Proton dynamics in a spark-plasma sintered BaZr0.7Ce0.2Y0.1O3-δ proton conductor investigated by quasi-elastic neutron scattering.

The thermally activated proton dynamics in the perovskite lattice of spark-plasma sintered BaZr0.7Ce0.2Y0.1O3-δ was investigated by quasi-elastic neutron scattering (QENS) and electrochemical impedance spectroscopy (EIS) in the temperature range from 200-600 °C. The quasi-elastic signal could be resolved into two components corresponding to a translational and rotational motion. From a description of the diffusive movements with the Chudley-Elliot jump diffusion model a jump distance of 3.12 Å and residence time of 13.6 ps were found for the translational protonic diffusion at 600 °C. The diffusion coefficients for QENS and EIS follow an Arrhenius law with activation energies of 0.16 eV, 0.58 eV and 0.88 eV for the microscopic proton self-diffusion, the bulk and grain boundaries, respectively. The rotational motion was analyzed using a two-site jump and a spherical rotation model which resulted in O-H distances of 0.89 Å and 0.71 Å, respectively. The data provided by the two-site jump model evidences the Grotthuss-type mechanism behind the translational proton dynamics.

Modified Landau-Placzek ratio of the liquid metal rubidium beyond hydrodynamics.

The intensity ratio of the Rayleigh line and the Brillouin lines can be derived within hydrodynamics and is known as the Landau-Placzek (LP) ratio. This ratio is directly related to the ratio of specific heats of the fluid. Within the microscopic wave vector range, which can be probed by inelastic neutron scattering, the intensity ratio for simple liquid metals deviates distinctly from the hydrodynamic prediction of the LP-ratio. We derive the intensity ratio from experimental data of liquid rubidium, which shows an enhanced LP-ratio by a factor 8 compared to the hydrodynamic prediction. This strong deviation indicates a further relaxation process in the microscopic wave vector range beyond hydrodynamics. That relaxation process is the viscoelastic reaction of the simple liquid to density fluctuations. Taking this process into account a modified LP-ratio is able to describe the data quite well.

Collective dynamics of liquid sulfur scrutinized over three decades in frequency.

Liquid sulfur consists mainly of eight-membered rings and hence can be regarded as a model of a molecular liquid. A liquid, which is built from different molecular structures, will demonstrate a wide range in relaxation processes and excitation modes. Three inelastic neutron scattering experiments have been performed to study the collective dynamics of liquid sulfur over three decades in frequencies. A wide range of wave vectors was studied to reveal the response of density fluctuations over different lengthscales. A viscoelastic model with a two-times memory function was applied to the data. The analysis revealed a slow relaxation mode, an acoustic-type excitation, and a high-frequency mode, which resembles an optic-type excitation. The wave-vector dependence of the slow relaxation mode width exhibits the signs of a de Gennes narrowing around the wave vector where the structure factor has a shoulder. This slow relaxation process could be related to diffusive particle movements. The acoustic-type modes evidence a viscoelastic reaction with a 50% enhancement of the sound velocity. This enhancement of the sound velocity and the spectral line shape is qualitatively similar to spectra of molecular liquids. The two relaxation times of the memory function are separated by about two orders of magnitude and underpin the need for a wide frequency range investigation of this complex liquid. The high-frequency response can be interpreted as optic-type modes in the liquid.

Non-Arrhenius behaviour of nickel self-diffusion in liquid Ni77Si23.

Nickel self-diffusion was measured for a Ni77Si23alloy in the liquid state over a temperature range of about 400 K through quasielastic neutron scattering. At the two lowest temperature points the derived diffusion coefficients deviate from a high-temperature Arrhenius-type behaviour and indicate a change in dynamics above the liquidus temperature. A fit with a power-law temperature dependence as predicted by the mode coupling theory for the liquid to glass transition can describe the diffusion coefficients quite well over the whole measured temperature range. The obtained results agree with predictions from a classical molecular dynamics (MD)-simulation, which evidenced an increasing glass forming ability with increasing silicon content. A crossover to a super-Arrhenius behaviour was reported for metallic glass formers above the liquidus temperature and the here investigated NiSi alloy demonstrates the same signature.

