Ewald's Sphere

Ewald's Sphere

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

• the wavevector of the incident and diffracted x-ray beams,
• the diffraction angle for a given reflection,
• the reciprocal lattice of the crystal

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

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.