Intercalation compounds are popular candidate electrode materials for sodium-ion batteries and other ‘beyond lithium-ion’ technologies including potassium- and magnesium-ion batteries. We summarize first-principles efforts to elucidate the behaviour of such compounds in the layered and spinel structures. Trends based on the size and valence of the intercalant and the ionicity of the host are sufficient to explain phase stability and ordering phenomena, which in turn determine the equilibrium voltage profile. For the layered structures, we provide an overarching view of intercalant orderings in prismatic coordination based on antiphase boundaries, which has important consequences for diffusion. We examine details of stacking sequence transitions between different layered structures by calculating stacking fault energies and discussing the nature of dislocations. A better understanding of these transitions will likely aid the development of batteries with improved cyclability. This article is part of a discussion meeting issue ‘Energy materials for a low carbon future’.

The recent surge of interest in K-ion batteries necessitates a fundamental understanding of phase stability and K ordering tendencies in common electrode materials. We report on a first-principles study of phase stability in layered K x CoO2 (0 ≤ x ≤ 1) in the O1/P3/O3 family of host structures and identify K ordering preferences within each host. We find that the P3 host is stable at intermediate K concentrations and exhibits a multitude of hierarchical orderings characterized by well-ordered domains separated by antiphase boundaries. We also predict the stability of a new family of layered structures at high K concentrations that are highly distorted and host both octahedrally and prismatically coordinated K within each intercalation layer.

Electrode materials for Li + -ion batteries require optimization along several disparate axes related to cost, performance, and sustainability. One of the important performance axes is the ability to retain structural integrity though cycles of charge/discharge. Metal-metal bonding is a distinct feature of some refractory metal oxides that has been largely underutilized in electrochemical energy storage, but that could potentially impact structural integrity. Here LiScMo 3 O 8 , a compound containing triangular clusters of metal-metal bonded Mo atoms, is studied as a potential anode material in Li + -ion batteries. Electrons inserted though lithiation are localized across rigid Mo 3 triangles (rather than on individual metal ions), resulting in minimal structural change as suggested by operando diffraction. The unusual chemical bonding allows this compound to be cycled with Mo atoms below a formally +4 valence state, resulting in an acceptable voltage regime that is appropriate for an anode material.Several characterization methods including potentiometric entropy measurements indicate two-phase regions, which are attributed through extensive first-principles modeling to Li + ordering. This study of LiScMo 3 O 8 provides valuable insights for design principles for structural motifs that stably and reversibly permit Li + (de)insertion.

The size dependence of the dielectric constants of barium titanate or other ferroelectric particles can be explored by embedding particles into an epoxy matrix whose dielectric constant can be measured directly. However, to extract the particle dielectric constant requires a model of the composite medium. We compare a finite element model for various volume fractions and particle arrangements to several effective medium approximations, which do not consider particle arrangement explicitly. For a fixed number of particles, the composite dielectric constant increases with the degree of agglomeration, and we relate this increase to the number of regions of enhanced electric field along the applied field between particles in an agglomerate. Additionally, even for dispersed particles, we find that the composite method of assessing the particle dielectric constant may not be effective if the particle dielectric constant is too high compared to the background medium dielectric constant.

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The success of K-ion battery technology will rely on the development of robust cathode materials that can incorporate and shuttle large amounts of K reversibly.Recent experimental work has demonstrated the viability of layered KCrO 2 as a cathode material for K-ion batteries; however, some fundamental details of structural phase transitions and K ordering during cycling remain unknown. We report on a first-principles thermodynamic investigation of layered K x CrO 2 (0 ≤ x ≤ 1) in the O3 and P3 host structures. We predict that P3 is preferred at intermediate x, with the stable K orderings belonging to staircases of phases that contain antiphase boundaries between ordered regions. Varying densities of these boundaries allow for smooth changes in composition. At high x, we predict the stability of "M" phases containing a mixture of octahedral and prismatic K coordination within each layer, which is accommodated by undulations of the oxide host. Our calculated voltage curve and analysis of structural evolution indicate that the predicted phase stability, including the formation of the M phases, is mostly compatible with experimental observations.

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