Nonisothermal Kinetics Study with Isoconversional Procedure and

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Non-isothermal kinetics study with isoconversional procedure and DAEM: LiCoPO4 synthesized from thermal decomposition of the precursor Yu He, Sen Liao, Zhipeng Chen, Yu Li, Yao Xia, Wenwei Wu, and Bin Li Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie302743h • Publication Date (Web): 11 Jan 2013 Downloaded from http://pubs.acs.org on January 13, 2013

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Industrial & Engineering Chemistry Research

Non-isothermal kinetics study with isoconversional procedure and DAEM: LiCoPO4 synthesized from thermal decomposition of the precursor Yu He, Sen Liao*, Zhipeng Chen, Yu Li, Yao Xia, Wenwei Wu, and Bin Li School of Chemistry and Chemical Engineering, Guangxi University, Nanning, Guangxi, 530004, China

Corresponding Author *Tel.: +86 771 3233718. Fax: +86 771 3233718. E-mail: [email protected]; [email protected].

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ABSTRACT: The precursor of LiCoPO4 was synthesized by solid-state reaction at low-heating temperature using LiOH·H2O and NH4CoPO4·H2O as raw materials. LiCoPO4 was obtained by calcining the precursor. Based on isoconversional procedure and the distributed activation energy model (DAEM), the activation energies calculated indicate that the thermal process involves two regions which Region II (α = 0.38～0.90) is a kinetically complex process , but Region I (α = 0.10～0.38) is single-step process. The most probable mechanism for the Region I is two-dimensional diffusion. The distributed activation energy model (DAEM) was applied to study the Region II of decomposition process of the precursor. The distributions of activation energy, f(Ea) and values of pre-exponential factor A of the Region II of the thermal decomposition of precursor were obtained on the basis of DAEM. The reliability of the DAEM for the Region II was tested by the comparison between experimental plots and calculated plots. The results show that the prediction of DAEM is reliable. Keywords LiCoPO4; Synthesis; Non-isothermal kinetics; Solid-state reaction; distributed activation energy mode

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1. INTRODUCTION The successful development and commercialization of LiFePO4 as a cathode for lithium-ion batteries has provoked strong interest on other transition metal phosphates such as LiMnPO4 and LiCoPO4.1-3 Owing to high operating potential close to 4.8V vs. Li/Li+ and relatively high theoretical specific capacity (167 mAhg−1),4 LiCoPO4 is regarded as a promising 5V electrode material for high power batteries. So, recently, various methods have been developed to synthesize LiCoPO4 compounds, including solid-state reaction,5-9 hydrothermal synthesis (or Solvothermal synthesis),10-13 sol-gel method,14-18 co-precipitation,19 optical floating zone method,20 radio frequency magnetron sputtering,21 electrostatic spray deposition technique,22 spray pyrolysis method,23, 24 rheological phase method25 and microwave heating method.26 Different raw materials and synthesis methods will result in different electrochemical properties of LiCoPO4 associated with the crystallization temperature, crystallite size, and morphology. Therefore, new synthesis methods for LiCoPO4 still need to be studied and innovated further. Kinetic analysis is a modern technique widely used to study the thermal decomposition process of substances. The technique has received considerable attention all along the modern history of thermal decomposition study.27-31 For example, recently, kinetic analysis of thermal decomposition process has been applied in the determination of the activation energy for different thermal decomposition reaction.28-31 Kinetic analysis can have either a practical or theoretical application. A major practical

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application is the prediction of process rates and material lifetimes. Hence, different methods such as isoconversional procedure32-34 and distributed activation energy model (DAEM)35-37 have been employed to study the kinetics of the thermal decomposition process of substances. For this reason, kinetic analysis is very essential and useful for the preparation and application of various materials. In this study, olivine-type LiCoPO4 was synthesized after thermal decomposition of the precursor that prepared by a novel synthetic technique. Kinetic data were collected using simultaneous TG/DTG technique. Non-isothermal kinetics of the decomposition process was analyzed using isoconversional procedure32-34 and DAEM.35-37 The values of Ea were obtained from both isoconversional procedure and DAEM. The pre-exponential factor A and distributions of activation energy f(Ea) were calculated using DAEM. Utilizing the f(Ea) and A obtained by DAEM, the calculated TG curve was obtained and discussed.

