Solid State Communications

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1 Solid State Communications ) Contents lists available at ScienceDirect Solid State Communications journal homepage: X-ray peak broadening analysis in ZnO nanoparticles Rajeswari Yogamalar a, Ramasamy Srinivasan a, Ajayan Vinu b, Katsuhiko Ariga b, Arumugam Chandra Bose a, a Nanomaterials Laboratory, Department of Physics, National Institute of Technology, Tiruchirappalli , India b International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Ibaraki , Japan a r t i c l e i n f o a b s t r a c t Article history: Received 14 April 009 Received in revised form 5 June 009 Accepted 7 July 009 by P. Chaddah Available online 30 July 009 PACS: cc cp 6.0.-x 6.0.dq Keywords: A. Semiconductor B. Chemical synthesis C. Crystal structure C. Dislocation Zinc oxide ZnO) nanoparticles were synthesized by a hydrothermal process at 10 C. XRD results reveal that the sample product is crystalline with a hexagonal wurtzite phase. TEM results confirm that the morphology of the annealed ZnO is rod shaped with an aspect ratio length/diameter) of 3.. We also investigate the crystallite development in nanostructured ZnO by X-ray peak broadening analysis. The individual contributions of small crystallite sizes and lattice strain to the peak broadening in as-prepared and annealed ZnO nanoparticles were studied using Williamson-Hall W H) analysis. All other relevant physical parameters including strain, stress and energy density value were calculated more precisely for all the reflection peaks of XRD corresponding to wurtzite hexagonal phase of ZnO lying in the range 0 65, from the modified form of W H plot assuming the uniform deformation model UDM), uniform stress deformation model USDM) and uniform deformation energy density model UDEDM). The root mean square RMS) lattice strain ε RMS calculated from the interplanar spacing and the strain estimated from USDM and UDEDM are different due to consideration of anisotropic crystal nature. The results obtained show that the mean particle size of ZnO nanoparticles estimated from TEM analysis, Scherer s formula and W H method are highly inter-correlated. All the physical parameters from W H plot are tabulated, compared, and found to match well with the value of bulk ZnO. 009 Elsevier Ltd. All rights reserved. 1. Introduction A perfect crystal would extend in all directions to infinity, so no crystals are perfect due to their finite size. This deviation from perfect crystallinity leads to a broadening of the diffraction peaks. The two main properties extracted from peak width analysis are the crystallite size and lattice strain. Crystallite size is a measure of the size of coherently diffracting domain. The crystallite size of the particles is not generally the same as the particle size due to the presence of polycrystalline aggregates [1]. The most common techniques used for the measurement of particle size, rather than the crystallite size, are the Brunauer Emmett Teller BET), light laser) scattering experiment, scanning electron microscopy SEM) and TEM analysis. Lattice strain is a measure of the distribution of lattice constants arising from crystal imperfections, such as lattice dislocation. The other sources of strain are the grain boundary triple junction, contact or sinter stresses, stacking faults, coherency stresses etc. []. X-ray line broadening is used for the investigation of dislocation distribution. Crystallite size and lattice strain affect the Bragg peak in different ways. Both these effects increase the peak width, the intensity of the peak and shift the θ peak position accordingly. Corresponding author. Tel.: address: acbose@nitt.edu A.C. Bose). However the peak width from crystallite size varies as 1/ cos θ, whereas strain varies as tan θ. This difference in behavior as a function of θ enables one to discriminate between the size and strain effect on peak broadening. The Bragg width contribution from crystallite size is inversely proportional to the crystallite size [3]. W H analysis is a simplified integral breadth method where, both size induced and strain induced broadening are deconvoluted by considering the peak width as a function of θ [4]. Although X-ray profile analysis is an average method, they still hold an unavoidable position for grain size determination, apart from TEM micrographs. This paper accounts for the synthesis of ZnO nanorods by a hydrothermal process. In addition, a comparative evaluation of the mean particle size of ZnO nanorods obtained from direct TEM measurements and from powder XRD procedures is been reported. The strain associated with the as-prepared and annealed ZnO sample at 800 C due to lattice deformation was estimated by a modified form of W H, namely UDM. The other modified models, such as USDM and UDEDM, give an idea of the stress strain relation and the strain ε as a function of energy density u. In UDM, the isotropic nature of the crystal is considered, whereas USDM and UEDM assume that the crystals are of an anisotropic nature. The strain associated with the anisotropic nature of the hexagonal crystal is compared and plotted with the strain resulting from the interplanar spacing /$ see front matter 009 Elsevier Ltd. All rights reserved. doi: /j.ssc

