Determination of the short-wavelength propagation threshold in the collective excitations of liquid ammonia

The dynamics structure factor S(Q,E) of liquid ammonia l-NH3 at T = 200 K and at its vapor pressure has been measured by inelastic x-ray scattering (IXS) in the 1-15 nm(-1) momentum transfer ( Q) range. Contrary to previous IXS studies on other associated liquids and glasses, in l-NH3 a large inelastic signal is observed up to Q = 15 nm(-1). This, enabling S(Q,E) measurements as a function of Q at constant E transfer, allows us to demonstrate experimentally the transition from a propagating dynamics regime, where the acoustic excitation energy linearly disperses with Q, to a high-Q regime, where it is no longer possible to observe a dominant excitation in the S(Q,E).     

Analysis of inelastic x-ray scattering spectra of low-temperature water

We analyze a set of high-resolution inelastic x-ray scattering (IXS) spectra from H2O measured at T=259, 273, and 294 K using two different phenomenological models. Model I, called the "dynamic cage model," combines the short time in-cage dynamics described by a generalized Enskog kinetic theory with a long-time cage relaxation dynamics described by an alpha relaxation. This model is appropriate for supercooled water where the cage effect is dominant and the existence of an alpha relaxation is evident from molecular-dynamics (MD) simulation data of extended simple point charge (SPC/E) model water. Model II is essentially a generalized hydrodynamic theory called the "three effective eigenmode theory" by de Schepper et al. 11. This model is appropriate for normal liquid water where the cage effect is less prominent and there is no evidence of the alpha relaxation from the MD data. We use the model I to analyze IXS data at T=259 K (supercooled water). We successfully extract the Debye-Waller factor, the cage relaxation time from the long-time dynamics, and the dispersion relation of high-frequency sound from the short time dynamics. We then use the model II to analyze IXS data at all three temperatures, from which we are able to extract the relaxation rate of the central mode and the damping of the sound mode as well as the dispersion relation for the high-frequency sound. It turns out that the dispersion relations extracted from the two models at their respective temperatures agree with each other giving the high-frequency sound speed of 2900+/-300 m/s. This is to be compared with a slightly higher value reported previously, 3200+/-320 m/s, by analyzing similar IXS data with a phenomenological-damped harmonic oscillator model 22. This latter model has traditionally been used exclusively for the analysis of inelastic scattering spectra of water. The k-dependent sound damping and central mode relaxation rate extracted from our model analyses are compared with the known values in the hydrodynamic limit.     

Workshop on “very bright infrared sources and applications”

The study of electronic excitations by inelastic X-ray scattering (IXS) has a rich history. Very early IXS work, for example, provided seminal demonstrations of the validity of relativistic kinematics and the quantum hypothesis [1] and of Fermi-Dirac statistics [2]. While there have been many important results in the interim [3], it has been the development of the third generation light sources together with continuing innovations in the manufacture and implementation [4–6] of dispersive X-ray optics that has led to the rapid growth of IXS studies of electronic excitations.     

Inelastic X-ray scattering studies of phonons propagating along the axial direction of a DNA molecule having different counter-ion atmosphere

Shear-aligned 40 wt% calf-thymus Na-DNA molecules in aqueous solutions are prepared in their liquid crystalline phases and studied by high resolution inelastic X-ray scattering (IXS). Measured IXS spectra are analyzed with the generalized three effective eignmode (GTEE) theory. The phonon dispersion relations along the axial direction of DNA molecules with different MgCl₂ concentrations are constructed and compared. It is found that the sound speed along the axial direction of DNA molecules varies only slightly, but the phonon dampening is greatly affected with the increase amount of MgCl₂ concentration. Using the GTEE theory, we are able to extract the longitudinal viscosity in the hydrodynamic limit from the Q-dependence of a fitted parameter. We make a comprehensive review of the GTEE theory and discuss detailed analyses of IXS spectra taking into account finite energy resolution of the instrument.     

Inelastic x-ray scattering study of exciton properties in an organic molecular crystal

Excitons in a complex organic molecular crystal were studied by inelastic x-ray scattering (IXS) for the first time. The dynamic dielectric response function is measured over a large momentum transfer region, from which an exciton dispersion of 130 meV is observed. Semiempirical quantum chemical calculations reproduce well the momentum dependence of the measured dynamic dielectric responses, and thus unambiguously indicate that the lowest Frenkel exciton is confined within a fraction of the complex molecule. Our results demonstrate that IXS is a powerful tool for studying excitons in complex organic molecular systems. Besides the energy position, the IXS spectra provide a stringent test on the validity of the theoretically calculated exciton wave functions.     

