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Lattice deformation and phase transformation from nano-scale anatase to nano-scale rutile TiO2 prepared by a sol-gel technique
CHINA PARTICUOLOGY Vol. 2, No. 3, 119-123, 2004
LATTICE DEFORMATION AND PHASE TRANSFORMATION FROM NANO-SCALE ANATASE TO NANO-SCALE RUTILE TiO2 PREPARED BY A SOL-GEL TECHNIQUE Yanqun Shao1,2,*, Dian Tang2,3, Jinghua Sun3,Yekun Lee3 and Weihao Xiong1 1
State Key Laboratory of Die & Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, P. R. China 2 Institute for Materials Research, Fuzhou University, Fuzhou 350002, P. R. China 3 Materials Research Center, University of Missouri-Rolla, Missouri, Rolla, MO65401, USA *Author to whom correspondence should be addressed. E-mail: [email protected]
Abstract
Nano-scale rutile phase was transformed from nano-scale anatase upon heating, which was prepared by a sol-gel technique. The XRD data corresponding to the anatase and rutile phases were analyzed and the grain sizes of as-derived phases were calculated by Sherrer equation. The lattice parameters of the as-derived anatase and rutile unit cells were calculated and compared with those of standard lattice parameters on PDF cards. It was shown that the smaller the grain sizes, the larger the lattice deformation. The lattice parameter a has the negative deviation from the standard and the lattice parameter c has the positive deviation for both phases. The particles sizes had preferential influence on the longer parameter between the lattice parameters of a and c. With increasing temperatures, the lattice parameters of a and c in both phases approached to the equilibrium state. The larger lattice deformation facilitated the nucleation process, which lowered the transformation temperature. During the transformation from nano-scale anatase to rutile, besides the mechanism involving retention of the {112} pseudo-close-packed planes of oxygen in anatase as the {100} pseudo-close-packed planes in rutile, the new phase occurred by relaxation of lattice deformation and adjustment of the atomic sites in parent phase. The orientation relationships were suggested to be anatase {101}//rutile {101} and anatase <201>//rutile<111>, and the habit plane was anatase (101).
Keywords
nano-scale materials, anatase, rutile, phase transformation, TiO2 , sol-gel technique
1. Introduction Titania TiO2 is a polymorphic oxide, inclusive of two common polymorphs: anatase (space group I41/amd, a0=0.37852 nm, c0=0.95139 nm) and rutile (space group P42/mnm, a0=0.45933 nm, c0=0.29592 nm) , both with octahedrally coordinated tetragonal structures. Anatase is a metastable structure and readily transforms to the stable morphic rutile upon heating (Gribb & Banfield, 1997). Because of their wide application in ceramics, catalysis, electronics, sensors and electrodes, they have been the subjects of keen investigations. With the increasing demand for nanostructured materials, a large amount of research has been carried out on nano-scale particles of titania (Hahn et al., 1990), such as microstructure, low- temperature sintering, plasticity and strain rate, catalysis, etc (Li et al., 2002; Shao et al., 2000). All results show that the smaller the particle size, the better the various properties, revealing the superior performance of nanocrystalline titania. When heated, nanocrystalline anatase will coarsen and transform to rutile, which will continue to coarsen though much faster. In spite of the considerable amount of work on the transformation of anatase to rutile (Won et al., 2001; Zhang & Banfield, 1999; Oomman, 2003), the lattice deformation behavior and mechanics of transformation from nano-scale monophase anatase to nano-structured rutile have not been discussed in detail. The purpose of the present work was to analyze the transformation process from the aspect of lattice deformation. A nano-scale mo-
nophase anatase was prepared by a sol-gel method and the product rutile was controlled in the nano-scale status by heat treatment. Using XRD, a series of lattice deformation values were obtained from which the grain size and the trend of lattice deformation were analyzed. The mechanisms of nucleation and growth from anatase to rutile were suggested.
2. Experiments and Data Analysis 2.1 Sample preparation and test The source material (C4H9O)4Ti was diluted in C2H5OH to a molar ratio of 1:8.5 to form a (C4H9O)4Ti solution. The hydrolytic reactant was a solution with a ratio of water and C2H5OH being 0.3:8.5. Hydrolysis started by adding the C2H5OH solution to the (C4H9O)4Ti solution with intensive magnetic stirring. The resulting clear solution was kept undisturbed for 48 h to become a transparent pale yellowo ish sol which was then dried in a desiccator at (60 ± 2) C to form a gel. The dried powder gel was calcined at 250, o 360, 600, 680, 750, 950, and 1200 C for 1, 3, 5, 7, and 10 h respectively in an oven to prepare the TiO2 powder samples. XRD examination of the powder samples was carried out using a Rigaku D/max-3C diffractometer equipped with a current-voltage stabilizer, counters, and a strip chart recorder. The instrument was operated at 35 kV with a filament current of 15 mA and copper Kα radiation. Scanning operation covered a wide range of 2θ from 20~90° with a scanning speed 4°/min at 0.02°steps.
