Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process

Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process

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Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process Cheng-Li Wang a, Weng-Sing Hwang a,b, Hsueh-Liang Chu a, Huey-Jiuan Lin c, Horng-Huey Ko d,n, Moo-Chin Wang d,n a

Department of Materials Science and Engineering, National Cheng Kung University, 1 Ta-Hsueh Road, Tainan 70101, Taiwan Institute of Nanotechnology and Microsystems Engineering, National Cheng Kung University, 1 Ta-Hsueh Road, Tainan 70101, Taiwan c Department of Materials Science and Engineering, National United University, 1 Lien-Da, Kuan-Ching Li, Miao-Li 36003, Taiwan d Department of Fragrance and Cosmetic Science, Kaohsiung Medical University,100 Shih-Chuan 1st Road, Kaohsiung 80708, Taiwan b

art ic l e i nf o

a b s t r a c t

Article history: Received 11 April 2016 Received in revised form 11 May 2016 Accepted 16 May 2016

Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process have been studied using differential thermal analysis (DTA), X-ray diffraction, transmission electron microscopy (TEM), selected area electron diffraction (SAED), nano beam electron diffraction (NBED) and high resolution TEM (HRTEM). The DTA result shows residual organic matter decomposed at 436 K. The transition temperature for amorphous precursor powders converted to anatase TiO2 occurred at 739 K. Moreover, the full anatase transition to rutile TiO2 occurred at 1001 K. The activation energy of anatase TiO2 formation was 128.9 kJ/mol. On the other hand, the activation energy of anatase transition to rutile TiO2 was 328.4 kJ/mol. Mesoporous structures can be observed in the TEM image. & 2016 Published by Elsevier Ltd.

Keywords: Anatase TiO2 Rutile TiO2 Transition Activation energy

1. Introduction The wavelength of ultraviolet radiation (UV) that reaches the earth and damages skin can be divided into three regions of 200– 280 nm (UVC), 280–320 nm (UVB) and 320–400 nm (UVA). A major culprit of photoaging and skin cancers can be UVA radiation [1]. On the other hand, the skin is also susceptible to acute photodamage such as sunburn and some non-melanoma skin cancers when the top-most layer of skin suffers from UVB radiation [1]. Therefore, protection against harmful UVA and UVB radiations becomes very important. In order to protect against the adverse effects of UVA and UVB radiation, some minerals and metal oxides can be used as sunscreen or sun-attenuating agents. As mentioned above, among these materials, an important material frequently used as an inorganic physical sun-attenuating or sun-blocker is titanium dioxide (TiO2) due to its increased effectiveness in the UVB region [2]. TiO2 in nature has three different crystal structures: the orthorhombic phase of brookite, and the tetragonal phases of anatase and rutile [3]. However, when the micron-sized TiO2 powders used as a UV-attenuation agent are applied to the skin surface, sometimes they create an opaque layer n

Corresponding authors. E-mail addresses: [email protected] (H.-H. Ko), [email protected] (M.-C. Wang).

on the skin. In order to solve the cosmetic drawback of TiO2 causing this opaque layer and to enhance the transparency and increase the effect of attenuating UV radiation with a low content of TiO2 particles, nanosized TiO2 particles must be used instead of micron-sized particles [4–6]. On the other hand, when the TiO2 particles are used as a sunscreen agent for cosmetic application, they must possess high purity with controlled size, excellent surface properties, definite phase content and suitable morphology. The UV protection effect of TiO2 is dependent on the crystalline structure, also reported by Lee et al. [7]. Therefore, for the TiO2 particles used for cosmetic application, the various phase contents and crystallite size become very significant. In recent years, synthesized TiO2 powders with control over the crystalline phase, crystallite size, morphology and surface area have been used in various synthesized methods, such as sol-gel [8,9], hydrolysis [10,11], coprecipitation [5,6,12,13] and hydrothermal process [14,15], etc. Moreover, Liu et al. [15] have pointed out that the activation energy of anatase TiO2 nanocrystalline growth was 39 kJ/mol when the titanium dioxide precursor powders prepared were by a microemulsion-modified reaction of TiCl4. The activation energy of anatase TiO2 nanocrystallines was 32 kJ/mol for high purity anatase TiO2 nanocrystals prepared by a sol-gel process, also reported by Lu et al. [13]. The activation energies of anatase and rutile TiO2

http://dx.doi.org/10.1016/j.ceramint.2016.05.101 0272-8842/& 2016 Published by Elsevier Ltd.

