Diffusion mechanism in the sodium-ion battery material sodium cobaltate

High performance batteries based on the movement of Li ions in Li_xCoO₂ have made possible a revolution in mobile electronic technology, from laptops to mobile phones. However, the scarcity of Li and the demand for energy storage for renewables has led to intense interest in Na-ion batteries, including structurally-related Na_xCoO₂. Here we have determined the diffusion mechanism for Na_0.8CoO₂ using diffuse x-ray scattering, quasi-elastic neutron scattering and ab-initio molecular dynamics simulations, and we find that the sodium ordering provides diffusion pathways and governs the diffusion rate. Above T ~ 290 K the so-called partially disordered stripe superstructure provides channels for quasi-1D diffusion, and melting of the sodium ordering leads to 2D superionic diffusion above T ~ 370 K. We obtain quantitative agreement between our microscopic study of the hopping mechanism and bulk self-diffusion measurements. Our approach can be applied widely to other Na- or Li-ion battery materials.

Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores

The idea of magnetic monopoles in spin ice has enjoyed much success at intermediate temperatures, but at low temperatures a description in terms of monopole dynamics alone is insufficient. Recently, numerical simulations were used to argue that magnetic impurities account for this discrepancy by introducing a magnetic equivalent of residual resistance in the system. Here we propose that oxygen deficiency is the leading cause of magnetic impurities in as-grown samples, and we determine the defect structure and magnetism in Y2Ti2O7-δ using diffuse neutron scattering and magnetization measurements. These defects are eliminated by oxygen annealing. The introduction of oxygen vacancies causes Ti(4+) to transform to magnetic Ti(3+) with quenched orbital magnetism, but the concentration is anomalously low. In the spin-ice material Dy2Ti2O7 we find that the same oxygen-vacancy defects suppress moments on neighbouring rare-earth sites, and that these magnetic distortions markedly slow down the long-time monopole dynamics at sub-Kelvin temperatures.

Suppression of thermal conductivity by rattling modes in thermoelectric sodium cobaltate

The need for both high electrical conductivity and low thermal conductivity creates a design conflict for thermoelectric systems, leading to the consideration of materials with complicated crystal structures. Rattling of ions in cages results in low thermal conductivity, but understanding the mechanism through studies of the phonon dispersion using momentum-resolved spectroscopy is made difficult by the complexity of the unit cells. We have performed inelastic X-ray and neutron scattering experiments that are in remarkable agreement with our first-principles density-functional calculations of the phonon dispersion for thermoelectric Na(0.8)CoO2, which has a large-period superstructure. We have directly observed an Einstein-like rattling mode at low energy, involving large anharmonic displacements of the sodium ions inside multi-vacancy clusters. These rattling modes suppress the thermal conductivity by a factor of six compared with vacancy-free NaCoO2. Our results will guide the design of the next generation of materials for applications in solid-state refrigerators and power recovery.

Room temperature single-crystal diffuse scattering and ab initio lattice dynamics in CaTiSiO5

Single-crystal diffuse scattering data have been collected at room temperature on synthetic titanite using both neutrons and high-energy x-rays. A simple ball-and-springs model reproduces the observed diffuse scattering well, confirming its origin to be primarily due to thermal motion of the atoms. Ab initio phonons are calculated using density-functional perturbation theory and are shown to reproduce the experimental diffuse scattering. The observed diffuse x-ray and neutron scattering patterns are consistent with a summation of mode frequencies and displacement eigenvectors associated with the entire phonon spectrum, rather than with a simple, short-range static displacement. A band gap is observed between 600 and 700 cm(-1) with only two modes crossing this region, both associated with antiferroelectric Ti-O motion along a. One of these modes (of Bu symmetry), displays a large LO-TO mode-splitting (562-701.4 cm(-1)) and has a dominant component coming from Ti-O bond-stretching and, thus, the mode-splitting is related to the polarizability of the Ti-O bonds along the chain direction. Similar mode-splitting is observed in piezo- and ferroelectric materials. The calculated phonon dispersion model may be of use to others in future to understand the phase transition at higher temperatures, as well as in the interpretation of measured phonon dispersion curves.

