Title: The Mechanistic Description of the Open Circuit Potential for the Lithiation of Magnetite Nanoparticles
Description: Batteries are ubiquitous in modern society, from the portable devices we use daily to the yet-to-be realized integration of batteries into the electrical grid and electrical vehicle markets. One of the primary roles of batteries to date has been to enable portability of devices, and as chemical energy storage becomes more affordable, batteries will play a larger role in how society cares for the environment by enabling technologies that are poised to decrease greenhouse gas emissions. Low cost and environmentally conscious materials are pivotal for the economic feasibility and widespread integration of batteries into new markets. Batteries operate far from equilibrium and may operate under extreme stress and varying loads, therefore, for a material to be successful in an operational battery it must meet multiple design criteria. Here, an in-depth analysis of magnetite, a low cost and abundant iron oxide studied for use as an electrode material in lithium-ion batteries, is presented. In the second Chapter, an in-depth analysis into how magnetite accepts lithium into the solid state at low depths of discharge is examined with density functional theory and a mechanistic understanding of a phase change from the parent spinel to a rocksalt-like material is presented.

When magnetite is used as an electrode material in a lithium-ion battery, lithium must enter into and eject from the solid state of the host material, where the direction of lithium movement is a function of the current in the battery. In many electrode materials, magnetite included, large structural rearrangements can occur in the host material as lithium moves into and out of the lattice. These structural rearrangements can be irreversible and can contribute to overpotentials, decreasing efficiency and lifecycle for the battery. The structural rearrangements in bulk magnetite occurring due to lithium insertion are found to be driven primarily by Coulombic interactions. Additionally, the energetics and structural rearrangements for lithium insertion into defective magnetite and maghemite are examined, as these derivative structures commonly co-exist with magnetite, especially when the material is nanostructured. It is found that defective magnetite and maghemite accept lithium by a different mechanism, one that does not initially result in substantial structural rearrangement, as is the case in magnetite.

In Chapter three, the effects of nanostructuring magnetite on the reversible potential are examined as a function of nanoparticle size. Due to solid-state mass-transport resistances, active electrode materials in batteries are commonly nanostructured. When a material is nanostructured, the bulk properties are often replaced due to interesting phenomena that can occur as a result of stark differences between the nanostructured material and the bulk counterpart. These differences are often attributed to surface area to volume ratios, the exaggerated role of surface energies, lattice defects, and the variation in electronic behavior, all properties which change between a bulk and nanostructured material. The reversible potential is found to be particle size dependent, and this dependence is explained, in part, by the cationic defective surfaces in the particles and the differences in surface area to volume ratio between varying particle sizes. Evidence for these defects is presented with materials characterization techniques such as XRD and EELS studies.

Finally, the reversible potential at low lithiation states is predicted theoretically and found to match well to the experimentally measured potential. A study of the DFT predicted potentials and XRD characterization for multiple metastable pathways is examined in the fourth Chapter. Room temperature and long-time scale persistence of metastable phases is a pervasive phenomenon in nature. Magnetite is known to undergo both phase change and conversion reactions upon lithiation. Due to large mass transport and kinetic resistances, multiple phase changes are often observed in parallel during discharge, resulting in heterogenous phase formation in particles which can have large local lithium concentration variations. Phases which form during discharge can become kinetically trapped and the equilibrium state can therefore follow a metastable pathway. Theoretical potentials and XRD patterns are compared to the experimental patterns taken following 600 hours of relaxation following discharge at the slow rate of C/600.

The evidence presented supports a metastable pathway occurring on the first voltage plateau. In the fifth Chapter, the methodologies for the density functional theory calculations are presented in full detail. This includes various studies on the more subtle electronic properties of magnetite and its lithiated derivates studied herein. These studies include examination of the charge and orbital ordering problem related to the Verwey transition in magnetite, the charge and magnetic order in the rocksalt-like lithiated magnetite, and a full theoretical description of the various phases in the Li-Fe-O ternary phase diagram that were calculated to make the relevant conclusions in Chapters 2-4. Finally, corrections to DFT predicted formation energy and volume are presented. The aim of this thesis is to use theoretical techniques to examine the lithiation of magnetite on the atomic scale and make meaningful connections to the experimentally observed electrochemical behavior of the material. To accomplish this, magnetite and the structural derivatives of magnetite that co-exist with the material under physically realistic conditions must be treated theoretically.

In this thesis, ties between phenomena occurring on the atomic scale and the measurable properties of the macroscopic system, such as voltage, will be related. It will be illustrated that as a function of nanoparticle size, the magnetite system can vary in its atomic structure and the resultant electrochemistry and phase change characteristics are both affected. The findings indicate the relevance of the atomic properties and nanostructure for magnetite to the observed and measured electrochemical properties of the material.