First-Principles Analysis of Cation Diffusion in Mixed Metal Ferrite Spinels

Ferrite spinels are metal oxides used in a wide variety of applications, many of which are controlled by the diffusion of metal cations through the metal oxide lattice. In this work, we used density functional theory (DFT) to examine the diffusion of Fe, Co, and Ni cations through the Fe₃O₄, CoFe₂O₄, and NiFe₂O₄ ferrite spinels. We apply DFT and crystal field theory to uncover the principles that govern cation diffusion in ferrite spinels. We found that a migrating cation hops from its initial octahedral site to a neighboring octahedral vacancy via a tetrahedral metastable intermediate separated from octahedral sites by a trigonal planar transition state (TS). The cations hop with relative activation energies of Co ≈ < Fe < Ni; the ordering of the diffusion barriers is controlled by the crystal field splitting of the diffusing cation. Specifically, the barriers depend on the orbital splitting and number of electrons which must be promoted into the higher energy t_2g orbitals of the tetrahedral metastable intermediate as the cations move along the minimum energy pathway of hopping. Additionally, for each diffusing cation, the barriers are inversely proportional to the spinel lattice parameter, leading to relative barriers for cation diffusion of Fe₃O₄ < CoFe₂O₄ < NiFe₂O₄. This results from the shorter cation-O bonds at the TS for spinels with smaller lattices, which inherently possess shorter bond lengths, and consequently higher system energies at their more constricted TS geometries.