Materials Chemistry and Physics 123 (2010) 791–794

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Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys

Study of dimension dependent diffusion coefficient of titanium dioxide nanoparticles Shree Mishra a,b , Sanjeev K. Gupta a , Prafulla K. Jha a,∗ , Arun Pratap c a b c

Department of Physics, Bhavnagar University, Bhavnagar 364 022, India Tolani F.G. Polytechniqic, Adipur 370 205, India Applied Physics Department, Faculty of Technology and Engineering, The M.S. University of Baroda, Vadodara 390 001, India

a r t i c l e

i n f o

Article history: Received 29 October 2009 Received in revised form 1 April 2010 Accepted 21 May 2010 PACS: 66.30.Dn 61.46 +w

a b s t r a c t In the present paper, we have studied size and dimension effect on diffusion coefficient of nitrogen and platinum doped TiO2 nanoparticle using Arrhenius relation and Lindeman’s criteria under their dynamic limit. The activation energy and melting point decreases with decrease in size. The TiO2 diffused with metal and nonmetal gives rise to (meta-) stable structure and mid-gap state helps to increase surface to volume ratio and quantum confinement effects, and results in the increase of diffusion coefficient. The calculated diffusion coefficient of undiffused TiO2 with size is in good agreement with available experimental data. © 2010 Elsevier B.V. All rights reserved.

Keywords: Nanostructures Theoretical Diffusion Thermal properties

1. Introduction Recently, there has been great interest in the nanocrystals due to both fundamental scientific interest and technological applications. Among the various shape and size dependent properties arising due to quantum confinement and large surface to volume ratio, the thermal properties such as surface energy, diffusion coefficient, melting temperatures represent an important class of properties which raises expectation for many novel applications in devices [1–5]. The melting temperature of nanoparticles is lower than the bulk and varies with size and shape. Further, it depends on the matrix/particle interface, which corresponds to superheating if matrix/particle interface is coherent or semicoherent and to supercooling if matrix/particle interface is non-coherent. For technological point of view, the knowledge of thermodynamical properties at nanoscale is necessary for the reliability of the device [6–10]. Titanium dioxide (TiO2 ) is a popular material with many applications due to its high permittivity, refractive index, efficiency, low cost, chemical inertness, photocatalytic, photostability and capability of decomposing a wide variety of organics [11–17]. The very important use of TiO2 as a photocatalyst has been hampered by its

∗ Corresponding author. Present address: Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100 190, China. Tel.: +91 278 2422650. E-mail addresses: [email protected], [email protected] (P.K. Jha). 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.05.061

wide band gap (3.2 eV for anatase TiO2 ) and it requires an ultraviolet radiation (UV) for its photocatalytic activation. Diffusion is an efficient process which shifts the optical response of TiO2 from the UV to the visible spectral range, i.e. to longer wavelength and gives maximum utilization of the solar induced photocatalytic properties of this material. Further, the diffusion for any TiO2 photocatalytic system helps in controlling electron–hole transport which may be hindered by any material interfaces, and hence it may lead to great interest in TiO2 based electronics [14–16]. The shortcoming of TiO2 can be overcome by diffusing certain element like metal or nonmetals in TiO2 which shows different properties like ferromagnetism in metal doped TiO2 [18], capacity to absorb visible light, decrease in working temperature, increase in field emission, etc. This may be due to the formation of new dbands as a consequence of the interaction of interstitial metal ions in the TiO2 lattice with host material. The metal dopant, which acts as an electron–hole recombination centers, photocatalyst tends to decrease [18]. Further, it is well known that the diffusion activation energy decreases which results an increase in the diffusion coefficient of atoms in nanocrystals than its bulk counterpart [19–22]. The band gap of TiO2 can be narrowed by doping it with nonmetals like O [23], C [24–26] and N [27,28], which can replace the lattice oxygen atoms. The size and shape dependent diffusion coefficient function is an important parameter for any phase transition process, and is related to the thermodynamical properties of material. The under-

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standing of this kind of scientific problem is a challenge particularly in the field of nanotechnology. Until now, to the best of our knowledge there is no study with consideration of shape and size on diffusion coefficient in the case of TiO2 nanocrystals particularly to see the effect of diffusion of any metal/nonmetal nanoparticles in the TiO2 nanocrystal. In the present work we propose to study, theoretically the effect of size and shape on diffusion process using a simple-empirical method within thermodynamical limit. In order to understand the effect of diffusion of metal/nonmetal in TiO2 , diffusion activation energy, diffusion time and diffusion coefficient are also calculated at the nanoscale in undiffused and diffused TiO2 . The size effect on the diffusion activation energy is analyzed through the size effect on the melting temperature. In the present study, we have considered the doping of nitrogen and platinum nanoparticles in the TiO2 nanoparticle. 2. Methodology and computation The size-dependent properties of the kinetic parameters are so useful, a unique attempt to establish a quantitative model for describing the size and shape dependent thermal properties using surface/volume ratio is necessary. To model quantitatively the size and temperature dependence of the diffusion coefficient D(r, T) with r being the radius of nanoparticles or grains and T being the temperature, the diffusion coefficient D(r, T) can be written as [29]: D(r, T ) = D0 exp

