Influence of particle size on the phonon confinement of TiO₂ nanoparticles

Abstract

Titanium dioxide nanocrystals are prepared by a hydrolysis process of Titanium tetraisopropoxide. Nano crystals of various sizes are obtained after annealing from 300 to 450°C. Raman scattering was employed to investigate the evolution of the anatase phase in the nano crystals during annealing. X-ray diffraction, transmission electron microscopy and dynamic light scattering studies were done to supplement the Raman scattering results on particle size. Phonon confinement and non-stoichiometry effects are responsible for the blue shift and broadening of the lowest-frequency E_g Raman mode.

Keywords:

• nanomaterials
• titanium dioxide
• Raman spectroscopy
• phonon confinement model

1. Introduction

Nanophase materials have been attracting great interest for several years because of their unique mechanical, electrical, optical, biological and magnetic properties [1]. The properties of nanophase materials are strongly related to their structure, therefore the structure of nanophase materials is studied on a variety of length scales in order to develop an understanding of the structure–property relations [2]. Titanium dioxide (TiO₂) is a main component of paints, pigments, a variety of glass products, biomedical implants and in cosmetics [3,4]. TiO₂ exists in three natural phases. They are anatase, rutile, and brookite. Anatase is tetragonal () with two formula units per unit cell and six Raman active modes (A _{1 g}  + 2B _{1 g}  + 3E_g ), whereas rutile ∼tetragonal, ) has two units and four Raman active modes (A _{1 g}  + B _{1 g}  + B _{2 g}  + E_g ). Brookite is orthorhombic (), has eight formula units per unit cell and shows 36 Raman active modes (9A _{1 g} + 9B _{1 g} + 9B _{2 g} + 9B _{3 g} ) [5]. The phonons are confined in nanocrystals. In the bulk material Raman modes obey the fundamental selection rule  = 0, where is the wave vector of the scattered phonon. In finite domains this selection rule is relaxed. All phonon modes with π/d, where d is the dimension of the crystalline domine, contribute to the Raman intensity [6]. An important property of nanocrystals is the appearance of surface phonon modes. In the frequency range between bulk longitudinal optical phonon frequency, ω _LO transverse optical mode frequency, ω _TO a new mode know as surface phonon mode, appears in the nanocrystals, which is absent in corresponding bulk material [7].

Fabrication techniques and the processing conditions have a strong influence on the microstructures and electronic and vibrational properties of the materials. Changes in the Raman spectra TiO₂ nanocrystals were related to non-stoichiometry, surface pressure and the phonon confinement effect [8–11]. In this study, we investigate the Raman spectra of TiO₂ nanocrystals at various annealing temperatures and particle sizes in order to get a better understanding of the lattice vibration characters in ultrafine particle TiO₂ systems. Particle size were also studied by X-ray diffraction (XRD), transmission electron microscopy (TEM) and dynamic light scattering (DLS) to confirm the results of Raman scattering.

2. Experimental procedure

2.1. Synthesis of TiO₂ nanoparticles

A 7.4 ml of titanium tetraisopropoxide was added, drop by drop, to 30 ml of 1 M HNO₃ aqueous solution, and then agitated for 2 h to give a transparent sol, in which 2.0 g TiO₂ are contained. The pH of the colloidal solution was adjusted to pH 3, with the addition of 1 M NaOH solution after dilution of the colloid with 100 ml water, resulting in a turbid TiO₂ colloid. The suspension was agitated at room temperature, centrifuged and then washed with distilled water. The isolated TiO₂ was dried for 1 h at 100°C in air. The resulting powder was then calcinated at 300, 350, 400, 450°C for 3 h [12,13].

The micro-Raman spectra were recorded at room temperature using a laser Raman confocal microprobe (LabRam HR 800). A He–Ne laser (λ = 633 nm) was used as the excitation source with an output power of 17 mW and was focused to a spot of 1 µm. Before measurement, the system was calibrated using the 521 cm⁻¹ Raman line of a silicon (Si) wafer. The confocal hole of the spectrograph was 100 µmin diameter. All Raman spectra were recorded in the back scattering geometry. Powder XRD (Seifert, JSO-DE BYEFLEX 2002, Germany) was utilised to identify the crystalline phase composition. The morphology and crystal structure of the product were observed by TEM. The instrument was JEOL 2000Fx-II operated at 200 kV, high resolution, analytical TEM with a W-source and a point–point resolution of 2 Å. Particle size distribution is analysed by Zeta sizer Nano S90 series.

