Inelastic neutron scattering from amorphous solids

Utilization of the inelastic neutron scattering technique for the study of the dynamics of amorphous solids is discussed. Excitation energies of interest range from a fraction of a milli-electron-volt (meV) to several hundred meV. For coherent scatterers, the scattering-vector dependence of the cross section gives information on the correlation between the motions of different atoms. Progress in the application of the technique to several classes of materials is reviewed, and the possibilities offered by the new generation of pulsed-spallation neutron sources are considered. Existing instrumentation on presently operating sources should already be able to measure wide-ranging scattering functions for comparison to model predictions for several types of amorphous solids. Higher flux sources, now at the proposal stage, would allow greater detail in the scattering to be observed and thus aid in discriminating between models.     

The Rayleigh scattering loss in silicate glasses containing PbO

The Rayleigh scattering coefficients of a number of glasses in the K₂OMgOPbOSiO₂ system have been determined. The scattering by density fluctuations and by concentration fluctuations was calculated using theories which were developed for ideal multicomponent liquids. In order to investigate how these theories could be applied to multicomponent glasses, the scattering by concentration fluctuations was calculated making different assumptions. It was found that reasonable agreement, both in trends and in order of magnitude, was obtained between the calculated and observed scattering coefficients when the glass was considered to be a frozen-in mixture of silicate units with compositions corresponding to those of crystalline silicates.     

On the Determination of the Size Distribution Functions of Spherical Precipitations in Al–Zn Alloys by Neutron Small-angle Scattering

The size distribution of approximately spherical incoherent precipitations of Zn in AlZn-alloys is calculated and experimentally tested by means of neutron small angle scattering (NSAS) at a double-crystal diffractometer (DCD). The scattering curves can be approximated by a Gaussian function, so that the size distribution is directly calculated for the experimentical scattering curves under application of a particular LAPLACE-transformation. The size distributions of the α′_m-phase of AlZn(16)-samples of different averaged radii of precipitations are calculated by means of FWHM which are determined by the fitting procedure of a computer programme and compared with TEM micrographs.     

Structural relaxation and optical properties in transparent nanocrystalline β-quartz glass-ceramic

We studied structural relaxation in a nanocrystalline β-quartz solid solution (s.s.) glass-ceramic through density measurement, and the effect of structural relaxation on its optical properties. The density of the glass-ceramic changed as structural relaxation proceeded in the glass phase. It was found that the glass-ceramic whose glass phase has a high fictive temperature shows a high optical transmittance because of less optical scattering. We also demonstrated that the refractive index difference between the crystal and glass phases can be calculated from the scattering coefficients of the specimens with different fictive temperatures. The calculated refractive index of the crystalline phase was in fair agreement with the indices of a high-quartz crystal.     

Brillouin light scattering study of polymeric glassy sulfur

We present here a study of the acoustic dynamics of polymeric glassy sulfur. The data have been collected in the GHz frequency range by means of Brillouin light scattering for different scattering geometries. The choice of the experimental setup allows us to obtain information on the refractive index, n, that comes out to be close to that corresponding to the high temperature polymeric liquid phase. The longitudinal acoustic excitations have been investigated as a function of temperature from deep into the glassy state up to the glass transition temperature. The temperature dependence of the sound velocity is compared to the one measured in the liquid phase. We find that the sound velocity of the glass can be linearly extrapolated from that of the polymeric liquid measured in the THz frequency range with inelastic X-ray scattering.     

A neutron small angle scattering study of SiO2Na2 O glasses

The first results obtained by small-angle neutron scattering (SANS) study of sub-liquidus immiscibility of glasses are presented. Measurements were performed on the neutron small-angle scattering spectrometer of the Institut Laue-Langevin (Grenoble, France). The glass studied was 0.88 (SiO₂), 0.12 (Na₂O) from SiO₂Na₂O system which presents a well-known miscibility gap already explored by small-angle X-ray scattering (SAXS) method. Absolute values of the neutron scattering cross section as a function of scattering vector were obtained for this glass quenched and heat treated at 560°C for various lengths of time. It is shown that the ANS method can be used to follow phase separation kinetics and the comparison with SAXS results can in principle be used to separate the effects of density and concentration fluctuations in this system.     

Dynamic Scattering and Material Flow in a Nematic Liquid Crystal

Results are presented which show how defects in a nematic liquid crystal can be used to investigate material flow when external electric fields are applied. These results include measurements of the size of flow cells, which were created between the electrodes by an electric field. The electrodes, which were made of transparent conductive coated glass, were placed in a vertical position so that flow cells could be observed from the top while dynamic scattering was observed when viewing normal to the electrodes.     

