Quasielastic neutron scattering

Quantitative insights into atomic-scale ionic conduction mechanisms
Quantitative fitting of quasielastic neutron scattering reveals liquid-like oxide ion diffusion through a solid.

The exceptional oxide-ionic conductivity of the high-temperature phase of bismuth oxide gives rise to a characteristic “quasielastic” broadening of its neutron scattering spectrum. We show that the oscillating form of this broadening can be fit using a modified version of a jump-diffusion model previously reserved for liquid ionic conductors. Fit parameters include a quantitative jump distance and a semi-quantitative diffusion coefficient. The results show that diffusion is liquid-like in this material. More broadly, they show for the first time that quasielastic neutron scattering can give quantitative insights into atomic-scale ionic conduction mechanisms in solid-oxide fuel cell and, potentially, lithium-ion battery materials.

The search for new and improved solid-state ionic conductors (SSICs) is one of the most active and important fields in materials chemistry, driven by the key role they play in solid-state battery and fuel cell technologies. The paradoxical chemical and structural requirements of SSICs are challenging: long-range order to provide a mechanically stable framework, together with short-range disorder so that selected atoms can migrate through it. Rational design and optimization of SSICs depends on a detailed understanding of the atomic-scale mechanisms by which this paradox is resolved.

Left: Locally relaxed average crystal structure of δ-Bi2O3. Bi atoms (4a site) are shown as large purple spheres. Red tetrahedra represent disordered O positions: a central O on the 8c site (25% occupancy) surrounded by four 32f sites (12.5% occupancy). Black arrows indicate possible oxygen jumps in ⟨100⟩ ⟨110⟩ and ⟨111⟩ directions. 

Right: Possible jumps between tetrahedral cavities, and the fit of a coherent modification of the Chudley-Elliot jump-diffusion model to the experimental QENS (X symbols) using the weighted average jump length (solid black line). Colored lines are the fits for individual jumps matching the colors in (b), along the ⟨100⟩ (dashed), ⟨110⟩ (dash-dot) and ⟨111⟩ (dotted) directions.

Inelastic neutron scattering is the only experimental technique that simultaneously probes ionic diffusion (as quasielastic neutron scattering, QENS) and lattice dynamics (as a generalised density of states, GDOS). In solid-state ionic conductors where the diffusing species has a predominantly incoherent neutron scattering cross section – the exemplar of which is hydrogen – key parameters describing the atomistic nature of diffusion, such as jump lengths and residence times, can be extracted directly by modelling the form of the QENS. However, this is a far more challenging problem when the diffusing species have significant coherent cross-sections, such as oxygen and lithium. In this work, we showed that it is possible to quantitatively model coherent QENS from a solid-state ionic conductor, by starting with the ideal case – high-temperature cubic δ-Bi2O3 – for which the diffusing species (oxygen) is an almost purely coherent scatterer, the structure is simple, and the conductivity (hence the QENS signal) is high.

Our results show for the first time that oxide-ionic diffusion in δ-Bi2O3 is isotropic (liquid-like), even though some directions present shorter oxygen-vacancy distances, an insight corroborated by computational dynamics simulations.

Coherent QENS analysis can now be applied to more complex solid-state oxide ionic conductors of direct practical interest for solid-oxide fuel cells, to inform the rational design of new and improved materials. It should nevertheless be noted that δ-Bi2O3 is the best-case scenario for coherent QENS analysis, due to its exceptionally high conductivity (and therefore strong QENS signal) from a purely coherent scatterer (O) in a very small unit cell (fluorite-type). The next logical steps will be to systematically move to larger unit cells with high conductivity (doped variations of δ-Bi2O3), and lower conductivity materials with small unit cells (yttria- and ceria-stabilised zirconia). The limiting factors will be instrumental: the sensitivity and resolution of the detectors; the experimentally accessible temperatures range; and the accessible time window, which must match the scale of diffusion.

Ultimately, we hope to apply this approach to mixed coherent-incoherent scatterers. This will be challenging due to the need to separate the components using polarization analysis, further weakening the signal. The case of lithium is the most promising, because its lighter mass as a mobile ion makes the dynamics more accessible to current instrumentation, and the lower operating temperatures of lithium-ion batteries opens a wider range of materials design possibilities through which to capitalize on the insights gained.

Recent publications

Wind, J., Mole, R.A., Yu, D., Ling, C.D., 2017., Liquid-like Ionic Diffusion in Solid Bismuth Oxide Revealed by Coherent Quasielastic Neutron Scattering, Chemistry of Materials

Chris Ling

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