Please cite this article as: C.-L. Wang, et al., Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process, Ceramics International (2016), http://dx.doi.org/10.1016/j.ceramint.2016.05.101i

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nanocrystalline growth were 21.5 and 32.5 kJ/mol respectively for titanium dioxide precursor powders synthesized by a coprecipitation route [5]. In addition, the activation energy of phase transition from anatase TiO2 to rutile TiO2 was 147 kJ/mol for titanium dioxide membranes prepared by the sol-gel process [16,17]. The aging effect on the activation energies of crystalline growth and the phase transition of titanium dioxide of nanocrystalline have been reported by Hsiang et al. [18,19]. They pointed out that the activation energy of anatase TiO2 nanocrystalline growth with aging between 873 and 923 K for 12 h was 250 kJ/mol, which was greater than the 53 kJ/mol for the sample without the aging treatment [18]. On the other hand, the activation energy of phase transition from anatase TiO2 to rutile TiO2 for the sample with aging between 1073 and 1123 K for 12 h was 506 kJ/mol, which was greater than that without the aging treatment of 205 kJ/mol [19]. The thermal behavior and phase transformation of titanium dioxide nanocrystallines prepared by a coprecipitation process have been reported by Yeh et al. [12]. They also reveal that the activation energy of phase transition from anatase TiO2 to rutile TiO2 was 267.5 kJ/mol. However, the kinetic of anatase TiO2 transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process have not been discussed in detail. In the present study, the titanium dioxide precursor has been successfully synthesized by a sol-gel process using TiCl4 as the initial material. The precursor powders were characterized using differential thermal analysis (DTA), X-ray diffraction (XRD), transmission electron microscopy (TEM), selected area electron diffraction (SAED), nano beam electron diffraction (NBED) and high resolution TEM (HRTEM). The purposes of this work were: (i) to study the thermal behavior of the titanium dioxide precursor powders; (ii) to evaluate the phase development of titanium dioxide precursor powders after being calcined at various temperature for different times; (iii) to identify the activation energy from anatase TiO2 transition to rutile TiO2 of titanium dioxide precursor powders after calcination; and (iv) to examine the microstructures of anatase TiO2 and rutile TiO2 nanocrystallines.

2. Experimental procedure 2.1. Sample preparation The titanium dioxide precursor powders were synthesized using a sol-gel process. The initial materials were reagent-grade titanium tetraisopropoxide (TTIP, purity Z97.0%, supplied by Aldrich, Germany), and absolute ethanol (purity Z99.9%, supplied by J. T. Baker, USA). The schematic flow chart of the titanium dioxide precursor powders synthesized by a sol-gel process is shown in Fig. 1. The “A” solution was made by mixing TTIP and absolute ethanol in a volume of 20 ml and 30 ml, respectively. The “B” solution was made by mixing acetone and absolute ethanol in a volume of 7.5 ml and 15 ml, respectively. The titanium dioxide solgel was prepared by sequentially premixing the “B” solution into the “A” solution and stirring at room temperature for 10 min to form sol 1. The mixture of the solutions was stirred at room temperature for 90 min to form an insoluble gel. The gel was then aged at room temperature for 72 h. Finally, the gel was dried at 323 K for 72 h, and then ground to powder. The alumina grinding balls were used as the grinding medium. 2.2. Analysis of the precursor powders The precursor powders of titanium dioxide gels, dried at 323 K for 72 h and calcined under various conditions, were analyzed. Differential thermal analysis (DTA, SETARAM TG24 Simultaneous

Fig. 1. The schematic flow chart of the titanium dioxide precursor powders synthesized by a sol-gel process.

