Oxidation-State Dynamics and Emerging Patterns in Magnetite

Abstract

Magnetite is an important mineral with many interesting applications related to its magnetic, electrical, and thermal properties. Typically studied by electronic structure calculations, these methods are unable to capture the complex ion dynamics at relevant temperatures, time, and length scales. We present a hybrid Monte Carlo/molecular dynamics (MC/MD) method based on iron oxidation-state swapping for accurate atomistic modeling of bulk magnetite, magnetite surfaces, and nanoparticles that captures the complex ionic dynamics. By comparing the oxidation-state patterns with those obtained from density functional theory, we confirmed the accuracy of our approach. Lattice distortions leading to the stabilization of excess charges and a critical surface thickness at which the oxidation states transition from ordered to disordered were observed. This simple yet efficient approach paves the way for elucidating aspects of oxidation-state ordering of inverse spinel structures in general and battery materials in particular.

Figure 1

First peaks of bulk magnetite RDFs, g(r), between the iron species indicated in the legend. (a) RDF obtained from a hybrid MD/MC simulation starting from an initially minimized oxidation-state configuration and keeping the MC temperature T^MC below the critical temperature T_c^MC and (b) with T^MC at an elevated MC temperature of 10⁵ K above the critical MC temperature while maintaining 300 K in the MD in both cases. In addition, the first RDF peak of an ideal (i.e., undistorted) lattice is shown by a dashed black line. Full RDFs are shown in Figure S1.

Figure 2

(a) Stoichiometry of magnetite surfaces. Ideal magnetite stoichiometry is indicated by the black dashed line. n_Fe²⁺/n_Fe³⁺ ratios derived from charge neutrality, given by eq 3, are represented by lines; ratios derived from DFT are represented by crosses. (b) Potential energy differences (ΔE) between layered and minimized oxidation-state configurations of (001)-DBT surfaces of varying thickness. (c) Octahedral iron layer spacings (d_oct) of (001)-DBT surfaces as a function of the number of atomic layers. Layer spacing in bulk magnetite is indicated by the black dashed line.

Figure 3

(left) Minimized oxidation-state configuration of three exemplary (001)-DBT surfaces. Number of atomic layers is indicated in the top-left corner. (right) Ratio of Fe_oct³⁺ ions in each octahedral layer, denoted by n_Feoct³⁺/n_Feoct. Fe_tet and O are omitted. Colors: Fe_oct³⁺, dark blue; Fe_oct²⁺, light blue.

Figure 4

(a) Schematic representation of the corners reconstructed in a cubic nanoparticle (triangles). Pink areas correspond to cross-sectional views of a minimized oxidation-state configuration found for cubic magnetite nanoparticles on the right. (b) Corner before reconstruction; relevant Fe_oct ions are highlighted. (c) Corner after reconstruction. (d) Cross-sectional views of a minimized oxidation-state configuration found for spherical magnetite nanoparticles. Colors: Fe_oct³⁺ – dark blue, Fe_oct²⁺ – light blue, Fe_tet³⁺ – purple, Fe_tet²⁺ – mauve, and O – red. Oxygen is omitted in (a) and (d).