The Ewald X-Rays Diffraction Rationalization

A crystal arbitrary oriented in the way of an X-ray beam does not necessary produce a scattering beam and respectively its diffraction picture. Instead, diffraction can be rationalized through a construction in the reciprocal space, where the diffraction occurs, through the so-called Ewald reflection sphere that allows the prediction of the necessary orientation for satisfying the condition of Bragg s diffraction (Ewald, 1965, 1969). 

FIGURE 5.12 The construction (left) of the Ewald s sphere of diffraction (right), after (Matter Diffraction, 2003 X-Rays, 2003 Putz Lacrama, 2005). 

the Ewald s reflection sphere corresponds to the geometrical place of the elastic scattering of incident X photons on the electrons of a crystalline lattice if the momentum conservation law is applied to the elastic scattering the relation will next be written at Ihe level of the associated wave vectors  

Therefore, when the Ewald s sphere contains, passes by, or touches points of the reciprocal lattice the possibility of Bragg s reflection is predicted the point from the reciprocal space, on the Ewald sphere, touched 

Therefore, one notes how the Ewald s sphere rationalizes the X-ray diffraction, by the reflection on the crystallographic planes (hkl), along the Bragg s law in terms of wavelengths of incident X-radiation on crystal, through the HX radius of reflection s sphere. 

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