Transformation towards renewable energy sources and reduction of greenhouse gas emissions to mitigate climate change are among the most severe challenges of humankind today. Energy storage bears the potential to enable this transformation when applied as grid energy storage, which could enhance the utilization of renewable energy sources. Electrification of the transport sector by energy storage can potentially further reduce greenhouse gas emissions. Secondary batteries are promising energy-storage systems for these purposes and lithium-ion batteries (LIBs) are already applied. However, LIBs often rely on critical raw materials such as cobalt, raising sustainability concerns for growing larger-scale application. To partially overcome these issues, materials that do not contain critical raw materials are researched. Under these sustainability measures sodium-ion batteries (SIBs) are discussed as a promising alternative to LIBs due to the high abundance of sodium and the possibility to reduce the critical/costly elements in batteries. For both of these battery technologies, the cathode materials dominate their electrochemical performance and layered oxides are among the most promising materials. In general, layered oxides allow for tailored tuning, raising the demand for rational design approaches by in-depth characterisation and efficient pre-selection of interesting compositions. This can be achieved by first principles simulation studies on the atomistic scale that usually involve three simulation steps, namely configuration selection, geometry relaxation/evolution, and electronic structure calculation. In this thesis, computational techniques to study cathode materials are discussed and for each of these simulation steps relevant methods are developed, tested, and applied. The last chapter describes several practical examples how computational studies, in concert with experimental results, can advance the understanding of cathode materials for LIBs and SIBs. The contents of the chapters are as follows: In Chapter 2 the first simulation step of configuration selection is discussed. This problem arises due to partial occupations on crystal sites that need to be described by just full occupancies to apply further simulation steps. For complex materials (many substituents) configurational optimization is a formidable combinatorial problem. First, it is highlighted that the relative energy of various configurations in ionic crystals such as layered oxide cathodes can be efficiently assessed in terms of simple pairwise electrostatic interactions. Due to the pairwise character of electrostatic energies, an optimization problem with pre-computed energy terms can be formulated. This implies that there is a computationally inexpensive proxy to obtain low(est) energy configurations for follow-up simulations by optimizing the total electrostatic energy. The optimization is enabled by implementation of various efficient Monte Carlo-based and Genetic Algorithm-based optimizers and also an interface to external solvers is pointedout. These implementations ultimately result in a new code, GOAC (Global Optimization of Atomistic Configurations by Coulomb), that is significantly faster than existing software for the given problem. Application to multiple extremely large configurational optimization problems proves the efficiency of the code, providing a valuable tool for computational material, and especially cathode material, research. Chapter 3 discusses the selection of a structural model but with a focus on stacking phase. Layered oxide cathodes in SIBs show various phases in terms of the stacking sequence and relative shift of the layers towards each other. These phases significantly influence their electrochemical performance such as capacity and/or sodiumdiffusivity. Moreover, transitions between the phases happen during operation of the cathode materials, causing degradation and capacity fading. However, the phase stability and phase transitions can be optimized by tuning the cathode composition and therefore it would be highly desirable to relate compositions to the associated most stable stacking phase. Here, it is shown that comparing the electrostatic energies of different stacking phases at their respective lowest energy configurations can be an efficient ab initio predictor of phase stability. In order to increase the predictive power of this computationally inexpensive approach, electrostatic parameters such as lattice parameters and inter-layer distances are optimized to maximize the correlation of relative phase energies to density functional theory (DFT) calculations. The established prediction scheme allows for high-throughput studies while still being fully ab initio and achieves a prediction accuracy of 80 % on experimental data. Moreover, the method allows to capture ordering phenomena (transition metals (TM) and sodium) and to consider all kinds of stacking phases, e.g., O1, O2, O3, P2, P3, OP2, OP4. Therefore, the method is useful to design novel cathode materials with tailored phase stabilities for further experimental or simulational studies. In Chapter 4 the phase stability in layered oxide cathodes for SIBs is studied further. Next to the thermodynamic phase stability also the process and mechanism of phase transitions (kinetics) is important to understand. In order to simulate phase transitions, a Coulomb-Buckingham potential is fitted to reproduce interatomic interactions in the NaxCoO2 cathode material. An extensive dataset of DFT reference calculations is created and the potential is fitted to energies and forces. As a novelty, the potential was fitted as a function of sodium-concentration, thus allowing to capture the cathode material at all states of charge. Results show that the phase-transition barrier for the O2-P2 phase transition decreases on desodiation (charging). It is further shown that in dynamic molecular dynamics (MD) simulations at finite temperatures the barrier is lowered even further and that the transition mechanism involves gliding of a TMO6 layer. As a highlight, the O2-P2 phase transition inNa0.67CoO2 is directly observed on atomistic scale and at standard lab conditions (NpT with 300 K and 1 bar) on the μs time-scale. Finally, the sodium diffusivity as function of progress of phase transition is analyzed, showing satisfactory agreement to experimental values reported in the literature. In conclusion, new insights on the phase transitions of layered oxide cathodes for SIBs are described and the applied classical potential approach is shown to boost computational battery materials research by allowing for larger and longer simulations. Chapter 5 is about the electronic structure calculation of layered oxide cathode materials. Electronic structure calculations of TM oxides are known to be challenging but are extremely important for cathode materials to comment about their redox mechanism. To improve on this issue, different electronic structure calculations are thoroughly benchmarked here. Namely, hybrid functionals and their Hartree-Fock mixing parameter α is assessed and optimized by the so-called GW calculations. It is shown that especially the hybridization of 2p oxygen orbitals and 3d TM orbitals is affected by α, which substantially influences the assigned redoxmechanism of a cathode material. By applying different levels of GW calculations and providing various hybrid functional startingpoints, two promising ranges for α are determined. The first range is highlighted to show satisfactory agreement to experimentally reported band gaps but corresponding α values of approximately 8.5 % are significantly lower than the default of 25 % employed in most hybrid functionals. However, the other determined range yields an α of approximately 22 % which is fairly close to the aforementioned default value. Finally, the results give some guidance on electronic structure calculations of layered oxide cathodes by summarizing effects and optimization strategies for varying the α parameter. The last chapter (Chapter 6) focuses on the combination of experimental and theoretical studies on cathodematerials. First, awork on a lithium-rich layered oxide cathode for LIBs is shown that aims to improve energy density over conventional cathodes. Especially the determination of the redox mechanism by computational studies is discussed while also configurational optimization by electrostatics andMD simulations to observe structural evolutions are performed. In the second work, large-scale configurational optimizations are leveraged to study lithium iron phosphate (LFP) that is discussed as a more sustainable LIB cathode material. The optimizations successfully reproduced the single-phase/two-phase charging mechanism in LFP on the multi-nanometer lengthscale, proving the value and necessity of large-scale configurational optimizations by electrostatics. In the third example, it is shown how a layered oxide SIB cathode can be stabilized by surface modification in terms of a coating. Experimental results highlight significantly improved cycling stability due to the coating and ab initio MD simulations reveal the degradation of the bare cathode material by electrolyte species while the coating is found to be mostly inert. The last presented study focuses mainly on the determination of the redox process from electronic structure calculations in layered oxide SIB cathodes. It is highlighted that detailed electronic structure analysis can be directly related to experimentally observed effects such as subtle, yet important, changes in the shape of the voltage curve. In summary, all of the case studies presented in the last chapter highlight how the methodologies developed in the previous chapters and computational methods in general can contribute to improved characterization of novel cathode materials. Ultimately, these introduced methodologies in conjunction with the detailed insights on specific cat
Konstantin Köster (Thu,) studied this question.