ZnAl_xFe_2-xO₄ (x = 0.0, 0.2, 0.4) were prepared by the solid state reaction. Powder of ZnO (99% pure), Al₂O₃ (99% pure), Fe₂O₃ (99% pure) were used as initial chemicals in precise stoichiometric ratios. The chemicals were weighed individually using a digital micro balance and then thoroughly mixed in an agate mortar for two hours of each sample. Then the samples were milled intimately in a stainless steel ball-milling for about 6 hours. For fine mixing of the ingredients, a small amount of distilled water was used. Then the mixtures were dried on a magnetic heater and then calcinated in an alumina crucible at 800˚C in air for 8 hours inside a muffle furnace to homogenize the product. Little amount of polyvinyl alcohol (PVA) was added to each dried powder as binder and was again closely grinded. The powders were then pressed into pellets of 13 mm dia using a hydraulic press with 5 tons pressure. All pellets were slightly brick reddish in color and were finally sintered at 1350˚C for 6 hours in air with the rate of 5˚C/min and then converted into powder again for X-ray diffraction experiment.

The X-ray diffraction experiments were performed on all the samples using X’ Pert PRO XRD system (Manufacturer: PANalytical, Frankfurt, Germany) with CuK_α1 radiation of wavelength λ = 1.54056 Å in the angular range of 2θ = 15˚ to 90˚ with a step size of 0.025˚ at room temperature. The X-ray diffraction patterns for all the samples have been indexed using the indexing program TREOR90 [20] . The lattice constants, oxygen position parameters and cation distributions been determined precisely by using the Rietveld refinement [21] program RIETAN-2000 [22] .

Figure 1 shows the Rietveld analysis profile of X-ray diffraction data of ZnAl_0.2Fe_1.8O₄ at room temperature.

Rietveld analysis of the X-ray diffraction patterns confirms the single phase spinel structure for all the three samples. It was found that (311) Bragg reflection has the highest intensity for all samples. The crystal structure of spinel oxide is defined by three crystallographic parameters, namely the lattice constant (a₀), oxygen position parameter (u) and cation distribution on the A and B sites.

The spinel structure exhibits the symmetry of the space group Fd3m and this space group has been used in the data refinement process for generating the calculated diffraction profile. The occupation numbers of cations at A and B sites and other structural parameters have been obtained from the basis of the best fit to the observed data. It is evident from the agreement factors that the observed and calculated intensities are quite satisfactory.

In the refinement process lattice constants, oxygen position parameters and cation distribution have been determined and presented in Table 1. In the table we see that the lattice constants decrease with the increase of Al contents. This is due to the effect of the size or radius of the aluminum atom in comparison with the iron (iron is bigger than the aluminum).

The agreement factors (R-factors) and χ² are the indicators of the goodness of fit of the refinement parameters. The values of R-factors (%) and χ² obtained from the Rietveld refinement of the X-ray data by using the program RIETAN-2000 are given in Table 2. The goodness of fits (χ²) is increased with the increasing of aluminum and may be due to the ratio or number of aluminum atoms increased or decreasing of iron atoms from the zinc ferrite. The profile R factor, weighted R factor is increased with the increasing of aluminum, on the other hand the expected R factor decreased with the increasing of it.

The site occupancies of different cations have been determined by varying them within the stoichiometric constraint. The occupation of oxygen ions for all the samples have been kept fixed during the refinement.

The positions of the several diffraction peaks, d-spacing, lattice parameters, N-R functions, relative intensities and corresponding Miller indices of ZnAl_0.4Fe_1.6O₄ are given in Table 3.

Lattice parameter decreases with Al doping. The decrease in lattice parameter is due to the smaller ionic radius of Al in comparison to Fe. The change in lattice parameters with doping follows the Vegard’s law with a very small deviation for x = 0.2 composition. Figure 2 shows the plot of lattice parameter versus doping concentration. Nelson-Riley [23] function was calculated to find the greater range of linearity. The calculated values of Nelson-Riley (N-R) functions are plotted against the lattice parameters in Figures 3-5 for the three composition of x = 0.0, 0.2 and 0.4 respectively.

The bulk density (ρ_B) has been calculated by using the usual mass volume ratio; X-ray density (ρ_x) by using molecular weight, Avogadro’s constant & lattice constants and porosity (ρ) has been calculated by using both bulk density and X-ray density.

The calculated bulk density, X-ray density and porosity of the three samples are given in Table 4. The bulk density increases with the increases of aluminum, due to the smaller size of aluminum which create less porous inside the material around the spheres of aluminum.