Neutron line shape

The coherent tunneling case is experimentally dealt with in spectroscopic studies. For example, the neutron-scattering structure factor determining the spectral line shape is... 

Time-dependent correlation functions are now widely used to provide concise statements of the miscroscopic meaning of a variety of experimental results. These connections between microscopically defined time-dependent correlation functions and macroscopic experiments are usually expressed through spectral densities, which are the Fourier transforms of correlation functions. For example, transport coefficients1 of electrical conductivity, diffusion, viscosity, and heat conductivity can be written as spectral densities of appropriate correlation functions. Likewise, spectral line shapes in absorption, Raman light scattering, neutron scattering, and nuclear jmagnetic resonance are related to appropriate microscopic spectral densities.2... 

Both Pecora (16) and Komarov and Fisher (17) adapted van Hove s space-time correlation function approach for neutron scattering (18) to the light-scattering problem to calculate the spectral distribution of the light scattered from a solution. Using a molecular analysis, Pecora assumed the scattering particles to be undergoing Brownian motion, and predicted a Lorentzian line shape for the spectral distribution of the... 

In PB networks, the variation of the line shape as a function of the applied stress was interpreted in terms of a chain length distribution. Shorter chains may be more oriented than longer ones, at a given elongation [18], which may lead to a non-affine behaviour at the chain scale. The question of the spatial scale to which the deformation is affinely transmitted, has been investigated intensively by small angle neutron scattering [64]. However, it may happen as well that the chain portions close to junction points are more oriented (have a more restricted mobility) than those in the middle of the chains [19]. 

Neutron diffraction patterns of powder samples were taken on a neutron diffractometer (X = 1.085 A) mounted on the thermal column of a WR-SM nuclear reactor [3]. The DBW-3.2 program for the Rietveld neutron diffraction line shape analysis was used in calculations and structure refinement [4]. A DRON-3M X-ray diffractometer (CuK - radiation) was used to measure X-ray powder diffraction patterns. 

When the H- H dipole-dipole interaction can be measured for a specific pair of H nuclei, studies of the temperature dependence of both the H NMR line-shape and the H NMR relaxation provide a powerful way of probing the molecular dynamics, even in very low temperature regimes at which the dynamics often exhibit quantum tunnelling behaviour. In such cases, H NMR can be superior to quasielastic neutron scattering experiments in terms of both practicality and resolution. The experimental analysis can be made even more informative by carrying out H NMR measurements on single crystal samples. In principle, studies of both the H NMR lineshape and relaxation properties can be used to derive correlation times (rc) for the motion in practice, however, spin-lattice relaxation time (T measurements are more often used to measure rc as they are sensitive to the effects of motion over considerably wider temperature ranges. 

Figure 65 Evidence for short range, two dimensional order from neutron scattering for the jarosite, D30Fe3(S04)2(0H)6. Note the asymmetric Warren line shape. (Ref 138. Reproduced by permission from EDP Sciences)...

Experimentally, the EISF is the fraction of the total quasielastic intensity contained in the purely elastic peak. For an exact experimental determination of the EISF the neutron spectra have to be fitted with the correct scattering function which consists of the elastic and a series of quasielastic terms (see [14, 28, 29]). Approximately, however, the EISF can be determined in a kind of model-indepen-dent data evaluation by fitting the neutron spectrum with a single Lorentzian plus an elastic term. Although in this way the line shape is not correct (except for N = 2 and 3), the EISF thus obtained allows statements to be made about the geometry for the localized motion. For the present chapter two EISFs, both spatially averaged (for powder samples), are of particular relevance ... 

Figure 62. Neutron diffraction intensity after subtraction of the background from CO on graphite (Papyex) at 1.58 K and at a coverage of 0.78 monolayers (see also Fig. 25 for comparison). Note the presence of the (20) and (21) reflections (at Q = 1.703 A and 2.253 A , respectively) and the absence of the (10) and (11) reflections (at Q = 0.852 A" and 1.475 A", respectively) as marked by the arrows the solid line is a two-dimensional line-shape fit [309]. The diffraction pattern reveals that CO on graphite remains in the commensurate herringbone stmcwre down to very low temperatures. (From Refs. 177 and 381.)...

Diffusion measurements fall into two broad classes. Under macroscopic equilibrium, i.e. if the overall concentration within the sample remains constant, molecular diffusion can only be studied by following the diffusion path of the individual molecules ( microscopic measurement by quasielastic neutron scattering (QENS) [48,183,184], nuclear magnetic relaxation and line-shape analysis, PFG NMR) or by introducing differently labelled (but otherwise identical) molecules into the sample and monitoring their equilibration over the sample ( macroscopic measurements by tracer techniques) [185,186]. The process of molecular movement studied under such conditions is called self-diffusion. 

Fig. 13. Inelastic neutron-scattering spectra of Ar/MgO(100) at 10 K. (a) Experimental spectra at incident energy of 7 meV for a 1.16 layer (hexagonal structure) the vertical bars and the triangle represent experimental errors and the experimental broadening (reduced by a factor of 1/10), respectively (b) calculated spectrum for the hexagonal incommensurate structure after convoluting with the instrumental line shape of 0.3 meV at a neutron gain of 5 meV. Units are arbitrary and the basehne is shifted with respect to curve (a) (fiomRef 99).

The M —H distances are approximately equal to the sum of covalent radii as shown by neutron and X-ray studies. In order to find out the precise structure of metal hydrides, both neutron and X-ray studies are needed. The distances obtained from NMR studies in the solid state based on the second moment calculated from the line shape are too small. This results from the inaccuracy of the Van Vleck equation. The Mn-H distance in [MnH(CO)5] calculated from the second moment of the Van Vleck equation is 128 pm. The longer distance (144 pm) was calculated from NMR data based on the modified Van Vleck equation. " A similar distance was calculated from electron diffraction studies in the gas phase. All these distances are lower than the sum of covalent radii which equals 157 pm. The Mn-H distance in [MnH(CO)5] obtained from neutron diffraction studies equals 160.1 pm. Similar distances were found for other hydride complexes. 

Fig. 4. Neutron spectra of UOj measured at the ISIS spallation source with i = 290meV for different temperatures. The Neel temperature of UOj is 30.8 K. The smooth line is the fit to four Gaussian line shapes and a sloping background. These five components are shown by the dashed lines. (From Amoretti et al. 1989.)...

Stassis et al. (1979c) have observed a neutron scattering line shape similar to fig. 50 at the zone boundary point [111] of the mixed valence material y-Ce. 

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