Symmetrical Thermoanalyzer, France) was conducted on 50 mg as-dried titanium dioxide precursor powders in static air with Al2O3 as a reference material. The calcination temperature was determined from DTA results. The crystalline phase was identified using an X-ray diffractometer (XRD, Model Rad Ⅱ A, Rigaku, Tokyo) with Cu Kα radiation and a Ni filter, operated at 40 kV, 30 mA and a scanning rate (2θ) of 1°/min. To determine the content of anatase TiO2, the intensity ratio of rutile TiO2 in the matrix was determined from the following formula [20]:

fr =

1.265Ir Ia + 1.265Ir

(1)

where fr is the fraction of the rutile TiO2, and Ia and Ir denote the intensities of the (101) and (110) reflections of anatase TiO2 and rutile TiO2, respectively. The morphology of the calcined TiO2 nanocrystallite powders was examined by transmission electron microscopy (TEM, JEOL JEM-1400) operated at 200 kV. Selected area electron diffraction (SAED) and nano beam electron diffraction (NBED) were utilized to confirm the phases of the calcined TiO2 nanocrystallite powders, and high resolution TEM (HRTEM) examination was also conducted for calcined products.

3. Results and discussion 3.1. The thermal behavior of titanium dioxide precursor powders The DTA/TG result is shown in Fig. 2, where the titanium dioxide precursor powder was heated from room temperature to 1073 K at a rate of 10 K/min. The DTA curve of titanium dioxide precursor powders reveals that one endothermic peak was around 380 K. The DTA curve also shows the apparent first, second and third exothermic peaks were at 436 K, 739 K, and 1001 K, respectively. In Fig. 2, the endothermic reaction occurred due to the dehydration of the precursor powders. The first exothermic reaction was attributed to the decomposition of residual organic matters. The second exothermic reaction was due to the formation of the anatase TiO2. The third exothermic reaction was owed to the

Please cite this article as: C.-L. Wang, et al., Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process, Ceramics International (2016), http://dx.doi.org/10.1016/j.ceramint.2016.05.101i

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Fig. 2. The DTA curves of the titanium dioxide precursor powders heated at 10 K/ min.

occurrence of the phase transformation from anatase TiO2 to rutile TiO2. Moreover, some broad peaks at 482, 519, 582 and 680 K are also observed in Fig. 2. The exothermic peaks appear at 482 and 519 K caused by the decomposition of residual unhydrolyzed alkyls during gelation [21], and the exothermic peak at about 582 K is either attributed to the oxidation of residual –OC2H5 groups and/ or the decomposition of titanium alkoxy constituents (Ti–O–C) [22]. The exothermic peak at 680 K is related to loss of carbon groups in the structure [23] or the bond of Ti–O–CH(CH3)2 disappear [24]. The DTA curves of the titanium dioxide precursor powders between 400 and 1073 K at various heating rates in the static air are shown in Fig. 3. It reveals that the anatase TiO2 crystallized at temperature between 716 K and 766 K. The phase transition temperature for anatase TiO2 transferred to rutile TiO2 was found at temperature between 946 K and 1009 K. As mentioned above, all the exothermic peaks of Fig. 3 shifted to a higher temperature as the heating rate raising. This result was due to the higher heating rate causing the equilibrium state shifted to a higher temperature [12].

3

Fig. 4. The XRD patterns of titanium dioxide precursor powders before calcination and after calcination at various temperatures for 1 h: (a) before calcination, (b) 673 K, (c) 773 K, (d) 873 K, (e) 973 K and (f) 1273 K (“n” denotes NH4NO3, “a” denotes anatase TiO2 and “r” denotes rutile TiO2).

