Magnetite, Fe₃O₄ is a low-cost inverse-spinel material with high theoretical capacity, 926 mAh/g. Magnetite exhibits solid-state transport resistances, that have been alleviated through nanostructuring. However, the nanoparticles have been observed to form secondary structural motifs upon electrode fabrication. Physics-based modeling has revealed that resistances on both the nano (crystal) scale and on the scale of the secondary micron-sized structural motifs both contribute to the overpotential observed upon discharge.^1,2 These resistances are found to be a function of cycle rate and also electrode fabrication methods, as synthetic methods have been utilized to eliminate the secondary structural motifs.³ Modeling the interaction of lithium and the Fe₃O₄ crystal lattice at the atomic scale has also been employed utilizing DFT, and it has been found that atomic scale effects have measurable performance implications at the device-scale. DFT calculations have revealed that the high potentials (~3.0 V) initially observed at low discharge concentrations of lithium into magnetite (x~1.0) cannot be due to Li insertion into the pristine Fe₃O₄ lattice, due to phase instability and poor voltage prediction agreement of the resultant intercalated structures, Li_xFe₃O₄. Instead, DFT calculations and pre-edge XANES experiments have indicated that there exist Fe cationic defects, the concentration of which occur as a function of nanoparticle size, where smaller particles are observed to have a higher volume fraction of defects.⁴ DFT has predicted that lithium insertion into these Fe cationic defects are responsible for the initial high intercalation voltages. The nanoparticle size dependence of cationic defects, leads to the prediction of a nanoparticle-size-dependent reversible potential, corroborated experimentally. Additionally, the experimental observation of increased capacity of smaller nanoparticles over larger nanoparticles can also be partly explained by the increased concentration of cationic defects in the smaller particles. Here, we show that modeling at the atomic scale gives insight into the high potentials occurring at low lithium concentrations and the nanoparticle size-dependence of the reversible potential. Coarse grained modeling at the nano and micron scales have identified the unexpected impact of the secondary micron sized motifs on the overpotentials. The use of modeling at atomic, nano, and micron scales has revealed that all three length scales have nontrivial and measurable implications at the device scale. Understanding of these complex nonequilibrium devices over multiple length and time scales and is a requirement if we are to realize the next generation of lithium-ion batteries.

In addition to atomic scale modeling, continuum level modeling of batteries is an established method for interrogating performance. Previous efforts have focused on obtaining good model agreement with experimentally observed electrochemical measurements; where good agreement is usually used to validate the model and the concentration profiles predicted by the models are analyzed. Efforts have been made to directly interrogate the concentration profiles derived from battery operation, however, because these systems are highly dynamic even short time gaps between operation and characterization can result in significantly different profiles. Operando EDXRD characterization of battery electrodes has enabled us to directly compare the battery environment during operation to the results predicted from simulations.

The final part of my talk will be about how to leverage techniques from the rapidly advancing field of computer science, specifically machine learning, to assist in development of physics-based modeling. The utility of physics-based models is well known, however, good models require significant time and expertise to develop, and while the results of the models are accessible to experimentalists, model development is practically restricted to those with the expertise. Using relatively simple and well-established computer science techniques such as sampling and cross-validating we believe we can significantly reduce the time necessary for model development and outsource parameter estimation and model selection to a computer program.

(1) Knehr, K. W.; Brady, N. W.; Cama, C. A.; Bock, D. C.; Lin, Z.; Lininger, C. N.; Marschilok, A. C.; Takeuchi, K. J.; Takeuchi, E. S.; West, A. C., J. Electrochem. Soc. 2015, 162 (14), A2817–A2826.

(2) Knehr, K. W.; Brady, N. W.; Lininger, C. N.; Cama, C. A.; Bock, D. C.; Lin, Z.; Marschilok, A. C.; Takeuchi, K. J.; Takeuchi, E. S.; West, A. C., ECS Trans. 2015, 69 (1), 7–19.

(3) Bock, D. C.; Pelliccione, C. J.; Zhang, W.; Wang, J.; Knehr, K. W.; Wang, J.; Wang, F.; West, A. C.; Marschilok, A. C.; Takeuchi, K. J.; Takeuchi, E. S. D ACS Appl. Mater. Interfaces 2016, 8 (18), 11418–11430.

(4) Menard, M. C.; Marschilok, A. C.; Takeuchi, K. J.; Takeuchi, E. S., Electrochim. Acta 2013, 94 (42), 320–326.