Collective dynamics of liquid sulphur across the polymerisation transition temperature probed by inelastic x-ray scattering.

Inelastic x-ray scattering (IXS) experiments on liquid sulphur were carried out below (140◦C) and above (180◦C) the polymerisation temperature Tλ of about 159◦C to investigate changes in the collective dynamics of this unique liquid, that exhibits a liquid‒liquid transition. As reported earlier, broad longitudinal acoustic excitation signals were observed at both temperatures, and only the width of the quasielastic peaks slightly decreased when the temperature crossed the transition temperature. A model analysis was performed using a generalised Langevin formalism with a memory function having one thermal and two viscoelastic decay channels with the help of simple sparse modelling, and large positive deviations from the hydrodynamic sound velocity by 51‒54% were observed. The fast viscoelastic relaxation time τµis close to the correlation times of intermolecular stretching and bending motions of local sulphur connections in both ring and chain structures, and is similar to those of other molecular liquids. The small contrasts in the IXS spectra across the λ transition result in large changes in only the slow viscoelastic decay time τα of the memory function. The τα value at 140◦C matches the mixed internal/external torsional modes of S8 molecules well, whereas that at 180◦C has no corresponding molecular motion mode. The kinematic viscosity values at thesmaller than the minimum values of macroscopic shear viscosity, in⃗dicating that largeQ 0 limit are much changes in relaxation dynamics are expected with Q in the GHz and MHz excitation regimes. .

Density deficit of Earth's core revealed by a multimegabar primary pressure scale.

An accurate pressure scale is a fundamental requirement to understand planetary interiors. Here, we establish a primary pressure scale extending to the multimegabar pressures of Earth's core, by combined measurement of the acoustic velocities and the density from a rhenium sample in a diamond anvil cell using inelastic x-ray scattering and x-ray diffraction. Our scale agrees well with previous primary scales and shock Hugoniots in each experimental pressure range and reveals that previous scales have overestimated laboratory pressures by at least 20% at 230 gigapascals. It suggests that the light element content in Earth's inner core (the density deficit relative to iron) is likely to be double what was previously estimated, or Earth's inner core temperature is much higher than expected, or some combination thereof.

Dynamic Lone Pair Expression as Chemical Bonding Origin of Giant Phonon Anharmonicity in Thermoelectric InTe.

Loosely bonded ("rattling") atoms with s2 lone pair electrons are usually associated with strong anharmonicity and unexpectedly low thermal conductivity, yet their detailed correlation remains largely unknown. Here we resolve this correlation in thermoelectric InTe by combining chemical bonding analysis, inelastic X-ray and neutron scattering, and first principles phonon calculations. We successfully probe soft low-lying transverse phonons dominated by large In1+ z-axis motions, and their giant anharmonicity. We show that the highly anharmonic phonons arise from the dynamic lone pair expression with unstable occupied antibonding states induced by the covalency between delocalized In1+ 5s2 lone pair electrons and Te 5p states. This work pinpoints the microscopic origin of strong anharmonicity driven by rattling atoms with stereochemical lone pair activity, important for designing efficient materials for thermoelectric energy conversion.

Sound velocity of hexagonal close-packed iron to the Earth's inner core pressure.

Here we determine the compressional and shear wave velocities (vp and vs) of hexagonal close-packed iron, a candidate for the main constituent of the Earth's inner core, to pressures above 300 gigapascals using a newly designed diamond anvil cell and inelastic X-ray scattering combined with X-ray diffraction. The present results reveal that the vp and vs of the Preliminary reference Earth model (PREM) inner core are 4(±2)% and 36(±17)% slower than those of the pure iron, respectively at the centre of the core. The density and sound velocity of the PREM inner core can be explained by addition of 3(±1) wt% silicon and 3(±2) wt% sulphur to iron‒5 wt% nickel alloy. Our suggested inner core composition is consistent with the existing outer core model with oxygen, as the growth of the inner core may have created a secular enrichment of the element in the outer core.

Effects of molecular shape and flexibility on fast sound of organic liquids.

