The Ewald sphere is a geometric construction used in electron, neutron, and X-ray crystallography which demonstrates the relationship between:

It was conceived by Paul Peter Ewald, a German physicist and crystallographer.^[1] Ewald himself spoke of the sphere of reflection.^[2]

Ewald's sphere can be used to find the maximum resolution available for a given x-ray wavelength and the unit cell dimensions. It is often simplified to the two-dimensional "Ewald's circle" model or may be referred to as the Ewald sphere.

When the wavelength of the radiation to be scattered is much smaller than the spacing between atoms, the Ewald sphere radius becomes large compared to the spatial frequency of atomic planes. This is common, for example, in transmission electron microscopy. In this approximation, diffraction patterns in effect illuminate planar slices through the origin of a crystal's reciprocal lattice. However, it is important to note that while the Ewald sphere may be quite flat, a diffraction pattern taken perfectly aligned down a zone axis (high-symmetry direction) contains precisely zero spots that exactly satisfy the Bragg condition. As one tilts a single crystal with respect to the incident beam, diffraction spots wink on and off as the Ewald sphere cuts through one zero order Laue zone (ZOLZ) after another.