Collective particle dynamics of molten NaCl by inelastic x-ray scattering.

An inelastic x-ray scattering experiment has been performed on molten NaCl over wide wave vector and energy transfer ranges. Data of high statistical quality are analyzed using a memory function approach within a generalized Langevin equation. The approach with two relaxation times for the memory function provides a very good data description over the whole wave vector range beyond the hydrodynamic regime. A slow thermal and a fast structural relaxation process in the memory function completely define the density fluctuations in molten NaCl and evidences the thermal-viscoelastic model as the minimal description for collective particle dynamics in molten alkali halides. The obtained excitation frequencies demonstrate a large positive dispersion effect, which can be related to the viscoelastic reaction of the molten salt. A transition from the viscoelastic to a hydrodynamic response of the molten salt at small wave vectors is observed. In the hydrodynamic regime the resulting thermal diffusivity agrees well with values obtained through light scattering. The modeling indicates some deficiencies at small wave vectors and large energy transfers and the spectra of the current correlation function evidences additional intensity at high frequency. The frequency of these additional modes approach a non-zero value at zero wave vector and indicates a non-acoustic character of these excitations. The frequency center of this additional inelastic intensity coincides with optic-type modes in molten NaCl predicted by simulations.

Sodium ion self-diffusion in molten NaBr probed over different length scales.

The single-particle dynamics of sodium ions in molten sodium bromide has been investigated with quasielastic neutron scattering. A detailed and rather extensive data analysis procedure allowed determination of the pure sodium ion dynamics with increasing wave vector. Two different evaluation procedures agree perfectly on the resulting diffusion coefficient of sodium ions on long distances. A simple kinetic theory based on binary collisions of hard spheres is not able to reproduce the sodium diffusion coefficient. The derived reduced linewidth from modeling with a Lorentzian spectral function decreases with increasing wave vector towards the first structure factor maximum. That deviation from the hydrodynamic behavior signals the hindrance of the microscopic diffusion process due to the so-called cage effect when microscopic length scales are probed in a dense fluid. The observed quadratic wave-number-dependent decrease might be evidence for a coupling to density fluctuations as the source of the changes in the diffusion process. The results indicate that in the molten salt NaBr near the melting point the self-diffusion process might be governed by similar processes as already observed in dense metallic liquids.

Spinon confinement and a sharp longitudinal mode in Yb2Pt2Pb in magnetic fields.

The fundamental excitations in an antiferromagnetic chain of spins-1/2 are spinons, de-confined fractional quasiparticles that when combined in pairs, form a triplet excitation continuum. In an Ising-like spin chain the continuum is gapped and the ground state is Néel ordered. Here, we report high resolution neutron scattering experiments, which reveal how a magnetic field closes this gap and drives the spin chains in Yb2Pt2Pb to a critical, disordered Luttinger-liquid state. In Yb2Pt2Pb the effective spins-1/2 describe the dynamics of large, Ising-like Yb magnetic moments, ensuring that the measured excitations are exclusively longitudinal, which we find to be well described by time-dependent density matrix renormalization group calculations. The inter-chain coupling leads to the confinement of spinons, a condensed matter analog of quark confinement in quantum chromodynamics. Insensitive to transverse fluctuations, our measurements show how a gapless, dispersive longitudinal mode arises from confinement and evolves with magnetic order.

Dynamics on next-neighbour distances in liquid and undercooled gallium.

