Scattering neutron inelastic

Sun and Wang report a series of studies of polystyrene polymethylmethacrylate mixtures (in benzene, dioxane, and toluene, respectively) using light scattering spectroscopy as the major experimental technique(78-80). Both polymers were in general nondilute. Neither polymer is isorefiractive with any of the solvents. The objective was to study the bimodal spectra that arise under these conditions and to show that the two relaxation times and the mode ampUtude ratio can be used to infer diffusion and cross-diffusion coefiBcients of the two components. Experimental series varied both the total polymer concentration and the concentration ratio of the two components. The theoretical model predicts a biexponential spectrum. The experimental data were fitted by a bimodal distribution of relaxation rates or by a sum of two Williams-Watts functions. The inferred self-diffusion coefiBcients of both species fall with increasing polymer concentration. 

Roberts, et at. used PFGNMR to examine a model Uquid-filled-polymer system, formed from silica nanoparticles suspended in monodisperse polydimethylsilox-ane(81). Silica particles had diameters 0.35 and 2.2 nm polymers had molecular weights 5.2 and 12.2 kDa, with M /Mn of 1.07 and 1.03, respectively. These are not probe measurements. The volume firacfions of probes and matrix polymers were both always substantial. The of the small siUca particles and the 5.2 kDa poly- 

Borsali, et al. applied NSE to a polystyrene perdeuteropolystyrene block copolymer and to a mixture of polystyrene and perdeuteropolystyrene copoly-mers(85). By using a benzene perdeuterobenzene contrast-matching solvent, it was possible to arrange matters so that fluctuations in the number density of the block copolymer scattered no neutrons. Under these conditions, NSE spectra revealed a single mode for the block copolymer with relaxation rate linear in q and a nonzero intercept as 0. NSE spectra of the homopolymers instead revealed a mode with relaxation rate linear in and a zero intercept as 0. This result is very close to the predictions of Pecora(l-3) as confirmed with light scattering by Han and Akcasu(l 1) and Ellis, et a/.(14), but here the incident neutron waves had X = 8.5A, and the observed time range was 0.3-17 ns. 

Besides thermal excitation of phonons, they can also be excited systematically by inelastic neutron scattering, by Raman scattering, by infrared absorption, by coup-Ung to optical transitions or by coupUng to charge carriers within the crystal. The first three of these methods can be apphed to determine the phonon frequencies or the entire dispersion relations S2(K) quantitatively. This will be treated in the following Sect 5.4. 

For the experimental determination of the phonon dispersion relations S2(K), inelastic neutron scattering is by far the most powerful method, but it also requires the most effort Important complements to this method are however Raman scattering of light and infrared absorption spectroscopy. In particular, Raman scattering permits a precise determination of the frequencies of the Raman-active optical phonons with wavevectors K 0. It is thus particularly well suited to the evaluation of pressure and temperature dependences, which are especially prominent in the case of the soft organic molecular crystals. 

In inelastic neutron scattering, neutrons from a cold source are selected by a monochromator M and coUimated to yield a monoenergetic beam (Fig. 5.6). The neutron matter wave thus has a well-defined wavevector kj and a quantum energy b k /2M , before it reaches the crystal Cr which is to be investigated. In the crystal, it is scattered elastisically and inelastically. In the case of the inelastic scattering. 

G is a lattice vector in the reciprocal-space lattice. Fig. 5.7 illustrates the principle of the experiment in reciprocal space. Only when Eqns. (5.2) and (5.3) are simultaneously fulfiUed is there a finite intensity of the inelastically-scattered neutron wave. The observable quantity in the experiment is the intensity of the scattered neutron wave as a function of the energy loss and of the scattering vector 

By rotating the sample crystal, one can in principle investigate any arbitrary direction in the reciprocal lattice and any magnitude of K, thus the entire first Brillouin 

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Vibrational spectroscopy provides detailed infonnation on both structure and dynamics of molecular species. Infrared (IR) and Raman spectroscopy are the most connnonly used methods, and will be covered in detail in this chapter. There exist other methods to obtain vibrational spectra, but those are somewhat more specialized and used less often. They are discussed in other chapters, and include inelastic neutron scattering (INS), helium atom scattering, electron energy loss spectroscopy (EELS), photoelectron spectroscopy, among others. 