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2.2 Data analysis
compared with a0 and c0, i.e, let Δa = a − a0 and Δc = c − c0 ,
The breadth of the half maximum intensity of the pure diffraction profile was estimated after separating the ka1 and ka2. This calibration is important for comparing peak intensities obtained from an annealed coarse-grained sample of silicon dioxide with the intensities from samples in as-produced nanophase form. The preferred orientation coincided with those reported in the corresponding PDF (Powder Diffraction Files) cards was indexed. The particle size D was determined from the X-ray diffraction data by Sherrer equation. It is known that when measuring the lattice parameter a and c of the crystalline cell, there is a close relationship between the relative error and 2θ angle. For example, the
the tendency of the lattice deformations versus the crystalline sizes D could be obtained.
relationship between the relative error
Δa a
and the 2θ
angle can be expressed as follows: Δa (1) = − cos θ ⋅ Δθ , a where Δθ is the error including systematic error and incidental error from instrument and 2θ and Δa = a − a0 . To ensure the accuracy, the higher diffraction angle θ is required to have cosθ reach the minimum value. Thus
Δa a
can reach the value as little as possible. Theoretically, 2θ diffraction angle is wanted to exceed 120°. It is the same for measuring the lattice parameter c. In our experiments, all angles that can be tested were below 90°. Each pointed datum was weighted equally because errors surely exist. The crystallite lattice deformation normal to the reflection planes (101), (200) and (204) of anatase and (110), (101) and (211) of rutile were calculated by measuring the X-ray diffraction peak broadening of the samples. As mentioned above, because the crystalline sizes are small, the diffraction intensity of higher angle became too weak to precisely decide. Consequently, the lattice parameters were difficult to be calculated accurately using the typical method. But it is necessary to learn the effect of lattice parameters on the novel nanostructured materials, especially on the properties that were brought from the smaller sizes. We would get the values introducing the following equation for tetragonal structures: 1 h2 + k 2 l 2 = + 2, (2) 2 d hhkl a2 c
where d is the measured value, h, k and l are the indexes of crystalline plane relevant to the measured d-spacing respectively, and a and c are the lattice parameters of a tetragonal structure, which would be calculated from Eq. (2). The crystalline planes (hkl) corresponding to the first three intensive diffraction peaks of the two phases and their d-spacing values were selected and united each other to be an equation group, from which a series of a and c values could be obtained. The averages of the above a and c values were denoted as a and c respectively. If they were
3 Results and Discussion 3.1 Phase transformation and particle sizes Fig. 1 shows the XRD patterns of powders calcined at different temperatures for 1 hour. Below 250 oC TiO2 exists in its amorphous state, for which only the reflection plane (101)A could be seen. Upon heating, the characteristic peak intensities of anatase increase significantly while the peak widths diminish. Below 600 oC, only the anatase phase exists. By the Sherrer equation, the average crystal size is calculated to be about 13 nm at 360 oC, and about 60 nm at 600 oC when the rutile phase begins to appear. Above 600 oC, anatase and rutile co-exist, while the volumetric fraction of the former decreases. At 750 oC, within 1 hour, the anatase crystal are measured about 48 nm, and for rutile, about 70 nm. When the temperature reaches 900 oC, anatase has totally transformed to rutile with a crystal size of less than 100 nm, that is, still within the nano-scale range. When calcined at 950 oC, the crystal size increases to around 115 nm, and the rutile particles coarsen rapidly above 1200 oC. The as-derived rutile sizes are close to those of the anatase at 600 oC. The co-existence of both crystalline phases has been known to lead to greatly deformed structures, which might be responsible for raising the annealing temperature to exceed that for complete transformation into the new phases. In the present work, the final temperature for 100% transformation to rutile is considered to be 950 oC.
Fig. 1
XRD patterns of powders heat treated at different temperatures for 1 h.
3.2 Lattice parameters and crystal deformation Fig. 2 shows the influence of particle size D on the lattice parameters a and c and their deviations, Δa and Δc. Lattice deformation could not be ignored for small particle sizes. It
Shao, Tang, Sun, Lee & Xiong: Phase Transformation from Nano-scale Anatase to Rutile is interesting to note that for anatase both a and c have greater deviations from their standards a0 and c0 than rutile. It might be due to the smaller sizes of anatase. The a values were below a0, while c ones were above c0 for both phases.
Fig. 2
Plot of lattice deformation (
121
and oxygen ions, which changes the lattice parameters of the parent phase. As a rule, nanostructured materials consist of a large number of surface atoms arrayed in disorder which possess superficial energy greater than those of the inner atoms. As a grain size gets smaller, its surface area increases, and the surface atoms exhibit easier mobility, which leads to greater defects, thus further enlarging lattice deformation. Previous studies have shown that nanophase TiO2 is typically oxygen-deficient. Coarse-grained rutile with an oxygen nonstoichiometry corresponding to the composition TiO1.983 was found to have a smaller a and a larger c for lattice parameters as compared to stoichiometric materials. The parameters of the unit cells must be adjusted to suitable sites in order to maintain the system in the lowest energy situation.
