 [1 − (1 − ˛)1/3 ]−1 n(1 − ˛)[−ln(1 − ˛)]−(1/n−1) 1 2(1 − ˛)1/2 3(1 − ˛)2/3 2˛1/2 3˛2/3 4˛3/4

at 353 K for 10 h. The dried precursors were ground in a mortar for about 30 min, and the resulting powders were used as the raw materials in the subsequent thermal experiments. Thermal analysis experiments: For each experiment, 3–6 mg LiFePO4 precursors were put into an aluminum crucible with the different heating rates 5, 10, 15, 20 K min−1 , under argon with a gas-flow rate of 50 mL min−1 on Netzsch Model 449C analyzer. The measured TG/DSC data was analyzed by using Origin8.0 software. The crystallographic structure of the samples were measured by ˚ X-ray diffraction (XRD: Siemens D-500, Cu K␣ radiation,  = 1.8 A) under the scan rate 2(◦ ) min−1 and step 0.02◦ , and the morphology of the samples were observed by using a JXA-8800R scanning electron microscope (SEM). 4. Results and discussion 4.1.1. 4.1Decomposition of LiFePO4 precursors The TG–DSC curves of LiFePO4 precursors at the heating rate of 10 K min−1 were represented in Fig. 1. According to the DSC curve, one endothermic peak and another exothermic peak were observed. Combining with the percentages of weight losses (TG curve), two-step reaction was proposed for this synthesis process. At the first stage, the weight loss (18.15%) corresponding to the exothermic peak (428.05 K) in DSC curve was observed from 300 to 480 K, which can be attributed to the crystal water losing of FePO4 ·2H2 O [26,27] and C6 H12 O6 ·2H2 O (theoretical mass loss: 17.33%), just as shown in Eqs. (7) and (8). For the second stage, which occurred in the temperature range 480–850 K, corresponding to the mass loss 13.77% (theoretical value 14.25%) and exothermic temperature 720.15 K, the glucose was decomposed (Eq. (9)), meanwhile FePO4 , Li2 CO3 , and pyrolytic carbon were

Fig. 1. TG–DSC curves of LiFePO4 precursors at 10 K min−1 heating rate.

reacted to form LiFePO4 , just as listed in Eq. (10). To summarize, these two stages can be roughly summarized as dehydration and LiFePO4 formation. Notably, with the temperature increasing over 750 K, though there was no obvious weight loss in TG curve, endothermic phenomenon still appeared in the system, which means that the initial formed LiFePO4 crystal could be crystallized perfectly with the temperature increase. FePO4 ·2H2 O = FePO4 + 2H2 O

(7)

C6 H12 O6 ·2H2 O = C6 H12 O6 + 2H2 O

(8)

C6 H12 O6 = 6C + 6H2 O

(9)

FePO4 + 2Li2 CO3 + 2C = 2LiFePO4 + 3CO ↑

(10)

Fig. 2 showed the XRD patterns of the precursors and the precursors sintered at 473, 673, 773 and 873 K for 10 h under N2 atmosphere. As can be seen from the diagram, when the precursors were heated at 473 K, the obtained particles were amorphous. As the temperature rose to 673 K, the X ray diffraction peaks of the sample matched well with that of pure LiFePO4 (PDF#40-1499), the higher sintering temperature, the stronger of the diffraction peaks will be. So the main phase of the samples can be identified as LiFePO4 with olivine structure indexed to orthorhombic Pnmb, which means that the carbothermal reduction reaction happened as the sintering temperature over 673 K, corresponding with the LiFePO4 being formed. Table 2 listed the lattice parameters of the samples sintered at 673, 773, 873 K, which are very close to the ˚ b = 10.334 A, ˚ c = 4.693 A, ˚ V = 291.392 A˚ 3 ) standard data (a = 6.008 A,

Fig. 2. XRD patterns of LiFePO4 precursor and olivine LiFePO4 : a – LiFePO4 precursor; b – 473 K; c – 673; d – 773 K; e – 873 K sintered.

