Cation Distributions in Magnesium-Nickel Ferrites

Abstract

The dependence of the nonthermal part of the internal energy ${\mathrm{(u}}_1)$ of mixed magnesium-nickel ferrites, ${\mathrm{Mg}}_y{\mathrm{Ni}}_{\text{1−y}}{\mathrm{Fe}}_2{\mathrm{O}}_4$ on the cation distribution has been studied. The cation distribution, which is charactered by the parameters $\eta$ (the fraction of Mg ions on tetrahedral sites) and $\xi$ (the fraction of Ni ions on tetrahedral sites), is determined from measurements of the saturation magnetization of samples quenched from temperatures between 1400° and 400°C. As in the case of magnesium-manganese ferrites it is found that $$u_1{\mathrm{\hspace{0.17em}=\hspace{0.17em}u}}_0\mathrm{+R}\left({\theta }_0-\frac{1}{2}{\theta }_1{\eta }^2\right)$$ . The parameters ${\theta }_0$ and ${\theta }_1$ are related to the energies necessary to transport Mg ions from octahedral (B) to tetrahedral (A) sites. The Madelung energy portion of ${\theta }_0$ predicts a linear dependence of ${\theta }_0$ on $y$ and this is observed experimentally. It is also demonstrated that ${\theta }_0$ is increased considerably by the substitution of Ni ions for Mn ions in the spinel lattice as dictated by the Madelung energy. The dependence of ${\theta }_1$ on $y$ can also be qualitatively explained. It is shown that the magnetic moment data considered as a function of composition can give useful information about the degree of inversion in the spinel lattice despite the two degrees of inversional freedom ($\xi$ and $\eta$ ). The variation of the maximum attainable value of $\eta$ with composition depends on $\xi$ and the magnetic moment of the Ni ion. Values of ξ and the Ni ionic magnetic moment compatible with the observed data are discussed.