2. EXPERIMENTAL 2.1. Reagent and Apparatus. All chemicals were of reagent grade purity. X-ray powder diffraction (XRD) was performed at a scanning rate of 5°/min from 5° to 70° for 2θ at room temperature using a Rigaku D/max 2500 V diffractometer equipped with a graphite monochromator utilizing monochromatic CuKα radiation (λ = 0.154178 nm). TG/DTG measurements were made using a NETZSCH STA 409 PC/PG thermogravimetric analyzer. High purity nitrogen gas (99.999 %) was used as protective

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atmosphere, flowing at 20 mL min-1. Samples of 6 ± 0.1 mg mass were used for the experiments varied out at heating rates of 5, 8, 11, 15 K min-1 up to 1000 K. The samples were loaded without pressing into a platinum crucible. Fourier transform-infrared (FT-IR) spectra of the precursor and its calcined products were recorded on a Nexus 470 FT-IR spectrometer in the wavenumbers range of 4000-400 cm-1 for samples made in KBr pellet form. The results of isoconversional procedure and DAEM presented in the paper were obtained using the programs compiled by ourselves. 2.2. Preparation of LiCoPO4. The precursor of LiCoPO4 was synthesized by solid-state reaction at low-heating temperature. This preparation technique has been developed in recent decades and it is of simplicity, low cost, high output and little pollution.34, 38-42 NH4CoPO4·H2O was prepared with the reported method.40 In a typical synthesis, NH4CoPO4·H2O (70 mmol, 13.30 g) and LiOH·H2O (73.5 mmol, 3.08 g) were put in a mortar, fully ground for 30 min and dried at 373 K for 3 h to form the precursor. LiCoPO4 was obtained after calcining the precursor.

3. THEORETICAL 3.1. Isoconversional Procedure. In thermogravimetric analysis, the extent of conversion may be defined as the ratio of actual mass loss to the total mass loss corresponding to the investigated process:



mo  m mo  m f

(1)

where m, m0 and mf are the actual, initial and final masses of the sample, respectively.

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According to non-isothermal kinetic theory, thermal decomposition kinetic equation27 of solid-state material is: d A  E   exp   a  f ( ) dT   RT 

(2)

where α is the degree of conversion, β is the heating rate (K min-1), Ea is the apparent activation energy (kJ mol-1), A is the pre-exponential factor, R is the gas constant (8.314 × 10-3 kJ mol-1 K-1). From eq 1 Starink equation32 and Tang equation33 are deduced by a series of transforms: Tang equation: ln

 T

1.894661

Starink equation: ln

 T

1.92

 ln[

AE E ]  3.635041  1.894661ln E  1.001450 a Rg ( ) RT

 C  1.0008

(3)

Ea RT

(4)

The activation energy Ea can be estimated with above isoconversional procedure equations. The isoconversional procedure performed involved the following steps: (i) Measure α vs T relationships at three different heating rates at least. (ii) Calculate the values of (β/T1.894661) or (β/T1.92) at the selected α values from α vs T relationships obtained from different heating rates. (iii) Plot ln(β/T1.894661) vs 1/T or plot ln(β/T1.92) vs 1/T at the selected α values, and determine the Ea values from the slope of the Arrhenius plots at different α values using the relationship in eq 3 or 4. These plots are model independent since the estimation of the apparent activation energy does not require selection of particular kinetic model (type of g(α) function). Therefore, the activation energy values obtained by this method are usually regarded as more reliable than these

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obtained by a single TG curve. The following equation is used to estimate the most correct reaction mechanism, i.e. g(α) function: 43-49

 AEa  e x ln g ( )  ln  ln 2  ln h( x)   ln  R x  

(5)

The degrees of conversion α corresponding to multiple rates at the same temperature are put into the left side of eq 5, combined with thirty-one types of mechanism functions,43-49 the slope km of the straight line and the linear correlation coefficient r are obtained from the plot of ln[g(α)] vs ln β. The probable mechanism function is the one for which the value of the slope km is near to -1.00000 and the correlation coefficient r is better. If several g(α) functions meet this requirement, the degrees of conversion corresponding to multiple heating rates at several temperatures are applied to calculate the probable mechanism by the same method. The function, whose km value is the closest to -1.00000 and the correlation coefficient r is high too at all these temperatures, is considered to be the most probable mechanism function. The pre-exponential factor A can be estimated from the intercept of the plots of eq 3 by inserting the g(α) function determined to be the most probable. 3.2. Distributed Activation Energy Model. The distributed activation energy model (DAEM) has been proved very successful in kinetic analysis of complex material.35-37 The model assumes that many irreversible first-order parallel reactions that have different rate parameters occur simultaneously. The distributed activation energy model is represented as follows when it is applied to represent the change in total volatiles:

