Scattering absolute intensity

Figure 9.7 (a) Scattered absolute intensity for = 120°C and T = 78°C for PE. The continuous lines represent the Porod fit. (b) Corresponding K" z) for both temperatures. Reprinted with permission from [13]. Copyright 1995 American Chemical Society. 

Practically it is more convenient to measure intensity ratios instead of absolute intensities. Thus, e.g., Cu may serve as a reference material, relative to which the ion intensities back-scattered from the atoms of the surface under consideration are measured ... 

Calibration to absolute intensity means that the scattered intensity is normalized with respect to both the photon flux in the primary beam and the irradiated volume V. Thereafter the scattering intensity is either expressed in terms of electron density or in terms of a scattering length density. Both definitions are related to each other by Compton s classical electron radius. 

Electron Density. Continuing the preceding considerations, calibration to absolute intensity means normalization to the scattering of a single electron , Ie that can be expressed in electron units, [e.u.]. Inevitably a calibration to absolute units involves also a normalization with respect to the irradiated volume V. Thus, for the field of materials science a suitable dimension of the absolute intensity is [I/V] = e.u./nm3 - The intensity measured in the detector is originating from a material with an average electron density of 400 electrons per nanometers cubed . The electron density itself is easily computed from mass density and chemical composition of the material (cf. Sect. 2.2.1). 

In Eq. (7.21) the normalization to the scattering cross-section r2 leads to the definition of absolute intensity in electron units which is common in materials science. If omitted [90,91], the fundamental definition based on scattering length density is obtained (cf. Sect. 7.10.1). 

This procedure can only be applied for a Kratky camera with zero-dimensional detector. It shows the value of this classical step-scan device for studies of scattering in absolute intensity units. 

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... 

Pure liquids can be used for the purpose of calibration to absolute intensity, because their diffuse scattering Ipi (0) = limv qIFi (s) caused from density fluctuations can be computed theoretically. Some examples are in the literature [91,93-95],... 

Finally, calibration of an unknown scattering pattern is carried out by (1) reducing the intensity in the same way as was done with the scattering of the noble metal sol, (2) obtaining the absolute intensity by... 

We notice that anisotropic scattering patterns can be calibrated to absolute intensity, as well. 

It is also interesting to note that circular differential Raman scattering, circular intensity differential (CID), has been reported for a series of optically active sulfoxides and a correlation found between the absolute configuration at sulfur and the differential scattering (240). Thus, all (/ )-alkyl p-tolyl sulfoxides investigated show a common (positive) CID feature in the 300 to 400 cm" region. 

Calibration is required to convert measurements of scattered light intensity from arbitrary to absolute values, an essential step in the calculation of molecular weight. Fortunately, because the calibration constant of most photometers remains stable for long periods of time, the calibration procedure need be carried out only infrequently. Should it need to be calibrated, the procedure described in ASTM D4001-93 or that of the instrument vendor should be followed. 

A natural concern with a x J> process is the size of the signal to be measured. However, under realistic conditions, the absolute intensity of the Raman echo signal is easy to detect. The problem is scattered light from unintended FID processes. As Fig. 5 shows, the Raman echo signal grows... 

Better analytical results can be expected if relative instead of absolute intensities are used for quantitative analysis The determination of relative intensities of liquids has been discussed by Bernstein and Allen (1955). Relative scattering cross sections of gases have been described by Schrotter and Klockner (1979). There are certain cases in which the solvent can be used as an internal standard. Otherwise, the standard must be added to the investigated sample. In this case, the relation between the intensity of the standard and that of the compound to be determined must be known. 

To calculate the absolute intensity it is necessary to know the strength of the primary beam. This can be achieved by using a specially prepared standard sample that scatters X-rays in a known way such that the absolute intensity scattered by any sample is determined by a simple comparison calculation. It must be sufficiently insensitive to the action of X-rays (18) as well as being homogeneous throughout. The standard sample used here is Lupolen (a polyethelene platelet) supplied with the Kratky Camera. 

As the fluorescence cross sections are known, the absolute intensity of the incoming beam can be determined readily from a measurement of the fluorescence intensity. On this basis all scattering data can be put on an absolute scale. 

Keller and Sadler s model fits the shape of the scattering curve, but fails by a factor of two in absolute intensity but how reliable are the absolute intensities in neutronscattering measurements A factor of two is quite a lot to laugh off. Yoon and Flory produce a computer-generated stochastic model which buys agreement in shape and intensity at the expense of unacceptably large variation in real space density, as... 

J. H. R. Clarke and J. Bruining. The absolute intensity of depolarized light scattering from liquid argon. Chem. Phys. Lett., 30 42-44 (1981). 

The absolute intensity of the x-ray wave coherently scattered by a single electron, I, is determined from the Thomson equation ... 

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