3.12: Ewald sphere
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 s h , will satisfy the diffraction condition if the diffraction vector OH = IH – IO = s h /λ – s o /λ ( s o 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 λ min ≤ λ ≤ λ max , there will be a nest of Ewald spheres of radii 1/ λ max ≤ 1/λ ≤ 1/ λ min .