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

T

0

0

A 1     exp(  e Ea /( RT ) dT ) f ( Ea )dEa

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(6)



where α is the total conversion of decomposition reaction at temperature T, f(Ea) is the distribution curve of the activation energy to represent the differences in the activation energies of many first-order irreversible reactions, β is the linear heating rate of the decomposition reaction, and A is the pre-exponential factor. A new method was presented by Miura37 for estimating f(Ea) and A in the distributed activation energy model. With this new method, f(Ea) and A can be estimated accurately. The equation is expressed as follows: ln(β/T2) = ln(AR/Ea) + 0.6075 - (Ea /R) × (1/T)

(7)

The procedure to estimate f(Ea) and A using this method is as follows (The results presented in the paper were calculated by the programs compiled by ourselves): (i) Measure α vs T relationships at three different heating rates at least. (ii) Calculate the values of (β/T2) at the selected α values from α vs T relationships obtained from different heating rates. (iii) Plot ln(β/T2) vs 1/T at the selected α values, and determine the Ea and A values from the Arrhenius plots at different α values using the relationship in eq 6. Both the Ea and A values corresponding to α values can be obtained from the slope and the intercept in each Arrhenius plot. (iv) Plot the α values against the activation energies, Ea, obtained above, and differentiate the α vs Ea relationships to obtain f(Ea).

4. RESULTS AND DISCUSSION

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4.1. Characterization Results. Figure 1 shows the XRD patterns of the precursor dried at 373 K for 3 h and the products resulted from calcination at different temperature for 2 h. The results of Figure 1a, show that the precursor keeping at 373 K for 3 h is a mixture containing NH4CoPO4·H2O, LiOH·H2O, Co(OH)2, Li3PO4 and LiCoPO4. It suggests that the raw materials only partly react. Figure 1b shows that the products calcined at 673 and 973 K are crystals, but the product calcined at 473 K is an amorphous product. However, Figure 1b also shows that the diffraction peaks of Li3PO4 is still observed in XRD pattern of the product calcined at 673 K. Then, all the peaks of Li3PO4 are disappeared after calcination at 973 K for 2 h. All diffraction peaks in the pattern of product calcined at 973 K could be indexed to obtain lattice parameters: a = 1.021287(1) nm, b = 0.591902(1) nm, c = 0.470223(1) nm, α = β = γ = 90° that are in agreement with that of orthorhombic LiCoPO4, with space group Pnma (62) and lattice parameter a = 1.02001 nm, b = 0.59199 nm, c = 0.46899 nm, α = β = γ = 90°, Density = 3.772 g cm-3, from PDF card 85-0002. Figure 2 shows the TG curves of the precursor at four different heating rates, respectively, which the thermal decomposition of the precursor below 760 K only occurs in one main stage. So, it suggests there is no obvious step between dehydration and deamination for the decomposition reaction. It can be seen from the Figure 2 that the mass loss starts at about 320 K, ends at about 740 K. The observed mass loss in the TG curve (β = 11 K min-1) is 19.01 %. But, the theoretic mass loss is 30.6 % for the formation of LiCoPO4 with NH4CoPO4·H2O and LiOH·H2O as raw materials. The

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result of TG curves also indicates that have partly reacted to release some NH3 and H2O at 373 K, which is supported by the XRD results of the precursor. So, the obtained mass loss of 19.01% is not close with the theoretic mass loss of 30.6 %. The FT-IR spectra of the precursor and calcined product are shown in Figure 3. From the spectra of the precursor, the strong bands at 1070 and 939 cm-1 are attributed to the P–O stretching vibration. The bending OPO vibration appears in the region of 650–530 cm-1. The weak band at about 782 cm-1 is the water libration (hindered rotation), while the broad band between 3500-2700 cm-1 is assigned to the stretching OH vibration of the water molecule50-52 and the stretching vibration of NH4+. The bands at 1520-1360 cm-1 can be the bending mode of NH4+, and the band at about 1645 cm-1 is assigned to the bending mode of HOH. From the spectra of calcined product, the bands at 3280-2700, 1520-1360 and 782 cm-1 had disappeared, which suggests the product have experienced processes of dehydration and deammoniation after calcination at 973 K. The bands at 1070 and 939 cm-1 are split into three bands at 1150, 1080 and 977 cm-1, and the bands at 650–530 cm-1 are split into several bands, which indicates the structure of the calcined products takes place transform. The results from XRD, TG and FT-IR of the precursor and its calcined products suggest that the total reaction for formation of LiCoPO4 can be suggested as following: NH4CoPO4·H2O + LiOH·H2O → LiCoPO4 + 3H2O + NH3 4.2. Results of Thermal Decomposition Kinetics. 4.2.1. Isoconversional Procedure