Inelastic x-ray scattering spectra of four organic liquids, n-hexane, cyclohexane, ethylene glycol dimethyl ether, and 1,4-dioxane, were measured, and the sound velocity in the nm-1 wavenumber and meV energy regimes was determined. Compared with the corresponding values in the hydrodynamic limit, the sound velocity in the nm-1 regime was faster, and the positive dispersion of the longitudinal modulus was stronger in liquids composed of ring structures (cyclohexane and 1,4-dioxane) than in those of linear chain structures (n-hexane and ethylene glycol dimethyl ether). Molecular dynamics simulation of n-hexane and cyclohexane was also performed. The difference in the positive dispersion of the longitudinal modulus was reproduced by simulation, and it was elucidated by the difference in the longitudinal modulus in the q = 0 limit and the THz frequency regime. The excess part of the longitudinal modulus from the hydrodynamic limit was further divided into various contributions, and the smaller excess modulus of n-hexane was mainly ascribed to two reasons. The first one is that the shear modulus of n-hexane is smaller in the THz regime, and the second one is that the positive dispersion of the bulk modulus due to the vibrational energy relaxation is weaker. The second mechanism was further interpreted in terms of the fast vibrational energy relaxation of intramolecular modes associated with the chain deformation of n-hexane.

Calculating temperature-dependent X-ray structure factors of α-quartz with an extensible Python 3 package.

The design of X-ray optics based on diffraction from crystals depends on the accurate calculation of the structure factors of their Bragg reflections over a wide range of temperatures. In general, the temperature dependence of the lattice parameters, the atomic positions and the atomic thermal vibrations is both anisotropic and nonlinear. Implemented here is a software package for precise and flexible calculation of structure factors for dynamical diffraction. α-Quartz is used as an example because it presents the challenges mentioned above and because it is being considered for use in high-resolution X-ray spectroscopy. The package is designed to be extended easily to other crystals by adding new material files, which are kept separate from the package's stable core. Python 3 was chosen as the language to allow the easy integration of this code into existing packages. The importance of a correct anisotropic treatment of the atomic thermal vibrations is demonstrated by comparison with an isotropic Debye model. Discrepancies between the two models can be as much as 5% for strong reflections and considerably larger (even to the level of 100%) for weak reflections. A script for finding Bragg reflections that backscatter X-rays of a given energy within a given temperature range is demonstrated. The package and example scripts are available on request. Also discussed, in detail, are the various conventions related to the proper description of chiral quartz.

Structural changes across thermodynamic maxima in supercooled liquid tellurium: A water-like scenario.

Liquid polymorphism is an intriguing phenomenon that has been found in a few single-component systems, the most famous being water. By supercooling liquid Te to more than 130 K below its melting point and performing simultaneous small-angle and wide-angle X-ray scattering measurements, we observe clear maxima in its thermodynamic response functions around 615 K, suggesting the possible existence of liquid polymorphism. A close look at the underlying structural evolution shows the development of intermediate-range order upon cooling, most strongly around the thermodynamic maxima, which we attribute to bond-orientational ordering. The striking similarities between our results and those of water, despite the lack of hydrogen-bonding and tetrahedrality in Te, indicate that water-like anomalies may be a general phenomenon among liquid systems with competing bond- and density-ordering.

Universal Two-Component Dynamics in Supercritical Fluids.

Despite the technological importance of supercritical fluids, controversy remains about the details of their microscopic dynamics. In this work, we study four supercritical fluid systems─water, Si, Te, and Lennard-Jones fluid─via classical molecular dynamics simulations. A universal two-component behavior is observed in the intermolecular dynamics of these systems, and the changing ratio between the two components leads to a crossover from liquidlike to gaslike dynamics, most rapidly around the Widom line. We find evidence to connect the liquidlike component dominating at lower temperatures with intermolecular bonding and the component prominent at higher temperatures with free-particle, gaslike dynamics. The ratio between the components can be used to describe important properties of the fluid, such as its self-diffusion coefficient, in the transition region. Our results provide an insight into the fundamental mechanism controlling the dynamics of supercritical fluids and highlight the role of spatiotemporally inhomogeneous dynamics even in thermodynamic states where no large-scale fluctuations exist in the fluid.

Temperature-gradient analyzers for non-resonant inelastic X-ray scattering.