1 Δa Δc )* versus . , D a0 c0
*Subscripts A and R represent respectively anatase and rutile. The values of a0 and c0 come from ASTM cards. The solid line stands for the standard. All values of
Δa Δc are below zero while all values a0 c0
are above zero.
But the absolute deviations of these parameters for anatase differ from those of rutile, that is, for the former Δa > Δc and for the latter Δa < Δc . Contrary to previ-
20 nm Fig. 3
TEM morphology of anatase after heating for 1 h at 600 oC.
ous studies (Vydianathan et al., 2001; Chen et al., 1998), though both a and c decrease with particle size decreasing, the deviation of a is smaller than that of c. Here three important factors need to be considered. First, though the particles are quite uniform in size and well dispersed, as the size D decreases, it becomes increasingly difficult to get precise measurement of a and c, thus increasing the errors for the values of Δa and Δc . Second, the equiaxial crystalline morphologies of anatase and rutile, as seen in Figs. 3 and 4, affect their crystalline growth. Though the mentioned authors observed that the morphologies of the phases were somewhat round, the preferred orientation of the (101) plane of anatase and the (110) plane of rutile would result in anisotropic grains. Third, the interfacial atoms of the two phases must coordinate with each other to reach the lowest interfacial energy state, so as to reach the lowest energy state for the lattice deformation. Consequently, the longer parameters in the unit cell of the two phases should experience greater change than the shorter parameters. Above 600 oC, anatase phase growth and transformation to rutile proceed at the same time, accompanied by lattice reconstruction involving cooperative displacement of Ti
20 nm Fig. 4
TEM morphology of rutile after heating for 1 h at 950 oC.
3.3 Lattice correlations and orientational relationships For any transformation of a crystalline material, a two-stage process certainly takes place, nucleation and growth. It would be necessary to specify its particle size
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and surface area while defining the thermodynamic stabilities of its polymorphs. In nanostructured materials a large number of atoms are situated on the surfaces or grain boundaries, which can facilitate nucleation. The effect of particle sizes can not be ignored in the range of nanometer scale. In this experiment the transformation occurs above 600 oC from anatase to rutile. Even though there are many assumptions to explain the mechanism of the transformation by thermodynamics and kinetics, one more mechanism will be presented from the view of crystalline structures of anatase and rutile between which there are two equal interplanar spacings even though these atoms are not in the first close-packed planes. Both anatase and rutile are homogeneous isomers, their coordination is formed by Ti−O6 octahedron (Lu, 1996). The rutile structure consists of a distorted hexagonally close packing of oxygen atoms. Two of the six Ti−O bonds are slightly longer (1.98 Å) than the other four bonds in the rutile structure (1.95 Å) which is built up with Ti−O6 octahedrons arraying in chains sharing two edges. The anatase structure is based on a close packing of oxide ions. The metal atoms are arranged in zigzag rows. Two of the six Ti−O bonds are also longer than the other four bonds (1.96 Å versus 1.94 Å). The anatase structure arrays in chains sharing four edges of Ti−O6 octahedrons parallel along the (001) plane to form square slice or flat bi-pyramidal shapes. According to Pauling Law, The rutile structure is more stable than the anatase one. Their structural differences lead to the high activation energy, 418~752 kJ.mol-1 (Shannon & Pask, 1964). It supports the fact that the anatase-rutile transformation is reconstructive. Shannon and Pask (1964) also presented a transformation mechanism which was involved with the retention of the {112} pseudo-close-packed planes of oxygen in anatase like that of the {100} pseudo-close-packed planes in rutile, and rearrangement of the titanium and oxygen ions within these planes. But in the present work, as shown in XRD patterns of Fig. 1, the intensities of the peaks related to the preferred orientation of the anatase (101) plane and rutile (110) plane were observed. In other words, the phase transformation from anatase to rutile has a preferred orientation. This direct transformation can be understood intuitively by considering the titanium matrices in anatase and rutile shown in Fig. 5 and Fig. 6. The interatomic distance da1-a3 and da1-a2 in the anatase (101) plane is very close to db1-b2 and db1-b3 in the rutile (101) plane. It can be presumed that the crystalline structure of anatase with preferred orientation along the (101) plane can be easily deformed into rutile (110). Therefore, during the nucleation, as long as the Ti atoms of the anatase can displace spontaneously in collectivity, and the energy was enough to keep the displacement, the displacive phase transformation would progress (Feng, 1990). The energy for the displacive phase transformation is smaller than that for recomposing phase transformation.
The energy might be mainly from either the decrease of the lattice deformation or the increase of temperature. The smaller the crystalline size, the lower the barrier height, consequently the more easily the grain boundary movement takes place. The speciality of anatase and rutile phases in crystal structure favors the transformation.
