Quasielastic line

Specification of. S SkCG, CO) requires models for the diffusive motions. Neutron scattering experiments on lipid bilayers and other disordered, condensed phase systems are often interpreted in terms of diffusive motions that give rise to an elastic line with a Q-dependent amplitude and a series of Lorentzian quasielastic lines with Q-dependent amplitudes and widths, i.e.. 

The results of QENS measurements for TaV2H [76] are consistent with this microscopic picture of H motion. First, on the frequency scale of tf the measured QENS spectra S(Q, co) are well described by the sum of a narrow elastic line and a broader quasielastic line having Q-dependent intensity, but Q-independent width. These features are typical of the case of spatially-confined (localized) motion [14]. 

Figure 26.15 The full width at half-maximum of the Lorentzian quasielastic line for ScH ,5 as a function of temperature. The solid line shows the fit based on of Eq. (26.27) to the data below 100 K.

Quasi-elastic neutron scattering (QENS) is related to stochastic particle motions. Because the displacements are random, the diffusive motion of particles in liquids caimot be quantized, and the energies are continuously distributed. Unlike the case of cooperative motions like phonons in solids or molecular vibrational excitations, in the dynamic scattering function S(Q,(o), there are no 5-functions at finite momentum and energy transfers. Instead, the dynamic scattering function is centered at zero-energy transfer with a characteristic quasielastic line width proportional to the diffusivity of the particles. 

Fig. 26. Temperature dependence of the quasielastic line width of CePdj. Solid cicles Holland-Moritz et al. (1982) open circles Galera et al. (1987).

Fig. 35. Inelastic magnetic neutron spectrum of CeSnj obtained on D7 with o = 3.5mcV at a scattering angle of 20° and at T = 300 K (phonons are already subtracted using an appropriate, scaled LaSuj spectrum). The solid line is a fit with one broad quasielastic line of Lorentzian shape. Corrections due to the Q-variation of the intensity arc contained in the fitted curve, not in the data points (Holland-Moritz et al. 1982).

Fig. 57. Temperature dependence of the quasielastic line width for CcB and Ceo.sLa, 585, (open circles Horn et al. 1981c, other symbols Neuhaus 1987).

Fig. 3. The temperature dependence of the quasielastic line in DyoosYo sPdj and Dyoo7Y(,93Al2. (From Waller and Holland-Moritz 1981.)...

X = 0.35 for y and Xo> x = 0.32 for neutron data. Note that in this material the authors state that two quasielastic lines are present. 

Fig. 30. Background corrected spectra of Ceo,4-Tho.26 as function of temperature upper panel has i = 300meV and lower panel at 7 = 10K has j = 1200meV The solid lines in the upper panel are fits with quasielastic lines, whereas in the lower panel the solid is an inelastic line and the dashed is quasielastic. (From Loong et al. 1987.)...

Fig. 37. The QE linewidth of YbMCu4 systems as function of temperature. The solid circles for YbAgCu4 correspond to an analysis with a quasielastic line only, whereas the open circles give the width assuming an inelastic contribution (see text). The triangles and squares represent the isostructural systems with M = Au and Pd, respectively. (From Severing et al. 1990a.)...

In fig. 43 the width found for YbCuAl by an analysis with just one quasielastic line is plotted as a function of temperature (circles) together with the relaxation rates extracted from NMR data (open circles, MacLaughlin et al. 1982). Whereas the NMR rate shows a strong increase below T = 40 K, this increase is much smaller for the relaxation rates extracted from the neutron scattering data. With new experiments, and an improved analysis, Murani et al. (1985) showed the existence of at least two inelastic magnetic excitations in YbCuAl. They added to fig. 43 the quantity X n X"(( n)> where x is the static bulk susceptibility, represented by x (8> = 0- T) in eq. (5), is the peak... 

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