Quasi-localized vibrations and phonon damping in glasses

There is ample evidence both from computer simulation and experiments that the structural disorder characterizing glasses and amorphous materials leads to quasi-localized vibrations (QLVs). The effect of these modes on low temperature properties such as heat capacity and conduction or tunnelling can be calculated in the framework of the soft potential model. Recently it has been shown that this concept can be extended to describe the boson peak (BP). By interaction, the density of states of the QLVs is changed to a characteristic shape corresponding to the boson peak in inelastic scattering. The QLVs interact with the sound waves and dampen them. We show that resonant scattering between QLVs and sound waves can describe the strong damping observed experimentally.     

Sol–gel simulation—I: Scattering response

Scattering of sol–gel structures is investigated computationally. Sol-gels are recreated through an aggregation algorithm incorporating Brownian motion and chemical reactions. Using the fractal character of sol–gels, the concept of recursion is introduced as a tool to perform multi scale computation of the response of sol–gels through the different scales from the molecular level to the macro scale. The concept is illustrated with the prediction of scattering intensity. The relationship between scattering intensity and functionality is investigated, noting that the latter is a function of the Brownian motion and chemical reactivity. Computational simulation tools are developed to predict scattering intensity as a function of density and reactivity, the former represented by the number of particles, or clusters, in the simulation box. Then, the results are correlated to an analytical model that reveals the critical wave number, or critical scale, at which percolation occurs.     

X-ray scattering from an irregular surface: Two-scale model

X-ray scattering from an irregular surface, which is described within a two-scale model, has been considered. A method for calculating the differential scattering cross section based on the quasi-classical Kirchhoff approximation is proposed. Coherent scattering from a lateral surface with a periodic motif is analyzed, and the reduction factor is calculated; the latter differs from the well-known expressions of the perturbation theory (first Born approximation, distorted-wave Born approximation). It is shown that the surface profile deviations from a periodic law, edge effects, and the interference of waves reflected from surface areas with different inclination angles significantly affect scattering from lateral structures.     

Neutron Scattering by Copolymers

Abstract

Neutron scattering is a very efficient tool for studying polymers in bulk as well as in solution. This is mainly due to the difference of scattering length between hydrogen and deuterium which allows the possibility of changing the contrast without too serious alteration in the conformation and thermodynamics of the systems.

In order to take full advantage of this possibility, one has to remember the general rules which allow the evaluation of the total scattering function S(q) as a function of the partial scattering functions S _pq (q) which describes the contributions of the interferences between scattering center of species p and q.^1.2 In a first part we shall briefly establish these rules for incompressible systems introducing what has been called by J. Koberstein³ the molecular contrast and the phase contrast.

In the second part of this talk we shall discuss the problem of copolymers. S(o) the intensity scattered at zero angle depends on the heterogeneity in composition of the sample,⁴ for homogeneous composition S(o) = o. This gives the possibility of studying trans-esterification in polyester, for example.

At finite q for a monodisperse system, S(q) is not zero and it will be shown how it depends on the length of the sequences and the architecture of the copolymers. If the number of blocks is large S _pq (q) is practically not affected by the total length of the polymer.⁵

The condition I ^?1(q) = o allows one to write the equation of a q dependent generalized spinodal and therefore to determine the parameters which govern the stability of a multiphase system.

In the last part we shall discuss the problem of the application of this formalism to networks and gels made of different types of units. It will be shown that the scattering is mainly sensitive to the local conformation and that the introduction of translational order between the units does not affect significantly the scattering curves but can explain the occurrence of secondary maxima which have been observed in polyurethane and ionomers.⁶     

Spinodal decomposition in amorphous systems

The theory of spinodal decomposition in amorphous systems is extended to include the effect of internal stress due to coherency strain. A quantitative treatment is developed for the kinetics of internal stress relaxation via plastic deformation. The general solution for the evolution of the composition and internal stress distributions during the early stage of spinodal decomposition is derived for a system obeying the visco-elastic constitutive relations of a Maxwell solid. A kinetic equation for the structure factor is obtained for the limiting case in which coherency strain is relatively large. In this case, it is found that plastic deformation to relieve internal stress can become the rate-limiting step in the evolution of Fourier components having large wavenumbers. The predicted shape of the structure factor as a function of wavenumber, time, and temperature can be very different from that obtained when the kinetics of internal stress relaxation are neglected. The theory is expected to be particularly applicable to amorphous systems in which the species of interest have very different mobilities, and can explain the discrepancies found in previous analyses of scattering data for the lead-aluminum-borate system and alkali-silicate systems.     

Neutron measurements of magnetic correlations in metallic glasses

Neutron diffraction experiments have been made on FeB and PdSi transition metal alloy glasses prepared by melt-spinning. The magnetic neutron scattering has been analysed to provide information about the magnetic order in the specimens. An Fe₈₃B₁₇ metallic glass has magnetic correlations at room temperature with a range commensurate with the variations in atomic structure. These correlations appear to have a structure based on fcc gamma-iron, and the magnetic disorder is small - given that the specimen was in a field of 1 kG. Magnetic scattering was observed from Pd₇₀Si₂₀Co₁₀ and Pd₆₇Si₂₀Fe₁₃ at room temperature, which indicated a large magnetic moment value for the transition metal atoms. Cooling the PdSiCo sample to 80 K induced an antiparallel moment correlation, while further cooling to 7 K produced little obvious change in the scattering. These latter results are discussed in the light of the considerable disagreement which exists between different investigations of these alloys.     