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(8)

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4.2.1.1. Calculation of Activation Energy Ea by Isoconversional Procedure. According to eqs 3 and 4, the isoconversional procedure of Starink and Tang equation were used. The Ea values of thermal decomposition of the precursor corresponding to different degrees of conversion α are shown in Figure 4 and Table 1 (interval of degrees of conversion, Δα, is 0.02). As shown in Figure 4, it can be discovered that the curves of the Starink and Tang method almost overlapped together. After carefully study, Starink32 indicated the difference in the Ea values between Starink and other isoconversional procedure methods was only due to the difference in the accuracy of the approximation to the T-integral. From eqs 3 and 4, it is not difficult to find that the difference of the approximation to the T-integral between Starink (ln(β/T1.92)) and Tang (ln(β/T1.894661)) procedure methods is very small. So, both theoretical and experimental results all indicate that the results obtained from Starink and Tang method are very close to each other. If Ea values are independent of α, the decomposition process is dominated by a single reaction step,52 on the contrary, a significant variation of Ea with α should be interpreted in terms of multi-step mechanism.53, 54 If Ea values are roughly constant, it is likely that a process is dominated by a single reaction step and can be adequately described by a single-step model.27 From Figure 4 and Table 1, it can be seen that the α-Eα curve has two regions: (I) Region I, α = 0.10～0.38 that the Ea values are roughly constant (the relative error is 18.9 %); (II) Region II, α = 0.38～0.90 that the Ea values are significant variation with

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α (the relative error is 60.9 %). So, from Figure 4 and Table 1, it is obvious that thermal decomposition of Region II (α = 0.38～0.90) is a kinetically complex process and cannot be considered as a single reaction step; however, Region I (α = 0.10～0.38) could be considered as single-step process and can be described by a unique kinetic triplet [Eα, g(α) and A]. The average Ea values of the Region I that calculated with Starink and Tang equation were determined to be 90.67 and 90.70 kJ mol-1, respectively. 4.2.1.2. Determination of the Most Probable Reaction Mechanism Function for Region I. eq 5 is used to find the most probable reaction mechanism. The degrees of conversion for β = 5, 8, 11 and 15 K min-1 at the same temperature are illustrated in Table 2. The appropriate temperatures are randomly selected, the range of the degrees of conversion corresponding to the temperature should be within 0.10～0.38. The corresponding degrees of conversion of four temperatures are chosen as examples to put into thirty-one types of mechanism functions.43-49 The slope km, correlation coefficient r and intercept B of linear regression of ln[g(α)] vs lnβ are obtained. The results of the linear regression show that the slopes of No. 28 ( g(α) = [-ln(1-α)]3 ) and No. 29 ( g(α) =[-ln(1-α)]4 ) mechanism functions are the most adjacent to -1.00000 and the correlation coefficients r are better, which are shown in Table 2. Therefore, No. 29 ( g(α) = [-ln(1-α)]4 ), which belongs to two-dimensional diffusion, is determined to be the most probable mechanism function of the Region I. The mechanism of two-dimensional diffusion is physical process. The results indicates the total process of the Region I is controlled by physical process, though the decomposition process of the Region I

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includes chemical reactions. 4.2.1.3. Calculation of Pre-exponential Factor A. The pre-exponential factor A for the Region I is estimated from the intercept of the plots of eq 3 (the intercept, B, is shown in Table 1), inserting the determined most probable g(α) function (No. 29). The pre-exponential factor A for the Region I is shown in Figure 5. The results show that the range of pre-exponential factor A is 1.13×106～7.01×1010 min-1 and average value of A is 9.17×109 min-1. From Figure 5, a functional dependence between lnA (A / min-1) and Ea of the Region I can be obtained as following empirical equation: lnA = -9.8647+0.32628 Ea According to the some authors49,

(9) 55-59

the so-called kinetic compensation effect,

isokinetic effect, or θ-rule may be described with the equation: ln A = ln kiso + E/(RTiso)

(10)

