Theory of inelastic neutron scattering from molecular fluids

The time-dependent angular pair correlation function is discussed and its use in the analysis of inelastic neutron scattering experiments from polyatomic fluids is described, including both the coherent and incoherent spectra. The set of formal results given here permits a systematic interpretation of neutron inelastic scattering spectra on simple molecular liquids. Neutron spectra second moments are reviewed, and a new result for the fourth moment is given for the incoherent spectrum. Numerical results for the moments are obtained. The fourth moment depends on the mean squared torque and the mean squared force acting on a molecule in the fluid, and may provide a means for studying intermolecular forces in dense fluids. In addition, a method of calculating the correlation function for weak anisotropic forces is outlined.     

Incoherent inelastic neutron scattering from hexamethylene-tetramine and adamantane

The incoherent inelastic neutron scattering spectra of hexamethylene tetramine (HMT) and adamantane have been measured at high resolution between 200 and 1000 cm^-1. The agreement between the frequencies of the observed spectra and the optical spectra of Mecke and Spieseche (HMT) and Bailey (adamantane) is good. The observed neutron spectra are also matched very closely by the calculated one-phonon spectra, computed from a normal-coordinate analysis. There is some additional structure in the neutron spectra which appears to be due to multiphonon scattering involving lattice modes.     

Elastic and inelastic scattering components in the angular intensity distribution of He scattered from graphite

The angular intensity distribution of thermal energy He beam scattered from highly oriented pyrolytic graphite (HOPG) surface has been measured by means of supersonic molecular beam scattering technique in the wide surface temperature range. To separate the elastic and inelastic scattering components, simple analysis method has been developed by applying the classical binary collision theory of the hard cube model (HCM). From the extracted elastic scattering component in the scattering distribution, the Debye temperature of the HOPG surface has been derived as 590 ± 30 K. On the basis of the HCM analysis for the extracted inelastic scattering components of He beam, the effective mass for the HOPG surface has been found to be 72 u (six carbon atoms).     

The lineshape of inelastic neutron scattering in relaxor ferroelectrics

We show that a microscopic reason for the steep drop of the optical phonon branch into an acoustic one (the so-called waterfall effect) in relaxor ferroelectrics may be the coupling of phonons with defects and impurities of different kinds, which is always present in relaxors. Namely, we do not specify the type of impurities but rather represent them as an ensemble of so-called two-level systems (TLS). This approach makes it possible to trace the evolution of the “waterfall” with temperature and the TLS concentration. To facilitate the planning of experiments on inelastic neutron scattering, we present a modification of the so-called Latin hypercube sampling method, which, based on some significance criteria, allows one to perform measurements that are highly significant for elucidating the physical nature of, e.g., phonon dispersion laws in relaxor ferroelectrics.     

Quasielastic and inelastic neutron scattering from AgPO3-AgI glass

A quasielastic neutron scattering experiment was performed on the fast ionic conductor AgPO₃-Agl, which is a vitreous electrolyte. This experiment was performed on the time-of-flight spectrometer IN 6 of the Institut Laue-Langevin in Grenoble, with the following parameters: λ=5.1 Å; 1.25 Å;^-1<Q<2.04^-1; instrumental resolution— FWHM=0.070 meV; sample thickness: 1.5 mm, 299 K <T< 368 K. The spectra generally show a quasielastic broadening of the elastic peak and a long tail up to 10 meV which is due to an inelastic distribution. In order to obtain the quasi-elastic contribution, the profile of the central peak was fitted within ± 0.6 meV for nine different spectra and for five temperatures. The elastic incoherent structure factor (EISF) was constant at 85%. The profile of the quasielastic contribution was found to be Lorentzian. When plotting the energy width ΔE times S(Q), the coherent structure factor, versus Q², a straight line is obtained for all temperatures. This means that the mechanism of the conductivity is certainly a translational diffusion with a coefficient of self-diffusion of the silver ions D=1.32x10^-5exp(-2080⧸RT) (activation energy being in calories). The value of the activation energy is very close to that of α-AgI measured by electric conductivity. The value of EISF: 0.85 indicates that the observed quasielastic scattering is due to half of the silver ions. These two results seem to confirm our hypothesis on the structure of these glasses: small “clusters” of AgI with tetrahedral coordination are dispersed in the AgPO₃ host glass. The two peaks observed in the inelastic frequency distribution function can be related to vibrations of the AgPO₃ host glass and of AgI₄ structural units respectively.     

Width-fluctuation effects in angular correlation in inelastic nucleon scattering

The effects of level-width fluctuations on the nucleon-gamma angular correlations and double-differential cross sections have been studied on the basis of Moldauer's formulation. Computational procedures for pursuing the width-fluctuation studies on a routine basis for reactions following the compound nucleus mechanism have been developed. The width-fluctuation effects in (n, n'γ) reactions with ²⁴Mg and ⁵⁶Fe have been calculated. These calculations indicate that the inclusion of width-fluctuation considerations significantly reduces the double differential cross sections compared to those made on the basis of Hauser-Feshbach theory. However, as expected, the shape of the angular correlation function is not siginificantly altered by the width-fluctuation corrections.     

Crystal field spectroscopy by inelastic neutron scattering

We present a review of inelastic neutron scattering results on very diluted rare earth (RE)-Laves phases. A systematic investigation to study crystal electric fields, experienced by single rare earth ions in a metallic environment, was done on (RE,R)Al₂, with RE=Pr, Nd, Tb, Dy, Ho, Er, Tm andR=Sc, Y, La. We show the influence of the 4f-ions on the crystal fields as well as the influence of the host lattices. The rare earth atoms in ScAl₂ have been studied for the first time and most of the other alloys, with LaAl₂ and YAl₂ as hosts, have been studied for the first time with magnetic atom concentrations below 1 at% and/or with good resolution for low energy excitations. Furthermore we studied the dynamics of 4f-moments, which are coupled to the conduction electrons by determining the coupling constants. We present a comprehensive set of crystal field parameters and coupling constants from these systematic studies and discuss them qualitatively within the available theoretical models. The influence of magnetic atom concentration on crystal field spectra will be shown in part II.     

