Peak positions factors affecting

The change in the intensity with temperature is calculated with the temperature factor. This change is produced by the crystal lattice vibrations, that is, the scattering atoms or ions vibrate around their standard positions as was previously explained (see Section 1.4) consequently, as the crystal temperature increases, the intensity of the Bragg-reflected beams decreases without affecting the peak positions [25], Debye and Waller were the first to study the effect of thermal vibration on the intensities of the diffraction maxima. They showed that thermal vibrations do not break up the coherent diffraction this effect merely reduces the intensity of the peaks by an exponential correction factor, named the temperature factor, D(0) [2,26], given by... 

From the above remarks it may be seen that many factors affect the observed results. This means that although thermogravimetry can identify a substance from its decomposition temperature it should not be thought of as a finger print method like spectroscopy. In that technique a peak will always be at the same position in the spectrum, regardless of the make of the instrument or size of sample. 

In conventional polymer composites, the interlayer spacing will remain the same, similar to clay, and there will therefore be no shift of the diffraction peak. But if there is intercalation, the peak position will shift to a lower angle than in the original nanomaterial. The absence of a characteristic diffraction peak is usually the first indication of exfoliation of the nanomaterial, although it is not conclusive. However, several other factors such as a decrease in the degree of coherent layer stacking, very low concentration of nanomaterial and strong absorption by heavy atoms/ions (e.g. bromide) may also affect the accuracy of this analysis. 

Nevertheless, when we carry out x-ray crystallinity measurements on textile fibers, we must consider distortions that always affect crystalline material. Even in a completely crystalline material, the scattered x-ray intensity is not located exclusively in the diffraction peaks. That is because the atoms move away from their ideal positions, owing to thermal motion and distortions. Therefore, some of scattered x-rays are distributed over reciprocal space. Because of this distribution, determinations of crystallinity that separate crystalline peaks and background lead to an underestimation of the crystalline fraction of the polymer. In this paper, we attempt to calculate the real crystallinity for textile fibers from apparent values measured on the x-ray pattern. This is done by taking into account the factor of disorder following Ruland s method (3). 

Section 2.2.3 described factors that can affect relative intensities of peaks. These include the preferential orientation of crystal grains, residual stress and other crystal defects. Eventually, we must rely on human judgment to make the final identification. In this case, the matches of relative intensities are very good in general and no other calcium phosphate PDFs can provide matches as good as hydroxyapatite. Thus, hydroxyapatite can be positively identified. 

Since the integrand is strongly peaked about t = 0, we may multiply it by a factor with a very small positive rj without affecting the result. This, however, makes it possible to perform the r integral before the summation, leading to (in analogy... 

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