2 190 R. Yogamalar et al. / Solid State Communications ) Experimental.1. Sample synthesis The following reagents were used: zinc nitrate hexahydrate ZnNH 3 ).6H O, ammonia NH 3 ) and poly-ethylene glycol PEG). A known ratio of PEG is dissolved in 50 ml distilled water, followed by the slow addition of zinc nitrate to the solution. The resulting reaction mixture was simultaneously stirred and heated for 4 h continuously using a magnetic stirrer; it was followed by the drop-wise addition of NH 3. After a few minutes, a turbid white precipitation was formed. The mixture was then transferred to a teflon-lined autoclave for hydrothermal treatment to a temperature of 10 C for 8 h. After the reaction, the sample was allowed to cool down to room temperature naturally. The obtained white precipitate was collected, washed with distilled water and ethanol several times, and further dried at 60 C in order to remove the organic impurities. Finally, the as-prepared ZnO white nanopowder was annealed at 800 C for 15 min... Geometric characterization XRD and TEM were used to obtain the textural parameters of the materials, such as size, shape, composition and crystal structure, in order to understand the enhanced properties of as-prepared and annealed ZnO nanoparticles. XRD was performed by powder X-ray diffraction Rigaku diffractrometer) using Cu K α1 radiation Å) in a θ θ configuration. For TEM analysis, Jeol JEM 000 FX-II operating at 00 kv was used to examine the morphology of the annealed ZnO nanorods. Microscopy measurements were not carried out for as-prepared ZnO nanoparticles. 3. Results and discussion 3.1. XRD analysis Diffraction from the as-prepared and annealed ZnO nanoparticles sample occurs, based on Bragg s law nλ = d sin θ, where n is an integer, λ is the wavelength of Cu K α1 radiation, d is the interplanar spacing and θ is the diffraction angle [5]. The output from XRD analysis of the as-prepared and annealed ZnO nanoparticles sample yields a plot of intensity versus angle of diffraction as shown in Fig. 1. The ZnO nanoparticles exhibit several diffraction peaks which can be indexed as hexagonal wurtzite ZnO with lattice parameters a = 3.44 Å, c = Å. No diffraction peaks corresponding to Zn, ZnOH) or other ZnO phases were detected, indicating that pure ZnO nanoparticles with a hexagonal wurtzite phase were formed. However, the XRD pattern of ZnO samples annealed at 800 C for 15 min show a small peak at θ 44.5, corresponding to the sample holder and it has no relation with wurtzite hexagonal phase ZnO. It must be further noted that the intensities of the Bragg peaks of annealed ZnO samples were sharp and narrow when compared to as-prepared ZnO nanoparticles, confirming that the sample was of high quality with excellent crystallinity and increased particle size. 3.. Crystallite size and strain XRD can be utilized to evaluate peak broadening with crystallite size, and lattice strain due to dislocation [6 9]. The breadth of the Bragg peak is a combination of both instrument and sample dependent effects. To decouple these contributions, it is necessary to collect a diffraction pattern from the line broadening of a standard material such as silicon to determine the instrumental broadening [10]. The instrumental corrected broadening [11] β hkl Fig. 1. XRD pattern of as-prepared and annealed 800 C) ZnO nanoparticles. corresponding to the diffraction peak of ZnO was estimated by using the relation β hkl = [ β hkl ) measured β instrumental] 1/. 1) Scherer formula = kλ β hkl cos θ where = volume weighted crystallite size, k = shape factor 0.9), λ = wavelength of Cu K α1 radiation, β hkl = instrumental corrected integral breadth of the reflection in radians) located at θ, and θ = angle of reflection in degrees) was utilized to relate the crystallite size to the line broadening. The average crystallite size of the annealed ZnO nanoparticles was found to be 9 nm and that of the as-prepared ZnO nanoparticles was 4 nm. Strain induced broadening arising from crystal imperfection and distortion were related by ε = β hkl tan θ From Eqs. ) and 3) it was clear that the peak width from 1 crystallite size varies as, whereas strain varies as tan θ. cos θ Williamson and Hall proposed a method of deconvoluting size and strain broadening by looking at the peak width as a function of diffracting angle θ and obtained a mathematical expression as ) kλ β hkl = + 4ε tan θ) 4) cos θ or by rearranging ) kλ β hkl cos θ = + 4ε sin θ). 5) A plot is drawn with 4 sin θ along the x-axis and β hkl cos θ along the y-axis for as-prepared and annealed ZnO nanoparticles. For the entire experiment, the plot is drawn only for the preferred orientation peaks of ZnO with the wurtzite hexagonal phase. The lattice planes corresponding to those preferred peaks are 1 0 0), 0 0 ), 1 0 1), 1 0 ), 1 1 0) and 1 0 3). From the linear ) 3)