Fig. 5
Theoretical simulation of a unit cell of ideal crystal structure in anatase: (a) array of [TiO6] octahedrons; (b) distance of titanium matrix for (101) plane; (c) interatomic distance da1-a3=0.54582 nm and da1-a2=0.37853 nm of the titanium matrix in anatase (101) plane. Titanium: solid circle; oxygen: open circle.
Fig. 6
A unit cell of ideal crystal structure in rutile: (a) array of [TiO6] octahedrons; (b) distance of titanium matrix for (101) plane; (c) interatomic distance db1-b2=0.54640 nm and db1-b3=0.35691 nm of the titanium matrix in rutile (101) plane.
The anatase-rutile transformation implies that two of the six Ti-O bonds of the anatase structure are broken to form a rutile structure. During the growth, reconstruction is the key step. The atoms among the anatase displace coordinately in collectivity, and the plane {101}A of parent phase is turned into {101}R of as-produced rutile phase. Finally the rutile structure forms through rearranging Ti atoms on plane {101}R. The orientational relationship between the lattices of anatase and rutile was expressed as follows: {101}A//{101}R,<201>A//<111>R It shows that there not only exists the certain orientational relationship, but also rutile forms in the certain lattice direction of parent lattices in anatase, i.e., a habit plane (101)A.
Shao, Tang, Sun, Lee & Xiong: Phase Transformation from Nano-scale Anatase to Rutile
123
4. Conclusions
References
(1) Nano-scale rutile phase was obtained from heating nano-scale anatase which was prepared by a sol-gel technique. The transformation occured within the nano-scale range. It was shown that the smaller the particle size, the larger the lattice deformation. For both phases, lattice parameter a has negative deviation from the standard (ac0). But the absolute deviations of the parameters in anatase are different from those in rutile: Δa > Δc for anatase and Δa < Δc for rutile. The ef-
Chen, S. R., Shao, Y. Q. & Tang, D. (1998). TiCl3 oxidation and sintering to prepare nanomaterials. Chin. J. Nonferrous Met., 8(2), 250-253. (in Chinese) Feng, D. (1990). Physics of Metals, Vol. 2: Phase Transformation. Beijing: Science Press. (in Chinese) Gribb, A. A. & Banfield, J. F. (1997). Particle size effects on transformation kinetics and phase stability in nanocrystalline TiO2. Am. Mineral., 82, 717-728. Hahn, H., Logas, J. & Averback, R. S. (1990). Sintering characteristics of nanocrystalline TiO2. J. Mater. Res., 5(3), 609-614. Li, W., Ismat Shah, S., Huang, C.-P., Jung, O. & Ni, C. (2002). Metallorganic chemical vapor deposition and characterization of TiO2 nanoparticles. Mater. Sci. Eng., B, 96, 247-253. Lu, P. W. (1996). Fundamentals of Inorganic Chemistry: Physical Chemistry of Silicates (pp.68-70). Wuhan: Wuhan University of Technology Press. (in Chinese) Oomman, K. V. (2003). Crystallization and high-temperature structural stability of titanium oxide nanotube arrays. J. Mater. Res., 18(1), 156-165. Shannon, R. D. & Pask, J. A. (1964). Topotaxy in the anatase-rutile transformation．Am. Mineral., 49(11-12), 170-171. Shao, Y. Q., Tang, D. & Ding, Y. D. (2000). Thermal stability of nano-scale rutile TiO2 prepared under low temperatures. Chin. J. Nonferrous Met., 10 (Suppl.1), 227-229. (in Chinese) Won, D. J., Wang, C. H., Jang, H. K. & Choi, D.-J. (2001). Effects of thermally induced anatase-to-rutile phase transition in MOCVD-grown TiO2 films on structural and optical properties. Appl. Phys. A, 73, 595-600. Vydianathan, K., Nuesca, G., Peterson, G., Eisenbraun, E. T., Kaloyeros, A. E., Sullivan, J. J. & Han, B. (2001). Metallorganic chemical vapour deposition of titanium oxide for microelectronics applications. J. Mater. Res., 2001,16(6), 1838-1849. Zhang, H. Z. & Banfield, J. F. (1999). New kinetic model for the nanocrystalline anatase-to-rutile transformation revealing rate dependence on number of particles. Am. Mineral., 84, 528-535.
fect of particle sizes on the shorter lattice parameter is larger as compared to the longer lattice parameter. (2) During the phase tranformation from anatase to rutile, nucleation of rutile takes place by atom movement in anatase, followed by local adjustments of atoms to conform to the new structure. The orientational relationship between the lattices of anatase and rutile can be expressed as follows: anatase {101} // rutile {101} and anatase <201> // rutile <111> for which the habit plane is (101)A.
Acknowledgement Financial support for this work was derived from Science & Technology Development Foundation of Fuzhou University (XKJ(YM)0112) and International Cooperation Projects of Science & Technology Committee of Fujian Province(2002I011).
