A Machine Learning Based Computational Approach for Prediction of Cation Distribution in Spinel Crystal

Spinel ferrites with a general chemical formula of AB2O4 (A, B = Fe, Mg, Co, Ni, Cu, or Al) have interesting and technologically relevant magnetic and electrical properties. The crystal structure of spinel AB2O4 can be viewed as a superlattice consisting of eight (2x2x2) face-centered cubic unit cells with the lattice sites occupied by oxygen ions. In addition, one eighth of the tetrahedral and one half of the octahedral sites of the lattice are occupied by the A and B cations. In a normal spinel structure, all A ions will lie at the tetrahedral sites whereas all B ions at the octahedral sites. By contrast, half of the B ions will lie at the tetrahedral sites, whereas the octahedral sites are occupied by both A and B ions in an inverse spinel structure. Varying from the normal to inverse structures, the cation distribution in spinel AB2O4 could be quantified using degree of inversion which is the fraction of the tetrahedral sites occupied by B ions.<br/><br/>It has been found that both cation chemistry and degree of inversion play an important role in technically relevant properties of spinel oxides. In this study, we have developed and applied a machine learning based computational approach to predict the equilibrium cation distribution in multi-cation spinel oxides at high temperature. The computational approach integrates the construction of datasets consisting of the energies calculated from the density functional theory of the spinel oxides with various cation distributions, the training of the support vector machine model to derive relationship between system energy and structural features, and atomistic Monte Carlo simulations to sample the thermodynamic equilibrium structures of spinel crystal as a function of temperature We have applied our computational approach to predict the cation distributions for material systems of single spinel CoFe₂O₄, NiFe₂O₄, MgAl₂O₄, MgFe₂O_4, and double spinel MgAl_2-xFe_xO_4. Our predictions are found to agree well with available experimental results. Therefore, this study presents a reliable computational approach that can be extended to study the variation of cation distribution with processing temperature and chemical composition in complex multi-cation spinel oxides.