Sn$_{0.97-y}$Co$_{0.03}$Ni$_{y}$O$_{2}$ (0 $leq y leq$ 0.04) nanocrystals, with average crystallite size in the range of 7.3 nm ($y$=0.00) to 5.6 nm ($y$=0.04), have been synthesized using pH-controlled chemical co-precipitation technique. The non-stoichiometric Sn related defects and the O related stoichiometric Frenkel defects arising in the nanocrystals because of co-doping have been identified and their effect on the structural and optical properties of the nanocrystals have been extensively studied. It has been observed, using XPS that on increasing the Ni co-doping concentration ($y$), the non-stoichiometric Sn defect Sn$_{text{Sn}}^{}$ increases in compensation of existing defect Sn$_{i}^{....}$ for $y$ = 0.00 nanocrystals. High resolution transmission electron microscopy (HR-TEM) also confirms the existence of Sn$_{text{Sn}}^{}$. Regarding the Frenkel defect, XPS results indicate that the concentration of $V_{text{O}}$ and O$_{i}$, manifested in the form of dangling bond related surface defect states,increases with increase in $y$. Temperature dependent magnetisation measurement of the nanocrystals confirm the charge state of $V_{text{O}}$. The point defects have been found to affect the structural properties in a way that distortion in octahedral geometry of complete Sn-O octahderon effectively reduces whereas distortion in the trigonal planar coordination geometry of O increases. The investigation of Urbach edge indicates an enhancement in the disorder in the nanocrystals on co-doping. The optical band gap of the nanocrystals has been found to be red shifted upto $y$=0.02 and then a gradual blue shift has been observed. A direct effect of the O related defect has been observed on the blue luminescence of the nanocrystals such that the spectral contribution of blue luminescence in the total emission intensity increases by 72% for $y$=0.04 as compared to $y$=0.00.
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