On the basis of eqs 9 and 10 the values of kiso and Tiso may be calculate. In the case of the Region I, they are 5.198×10-5 min-1 and 369 K, respectively. This temperature is very near the beginning temperature (373 K for 5 K min-1) of the thermal decomposition of the Region I, and it is roughly in the range between the temperature of the beginning and the temperature of the end of the thermal decomposition of the Region I. Therefore, it is concluded that kiso of a single-step process reaction is in the temperature interval of thermal decomposition. 4.2.2. Study Thermal Decomposition Kinetics using the Distributed Activation Energy Model (DAEM). As mentioned above, the thermal decomposition of the Region II is a

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kinetically complex process that controls by both chemical and physical processes, and can not be considered as a single reaction step. So, the distributed activation energy model (DAEM) is applied to study its thermal decomposition kinetics. According to eq 7, a new simple method was used. The Ea and A values of thermal decomposition of the precursor corresponding to different degrees of conversion α are obtained simultaneously. The Ea values of DAEM are also shown in Figure 4 (Δα = 0.02). As shown in Figure 4, that the Ea values of DAEM are only slight smaller than those of the Starink and Tang equation at corresponding degrees of conversion α. The variation of the pre-exponential factor with activation energy is given in Figure 5. From Figure 5, a functional dependence between lnA (A / min-1) and Ea at range of the Region II can be obtained as following empirical equation: lnA =3.04928+0.1614Ea

(11)

On the basis of eqs 10 and 11 the values of kiso and Tiso may be calculate. For the Region II, they are 21.10 min-1 and 745 K, respectively. This temperature is much higher than the end temperature (599 K for 15 K min-1) of the thermal decomposition of the Region II, and it is not in the range between the temperature of the beginning and the temperature of the end of the thermal decomposition of the Region II. The results also indicate that kiso of a complex process reaction is far away from the temperature interval of thermal decomposition. The distribution of activation energy of the Region II is shown in Figure 6. Utilizing the f(Ea) and A obtained by DAEM, a calculated TG curve of the Region II could be

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obtained as shown in Figure 7 without any mathematical fitting technique. From Figure 7, it can be found that the model predicted plots agree with the experimental plots, indicating that the DAEM prediction for thermal decomposition of the Region II of the LiCoPO4 precursor is reliable.

5. CONCLUSIONS This work has successfully achieved a simple synthesis of olivine-type LiCoPO4 from thermal decomposition of the precursor that is prepared using the novel solid-state reaction. The non-isothermal kinetics for the thermal decomposition process of the precursor is studied with isoconversional procedure and DAEM. The activation energies calculated indicate that the thermal process involves two regions which Region II (α = 0.38～0.90) is a kinetically complex process , but Region I (α = 0.10～0.38) is single-step process. The most probable mechanism for the Region I is two-dimensional diffusion. The distributed activation energy model (DAEM) was applied to study the Region II of decomposition process of the precursor.

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ACKNOWLEDGEMENTS This study was financially supported by the Key laboratory of new processing technology for nonferrous metals and materials, Ministry of Education, Guangxi University (No. GXKFZ-02); the Guangxi Natural Scientific Foundation of China (Grant No. 2012GXNSFAA053019 and No. 0991108); and the Guangxi Science and Technology Agency Research Item of China (Grant No. 0895002–9).

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321. (9) Wolfenstine, J.; Read, J.; Allen, J. L. Effect of carbon on the electronic conductivity and discharge capacity LiCoPO4. J. Power Sources 2007, 163, 1070. (10) Huang, X.; Ma, J. F.; Wu, P. W.; Hu, Y. M.; Dai, J.H.; Zhu, Z. B.; Chen, H.Y.; Wang, H. F. Hydrothermal synthesis of LiCoPO4 cathode materials for rechargeable lithium ion batteries. Mater. Lett. 2005, 59, 578. (11) Chen, J. J.; Wang, S. J.; Whittingham, M.S. Hydrothermal synthesis of cathode materials. J. Power Sources 2007, 174, 442. (12) Zhao, Y. J.; Wang, S. J.; Zhao, C. S.; Xia, D. G. Synthesis and electrochemical performance of LiCoPO4 micron-rods by dispersant-aided hydrothermal method for lithium ion batteries. Rare Met. 2009, 28, 117. (13) Wang, F.; Yang, J.; NuLi, Y. N.; Wang, J. L. Novel hedgehog-like 5V LiCoPO4 positive electrode material for rechargeable lithium battery. J. Power Sources 2011, 196, 4806. (14) Bhuwaneswari, M. S.; Dimesso, L.; Jaegermann, W. Preparation of LiCoPO4 powders and films via sol–gel. J. Sol-gel Sci. Technol. 2010, 56, 320. (15) Wu, X. B.; Gong, Z. L.; Tan, S.; Yang, Y. Sol-gel synthesis of Li2CoPO4F/C nanocomposite as a high power cathode material for lithium ion batteries. J. Power Sources 2012, 220, 122. (16) Poovizhi, P. N.; Selladurai, S. Study of pristine and carbon-coated LiCoPO4 olivine material synthesized by modified sol-gel method. Ionics 2011, 17, 13.

