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The as precursor, HMTA as fuel material and non-ionic surfactant (Triton-X 100). The X-Ray diffraction (XRD) analysis revealed that the synthesized ZnO nanopowder has the pure wurtzite structure. The ZnO powder shows polycrystalline nature having the crystallite size 21.25 nm. Crystallite size is calculated using Debye-Scherrer’s and Williamson-Hall equations. Porosity, Cell Volume, Micro strain, Morphology Index, Lorentz factor and Lorentz Polarization factor are also studied. From differential thermal analysis (DTA) & thermo gravimetric (TGA) it has been confirmed that nano powder has the phase purity. The weight loss percentage of the sample is 2.8385%. The particle size obtained 29 nm is in good agreement with the crystallite size calculated from X-Ray Diffraction pattern with the Particle Size Analyzer. The morphology of as prepared Zinc oxide nanopowders are characterized by scanning electron microscope (SEM). From specific area electron diffraction (SAED) pattern has specified the d-spacing and corresponding planes which coincide with the XRD d-spacing and planes.

Zinc Oxide (ZnO) is a wide band gap semiconductor with wurtzite structure. The physical and chemical properties of nano-scale particles are different when compared with the bulk materials. Nano powders controlled to nanocrystalline size can show atom-like behavior which results from higher surface energy. It is due to the large surface area and wider band gap between the conduction and valence band [

The starting materials such as zinc nitrate, HMTA and non-ionic surfactant are used. Freshly prepared aqueous solutions of the chemicals were used for the synthesis of nanoparticles. At room temperature the chemicals are mixed by dropping simultaneously 50 ml of 0.1 M solution of zinc nitrate, 50 ml of 0.15 M solution of HMTA and 0.025 M solution of non-ionic surfactant. The mixture of chemicals was then heated on a hot plate which led the chemical mixture to self-combustion. After combustion the final precipitate is subjected to calcination for 1 hr at 4000 C. Thus we successfully obtained a pure ZnO nano powder in this synthesis. Addition of nonionic surfactant with molecules composed of the hydrophilic head and hydrophobic tail, into precursor solution results in formation of reverse micelles in the gel. Placing the aqueous ions inside these micelles can be effective for controlling the growth of the particles. Surfactant has also the role of fuel in the combustion process. The powder characteristics like crystallites size, particles morphology and agglomeration are dependent on flame temperature generated during combustion, which is dependent on nature of the fuel and other starting materials such as oxidant.

The XRD pattern of the powder is studied with the diffraction angle 25˚ - 80˚. All the peaks are in 100% phase matching with the ZnO hexagonal phase of JCPDF No. 36-1451. It is shown in

where D is the average crystalline size λ is the X-ray wavelength of 1.54 Ǻ, θ is the Bragg diffraction angle and β is the FWHM.

The Willliamson-Hall Equation (2) is

where β is the full width at half maximum (FWHM) of the XRD all peaks, K is Scherrer’s constant, D is the crystallite size, λ the wavelength of the X-ray, ε the lattice strain, and θ the Bragg angle. βcosθ is plotted against 2sinθ along y and x axis respectively. Linear extrapolation is employed to this plot, the crystallite size is given by the intercept Kλ/D and the strain (ε) is given by slope. Here the average size of the crystal is 21.82 nm. Micro strain is calculated from Williamson-Hall plot equation. The micro strain from the

average crystallite size decreased the micro strain increased. This might be because of the mechanical surface-free energy of the metastable nanoparticles. Chemical combustion synthesis produced highly porous materials as the synthesized material has less density than the theoretical values [_{T} is theoretical density and D is calculated density from X-ray data using the formula (D = 8 M/Na_{3}) where M is the molecular weight, N is Avogadro’s number, and “a” is the lattice parameter.

From

Units Morphology Index (MI) is developed from FWHM of XRD data. The FWHM of two peaks are related with MI to its particle morphology. MI is obtained from Equation (4). The MI range for HMTA is from 0.5 to 0.61. It correlates with its particle sizes. Details are present in

where M.I is morphology index, FWHM_{h} is highest FWHM value obtained from peaks and FWHM_{p} is value of particulars peak’s FWHM for which M.I is to be calculated. The Lorentz-polarization factor is the most important of the experimental quantities that control X-ray intensity with respect to diffraction angle. In the intensity calculations Lorentz factor is combined with the polarization factor and further the variation of the Lorentz’s factor with the Bragg angle (θ) is shown [6-8]. The overall effect of Lorentz factor is to decrease the intensity of the reflections at intermediate angles compared to those in the forward or backward directions. Lorentz factor and Lorentz Polarization factor are calculated from Equations (5) and (6) respectively and tabulated in

In the

where

R∞ (1/10) is the diffused reflectance of a given wavelength, of a dense layer of non transparent infinite material, α is the absorption coefficient (cm^{−1}) and S is the dispersion factor, which is independent of the wavelength for particles larger than 5 μm. α is related to the incidental photon energy by means of the following equation [

where A is a constant that depends on the properties of the material, E is the photon energy, E_{g} is the bandgap and γ is a constant that can take different values depending on the type of electronic transition, for a permitted direct transition γ = 1/2, a prohibited direct transition γ = 3/2, a permitted indirect transition γ = 2 and for a prohibited indirect transition γ = 3 [17,18]. Therefore:

h is the plank’s constant and c is the velocity of light.

For direct transition equation is

For an indirect transition the equation is

The direct band gap energy (E_{g}) for the ZnO nanoparticles is determined by fitting the reflection data to the direct transition equation F(R'α)^{2} vs E (eV). The exact value of the band gap is determined by extrapolating the linear part of the graphics to the axis of the abscissa. The direct band gap found to be 3.5 eV which is shown in

The average particle size present in the nanoparticles can be determined by using the mathematical model of effective mass approximation Equation (13) [19,20] where the particle size (r, radius) and peak absorbance wavelength (p) for monodispersed ZnO nanoparticles.

During the derivation of Equation (13), me = 0.26 mo, mh = 0.59 mo, mo is the free electron mass, ε = 8.5, and E_{g} bulk = 3.3 eV. The prepared ZnO nanoparticles show peak absorbance at 372 nm which corresponds to average particle size of 5 nm.

Typical TGA and DTA curves of the prepared sample powder are subjected to 8000 C are shown in the

In the

The scanning electron microscopy studies were undertaken for the sample and the image is shown in the

From the dark field TEM

In this paper we have reported the synthesis of ZnO nano powder by fast and efficient combustion method. Using XRD data crystallite size is calculated as 21 nm which are in good agreement with TEM results. Further analysis showed that synthesized ZnO nano powder has the pure wurtzite structure with hexagonal phase. From TG/DTA weight loss was calculated to be 2.8385% which revealed that sample has high purity. Particle Analyzer supported the XRD calculations of crystallite size. SEM picture showed that particles were arranged on one another.