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(3) Where l is the wave length of incident X-ray (1.5406 A0) and q is the Bragg's angle. The average crystallite size of Zn1-xCoxO samples lie in the range of 33-36 nm. The average crystallites size of samples are go on decreasing with increasing Co concentrations. It may be due to the induced growth of particle and large surface to volume ratio. Crystallite sizes of Zn1-xCoxO samples are decreasing which increase the surface to volume ratio. If particle size decreases, it would cause deformation of particles to anisotropic shape. 3.2 Williamson – Hall methods The strain induced broadening is arised due to crystal imperfections and distortion. The strain is evaluated using the relation [10] (4) A remarkable property of Eq. 4 is the dependence on the diffraction angle q and W-H method which does not follow a 1/cosq dependency as in the Scherrer's equation instead of varing with tanq. This fundamental difference allows for a separation of reflection broadening when both microstrain causes small crystalline size and microstrain occurs togother. The different approaches are presented in the following assumation that size strain broadening is additive component of the total integral breadth of a Bragg's peak [11]. The distinct values of q are dependent on strain owing to this strain separation is being clearly observed which reflects broadening in the analysis of Williamson – Hall method [12]. Addition of the Scherrer's equation with Eq. 4 one gets instrumental broadening βhkl = [(βhkl)2Measured – (βhkl)2Instrumental]1/2 (5) (6) Rearranging the above equation, one gets (7) Eq. 7 represents the uniform deformation model (UDM), where the strain was assumed to be uniform in all crystallographic directions. The strain of all samples are measured considering the isotropic nature of the crystal. The term bcosq was plotted with respect to 4sinq for the preferred orientation peaks of samples with wurtzite hexagonal phase. Fig. 2 shows the slope and Y intercept of the fitted lines represent strain and particle sizes respectively. The strain was calculated using the UDM analysis. It is found that the lattice strain goes on decreasing with enhancing Co concentration. The crystallite sizes of Zn1-xCoxO samples are determined using UDM analysis and these values are tabulated in Table 1. It indicates that the crystalline sizes are decreasing with increasing Co content. The crystallite sizes obtained from W-H analysis are highly intercorrrelated with Scherrer's formula. Table 1: Lattice parameters, grain size, volume of unit cell, X-ray density, W-H grain szie and strain of the Co doped ZnO nano-sized samples. Samples a (A0) c (A0) Grain Size Volume X- density W-H Strain (ε ) D (nm) (A0)3 (gm/cm3) Grain size(nm) (10-4)
0.00 3.2485 5.2030 35.03 47.5500 5.6859 42.66 8.1568 0.10 3.2461 5.1974 34.76 47.4286 5.6727 40.42 6.1867 0.20 3.2459 5.1970 33.34 47.4191 5.6055 35.28 4.6298
Fig. 2 Plot of βhklCosθ vursus 4Sinθ of Zn1-xCoxO nanosized samples Conclusions Co doped ZnO nano-sized powders were synthesized by co-precipitation method. The XRD reveals that all the samples exhibit wurtzite structure and the lattice parameter decreases with increasing Co concentration, owing to the larger ionic radii of Zn than Co ions. The unit cell volume increases with increasing Mn concentration, it indicates that the incorporation of Co at Zn sites. The avearge grain sizes of the samples decrease with increasing Co concentration. The line broadening was analyzed by the Scherrer's formula and modified forms of W-H analysis. It was observed that the lattice strain and crystallite size values are decreasing with increasing Co concentration. The avearge grain size calculated from Scherrer's formula are in good agreement with the results obtanied by W-H method. Refernces
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