L. He et al. / Thermochimica Acta 566 (2013) 298–304

301

Table 2 Structure parameters of samples sintered at different temperatures. Samples

673 K 773 K 873 K Standard

Cell parameters a (Å)

b (Å)

c (Å)

Volume (Å3 )

Space group

6.001 6.001 6.008 6.008

10.331 10.332 10.333 10.334

4.688 4.693 4.693 4.693

290.639 290.853 291.344 291.392

Pnmb Pnmb Pnmb Pnmb

[1], but slightly increase with the synthesis temperature increasing. According to the formation temperatures of LiFePO4 products, we can see that these XRD results were consistent with that of TG–DSC. 4.2. Kinetic analysis Fig. 3 showed the DSC curves of the LiFePO4 precursors measured at heating rates 5, 10, 15, 20 K min−1 . It can be seen, the shape and tendency of the curves followed the similar pattern, and with the heating rate rising up gradually, the peaks moved to a high temperature. According to the DSC data illustrated in Fig. 3, the relationship between fractional conversions and heating temperature were obtained via integral method, and the results were shown in Fig. 4. Based on the data of fractional conversions under different temperatures, heating rates and peak temperatures, the kinetics of LiFePO4 synthesis was analyzed via Ozawa–Flynn–Wall and/or Kissinger methods. By means of Ozawa–Flynn–Wall method, the diagrams of lg ˇ ∼ 1/T for two stages were showed in Fig. 5. The slopes, correlation coefficients (R2 ), residual standard deviation (S) and activation energy of each line were listed in Table 3. It can be easily seen that with ˛ increased from 10% to 100%, the apparent activation energy decreased from101.3 kJ mol−1 to 59.3 kJ mol−1 for the dehydration stage and from 203.9 kJ mol−1 to 169.4 kJ mol−1 for the LiFePO4 formation stage. Additionally, the average apparent activation energy of the two stages was 87.3 ± 5.7 kJ mol−1 and 182.2 ± 12.4 kJ mol−1 , respectively. For the Kissinger method, the curves of ln(ˇTP−2 ) vs. 1/T for each reaction were plotted in Fig. 6, with its corresponding kinetic parameters being listed in Table 4. The results showed that apparent activation energy and natural logarithmic frequency factor of the dehydration reaction were 76.6 ± 6.2 kJ mol−1 and 20.7 ± 1.7 s−1 , respectively. And that of the LiFePO4 formation reaction were 189.4 ± 14.1 kJ mol−1 and 30.7 ± 2.3 s−1 , respectively. As

Fig. 3. DSC curves of LiFePO4 precursors at different heating rates: a – 5; b – 10; c – 15; d – 20 K min−1 .

Fig. 4. Fractional conversions ˛ vs. T for the reaction of LiFePO4 precursors at different heating rates: a – endothermic peak; b – exothermic peak.

compared with the results listed in Table 3, it indicated that the values obtained by Ozawa–Flynn–Wall method were close to the one gained via Kissinger methods. The kinetic parameters frequency factor, A, and apparent activation energy, E, were calculated via Ozawa–Flynn–Wall and Kissinger methods. Nevertheless, just as the brief introductions above, in order to obtain a reliable and accurate value, these two methods have been avoided the choosing of reaction mechanism. Herein, Coats–Redfern method was used to determine the reaction mechanism and its results matching to the dehydration stage and LiFePO4 formation stage were illustrated in Table 5. Comparing the value with that obtained via Ozawa–Flynn–Wall and/or Kissinger methods, we deduced the most probable mechanism for dehydration and LiFePO4 formation stages was A1.5 and A4 , corresponding with the value of E and ln A 86.3 ± 2.1 kJ mol−1 , 23.4 ± 1.2 s−1 and 180.9 ± 4.8 kJ mol−1 , 25.9 ± 1.5 s−1 , respectively. Furthermore, the apparent activation energies and frequency factors which were calculated via different method for each stage were listed in Table 6, and the average value of E and ln A for lowtemperature dehydration reaction and LiFePO4 formation reaction was 83.4 ± 4.7 kJ mol−1 , 22.1 ± 1.5 s−1 and 184.2 ± 10.4 kJ mol−1 , 28.3 ± 1.9 s−1 , respectively. Based on the values of E and A, and reaction mechanism, the kinetic equation for each stage was described as Eqs. (11) and (12). Dehydration stage :

[− ln(1 − ˛)]

2/3

 = 3.96 × 109 exp

−

8.34 × 104 RT

 t

(11)

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L. He et al. / Thermochimica Acta 566 (2013) 298–304

Table 3 Slopes, linear coefficients, residual standard deviation and apparent activation energy of each reaction degree by Ozawa–Flynn–Wall method. ˛

Dehydration stage

10 20 30 40 50 60 70 80 90 100

LiFePO4 formation stage

Slope

E (kJ mol−1 )

S

R2

Slope

E (kJ mol−1 )

S

R2

−5.56 −5.32 −5.17 −5.05 −4.97 −4.88 −4.77 −4.61 −4.34 −3.26

101.3 96.8 94.1 92.0 90.6 88.8 86.8 83.9 79.0 59.3

8.8 × 10−5 3.3 × 10−4 5.49 × 10−4 9.0 × 10−4 1.3 × 10−3 1.8 × 10−3 2.3 × 10−3 3.1 × 10−3 3.7 × 10−3 2.1 × 10−3