Manuscript received April 4, 2004 and accepted May 15, 2004.
LATTICE DEFORMATION AND PHASE TRANSFORMATION FROM NANO-SCALE ANATASE TO NANO-SCALE RUTILE TiO2 PREPARED BY A SOL-GEL TECHNIQUE Yanqun Shao1,2,*, Dian Tang2,3, Jinghua Sun3,Yekun Lee3 and Weihao Xiong1 1
State Key Laboratory of Die & Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, P. R. China 2 Institute for Materials Research, Fuzhou University, Fuzhou 350002, P. R. China 3 Materials Research Center, University of Missouri-Rolla, Missouri, Rolla, MO65401, USA *Author to whom correspondence should be addressed. E-mail: [email protected]
Abstract
Nano-scale rutile phase was transformed from nano-scale anatase upon heating, which was prepared by a sol-gel technique. The XRD data corresponding to the anatase and rutile phases were analyzed and the grain sizes of as-derived phases were calculated by Sherrer equation. The lattice parameters of the as-derived anatase and rutile unit cells were calculated and compared with those of standard lattice parameters on PDF cards. It was shown that the smaller the grain sizes, the larger the lattice deformation. The lattice parameter a has the negative deviation from the standard and the lattice parameter c has the positive deviation for both phases. The particles sizes had preferential influence on the longer parameter between the lattice parameters of a and c. With increasing temperatures, the lattice parameters of a and c in both phases approached to the equilibrium state. The larger lattice deformation facilitated the nucleation process, which lowered the transformation temperature. During the transformation from nano-scale anatase to rutile, besides the mechanism involving retention of the {112} pseudo-close-packed planes of oxygen in anatase as the {100} pseudo-close-packed planes in rutile, the new phase occurred by relaxation of lattice deformation and adjustment of the atomic sites in parent phase. The orientation relationships were suggested to be anatase {101}//rutile {101} and anatase <201>//rutile<111>, and the habit plane was anatase (101).
Keywords
nano-scale materials, anatase, rutile, phase transformation, TiO2 , sol-gel technique
1. Introduction Titania TiO2 is a polymorphic oxide, inclusive of two common polymorphs: anatase (space group I41/amd, a0=0.37852 nm, c0=0.95139 nm) and rutile (space group P42/mnm, a0=0.45933 nm, c0=0.29592 nm) , both with octahedrally coordinated tetragonal structures. Anatase is a metastable structure and readily transforms to the stable morphic rutile upon heating (Gribb & Banfield, 1997). Because of their wide application in ceramics, catalysis, electronics, sensors and electrodes, they have been the subjects of keen investigations. With the increasing demand for nanostructured materials, a large amount of research has been carried out on nano-scale particles of titania (Hahn et al., 1990), such as microstructure, low- temperature sintering, plasticity and strain rate, catalysis, etc (Li et al., 2002; Shao et al., 2000). All results show that the smaller the particle size, the better the various properties, revealing the superior performance of nanocrystalline titania. When heated, nanocrystalline anatase will coarsen and transform to rutile, which will continue to coarsen though much faster. In spite of the considerable amount of work on the transformation of anatase to rutile (Won et al., 2001; Zhang & Banfield, 1999; Oomman, 2003), the lattice deformation behavior and mechanics of transformation from nano-scale monophase anatase to nano-structured rutile have not been discussed in detail. The purpose of the present work was to analyze the transformation process from the aspect of lattice deformation. A nano-scale mo-
nophase anatase was prepared by a sol-gel method and the product rutile was controlled in the nano-scale status by heat treatment. Using XRD, a series of lattice deformation values were obtained from which the grain size and the trend of lattice deformation were analyzed. The mechanisms of nucleation and growth from anatase to rutile were suggested.
2. Experiments and Data Analysis 2.1 Sample preparation and test The source material (C4H9O)4Ti was diluted in C2H5OH to a molar ratio of 1:8.5 to form a (C4H9O)4Ti solution. The hydrolytic reactant was a solution with a ratio of water and C2H5OH being 0.3:8.5. Hydrolysis started by adding the C2H5OH solution to the (C4H9O)4Ti solution with intensive magnetic stirring. The resulting clear solution was kept undisturbed for 48 h to become a transparent pale yellowo ish sol which was then dried in a desiccator at (60 ± 2) C to form a gel. The dried powder gel was calcined at 250, o 360, 600, 680, 750, 950, and 1200 C for 1, 3, 5, 7, and 10 h respectively in an oven to prepare the TiO2 powder samples. XRD examination of the powder samples was carried out using a Rigaku D/max-3C diffractometer equipped with a current-voltage stabilizer, counters, and a strip chart recorder. The instrument was operated at 35 kV with a filament current of 15 mA and copper Kα radiation. Scanning operation covered a wide range of 2θ from 20~90° with a scanning speed 4°/min at 0.02°steps.