3 R. Yogamalar et al. / Solid State Communications ) fit to the data, the crystallite size was extracted from the y-intercept and the strain ε from the slope of the fit. Eq. 5) represents the UDM, where the strain was assumed to be uniform in all crystallographic directions, thus considering the isotropic nature of the crystal, where all the material properties are independent of the direction along which they are measured. The UDM for as-prepared nanoparticles and annealed ZnO nanorods are shown in Fig.. From the plot it is clear that the strain associated with as-prepared and annealed samples are more or less similar and small, indicating that the annealing of ZnO samples does not produce any significant effect on strain. The generalized Hooke s law referred to the strain, keeping only the linear proportionality between the stress and strain, is given by σ = Eε. This equation is merely an approximation that is valid for a significantly small strain. Assuming a small strain to be present in the as-prepared and annealed ZnO nanoparticles, then the ZnO samples obeys Hooke s law to a reasonable approximation. Here, the stress σ is proportional to the strain ε with the constant of proportionality being the modulus of elasticity or Young s modulus, denoted by E. With a further increase in strain the particles deviate from this linear proportionality. As a result, Eq. 5) may be modified as ) ) kλ 4 sin θσ β hkl cos θ = +. 6) Eq. 6) represents USDM, where ε is replaced by σ and is the Young s modulus in the direction perpendicular to the set of crystal lattice planes hkl). The uniform stress can be calculated from the slope line plotted between 4 sin θ and β hkl cos θ, and the crystallite size from the intercept. The strain ε can be measured if of hexagonal ZnO nanoparticles are known. For samples with a hexagonal crystal phase, Young s modulus [1,13] is related to their elastic compliances s ij as = ) s 11 h + h+k) + s 3 33 [ ) ] h + h+k) + al 3 c al c ) 4 + s13 + s 44 ) h + h+k) 3 ) ). 7) al c Here s 11, s 13, s 33, s 44 are the elastic compliances of ZnO and their values are , , , m N 1 respectively [14]. USDM for as-prepared and annealed ZnO nanoparticles are shown in Fig. 3. The stress calculated from the slope of the line is slightly greater for the asprepared ZnO sample than for the annealed ZnO nanoparticles. In Eq. 5) we have considered the homogeneous isotropic nature of the crystal. But, in many cases, the assumption of homogeneity and isotropy is not fulfilled. Moreover, all the constants of proportionality associated with the stress strain relation are no longer independent when the strain energy density u is considered. According to Hooke s law the energy density u energy per unit volume) as a function of strain ε is u = ε.therefore, Eq. 6) can be modified to the form ) ) ) kλ 1/ u β hkl cos θ = + 4 sin θ. 8) ) 1/ A plot of β hkl cos θ versus 4 sin θ gives the UDEDM asprepared and annealed ZnO nanoparticles) as displayed in Fig. 4. The anisotropic energy density u can be estimated from the slope of the line, and the crystallite size from the intercept, and the strain ε from σ. From the above equations the energy density u and stress σ are related by the equation u = σ. There is a slight difference in the energy density value u obtained in the case of asprepared and annealed ZnO nanoparticles. Fig.. The W H analysis of as-prepared and annealed ZnO nanoparticles assuming UDM. Fig. 3. Modified form of W H analysis assuming USDM for as-prepared and annealed ZnO nanoparticles along with a plot of RMS lattice strain ε RMS and the strain estimated from USDM shown as an inset). To calculate the residual or applied stresses in a polycrystalline specimen from the XRD method, it is necessary to consider only those grains which are properly oriented to diffract the incident X-ray beam. As a result, the X-ray elastic constants s ij connecting dhkl) d the lattice strain, ε = 0hkl) ), where d d hkl) and d 0hkl) 0hkl) are the calculated and observed interplanar spacings of the ZnO nanoparticles, to the stresses will vary with the particular set of planes hkl) chosen for the calculation [15]. Hence, in anisotropic