3.2. The phase formation of titanium dioxide precursor powders after calcination The XRD patterns of titanium dioxide precursor powders after calcination at various temperatures for 1 h are shown in Fig. 4. The XRD pattern of the precursor powder before calcination is shown in Fig. 4(a). It reveals the presence of NH4NO3 in the precursor powder by the appearance of reflection peaks at (011), (111), (002), (020), (110) and (210) (JCPDS Card No. 47-0867). Fig. 4(b) shows the XRD pattern of the precursor powders after calcination at 673 K for 1 h, where the reflection peaks of the crystalline phases of the calcined powders show the single phase of anatase TiO2. When the titanium dioxide precursor powders were calcined at 773 and 873 K for 1 h, the XRD patterns are shown in Fig. 4(c) and (d), respectively. The reflection peaks still maintain the single phase of anatase TiO2. Fig. 4(e) shows the XRD pattern of titanium dioxide precursor powders calcined at 973 K for 1 h, it is seen that the crystalline phases of the calcined powders are composed of the coexisting anatase TiO2 and rutile TiO2, but the intensity of anatase TiO2 still increased and the rutile TiO2 is very poor. The XRD pattern of titanium dioxide precursor powders calcined at 1273 K for 1 his shown in Fig. 4(f). It is seen that only a single phase of rutile TiO2 peaks appeared. Fig. 5 shows the XRD patterns of titanium dioxide precursor powders calcined at 1073 K for various durations. Fig. 5(a) reveals the XRD pattern of the titanium dioxide precursor powders calcined at 1073 K for 20 min. It is seen that the reflection peaks are composed of the coexisting anatase TiO2 and rutile TiO2, but the weak intensities and broaden peaks are due to the anatase TiO2 and rutile TiO2 maintaining poor crystallinity and fine crystallite [25]. Fig. 5(b) and (c) show the XRD patterns of the titanium dioxide precursor powders calcined at 1073 K for 40 and 60 min respectively. It is seen that the intensities of anatase TiO2 decreased rapidly, but the rutile TiO2 increased abruptly when calcined at 1073 K for 90 min. When the calcination time increased to 90 min, the crystallinity of rutile TiO2 only increased slowly. 3.3. Kinetics of anatase TiO2 formation and phase transition from anatase TiO2 to rutile TiO2

Fig. 3. The DTA curves of the titanium dioxide precursor powders heated at different heating rates: (a) 5, (b) 10, (c) 15 and (d) 20 K/min.

The kinetics of anatase TiO2 crystallization could be evaluated by the amount of peak shift with various heating rates. Taking into

Please cite this article as: C.-L. Wang, et al., Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process, Ceramics International (2016), http://dx.doi.org/10.1016/j.ceramint.2016.05.101i

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Fig. 5. The XRD patterns of titanium dioxide precursor powders calcined at 1073 K for various times: (a) 20 min, (b) 40 min, (c) 60 min and (d) 90 min.

account the exothermic peak temperature, Tch, at a corresponding heating rate h, the following relation holds as described by the Johnson-Mehl-Avrami equation:

ln h = −

Qc + constant RTch

(2)

where Qc is the apparent activation energy of anatase TiO2 crystallization and R is the gas constant. The relation of ln h and 1/Tch is shown in Fig. 6 and a straight line is obtained. The apparent activation energy of anatase TiO2 crystallization is calculated from the slope of the straight line; then the 128.9 kJ/mol is obtained. This value is smaller than the activation energy of 242.4 kJ/mol for anatase TiO2 crystallization by a coprecipitation process [12]. When the titanium dioxide precursor powders were calcined at various temperatures for different times, the calculated crystallinity of rutile TiO2 using Eq. (1) is shown in Fig. 7. It reveals that the crystallinity of rutile TiO2 increases with calcined temperature. When calcined at 1073 K for 20–90 min, the crystallinity rapidly increased from 39.2 to 96.9%, but the crystallinity increased slightly from 96.9 to 100% when calcined at 1073–1273 K for

Fig. 7. The calculated crystallinity of rutile TiO2 when the titanium dioxide precursor powders were calcined at various temperatures for different times.

90 min. From the results of Fig. 7, it is also found that when calcined at 1173 K and 1273 K for 20–90 min, the crystallinity of rutile TiO2 is nearly the same. The following formula of the Johnson-Mehl-Avrami equation [26–29] can be applied to determine the kinetics of phase transition by using an isothermal method:

fr = 1−exp (−kt n)

(3)

where k is the reaction rate constant, and n denotes the Avrami exponent which is a dimensionless constant related to the nucleation and growth mechanism. The reaction rate constant, k, is related to the activation energy for the transition process, E, through the Arrhenius temperature dependence. Therefore k can be expressed as:

k = k 0 exp (−

E ) RT

(4)

where k0 is a constant, R is the universal gas constant, and T is the isothermal absolute temperature. The natural logarithms of both sides of Eq. (4) are taken, and Eq. (5) is obtained:

ln k = ln k 0−

E RT

(5)

The appropriate values of k were found by plotting the fraction crystallized, fr, versus the isothermal time for a range of temperatures. Therefore, the time of attained a given fr can be obtained from a range of fr values. Subsequently, the values of k and n were determined by taken double natural logarithms from both sides of Eq. (3).

ln [− ln (1−fr )] = ln k + n ln t

Fig. 6. ln h vs. 1/Tc.

