Density functional theory (DFT) is used to reveal that the polycrystalline Young’s modulus (E) of graphite triples as it is lithiated to LiC6 . This behavior is captured in a linear relationship between E and lithium concentration suitable for continuum-scale models aimed at predicting diffusion-induced deformation in battery electrode materials. Alternatively, Poisson’s ratio is concentration-independent. Charge-transfer analyses suggest simultaneous weakening of carbon–carbon bonds within graphite basal planes and strengthening of interlayer bonding during lithiation. The variation in bond strength is shown to be responsible for the differences between elasticity tensor components, Cij , of lithium–graphite intercalation (Li-GIC) phases. Strain accumulation during Li intercalation and deintercalation is examined with a core–shell model of a Li-GIC particle assuming two coexisting phases. The requisite force equilibrium uses different Young’s moduli computed with DFT. Lithium-poor phases develop tensile strains, whereas Li-rich phases develop compressive strains. Results from the core–shell model suggest that elastic strain should be defined relative to the newest phase that forms during lithiation of graphite, and Li concentration-dependent mechanical properties should be considered in continuum level models.

The widespread nanostructures of iron oxides and oxyhydroxides are important reagents in many biogeochemical processes in many parts of our planet and ecosystem. Their functions in various aspects are closely related to their shapes, sizes, and thermodynamic surroundings, and there is much that we can learn from these natural relationships. This review covers these subjects of several phases (ferrihydrite, goethite, hematite, magnetite, maghemite, lepidocrocite, akaganéite and schwertmannite) commonly found in water, soils and sediments. Due to surface passivation by ubiquitous water in aquatic and most terrestrial environments, the difference in formation energies of bulk phases can decrease substantially or change signs at the nanoscale because of the disproportionate surface effects.Phase transformations and the relative abundance are sensitive to changes in environmental conditions.Each of these phases (except maghemite) displays characteristic morphologies, while maghemite appears frequently to inherit the precursor's morphology. We will see how an understanding of naturally occurring iron oxide nanostructures can provide useful insight for the production of synthetic iron oxide nanoparticles in technological settings.

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Iron oxides and oxyhydroxides are challenging to model computationally as competing phases may differ in formation energies by only several kJ mol −1 , they undergo magnetization transitions with temperature, their structures may contain partially occupied sites or long-range ordering of vacancies, and some loose structures require proper description of weak interactions such as hydrogen bonding and dispersive forces. If structures and transformations are to be reliably predicted under different chemical conditions, each of these challenges must be overcome simultaneously, while preserving a high level of numerical accuracy and physical sophistication. Here we present comparative studies of structure, magnetization, and elasticity properties of iron oxides and oxyhydroxides using density functional theory calculations with plane-wave and locally-confined-atomic-orbital basis sets, which are implemented in VASP and SIESTA packages, respectively. We have selected hematite (α-Fe 2 O 3 ), maghemite (γ-Fe 2 O 3 ), goethite (α-FeOOH), lepidocrocite (γ-FeOOH), and magnetite (Fe 3 O 4 ) as model systems from a total of 13 known iron oxides and oxyhydroxides; and use same convergence criteria and almost equivalent settings in order to make consistent comparisons. Our results show both basis sets can reproduce the energetic stability and magnetic ordering, and are in agreement with experimental observations. There are advantages to choosing one basis set over the other, depending on the intended focus. In our case, we find the method using PW basis set most appropriate, and combine our results to construct the first phase diagram of iron oxides and oxyhydroxides in the space of competing chemical potentials, generated entirely from first principles.keywords: iron oxides and oxyhydroxides; phase diagram; density functional theory; modeling and simulation.