Ewald sphere
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- 17704
The Ewald sphere, or sphere of reflection, is a sphere of radius 1/λ passing through the origin O of the reciprocal lattice. The incident direction is along a radius of the sphere, IO (Figure 1). A reflected direction, of unit vector sh, will satisfy the diffraction condition if the diffraction vector OH = IH – IO = sh/λ – so/λ (so unit vector in the direction IO) is a reciprocal lattice vector, namely if H is a node of the reciprocal lattice (see Diffraction condition in reciprocal space) . If other reciprocal lattice nodes, such as G, lie also on the sphere, there will be reflected beams along IG, etc. This construction is known as the Ewald construction. When the wavelength is large, there are seldom more than two nodes, O and H, of the reciprocal lattice simultaneously on the Ewald sphere. When there are three or more, one speaks of multiple diffraction, multiple scattering or n-beam diffraction. This situation becomes increasingly frequent as the wavelength decreases and is practically routine for very short wavelengths such as those of γ-rays and electrons. The curvature of Ewald sphere then becomes negligible and it can often be approximated by a plane. Many reflections must then be taken into account at the same time.
When the wavelength changes, the radius of the Ewald sphere changes. If the incident beam is a white beam, with a wavelength range λmin ≤ λ ≤ λmax, there will be a nest of Ewald spheres of radii 1/λmax≤ 1/λ ≤ 1/λmin.