Density fluctuations of liquid and 20 K undercooled gallium have been studied by neutron spectroscopy. The decay of density fluctuations has been recorded at the structure factor maximum over a wide temperature range up to twice the melting temperature. The amplitude of the scattering function falls off with rising temperature in a nonlinear way with a changing slope around [Formula: see text]. The derived generalized longitudinal viscosity shows an upturn with decreasing temperature in the same temperature range. This increase in viscosity can be understood that liquid gallium transforms from a more fluid liquid metal to a more viscous liquid metal in that temperature range upon cooling. The change in the amplitude shows a remarkable agreement with results from liquid aluminium, lead and rubidium. This study suggests a universal crossover in dynamics of liquid monatomic metals, despite the many peculiar properties of gallium.

From Ising Resonant Fluctuations to Static Uniaxial Order in Antiferromagnetic and Weakly Superconducting CeCo(In_{1-x}Hg_{x})_{5}(x=0.01).

CeCo(In_{0.990}Hg_{0.010})_{5} is a charge doped variant of the d-wave CoCoIn_{5} superconductor with coexistent antiferromagnetic and superconducting transitions occurring at T_{N}=3.4 and T_{c}=1.4 K, respectively. We use neutron diffraction and spectroscopy to show that the magnetic resonant fluctuations present in the parent superconducting phase are replaced by collinear c-axis magnetic order with three-dimensional Ising critical fluctuations. No low-energy transverse spin fluctuations are observable in this doping-induced antiferromagnetic phase and the dynamic resonant spectral weight predominately shifts to the elastic channel. Static (τ>0.2 ns) collinear Ising order is proximate to superconductivity in CeCoIn_{5} and is stabilized through hole doping with Hg.

Stokes-Einstein relation of the liquid metal rubidium and its relationship to changes in the microscopic dynamics with increasing temperature.

For liquid rubidium the Stokes-Einstein (SE) relation is well fulfilled near the melting point with an effective hydrodynamic diameter, which agrees well with a value from structural investigations. A wealth of thermodynamic and microscopic data exists for a wide range of temperatures for liquid rubidium and hence it represents a good test bed to challenge the SE relation with rising temperature from an experimental point of view. We performed classical molecular dynamics simulations to complement the existing experimental data using a pseudopotential, which describes perfectly the structure and dynamics of liquid rubidium. The derived SE relation from combining experimental shear viscosity data with simulated diffusion coefficients reveals a weak violation at about 1.3T_{melting}≈400 K. The microscopic relaxation dynamics on nearest neighbor distances from neutron spectroscopy demonstrate distinct changes in the amplitude with rising temperature. The derived average relaxation time for density fluctuations on this length scale shows a non-Arrhenius behavior, with a slope change around 1.5T_{melting}≈450 K. Combining the simulated macroscopic self-diffusion coefficient with that microscopic average relaxation time, a distinct violation of the SE relation in the same temperature range can be demonstrated. One can conclude that the changes in the collective dynamics, a mirror of the correlated movements of the particles, are at the origin for the violation of the SE relation. The changes in the dynamics can be understood as a transition from a more viscous liquid metal to a more fluid-like liquid above the crossover temperature range of 1.3-1.5 T_{melting}. The decay of the amplitude of density fluctuations in liquid aluminium, lead, and rubidium demonstrates a remarkable agreement and points to a universal thermal crossover in the dynamics of liquid metals.

Diffusion mechanism in the sodium-ion battery material sodium cobaltate.

High performance batteries based on the movement of Li ions in Li x CoO2 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 x CoO2. Here we have determined the diffusion mechanism for Na0.8CoO2 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.

Quasielastic and low-energy inelastic neutron scattering study of HoCrO3 by high resolution time-of-flight neutron spectroscopy.