Figure 4 Schematic vector diagrams illustrating the use of coherent inelastic neutron scattering to determine phonon dispersion relationships, (a) Scattering m real space (h) a scattering triangle illustrating the momentum transfer, Q, of the neutrons in relation to the reciprocal lattice vector of the sample t and the phonon wave vector, q. Heavy dots represent Bragg reflections.

If the displacements of the atoms are given in terms of the harmonic normal modes of vibration for the crystal, the coherent one-phonon inelastic neutron scattering cross section can be analytically expressed in terms of the eigenvectors and eigenvalues of the hannonic analysis, as described in Ref. 1. 

Figure 7 Experimental and theoretical inelastic neutron scattering spectrum from staphylococcal nuclease at 25 K. The experimental spectrum was obtained on the TFXA spectrometer at Oxford. The calculated spectrum was obtained from a normal mode analysis of the isolated molecule. (From Ref. 28.)...

At T < tunneling occurs not only in irreversible chemical reactions, but also in spectroscopic splittings. Tunneling eliminates degeneracy and gives rise to tunneling multiplets, which can be detected with various spectroscopic techniques, from inelastic neutron scattering to optical and microwave spectroscopy. The most illustrative examples of this sort are the inversion of the... 

Figure 3 Phonon dispersion curves obtained by inelastic neutron scattering revealing precursor behaviour prior to the 14M transformation in Ni-AI. The dip at q = 1/6 [110] (a) deepens upon cooling and (b) shifts under an external load .

Role of adsorbed hydrogen species on ruthenium and molybdenum sulfides. Characterization by inelastic neutron scattering, thermoanalysis methods and model reactions. 

Kearley, G. J., Pressman, H. A. Slade, R. C. T. (1986). The geometry of the HjOJ ion in dodecatungstophosphoric acid hexahydrate, (HjOJ)j (PWjjOfo), studied by inelastic neutron scattering vibrational spectroscopy. Journal of the Chemical Society Chemical Communications, 1801-2. 

As for oxygen species, significantly important knowledge has been accumulated both by experimental and theoretical investigation. Goodman and his coworkers reported inelastic neutron scattering evidence (Figure 22)... 

Also known for some time is a phase transition at low temperature (111K), observed in studies with various methods (NQR, elasticity measurement by ultrasound, Raman spectrometry) 112 temperature-dependent neutron diffraction showed the phase transition to be caused by an antiphase rotation of adjacent anions around the threefold axis ([111] in the cubic cell) and to lower the symmetry from cubic to rhombohedral (Ric). As shown by inelastic neutron scattering, this phase transition is driven by a low-frequency rotatory soft mode (0.288 THz 9.61 cm / 298 K) 113 a more recent NQR study revealed a small hysteresis and hence first-order character of this transition.114 This rhombohedral structure is adopted by Rb2Hg(CN)4 already at room temperature (rav(Hg—C) 218.6, rav(C—N) 114.0 pm for two independent cyano groups), and the analogous phase transition to the cubic structure occurs at 398 K.115... 

The Debye temperatures of stages two and one were determined by inelastic neutron scattering measurements [33], The total entropy variation using equation 8 is in the order of about 2 J/(mol.K). Although smaller in value, such variation accounts for 10-15% of the total entropy and should not be neglected. We are currently carrying on calculations of the vibrational entropy from the phonon density of states in LixC6 phases. 

Highly energetic compounds with potential use in explosive devices must be characterized completely and safely, particularly as the explosive character may be linked directly to vibrational modes in the molecular structure, hence the application of computational methods to complement experimental observations. ANTA 5 has been the subject of various studies and, as an adjunct to one of these and to confirm the results of an inelastic neutron scattering experiment, an isolated molecule calculation was carried out using the 6-311G basis set <2005CPL(403)329>. 

Supplementary to other vibrational spectroscopies, inelastic neutron scattering (INS) spectroscopy is a very useful technique for studying organic molecules as it is extremely sensitive to the vibrations of hydrogen atoms. INS spectroscopy has been used to analyze the molecular dynamics of the energetic compound ANTA 5 <2005CPL(403)329>. 

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