Elastic properties and anisotropic effects on waves propagation of zinc-ferrite spinel systems as a function of pressure

Abstract

Classical Buckingham potentials are used to obtain information on how physical quantities change under lattice and pressure variations at zero temperature in zinc ferrites (Zn1−x2+Fex3+)[Znx2+Fe2−x3+]O4. Elastic constants, sound velocities and Debye's temperature, θD, are obtained numerically and compared to literature. The potentials predict pressure vs lattice dependencies in agreement with experiments. Additionally, sound velocities along the [100], [110] and [111] crystallographic directions are compared to those in the polycrystalline counterparts to evaluate the anisotropy as a function of pressure. The fastest propagation is predicted along [111] direction and the lowest one along [100], in agreement with experiments. The transverse velocities are predicted asymmetric with respect to the zero-pressure point where they have a maximum and under compression they remain almost constant. In contrast, the longitudinal velocities increase almost linearly under compression. Both transverse and longitudinal velocities decrease quadratically under expansion. Thus, the average sound velocity in the polycrystalline and therefore θD, which depends on it, have similar trends. The spinel structure is also investigated as function of the inversion parameter x to address the effect of crystallographic inversion upon sound waves propagation. The average sound velocity and θD are barely affected by x as their biggest changes are ∼1.9% and ∼1.4% respectively, with respect to a normal spinel. Besides, it is found that fluctuations due to ion randomness of octahedral/tetrahedral sites at each fixed x have a smaller role, therefore they can be neglected.