Excitation of levels by inelastic neutron scattering

A scintillation spectrometer in ring geometry was used to study the gamma rays accompanying the inelastic scattering of fast neutrons on Na, Mg, Mn, Fe and I. The energies of the gamma rays were in most cases arranged into the cascade decay schemes of excited nuclei. Some of the transitions, which had not yet been described, were also found. These are the lines (2147±21) keV for Mg²⁵, (2135±22) keV, (2750±40) keV, (3040±50) keV and (3200±50) keV for Mn⁵⁵ and a series of other gamma rays emitted during the interaction of fast neutrons with I¹²⁷, which are given in the paper.

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-, Na, Mg, Mn, Fe I. - . , , . (2147±21) keV y Mg²⁵, (2135±22) keV, (2750±40) keV, (3040±50) keV (3200±50) keV y Mn⁵⁵ -, c I¹²⁷, .

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In conclusion the authors thank Z. Janout for contributing to the experimental work, J. Vrzal for the design of some of the apparatus, and F. trba, lecturer at the Faculty of Technical and Nuclear Physics, for help during the measurements. Thanks go to members of the accelerator laboratory staff of the Institute of Nuclear Research J. SchÄferling, J. Filípek and particularly J. Jirou, and to J. Zikmund from the same institute for valuable advice and help in the chemical problems connected with the measurements.     

Phonon eigenvectors in Si determined by inelastic neutron scattering

We have determined the eigenvectors of longitudinal phonons with wavevectors in the direction in Si at 12 K from inelastic neutron scattering intensities. The eigenvectors obtained from different model and quantum-mechanical calculations are at variance. Comparison of experimental and theoretical results shows that of the various theoretical predictions the ones from the bond-charge model are in best agreement with experiment. Internal-strain constants from these models and from experiment are compared.     

Some applications of polarized inelastic neutron scattering in magnetism

A brief account of applications of polarized inelastic neutron scattering in condensed matter research is given. We show that full polarization analysis is the only tool allowing to discriminate unambiguously between different magnetic modes in various magnetic materials. We show by means of recent results in the Heisenberg ferromagnet EuS that the effects of dipolar interactions can be studied on a microscopic scale. Moreover, we have found for the first time indications for the divergence of the longitudinal fluctuations belowT _c. In the itinerant antiferromagnet chromium we demonstrate that the dynamics of the longitudinal and transverse excitations are very different, resolving a long standing puzzle concerning the slope of their dispersion. Finally, we show that a measurement of the polarization-dependent part of the cross section of non-centrosymmetric MnSi proves directly that the chirality of the magnetic fluctuations is left-handed.     

Angular distribution of neutrons from precompound decay in inelastic scattering

Precompound angular distribution in inelastic scattering of 14 MeV neutrons are analysed in terms of surface interaction with the higher exciton states taken into account. This model is applied to some (p, α) reactions also.     

Internal inelastic scattering satellite probed by molecular-frame photoelectron angular distributions from CO2

The molecular-frame photoelectron angular distribution (MFPAD) of the satellite accompanying the C 1s photoline of the CO2 molecule has been measured at the C 1s(2sigmag)-->4sigmau* shape resonance, using electron-ion multicoincidence momentum spectroscopy. The observed MFPAD indicates that the conjugate satellite is excited by internal inelastic scattering. In this scenario, a photoelectron is ejected from the C 1s(2sigmag) orbital along the molecular axis and collides with an O lone-pair electron in the highest occupied molecular orbital 1pig. Then one of the colliding electrons is trapped to the lowest unoccupied molecular orbital 2piu*, while the other is emitted as a satellite photoelectron of sigmag symmetry, losing the information of the original photoelectron emission direction and parity.     

Measurement of momentum distribution of lightatoms and molecules in condensed matter systems using inelastic neutron scattering

Studies of single-particle momentum distributions in light atoms and molecules are reviewed with specific emphasis on experimental measurements using the deep inelastic neutron scattering technique at eV energies. The technique has undergone a remarkable development since the mid-1980s, when intense fluxes of epithermal neutrons were made available from pulsed neutron sources. These types of measurements provide a probe of the short-time dynamics of the recoiling atoms or molecules as well as information on the local structure of the materials. The paper introduces both the theoretical framework for the interpretation of deep inelastic neutron scattering experiments and thoroughly illustrates the physical principles underlying the impulse approximation from light atoms and molecules. The most relevant experimental studies performed on a variety of condensed matter systems in the last 20 years are reviewed. The experimental technique is critically presented in the context of a full list of published work. It is shown how, in some cases, these measurements can be used to extract directly the effective Born–Oppenheimer potential. A summary of the progress made to date in instrument development is also provided. Current data analysis and the interpretation of the results for a variety of physical systems is chosen to illustrate the scope and power of the method. The review ends with a brief consideration of likely developments in the foreseeable future. Particular discussion is given to the use of the VESUVIO spectrometer at ISIS.

Measurement of momentum distribution of lightatoms and molecules in condensed matter systems using inelastic neutron scattering

All authors

C. Andreani, D. Colognesi, J. Mayers, G. F. Reiter &; R. Senesi

https://doi.org/10.1080/00018730500403136

Published online:

19 February 2007

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