In order to understand the origin of the huge quasielastic magnetic scattering observed previously with a back-scattering neutron spectrometer, we have re-investigated the low energy excitations in HoCrO3 by inelastic neutron scattering in a much wider energy range with time-of-flight neutron spectrometers. The inelastic signals are due to the excitations between the ground state doublet of the Ho ion. The quasielastic signal is due to the fluctuation of the disordered Ho moments. At low temperature the intensity of quasielastic scattering is small. It starts increasing as the temperature increases above 30 K. At the same temperature, the elastic intensity due to Ho moment ordering decreases in a similar way. This observation strengthens the hypothesis that the quasielastic scattering is due the fluctuations of the disordered Ho moments. The time scale of fluctuations has been determine from the quasielastic scattering and was found to vary from about 22 ps at [Formula: see text] K to about 2.5 ps at [Formula: see text] K. The stretched exponential line shape indicates a distribution of decay rates at low temperatures.

Wave vector dependent damping of THz collective modes in a liquid metal.

Well-defined damped collective modes have been observed in liquid metals over a wide range of wave vectors. Hydrodynamics predicts that viscosity and thermal conductivity are the cause for the damping of the collective modes. Here we present experimental data from neutron spectroscopy on the damping of collective modes of liquid rubidium over a wide range of wave vectors. We propose a phenomenological model derived from generalized hydrodynamics to describe the damping of the modes and the evolution with increasing wave vector based on the viscoelastic picture of liquid response. As necessary ingredients a wave vector dependent high frequency shear modulus and shear relaxation time appear. We obtain a remarkable good agreement on a quantitative basis between experiment and calculation over a wide range of wave vectors. The emergent picture is that the lifetime of the collective modes in the THz regime is mainly limited through the diffusion of momentum. The proposed methodology might be applicable to a wide range of liquids.

On the microscopic mechanism behind the purely orientational disorder-disorder transition in the plastic phase of 1-chloroadamantane.

Globular molecules of 1-chloroadamantane form a plastic phase in which the molecules rotate in a restrained way, but with their centers of mass forming a crystalline ordered lattice. Plastic phases can be regarded as test cases for the study of disordered phases since, contrary to what happens in the liquid phase, there is a lack of stochastic translational degrees of freedom. When the temperature is increased, a hump in the specific heat curve is observed indicating a change in the energetic footprint of the dynamics of the molecules. This change takes place without a change in the symmetry of the crystalline lattice, i.e. no first-order transition is observed between temperatures below and above the calorimetric hump. This implies that subtle changes in the dynamics of the disordered plastic phase concerning purely orientational degrees of freedom should appear at the thermodynamic anomaly. Accordingly, we describe, for the first time, the microscopic mechanisms behind a disorder-disorder transition through the analysis of neutron diffraction and QENS experiments. The results evince a change in the molecular rotational dynamics accompanied by a continuous change in density.

Orphan Spins in the S=5/2 Antiferromagnet CaFe_{2}O_{4}.

CaFe_{2}O_{4} is an anisotropic S=5/2 antiferromagnet with two competing A (↑↑↓↓) and B (↑↓↑↓) magnetic order parameters separated by static antiphase boundaries at low temperatures. Neutron diffraction and bulk susceptibility measurements, show that the spins near these boundaries are weakly correlated and a carry an uncompensated ferromagnetic moment that can be tuned with a magnetic field. Spectroscopic measurements find these spins are bound with excitation energies less than the bulk magnetic spin waves and resemble the spectra from isolated spin clusters. Localized bound orphaned spins separate the two competing magnetic order parameters in CaFe_{2}O_{4}.

Solitary Magnons in the S=5/2 Antiferromagnet CaFe_{2}O_{4}.

CaFe_{2}O_{4} is a S=5/2 anisotropic antiferromagnet based upon zig-zag chains having two competing magnetic structures, denoted as the A (↑↑↓↓) and B (↑↓↑↓) phases, which differ by the c-axis stacking of ferromagnetic stripes. We apply neutron scattering to demonstrate that the competing A and B phase order parameters result in magnetic antiphase boundaries along c which freeze on the time scale of ∼1 ns at the onset of magnetic order at 200 K. Using high resolution neutron spectroscopy, we find quantized spin wave levels and measure 9 such excitations localized in regions ∼1-2 c-axis lattice constants in size. We discuss these in the context of solitary magnons predicted to exist in anisotropic systems. The magnetic anisotropy affords both competing A+B orders as well as localization of spin excitations in a classical magnet.