 −E(∞) 

(1)

RT

where D0 is a pre-exponential factor, E(∞) is thermal activation energy without considering size and shape effect (i.e. for bulk crystal), R is the ideal gas constant and T is temperature. The diffusion coefficient in Eq. (1) does not need any adjusting parameters. Thermal activation energy E(∞) which is different for different diffusion process is related to the melting temperature T(∞) via a coefficient C [30,31]. E(∞) = CTm (∞)

(2)

The coefficient C depends on a class of materials and type of diffusion process [30]. To obtain the diffusion coefficient at nanoscale, Eq. (1) can be modified by considering the two main responsible properties: (1) high surface to volume ratio and (2) quantum confinement effect. Considering no size effect on C, we can write the thermal activation energy at the nanoscale as [31], E(r) = CTm (r)

(3)

Tm (r) E(r) = E(∞) Tm (∞)

(4)

At the nanoscale, the activation energy decreases when the size decreases [31], which implies that diffusion is more activated at the nanoscale, hence we can write Eq. (1) as [32]



 T (r)  m Tm (∞)

/RT



(5)

To find a convenient means for correlating Tm (r)/Tm (∞) in Eq. (4), we can find Tm (r)/Tm (∞) function by considering the average mean square displacement (msd) of atoms in a nanocrystal  2 (r) using Lindemann’s criterion as [32] Tm (r) = exp T (∞)

 −2S (∞)  vib [3R(r/r0 − 1)]

condition for different surface states which in the case of nanocrystals is equal to unity [32]. Using Eqs. (6) and (5) we can find the expression for diffusion coefficient as, D(r, T ) = D0 exp

 −E(∞) RT

exp

 −2S (∞) vib 3R

1 r/r0 − 1



(7)

The diffusion time,  diff is the quantity which determines the rate of diffusion, critical temperature and critical stress and we can express it as [30], diff =

L2 , D

(8)

where  is a numerical constant equal to 2, 4, 6 for one, two, or three dimensions respectively. L is diffusion length, i.e. displacement of one atom by diffusion during a time  diff . To obtain a statistical limit, we have considered the relative temperature fluctuation inside a cube and the size limit nearly equal to 2 nm for the application of thermodynamics. Therefore any shape effect due to thermal fluctuation above 3% are not addressed in this work and other methods such as molecular dynamics simulation and density functional calculation can be considered for such small nanostructures [30]. 3. Results and discussion

Dividing Eq. (3) by Eq. (2), we get

D(r, T ) = D0 exp −E(r)

Fig. 1. Tm (r)/Tm (∞) functions of TiO2 denoted as a solid lines in terms of Eq. (6). The related parameter in Eq. (6) are h = 0.3768 nm [38], Tm (∞) = 1200 K and Sm (∞) = 126.60 J mol−1 K−1 [39].

(6)

where Svib (∞) is the bulk melting entropy and essential contribution on the overall bulk melting entropy, r0 = c1 (3 − d)h, where d is extended for different dimension with d = 0 for nanosphere, d = 1 for nanowires and d = 2 for thin films, c1 is added as an additional

The present paper reports the calculated results on the size and shape dependant thermal properties such as melting temperature, diffusion coefficient, and diffusion time of TiO2 nanoparticles. We present the variation of melting temperature with size for the TiO2 nanoparticles of different dimension (shapes) in Fig. 1 and observe that the melting temperature of TiO2 nanoparticles decreases as the size of the particle decreases similar to earlier results on some metal nanoparticles [33–35]. We observe a considerable difference in the behavior of melting temperature of nanoparticle of different dimensions in the case of particles of smaller size. As the particle size increases, melting temperature increases and approaches to bulk melting temperature point, of 1160 K irrespective of the shape. We find a rapid drop of the melting temperature below the size nearly 5 nm which is consistent with earlier findings [33–35]. We further observe that the melting temperature which decreases with size is minimum for 0D structure and maximum for 2D structure, for the same size. This is due to the fact that the size of nanoparticles decreases, surface to volume ratio increases, so there are more number of surface atoms which are loosely bound and are

S. Mishra et al. / Materials Chemistry and Physics 123 (2010) 791–794

Fig. 2. D(r, T) function of TiO2 as a function of size. The related parameter in Eq. (7) are h = 0.3768 nm [37], Tm (∞) = 600 K and Sm (∞) = 78.22 J mol−1 K−1 [40], D0 = 2.75 × 10−5 m2 s−1 [41], and E(∞) = 18.33 kJ mol−1 [41]. Inset figure is the plot of diffusion coefficient of TiO2 as a function of size for 2D. The parameter are h = 0.3768 nm [38], Tm (∞) = 453 K, Sm (∞) = 78.22 J mol−1 K−1 [40], D0 = 2.75 × 10−5 m2 s−1 [41], and E(∞) = 18.33 kJ mol−1 [41]. Inset diffusion coefficient of TiO2 at 453 K is also shown.