4 19 R. Yogamalar et al. / Solid State Communications ) Fig. 5. TEM micrographs and SAED pattern insert on the upper left) of annealed ZnO nanorods. Fig. 4. The modified form of W H analysis assuming UDEDM for as-prepared and annealed ZnO nanoparticles and a plot of RMS lattice strain ε RMS and the strain estimated from UDEDM shown as an inset). hexagonal crystal the strain calculated from the peak position is different from the uniform stress deformation model and uniform deformation energy density model. This result is confirmed from ) 1/ the plot of RMS lattice strain ε RMS = d where, π d = d hkl) d 0hkl) ) as a function of interplanar spacing, and the strain estimated from USDM and UDEDM for the as-prepared and annealed ZnO nanoparticles which are shown in Figs. 3 and 4 as an inset) respectively. The strain values estimated from the peak position in USDM and UDEDM differ to a greater extent due to the inclusion of anisotropic nature and their values are tabulated in Table 1. Crystalline matter can contain a number of varieties of imperfections, each of which affects the properties of a polycrystalline aggregate. By W H models the strain due to the dislocation received at the time of synthesis of ZnO nanoparticles were calculated and tabulated in Table. The main contribution is from the chemical reaction, and synthesis parameters such as temperature, pressure and time factor. However, the strain arising from these contributions as calculated from W H models are very small and have a negligible effect on peak broadening Particle size from TEM d 0hkl) ) TEM micrographs was considered to be a better tool for size and shape data as it yields real images from which measurements can be made [16,17]. In TEM, electron beams focused by electromagnetic lines are transmitted through a thin sample of ZnO nanopowders. Fig. 5 displays the TEM image and selected area electron diffraction SAED) pattern of annealed ZnO nanoparticles. It is observed that the morphology of the annealed ZnO is rod shaped with a smooth surface. The micrographs comprise of an assembly of ZnO nanorods and are of varying size with an aspect ratio of 3.. TEM micrographs, along with the SAED pattern, of ZnO nanorods are shown in the inset on the upper left of Fig. 5. The figure clearly indicates that the annealed ZnO nanorods are crystalline with a wurtzite structure and no other impurities were observed; this is in close agreement with the results obtained from powder XRD measurements. In addition, the rings with a dotted pattern in SAED confirm the wide size distribution of ZnO nanoparticles. Young s modulus E, for hexagonal as-prepared and annealed ZnO nanoparticles was calculated to be 17 GPa from Eq. 7) Ref. Table 1), which is in agreement with the bulk ZnO [18]. Table summarizes the geometric parameters of as-prepared and annealed ZnO nanoparticles obtained from Scherer formula, various modified forms of W H analysis and TEM results respectively. Comparing the values of average crystallite size of as-prepared and annealed ZnO nanoparticles, obtained from UDM, USDM and UDEDM are more or less similar, implying that the inclusion of strain in various forms has a very small effect on the average crystallite size of ZnO nanoparticles. However, the average crystallite size obtained from Scherer formula and W H analysis shows a variation, this is because of the difference in averaging the particle size distribution. The values of strain from each model are calculated by considering Young s modulus to be 17 GPa. From the graphs plotted for various forms of W H analysis, the average crystallite size and the strain values obtained from UDM, USDM and UDEDM were found to be accurate, comparable and reasonable, as their entire preferred high intensity points lie close to the linear fit. 4. Conclusion In conclusion, pure ZnO nanoparticles were synthesized by a hydrothermal process and characterized by powder XRD and TEM. The line broadening of as-prepared and annealed ZnO nanoparticles due to small crystallite size and lattice strain were analyzed by Scherer formula and modified forms of W H analysis. A modified W H plot has been worked out and accepted as determining the crystallite size and strain-induced broadening due to lattice deformation. With the assumption of hexagonal anisotropic crystalline nature, the RMS lattice strain differs from that of the strain calculated from USDM and UDEDM. TEM image of annealed ZnO nanorods reveals the nanocrystalline nature, and their aspect ratio was found to be 3.. The three modified forms of W H analysis were helpful in determining the strain, stress, and energy density value with a certain approximation and hence these models are highly preferable to define the crystal perfection.