(6)

Fig. 8 shows the plot of ln[-ln(1-fr)] versus ln t for various temperatures, where straight lines were obtained. The values of n and ln k were calculated from the slope of the straight lines and each line's intersection extrapolated to the vertical axis. The obtained values of n are listed in Table 1. Then, the activation energy of anatase TiO2 transition to rutile TiO2 was determined using Eq. (5), plotting the ln k against the reciprocal of absolute temperature, 1/T, yielding straight lines as shown in Fig. 9. The obtained value of activation energy and constant k0 are also listed in Table 1. Therefore, the kinetics of anatase TiO2 transition to rutile TiO2

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is caused by the different synthesized process. 3.4. Microstructure of anatase TiO2 transition to rutile TiO2

Fig. 8. Plot of ln[-ln(1-fr)] versus ln t for various temperatures.

Table 1. The activation energy and parameters of anatase TiO2 transition to rutile TiO2. Temperature (K)

n

k0

Ea (kJ/mol)

973 1073

1.48 1.26

2.85  10  4 1.24  10  2

328.4

The TEM micrographs, SAED and NBED patterns, and HRTEM of TiO2 precursor powders after calcination at 673 K for 1 h are shown in Fig. 10. Fig. 10(a) and (b) show the bright field (BF) and dark field (DF) images respectively. It is seen that agglomerated TiO2 crystallites synthesized by a sol-gel route occurred. This phenomenon is due to the TiO2 precursor powders being prepared through drying and/or subsequent steps, where agglomeration can take place [30,31]. Fig. 10(c) shows the SAED pattern for the location area marked by “03sadp” in Fig. 10(a), which is indexed corresponding to anatase TiO2 because of the (101), (103), (200), (105), (213), (116) and (107) reflections of anatase TiO2 (JCPDS Cards 89-4921). The polycrystalline nature of the powders was indicated by the Debye rings. The SAED pattern of the anatase TiO2 reveals that a lot of crystallite had been incorporated and crystallized. The NBED pattern of the location area marked by “08nbdp” in Fig. 10(a) is shown in Fig. 10(d), which is also indexed corresponding to TiO2 with zone axis (ZA) of [010]. An HRTEM image of the location area marked by “06hrtem” in Fig. 10(a) is shown in Fig. 10(e). The lattice image is indexed corresponding to the anatase TiO2 (200) and (101) with d-spacings of 1.886 and 3.502 Å, respectively. It also shows the mesoporous structure in the anatase TiO2 crystallites as denoted by circles and indicated by arrows, the mesoporous structure without the addition of surfactant is caused by decomposition of organic substance when the precursor powders after calcination. Fig. 11 shows the TEM micrographs, SAED and NBED patterns and HRTEM image of TiO2 precursor powders calcined at 973 K for 1 h. The BF image of the crystallites with a size of about 10.0 nm is shown in Fig. 11(a). Fig. 11(b) shows the DF image of the calcined product using a circle marked by “22df” in Fig. 11(c), which shows that the isolated crystallites had a size of about 16 nm. The SAED pattern of the location area marked by “21sadp” in Fig. 11(a) is shown in Fig. 11(c), which can be indexed corresponding to the coexistence of anatase and rutile TiO2 due to the (101), (004), (200), (105), (213) and (107) reflections of anatase TiO2, and (110), (101), (201) and (301) reflections of rutile TiO2, respectively. Fig. 11 (d) and (e) show the NBED patterns of the location areas marked by “30nbdp” and “32nbdp” in Fig. 11(a), which are indexed corresponding to anatase TiO2 with ZA¼ [010], and rutile TiO2 with ZA¼[ 111], respectively. Fig. 11(f) shows the HRTEM image in the location area marked by “24hrtem” in Fig. 11(a), which shows the anatase (101) with d-spacing of 3.503 Å, and rutile (110) and (101) with the d-spacings of 3.296 and 2.462 Å, respectively.