responsible for the melting of nanoparticles. As far as the dimension dependent melting temperature is concerned, the melting for 0D structure is faster than other structured (dimension) material. We present size and dimension dependent coefficient of TiO2 nanoparticles in Fig. 2 and find that the diffusion coefficient in the case of TiO2 nanoparticles (spherical) is more than the nanostructure of other dimensions such as wire and films due to the fact that the activation energy as well as melting point temperature for spherical particle is lesser than the corresponding cylindrical wire (1D) and thin film (2D) structures. This suggests that the reaction or diffusion can be made faster in the case of spherical nanoparticles. The size and shape dependent activation energy shows the same behavior as of melting temperature. We observe a remarkable feature that the diffusion coefficient is nearly equal in the case of spherical and cylindrical structures for smaller size resulting from the shape instability effect due to the thermal fluctuation [30]. We could not compare the present result on the size and shape dependent diffusion coefficient with any experimental data due to their unavailability. However, to check the accuracy of approach we include the effect of temperature in the calculation of size dependent diffusion coefficient for the comparison with available experimental data at temperature 453 K (inset of Fig. 2). We observe a reasonably good agreement between calculated and only available experimental size dependent diffusion coefficient in the case 2D nanostructure for the size of 14 and 19 nm [36]. We present the diffusion coefficient of nitrogen-diffused TiO2 for different dimensions and sizes in Fig. 3. Nitrogen doping seems to be more attractive among all anionic elements because of its comparable atomic size with oxygen, small ionization energy, metastable center formation and stability [37–40]. We observe from Fig. 3 that the diffusion coefficient depends on both dimension and size of the TiO2 nanoparticles. We find that the diffusion coefficient increases with decrease in the size of the TiO2 nanoparticles. Furthermore, we observe a remarkable increase in the case of doped TiO2 nanoparticles. This increase in diffusion coefficient of nitrogen-diffused TiO2 is the consequence of the decrease in melting temperature and activation energy resulting from the decrease in band gap of TiO2 . The nitrogen octet rule is satisfied without

793

Fig. 3. D(r, T) function of N diffusing into anatase TiO2 shown as the solid lines in terms of Eq. (7) where r is the radius of the grain size of TiO2 . The parameter in Eq. (7) is as follows: h = 0.3768 nm, for nitrogen sublimation entropy Sc for N is used to substitute Sm(∞) with Sc = 36.106 J mol−1 K−1 [39], D0 = 7.46 × 10−7 m2 s−1 , and E(∞) = 78.3 kJ g atom−1 , and T = 573 K [31].

inducing any significant structural change as the nitrogen occupies the oxygen sites. In Fig. 4, we present the diffusion coefficient of TiO2 nanoparticles diffused with platinum (Pt) nanoparticles of different shapes. We have calculated the diffusion coefficient in the present case by considering the entropy and pre-exponential factor for different shape of Pt nanoparticles from the experimental work of Narayana et al. [37] which already considers the dimension effect d = 0. We observe from Fig. 4 that the diffusion coefficient rapidly increases in the case of diffused cubic Pt nanoparticles below the size of 4 nm. However, we do not find any variation for the diffusion coefficient in the case of tetrahedral shaped Pt nanoparticles. This may be due to the fact that the tetrahedral particle has sharp edges and corners corresponding to either very high value of activation energy or very low value of activation energy [37]. We know that in the case

Fig. 4. D(r, T) function of Pt diffusing into anatase TiO2 shown as the solid lines in terms of Eq. (7) where r is the radius of the grain size of TiO2 . The parameter in Eq. (7) is as follows: h = 0.3768 nm, For Pt. having tetrahedral shape Sm(∞) = 2.18 J mol−1 K−1 [37], D0 = 3.9 × 10−7 m2 s−1 [42] and E(∞) = 14 kJ g atom−1 [37], and for Pt having cubic shape Sm(∞) = 29.60 J mole−1 K−1 [37], D0 = 3.9 × 10−7 m2 s−1 [42] and E(∞) = 26.4 kJ g atom−1 [37]. Similarly for Pt having tetrahedral shape Sm(∞) = 21.37 J mol−1 K−1 [37], D0 = 3.9 × 10−7 m 2 s−1 [42] and E(∞) = 22.6 kJ g atom−1 [37].

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other, i.e. diffusion time increases as size and dimension of TiO2 nanoparticle decreases. 4. Conclusion In summary, we have systematically investigated the size and dimension dependent diffusion coefficient of undoped and doped TiO2 nanoparticles. We find that there is suppression in diffusion coefficient of TiO2 nanoparticles as its size or dimension decreases. The diffusion coefficient starts increasing near about 10 nm, however, the change is significant only for smaller size and dimension especially in the case of diffused TiO2 nanoparticles. The inverse relation between diffusion time and diffusion coefficient is also observed. Diffusion coefficient of TiO2 nanoparticles is in well agreement with the available experimental data. Acknowledgments

Fig. 5. D(r, T) function of Pt diffusing into anatase TiO2 shown as the solid lines in terms of Eq. (7) where r is the radius of the grain size of TiO2 . The parameter in Eq. (7) is as follows: h = 0.3768 nm, for Sm(∞) = 21.37 J mol−1 K−1 [37], D0 = 3.9 × 10−7 m2 s−1 [42] and E(∞) = 22.6 kJ g atom−1 , and T = 573 K [37].

