The maximum power output and minimum charging time of a lithium-ion battery depend on both ionic and electronic transport. Ionic diffusion within the electrochemically active particles generally represents a fundamental limitation to the rate at which a battery can be charged and discharged. To compensate for the relatively slow solid-state ionic diffusion and to enable high power and rapid charging, the active particles are frequently reduced to nanometre dimensions, to the detriment of volumetric packing density, cost, stability and sustainability. As an alternative to nanoscaling, here we show that two complex niobium tungsten oxides-Nb16W5O55 and Nb18W16O93, which adopt crystallographic shear and bronze-like structures, respectively-can intercalate large quantities of lithium at high rates, even when the sizes of the niobium tungsten oxide particles are of the order of micrometres. Measurements of lithium-ion diffusion coefficients in both structures reveal room-temperature values that are several orders of magnitude higher than those in typical electrode materials such as Li4Ti5O12 and LiMn2O4. Multielectron redox, buffered volume expansion, topologically frustrated niobium/tungsten polyhedral arrangements and rapid solid-state lithium transport lead to extremely high volumetric capacities and rate performance. Unconventional materials and mechanisms that enable lithiation of micrometre-sized particles in minutes have implications for high-power applications, fast-charging devices, all-solid-state energy storage systems, electrode design and material discovery.

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Niobium tungsten oxides for high-rate lithium-ion energy storage

The vast majority of materials have a positive coefficient of thermal expansion and their volume increases on heating. There has been considerable recent interest in materials which display the unusual property of contracting in volume on heating; i.e. those with a negative coefficient of thermal expansion. This Perspective gives an overview of some of the physical phenomena that can give rise to this unusual effect. Recent insights into negative thermal expansion materials and some of their unusual structural properties are discussed.

Negative thermal expansion materials

Vibrational thermodynamics of materials

Isostructural ZrW2O8 and HfW2O8 show strong negative thermal expansion from 0.3 K up to their decomposition temperatures of approximately 1050 K. This behavior is especially unusual because these compounds are apparently cubic over their entire existence range. Detailed structural studies of ZrW2O8 were conducted using high-resolution neutron powder diffraction data taken at 14 temperatures from 0.3 to 693 K. Below 428 K, ZrW2O8 adopts the acentric space group P213 and has a well-ordered structure containing corner-sharing ZrO6 octahedra and two crystallographically distinct WO4 tetrahedra. Above the phase transition at 428 K, which appears to be second order, the space group becomes centric Pa3. The structure is now disordered with one oxygen site 50% occupied, suggesting the possibility of high oxygen mobility. Oxygen motion above 428 K is also suggested by dielectric and ac impedance measurements. The negative thermal expansion of ZrW2O8 and HfW2O8 is related to transverse thermal vibrations of bridgi...

Negative Thermal Expansion in ZrW2O8 and HfW2O8

There has been substantial renewed interest in negative thermal expansion following the discovery that cubic ZrW2O8 contracts over a temperature range in excess of 1000 K. Substances of many different kinds show negative thermal expansion, especially at low temperatures. In this article we review the underlying thermodynamics, emphasizing the roles of thermal stress and elasticity. We also discuss vibrational and non-vibrational mechanisms operating on the atomic scale that are responsible for negative expansion, both isotropic and anisotropic, in a wide range of materials.

https://iopscience.iop.org/article/10.1088/0953-8984/17/4/R03/pdf

Negative thermal expansion

The rigid-unit mode model provides many new insights into the stability and physical properties of framework silicates. In this model the SiOo and AlO4 tetrahedra are treated as very stifl to a first approximation as completely rigid, in comparison with intertetrahedral forces. In this paper we apply the model to several important examples. The model is reviewed by a detailed study of quarlz, and it is shown that the a-B phase transition involves a rigid-unit mode that preserves the Si-O-Si bond angle. The model is used to explain the phase transitions in cristobalite and the diferent feldspar, sodalite, and leucite structures. We also use the model to explain the nature of the high-temperature disordered phases of cristobalite and tridymite, to interpret the observations of streaks of diffuse scattering in electron diffraction patterns, to interpret the structures in the kalsilite-nepheline solid solution, to explain volume anomalies in the cubic leucite structures, and to explain qualitatively the negative linear thermal expansion in cordierite. The results for the highest symmetry sodalite structure show that there is a rigid-unit mode at every wave vector, a finding with significant implications for the understanding of the sorption and catalytic behavior of zeolites.

Rigid-unit phonon modes and structural phase transitions in framework silicates

This paper describes a computational method for the determination of all possible phonon modes in framework crystal structures that leave the fundamental structural units (tetrahedra and octahedra) undistorted. Such rigid-unit modes (RUMs) are prime candidates as soft modes for displacive phase transitions, such as in the perovskite structure, and this computational method can be used to rationalize the phase transitions in any framework structure. The method has been programmed for general use. The RUM approach is illustrated by consideration of the perovskite, quartz and cristobalite structures.

The Determination of Rigid-Unit Modes as Potential Soft Modes for Displacive Phase Transitions in Framework Crystal Structures

Crush is a program designed to calculate the rigid-unit mode spectrum for any given framework structure. Release version 1.1 is now available and contains some new features compared with the prerelease version described elsewhere.

Crush; a Fortran program for the analysis of the rigid-unit mode spectrum of a framework structure

It is commonly observed that displacive phase transitions, including ferroelectric phase transitions, can be accurately described by mean-field theory and hence Landau theory. In same cases the reasons why can be deduced by renormalisation group theory, but there are many other cases where the reasons are less clear. We have developed a model for displacive phase transitions in silicates, called the rigid unit mode model, in which it is assumed that any change in the structure does not involve distortion of the SiO4 tetrahedra. This model can explain a wide range of phenomena associated with phase transitions in silicates, such as why phase transitions are so common, why they have their particular transition temperatures, and why they can be described by Landau theory over a wide range of temperatures including close to the transition temperature. The model can be generalised to a model of a crystal of atoms with nearly-constant contact distances, a rigid bond model. This is then applied to the p...

On the application of mean-field and landau theory to displacive phase transitions

Landau free-energy expansions are commonly used to describe systems undergoing structural phase transitions. The Landau free energy of a model solid with an anharmonic potential (often a double well) at each site and mean-field-like inter-site coupling has been calculated both analytically and from molecular dynamics simulation. The calculated free-energy function is not well described by a simple polynomial in the order parameter. This result is not due to critical fluctuations in the Ginzburg interval. If, however, such a polynomial is used the coefficient of the fourth-order term is found to be highly temperature dependent. For a certain range of model parameters this coefficient is small relative to that of the second-order term. These observations help to explain the occurrence of 'non-critical, non-standard' values of the exponent beta in the variation of the order parameter, x, with temperature: x varies as (Tc-T)beta . More importantly they also help to explain why so many natural systems behave in a tricritical-type manner with beta approximately=1/4.

https://iopscience.iop.org/article/10.1088/0953-8984/1/44/005/pdf

A. P. Giddy

Papers

Rigid-unit phonon modes and structural phase transitions in framework silicates

The Determination of Rigid-Unit Modes as Potential Soft Modes for Displacive Phase Transitions in Framework Crystal Structures

Crush; a Fortran program for the analysis of the rigid-unit mode spectrum of a framework structure

On the application of mean-field and landau theory to displacive phase transitions

What do Landau free energies really look like for structural phase transitions