3. Results and discussion

Raman spectra of TiO₂ samples annealed at different temperatures are given in Figure 1. In the spectra of all TiO₂ samples the dominant Raman modes can be assigned to the Raman active modes of the anatase crystal 144 (E_g (1)), 197 (E_g (2)), 399 (B _{1 g} (1)), 519 (combination of A _{1 g} and B _{1 g} (2) that cannot be resolved at room temperature) and 639 cm⁻¹ (E_g (3)) [14]. The dependence of the shape of the Raman peaks from the crystal dimension may have various explanations. A pressure effect on the grains, induced by the surrounding grains or by the surface tension, has been often invoked in similar cases. This mechanism usually gives large frequency shifts and, moreover, Raman measurements as a function of the external pressure show a behaviour, for some of the peaks, which is opposite that observed here. Therefore, we believe that the changes in the Raman line widths have a different origin. A possible cause of the Raman line broadening could be a non-stoichiometry of the sample i.e. an oxygen deficiency or the disorder induced by minor phases, which in titania samples obtained with other preparation methods play an important role. In our case, the thermal treatments are performed in air and the non-stoichiometry is expected to be negligible. In addition, Raman and XRD measurements suggest that only the anatase phase is present [15].

Figure 1. Raman spectrum of titanium dioxide nanoparticles annealed at different temperature.

Therefore, we attempt to explain the observed line broadening with the breakdown of the phonon momentum selection rule q = 0, specific of the Raman scattering in ordered systems. In the case of crystals of very small size, this rule is no longer valid as the phonons are confined in space and all the phonons over the Brillouin zone will contribute to the first order Raman spectra. The weight of the off-center phonons increases as the crystal size decreases and the phonon dispersion causes an asymmetrical broadening and the shift of the Raman peaks. A simple confinement model may then be used to calculate the shape of the 144 cm⁻¹ mode of the anatase at various nano crystal sizes. For spherical nano crystals and first-order scattering, the Raman intensity I(ω) can be written as

where q is wave vector expressed in units of π divided by value of unit cell parameter, L is the diameter of the particle and Γ₀ is the intrinsic line width of Raman mode at given temperature, d is the crystallite size, and ω(q) is q-dependent phonon frequency.

By taking a spherical Brillouin zone and an isotropic dispersion curve, the dispersion relationship for the E_g Raman mode in the anatase phase could be expressed as [16]

where ω ₀ is the zone-centre frequency of the E_g (1) mode at room temperature where Δ = 20 cm⁻¹, a = 0.3768 nm and ω ₀  = 144 cm⁻¹.

Figure 2 shows the Raman intensity calculated using phonon confinement model for different crystal sizes (diameter 6, 6.5, 7, 8.25 and 11 nm). As the crystallite size decreases, the frequency and line width of the E_g Raman peak blue shift and increase, respectively. At the crystallite size of 6 nm, the Raman peak exhibits a significant asymmetric broadening. Obviously, the calculated results based on the phonon confinement model are in qualitative agreement with our experimental data. The main E_g Raman modes of the TiO₂ nano crystals annealed at various temperatures are displayed in Figure 3. The broadening of the peak becomes important only for the smallest crystals, when the confinement involves the phonons far from the zone center. When the size is <3–4 nm the model cannot be used, as details of the dispersion curve and of the shape of the Brillouin zone becomes critical. The calculated broadening and blue shift of the Raman peak fairly describe those observed in nano crystals with different sizes. This indicates that the phonon confinement is the dominant mechanism responsible for the blue shift of the Raman peak in small-sized nano crystals, and the non-stoichiometry has only a little influence on the blue shift.

Figure 2. (Colour online) Raman intensity calculated using phonon confinement model for different crystal sizes.

Figure 3. (Colour online) Raman modes E_g of the TiO₂ nanoparticles annealed at various temperatures.