Captured Orientational Order in Polymer Network Assemblies

Abstract

The “marriage” between low molecular weight liquid crystals and polymers burgeoned in the 1980s with the idea of dispersing liquid crystal droplets in a rigid polymer matrix to create an electrically controllable light scattering medium. The orientation of the liquid crystal droplets, and hence the refractive index match and scattering, can be systematically controlled with an electric field. Today, dispersions of liquid crystals and polymers are found in many forms depending on the concentration of polymer, which can be as large as 70% or as small as 1%. The systems most understood are those of larger concentration where the liquid crystal is segregated out in the form of droplets randomly distributed throughout the surrounding polymer (see page 2). Dispersions of liquid crystals and polymers differ from macroscopic bulk liquid crystals because of the large surface-to-volume ratio and symmetry breaking non-planar geometry imposed by the polymer. Their composite nature profoundly affects the ordering of the liquid crystal, and their susceptibility to external fields makes them suitable for many new electro-optic applications, as well as intellectually challenging to study from the basic science perspective.     

Analysis of the applicability of the modified kinematic approximation to describe the off-specular neutron scattering from the surface of micro- and nanostructured objects

The applicability of the modified kinematic approximation to describe the off-specular neutron scattering from interfaces between media is analyzed. It is demonstrated that in some cases one can expect not only a qualitative but also a quantitative agreement between the data and the results of experiments and calculations based on more accurate techniques. Diffuse scattering from rough surfaces and thin films with correlated and noncorrelated roughness of the upper and lower interfaces and the neutron diffraction by stripe magnetic domains and magnetic domains with a random size distribution (magnetic roughness) are considered as examples.     

Phase Transitions of A Quasi-One-Dimensional Fermi Gas

Phase transitions of a quasi-one-dimensional Fermi gas are studied by the use of the renormalization group method for the fermion system without the bosonization. Intrachain backward and forward scatterings, pair electron hopping between different chains and exchange scattering of electrons in different chains are taken account of. Pair electron hopping gives rise to the singlet and triplet superconductor phase transitions. Electron exchange scattering gives rise to the spin density wave and charge density wave transitions. Calculation is made by the use of the one-dimensional dispersion. Following Menyhárd's method (Ref. 1) for the model with interchain backward scattering only, the change of the fluctuation from the one-dimensional region to the three-dimensional region is described. The transition temperatures are given by the bare couplings at high temperatures.     

X‐ray Reflectivity from Sinusoidal Surface Relief Gratings

The sinusoidal shape of light‐induced surface relief gratings of polymers can be probed by x‐ray scattering techniques. A particular approach of kinematic x‐ray scattering theory is developed to interpret experimental scattering curves. The simulations demonstrate the particular sensitivity of x‐ray reflectivity for very small grating amplitudes. At angles of incidence close to the critical angle of total external reflection a grating amplitude h < 2 nm already provides measurable grating peaks. In general the grating amplitude h can be measured from the envelope function over the grating peak maxima. The capability of the approach is demonstrated by simulation of the reflection curve recorded from a polymer sample with non uniform grating height.     

Porosity and structural parameters of Karelian shungites according to the data of small-angle synchrotron radiation scattering and microscopy

The nanoporosity and structure of natural carbons has been investigated on the example of Karelian carbon-rich shungites by comparing the data of small-angle synchrotron radiation scattering and highresolution microscopy. The analysis of small-angle scattering data is based on the model of scattering spheres with lognormal size distribution. It is found that the structure of samples from the Maksovo and Zazhogino deposits subjected to high temperatures in the geological medium and (also to a lesser extent) a sample from the Shunga deposit can be described as an aggregation of polydisperse scattering spheres with lognormal size distribution; the characteristic scatterer size is determined for them. A comparison with microscopy data shows that these scatterers are mainly associated with pores, and the character of their size distribution is similar to that previously established for nanoglobules in schungites.     

Structure analysis by normalized data. I. Increase of relative accuracy of diffraction data

A new method for obtaining physically reliable values of atomic parameters in the refinement of the structure model by the least squares method has been suggested. The method requires the use of experimental data reduced to a scale corresponding to the Bragg scattering from an ideal defect-free crystal. The reduced experimental data can be obtained by interexperimental-minimization (IEM) method—a new algorithm minimizing the difference “experiment 1-experiment 2” (between the data obtained in two experiments, 1 and 2) used in addition to the model-experiment minimization performed in the conventional least square procedure. The use of four different experimental data sets for alexandrite crystals, Al₂BeO₄: Cr³⁺, allowed us to show that the application of the IEM algorithm considerably increases the reproducibility level of the experimental data, which, in turn, increases by 30–60% the agreement between the model and the experiment.