Reflection profile function, peak

Peak Breadths And Reflection Profile Function. As has been mentioned, the individual reflection profiles tend to be broad for polymers. With both x-ray and neutron radiation the peaks exhibit large peak-widths. In a neutron diffraction pattern of isotactic polypropylene (A. Immirzi, work in progress) the peak width at half maximum, K j, had values ranging from 0.60° at 20= 14° to 1.00° at 26= 43° (X= 1.542 A), whilst, with the same... 

The used S5mbols are K, scale factor n, number of Bragg peaks A, correction factor for absorption P, polarization factor Jk, multiplicity factor Lk, Lorentz factor Ok, preferred orientation correction Fk squared structure factor for the kth reflection, including the Debye-Waller factor profile function describing the profile of the k h reflection. 

Outside the spectral region A (co) = 0. A (Si) reflects the average peak profiles in the spectral region and for small values of m the spectral function of the autocorrelation function can be approximated as... 

The integral breadth, defined as the ratio between integrated intensity (peak area) and peak maximum, is frequently considered as a measure of the peak width. For the case of (00/) reflections from cubic crystallites of edge D = Na, the IB of the PD peak profile is readily obtained using the properties of the profile function of Equation (2) ... 

The important information about the properties of smectic layers can be obtained from the relative intensities of the (OOn) Bragg peaks. The electron density profile along the layer normal is described by a spatial distribution function p(z). The function p(z) may be represented as a convolution of the molecular form factor F(z) and the molecular centre of mass distribution f(z) across the layers [43]. The function F(z) may be calculated on the basis of a certain model for layer organization [37, 48]. The distribution function f(z) is usually expanded into a Fourier series f(z) = cos(nqoz), where the coefficients = (cos(nqoz)) are the de Gennes-McMillan translational order parameters of the smectic A phase. According to the convolution theorem, the intensities of the (OOn) reflections from the smectic layers are simply proportional to the square of the translational order parameters t ... 

The calculated intensity z Xi, yj) at any point x, y, of a dififaction pattern is expressed as a function of the integrated intensity h of the reflections contained in the pattern and a normalized analytical peak shape function PS x, y) is used to model the individual profiles. It is given by... 

Fig. 13a and b. Intensity contour maps around the 5.9-nm and 5.1-nm actin layer lines (indicated by arrows) a resting state b contracting state. Z is the reciprocal-space axial coordinate from the equator. M5 to M9 are myosin meridional reflections indexed to the fifth to ninth orders of a 42.9-nm repeat, (c) intensity profiles (in arbitrary units) of the 5.9- and 5.1-nm actin reflections. Dashed curves, resting state solid curves, contracting state. Intensity distributions were measured by scanning the intensity data perpendicular to the layer lines at intervals of 0.4 mm. The area of the peak above the background was adopted as an integrated intensity and plotted as a function of the reciprocal coordinate (R) from the meridian... 

Figure 2. X-ray diffraction pattern of a POD film for HTT = 2800 C (a) and profiles of the (002) reflection peaks as a function of deviation from the Bragg angle (b). (Reproduced with permission from Ref. 10. Copyright 1986 American Institute of Physics.)...

Figure 4.17 Example for the one parameter asymmetry correction. Top a symme trical ML curve with the correction function added k= 0.8). This is an odd function that does not change either the integral intensity or the peak height. Moreover the 1st derivate of the correction is zero at the central part. Thereby, also the peak position is kept unchanged. Middle The sum of both curves yields an asymmetrical peak. The minimum of the 2nd derivative is slightly shifted to the narrow slope. Bottom Application of the asymmetrical profile (in total five parameters) on the Si(lll) reflection from Figure 4.14.

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