Br diffusion in molten NaBr explored by coherent quasielastic neutron scattering.

Molten sodium bromide has been investigated by quasielastic neutron scattering focusing on the wave vector range around the first structure factor peak. The linewidth of the scattering function shows a narrowing around the wave number of the structure factor peak, known as deGennes narrowing. In a monatomic system, this narrowing or in the time domain slowing down, has been related to a self-diffusion process of the caged particle. Here we show that this methodology can be applied to the molten alkali halide NaBr. The incoherent scattering from the sodium ions at small wave vectors provides the self-diffusion coefficient of sodium and the dynamics of bromine ions can be studied at wave numbers around the structure factor peak. With input from molecular dynamics simulations on the partial structure factors, diffusion coefficients of the bromine ions can be obtained. These experimentally derived diffusion coefficients are in good agreement with molecular dynamics simulation results. This methodology to extract self-diffusion coefficients from coherent quasielastic neutron scattering is applicable to binary fluids in general when one particle dominates the scattering response at the structure factor maximum.

Quasielastic neutron scattering measurements and ab initio MD-simulations on single ion motions in molten NaF.

The ionic stochastic motions in the molten alkali halide NaF are investigated by quasielastic neutron scattering and first principles molecular dynamics simulation. Quasielastic neutron scattering was employed to extract the diffusion behavior of the sodium ions in the melt. An extensive first principles based simulation on a box of up to 512 particles has been performed to complement the experimental data. From that large box, a smaller 64-particle box has then been simulated over a runtime of 60 ps. A good agreement between calculated and neutron data on the level of spectral shape has been obtained. The obtained sodium diffusion coefficients agree very well. The simulation predicts a fluorine diffusion coefficient similar to the sodium one. Applying the Nernst-Einstein equation, a remarkable large cross correlation between both ions can be deduced. The velocity cross correlations demonstrate a positive correlation between the ions over a period of 0.1 ps. That strong correlation is evidence that the unlike ions do not move completely statistically independent and have a strong association over a short period of time.

Experimental evidence for a dynamical crossover in liquid aluminium.

The temperature dependence of the dynamic structure factor at next-neighbour distances has been investigated for liquid aluminium. This correlation function is a sensitive parameter for changes in the local environment and its Fourier transform was measured in a coherent inelastic neutron scattering experiment. The zero frequency amplitude decreases in a nonlinear way and indicates a change in dynamics around 1.4 ∙ Tmelting. From that amplitude a generalized viscosity can be derived which is a measure of local stress correlations on next-neighbour distances. The derived generalized longitudinal viscosity shows a changing slope at the same temperature range. At this temperature the freezing out of degrees of freedom for structural relaxation upon cooling sets in which can be understood as a precursor towards the solid state. That crossover in dynamics of liquid aluminium shows the same signatures as previously observed in liquid rubidium and lead, indicating an universal character.

Transition from hydrodynamic to viscoelastic propagation of sound in molten RbBr.

Inelastic neutron scattering was applied to measure the acoustic-type excitations in the molten alkali halide rubidium bromide. For molten RbBr neutron scattering is mainly sensitive to the number density fluctuation spectrum and is not influenced by charge fluctuations. Utilizing a dedicated Brillouin scattering spectrometer, we focused on the small-wave-vector range. From inelastic excitations in the spectra a dispersion relation was obtained, which shows a large positive dispersion effect. This frequency enhancement is related to a viscoelastic response of the liquid at high frequencies. Towards small wave vectors we identify the transition to hydrodynamic behavior. This observation is supported by a transition of the sound velocity from a viscoelastic enhanced value to the adiabatic speed of sound for the acoustic-type excitations. Furthermore, the spectrum transforms into a line shape compatible with a prediction from hydrodynamics.