Raman scattering in defect chalcopyrite crystals

Summary Raman-scattering measurements on the defect chalcopyrite compounds CdGa₂Se₄, CdGa₂S₄, ZnGa₂S₄ are reported. The phonon picture is consistent with the space group. A comparison between corresponding phonons suggests a simple model for the vibrational dynamics. Preliminary Raman results in the mixed compound Cd _x Zn_1−x Ga₂S₄ and in resonance conditions in CdGa₂Se₄ are presented. Paper presented at the ?V International Conference on Ternary and Multinary Compounds?, held in Cagliari, September 14–16, 1982.     

Longitudinal sum rule for inelastic electron scattering and nucleon-nucleon correlations

We have considered the influence of short-range dynamical and statistical correlations on the inelastic scattering of electrons from light nuclei. The correlation effects are discussed on the example of the longitudinal sum rule for the ¹⁶O and ¹²C nuclei. A remarkable increase in the sum rule, caused by the short-range correlations at medium momentum transfers (100–200 MeV), is pointed out.     

Experimental investigation of inelastic neutron scattering structure factors of three dimensional rotators

High resolution inelastic neutron scattering experiments on tunnelling molecules in CH₄ II and NH ₄ ⁺ ions in (NH₄)₂PdCl₆ performed at high momentum transferQ are reported. TheQ dependence of the inelastic structure factors of the tunnelling transitions extracted from the results is compared with theoretical predictions.     

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.     

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.     

A neutron resonance spin echo spectrometer for quasi-elastic and inelastic scattering

We propose a modified neutron spin echo (NSE) spectrometer using high frequency spin flippers to replace the static spin flipper and the long magnetic precession field in each arm of the classicalspin echo setup. The spectrometer is suitable for quasi-elastic as well as inelastic scattering and can work with an arbitrary magnetic field on the sample. The restrictions on sample size and scattering angle can be relaxed, in comparison with the classical NSE method.     

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.     

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.     

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.     

Quasielastic neutron scattering and correlated self-diffusion in crystals

The effect of correlations between successive jumps of atoms during self-diffusion on the quasielastic neutron-scattering line wodth is investigated. Temporal and spatial aspects of these correlations are described in terms of the so-called “encounter model”, which had originally been developed for the interpretation of nuclear-magnetic resonance studies on self-diffusion. Owing to the rather high temperatures (i.e. large diffusivities) to which quasielastic neutron-scattering experiments on self-diffusion in crystals are restricted, the effect of both mono- and divacancies is considered. It is found that the line width associated with a correlated mechanism is smaller and in single crystals shows a different orientation dependence than expected for a random-walk diffusion mechanism. Numerical results are presented for (i) the monovacancy and two divacancy mechanisms of self-diffusion in a b.c.c. lattice, a situation likely to be encountered in sodium metal, and (ii) mono- and divacancies in the f.c.c. lattice. In the random-walk limit earlier results of Gissler and Rother and Chudley and Elliot are reproduced. All of the results derived also apply to the diffusion-induced broadening of Mössbauer lines. The article therefore presents a generalization of a recent theory in which only the effect of monovacancies on the Mössbauer line broadening has been considered.     

Spin-orbit sum rule for electric multipole transitions in nonresonant inelastic x-ray scattering

The sum rule for the branching ratio of dipole-excited core-valence transitions in isotropic x-ray absorption spectroscopy is extended to electric multipole transitions. The derived sum rule not only shows that the branching ratio is linearly related to the expectation value of the angular part of the spin-orbit operator in the valence states, but also shows a strong dependence on the rank of the multipole. The spin-orbit dependence vanishes in the weighted sum over the branching ratios. The effect can be an important diagnostic tool for high-energy spectroscopies.     

Zero- and first-sound damping in NaF observed by inelastic neutron scattering

The frequency and temperature dependence of the damping of transverse acoustic modes with 0.06 ? q/q_max ? 0.25 in NaF was determined by means of inelastic neutron scattering. The results clearly show a transition from the Akhiezer to the Landau-Rumer regime.     

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.     

Hydrodynamic effects in bicontinuous microemulsions measured by inelastic neutron scattering

The dynamical properties of bicontinuous microemulsions have been studied with neutron spin echo spectroscopy around length scales corresponding to the correlation peak q₀. Comparison of samples with different contrasts for neutrons shed light on the two modes dominated either by variation of the oil/water difference or surfactant concentration in the hydrodynamic regime. The results have been compared to theoretical predictions of the relaxation rates of bicontinuous microemulsions by Nonomura and Ohta [M. Nonomura, T. Ohta, J. Chem. Phys. 110, 7516 (1999)]. The influence of modification of the surfactant layer bending constants in the microemulsion by addition of homopolymers (polyethylenepropylene: PEP_X and polyethyleneoxide: PEO_X, X=5 kg/mol), dissolved in the oil phase and water, has been investigated.