A rotator for single-crystal neutron diffraction at high pressure

We present a modified Paris-Edinburgh press which allows rotation of the anvils and the sample under applied load. The device is designed to overcome the problem of having large segments of reciprocal space obscured by the tie rods of the press during single-crystal neutron-scattering experiments. The modified press features custom designed hydraulic bearings and provides controls for precision rotation and positioning. The advantages of using the device for increasing the number of measurable reflections are illustrated with the results of neutron-diffraction experiments on a single crystal of germanium rotated under a load of 70 tonnes.

Neutron diffuse scattering in deuterated para-terphenyl, C(18)D(14)

Neutron diffuse scattering is used to explore the short-range order (SRO) in deuterated para-terphenyl, C(18)D(14). The crystal shows SRO because the central of the three phenyl groups of each molecule can twist positively or negatively and these twists are correlated over the local scale. The presence of incipient Bragg peaks at [Formula: see text] at 200 K shows that these flips are negatively correlated along the a direction (nearest neighbour correlation coefficient of ∼-0.3) and b direction (nearest neighbour correlation coefficient of ∼-0.87) and appear essentially uncorrelated along c. Diffuse peak anisotropy indicates that the range of the correlations along b is found to be ∼3 times that along a. These correlations persist, although weaker, at room temperature. A Monte Carlo simulation was used to impose a correlation structure on the population of central ring twists that was deduced from Bragg scattering. By then allowing displacive relaxation of the structure, the observed diffuse scattering was well reproduced. Modelling the displacive motions of molecules showed that the positions of nearest ab-plane neighbour molecules are strongly positively correlated, particularly for motions approximately parallel to a, while the displacive correlations are weaker between molecules stacked along c. The apparent contradiction that the displacements are most strongly correlated along a while the occupancies are most strongly correlated along b is explained in terms of the connectivity of molecular interactions.

Revealing how interactions lead to ordering in para-terphenyl

How does the ordering in a crystal arise from the interactions present? Crystal structure determination shows what the crystal structure is, but in solving directly for atomic coordinates leaves questions as to why (or how) aspects of the structure arise. The answers to such questions are crucial in the study of what drives structural phase transitions or in crystal structure prediction. In this work, modeling of the neutron diffuse scattering from deuterated para-terphenyl, C18D14, shows directly how the observed short-range order arises out of intramolecular and intermolecular interactions. This approach provides real-space descriptions of cooperative molecular motions and correlations, and explains the two-dimensional critical behavior observed in other experiments. In doing so, it is found that intramolecular and intermolecular interactions, and the molecules themselves, can be thought of as acting as nanoscale mechanical linkages.

Patterning of sodium ions and the control of electrons in sodium cobaltate

Sodium cobaltate (Na(x)CoO2) has emerged as a material of exceptional scientific interest due to the potential for thermoelectric applications, and because the strong interplay between the magnetic and superconducting properties has led to close comparisons with the physics of the superconducting copper oxides. The density x of the sodium in the intercalation layers can be altered electrochemically, directly changing the number of conduction electrons on the triangular Co layers. Recent electron diffraction measurements reveal a kaleidoscope of Na+ ion patterns as a function of concentration. Here we use single-crystal neutron diffraction supported by numerical simulations to determine the long-range three-dimensional superstructures of these ions. We show that the sodium ordering and its associated distortion field are governed by pure electrostatics, and that the organizational principle is the stabilization of charge droplets that order long range at some simple fractional fillings. Our results provide a good starting point to understand the electronic properties in terms of a Hubbard hamiltonian that takes into account the electrostatic potential from the Na superstructures. The resulting depth of potential wells in the Co layer is greater than the single-particle hopping kinetic energy and as a consequence, holes preferentially occupy the lowest potential regions. Thus we conclude that the Na+ ion patterning has a decisive role in the transport and magnetic properties.

Simultaneous fitting of X-ray and neutron diffuse scattering data

Conventional crystallographic refinement uses the Bragg-peak intensities and gives the single-site average crystal structure. Information about short-range order and local order is contained in the diffuse scattering that is distributed throughout reciprocal space. Models of the short-range order in materials can now be automatically refined. The complementarity of X-ray and neutron diffraction data, and the value of simultaneously refining a structural model against both types of data, has long been known. This paper presents the first refinement of a short-range-order model against comprehensive X-ray and neutron diffuse scattering data simultaneously. The sample is the organic molecular crystal benzil, C(14)H(10)O(2) (for neutron work H is replaced by D). The technique gives new insights into local order in crystalline materials, including the dynamic correlation structure indicative of the dynamics of molecules in the crystalline state, and successfully overcomes limitations of using only the X-ray data set.

