Corrected intensity distributions

Figure 8. The corrected intensity distributions divided by the respective concentration from SAXS measurements (original data in inset, including background) for solutions of 57Tri07H with increasing concentration.

In addition to qualitative identification of the elements present, XRF can be used to determine quantitative elemental compositions and layer thicknesses of thin films. In quantitative analysis the observed intensities must be corrected for various factors, including the spectral intensity distribution of the incident X rays, fluorescent yields, matrix enhancements and absorptions, etc. Two general methods used for making these corrections are the empirical parameters method and the fimdamen-tal parameters methods. 

The most recent calculations, however, of the photoemission final state multiplet intensity for the 5 f initial state show also an intensity distribution different from the measured one. This may be partially corrected by accounting for the spectrometer transmission and the varying energy resolution of 0.12, 0.17, 0.17 and 1,3 eV for 21.2, 40.8, 48.4, and 1253.6 eV excitation. However, the UPS spectra are additionally distorted by a much stronger contribution of secondary electrons and the 5 f emission is superimposed upon the (6d7s) conduction electron density of states, background intensity of which was not considered in the calculated spectrum In the calculations, furthermore, in order to account for the excitation of electron-hole pairs, and in order to simulate instrumental resolution, the multiplet lines were broadened by a convolution with Doniach-Sunjic line shapes (for the first effect) and Gaussian profiles (for the second effect). The same parameters as in the case of the calculations for lanthanide metals were used for the asymmetry and the halfwidths ... 

To decide whether a surface effect is present and, if so which, the experimental spectra shown in Fig. 16 have been corrected for the spectrometer transmission. The secondary electron contribution and the emission from conduction band states have also been subtracted. Comparing this spectrum with calculated multiplet intensities it seems that a contribution from a divalent Am surface resulting in a broad structureless 5f 5f line at 1.8 eV is the most suitable explanation of the measured intensity distribution. Theory also supports this interpretation, since the empty 5f level of bulk Am lies only 0.7 eV above Ep within the unoccupied part of the 6d conduction band (as calculated from the difference of the Coulomb energy Uh and the 5 f -> 5 f excitation energy Any perturbation inducing an increase of Ep by that amount will... 

J3—ft. Strictly speaking, it depends on the intensity distribution in a line (Jones, 1938) and the ideal method of obtaining / is by a Fourier analysis of the line shape (Stokes, 1948) in practice it is doubtful whether such elaboration is worth while, and it is usually sufficient to use correction curves given by Jones (1938) for the relation between b/B and jS/JB for different line-shapes, or to use Warren s (1941) relation j32 = J52—6a which gives very similar results (King and Alexander, 1954). 

Structure Refinement. The habit of the selected crystal already showed its monoclinic symmetry, with well-developed faces. From the carefully measured intensities, structure factors were derived by routine methods. For absorption correction, -scans of 11 reflections were taken in steps of s 10 . As one of these reflections (115) showed a completely different intensity distribution, it was remeasured with 2 . This... 

The intensity calculation is based on the knowledge of qKpr), the primary X-ray intensity distribution function as a function of mass depth pz (Fig. 8.9). Some experimental calculations of (iKp ) have been conducted using the tracer method proposed by Castaing. These measurements have only covered a limited number of experimental situations but have enabled adjustment of the parameters used in simulations by the Monte Carlo method or matrix effect correction models using a parameterisation of the function [Pg.164]

A property of NMR that has been used extensively to study the details of phase transition dynamics is the time required for the nuclei to establish an equilibrium population distribution among the energy levels, called spin-lattice relaxation and denoted by the characteristic time constant Ti. This relaxation time is also important to solid-state NMR in a practical sense, because once a spectrum is acquired one must wait until the nuclei have at least partially re-equilibrated before the spectrum can be acquired again, or fully re-equilibrated to obtain quantitatively correct intensity ratios. Most solid-state NMR spectra represent lOO s to lOOO s of co-added acquisitions to improve the signal-to-noise ratio. 

In this way, separate meridional intensity profiles were generated for each dimer, corrected for polarization, and plotted in the range of 0comparison with calculated intensity distributions. Similarly, azimuthal intensity distributions passing through the equatorial reflections (measured as a function of azimuthal angle from the meridian) were used to determine the Hermans order parameters (8). 

Fig. la-d. Small-angle scattering from a dilute, random dispersion of membranes (vesicles), a corrected intensities or thickness factor obtained from the experimental intensity distribution 1(h) by multiplication with h. b Structure factor (amplitude function) with arbitrarily chosen signs (-k,—, +, —,).c Autocorrelation function of the electron density q(x) profile across the membrane obtained by cosine transformation of I,(h) (Eq. 5a) the insert shows the profile obtained by de-convolution. d Centrosymmetric electron density profile obtained by cosine transformation (Eq. 5b) of F,(h). From a study on lipoprotein X, an assembly of unilamellar vesicles (Ref. 84, with permission)... 

Here, d//dA denotes the spectral intensity distribution of the incident X-ray beam V is the volume of sample illuminated V0 is the sample unit cell volume 0 is the Bragg angle for the reflection h P is the polarisation factor A is an absorption correction for the sample in its capillaiy and D is a detector sensitivity and obliquity factor. Quantities such as P, A and D vary with any or all of A, 0 and x, the position of the diffracted beam on the detector the spectral intensity distribution is, in general, not precisely known in advance and the detector may suffer from spatial distortion and non-uniformity. Thus equation (7.17) may be written as... 

We have modified a 1 kW Oriel xenon light source to provide an 8 inch illuminated circle with light between 300 and 1,000 nm to simulate sunlight for our prototype device. We have measured the light intensity distribution in the circle so that we can correct for effects of non-uniformity in the light field on the performance of photocatalysts. 

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