4. Conclusion

Fig. 9. Plot of the ln k against the reciprocal of absolute temperature.

can be described by the following equations:

fr = 1−exp (−2. 74 × 10−4 × t1.48), as T = 973 K

(7)

fr = 1−exp (−1. 2 × 10−2 × t1.26), as T = 1073K

(8)

Hsiang et al. [19] have also reported the effects of aging on the kinetics for nanocrystalline anatase-to-rutile phase transformation, they obtained the activation energy of 152 kJ/mol for unaged samples was smaller than that for aged samples (206–275 kJ/mol). Moreover, Zhang and Banfield [32] have also proposed a new kinetic model for the nanocrystalline anatase-to-rutile transformation, the calculated activation energy of 165.6 kJ/mol for rutile nucleation within nanocrystalline anatase particles. The difference

Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process have been studied using DTA, XRD, TEM, SAED, NBED and HRTEM. The results are concluded as follows. (1) The XRD results show the single phase of anatase TiO2 when the titanium dioxide precursor powders are calcined at 673 K for 1 h. The anatase and rutile TiO2 coexist in precursor powders when the calcination temperature is below 1273 K. (2) The anatase TiO2 crystallization between 716 and 766 K, and the phase transition temperature of anatase TiO2 to rutile TiO2, occurred between 946 and 1009 K. (3) The activation energy of anatase TiO2 formation and anatase transition to rutile TiO2 was 128.9 and 328.4 kJ/mol, respectively.

Please cite this article as: C.-L. Wang, et al., Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process, Ceramics International (2016), http://dx.doi.org/10.1016/j.ceramint.2016.05.101i

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Fig. 10. TEM micrographs, SAED and NBED patterns, and HRTEM image of TiO2 precursor powders after calcination at 673 K for 1 h: (a) BF image;(b) DF image in circle denoted by “05df” in (c);(c) SAED pattern for the area denoted by “03sadp” in (a)indexed corresponding to anatase TiO2;(d) NBED pattern of the area denoted by “08nbdp” in (a), also indexed corresponding to anatase TiO2 with ZA ¼ [010]; and (e) HRTEM image of the area denoted by “06hrtem” in (a) shows d-spacings of anatase TiO2 (200) and (101) reflections were 1.886 and 3.502 Å, respectively, and indicates the mesoporous structure by arrows.

Please cite this article as: C.-L. Wang, et al., Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process, Ceramics International (2016), http://dx.doi.org/10.1016/j.ceramint.2016.05.101i

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Fig. 11. TEM micrographs of TiO2 precursor powders calcination at 973 K for 1 h: (a) BF image; (b) DF image in circle denoted by “22df” in (c); (c) SAED pattern of the area denoted by “21sadp” in (a), indexed corresponding to the phases of anatase and rutile TiO2 coexisting;(d) NBED pattern of area denoted by “30nbdp” in (a), indexed corresponding to anatase TiO2 with ZA ¼[010]; (e) NBED pattern of location area denoted by “32nbdp” in (a), indexed corresponding to rutile TiO2 with ZA ¼[ 111]; and (f) HRTEM image shows d-spacings of the anatase TiO2 (101) reflection was 3.503 Å, and rutile TiO2 (110)and (101) reflections were 3.296 and 2.462 Å, respectively, and indicates the mesoporous structure by arrows.

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(4) The kinetics of anatase TiO2 transition to rutile TiO2 can be described as: fr = 1−exp (−2. 74 × 10−4 × t1.48) , as T = 973K and fr = 1−exp (−1. 2 × 10−2 × t1.26) , as T = 1073K .

[15] [16]

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Please cite this article as: C.-L. Wang, et al., Kinetics of anatase transition to rutile TiO2 from titanium dioxide precursor powders synthesized by a sol-gel process, Ceramics International (2016), http://dx.doi.org/10.1016/j.ceramint.2016.05.101i