The authors acknowledge financial support from Department of Science and Technology, New Delhi and University Grants Commission, New Delhi. One of the authors (SM) acknowledges the support and encouragement from the college administration. References

of cubic nanoparticle most of its atoms are located on (1 0 0) facet and are not tightly bound results in to a high value of activation energy and entropy of activation. Similarly in the case of spherical nanoparticles most of the atoms are located on (1 1 1) and (1 0 0) facets with edges at the interface of these facets [37]. We observe a remarkable feature in Fig. 4 that the diffusion coefficient is between cylindrical and tetrahedral shape is due to the fact the activation energy of spherical nanoparticles is between cylindrical and tetrahedral shape which in our view is due to the fact of having similar trend in the activation energy. We present the calculated diffusion coefficient of platinum diffused TiO2 for 0D, 1D and 2D in Fig. 5 and observe a similar behavior as in the case of nitrogen-diffused TiO2 nanoparticle. However, we note that the diffusion coefficient in the case of platinum diffused TiO2 is more than the nitrogen-diffused TiO2 in agreement with the experiment [37]. This is due to the fact that the activation energy of platinum is lower than the nitrogen which results to higher value of diffusion coefficient in the case of platinum diffused TiO2 as compare to the nitrogen-diffused TiO2 . We present the diffusion time for 1D, 2D and 3D nanostructures in Fig. 6 obtained using Eq. (8) and observed that the diffusion time and dimension of nanostructures are inversely proportional to each

Fig. 6. Diffusion time of TiO2 as a function of size and dimension.

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Thermal Analysis of Nanocrystallization of Anatase TiO2 Shree Mishraa, c, Sanjeev K. Guptaa, Rucha Desaia, Prafulla K. Jhaa and Arun Pratapb a Department of Physics, Bhavnagar University, Bhavnagar-364 022, India b Condensed Matter Physics Laboratory, Applied Physics Department, Faculty of Technology and Engineering, The M. S. University of Baroda, Vadodara-392 001, India. c Tolani F. G. Polytechnique, Adipur-370 205, India

Abstract. In the present paper, nanosized titanium dioxide (TiO2) is synthesized by wet-chemical technique, and characterized by x-ray diffraction (XRD), Fourier transform infrared reflectance (FTIR) and differential scanning calorimeter (DSC) thermograms. DSC thermogram shows a definite exothermic peak indicating the transformation from amorphous to crystalline phase. The FTIR spectra shows main peak around 1384 cm-1, which is attributed to the Ti-O bond in both the i.e. amorphous and crystalline samples.

Keywords: Titanium dioxide, X-ray diffraction (XRD), Fourier transform infrared reflectance (FTIR) PACS: 61.05.cp, 61.46.Hk, 65.80.-g

INTRODUCTION Titanium dioxide (TiO2) is a wide band gap semiconductor, crystalline as anatase, rutile or brookite. TiO2 is highly attractive material for variety of industrial applications such as solar cells, photocatalysis, charge spreading devices, chemical sensors, microelectronics, and electrochemistry, and dye sensitized solar cell etc [1-3]. However, the challenge for so-called nanotechnologies is to achieve perfect control of nanoscale-related properties. Therefore, scientists have focused on the nucleation and growth of titanium dioxides since these processes may involve changes in phase stability that accompanies the transition from nanoparticles to bulk phase. In recent, a continued focus on titanium dioxide has been paid, because of its efficiency, low cost, chemical inertness, photostability and capable of decomposing a wide variety of organics [3]. The use of TiO2 as a photocatalyst has been hampered by its wide bandgap (3.2 eV for anatase TiO2) and it needs ultraviolet radiation for its photocatalytic activation. An efficient process which shifts the optical response of TiO2 from the UV to the visible spectral range i.e. to longer wavelength give maximum utilization of the solar induced photocatalytic properties of this materials, which also led to the development of an photovoltaic devices for dye-sensitized solar cell (DSSC) [3, 5]. For the low-cost alternative to conventional semiconductor device, much effort has been put on the investigation and development of the materials. The nanoparticles of TiO2 posses superior quality than its bulk counterpart and hence is a better candidate to be used in the application of solar cell and photocatalytic properties of TiO2. Further, the TiO2 nanocrystal in its anatase phase has higher photocatalytic activity than other phases and its bulk counterpart [4]. The anatase nanocrystals is easily prepared in a range of sizes, shapes, and forms (as nanocrystals, rods, wires, etc.) by using a varieties of physical and chemical methods. It is important to develop synthesis methods in which the morphology and the

CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE OF EACH PAPER CP1249, 5th National Conference of Thermophysical Properties (NCTP-09), edited by A. Pratap and N. S. Saxena © 2010 American Institute of Physics 978-0-7354-0796-1/10/$30.00

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structure of nanotitania can be controlled or the fine structure can be mimicked at the nanoscale, owing to its technological importance, which is due to its strong oxidizing power, chemical inertness, and non-toxicity [5-7]. Recently we have reported structural characterizations of TiO2 nanocrystals, synthesized using a cost effective chemical route [8]. XRD, TEM, Raman spectroscopy and photoluminescence (PL) results confirm a single phase anatase TiO2 nanocrystal. The phonon confinement was found the main cause of the broadening and blue shift of the main Raman peak in anatase nanocrystals. The present paper effect of annealing temperature of the amorphous titanium dioxide is studied using x-ray diffractogram, differential scanning calorimetry (DSC) and Fourier transform infrared reflectometry (FTIR) techniques. Determination of crystallization of kinetics through DSC has been widely utilized and discussed in the literature. The purpose of DSC is to ascertain the mechanism of crystallization and separate the activation energy of crystallization.