The detailed fabrication and performance of the temperature-gradient analyzers that were simulated by Ishikawa & Baron [(2010). J. Synchrotron Rad. 17, 12-24] are described and extended to include both quadratic and 2D gradients. The application of a temperature gradient compensates for geometric contributions to the energy resolution while allowing collection of a large solid angle, ∼50 mrad × 50 mrad, of scattered radiation. In particular, when operating relatively close to backscattering, π/2 - θB = 1.58 mrad, the application of a gradient of 1.32 K per 80 mm improves the measured total resolution from 60 to 25 meV at the full width at half-maximum, while when operating further from backscattering, π/2 - θB = 6.56 mrad, improvement from 330 to 32 meV is observed using a combination of a gradient of 6.2 K per 80 mm and dispersion compensation with a position-sensitive detector. In both cases, the operating energy was 15.8 keV and the incident bandwidth was 22 meV. Notably, the use of a temperature gradient allows a relatively large clearance at the sample, permitting installation of more complicated sample environments.

Practical measurement of the energy resolution for meV-resolved inelastic X-ray scattering.

Several different ways of measuring the energy resolution for meV-resolved inelastic X-ray scattering (IXS) are compared: using scattering from poly(methyl methacrylate), PMMA, using scattering from borosilicate glass (Tempax), and using powder diffraction from aluminium. All of these methods provide a reasonable first approximation to the energy resolution, but, also, in all cases, inelastic contributions appear over some range of energy transfers. Over a range of ±15 meV energy transfer there is good agreement between the measurements of PMMA and Tempax at low temperature, and room-temperature powder diffraction from aluminium, so we consider this to be a good indication of the true resolution of our ∼1.3 meV spectrometer. The resolution over a wider energy range is self-consistently determined using the temperature, momentum and sample dependence of the measured response. The inelastic contributions from the PMMA and Tempax, and their dependence on momentum transfer and temperature, are then quantitatively investigated. The resulting data allow us to determine the resolution of our multi-analyzer array efficiently using a single scan. The importance of this procedure is demonstrated by showing that the results of the analysis of a spectrum from a glass are changed by using the properly deconvolved resolution function. The impact of radiation damage on the scattering from PMMA and Tempax is also discussed.

Local self-motion of water through the Van Hove function.

We show that the self-part of the Van Hove function-the correlation function describing the dynamics of a single molecule-of water can be determined through a high-resolution inelastic x-ray scattering experiment. The measurement of inelastic x-ray scattering up to 10Å^{-1} makes it possible to convert the inelastic x-ray scattering spectra into the Van Hove function, and its self-part is extracted from the short-range correlations. The diffusivity estimated from the short-range dynamics of water molecules is different from the long-range diffusivity measured by other methods. This approach using the experimentally determined self-part of the Van Hove function will be useful to the study of the local dynamics of atoms and molecules in liquids.

Equation of State of Liquid Iron under Extreme Conditions.

The density of liquid iron has been determined up to 116 GPa and 4350 K via static compression experiments following an innovative analysis of diffuse scattering from liquid. The longitudinal sound velocity was also obtained to 45 GPa and 2700 K based on inelastic x-ray scattering measurements. Combining these results with previous shock-wave data, we determine a thermal equation of state for liquid iron. It indicates that Earth's outer core exhibits 7.5%-7.6% density deficit, 3.7%-4.4% velocity excess, and an almost identical adiabatic bulk modulus, with respect to liquid iron.

Two-Component Dynamics and the Liquidlike to Gaslike Crossover in Supercritical Water.

Molecular-scale dynamics in sub- to supercritical water is studied with inelastic x-ray scattering and molecular dynamics simulations. The obtained longitudinal current correlation spectra can be decomposed into two main components: a low-frequency (LF), gaslike component and a high-frequency (HF) component arising from the O-O stretching mode between hydrogen-bonded molecules, reminiscent of the longitudinal acoustic mode in ambient water. With increasing temperature, the hydrogen-bond network diminishes and the spectral weight shifts from HF to LF, leading to a transition from liquid- to gaslike dynamics with rapid changes around the Widom line.

Identifying Water-Anion Correlated Motion in Aqueous Solutions through Van Hove Functions.

Electrolyte solutions are ubiquitous in materials in daily use and in biological systems. However, the understanding of their molecular and ionic dynamics, particularly those of their correlated motions, are elusive despite extensive experimental, theoretical, and numerical studies. Here we report the real-space observations of the molecular/ionic-correlated dynamics of aqueous salt (NaCl, NaBr, and NaI) solutions using the Van Hove functions obtained by high-resolution inelastic X-ray scattering measurement and molecular dynamics simulation. Our results directly depict the distance-dependent dynamics of aqueous salt solutions on the picosecond time scale and identify the changes in the anion-water correlations. This study demonstrates the capability of the real-space Van Hove function analysis to describe the local correlated dynamics in aqueous salt solutions.

