Total scattering measurements

Figure 11. T(r) functions for the high and low temperatures phases of cristobalite obtained from neutron total scattering measurements. The two peaks at low-r correspond to the Si-0 and 0-0 bonds. The dashed lines trace features in T(r) for p-cristobalite that are not seen in the T(r) for a-cristobalite.

Direct calibration to absolute intensity is not a usual procedure at synchrotron beamlines. Nevertheless, the technical possibilities for realization are improving. Therefore the basic result for the total scattering intensity measured in normal transmission geometry is presented. At a synchrotron beamline point-focus can be realized in good approximation and the intensity /(s) is measured. Then integration of Eq. (7.19) results in... 

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. 

For light-scattering measurements, the total amount of scattered light is deduced from the decrease in intensity of the incident beam as it passes through a polymer sample. This can be described in terms of Beer s law for the absorption of light as follows ... 

Figure 17 Total scattering cross section Cp (left axis) and rate (right axis) for the production of CO by electron impact on a 5-ML film of methanol condensed on an Ar spacer as a function of the incident electron energy. The dashed line is the intrinsic minimum rate of CO production due to the measurement at i = 14 eV. (From Ref. 37.)...

Light scattering is due to fluctuations in the local dielectric tensor e of the medium. In fluids these fluctuations are dynamic and the scattered intensity will be a function of time and the frequency spectrum of the scattered light will differ from that of the incident light. The time dependence of the total scattered intensity is analyzed by measuring the intensity autocorrelation function... 

This method, although well established, is not entirely satisfactory, since the experimental scatter is difficult to measure accurately over a small range of the two theta scale. We prefer to use a normalisation procedure based on Vainshtein s law of conservation of intensity. This law states that total scatter over identical regions of reciprocal space will be equal despite different degrees of lattice order (2). 

Fig. 2.2. Schematic diagram, not to scale, of the time-of-flight localized scattering system used by the UCL group for total scattering cross section measurements.

Fig. 2.5. Schematic illustration of the apparatus used by the Bielefeld group to measure total scattering cross sections. Reprinted from Journal of Physics B 13, Sinapius, Raith and Wilson, Low-energy positrons scattering from noble gas atoms, 4079-4090, copyright 1980, with permission from IOP Publishing.

Positron total scattering cross sections have been measured and calculated for a variety of atomic and molecular gases, and in this section we present a selection of results. In the light of the discussion given in section 2.4, particularly concerning small-angle elastic scattering, a critical evaluation... 

Positronium formation cross sections for atomic hydrogen have also been reported by Zhou et al (1997), who used the special hydrogen scattering cell described in subsection 2.5.4 with reference to their measurements of total scattering cross sections. Details were given by Zhou et al. (1997) and descriptions can be found below, since the same methods were used by the Detroit group (e.g. Zhou et al., 1994b) in their alkali metal work. 

Smart, J.H. and Stein, T.S. (1980). Measurements of total scattering cross sections for low-energy positrons and electrons colliding with krypton and xenon. Phys. Rev. A 22 1872-1877. 

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