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Sodium-ion batteries based on Prussian blue analogues (PBAs) are ideal for large-scale energy storage applications due to the ability to meet the huge volumes and low costs required. For Na 2−x Fe[Fe(CN) 6 ] 1−y •zH 2 O, realizing its commercial potential means fine control of the concentration of sodium, Fe(CN) 6 vacancies, and water content. To date, there is a huge variation in the literature of composition leading to variable electrochemical performance. In this work, we break down the synthesis of PBAs into three steps for controlling the sodium, vacancy, and water content via an inexpensive, scalable synthesis method. We produce rhombohedral Prussian white Na 1.88( 5) Fe[Fe-(CN) 6 ]•0.18(9)H 2 O with an initial capacity of 158 mAh/g retaining 90% capacity after 50 cycles. Subsequent characterization revealed that the increased polarization on the 3 V plateau is coincident with a phase transition and reduced utilization of the high-spin Fe(III)/Fe(II) redox couple. This reveals a clear target for subsequent improvements of the material to boost longterm cycling stability. These results will be of great interest for the myriad of applications of PBAs, such as catalysis, magnetism, electrochromics, and gas sorption.

Since their commercialization in 1991, lithium-ion batteries (LIBs) have revolutionized our way of life, with LIB pioneers being awarded the 2019 Nobel Prize in Chemistry. Despite the widespread use of LIBs, many LIB applications are not realized due to performance limitations, determined largely by the ability of electrode materials to reversibly host lithium ions. Overcoming such limitations requires knowledge of the fundamental mechanism for reversible ion intercalation in electrode materials. In this work, the still-debated structure of the most common commercial electrode material, graphite, during electrochemical lithiation is revisited using in operando neutron powder diffraction of a commercial 18650 lithium-ion battery. We extract new structural information and present a comprehensive overview of the phase evolution for lithiated graphite. Charge–discharge asymmetry and structural disorder in the lithiation process are observed, particularly surrounding phase transitions, and the phase evolution is found to be kinetically influenced. Notably, we observe pronounced asymmetry over the composition range 0.5 > x > 0.2, in which the stage 2L phase forms on discharge (delithiation) but not charge (lithiation), likely as a result of the slow formation of the stage 2L phase and the closeness of the stage 2L and stage 2 phase potentials. We reconcile our measurements of this transition with a stage 2L stacking disorder model containing an intergrown stage 2 and 2L phase. We resolve debate surrounding the intercalation mechanism in the stage 3L and stage 4L phase region, observing stage-specific reflections that support a first-order phase transition over the 0.2 > x > 0.04 range, in agreement with minor changes in the slope of the stacking axis length, despite relatively unchanging 00l reflection broadening. Our data support the previously proposed /ABA/ACA/ stacking for the stage 3L phase and an /ABAB/BABA/ stacking sequence of the stage 4L phase alongside experimentally derived atomic parameters. Finally, at low lithium content 0 < x < 0.04, we find an apparently homogeneous modification of the structure during both charge and discharge. Understanding the phase evolution and mechanism of structural response of graphite to lithiation under battery working conditions through in operando measurements may provide the information needed for the development of alternative higher performance electrode materials.

Crystalline solids consisting of three-dimensional networks of interconnected rigid units are ubiquitous amongst functional materials. In many cases, application-critical properties are sensitive to rigid-unit rotations at low temperature, high pressure or specific stoichiometry. The shared atoms that connect rigid units impose severe constraints on any rotational degrees of freedom, which must then be cooperative throughout the entire network. Successful efforts to identify cooperative-rotational rigid-unit modes (RUMs) in crystals have employed split-atom harmonic potentials, exhaustive testing of the rotational symmetry modes allowed by group representation theory, and even simple geometric considerations. This article presents a purely algebraic approach to RUM identification wherein the conditions of connectedness are used to construct a linear system of equations in the rotational symmetry-mode amplitudes.

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The development of electrodes for ambient temperature sodium-ion batteries requires the study of new materials and the understanding of how crystal structure influences properties. In this study, we investigate where sodium locates in two Prussian blue analogues, Fe[Fe(CN)6]1-x·yH2O and FeCo(CN)6. The evolution of the sodium site occupancies, lattice and volume is shown during charge-discharge using in situ synchrotron X-ray powder diffraction data. Sodium insertion is found to occur in these electrodes during cell construction and therefore Fe[Fe(CN)6]1-x·yH2O and FeCo(CN)6 can be used as positive electrodes. NazFeFe(CN)6 electrodes feature higher reversible capacities relative to NazFeCo(CN)6 electrodes which can be associated with a combination of structural factors, for example, a major sodium-containing phase, ∼Na0.5FeFe(CN)6 with sodium locating either at the x = y = z = 0.25 or x = y = 0.25 and z = 0.227(11) sites and an electrochemically inactive sodium-free Fe[Fe(CN)6]1-x·yH2O phase. This study demonstrates that key questions about electrode performance and attributes in sodium-ion batteries can be addressed using time-resolved in situ synchrotron X-ray diffraction studies.

The high-temperature cubic form of bismuth oxide, δ-Bi2O3, is the best intermediate-temperature oxide-ionic conductor known. The most elegant way of stabilizing δ-Bi2O3 to room temperature, while preserving a large part of its conductivity, is by doping with higher valent transition metals to create wide solid-solutions fields with exceedingly rare and complex (3 + 3)-dimensional incommensurately modulated "hypercubic" structures. These materials remain poorly understood because no such structure has ever been quantitatively solved and refined, due to both the complexity of the problem and a lack of adequate experimental data. We have addressed this by growing a large (centimeter scale) crystal using a novel refluxing floating-zone method, collecting high-quality single-crystal neutron diffraction data, and treating its structure together with X-ray diffraction data within the superspace symmetry formalism. The structure can be understood as an "inflated" pyrochlore, in which corner-connected NbO6 octahedral chains move smoothly apart to accommodate the solid solution. While some oxide vacancies are ordered into these chains, the rest are distributed throughout a continuous three-dimensional network of wide δ-Bi2O3-like channels, explaining the high oxide-ionic conductivity compared to commensurately modulated phases in the same pseudobinary system.

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