X-ray diffraction (XRD) analysis The X-ray diffraction is a very important techniquethat has been used to address all issues                                                                                             related to the crystal of solids, including lattice constant andidentification the geometry of unknown materials.

The XRD pattern of theprepared ZnO, Co- doped, and Ni- doped ZnO are given in Figure 5(a,b,and c).The XRD of the ZnO shows diffraction peak at 2  31.80 , 34.45 , 36.28 , 47.

57 ,and 56.62  which can be indexed to (100),(002), (101)(102) (110) and (200) crystal plane respectively, the position of these peakindicate the formation of hexagonal wurtzite structure which are very agreementwith standard JCPDS(NO-36-1451)(2157-7439). Similar characteristic peaks andassigned lattice plane were observed by some other research 15.

XRD pattern ofCo-doped ZnO consists of diffraction peaks located in 2? = 19.7785, 23.4242,27.5667, 28.9447, 33.2112, 33.

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6991, 48.5689, 59.1846, and 69.5614 respectively asshown in Fig. 5(b) . No peaks associated with Co was detected in the XRDpattern indicating that Co2+ ions have substitutionally replaced theZn2+ ions  16. Figure 5(c)presented the XRD pattern of Ni-doped ZnOthe pattern show peaks in (100) and (101). No signals of the metallic Zn aredetected by XRD.

Also, there is no peak attributed to Ni, suggesting that theNi+2 ion may be doped into ZnO  17  From results it was evident that incorporationof  Co and Ni into ZnO lattice improvescrystalline quality. The average crystalline size iscalculated using Debye–Scherrer equation 18, D                        (1)Where D = is theaverage crystalline size of the nanoparticles, k = is geometric factor (0.94), ?= is the wavelength of X-ray radiation source  = is the angular (full-width at half maximum)FWHM  of the XRD peak at the diffractionangle. The calculated average crystalline size of theundoped,Co-doped,and Nidoped ZnO are about (    ) nm, respectively.