Multiplicative scatter factor

Here, Aq(X), a, /3, and e(k) are a real spectrum, multiplicative scatter factor (amplification factor), additive scatter factor (offset deviation), and noise, respectively. There are several methods to eliminate or reduce the effects of a and /3. Here, we describe three of them. 

Equation (Bl.8.6) assumes that all unit cells really are identical and that the atoms are fixed hi their equilibrium positions. In real crystals at finite temperatures, however, atoms oscillate about their mean positions and also may be displaced from their average positions because of, for example, chemical inlioniogeneity. The effect of this is, to a first approximation, to modify the atomic scattering factor by a convolution of p(r) with a trivariate Gaussian density function, resulting in the multiplication ofy ([Pg.1366]

A teclmique that employs principles similar to those of isomorphous replacement is multiple-wavelength anomalous diffraction (MAD) [27]. The expression for the atomic scattering factor in equation (B1.8.2h) is strictly accurate only if the x-ray wavelength is well away from any characteristic absorption edge of the element, in which case the atomic scattering factor is real and Filiki) = Fthkl V- Since the diffracted... 

I is the measured intensity, J the Compton profile, M the multiple scattering contribution, K the energy dependent correction factor, B the background, C the normalization constant and Zvai the mean number of valence electrons. Figure 3 shows a valence Compton profile of Cu obtained by this procedure. 

One of the most serious difficulties for experimentally accessing the dynamics in the low Q plateau is the presence of multiple scattering [210]. In order to assess this effect, NSE spectra were taken above and below the multiple scattering threshold. For neutron wavelengths A 14 A the first structure factor peak cannot be seen with neutrons and therefore multiple scattering contributions... 

After a correction similar to that for the PDF for sample independent scattering, absorption, multiple scattering, and incoherent scattering one obtains a dynamic structure factor ... 

Martin et al. [102] reported a study in which LIBS was applied for the first time to wood-based materials where preservatives containing metals had to be determined. They applied PLS-1 block and PLS-2 block (because of the interdependence of the analytes) to multiplicative scattered-corrected data (a data pretreatment option of most use when diffuse radiation is employed to obtain spectra). They authors studied the loadings of a PCA decomposition to identify the main chemical features that grouped samples. Unfortunately, they did not extend the study to the PLS factors. However, they analysed the regression coefficients to determine the most important variables for some predictive models. 

Since 1992 the two Italian stations of Rome, urban site (latitude 41.9° N, longitude 12.5° E, altitude 60 m), and Ispra, semi-rural site (latitude 45.8° N, longitude 8.6° E, altitude 240 m), collect regular continuous measurements of spectral UV (290-325 nm) irradiance by means of Brewer Spectrophotometry. The measured data are compared with the output of the STAR model (System for Transfer of Atmospheric Radiation) [1], STAR is a multiple scattering radiative transfer model which considers all atmospheric factors modulating UV radiation at ground (ozone, aerosol, clouds, pollutants, albedo, pressure, temperature, humidity) [2], The model involves combination of a radiative transfer code, an initialisation procedure and an integration scheme. 

Joyce-Loebel MK III C flat-bed microdensitometer. The structure factor magnitudes were derived from the integrated intensities according to F(hk ) 2 = I(hk ). The largest errors in the intensity measurements were for the darkest spots. The scattering factors of C, 0 H for the diffraction of electrons were taken from the International Tables for X-Ray Crystallography, vol. IV (7). No correction for multiple scattering and n-beam dynamical interactions were applied because the thickness of the crystals was of the order of 100 X (6). 

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