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Nous expliquons la difference entre la diffusion coherente et la diffusion incoherente des neutrons par une analogie avec l'experience de diffraction par une double fente de Young. Nous montrons que le langage adequat pour calculer les signaux coherents est base sur une description en termes de configurations dans lesquelles les particules identiques qui peuvent etre echangees sont considerees comme indiscernables. Nous illustrons notre demarche avec un exemple tire de la physique des quasicristaux.

We have performed inelastic magnetic neutron scattering experiments on ${\mathrm{La}}_{2\ensuremath{-}x\ensuremath{-}y}{\mathrm{Sr}}_{x}{\mathrm{Nd}}_{y}{\mathrm{CuO}}_{4} (0l~xl~0.2$ and $0.1l~yl~0.6)$ in order to study the Nd $4f$-spin dynamics at low energies $(\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\lesssim}1 \mathrm{meV}).$ In all samples we find at high temperatures a quasielastic line (Lorentzian) with a linewidth which decreases on lowering the temperature. The temperature dependence of the quasielastic linewidth $\ensuremath{\Gamma}/2(T)$ can be explained with an Orbach process, i.e., a relaxation via the coupling between crystal field excitations and phonons. At low temperatures the $\mathrm{Nd}\ensuremath{-}4f$ magnetic response $S(\mathbf{Q},\ensuremath{\omega})$ correlates with the electronic properties of the ${\mathrm{CuO}}_{2}$ layers. In the insulator ${\mathrm{La}}_{2\ensuremath{-}y}{\mathrm{Nd}}_{y}{\mathrm{CuO}}_{4} (y=0.1,0.3)$ the quasielastic line vanishes below 80 K and an inelastic excitation occurs. This directly indicates the splitting of the ${\mathrm{Nd}}^{3+}$ ground state Kramers doublet due to the static antiferromagnetic order of the Cu moments. In ${\mathrm{La}}_{1.7\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{Nd}}_{0.3}{\mathrm{CuO}}_{4}$ with $x=0.12,0.15$ and ${\mathrm{La}}_{1.4\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{Nd}}_{0.6}{\mathrm{CuO}}_{4}$ with $x=0.1,0.12,0.15,0.18$ superconductivity is strongly suppressed. In these compounds we observe a temperature independent broad quasielastic line of Gaussian shape below $T\ensuremath{\approx}30 \mathrm{K}.$ This suggests a distribution of various internal fields on different Nd sites and is interpreted in the frame of the stripe model. In ${\mathrm{La}}_{1.8\ensuremath{-}y}{\mathrm{Sr}}_{0.2}{\mathrm{Nd}}_{y}{\mathrm{CuO}}_{4} (y=0.3,0.6)$ such a quasielastic broadening is not observed even at lowest temperature.

We present here new results on phason dynamics (atomic hopping) in quasi-crystals. An iron jump has been observed by spectroscopy Mossbauer in the system AlFeCu. Its relaxation time is very different from the one of the 3.9 A Cu jump previously determined by neutron scattering. Two distinct atomic jump times have also been observed by neutron scattering in the system AlMnPd. They exhibit the same unusual temperature dependence as the Cu one, such that it seems to be universal.

Incoherent quasi-elastic neutron scattering is applied to study the local diffusion and chain dynamics of L-alpha-diplamiotylphosphatidylcholine molecules in oriented model membranes. Different motions are distinguished by changing the hydration of the multilayers as well as by measuring below and above the gel-to-liquid crystalline phase transition. The time range of the utilized time-of-flight spectrometer permits to observe two types of motion to be observed more closely: chain defect motions and the local diffusion of the whole molecule in its solvation cage. Oriented lipid membranes are a useful system for the observation of chain defects, as they can be macroscopically oriented, in contrast to most polymers. As a representative model for a chain defect a kink is chosen and the corresponding scattering functions are derived. The kink motion can explain the entire dynamics seen in the gel phase, and the lifetime of such a defect was found to be 10–15 ps, in good agreement with theoretical predictions. On the other hand the dynamics in the liquid crystalline phase cannot be explained even by a superposition of several kinks and thus requires the consideration of an additional motion: the local diffusion of the molecule in its solvation cage. The size of the solvation cage is increasing with multilayer hydration and reduced temperature. Particularly interesting in view of recent discussions about the origin of the short-range repulsive forces between membranes is the experimental finding of an out-of-plane motion with an amplitude of 1–1.5 A, which cannot be explained by the undulation of the whole membrane.