Phase imaging using time-of-flight neutron diffraction

A technique that allows the spatial distribution of crystallographic phases in the interior of an object to be reconstructed from neutron time-of-flight (TOF) diffraction is described. To this end, the shift of the Bragg peaks due to the so-called `geometrical aberration' is exploited. A collimated incident white beam is used to perform a translational or rotational scan of the object whilst collecting a TOF data set for each sample position or orientation. Depending on the location of any scattering material along the line of the incident beam path through the object, the measuredd-spacings of the corresponding Bragg peaks are shifted with respect to their nominal values, which are attained only at the geometrical centre of the instrument. Using a formula that is usually employed to correct for sample offset, the phase distribution along the incident beamline can be directly reconstructed, without the need to perform a tomographic reconstruction. Results are shown from a demonstration experiment carried out on a cylindrical Al container enclosing an arrangement of Cu and Fe rods. On the basis of this formalism, an optimized experimental geometry is described and the potential and limits of this technique are explored, as are its applicability to X-ray and constant-wavelength neutron diffraction.

Single-crystal neutron diffuse scattering and Monte Carlo study of the relaxor ferroelectric PbZn1/3Nb2/3O3(PZN)

Full three-dimensional diffuse neutron scattering data have been recorded from a single crystal of Pb(Zn1/3Nb2/3)O3(PZN) at 300 K using the time-of-flight Laue technique on the SXD single-crystal instrument at ISIS. The data show a series of diffuse rods of scattering oriented parallel to each of the six 〈1 1 0〉 crystal directions. Monte Carlo simulation has been used to demonstrate that the diffuse rods are caused by planar nanodomains oriented normal to the 〈1 1 0〉 directions. Within these domains, there are correlated displacements of the atoms away from their average site positions. In order to explain the systematic absence of some rods of scattering in the (h k 1) data but the presence of all rods in the (h k 0) data, it is necessary that the displacement of an O atom is of opposite sign to that of its neighbouring Pb atoms. This is explained in terms of a model based on the fact that Pb2+possesses a lone pair of electrons, giving the Pb ion directionality.

Structural anomalies and multiferroic behavior in magnetically frustrated TbMn2O5

We have studied the magnetostructural phase diagram of multiferroic TbMn2O5 as a function of temperature and magnetic field by neutron diffraction. Dielectric and magnetic anomalies are found to be associated with steps in the magnetic propagation vector, including a rare example of a commensurate-incommensurate transition on cooling below 24 K, and in the structural parameters. The geometrically frustrated magnetic structure is stabilized by "canted antiferroelectric" displacements of the Mn3+ ions, an example of the magnetic Jahn-Teller effect. The Tb moments order ferromagnetically at low temperatures in an applied field, while the Mn magnetic structure is largely unchanged.

Diffuse neutron scattering in benzil, C14D10O2, using the time-of-flight Laue technique

Diffuse neutron scattering data have been recorded for the molecular crystald-benzil, C14D10O2, using the time-of-flight Laue technique on the SXD and PRISMA instruments at ISIS. Using SXD it was possible to access a large fraction of the total three-dimensional reciprocal space out to aQvalue of 15 Å−1, using only four individual exposures and by making use of the \bar{3}m Laue symmetry of the crystal. By segregating the scattered data according to the incident neutron energy used, patterns were obtained from those neutrons in the range of ∼20 meV to 150 meV, which showed little sign of inelastic effects and so could be compared with previously analysed X-ray data. For neutron energies of <20 meV, interesting inelastic effects were observed, which have been used to obtain an estimate for the energy of phonons associated with a vibrational mode in which an intramolecular mode couples to a low-energy shearing motion of the hydrogen-bonded network linking neighbouring molecules. The estimated value of 8.95 cm−1(1.11 meV) for this mode is less than the lowest energy mode reported from spectroscopic measurements for hydrogenous benzil (∼16 cm−1). A model previously derived from analysis of X-ray data observed over a limited range ofQhas been used to calculate neutron patterns over the fullQrange. Comparison with the present neutron data has shown that while the model gives a good description of the form of the diffuse patterns, the magnitudes of the atomic displacements are underestimated by a factor of ∼2.25.