Lithium ion batteries have been a central part of consumer electronics for decades. More recently, they have also become critical components in the quickly arising technological fields of electric mobility and intermittent renewable energy storage. However, many fundamental principles and mechanisms are not yet understood to a sufficient extent to fully realize the potential of the incorporated materials. The vast majority of concurrent lithium ion batteries make use of graphite anodes. Their working principle is based on intercalation, the embedding and ordering of (lithium-) ions in two-dimensional spaces between the graphene sheets. This important process, it yields the upper bound to a battery’s charging speed and plays a decisive role in its longevity, is characterized by multiple phase transitions, ordered and disordered domains, as well as nonequilibrium phenomena, and therefore quite complex. In this work, we provide a simulation framework for the purpose of better understanding lithium-intercalated graphite and its behavior during use in a battery. To address large system sizes and long time scales required to investigate said effects, we identify the highly efficient, but semiempirical density functional tight binding (DFTB) as a suitable approach and combine particle swarm optimization (PSO) with the machine learning (ML) procedure Gaussian process regression (GPR) as implemented in the recently developed package for DFTB repulsion fitting to obtain the necessary parameters. Using the resulting parametrization, we are able to reproduce experimental reference structures at a level of accuracy which is in no way inferior to much more costly ab initio methods. We finally present structural properties and diffusion barriers for some exemplary system states.
Lithium ion batteries play a key role in the implementation of fully sustainable electrical mobility. Long lifetime, fast recharging and safety are required for the acceptance of any battery powered vehicle. Graphite is still the state of art as negative electrode. Despite decades of investigation into the mechanism of lithium intercalation, the ion mobility and the underlying microscopic processes are still not fully understood, limiting progress in performance and lifetime prediction of a battery. In particular, improvements in fast charging of batteries mandates a deeper understanding of the lower states of charge (SoC), bellow or around 20 %. We propose a combination of advanced NMR experiments, i.e spin alignment echo (SAE), with a theoretical multi scale modelling approach to investigate relevant phenomena such as lithium ion diffusion in graphite. Here, we present a novel multi-level accelerated first-principles kinetic Monte Carlo (1p-kMC) model to assess in detail the mobility at a low SoC, i.e LiC108. In particular, an external potential is applied in order to mimic the driving force causing (dis)charge of the battery.
Lithium-graphite intercalation compounds (Li-GICs) are the most popular anode material for modern lithium-ion batteries and have been subject to numerous studies—both experimental and theoretical. However, the system is still far from being consistently understood in detail across the full range of state of charge (SOC). The performance of approaches based on density functional theory (DFT) varies greatly depending on the choice of functional, and their computational cost is far too high for the large supercells necessary to study dilute and non-equilibrium configurations which are of paramount importance for understanding a complete charging cycle. On the other hand, cheap machine learning methods have made some progress in predicting, e.g., formation energetics, but fail to provide the full picture, including electrostatics and migration barriers. Following up on our previous work, we deliver on the promise of providing a complete and affordable simulation framework for Li-GICs. It is based on density functional tight binding (DFTB), which is fitted to dispersion-corrected DFT data using Gaussian process regression (GPR). In this work, we added the previously neglected lithium–lithium repulsion potential and extend the training set to include superdense Li-GICs (LiC6−x; x>0) and lithium metal, allowing for the investigation of dendrite formation, next-generation modified GIC anodes, and non-equilibrium states during fast charging processes in the future. For an extended range of structural and energetic properties—layer spacing, bond lengths, formation energies and migration barriers—our method compares favorably with experimental results and with state-of-the-art dispersion-corrected DFT at a fraction of the computational cost. We make use of this by investigating some larger-scale system properties—long range Li–Li interactions, dielectric constants and domain-formation—proving our method’s capability to bring to light new insights into the Li-GIC system and bridge the gap between DFT and meso-scale methods such as cluster expansions and kinetic Monte Carlo simulations.
Lithium ion batteries have been a central part of consumer electronics for decades. More recently, they have also become critical components in the quickly arising technological fields of electric mobility and intermittent renewable energy storage. However, many fundamental principles and mechanisms are not yet understood to a sufficient extent to fully realize the potential of the incorporated materials. The vast majority of concurrent lithium ion batteries make use of graphite anodes. Their working principle is based on intercalation–the embedding and ordering of (lithium-) ions in the two-dimensional spaces between the graphene sheets. This important process–it yields the upper bound to a battery's charging speed and plays a decisive role for its longevity–is characterized by multiple phase transitions, ordered and disordered domains, as well as non-equilibrium phenomena, and therefore quite complex. Such complexity emerges particularly at low states of charge (SOC), and complicates both the interpretation of experiments and the computational modelling. From a computational standpoint, targeted system sizes compatible with the SOC range of interest are inaccessible to first-principles calculations, yet require first-principles treatment of key effects such as dispersion and long-range electrostatics. Density Functional Tight Binding (DFTB), a semi-empirical approximation to DFT, offers a high-quality trade-off between accuracy and speed. However, this advantage comes at the cost–or rather initial investment–of pairwise parametrization. As no Li-C DFTB parameters were publicly available yet, we produced a parameter set specifically tailored to this system, employing a parametrization strategy [1] that combines global optimization of electronic parameters via Particle Swarm Optimization (PSO) [2] with our recently developed approach that uses Gaussian Process Regression (GPR) [3] to machine-learn the repulsive potential. Using the resulting parametrization, we are able to reproduce experimental reference structures at a level of accuracy which is in no way inferior to much more costly ab initio methods. We present structural properties and diffusion barriers for some exemplary system states. Additionally, we are able for the first time to resolve the full Potential Energy Surface (PES) of Li motion in stage-I and stage-II LiC108 (SOC 5%). The PES contains information that enables us to implement, and in perspective discuss, both kinetic Monte Carlo (kMC) models of Li-ion mobility in the graphite host, and free-energy sampling which ultimately yields the computed voltage profile of the anode. [1] Panosetti et al., https://arxiv.org/abs/1904.13351 [2] Chou et al., J. Chem. Theory Comput. 2016, 12, 1, 53–64 [3] Panosetti et al., J. Chem. Theory Comput. 2020, 16, 4, 2181–2191 Figure 1
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