Structure factors and phonon dispersion in liquid Li<Subscript>0.61</Subscript>Na<Subscript>0.39</Subscript> alloy

The phonon spectra for liquid Li and Na have been computed through the phenomenological model of Bhatia and Singh for disordered systems like liquids and glasses and the obtained results have been compared with the available data obtained by inelastic neutron scattering (INS) and inelastic X-ray scattering (IXS) experiments. The effective pair potentials and their space derivatives are important ingredients in the computation of the dispersion curves. The pair potentials are obtained using the pseudo-potential theory. The empty core model proposed by Ashcroft is widely used for pseudo-potential calculations for alkali metals. But, it is thought to be unsuitable for Li because of its simple 1s electronic structure. However, it can be used with an additional term known as Born-Mayer (BM) core term. The influence of the BM core term on the phonon dispersion is discussed. The same pseudo-potential formalism has been employed to obtain the dispersion relation in liquid Li_0.61Na_0.39 alloy. Apart from the phonon spectra, the Ashcroft-Langreth structure factors in the alloy are derived in the Percus-Yevick approximation.     

Structure of alkali borate glasses at high pressure: B and Li K-edge inelastic X-ray scattering study

We report the first in situ boron K-edge inelastic x-ray scattering (IXS) spectra for alkali borate glasses (Li2B4O7) at high pressure up to 30 GPa where pressure-induced coordination transformation from three-coordinated to four-coordinated boron was directly probed. Coordination transformation (reversible upon decompression) begins around 5 GPa and the fraction of four-coordinated boron increases with pressure from about 50% (at 1 atm) to more than 95% (at 30 GPa) with multiple densification mechanisms, evidenced by three distinct pressure ranges for (d[4]B/dP)T. The lithium K-edge IXS spectrum for Li-borate glasses at 5 GPa shows IXS features similar to that at 1 atm, suggesting that the Li environment does not change much with pressure up to 5 GPa. These results provide improved understanding of the structure of low-z glass at high pressure.     

Collisional properties of cold spin-polarized metastable neon atoms

We measure the rates of elastic and inelastic two-body collisions of cold spin-polarized neon atoms in the metastable 3P2 state for 20Ne and 22Ne in a magnetic trap. From particle loss, we determine the loss parameter of inelastic collisions beta=6.5(18) x 10(-12) cm(3) s(-1) for 20Ne and beta=1.2(3) x 10(-11) cm(3) s(-1) for 22Ne. These losses are caused by ionizing (i.e., Penning) collisions and occur less frequently than for unpolarized atoms. This proves the suppression of Penning ionization due to spin polarization. From cross-dimensional relaxation measurements, we obtain elastic scattering lengths of a=-180(40)a(0) for 20Ne and a = +150(+80)(-50)a(0) for 22Ne, where a(0)=0.0529 nm.     

Plasmons in sodium under pressure: increasing departure from nearly free-electron behavior

We have measured plasmon energies in Na under high pressure up to 43 GPa using inelastic x-ray scattering (IXS). The momentum-resolved results show clear deviations, growing with increasing pressure, from the predictions for a nearly free-electron metal. Plasmon energy calculations based on first-principles electronic band structures and a quasiclassical plasmon model allow us to identify a pressure-induced increase in the electron-ion interaction and associated changes in the electronic band structure as the origin of these deviations, rather than effects of exchange and correlation. Additional IXS results obtained for K and Rb are addressed briefly.     

q-Dependence of the giant bond-stretching phonon anomaly in the stripe compound La1.48Nd0.4Sr0.12CuO4 measured by IXS

Inelastic X-ray scattering (IXS) was used to study the Cu-O bond-stretching vibrations in the static stripe phase compound La_1.48Nd_0.4Sr_0.12CuO₄. It was found that the intrinsic width in Q-space of the previously reported huge anomalous phonon softening and broadening is approximately 0.08 r.l.u. HWHM. A detailed comparison was also made to inelastic neutron scattering (INS) studies, which indicate a two-peak lineshape (with superimposed broad and narrow peaks) in the vicinity of the anomaly. The high resolution IXS data show that the narrow peak is mostly an artifact of the poor transverse Q-resolution of INS. Otherwise, the agreement between the INS and IXS was excellent.     

Electron-hole excitations in NiO: LSDA+U-based calculations vs. inelastic X-ray scattering and ellipsometry measurements

The performance of the LSDA+U functional—in particular, the quality of the ground-state—is tested via calculations of the electron-hole excitations of NiO, which are compared with (non-resonant) inelastic X-ray scattering (IXS) and ellipsometry measurements. The dynamical density-response calculations are performed within the random-phase approximation (RPA), defining an LSDA+U/RPA density-response method. A significant success of this method is the insight it provides into the main loss present in the IXS data above the NiO optical gap, namely, a peak lying at ∼7.5 eV. This excitation, which is shown to be collective in nature, and to be induced by e_g-e_g transitions, provides a direct link between the correlated e_g-states and the IXS data. This finding illustrates the power of IXS, combined with correlated-band-structure theory (here, LSDA+U theory), for the investigation of the electronic structure of strongly correlated materials. At the same time, our results indicate that the LSDA+U/RPA response method does not represent a complete theory.     

