X-ray Analysis of NiCrxFe2 – xO4 Nanoparticles Using Debye- Scherrer, Williamson-Hall and Size-strain Plot Methods

The aim of this work is to create and study NiCrxFe2 – xO4 nanoparticles using sol-gel technology with participation of auto-combustion (SGA). After completing the auto-combustion process, the phase which corresponds to the cubic structure of spinel space group Fd3m was obtained. The dependences of the lattice parameter and X-ray density of the ferrite powders on the nickel content were found. The values of the lattice parameter decrease from 0.8343 nm to 0.8306 nm with an increase in Cr3+ ions content. The decrease in lattice parameters by increasing Cr concentration can be attributed to replacement of the bigger ionic radius of Fe3+ by smaller ionic radius of Cr3+. The X-ray density dx increases from 5.360 g·cm–3 to 5.387 g·cm–3 with increasing degree of substitution x. The cation distribution study indicates that nickel and chromium ions have a tendency to occupy octahedral sites, whereas iron ions have a tendency to occupy both tetrahedral and octahedral sites. Morphological observations reveal that the particle size decreases significantly with increasing Cr content mean while the particle size becomes more uniform. The dimension of the particles and micro-deformations of crystal lattice was calculated from width of X-ray profile and angle. The integral width of Kα1-line was getting by division the integral width of the Kα-doublet obtained from the experiments on coefficient K. The ignoring a doublet in determining the integral width leads to increase of the calculated block sizes by 6 %. The particle size of NiCrxFe2 – xO4 powders was analyzed by the Scherrer formula, Williamson-Hall and the SSP methods. In determining particle average size by the Williamson-Hall method (24-43 nm), there is a larger scatter of experimental points on the straight line than by the SSP method (19-42 nm). The substitution of Cr3+ ions resulted in decrease of nanoparticle sizes. The values of micro-deformations ε obtained using the SSP method are within the range of 4.69·10–4 to 2.69·10–3. The average particle size of NiFe2O4 was found from the least-square fit of the lognormal distribution to the measured points obtained by the SEM micrographs. This average particle size was found in the range 41-42 nm.