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CHINA PARTICUOLOGY Vol. 2, No. 3, 2004
2.2 Data analysis
compared with a0 and c0, i.e, let Δa = a − a0 and Δc = c − c0 ,
The breadth of the half maximum intensity of the pure diffraction profile was estimated after separating the ka1 and ka2. This calibration is important for comparing peak intensities obtained from an annealed coarse-grained sample of silicon dioxide with the intensities from samples in as-produced nanophase form. The preferred orientation coincided with those reported in the corresponding PDF (Powder Diffraction Files) cards was indexed. The particle size D was determined from the X-ray diffraction data by Sherrer equation. It is known that when measuring the lattice parameter a and c of the crystalline cell, there is a close relationship between the relative error and 2θ angle. For example, the
the tendency of the lattice deformations versus the crystalline sizes D could be obtained.
relationship between the relative error
Δa a
and the 2θ
angle can be expressed as follows: Δa (1) = − cos θ ⋅ Δθ , a where Δθ is the error including systematic error and incidental error from instrument and 2θ and Δa = a − a0 . To ensure the accuracy, the higher diffraction angle θ is required to have cosθ reach the minimum value. Thus
Δa a
can reach the value as little as possible. Theoretically, 2θ diffraction angle is wanted to exceed 120°. It is the same for measuring the lattice parameter c. In our experiments, all angles that can be tested were below 90°. Each pointed datum was weighted equally because errors surely exist. The crystallite lattice deformation normal to the reflection planes (101), (200) and (204) of anatase and (110), (101) and (211) of rutile were calculated by measuring the X-ray diffraction peak broadening of the samples. As mentioned above, because the crystalline sizes are small, the diffraction intensity of higher angle became too weak to precisely decide. Consequently, the lattice parameters were difficult to be calculated accurately using the typical method. But it is necessary to learn the effect of lattice parameters on the novel nanostructured materials, especially on the properties that were brought from the smaller sizes. We would get the values introducing the following equation for tetragonal structures: 1 h2 + k 2 l 2 = + 2, (2) 2 d hhkl a2 c
where d is the measured value, h, k and l are the indexes of crystalline plane relevant to the measured d-spacing respectively, and a and c are the lattice parameters of a tetragonal structure, which would be calculated from Eq. (2). The crystalline planes (hkl) corresponding to the first three intensive diffraction peaks of the two phases and their d-spacing values were selected and united each other to be an equation group, from which a series of a and c values could be obtained. The averages of the above a and c values were denoted as a and c respectively. If they were
3 Results and Discussion 3.1 Phase transformation and particle sizes Fig. 1 shows the XRD patterns of powders calcined at different temperatures for 1 hour. Below 250 oC TiO2 exists in its amorphous state, for which only the reflection plane (101)A could be seen. Upon heating, the characteristic peak intensities of anatase increase significantly while the peak widths diminish. Below 600 oC, only the anatase phase exists. By the Sherrer equation, the average crystal size is calculated to be about 13 nm at 360 oC, and about 60 nm at 600 oC when the rutile phase begins to appear. Above 600 oC, anatase and rutile co-exist, while the volumetric fraction of the former decreases. At 750 oC, within 1 hour, the anatase crystal are measured about 48 nm, and for rutile, about 70 nm. When the temperature reaches 900 oC, anatase has totally transformed to rutile with a crystal size of less than 100 nm, that is, still within the nano-scale range. When calcined at 950 oC, the crystal size increases to around 115 nm, and the rutile particles coarsen rapidly above 1200 oC. The as-derived rutile sizes are close to those of the anatase at 600 oC. The co-existence of both crystalline phases has been known to lead to greatly deformed structures, which might be responsible for raising the annealing temperature to exceed that for complete transformation into the new phases. In the present work, the final temperature for 100% transformation to rutile is considered to be 950 oC.
Fig. 1
XRD patterns of powders heat treated at different temperatures for 1 h.
3.2 Lattice parameters and crystal deformation Fig. 2 shows the influence of particle size D on the lattice parameters a and c and their deviations, Δa and Δc. Lattice deformation could not be ignored for small particle sizes. It
Shao, Tang, Sun, Lee & Xiong: Phase Transformation from Nano-scale Anatase to Rutile is interesting to note that for anatase both a and c have greater deviations from their standards a0 and c0 than rutile. It might be due to the smaller sizes of anatase. The a values were below a0, while c ones were above c0 for both phases.
Fig. 2
Plot of lattice deformation (
121
and oxygen ions, which changes the lattice parameters of the parent phase. As a rule, nanostructured materials consist of a large number of surface atoms arrayed in disorder which possess superficial energy greater than those of the inner atoms. As a grain size gets smaller, its surface area increases, and the surface atoms exhibit easier mobility, which leads to greater defects, thus further enlarging lattice deformation. Previous studies have shown that nanophase TiO2 is typically oxygen-deficient. Coarse-grained rutile with an oxygen nonstoichiometry corresponding to the composition TiO1.983 was found to have a smaller a and a larger c for lattice parameters as compared to stoichiometric materials. The parameters of the unit cells must be adjusted to suitable sites in order to maintain the system in the lowest energy situation.