EXPERIMENTAL The titanium dioxide nanoparticles were synthesized using wet chemical technique. The analytical grade titanium tetrachloride (TiCl4) was used to prepare nano titanium dioxide particles. Other chemicals used were analytical grade ethylene glycol, polyethylene glycol and sodium acetate. With vigorous stirring titanium chloride (2 ml) was drop wise mixed in ethylene glycol and continued stirred for 10 mins. The reaction was exothermic and carried out in 100 ml beaker. This mixed precursor was heated to 333K. On refluxing white precipitates of titanium were observed, further it was collected by centrifugation. In order to remove chlorine impurities from this white particles, they were washed several times using warm water followed by acetone wash. Finally acetone wet particles were dried naturally. Structural characterization was carried out using D8 Advanced model powder x-ray diffractometer (Bruker) at room temperature. X-ray spectra were measured in 2theta range of 200 to 700 in steps of 0.020 with scan rate of 2 steps/sec. Infrared spectra were recorded on the powder samples in KBr matrix using thermonicolate FTIR spectrophotometer model IR200 at 300 K. Spectra were recorded for the wavenumber range of 400 to 4000 cm-1. Diffused scanning calorimetric (DSC) measurement was carried our using Shimadzu DSC-50 instrument. Sample was sandwiched in aluminum-sealed cell. Samples were scanned in the temperature range of 317 K to 890 K with scan rate of 10 K/min.

RESULTS AND DISCUSSION Structural phase determination is carried out using x-ray diffraction (XRD) measurement. Figure 1 shows XRD pattern of an as prepared sample (sample 1). It shows broad hump in the range of 200 to 370, which indicates the amorphous nature of material. In order to convert amorphous nature into crystalline phase, powder sample was annealed at 623 K for 2 hours, and henceforth sample is designated as sample 2. 1600

Sample 2

(204)

(112)

800

(211)

1200

(200)

(101)

Intensity (arb. unit)

TiO2

400 Sample 1 0

20

30

40 50 2θ (degree)

60

70

FIGURE 1. XRD spectra of samples 1 and 2.

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The XRD pattern of sample 2 shows all the lines corresponding to anatase crystalline phase and indexed accordingly. Particle size is calculated using Debye-Scherrer formula given by,

DX =

0 .9 λ BCosθ

(1)

Where, λ is X-ray wavelength, here 1.5414 Å, 0.9 is the Scherer factor, B is full width at half maxima and the Bragg angle. The calculated X-ray crystallite size for sample 2 is ~ 15 nm.

θ

is

FIGURE 2. DSC thermograms of sample 1 and 2.

Figure 2 shows the differential scanning calorimeter (DSC) thermograms of sample 1 and sample 2. DSC data of sample 1 shows two major peaks around 405 K and 666 K, which indicate the endothermic and exothermic reactions respectively. The thermogram of sample 1 shows definite exothermic peak indicating the transformation from amorphous to crystalline phase. Thermal energy required for the phase transformation is -6.18 kJ/g and 2.15 kJ/g for respective endothermal and exothermal peak area. In sample 2 typical endothermic peak is observed, however no any other impurity and/or secondary phase is observed. Thermal energy involved in the process is -694.25 J/g, which is one order to magnitude less than the sample 1. This shows that the phase formation process is complete in sample 2. These results of sample 1 and 2 are in agreement with the XRD results. The peak crystallization temperature is found to be 666 K. As the sample 2 is already in the crystalline state it does not exhibit any peak corresponding to crystallization. Other noteworthy features in the DSC thermograms of these two samples are the endothermic events at 405 K and 365 K for samples 1 and 2 respectively. The Fourier transform infrared reflectance (FTIR) is used to analyze the sample 1 and 2 as shown in figure 3. The main peak observed around 1384 cm-1 is attributed to the Ti-O bond in both the samples. The spectra exhibit that with increasing annealing temperature sample becomes more crystalline, hence a small shoulder around 1353 cm-1 is converted into a peak in sample 2. The broad hump observed > 2000 cm-1 is attributed to the presence of OH- ion on the surface of the particles.

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Transmittance (%)

60

50

2 40

30

1 20

500

1000

1500

2000

2500

3000

3500

4000

-1

Wavenumber (cm ) FIGURE 3. FTIR spectrum of TiO2 nanocrytals. samples 1 and 2.

CONCLUSION Nanocrystals of anatase TiO2 have been synthesized through a cost effective chemical route. DSC thermogram provides consistent crystallization curves and important information regarding crystallization, which is well, agrees with FTIR results and main peak observed around 1384 cm-1 is attributed to the Ti-O bond in both samples indicating formation of TiO2. It can be concluded from the thermogram analysis that the crystallinity increases with annealing time.

