Wave Vector Transfer Research Articles

Dynamic Structure Factor on Liquid Na

The dynamic structure factor S(Q, E) has been measured on liquid sodium at 413 K by inelastic neutron scattering. The data present at constant values of the wave vector transfer in the range 0.9 Å-1 ⩽ Q ⩽ 9 Å-1 are corrected for multiple scattering. This has an essential contribution to the obtaining of reliable experimental data especially in the range of the small Q and large energy transfers. A comparison of the data in terms of some theoretical models proposed for simple liquids is performed. It is shown that the dynamics of liquid sodium is fairly well described by these models. Conclusion is that the dynamic behaviour of the liquid sodium is like a classical liquid.

Brillouin spectroscopy of incommensurate Ba2NaNb5O15

Abstract We have measured the Brillouin spectra of barium sodium niobate in its incommensurate phase at temperatures just above and below TI = 573 K. The longitudinal sound velocities along the a- and b- axes exhibit lambda-shaped dips near TI with significant dispersion, ranging from 4 % at small angles (5 GHz) to 1.8 % at large angles (63 GHz). In the same temperature region the linewidths increase by 300 % as TI is approached from above or below. The C11 data can be analyzed by assuming a relaxation time of form with τ0 = 1.7 × 10−13 sec. TI varies as A + Dq2, where A = 5.2 × 10−12 sec. and q is the wave vector transfer. The diffusion constant is ten times that measured in BaMnF4 by Lyons et al. and about 300 times the thermal diffusivity C22 has the same value and q-dependence of τ−1 1, but τ−1 0 for C22 is negligible.

Wavevector-resolved electron-energy-loss spectroscopy on the dangling-bond states of Ge(111)-(2 × 1)

Electronic surface state transitions at loss energies up to about 1.5 eV are studied by high resolution electron energy loss spectroscopy on Ge(111)-(2 × 1) surfaces prepared by cleavage in UHV. By variation of the primary energy and the detection angle the dependence of the transition energy hω on the wavevector transfer q ∥ is measured. The obtained “dispersion” hω( q ∥) is compared with results from angular resolved photoemission spectroscopy and with band structure calculations for the dangling bond bands.

Quasielastic neutron scattering from a large single crystal of α - Ag2Se

A quasielastic neutron scattering experiment has been performed on a large single crystal of α-Ag2Se. Spectra were taken at 250 °C, under different orientations of the crystal. The range of wavevector transfer was 1.0 Å−1 ⪅ |Qo| ⪅ 1.8 Å−1 for elastic scattering. The spectra typically contain a narrow and a broad quasielastic component, plus some broad medium-energy-transfer inelastic scattering. The narrow component is consistent with a continuous model in which the silver ions are assumed to diffuse within a system of <100> channels. The broad component is essentially ascribed to a localized irregular movement of the silver ions. The broad inelastic contributions to the spectra reflect highly damped periodic motions of the ions.

The π-bonded chain-model for Si(111)-(2 × 1) in view of recent wavevector-resolved electron energy loss spectra

Transition energies between the occupied and empty dangling bond surface state bands of cleaved Si(111)-(2 × 1) surfaces are measured by means of high resolution electron energy loss spectroscopy. The wavevector transfer q ∥ is parallel to the Γ-J and J'-K' lines of the surface Brillouin zone. Near the energy gaps relatively large dispersion of the bands is found. This is in contradiction to band structure calculations for the buckling model but supports the recently suggested π-bonded chain model for the (2 × 1) reconstruction.

On the dynamics in compressed methane gas at 3 kbar by inelastic neutron scattering

The scattering function for methane gas at 295K and 3.0 kbar has been measured for wavevector transfers (Q) from 0.8 to 2.0 AA-1. The maximum energy transfers vary over the range of Q from 13 to 26 meV. The second energy moments of the scattering function were evaluated for 1.6 AA-1<or=Q<or=2.0 AA-1 showing a somewhat lower value, on average, than predictions based on decoupled translational and rotational motions. Combining this observation with the discrepancies between the measured scattering function and the calculated one, again assuming decoupled motions, there is an indication of weak coupling effects in the system. The frequency spectrum, reflecting the dynamics of the methane molecule, is estimated for energy transfers up to 17 meV, showing clear discrepancies compared with simple physical models which do not include coupling effects, e.g. the Langevin or rigid-sphere motion.

