Quasi-elastic scattering measurements

The neutron quasi-elastic scattering measurements have been made from room temperature to glassy transition temperature on LAM-40 spectrometer at KENS. The details of the spectrometer and the data analysis have been described elsewhere. ... 

The nuclear resonant inelastic and quasi-elastic scattering method has distinct features favorable for studies concerning the microscopic dynamics (i.e., lattice vibration, diffusion, and molecular rotation) of materials. One advantageous feature is the ability to measure the element-specific dynamics of condensed matter. For example, in solids the partial phonon density of states can be measured. Furthermore, measurements under exotic conditions -such as high pressure, small samples, and thin films - are possible because of the high brilliance of synchrotron radiation. (For the definition of brilliance, see O Sect. 50.3.4.5 of Chap. 50, Vol. 5, on Particle Accelerators. ) This method is applicable not only to solids but also to liquids and gases, and there is no limitation concerning the sample temperature. 

In the non-densified xerogels, the Raman spectra show a relatively sharp band centered at about 16 cm , for the xerogel with % = 800°C, and at about 18 cm, for the xerogel with % = 860°C. In the samples treated below 800°C, it is not possible to observe the low frequency bump. The strong quasi-elastic scattering is due to vibrational dynamics of the porous fractal-like system, but probably also to residual water inside the pores. The low frequency bumps are attributed to surface vibrations of the particle-pore structure. The peak frequency increases with the annealing temperature, as the mean pore size, measured by SAXS experiments, decreases (see Raman Spectroscopy ofNanocrystals ). The Raman... 

The index of refraction of the material in the layer can be estimated to be 1.333. The total intensity of the quasi elastically scattered light is proportional to the isothermal compressibility. From intensity measurements we estimate it to be about a factor 500 higher than the compressibility of water at O C. A diffusion constant, which describes the dynamics of the entropy fluctuations, has been determined to be about 3 10" cm /s. This value has to be compared with the thermal diffusivity in water a 10 cm /s or the constant for self diffusion in water Djj20 lO" cm /s. 

Figure 10. Incoherent quasi-elastic scattering law for a particle undergoing simple translational diffusion (D(= 1.5 X10" ° m s" ). This is normally measured as a series of constant Q spectra.

The figure shows that the proportion of elastic scattering decreases as Q increases from zero. In fact the ratio of elastic to total (elastic plus quasi-elastic) scattering intensity provides a very useful quantity which is known as the elastic incoherent structure factor (EISF). It is often experimentally measurable and can be calculated easily from a theoretical model of the molecular motion... 

The very detailed picture of the diffuse translational and rotational molecular motions described above was revealed because of the high energy transfer resolution (typically less than 20 ieV) that is available with the instruments at ILL. However, useful results have also been obtained from medium resolution (-100 peV) quasi-elastic scattering instruments by skilful choice of samples and by fitting different models. It is not generally possible to measure experimentally the EISF for the whole molecule rotational diffusion, because this motion is too slow to give quasi-elastic scattering that is clearly distinct from the elastic peak. 

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