ACKNOWLEDGMENTS Authors are thankful to Department of Science and Technology, Govt. of India, UGC-New Delhi, India, DAEBRNS, Govt. of India, for financial assistance.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

M. Gratzel, Nature (London) 414, 338 (2001). X. Chen and S. S. Mao, Chem. Rev. (Washington, D. C.) 107, 2891 (2007). Q. Xu and M. A. Anderson, J. Am. Ceram. Soc. 77, 1939 (1994). L. Gao and Q. Zhang, Scr. Mater. 44, 1195 (2001). H. Zhang and J. F. Banfield, J. Phys. Chem. B 104, 3481 (2000). H. Zhang and J. F. Banfield, J. Mater. Chem. 8, 2073 (1998). A. Pottier, S. Cassaignon, C. Chanéac, F. Villain, E. Tronc and J. Jolivet, J. Mater. Chem 13, 877 (2003). S. K. Gupta, R. Desai, P. K. Jha, S. Sahoo and D. Kirin, J. Raman Spect. 40, xxxx (2009). DOI 10.1002/jrs.2427. S. K. Gupta, R. Desai, P. K. Jha, ICMAT proceedings, A01907-03290 (2009).

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Proceedings of the 54th DAE Solid State Physics Symposium (2009)

Diffusion coefficient of TiO2 structure diffused with metal/non-metal nanoparticles Shree Mishra1,2, Sanjeev K. Gupta1, Prafulla K. Jha1 and Arun Pratap3 1

Department of Physics, Bhavnagar University, Bhavnagar-364 022, India 2 Tolani F. G. Polytechniqic, Adipur-370 205, India 3 Condensed Matter Physics Laboratory, Applied Physics Department, Faculty of Technology & Engineering, The M. S. University of Baroda, Vadodara-392 001, INDIA. Email: [email protected] Abstract Size and dimension effect on diffusion coefficient of TiO2 nanoparticle diffused with nitrogen and platinum of different shape and size is studied by using the Arrhenius relationship d Lindman’s criterion. It is found that activation energy and melting point decreases with decrease in size which corresponds to increase in diffusion coefficient and decrease in diffusion time. However, diffused with metal and nonmetal give rise to (meta-) stable structure and mid-gap states helps to increase surface to volume ratio and quantum confinement effects, responsible for further increase in diffusion coefficient.

METHODOLOGY AND COMPUTATION We have calculated diffusion coefficient of doped and undoped TiO2 nanostructure using Arrhenius equation and Lindman’s criterion which can be written as [2-3],

  E ( )   2S vib () 1  D(r , T )  D0 exp  exp   3R r / r0  1    RT Where D0 is a pre-exponential factor, E() is thermal activation energy without considering size and shape effect, R is the ideal gas constant and T is temperature, Svib () is the bulk melting entropy and essential contribution on the overall bulk melting entropy, r0=c1(3-d)h, where d is extended for different dimension with d = 0 for nanosphere, d = 1 for nanowires and d = 2 for thin films, c1 is added as an additional condition for different surface states, in the case of nanocrystals c1 =1 [7]. -4

10

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The TiO2 is a hot material for researcher due to its efficiency, low cost, chemical inertness, photocatalytic, photostability and capable of decomposing a wide variety of organics. Diffusion is an efficient process which shifts the optical response of TiO2 from the UV to the visible spectral range i.e. to longer wavelength and give maximum utilization of the solar induced photocatalytic properties of this material. Further, the diffusion for any TiO2 photocatalytic system helps in controlling electron-hole transport which may be hindered by any material interfaces, and hence it may lead to great interest for TiO2 based electronics. Further, it is well known that there are lower diffusion activation energy of atoms in nanocrystals or nanostructured materials and thus larger diffusion coefficient than the corresponding bulk counterpart due to the increase of surface/volume ratio of the nanocrystals or nanostructured materials [3]. The size and shape dependent diffusion coefficient function is an important parameter for any phase transition process, which is related to the thermodynamical properties of material. The understanding of this kind of scientific problem is a challenge particularly in the field of nanotechnology. Until now, to the best of our knowledge there is no study with consideration of shape and size on diffusion coefficient in the case of TiO2 nanocrystals particularly to see the effect of diffusion of any metal/non-metal nanoparticle [4-7].

D [m s ]

INTRODUCTION

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Figure 1: D(r, T) function of TiO2 as a function of size. Inset figure is the plot of diffusion coefficient of TiO 2 as a function of size for 0-D, 1-D and 2-D. The diffusion time can be calculated by using the relation diff = L2 /  D, where  is a numerical constant equal to 2, 4, 6, for one, two and zero dimensions respectively. L is diffusion length i.e. displacement of one atom by diffusion

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figure that the diffusion time and dimension of nanoparticle are inversely proportional to each other, i.e. diffusion time increases as size and dimension of TiO2 nanoparticles decreases. tetrahedral cubic spherical

1E-6 1E-7

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during a time diff. For our calculation, we have taken the parameters: h=0.3768nm, Tm()=600K, Sm()=78.22Jmole-1K-1, D0=2.7510-5m2sec-1 and E()=18.33KJmol-1 (for undoped TiO2 nanoparticle) and Tm() =453 K (inset of Fig. 1), sublimation entropy for N, is taken Sc=36.106Jmole-1K-1, D0=7.4610-7m2sec-1 and E()= 78.3 KJg-atom-1, T=573K (for nitrogen diffused TiO2 nanoparticle). For Pt having tetrahedral shape Sm()=2.18Jmole-1K-1, D0=3.910-7m2sec1 , and E()=14 KJg-atom-1, and for Pt having cubic shape Sm()=29.60 Jmole-1K-1 and E()= 26.4 KJg-atom-1, and Pt having tetrahedral shape Sm()=21.37Jmole-1K-1, and E()= 22.6 KJg-atom -1 (for Pt diffused TiO2 nanoparticle).