The dynamic scattering function for liquid bismuth at small wavevectors

The dynamic scattering function for liquid bismuth at 580K has been determined by neutron inelastic scattering for wavevector transfers, Q, in the range 0.5<or=Q<or=1.6 AA-1. The zeroth energy moment is satisfied within some ten per cent for all Q. No clear evidence of collective excitations is seen. Thus it is concluded that the molecular dynamics in liquid bismuth is different as compared to the classical liquid metals rubidium and lead.

Critical phenomena in a binary mixture ofn−hexaneand nitrobenzene. Analysis of viscosity and light-scattering data

Extensive measurements were made of light scattering intensity, quasielastic spectral width, and shear viscosity of the binary-liquid system $n\ensuremath{-}\mathrm{hexane}$ and nitrobenzene in the critical region. The measurements cover both the critical isochore and some other isochores in the temperature range $T=1 \mathrm{mK} \mathrm{to} 30 \mathrm{K}$ around the consolute temperature. The scattering experiments were made at five different angles covering a range of wave-vector transfer $q$ from 3.5\ifmmode\times\else\texttimes\fi{}${10}^{4}$ to 28.2\ifmmode\times\else\texttimes\fi{}${10}^{4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ with values of the scaling variable $q\ensuremath{\xi}$ ($\ensuremath{\xi}$ is the correlation length) spanning from 0.006 to 51. The data on viscosity and linewidth are analyzed in the light of recent theoretical predictions taking into account the background effects on the transport coefficients. The agreement between theory and the experiments is very good in the whole range of $q\ensuremath{\xi}$ when the background effect is included.

DC Transport Coeffcient Calculation by a Derivatives of Time Correlation Functions. II. Application to the Case of Liquid Metals and Alloys

Formula for electric resistivity ρ, derived in the first part of this work has developed to the case when the coupling of carriers to the rest part of many particle system, can be described by a local pseudo potential, like to the case of liquid metals and alloys. Resistivity of liquid alkali metals has been calculated, and specific lines of numerical calculations by the new formula have been analysed and comments given. According to our results, the scattering of carriers accompanied by the wave vector transfer in amount of q , is of essential importance, not only for q 2 k f , in opposite to the Ziman's formula, which takes into consideration and accounts only the region q <2 k f .

Dynamics of liquidN2studied by neutron inelastic scattering

Neutron inelastic-scattering data from liquid ${\mathrm{N}}_{2}$ at wave-vector transfer $\ensuremath{\kappa}$ between 0.18 and 2.1 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and temperatures ranging from $T=65\ensuremath{-}77$ K are presented. The data are corrected for the contribution from multiple scattering and incoherent scattering. The resulting dynamic structure factor $S(\ensuremath{\kappa},\ensuremath{\omega})$ is compared with $S(\ensuremath{\kappa},\ensuremath{\omega})$ determined by a molecular-dynamics calculation and with that calculated from a linearized Vlasov equation. For $\ensuremath{\kappa}\ensuremath{\le}0.3$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ the experimental $S(\ensuremath{\kappa},\ensuremath{\omega})$ is compared with the values predicted by hydrodynamic theory.

Dynamical structure factor for liquid bismuth

The scattering function $S(Q,E)$ for liquid bismuth at 305\ifmmode^\circ\else\textdegree\fi{}C has been determined by neutron inelastic scattering in the wave-vector transfer range $1.6lQl7.2$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and for energy transfers $E$ up to about 20 meV. The measured $S(Q,E)$ satisfies the zeroth- and the second-moment relations within some few percent. The shoulder in the static structure factor $S(Q)$ gives rise to clearly visible effects also in the dynamical-scattering function. The full width at half maximum of $S(Q,E)$ exhibits an oscillation at a $Q$ value corresponding to the position of the shoulder. This fact together with some particular features in the same $Q$ range regarding the experimentally obtained spectrum of the longitudinal current-current correlation function indicates that the nature of the molecular dynamics in liquid bismuth is different as compared with simple liquid metals.