We propose a monoatomic model for a quasicrystal transition as observed recently in systems with icosahedral [3] and decagonal [5] symmetry. It is developed here for the case of decagonal symmetry and is inspired by the experimental results on the system Al-Cu-Co-Si [5,6]. The model goes beyond the purely geometrical description by an important physical aspect: the transition mediates through a single atomic jump distance such that only one unique double-well potential has to be invoked to describe it; in conformity with the symmetry there are 10 jump vectors. In the framework of the model, the microcrystalline state is energetically more favourable than a monocrystalline approximant phase.

We have performed molecular-dynamics simulations of displacement cascades in copper in order to investigate the non-equilibrium ultra-short time damage and to evaluate the possibility of observing it experimentally in-situ (e.g. in a pump/probe laser experiment). The atomic trajectories have been analysed by calculating their X-ray diffraction patterns as a function of time. The results show that an integrated X-ray intensity can indeed be used to evidence the irradiation effects. Even though the number of Frenkel defects is large, the main effect of the irradiation showing up in the X-ray intensities at ultra-short times is an important alteration of the lattice vibrations. On the basis of these results, a new pump/probe set-up is proposed.

It has recently been claimed that the dynamics of long-wavelength phason fluctuations has been observed in i-AlPdMn quasicrystals. We will show that the data reported call for a more detailed development of the elasticity theory of Jaric and Nelsson in order to determine the nature of small phonon-like atomic displacements with a symmetry that follows the phason elastic constants. We also show that a simple model with a single diffusing tile is sufficient to produce a signal that (1) is situated at a "satellite position'' at a distance q from each Bragg peak, that (2) has an intensity that scales with the intensity of the corresponding Bragg peak, (3) falls off as 1/q-squared and (4) has a time decay constant that is proportional to 1/(D q-squared). It is thus superfluous to call for a picture of "phason waves'' in order to explain such data, especially as such "waves'' violate many physical principles., 36 pages, 0 figures, discussion about vacancies, fluctuating Fourier components, and difference between static and dynamical structure factors added, other additions

We previously derived a theorem about the {\em coherent} quasielastic neutron-scattering signal from a $d$-dimensional lattice of $N$ molecules that are undergoing rotational jump diffusion (around an $n$-fold axis), assuming that there are no correlations between the molecules. In the present paper molecular correlations are treated, but only in the sense that several molecules could reorient simultaneously as in a cog-wheel mechanism. Moreover, we do not examine the possibility that the relaxation times of these combined reorientations could depend on details of the local environment created by the neighbouring molecules. Finally also an ergodicity condition has to be fulfilled. Admitting for all these assumptions we can show that the correlations do not affect the coherent quasielastic scattering pattern in the following sense: The functions of $Q$ that intervene in the description of the intensities remain unaltered, while the functions of $\omega$ can undergo a renormalization of the time scales. The latter changes cannot be detected as the time scales that would occur if the dynamics were independent are not available for comparison. In other words: Coherent quasielastic neutron scattering is not able to betray the existence of correlations of the restricted type that occur in our model., Comment: 15 pages, 0 figures

We report on some Raman measurements of single wall carbon nanotubes (SWNT) prepared by laser ablation (LA) or electric arc discharge (EA). We correlate the Raman features with structural information and discuss the resonance behaviour of the Raman signal in terms of a distribution of tubes diameters and symmetries.

In two amorphous alloys ZrTiCuNiBe and ZrAlNiCu coherent neutron scattering has been measured over five decades in energy, including measurements in the metastable melt of a metallic alloy more than 80 K above Tg. In the vibrational spectra a pronounced "boson" peak is found: Even in crystallized samples the density of states exceeds the Debye ω2 model, and in the amorphous state low-frequency vibrations are further enhanced. The peak position shows no dispersion in q, while intensities are strongly correlated with the static structure factor. Over the full energy range the temperature dependence is strictly harmonic. From high-energy resolution measurements we establish lower bounds for the temperatures at which structural α and fast β relaxation become observable.

