However, if 0, and four crystallographic hard axes (directions) across the body diagonals denoted as. If δ = 0, the spinel ferrite is normal when δ = 1, the spinel ferrite is inverse. Delta ( δ) represents the degree of inversion (defined as the fraction of tetrahedral site occupied by Fe 3+ cations) which depends on the synthesis method and thermal treatment. Therefore, a whole range of distribution of cations is possible in spinel ferrites which can be represented by the general formula (M 2+ 1− δFe 3+ δ)O 4, where cations inside the round and square brackets are said to occupy the tetrahedral and octahedral site, respectively. Thus, the large fraction of empty interstitial sites makes its crystal structure a very open structure conducive to cation migration. Out of these, eight tetrahedral (A sites) and 16 octahedral (B sites) sites are occupied by the divalent and trivalent cations. The lattice consists of 32 divalent oxygen ions which are in direct contact to one another forming a closed pack face-centred cubic arrangement with 64 tetrahedral interstitial sites (A sites) and 32 octahedral interstitial sites (B sites). It crystallises in a face-centred cubic structure belonging to the space group Fd 3 − m composed of large unit cells containing eight formula units 8, i.e. Here, M 2+ and Fe 3+ are the divalent and trivalent cations, respectively. Spinel ferrites are isostructural with the mineral MgAl 2O 4 and have the general molecular formula (M 2+) O 4 2−. Crystal chemistry shows how the chemical composition, internal structure, distribution of cations, and physical properties are linked together, and it gives a clear understanding of magnetic properties of spinel ferrite nanoparticle. Magnetic nanoparticles of spinel ferrites are of great interest in fundamental science especially in addressing the relationship between magnetic properties and their crystal chemistry. The existence of constituents in the sample, i.e., Co, Fe and O has been authenticated using energy dispersive spectrum with the help of a FE-SEM. The vibrational modes of the octahedral and tetrahedral metal complex in the sample have been examined using FT-IR in the wave number range of 390 to 750 cm −1, and it shows an absorption band within this range, which confirms the spinel structure of the sample. It is observed that the distribution of cations and structural parameters are strongly dependent on synthesis method and annealing temperature. Distribution of cations among the two interstitial sites (tetrahedral and octahedral sites) has been estimated by analysing the powder X-ray diffraction patterns by employing Rietveld refinement technique, and the results reveal the existence of samples as a mixed type spinel with cubic structure. Structural characterization of the samples has been carried out using powder X-ray diffraction, Fourier transform infrared spectroscopy (FT-IR) and field emission scanning electron microscope (FE-SEM). Nanocrystalline cobalt ferrite powder has been synthesised by citrate precursor and co-precipitation methods.
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