On the Relation Between the Effective Pair-potential and the Static Structure Factor in Liquid Metals

Abstract Accurate neutron diffraction measurements of the static structure factor S(Q) for small wave-vector transfers Q have been used to obtain the ‘coarse’ structure of the long-range part of the effective inter-particle potential in liquid aluminium, lead and bismuth. An extended version of the random phase approximation developed by Gaskell has been used. It is found that for Al and Pb the potential is of simple oscillatory nature while for Bi it is of ledge type. Finer details of the shape of the potential could not be evaluated. Methods to determine a good pair-potential by combining experimental results and molecular dynamics calculations are suggested.

On the rotational motion of the ammonium ion in the CsCl-type phase of NH4Br: Results from quasielastic neutron scattering

The rotational motion of the ammonium ion in polycrystalline NH4Br has been investigated by quasielastic incoherent neutron scattering at 12 different temperatures between 297 and 409 K. The measured spectra were corrected for multiple scattering and compared to the C4-rotational jump model. The elastic incoherent structure factor was determined experimentally within the range 0.15⩽Q⩽1.72 Å−1 of elastic wave vector transfer. It yields a N-H bond length of 1.028±0.005 Å. The rotational jump rate was found to follow an Arrhenius law, 1 τC4[s−1] ±0.16)×1013 exp{(−1623±16)/T[K]}, with an activation energy of Ea=13.49±0.13 kJ/mole. Within the studied temperature interval the mean square hydrogen vibration amplitude can be described by the expression 〈u2〉 [Å2−]±1.6)×10−4 T[K] −(16.4±6)×10−2.

Lifetime of zero sound in liquid3He

Zero-sound excitations in liquid 3He at 0.02K and at the pressure of the saturated vapour have been studied using neutron inelastic scattering techniques. The results for the frequencies of the zero-sound excitations are in agreement with the measurements of Skold and co-workers. The results also show a non-zero linewidth for the excitations with wave-vector transfers 0.45 AA-1<Q<0.8 AA-1, which suggests that modification to the current theories is required.

The dynamics of the hydrogen atoms in LaNi5H≥3.0 studied by slow neutron scattering

Abstract The diffusion coefficient for hydrogen in LaNi 5 H x , 3.0 x −6 cm 2 /s and approximately follow the Arrhenius law. A pronounced anomaly in the Debye-Waller factors for the hydrogen motion has been observed for the quasi-elastic scattering at small wave-vector transfers.

Study of jump models for the diffusion of hydrogen in NbH0.02 by means of the quasielastic scattering of slow neutrons

The quasielastic scattering of slow neutrons in a NbH0.02 single crystal has been measured for a wavevector transfer Q between 0.5 ≤ |Q| ≤ 2.5 Å−1 at 293, 431 and 581 K for several sample orientations. The data have been analysed in terms of several jump models for the diffusion of hydrogen by comparing the spectral lineshape with the incoherent scattering law Sinc(Q, ω) of the models. The model of jumps to nearest-neighbor sites becomes progressively worse with increasing temperature. The discrepancy cannot be remedied by taking into account jumps to the second-neighbor sites. On the other hand the measured spectral lineshape can be well reproduced in the whole |Q| range by a double-jump model and a two-state model. For comparison, the method of fitting one Lorentzian to theory and experiment has also been used.

