The formation of crystals and symmetry on the atomic scale has persistently attracted scientists through the ages. The structure itself and its subtle dependence on boundary conditions is a reflection of three principles: atomic attraction, repulsion, and the limitations in 3D space. This involves a competition between simplicity and high symmetry on the one hand and necessary structural complexity on the other. This work presents a simple atomistic crystal growth model derived for equivalent atoms and a pair potential. It highlights fundamental concepts, most prominently provided by a maximum number of equilibrium distances in the atom’s local vicinity, to obtain high symmetric structural motifs, among them the Platonic Solids. In this respect, the harmonically balanced interaction during the atomistic nucleation process may be regarded as origin of symmetry. The minimization of total energy is generalized for 3D periodic structures constituting these motifs. In dependence on the pair potential’s short- and long-range characteristics the, by symmetry, rigid lattices relax isotropically within the potential well. The first few coordination shells with lattice-specific fixed distances do not necessarily determine which equilibrium symmetry prevails. A phase diagram calculated on the basis of these few assumptions summarizes stable regions of close-packed fcc and hcp, next to bcc symmetry for predominantly soft short-range and hard long-range interaction. This lattice symmetry, which is evident for alkali metals as well as transition metals of the vanadium and chromium group, cannot be obtained from classical Morse or Lennard-Jones type potentials, but needs the range flexibility within the pair potential.

The ferroelectric phase transition of the perovskite barium titanate as well as its technical importance regarding the switching of respective polar properties is well known and has been thoroughly studied, both experimentally and on theoretical grounds. While details about the phase diagram as well as transition temperatures are experimentally well known, the theoretical approaches still face difficulties in contributing a detailed description of these phase transitions. Within this work, a new methodological approach is introduced to revisit the ferroelectric phase transition with first-principles methods. With the chosen ab initio molecular dynamics (AIMD) method in combination with the applied NpT ensemble, we are able to join the accuracy of density functional theory (DFT) with ambient conditions, realized using a thermostat and barostat in an MD simulation. The derived phase diagram confirms recent corrections in the theoretical models and reproduces the phase boundary pressure dependence of T_C. In conclusion of the statistical atomistic dynamics, the nature of the transition can be described in a more detailed way. In addition, this work paves the way towards locally patterned piezoelectrica by means of acoustic standing waves as well as piezoelectrically induced acoustic resonators.

A description of the hydrogen occupation site in LiNbO₃ and LiTaO₃ is made based on theoretical structural models and validated by measured OH⁻ stretching vibrational modes.

Crystallography is a powerful descriptor of the atomic structure of solid-state matter and can be applied to analyse the phenomena present in functional materials. Especially for ion diffusion – one of the main processes found in electrochemical energy storage materials – crystallography can describe and evaluate the elementary steps for the hopping of mobile species from one crystallographic site to another. By translating this knowledge into parameters and search for similar numbers in other materials, promising compounds for future energy storage materials can be identified. Large crystal structure databases like the ICSD, CSD, and PCD have accumulated millions of measured crystal structures and thus represent valuable sources for future data mining and big-data approaches. In this work we want to present, on the one hand, crystallographic approaches based on geometric and crystal-chemical descriptors that can be easily applied to very large databases. On the other hand, we want to show methodologies based on ab initio and electronic modelling which can simulate the structure features more realistically, incorporating also dynamic processes. Their theoretical background, applicability, and selected examples are presented.

With an increasing diversity of electrical energy sources, in particular with respect to the pool of renewable energies, and a growing complexity of electrical energy usage, the need for storage solutions to counterbalance the discrepancy of demand and offer is inevitable. In principle, a battery seems to be a simple device since it just requires three basic components – two electrodes and an electrolyte – in contact with each other. However, only the control of the interplay of these components as well as their dynamics, in particular the chemical reactions, can yield a high-performance system. Moreover, specific aspects such as production costs, weight, material composition and morphology, material criticality, and production conditions, among many others, need to be fulfilled at the same time. They present some of the countless challenges, which make battery design a long-lasting, effortful task. This chapter gives an introduction to the fundamental concepts of batteries. The principles are exemplified for the basic Daniell cell followed by a review of Nernst equation, electrified interface reactions, and ionic transport. The focus is addressed to crystalline materials. A comprehensive discussion of crystal chemical and crystal physical peculiarities reflects favourable and unfavourable local structural aspects from a crystallographic view as well as considerations with respect to electronic structure and bonding. A brief classification of battery types concludes the chapter.