0.999 0.998 0.997 0.995 0.993 0.991 0.988 0.984 0.982 0.989

−11.20 −10.81 −10.29 −10.24 −10.13 −9.97 −9.78 −9.32 −9.05 −9.30

203.9 196.8 187.3 186.4 184.4 181.5 178.0 169.6 164.8 169.4

2.3 × 10−3 1.5 × 10−3 9.9 × 10−4 9.2 × 10−4 9.6 × 10−4 9.5 × 10−3 1.0 × 104−3 2.0 × 10−3 2.7 × 10−3 2.1 × 10−3

0.989 0.992 0.995 0.995 0.995 0.995 0.991 0.99 0.987 0.989

87.3 ± 5.7

Average

182.2 ± 12.4

Table 4 Kinetic parameters of each reaction calculated by Kissinger method. Reaction

Slope −9.21 −22.78

Dehydration reaction LiFePO4 formation reaction

Intercept

E (kJ mol−1 )

ln A (s−1 )

S

R2

11.61 20.72

76.6 ± 6.2 189.4 ± 14.1

20.7 ± 3.5 30.7 ± 4.2

0.077 0.073

0.987 0.989

Table 5 Model-fitting results by using Coats–Redfern method at a heating rate of 10 K min−1 . No.

Dehydration stage E (kJ mol

D1 D2 D3 A1.5 A2 A3 A4 R1 R2 R3 P2 P3 P4

193.7 215.4 243.2 86.3 62.9 39.6 27.9 93.3 111.2 118.1 43.1 26.4 18.1

± ± ± ± ± ± ± ± ± ± ± ± ±

−1

No. −1

)

ln A (s

15.5 13.4 10.0 2.1 1.6 1.0 0.8 7.7 5.8 5.0 3.8 2.6 2.0

53.1 58.9 65.6 23.4 16.6 9.7 6.1 25.0 29.7 31.3 10.5 5.4 2.7

± ± ± ± ± ± ± ± ± ± ± ± ±

LiFePO4 formation stage E (kJ mol−1 )

2

)

S

R

7.0 5.9 4.3 1.2 1.3 0.4 0.2 4.5 3.1 2.6 1.6 0.92 0.4

0.308 0.267 0.199 0.041 0.031 0.021 0.016 0.154 0.116 0.099 0.077 0.052 0.039

0.957 0.973 0.988 0.996 0.995 0.995 0.994 0.953 0.980 0.987 0.945 0.936 0.923

D1 D2 D3 A1.5 A2 A3 A4 R1 R2 R3 P2 P3 P4

97.9 108.6 122.3 449.0 333.7 218.5 180.9 483.5 571.7 605.3 235.8 153.2 111.9

± ± ± ± ± ± ± ± ± ± ± ± ±

7.7 6.8 5.2 11.5 8.6 5.7 4.8 38.6 29.8 26.0 19.3 12.9 10.4

ln A (s−1 ) 139.7 177.9 199.6 74.7 55.3 35.7 25.9 80.1 94.4 99.1 38.4 23.6 17.2

± ± ± ± ± ± ± ± ± ± ± ± ±

16.3 16.4 12.5 2.9 2.3 1.75 1.5 9.9 7.6 6.5 5.7 4.5 5.4

S

R2

0.310 0.273 0.209 0.046 0.035 0.023 0.017 0.015 0.120 0.105 0.078 0.052 0.039

0.958 0.973 0.987 0.995 0.995 0.995 0.995 0.957 0.981 0.987 0.955 0.952 0.95

Table 6 Average activation energy and frequency factor of each stage. Methods

Dehydration stage E (kJ mol

−1

LiFePO4 formation stage −1

)

ln A (s

)

E (kJ mol−1 )

ln A (s−1 )

Ozawa–Flynn–Wall Kissinger Coats–Redfern

87.3 ± 5.7 76.6 ± 6.2 86.3 ± 2.1

/ 20.7 ± 1.7 23.4 ± 1.2

182.2 ± 12.4 189.4 ± 14.1 180.9 ± 4.8

/ 30.7 ± 2.3 25.9 ± 1.5

Average

83.4 ± 4.7

22.1 ± 1.5

184.2 ± 10.4

28.3 ± 1.9

LiFePO4 formation stage : [− ln(1 − ˛)]