Effect of electron-phonon scattering on shot noise in nanoscale junctions

We investigate the effect of electron-phonon inelastic scattering on shot noise in nanoscale junctions in the regime of quasiballistic transport. We predict that when the local thermal energy of the junction is larger than its lowest vibrational mode energy eV(c), the inelastic contribution to shot noise (conductance) increases (decreases) with bias as V (sqrt[V]). The corresponding Fano factor thus increases as sqrt[V]. We also show that the inelastic contribution to the Fano factor saturates with increasing thermal current exchanged between the junction and the bulk electrodes to a value which, for V > V(c), is independent of bias. These predictions can be readily tested experimentally.     

Synchrotron X‐ray tests of an L‐shaped laterally graded multilayer mirror for the analyzer system of the ultra‐high‐resolution IXS spectrometer at NSLS‐II

Characterization and testing of an L‐shaped laterally graded multilayer mirror are presented. This mirror is designed as a two‐dimensional collimating optics for the analyzer system of the ultra‐high‐resolution inelastic X‐ray scattering (IXS) spectrometer at National Synchrotron Light Source II (NSLS‐II). The characterization includes point‐to‐point reflectivity measurements, lattice parameter determination and mirror metrology (figure, slope error and roughness). The synchrotron X‐ray test of the mirror was carried out reversely as a focusing device. The results show that the L‐shaped laterally graded multilayer mirror is suitable to be used, with high efficiency, for the analyzer system of the IXS spectrometer at NSLS‐II.     

Inelastic scattering of Ne atoms from a LiF(001) surface

Scattering experiments with a ²⁰Ne nozzle beam from a LiF(001) surface in the 〈100〉 azimuth are reported. The (11) and (1&#x0304;1&#x0304;) Bragg reflections show broad tails due to inelastic scattering. These tails can be attributed by time-of-flight measurements to single phonon scattering on acoustic modes. The inelastic contribution decreases rapidly with increasing energy of the phonons involved.     

Advances in crystal analyzers for inelastic X-ray scattering

The realization of spherical crystal analyzers for inelastic X-ray scattering experiments (IXS) is an ongoing project at the ESRF since 1992. We developed reliable techniques to routinely produce silicon spherical analyzers with very high (ΔE=1÷10 meV) and high energy resolution (ΔE=0.2÷1.5 eV), and with very good focal properties and efficiency. In this article we report the state of the art of the analyzer construction and the main improvements made during the last years.     

Fine structure of the cross section of contact inelastic scattering of an X-ray photon by an atom

The analytical structure of the double differential cross section of contact inelastic scattering of an X-ray photon by a free atom is established by the methods of the theory of irreducible tensor operators beyond impulse approximation. For the example of an Ne atom in the energy region of the ionization threshold of the 1 s shell, the existence of a fine structure of the cross section caused by transitions of electrons of the atomic core to excited states of the discrete spectrum is predicted theoretically. The results of the calculation with the effects of radial relaxation, inelastic scattering via the formation of intermediate states, and elastic Rayleigh scattering taken into account are predictive in character and, at the incident photon energy of 22 keV, are in good agreement with the results of the synchrotron experiment. Original Russian Text ? A.N. Khoperskiĭ, A.M. Nadolinskiĭ, A.S. Kasprzhitskiĭ, 2008, published in Optika i Spektroskopiya, 2008, Vol. 105, No. 1, pp. 5–10.     

Interaction of intermediate-energy protons with <Superscript>20</Superscript>Ne and <Superscript>24</Superscript>Mg nuclei within the multiple-scattering model

Observables of the elastic and inelastic scattering of 800- and 250-MeV protons on ²⁰Ne and ²⁴Mg nuclei were calculated on the basis of the theory of multiple diffractive scattering and the dispersive α-cluster model. The ²⁰Ne and ²⁴Mg nuclei were assumed to consist of a core (¹⁶O nucleus) and additional alpha-particle clusters, which could be situated with the highest probability both in the vicinity of the center of mass of the core and outside the core. The multiparticle densities of these nuclei and single-particle nucleon-distribution densities as obtained from the dispersive α-cluster model were used in the calculations. The differential cross sections and polarizations for elastic and inelastic p ²⁰Ne and p ²⁴Mg scattering at the energy of 800 MeV are in better agreement with experimental data than the analogous calculations at the energy of 250 MeV. The spin-rotation functions calculated in the singleparticle approximation for elastic p ²⁰Ne and p ²⁴Mg scattering at these two energy values differ qualitatively from their counterparts calculated on the basis of the dispersive α-cluster model.     

A quantum wavepacket study of three-dimensional Ne—H+ 2 scattering

The state-to-state and state-to-all reaction probabilities have been calculated for three-dimensional reactive and inelastic scattering of Ne + H⁺ ₂ (v = 0, j = 0, 1, 2) at zero total angular momentum. The time-dependent Schrödinger equation is solved by means of Fourier grid and discrete variable representation techniques. The inelastic and reactive scattering probabilities for a broad range of energies are calculated. Although the system has an open reactive channel, the results show that a high fraction of the flux is reflected back due to endoergicity and potential barriers leading to inelastic scattering.