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Figure 3: D(r, T) function of Pt diffusing into anatase TiO2 having tetrahedral, cubic and tetrahedral shape. 1E15 1E14 1E13

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The Fig. 1 presents diffusion coefficient of undoped TiO2 of different structures, diffusion coefficient for 0-D (spherical shape) is lesser than the corresponding 1-D and 2-D. The Fig. 1 reveals that the diffusion can be made faster in the case of spherical TiO2 nanoparticle. Further, in order to increase diffusion coefficient more and to shift optical response of TiO2, the TiO2 nanostructure is diffused with metal/nonmetal nanoparticles of different structures and shapes.

1-D 2-D 3-D

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CONCLUSION

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Figure 2: D(r, T) function of N diffusing into anatase TiO2. Fig. 2 and Fig. 3 present diffusion coefficient of TiO2 diffused with nitrogen and platinum respectively having different dimensions and structures. The behavior of diffusion coefficient is similar in both cases however, we found that the diffusion coefficient of platinum diffused TiO2 is more. This is due to the fact that the activation energy of platinum is lesser than nitrogen. The present results on the size and shape dependent diffusion coefficient could not be compared with any experimental data due to their unavailability. However to check the accuracy of approach we included the effect of temperature in the calculation of size dependent diffusion coefficient to compare with the available data at temperature 453 K. The plot is presented in the inset of Fig. 1 which shows a reasonably good agreement with the only available two experimental points [7]. Fig. 4 presents diffusion time for 0-D, 1-D and 2-D nitrogen doped TiO2. It is clear from the

Here, we report suppression in diffusion coefficient of TiO 2 as size of nanoparticle or dimension decreases. We note that the increment is in diffusion coefficient starts near about 10 nm but very remarkable for smaller size and dimension, specially when TiO2 is diffused with some metal and nonmetals. The inverse relation between diffusion time and diffusion coefficient is verified. ACKNOWLEDGEMENT The financial support from DST and UGC, New Delhi is highly appreciated. One of us (SM) is thankful to principal for support and encouragement. REFERENCES 1. H. Gleiter, Acta Mater. 48, 1 (2000). 2. Q. Jiang and C. C. Yang, Current Nanoscience 4, 179 (2008). 3. Jiang, S. H. Zhang and J. C. Li, Solid State Commun. 130, 581 (2004). 4. Q. Jiang, X. H. Zhou, M. Zhao, J. Chem. Phys. 117, 10269 (2002). 5. S. K. Gupta, Mina Talati, P. K. Jha, Mater. Sci. Forum, 570,132 (2008). 6. W. H. Qi, Physica B 368, 46 (2005).

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7. Narayana and M. A. (2008).

El-Sayed, Nano Lett. 4, 1343

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Proceedings of the 54th DAE Solid State Physics Symposium (2009)

Size Dependent Raman Shift and Linewidth of Silicon Nanocrystals Sanjeev K. Gupta, Venu Mankad, Shree Mishra, Sanjay D. Gupta and Prafulla K. Jha Department of Physics, Bhavnagar University, Bhavnagar, 364 022, India Email: [email protected] Abstract An improved phonon confinement model which includes a new phonon dispersion curve and a confinement function and size distribution function is developed for the calculation of size dependent Raman spectra of the silicon (Si) nanocrystals. The model is capable in simultaneous calculation of the Raman shift, intensity and linewidth. The rapid rise in the redshift and linewidth for relatively smaller Si nanocrystals are more accurately reported then in previous calculations. The asymmetric behavior of Raman spectra is also obtained from the present model.

INTRODUCTION

I    n   1 C q  L, q dq

In recent years the finite size effects on the Raman spectrum of a nanocrystal silicon have attracted considerable interest due to the role of Si in the current semiconductor industry and potential technological applications resulting from the optical properties of Si quantum dots [1-3]. When the size of Si reduces in the scale to few nm, its opto-electronic properties changes dramatically over its bulk value. However, most of the efforts are dedicated to interpret the experimental Raman spectra particularly in terms of confinement effect, which in 0D systems are difficult to evidence experimentally by Raman shift in contrast to 2D and 1D nanostructures. The quantization effect which is govern by many factors such as fluctuation in size, orientation and shape contributes in broadening of phonon peaks. Therefore, the majority of the published studies refer phonon confinement as the main mechanism responsible for the observed size-dependant Raman feature and a phonon confinement model (PCM) [46] has been proposed to interpret the Raman spectra. However, there are some reports on the limitations of the phonon confinement model (PCM) [5-7]. But these models do not satisfactorily describe the phonon confinement and are fail in explaining the experimental data particularly the shift and linewidth of the peak simultaneously [5-8].