1/4

 12

= 1.95 × 10

exp

1.84 × 105 − RT

 t

(12) where ˛ is the fractional conversion, T the calcination temperature (K), t the calcination time(s), R the gas constant (8.314 J mol−1 K−1 ). Fig. 7 showed the comparison between the experimental and simulated conversion data, indicating that the proposed rate equations, Eqs. (11) and (12), gave reasonably good fit to the raw conversion data. The comparison results also demonstrated that the kinetic parameters we determined were credible. It is worthy to note that both the processes of nucleation and its growth were derived by Avrami’s equation. For dehydration stage, the calculated reaction order, n, was 1.5, which means the

dehydration reaction probably occurred in the presence of high concentrations of noncrystallizable impurities, and its rate were diffusion controlled [28]. For this processes, the noncrystallizable impurities can be attributed to the formation of amorphous materials at 473 K, just as shown in Fig. 2b. And the diffusion controlled mechanism can be explained that on the decomposition (in the solid state) of FePO4 ·2H2 O and C6 H12 O6 ·2H2 O, a solid layer of FePO4 and C6 H12 O6 were formed, and then covered on the surface of FePO4 ·2H2 O and C6 H12 O6 ·2H2 O particles, respectively. So for further reaction to occur, the product molecules of H2 O must diffuse out through the solid layer of FePO4 and/or C6 H12 O6 . With the time extension the thickness of the product layer (i.e. diffusion path) will increase. Therefore, under such circumstances a diffusion-controlled mechanism can be used to describe the dehydration process. For the LiFePO4 formation stage, its reaction order,

L. He et al. / Thermochimica Acta 566 (2013) 298–304

303

Fig. 5. Curves of lg ˇ vs. 1/T for each reaction via Ozawa–Flynn–Wall method: a – dehydration reaction; b – LiFePO4 synthesis reaction.

Fig. 7. Comparison between the experimental fractional conversions data (, 䊉, ♦,  dots) and the simulated (the lines): (a) dehydration stage; (b) LiFePO4 formation stage.

Fig. 6. Curves of ln(ˇ/TP2 ) vs. 1/T for each reaction via Kissinger method: a – dehydration reaction; b – LiFePO4 formation reaction.

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n, was 4, which indicated that the crystallization of the process was proceed by nuclei being formed randomly and growing in threedimensions [29]. 5. Conclusions By using the thermogravimetry–differential scanning calorimetry (TG–DSC) technology, the non-isothermal kinetics of lithium ion phosphate precursors was studied. The whole synthesis processes could be divided into two stages of dehydration and LiFePO4 formation. The average value of apparent activation energy E and natural logarithmic frequency factor ln A obtained by Ozawa–Flynn–Wall, Kissinger and Coats–Redfern methods for dehydration reaction were 83.4 ± 4.7 kJ mol−1 and 22.1 ± 1.5 s−1 , and that for LiFePO4 formation reaction were 184.2 ± 10.4 kJ mol−1 and 28.3 ± 1.9 s−1 , respectively, corresponding with the actual reaction mechanisms A1.5 and A4 type. Comparing the experimental with simulated conversion data indicated that the proposed rate equations gave reasonably good fit to the raw conversion data. Moreover, the comparison results also demonstrate that the determined kinetic parameters were credible. Acknowledgements This work was supported by Science and Technology Bureau of Changsha City (Grant No. 328 K1205034-11) and Hunan Provincial Innovation Foundation For Postgraduate. References [1] A. Padhi, K. Nanjundaswamy, J.B. Goodenough, Phospho-olivines as positiveelectrode materials for rechargeable lithium batteries, J. Electrochem. Soc. 144 (1997) 1188–1194. [2] M.S. Whittingham, Y. Song, S. Lutta, P.Y. Zavalij, N.A. Chernova, Some transition metal (oxy) phosphates and vanadium oxides for lithium batteries, J. Mater. Chem. 15 (2005) 3362–3379. [3] A. Padhi, K. Nanjundaswamy, C. Masquelier, S. Okada, J.B. Goodenough, Effect of structure on the Fe3+ /Fe2+ redox couple in iron phosphates, J. Electrochem. Soc. 144 (1997) 1609–1613. [4] A. Ritchie, W. Howard, Recent developments and likely advances in lithium-ion batteries, J. Power Sources 162 (2006) 809–812. [5] W. Jiayuan, S. Zechang, W. Xuezhe, Performance and characteristic research in LiFePO4 battery for electric vehicle applications, in: Vehicle Power and Propulsion Conference, 2009, pp. 1657–1661. ´ D. Uskokovic, ´ A review of recent developments in the synthesis [6] D. Jugovic, procedures of lithium iron phosphate powders, J. Power Sources 190 (2009) 538–544. [7] H.H. Chang, C.C. Chang, H.C. Wu, Z.Z. Guo, M.H. Yang, Y.P. Chiang, H.S. Sheu, N.L. Wu, Kinetic study on low-temperature synthesis of LiFePO4 via solid-state reaction, J. Power Sources 158 (2006) 550–556.

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