1 Δa Δc )* versus . , D a0 c0
*Subscripts A and R represent respectively anatase and rutile. The values of a0 and c0 come from ASTM cards. The solid line stands for the standard. All values of
Δa Δc are below zero while all values a0 c0
are above zero.
But the absolute deviations of these parameters for anatase differ from those of rutile, that is, for the former Δa > Δc and for the latter Δa < Δc . Contrary to previ-
20 nm Fig. 3
TEM morphology of anatase after heating for 1 h at 600 oC.
ous studies (Vydianathan et al., 2001; Chen et al., 1998), though both a and c decrease with particle size decreasing, the deviation of a is smaller than that of c. Here three important factors need to be considered. First, though the particles are quite uniform in size and well dispersed, as the size D decreases, it becomes increasingly difficult to get precise measurement of a and c, thus increasing the errors for the values of Δa and Δc . Second, the equiaxial crystalline morphologies of anatase and rutile, as seen in Figs. 3 and 4, affect their crystalline growth. Though the mentioned authors observed that the morphologies of the phases were somewhat round, the preferred orientation of the (101) plane of anatase and the (110) plane of rutile would result in anisotropic grains. Third, the interfacial atoms of the two phases must coordinate with each other to reach the lowest interfacial energy state, so as to reach the lowest energy state for the lattice deformation. Consequently, the longer parameters in the unit cell of the two phases should experience greater change than the shorter parameters. Above 600 oC, anatase phase growth and transformation to rutile proceed at the same time, accompanied by lattice reconstruction involving cooperative displacement of Ti
20 nm Fig. 4
TEM morphology of rutile after heating for 1 h at 950 oC.
3.3 Lattice correlations and orientational relationships For any transformation of a crystalline material, a two-stage process certainly takes place, nucleation and growth. It would be necessary to specify its particle size
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and surface area while defining the thermodynamic stabilities of its polymorphs. In nanostructured materials a large number of atoms are situated on the surfaces or grain boundaries, which can facilitate nucleation. The effect of particle sizes can not be ignored in the range of nanometer scale. In this experiment the transformation occurs above 600 oC from anatase to rutile. Even though there are many assumptions to explain the mechanism of the transformation by thermodynamics and kinetics, one more mechanism will be presented from the view of crystalline structures of anatase and rutile between which there are two equal interplanar spacings even though these atoms are not in the first close-packed planes. Both anatase and rutile are homogeneous isomers, their coordination is formed by Ti−O6 octahedron (Lu, 1996). The rutile structure consists of a distorted hexagonally close packing of oxygen atoms. Two of the six Ti−O bonds are slightly longer (1.98 Å) than the other four bonds in the rutile structure (1.95 Å) which is built up with Ti−O6 octahedrons arraying in chains sharing two edges. The anatase structure is based on a close packing of oxide ions. The metal atoms are arranged in zigzag rows. Two of the six Ti−O bonds are also longer than the other four bonds (1.96 Å versus 1.94 Å). The anatase structure arrays in chains sharing four edges of Ti−O6 octahedrons parallel along the (001) plane to form square slice or flat bi-pyramidal shapes. According to Pauling Law, The rutile structure is more stable than the anatase one. Their structural differences lead to the high activation energy, 418~752 kJ.mol-1 (Shannon & Pask, 1964). It supports the fact that the anatase-rutile transformation is reconstructive. Shannon and Pask (1964) also presented a transformation mechanism which was involved with the retention of the {112} pseudo-close-packed planes of oxygen in anatase like that of the {100} pseudo-close-packed planes in rutile, and rearrangement of the titanium and oxygen ions within these planes. But in the present work, as shown in XRD patterns of Fig. 1, the intensities of the peaks related to the preferred orientation of the anatase (101) plane and rutile (110) plane were observed. In other words, the phase transformation from anatase to rutile has a preferred orientation. This direct transformation can be understood intuitively by considering the titanium matrices in anatase and rutile shown in Fig. 5 and Fig. 6. The interatomic distance da1-a3 and da1-a2 in the anatase (101) plane is very close to db1-b2 and db1-b3 in the rutile (101) plane. It can be presumed that the crystalline structure of anatase with preferred orientation along the (101) plane can be easily deformed into rutile (110). Therefore, during the nucleation, as long as the Ti atoms of the anatase can displace spontaneously in collectivity, and the energy was enough to keep the displacement, the displacive phase transformation would progress (Feng, 1990). The energy for the displacive phase transformation is smaller than that for recomposing phase transformation.
The energy might be mainly from either the decrease of the lattice deformation or the increase of temperature. The smaller the crystalline size, the lower the barrier height, consequently the more easily the grain boundary movement takes place. The speciality of anatase and rutile phases in crystal structure favors the transformation.