Rotational correlation functions of plastic-crystalline neopentane from neutron scattering experiments

The rotational motions of neopentane molecules in the orientationally disordered phase have been studied by incoherent neutron scattering. The measurements were performed with a rotating-crystal spectrometer (incoming wavelength 4.1 Å), covering a wave-vector transfer range of 0.23–2.18 A ̊ −1 . Its resolution leads to an observation time up to about 5 ps. From the time-of-flight spectra intermediate scattering functions and frequency distributions were obtained. The frequency distributions were fitted with a damped Debye-model for the translational motions. From the intermediate scattering functions the rotational part was deduced and, using the partial-wave expansion, rotational correlation functions could be determined up to third order. These first-and second-order correlation functions are compared with infrared and Raman data and they are found to be in good agreement. From the behaviour of the elastic intensity of the spectra it can be concluded that on the time-scale covered the distribution of the protons of the molecule does not randomize. A comparison of elastic intensities and rotational correlation functions with the predictions of several, symmetry adapted, jump reorientation models is made. The best fit is obtained for a model with D 2d symmetry where 90° reorientations about the fourfold axis occur more frequently than 180° jumps about the two perpendicular twofold axes.

Neutron scattering study of thermally excited density fluctuations in a dense classical fluid

Collective density fluctuations in $^{36}\mathrm{Ar}$ gas at 456 atm pressure and 295 K have been studied by thermal neutron scattering using time-of-flight techniques. Well-defined collective modes are observed for wave-vector transfers $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\lesssim}0.1$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ which become strongly damped at larger $k$. The data have been compared in detail with predictions of the generalized Enskog equation. Although extrapolation of the predictions to $k=0$ gives the correct transport coefficients to better than 5% accuracy, the generalized Enskog equation does not properly predict the wave-vector dependence of the scattering law.

Lattice dynamics of hcpHe4at high pressure

The neutron-inelastic-scattering technique was used to measure the phonon dispersion relations in two high-density crystals of hcp $^{4}\mathrm{He}$ with molar volumes of 11.61 and 9.41 ${\mathrm{cm}}^{3}$/mol. These densities are on the order of twice that of $^{4}\mathrm{He}$ at 30 bars. The crystals were grown from the melt in the fcc phase, and cooled across the fcc-hcp phase transition. The observed phonon spectra show anharmonic effects much less prominent than those observed in earlier measurements at 21 ${\mathrm{cm}}^{3}$/mol. In particular, multiphonon interference effects were not found to be very pronounced, while multiphonon scattering appeared to influence phonon line shapes strongly for large wave-vector and energy transfers. Elastic constants d\ifmmode \dot{e}\else \.{e}\fi{}termined from the initial slopes of the dispersion curves were found to be in good agreement with those calculated by Goldman using the first-order self-consistent-phonon theory. The dependence on volume of the phonon energies is discussed with reference to the earlier studies at 21.1 and 16.0 ${\mathrm{cm}}^{3}$/mol. No significant dispersion of mode Gr\uneisen parameters was found unlike the case of fcc He. Gr\uneisen parameters were found to depend on volume approximately in a manner given by Ahlers for the thermodynamic Gr\uneisen parameter.

Self-consistent phonons in fccHe4

The dynamic form factor, $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}, \ensuremath{\omega})$, of fcc $^{4}\mathrm{He}$ at high density is calculated, including the one-phonon, the two-phonon, and interference contributions, for comparison with the recent neutron-scattering measurements of Eckert et al. and of Thomlinson et al. The purpose is to test how well the standard self-consistent phonon (SCP) theory, which takes no account of short-range correlations in the atomic vibration, can describe a moderately anharmonic crystal such as fcc $^{4}\mathrm{He}$. The SCP theory is found to provide a good overall description of the neutron scattering data including both the one-phonon and multiphonon character. It is also found that the usual separation of $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}, \ensuremath{\omega})$, into a one-phonon and multiphonon contribution becomes difficult or impossible for wave-vector transfers $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}=(\frac{2\ensuremath{\pi}}{a})(\ensuremath{\zeta}, \ensuremath{\zeta}, \ensuremath{\zeta},)$ with $\ensuremath{\zeta}&lt;1.3$ at high-energy transfer. This is due to an unusually large frequency dependence of the two-phonon scattering contribution to $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}, \ensuremath{\omega})$.