Vibrational neutron

H.D. Middendorf, R.L. Hayward, S.F. Parker, J. Bradshaw A Miller (1995). Biophys. J., 69, 660-673. Vibrational neutron spectroscopy of collagen and model polypeptides. 

SANS Small-angle neutron scattering [175, 176] Thermal or cold neutrons are scattered elastically or inelastically Incident-Beam Spectroscopy Surface vibrational states, pore size distribution suspension structure... 

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. 

The dissociation energy is unaffected by isotopic substitution because the potential energy curve, and therefore the force constant, is not affected by the number of neutrons in the nucleus. However, the vibrational energy levels are changed by the mass dependence of 03 (proportional to where /r is the reduced mass) resulting in Dq being isotope-... 

Boron carbide is used in the shielding and control of nuclear reactors (qv) because of its neutron absorptivity, chemical inertness, and radiation stabihty. For this appHcation it may be molded, bonded, or the granular material may be packed by vibration. 

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. 

A procedure commonly used to extract dynamic data directly from experimental incoherent neutron scattering profiles is described in Ref. 17. It is assumed that the atomic position vectors can be decomposed into two contributions, one due to diffusive motion, fi /t), and the other from vibrations, Uijt), i.e.. 

The Q and ft) dependence of neutron scattering structure factors contains infonnation on the geometry, amplitudes, and time scales of all the motions in which the scatterers participate that are resolved by the instrument. Motions that are slow relative to the time scale of the measurement give rise to a 8-function elastic peak at ft) = 0, whereas diffusive motions lead to quasielastic broadening of the central peak and vibrational motions attenuate the intensity of the spectrum. It is useful to express the structure factors in a form that permits the contributions from vibrational and diffusive motions to be isolated. Assuming that vibrational and diffusive motions are decoupled, we can write the measured structure factor as... 

As with other diffraction techniques (X-ray and electron), neutron diffraction is a nondestructive technique that can be used to determine the positions of atoms in crystalline materials. Other uses are phase identification and quantitation, residual stress measurements, and average particle-size estimations for crystalline materials. Since neutrons possess a magnetic moment, neutron diffraction is sensitive to the ordering of magnetically active atoms. It differs from many site-specific analyses, such as nuclear magnetic resonance, vibrational, and X-ray absorption spectroscopies, in that neutron diffraction provides detailed structural information averaged over thousands of A. It will be seen that the major differences between neutron diffraction and other diffiaction techniques, namely the extraordinarily... 

Figure 3.2 The geometry of iner-/ran.v-[W(CO)3-(ij--H2)(Pf 3)2l from X-ray and neutron diffraction data r(H-H) 84pm (compared with 74.14 pm for free H2), I(W-H) 175 pm. Infrared vibration spectroscopy gives v(H-H) 2690cm compared with 4159cm (Raman) for free Hj.

Intimate information about the nature of the H bond has come from vibrational spectro.scopy (infrared and Raman), proton nmr spectroscopy, and diffraction techniques (X-ray and neutron). In vibrational spectroscopy the presence of a hydrogen bond A-H B is manifest by the following effects ... 

Kitagawa, T. and Miyazawa, T. Neutron Scattering and Normal Vibrations of Polymers. Vol. 9, pp. 335-414. 

The density of states (DOS) of lattice phonons has been calculated by lattice dynamical methods [111]. The vibrational DOS of orthorhombic Ss up to about 500 cm has been determined by neutron scattering [121] and calculated by MD simulations of a flexible molecule model [118,122]. 

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. 

Complementary to other methods that constimte a basis for the investigation of molecular dynamics (Raman scattering, infrared absorption, and neutron scattering), NIS is a site- and isotope-selective technique. It yields the partial density of vibrational states (PDOS). The word partial refers to the selection of molecular vibrations in which the Mossbauer isotope takes part. The first NIS measurements were performed in 1995 to constitute the method and to investigate the PDOS of... 

As at room temperature Bragg reflections contain both nuclear and magnetic structure factors, the nuclear structure was refined from a combination of polarized and unpolarized neutron data. Contrary to the ideal structure where only three atomic sites are present, it has been shown [11, 12] that some Y atoms were substituted by pairs of cobalt. These pairs, parallel to the c-axis are responsible for a structure deformation which shrinks the cobalt hexagons surrounding the substitutions. The amount of these substituted Y was refined to be 0.046 0.008. Furthermore, the thermal vibration parameter of Coi site appeared to be very anisotropic. The nuclear structure factors Fn were calculated from this refined structure and were introduced in the polarized neutron data to get the magnetic structure factors Fu. 

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