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(17) Dimesso, L.; Cherkashinin, G.; Spanheimer, C.; Jaegermann, W. Preparation and characterization of carbon foams-LiCoPO4 composites. J. Alloys Compd. 2012, 516, 119. (18) Kim, E. J.; Xu, H. Y.; Lim, J. S.; Kang, J. W.; Gim, J. H.; Mathew, V.; Kim, J. Impact of glucose on the electrochemical performance of nano-LiCoPO4 cathode for Li-ion batteries. J. Solid State Electrochem. 2012, 16, 149. (19) Sahnmukaraj, D.; Murugan, R. Synthesis and Characterization of LiNiyCo1-yPO4 (y=0-1) Cathode Materials for Lithium Secondary Batteries. Ionics 2004, 10, 88. (20) Saint-Martin, R.; Franger, S. Growth of LiCoPO4 single crystals using an optical floating-zone technique. J. Cryst. Growth 2008, 310, 861. (21) Xie, J.; Imanishi, N.; Zhang, T.; Hirano, A.; Takeda, Y.; Yamamoto, O. Li-ion diffusion kinetics in LiCoPO4 thin films deposited on NASICON-type glass ceramic electrolytes by magnetron sputtering. J. Power Sources 2009, 192, 689. (22) Shui, J. L.; Yu, Y.; Yang, X. F.; Chen, C. H. LiCoPO4-based ternary composite thin-film electrode for lithium secondary battery. Electrochem. Commun. 2006, 8, 1087. (23) Doan, T. N. L.; Taniguchi, I. Preparation of LiCoPO4/C nanocomposite cathode of lithium batteries with high rate performance. J. Power Sources 2011, 196, 5679. (24) Taniguchi, I.; Doan, T. N. L.; Shao, B. Synthesis and electrochemical characterization of LiCoxMn1-xPO4/C nanocomposites. Electrochim. Acta 2011, 56, 7680. (25) Tan, L.; Luo, Z. M.; Liu, H. W.; Yu, Y. Synthesis of novel high-voltage cathode

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Arrhenius temperature integral. Thermochimica Acta 2003, 408, 39. (34) Chen, Z. P.; Chai Q.; Liao, S.; Chen, X.; He, Y.; Li, Y.; Wu, W. W.; Li, B. Nonisothermal Kinetic Study: IV. Comparative Methods To Evaluate Ea for Thermal Decomposition of KZn2(PO4)(HPO4) Synthesized by a Simple Route. Ind. Eng. Chem. Res. 2012, 51, 8985. (35) Várhegyi, G.; Czégény, Z.;Liu, C.; McAdam, K. Thermogravimetric analysis of tobacco combustion assuming DAEM devolatilization and empirical char-burnoff kinetics. Ind. Eng. Chem. Res. 2010, 49, 1591. (36) Burnham A. K.; Braun R. L. Global kinetic analysis of complex materials. Energy Fuels 1999, 13, 1. (37) Miura K.; Maki T. A Simple Method for Estimating f(E) and k0(E)in the Distributed Activation Energy Model. Energy Fuels 1998, 12, 864. (38) Chen Z. P.; Chai Q.; Liao S.; He Y.; Wu W. W.; Li B. Preparation of LiZnPO4·H2O via a novel modified method and its non-isothermal kinetics and thermodynamics of thermal decomposition. J. Therm. Anal. Calorim. 2012, 108, 1235. (39) Liu C.; Wu X. H.; Wu W. W.; Cai J. C.; Liao S. Preparation of nanocrystalline LiMnPO4 via a simple and novel method and its isothermal kinetics of crystallization. J Mater Sci. 2011, 46, 2474. (40) Chen, Z. P.; Chai, Q.; Liao, S.; He, Y.; Li, Y.; Bo, X. H.; Wu, W. W.; Li, B. Application of isoconversional

calculation

procedure to

non-isothermal

kinetic study: III. Thermal decomposition of ammonium cobalt phosphate hydrate.

