Study of the glass transition order parameter in amorphous polybutadiene by incoherent neutron scattering

The temperature dependent elastic incoherent scattering from a glass forming polybutadiene was studied using high resolution neutron spectroscopy. This elastic scattering measures directly the non-ergodicity order parameter of the glass transition. We observed an anomalous decrease of this scattering setting in around 30 K below the thermodynamic glass transition,T _g , the temperature dependence of which is in agreement with the square root ofT prediction of the mode coupling approach. The critical temperature of 220 K lies about 30 K aboveT _g . The missing elastic intensity reappears as inelastic scattering in the 1 meV range. Within the eV resolution of the backscattering spectrometer no quasielastic scattering can be detected up to 20 K aboveT _g . The observed inelastic scattering may be interpreted as resulting from a continous shift of the density of states towards low frequencies as a consequence of a general softening of the structure.     

Debye-Waller factor in atom-surface scattering: Elastic and inelastic channels

Explicit expressions for the Debye-Waller factor for the elastic and one-phonon channels are presented to lowest order in the phonon displacement, using a hard wall model to represent the atom-surface interaction. The periodicity of the crystal is accounted for; thus we explicitly generalize to all elastic channels the reflectance result found by Garcia et al. within the plane-surface model, and we include the contribution of the umklapp processes to the inelastic channels. We show how for high incident energy of the atom all Debye-Waller factors reduce to the standard result.     

An incoherent inelastic neutron scattering study of NH4TaWO6

The incoherent inelastic neutron scattering spectrum of the defect pyrochlore, NH₄TaWO₆, has been determined at 20 K. The appearance of the spectrum indicates that the NH ₄ ⁺ ion is distorted from its free ion tetrahedral geometry. A profile refinement method has been used to fit a calculated spectrum to the data based on an ion of C _3v symmetry.     

Theory of transverse neutron inelastic scattering in the transition metals

A qualitative analysis of the transverse neutron inelastic cross section for the Hubbard model withs?d hybridization in the framework of RPA is considered. The poles of the transverse generalized spin susceptibility are studied. It is found that the acoustic spin wave pole exists among the set of poles of dynamical spin susceptibility and that the non-interacting susceptibility determines the four quasi-Stoner continuum.     

The anomalous Debye-Waller factor of hydrogen in niobium as determined by quasielastic neutron scattering

The integrated intensity of quasielastic neutron scattering by protons in polycrystalline NbH_0.16 and in a single crystal of NbH_0.045 was investigated as a function of the scattering vector Q. Strong deviations from a harmonic Debye-Waller factor behavior were observed at elevated temperatures. The results show a temperature dependent delocalization of the proton extending as far as the neighboring sites of the interstitial lattice. Experiments on the single crystal indicate a directional dependent mean-square amplitude of the proton even at room temperature.     

Elastic incoherent neutron scattering studies on glass forming hydrogen-bonded systems

Neutron incoherent elastic scattering data have been collected on homologues disaccharides (trehalose, maltose, sucrose)/H₂O mixtures as a function of temperature. The results show a dynamical transition at T238 K, T235 K and T233 K for trehalose, maltose and sucrose/H₂O mixtures, respectively, marking a cross-over in molecular fluctuations between harmonic and non-harmonic dynamical regimes, proving a higher ‘rigidity’ of trehalose mixture with respect to maltose and sucrose mixtures. This finding accounts for the higher cryptobiotic effectiveness of trehalose, namely a capability to encapsulate biostructures in a more rigid environment.     

A semiclassical approach to inelastic scattering from solid surfaces and to the Debye-Waller factor

A semiclassical formulation of inelastic atom-surface scattering is presented. This formulation is a mixture of classical S-matrix theory and a classical path model. A Debye-Waller factor enters this theory very naturally as the probability of elastic reflection in the presence of inelastic channels. Because of its importance the Debye-Waller factor is discussed in some detail. Finally, assuming a simplified model of the gas-surface system, the whole scattering problem is solved analytically.     

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.     

Elastic constants in RbI,determined by inelastic neutron scattering

Long-wavelength acoustic phonons have been studied in the whole (100)-plane of RbI at 295 K by means of inelastic neutron scattering. The raw data have been corrected for resolution effects taking into account the curvature of the dispersion surface and variations of the mode eigenvectors. The shifts of the neutron groups due to these resolution effects are discussed in detail. The analysis of the experimental results gives for the zero sound elastic constantsc ₁₁=28.15±0.5,c ₁₂=3.7±0.5 andc ₄₄=2.85±0.1 10¹⁰ dyn/cm². A comparison with first sound elastic constants taken from ultrasonic measurements yields significant differences between the high and low frequency elastic constantsc ₁₁ andc=(c ₁₁–c ₁₂)/2. The differences calculated from recent theories are in agreement with the experimental results for the elastic constantsc ₁₁,c ₄₄ andc, but not forc ₁₂. The dispersion surface in the (100)-plane is also shown for some out-of-symmetry data and compared with ultrasonic data as well as with theoretical results.Research supported by BMFT     

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.     

On the Debye-Waller factor for atom-surface scattering

The Debye-Waller factor in atom-surface scattering is considered. It is found that the equation suggested by Beeby is valid for soft potentials provided that (1) the attractive portion of the potential is stationary, (2) the repulsive portion of the potentials moves but does not distort, and (3) the effect of trajectories that reflect off the attractive well and multiply scatter from the repulsive wall is negligible.     

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.     

The Debye-Waller factor in helium scattering by a crystalline surface

On the dense face of a metallic crystal or the (001) face of lithium fluoride, the distance between nearest neighbours is of the same order of magnitude as the helium diameter. The hypothesis of simultaneous interaction between incident helium atoms of thermal kinetic energy and surface atoms belonging to a surface unit cell is therefore introduced. Then the exponent of the Debye-Waller factor contains mean square and mean correlated displacement between atoms of the cell. This gives for the (00) peak an apparent surface Debye temperature Θ_sa higher than the corresponding value usually deduced for instance from LEED measurements. For the (001) face of copper the calculated value is: 323 < Θ_sa < 354 K according to the value ascribed to bulk Debye temperature. On this face, recent experimental results show that helium atoms are coherently scattered in the specular (00) peak. From its intensity analysis is deduced an attractive well depth of 0.009 ± 0.002 eV and Θ_s = 370 ± 10 K, very close to the calculated result. The simultaneous interaction implies that the one phonon exchange can only take place with phonons of long wavelength. This theoretical expectation seems to be in qualitative agreement with experimental data.     

On the Debye-Waller factor in molecular beam scattering experiments

In the molecular beam scattering experiments against metal surfaces, one often obtains surface Debye temperatures larger than the bulk ones, in apparent contradiction to the larger thermal atomic motion at the surface. We point out that this is a consequence of that the thermal molecules scatter against the outer part of the electron distribution, and that the metal electrons do not follow the atomic motion rigidly. A self-consistent model calculation shows that this is a large enough effect to explain the experimental results.     

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.