By 57 Fe Mossbauer spectroscopy in a special experimental set-up we have shown the existence of Fe atomic jumps in Al 62 Fe 25.5 Cu 12.5 perfect icosahedral quasicrystals. The (preliminary) results indicate that at 790 °C 20% of the Fe atoms are jumping at a time scale corresponding to 4 μeV.

We investigate what the precise meaning is of a spinor in the rotation and Lorentz groups. We find that spinors correspond to a special coding of a group element. This is achieved by coding the whole reference frame into a special isotropic or “zero-length” vector. The precise form of that special vector in the Lorentz group is lacking in the literature, and this leads to some confusion, as the point that the coding can be complete has been missed. We then apply these ideas to quantum mechanics and find that the Dirac equation can be derived by just trying to describe a rotating electron.

The various methods to measure the density of states by neutron inelastic scattering are discussed. Purely incoherent scattering data on silica aerogels have been obtained by taking the difference spectra between protonated and identical deuterated samples. The results so far cover the particles modes and the upper part of the fracton regime. Complemented with Brillouin scattering information, these measurements provide an overall picture of the absolute density of states, from which low temperature thermal properties can be calculated, in remarkable agreement with experiments. 1 INTRODUCTION The theory of vibrational excitations in fractal structures predicts the existence of "fractons" 111. Those vibrational modes are localized. Also, in contrast to long-wavelength acoustic phonons, which obey a linear dispersion law, o = v q , where w is the frequency, q is the wavevector, -and v is the constant sound velocity, fractons are expected to exhibit dispersion according to o C C ~ ~ I ~ 11.21. Here D is the fractal (Hausdorff) dimension, and k is a characteristic length for the fracton. Finally, the density of states (DOS) of fractons Z(w) was predicted to be proportional to wa -1 /I/. The dimensions obey the inequality d 2 D > z, with d the Euclidean dimension. As an example, for 3-d percolation clusters and scalar waves the values are D = 2.5 and a = 413. The above predictions are at strong variance with the well-known behavior of acoustic phonons, a@ the differences should be observable experimentally. Silica aerogels are ideally suited for the experimental study of fracton dynamics. They are porous solid materials. Large pieces can be prepated, so that their elastic properties can be measured by static as well as by ultrasonic techniques. The optical transparency of aerogels in a broad range of densities and preparation conditions allows the study of their vibrational dynamics by Brillouin and Raman light scattering. (I) Supported by Neutron Scattering Project IIKW, Natuurkunde, University of Antwerp, 8-2610 Wilrijk, Belgium (2) Laboratoire mixte CNRS-Commissariat a I'Energie Atomique. (3) Laboratory associated to the Centre National de la Recherche Scientifique (CNRS). No 1129. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989424 Structural studies /3,4/ have demonstrated that silica aerogels are made of elementary particles, of typical size a, with more or less defined surfaces. Those particles assemble to form fractal networks, up to an average cluster size 5. At length scales above (, the material is an homogeneous assembly of such clusters. Corresponding to these different length scales, three distinct vibrational regimes are expected, namely, with increasing frequency : phonons, fractons, and particle modes. A crossover from phonons to fractons at oco,12n -1 GHz has been demonstrated by Brillouin scattering experiments 151. This technique also allowed the determination of the dispersion curve for fractons 16,7/, and gave indication for the occurrence of localization at the phonon-fracton crossover. Evidence of an extended fracton domain, ranging approximately from 40 peV to 1 meV, was obtained from very-low frequency Raman scattering IS/. It is obviously of interest to measure directly the DOS of these excitations. 2 EXPERIMENTAL APPROACHES There are several ways to measure a vibrational DOS by inelastic neutron scattering. One basic idea is that the DOS is reflected in the incoherently scattered neutrons. Taking only the one phonon terms in a multiphonon expansion, the expression for the double differential incoherent cross section of a Bravais lattice