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Thermochimica Acta 2012, 543, 205. (41) Chai, Q.; Chen, Z. P.; Liao, S.; He, Y.; Li, Y.; Wu, W. W.; Li, B. Preparation of LiZn0.9PO4:Mn0.1·H2O via a simple and novel method and its non-isothermal kinetics using iso-conversional calculation procedure. Thermochimica Acta 2012, 533, 74. (42) He, Y.; Liao, S.; Chen, Z. P.; Chai, Q.; Li, Y.; Su, Y. Y.; Wu, W. W.; Li, B. Application of isoconversional calculation procedure to non-isothermal kinetics study: II. thermal decomposition of NH4CuPO4·H2O. J. Therm. Anal. Calorim. DOI 10.1007/s10973-012-2306-6. (43) Liqing, L.; Donghua, C. Application of iso-themperature method of multiple rates to kinetic analysis. Dehydration for calcium oxalate monohydrate. J. Therm. Anal. Calorim. 2004, 78, 283. (44) Budrugeac, P.; Segal, E. Some methodological problems concerning nonisothermal kinetic analysis of heterogeneous solid-gas reactions. Int. J. Chem. Kinetics. 2001, 33, 564. (45) Gao, Z.; Amasaki, I.; Nakada, M. A description of kinetics of thermal decomposition of calcium oxalate monochydrate by means of the accommodated Rn model. Thermochim. Acta 2002, 385, 95. (46) Su, T.-T.; Jiang, H.; Gong, H. Thermal stabilities and the thermal degradation kinetics of poly(ε-caprolactone). Polym. Plast. Technol. Eng. 2008, 47, 398. (47) Vlaev, L.; Nedelchev, N.; Gyurova, K.; Zagorcheva, M. A comparative study of non-isothermal kinetics of decomposition of calcium oxalate monohydrate. J. Anal.

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(56) Atanassov, A.; Genieve, S.; Vlaeve, L. Study on the thermooxidative degradation kinetics of tetrafluoroethylene-ethylene copolymer filled with rice husks ash. Polym. Plast. Technol. Eng. 2010, 49,541. (57) Gorbachev, V. M. The compensation effect in the kinetics of the thermal decomposition of calcium carbonate. J. Therm. Anal. 1976, 9, 121. (58) Ray, H. S. The kinectic compensation effect in the decomposition of calcium carbonate. J. Therm. Anal. 1982, 24, 35. (59) Turmanova, S. C.; Genieva, S. D.; Dimitrova, A. S.; Vlaeve, L. T. Non-isothermal degradation kinectics of filled with rise husk ash polypropene composites. Express Polym. Lett. 2008, 2, 133.

Figure captions Figure 1. XRD patterns of the precursor and its calcined products at different temperature Figure 2. TG curves of the precursor at different heating rates Figure 3. FT-IR spectra of the precursor (a) and the product calcined at 973 K (b) Figure 4. Dependence of Ea on α for the thermal decomposition of the precursor. Figure 5. Dependence of lnA (A / min-1) on Ea the thermal decomposition of the

24


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precursor Figure 6. f(Ea) curve for the Region II of the thermal decomposition of the precursor. Figure 7. Comparison model result (symbol) with the experimental data (solid line) for the Region II of the thermal decomposition of the precursor (β =11 K min-1)

25



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Page 26 of 34

Table 1. Dependence of Eα (kJ mol-1), B (the intercept) and lnA(A/ min-1) on α for the thermal decomposition of the precursor α Eα1a Eα2b Eα3c Ba Bb lnAc 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 a

74.52 76.61 78.81 81.07 83.38 85.72 88.07 90.45 92.85 95.28 97.73 100.21 102.72 105.27 107.87 110.51 113.21 115.98 118.81 121.73 124.73 127.84 131.06 134.40 137.89 141.54 145.37 149.41 153.70 158.25 163.12 168.37 174.06 180.27 187.13 194.77 203.39 213.29 224.87 238.74 255.91

74.49 76.58 78.78 81.04 83.35 85.68 88.04 90.42 92.82 95.25 97.70 100.18 102.69 105.24 107.84 110.49 113.19 115.95 118.79 121.71 124.71 127.82 131.04 134.39 137.88 141.53 145.36 149.40 153.69 158.24 163.12 168.37 174.06 180.28 187.13 194.78 203.41 213.31 224.90 238.77 255.95