Fig. 5
Theoretical simulation of a unit cell of ideal crystal structure in anatase: (a) array of [TiO6] octahedrons; (b) distance of titanium matrix for (101) plane; (c) interatomic distance da1-a3=0.54582 nm and da1-a2=0.37853 nm of the titanium matrix in anatase (101) plane. Titanium: solid circle; oxygen: open circle.
Fig. 6
A unit cell of ideal crystal structure in rutile: (a) array of [TiO6] octahedrons; (b) distance of titanium matrix for (101) plane; (c) interatomic distance db1-b2=0.54640 nm and db1-b3=0.35691 nm of the titanium matrix in rutile (101) plane.
The anatase-rutile transformation implies that two of the six Ti-O bonds of the anatase structure are broken to form a rutile structure. During the growth, reconstruction is the key step. The atoms among the anatase displace coordinately in collectivity, and the plane {101}A of parent phase is turned into {101}R of as-produced rutile phase. Finally the rutile structure forms through rearranging Ti atoms on plane {101}R. The orientational relationship between the lattices of anatase and rutile was expressed as follows: {101}A//{101}R,<201>A//<111>R It shows that there not only exists the certain orientational relationship, but also rutile forms in the certain lattice direction of parent lattices in anatase, i.e., a habit plane (101)A.
Shao, Tang, Sun, Lee & Xiong: Phase Transformation from Nano-scale Anatase to Rutile
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4. Conclusions
References
(1) Nano-scale rutile phase was obtained from heating nano-scale anatase which was prepared by a sol-gel technique. The transformation occured within the nano-scale range. It was shown that the smaller the particle size, the larger the lattice deformation. For both phases, lattice parameter a has negative deviation from the standard (a
Chen, S. R., Shao, Y. Q. & Tang, D. (1998). TiCl3 oxidation and sintering to prepare nanomaterials. Chin. J. Nonferrous Met., 8(2), 250-253. (in Chinese) Feng, D. (1990). Physics of Metals, Vol. 2: Phase Transformation. Beijing: Science Press. (in Chinese) Gribb, A. A. & Banfield, J. F. (1997). Particle size effects on transformation kinetics and phase stability in nanocrystalline TiO2. Am. Mineral., 82, 717-728. Hahn, H., Logas, J. & Averback, R. S. (1990). Sintering characteristics of nanocrystalline TiO2. J. Mater. Res., 5(3), 609-614. Li, W., Ismat Shah, S., Huang, C.-P., Jung, O. & Ni, C. (2002). Metallorganic chemical vapor deposition and characterization of TiO2 nanoparticles. Mater. Sci. Eng., B, 96, 247-253. Lu, P. W. (1996). Fundamentals of Inorganic Chemistry: Physical Chemistry of Silicates (pp.68-70). Wuhan: Wuhan University of Technology Press. (in Chinese) Oomman, K. V. (2003). Crystallization and high-temperature structural stability of titanium oxide nanotube arrays. J. Mater. Res., 18(1), 156-165. Shannon, R. D. & Pask, J. A. (1964). Topotaxy in the anatase-rutile transformation．Am. Mineral., 49(11-12), 170-171. Shao, Y. Q., Tang, D. & Ding, Y. D. (2000). Thermal stability of nano-scale rutile TiO2 prepared under low temperatures. Chin. J. Nonferrous Met., 10 (Suppl.1), 227-229. (in Chinese) Won, D. J., Wang, C. H., Jang, H. K. & Choi, D.-J. (2001). Effects of thermally induced anatase-to-rutile phase transition in MOCVD-grown TiO2 films on structural and optical properties. Appl. Phys. A, 73, 595-600. Vydianathan, K., Nuesca, G., Peterson, G., Eisenbraun, E. T., Kaloyeros, A. E., Sullivan, J. J. & Han, B. (2001). Metallorganic chemical vapour deposition of titanium oxide for microelectronics applications. J. Mater. Res., 2001,16(6), 1838-1849. Zhang, H. Z. & Banfield, J. F. (1999). New kinetic model for the nanocrystalline anatase-to-rutile transformation revealing rate dependence on number of particles. Am. Mineral., 84, 528-535.
fect of particle sizes on the shorter lattice parameter is larger as compared to the longer lattice parameter. (2) During the phase tranformation from anatase to rutile, nucleation of rutile takes place by atom movement in anatase, followed by local adjustments of atoms to conform to the new structure. The orientational relationship between the lattices of anatase and rutile can be expressed as follows: anatase {101} // rutile {101} and anatase <201> // rutile <111> for which the habit plane is (101)A.
Acknowledgement Financial support for this work was derived from Science & Technology Development Foundation of Fuzhou University (XKJ(YM)0112) and International Cooperation Projects of Science & Technology Committee of Fujian Province(2002I011).
Manuscript received April 4, 2004 and accepted May 15, 2004.