Abstract
The Kinematic Theory covers any description of the X-ray scattering process by a distribution of electrons where rescattering (with phase coherence) of the already scattered waves by the distribution has negligible effects. In other words, the scattered radiation is composed by photons that interacted once with the sample. Under these conditions, the scattered intensity, often called the kinematic intensity, is proportional to the form factor square module, (1.25). Material samples in a gaseous, liquid, or solid state are nothing more than atom systems with different degrees of correlation between the atomic positions, ranging from disperse systems, such as a gas, until strongly correlated systems as in a crystals. The Kinematic Theory describes very accurately the X-ray scattering by any of these systems, except only by highly perfect crystals with dimensions larger than a few microns. In this chapter we will begin in fact to discuss analysis methods of atomic systems by kinematic scattering of X-rays starting with the disperse system of lowest possible degree of correlation.
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- 1.
Ideal gases under normal temperature and pressure conditions stand for ideally disperse systems (Guinier and Fournet 1955).
- 2.
With \(Q = (4\pi /\lambda )\sin (\gamma /2)\), \(\int G(Q)\,\mathrm{d}\Omega = 2\pi \int \exp \{ -\alpha \,\sin ^{2}(\gamma /2)\}\,\sin \gamma \,\mathrm{d}\gamma \simeq 4\pi /\alpha = 0.5\,\pi \,(\lambda /D)^{2}\).
- 3.
Assuming X-ray beams with finite coherence lengths.
- 4.
Useful range of a radiation detector in intensity scales or dose per pixel.
- 5.
It is an optional task to demonstrate that \(\lim \limits _{Q\rightarrow 0}\langle \vert \mathrm{FT}\{s({\boldsymbol r})\}\vert ^{2}\rangle = v_{p}^{2}\,e^{\,-\frac{1} {3} Q^{2}\langle r^{2}\rangle }\,.\) Such demonstration can be found in several books on SAXS, e.g. Giacovazzo (2002), Glatter and Kratky (1982), and Guinier (1994).
- 6.
Non-integer values occur in particles without defined interfaces, such as macromolecules and materials with fractal properties (Teixeira 1988).
- 7.
See Guinier (1994, p. 336).
- 8.
For large values of σ, such as σ > a 0∕3, the normalization constant is reset so that ∫ 0 ∞ p(a) da = 1.
Bibliography
Craievich, A.: Small-angle X-ray scattering by nanostructured materiais. In: Sakka, S. (ed.) Handbook of Sol-Gel Science and Technology: Processing, Characterization and Applications, vol. II, pp. 161–189. Kluwer Academic, New York (2002)
Giacovazzo, C. (ed.): Fundamentals of Crystallography, 2nd edn. Oxford University, Oxford (2002)
Glatter, O., Kratky, O. (eds.): Small Angle Scattering of X-Rays. Academic, London (1982)
Guinier, A.: X-ray Diffraction: In Crystals, Imperfect Crystals, and Amorphous Bodies. Dover, New York (1994)
Guinier, A., Fournet, G.: Small-Angle Scattering of X-Rays. Wiley, New York (1955)
Lindner, P., Zemb, T. (eds.): Neutrons, X-Rays and Light: Scattering Methods Applied to Soft Condensed Matter. Elsevier, Amsterdam (2002)
Teixeira, J.: Small-angle scattering by fractal systems. J. Appl. Crystallogr. 21, 781–785 (1988)
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Morelhão, S.L. (2016). Low Correlated Systems: Gases and Dilute Solutions. In: Computer Simulation Tools for X-ray Analysis. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-19554-4_2
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