Erratum: Viscosity and real-space molecular motion of water: Observation with inelastic x-ray scattering [Phys. Rev. E 98, 022604 (2018)].

This corrects the article DOI: 10.1103/PhysRevE.98.022604.

Compact hard x-ray split-delay system based on variable-gap channel-cut crystals.

We present the concept and a prototypical implementation of a compact x-ray split-delay system that is capable of performing continuous on-the-fly delay scans over a range of ∼10 ps with sub-100 nanoradian pointing stability. The system consists of four channel-cut silicon crystals, two of which have gradually varying gap sizes from intentional 5 deg asymmetric cuts. The delay adjustment is realized by linear motions of these two monolithic varying-gap channel cuts, where the x-ray beam experiences pairs of anti-parallel reflections, and thus becomes less sensitive in output beam pointing to motion imperfections of the translation stages. The beam splitting is accomplished by polished crystal edges. A high degree of mutual coherence between the two branches at the focus is observed by analyzing small-angle coherent x-ray scattering patterns. We envision a wide range of applications including single-shot x-ray pulse temporal diagnostics, studies of high-intensity x-ray-matter interactions, as well as measurement of dynamics in disordered material systems using split-pulse x-ray photon correlation spectroscopy.

Viscosity and real-space molecular motion of water: Observation with inelastic x-ray scattering.

Even though viscosity is one of the fundamental properties of liquids, its microscopic origin is not fully understood. We determined the spatial and temporal correlation of molecular motions of water near room temperature and its temperature variation on a picosecond timescale and a subnanometer spatial scale, through high-resolution inelastic x-ray scattering measurement. The results, expressed in terms of the time-dependent pair correlation function called the Van Hove function, show that the timescale of the decay of the molecular correlation is directly related to the Maxwell relaxation time near room temperature, which is proportional to viscosity. This conclusion validates our earlier finding that the topological changes in atomic or molecular connectivity are the origin of viscosity in liquids.

Pressure dependence of transverse acoustic phonon energy in ferropericlase across the spin transition.

We investigated transverse acoustic (TA) phonons in iron-bearing magnesium oxide (ferropericlase) up to 56 GPa using inelastic x-ray scattering (IXS). The results show that the energy of the TA phonon far from the Brillouin zone center suddenly increases with increasing pressure above the spin transition pressure of ferropericlase. Ab initio calculations revealed that the TA phonon energy far from the Brillouin zone center is higher in the low-spin state than in the high spin state; that the TA phonon energy depend weakly on pressure; and that the energy gap between the TA and the lowest-energy-optic phonons is much narrower in the low-spin state than in the high-spin state. This allows us to conclude that the anomalous behavior of the TA mode in the present experiments is the result of gap narrowing due to the spin transition and explains contradictory results in previous experimental studies.

Seeing real-space dynamics of liquid water through inelastic x-ray scattering.

Water is ubiquitous on earth, but we know little about the real-space motion of molecules in liquid water. We demonstrate that high-resolution inelastic x-ray scattering measurement over a wide range of momentum and energy transfer makes it possible to probe real-space, real-time dynamics of water molecules through the so-called Van Hove function. Water molecules are found to be strongly correlated in space and time with coupling between the first and second nearest-neighbor molecules. The local dynamic correlation of molecules observed here is crucial to a fundamental understanding of the origin of the physical properties of water, including viscosity. The results also suggest that the quantum-mechanical nature of hydrogen bonds could influence its dynamics. The approach used here offers a powerful experimental method for investigating real-space dynamics of liquids.

Effect of cation substitution on bridgmanite elasticity: A key to interpret seismic anomalies in the lower mantle.

Seismological observations show that, in some regions of the lower mantle, an increase in bulk sound velocity, interestingly, occurs in the same volume where there is a decrease in shear velocity. We show that this anti-correlated behavior occurs on cation substitution in bridgmanite by making single crystal elasticity measurements of MgSiO3 and (Mg,Fe,Al)(Si,Al)O3 using inelastic x-ray scattering in the ambient conditions. Cation substitution of ferrous iron and aluminum may explain large low shear velocity provinces in the lower mantle.