In 1913 Peter Ewald published details of a geometrical
construction which has been used ever since for interpreting diffraction patterns. When a
beam hits a crystal, Ewald's sphere shows which sets of planes are at (or close to) their
Bragg angle for diffraction to occur. In 2 D the sphere becomes a circle.
Click on the animation opposite to
show the construction of Ewald's sphere in 2 D.
• Consider a wave incident on a crystal. The crystal is represented by its
reciprocal lattice, with origin 0.
• The incident wave is represented by a reciprocal vector k. Draw the incident wave vector, k, ending at 0.
• Construct a circle with radius 1/l (i.e. |k|),
which passes through 0.
• Wherever a relpoint touches the circle, Bragg's Law is obeyed and a diffracted
beam will occur.
• CO represents the incident beam and CG is a diffracted beam. The angle between
them must be 2qB.
• OG is the g130
vector and thus has magnitude 1/d130,
and since |k| = 1/l:
• 0G = 2 × (1/l)sinqB
= 1/(d), rearranging this gives Bragg's equation with n = 1:
Click on the animation opposite to
show the construction of Ewald's sphere in 2 D.