74.29 76.38 78.58 80.84 83.14 85.48 87.83 90.21 92.61 95.04 97.48 99.96 102.48 105.03 107.62 110.27 112.97 115.74 118.57 121.49 124.50 127.60 130.82 134.17 137.66 141.31 145.14 149.19 153.47 158.02 162.90 168.15 173.84 180.06 186.92 194.57 203.20 213.11 224.69 238.58 255.76

a

14.41 14.57 14.80 15.06 15.36 15.68 16.02 16.37 16.73 17.10 17.48 17.87 18.26 18.66 19.07 19.50 19.93 20.37 20.82 21.28 21.76 22.26 22.77 23.31 23.86 24.44 25.05 25.69 26.36 27.08 27.84 28.66 29.55 30.52 31.58 32.75 34.08 35.59 37.35 39.45 42.03 b

14.24 14.40 14.62 14.89 15.19 15.51 15.84 16.19 16.55 16.92 17.30 17.69 18.08 18.48 18.89 19.31 19.74 20.18 20.64 21.10 21.58 22.08 22.59 23.12 23.68 24.26 24.86 25.50 26.18 26.89 27.66 28.48 29.36 30.33 31.39 32.57 33.89 35.41 37.17 39.27 41.84

15.2656 15.4482 15.6992 15.9948 16.3204 16.6676 17.0306 17.4058 17.7916 18.1858 18.5884 18.9986 19.4168 19.8429 20.2775 20.7214 21.1749 21.6389 22.1149 22.6037 23.1073 23.6263 24.1639 24.7210 25.3000 25.9051 26.5378 27.2032 27.9057 28.6503 29.4444 30.2959 31.2151 32.2150 33.3128 34.5301 35.8975 37.4570 39.2695 41.4251 44.0714

Eα1, B is the result of Tang method, bEα2, B is the result of Starink method, c

c

Eα2 and lnA is the result of DEAM method

26


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. The relation of temperature and conversion α at different heating rates β (K min-1) and lng(α) vs. lnβ curves of two types of probable mechanism functions for the Region I T/K 445

α β=5

β=8

β = 11

β = 15

Function No.

0.36844

0.33263

0.31517

0.29070

28

-1.07795

0.779605

0.997912

29

-1.43726

1.039472

0.997912

28

-1.03704

0.774671

0.997921

29 28 29 28 29

-1.38271 -0.99604 -1.32805 -0.95562 -1.27416

1.032895 0.769892 1.026523 0.764995 1.019994

0.997921 0.997935 0.997935 0.997953 0.997953

446

0.37318

0.33728

0.31973

0.29514

447

0.37795

0.34195

0.32431

0.29961

448

0.38272

0.34664

0.32891

0.30411

B

-k

R2

27



Figures



-NH4CoPO4 H2O 

o-Li3PO4



-Co(OH)

-LiCoPO4

2

-LiOH H2O







Intensity / a. u.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 34



 o

o





o 

 

20



 



 

373 K



473 K





10

o







673 K





973 K

 



30



  



40

50

2/

   

o

Fig. 1

28


60

70

Page 29 of 34

100 95 TG / %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-1

5 K min -1 8 K min -1 11 K min -1 15 K min

90 85 80 300

400

500

600

Temperature / K

Fig. 2

29


700


450 400

Transmittance / %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 34

350

(b) product

300 250

(a) precursor

200 150 100 50 0 4000

3500

3000

2500

2000

1500 -1

Wavenumbers / cm

Fig. 3

30


1000

500

Page 31 of 34

600 108

500 -1

300

TANG STARINK DAEM

106 Ea / kJ mol

-1

400 E / kJ mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


104 102 100 98 96 0.30

200

0.32

0.34

0.36

0.38



100 0 0.0

0.2

0.4

0.6

0.8



Fig. 4

31


1.0


45

ln A (A / min -1 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

40

Region I Region II

35 30 25 20 15 80 100 120 140 160 180 200 220 240 260 EkJ mol

-1

Fig. 5

32


Page 32 of 34

Page 33 of 34

0.008 0.007 0.006 f(E)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.005 0.004 0.003 0.002 0.001 0.000 100

150

200

250

300

E / kJ mol

350

-1

Fig. 6

33


400

450


94 92 90 TG / %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 34

11 K min

-1

88 86 84 82 80 450

500

550

600

650

700

Temperature / K

Fig. 7

34


750

800

Nonisothermal Kinetics Study with Isoconversional Procedure and

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