5 R. Yogamalar et al. / Solid State Communications ) Table 1 Young s modulus strain calculation for as-prepared and annealed ZnO nanoparticles. hkl GPa) Strain USDM 10 3 Strain UDEDM 10 3 RMS strain ε RMS = ) ) 1/ d Π d As-prepared Annealed As-prepared Annealed As-prepared Annealed As-prepared Annealed Table Geometric parameters for as-prepared and annealed ZnO nanoparticles. Samples Scherer method W H Method TEM Method nm) UD M USDM UDEDM nm) ε no unit 10 4 nm) σ MPa) εno unit 10 4 nm) u kjm 3 ) σ MPa) εno unit 10 4 Mean aspect ratio As-prepared ZnO Annealed ZnO Acknowledgements The authors thank Dr. M. Chidambaram, Director, National Institute of Technology, Tiruchirappalli for his constant encouragement and support. This research was financially supported by TEQIP and DST project SR/FTP/ETA-31/07), Government of India. References [1] K. Ramakanth, Basics of X-ray Diffraction and its Application, I.K. International Publishing House Pvt. Ltd., New Delhi, 007. [] T. Ungar, J. Mater. Sci ) [3] V.K. Pecharsky, P.Y. Zavalij, Fundamentals of Powder Diffraction and Structural Characterization of Materials, Springer, New York, 003. [4] C. Suryanarayana, M. Grant Norton, X-ray Diffraction: A Practical Approach, New York, [5] C. Kittel, Introduction to Solid State Physics, John Wiley & sons, London, 005. [6] J.D. Makinson, J.S. Lee, S.H. Magner, R.J. De Angelis, W.N. Weins, A.S. Hieronymus, JCPDS-International Centre for Diffraction Data 000 Advances in X-ray Analysis 4 000) 407. [7] T. Ungar, A. Borbely, G.R.G. Muginstein, S. Berger, A.R. Rosen, Nanostruct. Mater ) 103. [8] V.A. Drits, D.D. Eberl, J. Srodon, Clays clay Miner ) 38. [9] B. Marinkovic, R. Ribeiro, A. Saavedra, F.C. Rizzo, Mater. Res ) 71. [10] J.S. Lee, R.J. De Angelis, Nanostruct. Mater ) 805. [11] V. Biju, S. Neena, V. Vrinda, S.L. Salini, J. Mater. Sci ) [1] S. Adachi, Handbook on Physical Properties of Semiconductors, Springer, 004. [13] J. Zhang, Y. Zhang, K.W. Xu, V. Ji, Solid State Commun ) 87. [14] J.F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices, Oxford, New York, [15] C.S. Barrett, T.B. Massalski, Structure of Metals, Pergamon Press, Oxford, [16] J. Guerrero-Paz, D. Jaramillo-Vigueras, Nanostruct. Mater ) [17] X. Wang, J. Summers, Z.L. Wang, Nano Lett ) 43. [18] M.J. Weber, Handbook of Optical Materials, CRC Press, London, 003.