TiO₂ samples were annealed at various temperatures for 3 h. Figure 4 shows the X-ray diffraction patterns for TiO₂ as a function of annealing temperature. The diffraction peaks corresponds to anatase phase. From 300 to 450°C only peaks related to anatase structure were evident. Existence of strong crystalline peaks at 2θ values of 25.20°, 37.80°, 48.04°, 53.890° and 62.68° corresponding to the crystal planes of (101), (004), (200), (105) and (204) indicates the formation of anatase TiO₂ (JCPDS card No. 21-1272). As the annealing temperature increases above 300°C the intensity of (101) peak increases and the line width of the same decreases. This indicates that after annealing, the crystallinity of the sample becomes better and the crystallite size increases.

Figure 4. XRD images of TiO₂ nanoparticles annealed at different temperatures: (a) as prepared; (b) annealed at 300°C; (c) annealed at 350°C; (d) annealed at 400°C and (e) annealed at 450°C.

The TEM images of TiO₂ nanoparticles annealed for 3 h at different temperature are given in Figure 5. TEM images confirm the formation of spherical particles with uniform particle size. It is clearly seen that as the annealing temperature increases the average particle size increases. The increase in the average particle size is very little up to about 450°C. This agrees well with the results of Siegel et al. [17]. Grains with much agglomeration are clearly observable from the images of low temperature heat treated samples. The particle size of TiO₂ nanoparticles varies from 6 to 12 nm. The SAED analyses confirmed the formation of tetragonal structure of TiO₂. The particle size calculated from TEM agrees well with the particle size calculated in Raman spectroscopy.

Figure 5. TEM images of TiO₂ nanoparticles annealed at different temperatures.

The particle size distribution is shown in Figure 6. For the as prepared TiO₂, the size of particle is around 7 nm (60%). It is interesting that with the temperature rising, the size of particles increases. The size is around 8 nm (70%) at 300°C, while that is around 9 nm (75%) at °C, around 10 nm (78%) at 400°C and around 12 nm (80%) at 450°C. All the samples have a narrow size distribution.

Figure 6. Particle size distributions of TiO₂ nanoparticles annealed at different temperatures analysed by DLS.

Raman spectroscopy analysis shows that the TiO₂ nano crystals contain only tetragonal anatase phases. The evolution of the anatase phase in theTiO₂ nano crystals can be well characterised by the change of the lowest-frequency E_g Raman mode with annealing treatment. Phonon confinement has been found to be the main cause of the broadening and the blue shift of the main Raman peak in TiO₂ powders of pure anatase nano crystals. The particle size analysis by XRD, TEM and DLS is in agreement with the Raman spectroscopy analysis.

4. Conclusion

TiO₂ nanocrystals have been synthesised through chemical route. XRD, TEM, and Raman spectroscopy results confirm a single-phase anatase TiO₂ nano crystal. The evolution of the anatase phase in the TiO₂ nano crystals can be well characterised by the change of the lowest-frequency E_g Raman mode with annealing treatment. The phonon confinement has been found to be the main cause of the broadening and the blue shift of the main Raman peak in TiO₂ powders of pure anatase nano crystals. A combined mechanism involving phonon confinement and non-stoichiometry effects is proposed to well explain the blue shift and broadening of the lowest-frequency E_g Raman mode in TiO₂ nano crystals. The knowledge of the phonon dispersion curve in anatase could help in a more quantitative correlation between the band shape and the crystals size. The sizes of the particles obtained from TEM, particle size distribution and Raman scattering are consistent.

Acknowledgements

S. Ramasamy, CSIR Emeritus Scientist, acknowledges the financial support given to carry out this work under CSIR Emeritus Scientist Scheme number 21(0714)/08/EMR-II dated 28-04-2008 G. Devanand Venkatasubbu, CSIR-SRF, acknowledges the financial support given to him by CSIR. The authors V.S. and V.R. are thankful to UGC-UPE programme of Madurai Kamaraj University for the Micro Raman facility. The authors are grateful to Dr. G.S. Avadhani, Department of Materials Engineering, Indian Institute of Science, Bangalore, India for his help to do TEM analysis.