A geometric analysis of the cubic A2BX6 structure commonly formed by metal halides is presented. Using the 'hard sphere' approximation, where the ions are represented by spheres of a fixed radius, we derive four limiting models that each constrain the distances between constituent ions in different ways. We compare the lattice parameters predicted by these four models with experimental data from the Inorganic Crystal Structure Database (ICSD). For the fluorides, the maintenance of the AX bond length at the sum of the A and X radii gives the best approximation of the lattice parameter, leading to structures with widely separated BX6 octahedra. For the heavier halides, a balance between forming an A site cavity of the correct size, and maintaining suitable anion-anion distances determines the lattice parameter. It is found that in many A2BX6 compounds of heavier halides, the neighbouring octahedra show very significant anion-anion overlap. We use these models to predict a compound with A site rattling and use DFT to confirm this prediction. Lastly, we use the geometric models to derive formability criteria for vacancy ordered double perovskites.
The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT format from various tensor inputs: (1) Parallel-TTSVD for traditional format, (2) PSTT and its variants for streaming data, (3) Tucker2TT for Tucker format, and (4) TT-fADI for solutions of Sylvester tensor equations. We provide theoretical guarantees of accuracy, parallelization methods, scaling analysis, and numerical results. For example, for a d-dimension tensor in R nו••×n , a two-sided sketching algorithm PSTT2 is shown to have a memory complexity of O(n d/2 ), improving upon O(n d−1 ) from previous algorithms.
The heavy reliance of lithium-ion batteries has caused rising concerns on the sustainability of lithium and transition metal and the ethic issue around mining practice. Developing alternative energy storage technologies beyond lithium has become a prominent slice of global energy research portfolio. The alternative technologies play a vital role in shaping the future landscape of energy storage, from electrified mobility to the efficient utilisation of renewable energies and further to large-scale stationary energy storage. Potassium-ion batteries (PIBs) are a promising alternative given its chemical and economic benefits, making a strong competitor to lithium-ion and sodium-ion batteries for different applications. However, many are unknown regarding potassium storage processes in materials and how it differs from lithium and sodium and understanding of solid-liquid interfacial chemistry is massively insufficient in PIBs. Therefore, there remain outstanding issues to advance the commercial prospects of the PIB technology. This Roadmap highlights the up-to-date scientific and technological advances and the insights into solving challenging issues to accelerate the development of PIBs. We hope this Roadmap aids the wider PIB research community and provides a cross-referencing to other beyond lithium energy storage technologies in the fast-pacing research landscape.
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