Where the integral is extended to the entire first Brillouin zone, ω is the Raman frequency, n+1 is the Bose-Einstein factor, C(q) are Fourier coefficients of the phonon wave function and L(ω, q) is the Lorentzian function related to the phonon dispersion curve. The Raman scattering intensity, I(ω), for nanocrystals with the size distribution ρ(L) is given by [7-8],

PHONON CONFINEMENT EFFECT Due to the Heisenberg uncertainty principle, the fundamental q~ 0 (q is the phonon wave vector) Raman selection rule is relaxed for a finite size domain, allowing the participation of phonon away from the Brillouin zone center, also contribute to the Raman lineshape. The phonon uncertainty goes roughly as ∆q ~1/d, where ‘d’ is the quantum dot diameter. Consequently, the Raman spectrum [7-8] is calculated by the following integral over the momentum vector q,

2

  2     c q  d 3 q I      L dL  2   2       q    0 2      

(1)

(2)

Where Γ0 is the FWHM of the Raman line of bulk, ω(q) is the phonon dispersion curve, c(q) is the Fourier coefficients of the vibrational weighting function expanded in the Fourier integral and ρ(L) is the log-normal size distribution, which corresponds to the density of vibrational states, since each particle vibrates with a frequency that is inversely proportional to its diameter ‘D’. The complete model with the inclusion of new ω(q), confinement function and size distribution is presented elsewhere [8]. RESULTS AND DISCUSSION In Fig. 1, we plot the size dependent Raman frequency redshift for Si nanocrystals. This figure also includes the theoretical and experimental data reported from literature for the comparison. The Fig. 1 reveals the close agreement with the experiments in case of both smaller and larger particles. As can be seen from Fig. 1, except the present model none of the earlier models is able to satisfactorily produce the simultaneous observed a higher shift and a rapid increase around 2-3 nm size Si nanoparticles. This is

due to the fact that the present model includes the effect of size distribution and perhaps a most appropriate dispersion curves alongwith the confinement function. The present model is also used to calculate the linewidth of the Raman spectrum.

the way to get a better understanding of phonon confinement in nanoparticles. 30

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Figure 1: Raman line shape of Si as a function of particle size. Various symbols indicate the experimentally and calculated data for comparison. Inset is plot of dispersion curves. Symbols indicate the experimental data. In Fig. 2, we present the size dependent line broadening for Si nanocrystals alongwith the experimental and theoretical data from literature for comparison. An instrumental linewidth FWHM of 3.0 cm-1 is assumed. The present model is in general good agreement with the experimental data and better than the previous calculation similar to the redshift. The rapid rise around 2 nm is also produced well. The slight variation in magnitude which is probably the singular failure of the approach cannot be a drawback particularly in the case of large scatter experimental data. CONCLUSION In summary, we have presented a modified phonon confinement model which includes a new confinement function, size distribution and a dispersion curves representing accurately the most dispersive behavior of phonon branch to explain the size dependent Raman spectra for Si nanocrystals. The results obtained using the present model is in general fair agreement with the experimental data. The success of present calculation supports the idea of inclusion of size distribution in the phonon confinement model. The present calculation is also able to reproduce the asymmetric behavior of Raman spectra. Finally, in our opinion the results of the present work would be useful in

Figure 2: Plot of the Raman linewidth as a function of the Si nanocrystal size. The natural linewidth full width at half maximum (FWHM) Γ= 3 cm-1. Experimental and other calculated data from the literature are displayed for comparison. ACKNOWLEDGEMENTS The authors gratefully acknowledge Dr. A K Arora for fruitful discussion. The financial assistance from Department of Science and Technology, and Department of Atomic Energy, Govt. of India is highly appreciated. REFERENCES 1. M. Ehbrecht, H. Ferkel, F. Huisken, L. Holz, Yu. N. Polivanov, V. V. Smirnov, O. M. Steimakh and R. Schmidt, J. Appl. Phys. 78 (1995) 5302. 2. H. Xia, Y. L. He, L. C. Wang, W. Zhang, X. N. Liu, X. K. Zhang, D. Fang and Howard E. Jackson, J. Appl. Phys. 78 (1995) 6705. 3. A. A. Sirenko, J. R. Fox, I. A. Akimov, X. X. Xi, S. Rumirov and Z. Liliental-Weber, Solid State Commun. 113 (2000) 553. 4. V. Paillard, P. Puech, M. A. Laguna, R. Carles, B. Kohn and F. Huisken, J. Appl. Phys. 86 (1999) 1921. 5. I. H. Campbell and P. M. Fauchet, Solid State Commun. 58 (1986) 739. 6. H. Richter, Z. P. Wang and L. Ley, Solid State Commun. 39 (1981) 625. 7. G. Faraci, S. Gibilisco, P. Russo, A. R. Pennisi and S. La Rosa, Phys. Rev. B 73 (2006) 033307. 8. Sanjeev K. Gupta and Prafulla K. Jha; Solid State Commun. (In Commu.) (2009).