XRD diffractograms of the synthesized Mn0

XRD diffractograms of the synthesized Mn0.2Ni0.6 Zn0.2 Gdx Fe2-xO4 (x=0, 0.02, 0.04, 0.06) nanoparticles annealed at 400oC are shown in Fig.1. The obtained peaks in all the patterns correspond to that of single phase cubic spinel structure. There are no peaks corresponding to either secondary phases or impurity atoms in the patterns of any of the samples implying that the dopant ions, Gd3+ have completely been dissolved in the ferrite’s spinel structure. From the inter-planar spacing values (d), average value of lattice parameter (a) for each sample was calculated. The apparent density, ?a of the nanoparticles was calculated from the weight and bulk dimensions of the sintered pellets. The X-ray density, ?x was calculated using the formula 18,
?x = 8M/Na3
where M is the molecular weight (kg) of the sample, N is the Avogadro’s number (per mol) and ‘a’ is the lattice constant. The mean crystallite size, D of nanoparticles was calculated for all samples using Scherrer formula 19. Percentage of porosity was determined using the formula

The average lattice parameters, both experimental and theoretical, crystallite size, X-ray and apparent densities and porosity of the studied samples are given in Table 1.