Set of supplementary notes.

46 CHAPTER 3. FROM ATOMS TO SOLIDS
(3.19) defines a plane constructed perpendicular to the vector G and intersecting this vector
at its midpoint. The set of all such planes defines those incident wavevectors that satisfy the
conditions for diffraction (see Fig. 3.9).
Figure 3.9: Ewald construction. The points are the reciprocal lattice of the crystal. k 0 is the
incident wavevector, with the origin chosen so that it terminates on a reciprocal lattice point.
A sphere of radius |k 0 | is drawn about the origin, and a diffracted beam will be formed if this
sphere intersects any other point in the reciprocal lattice. The angle θ is the Bragg angle of
(3.21)
This condition is familiar as Bragg’s Law. The condition (3.19) may also be written as
2π
λ sin θ = π d
(3.20)
where λ = 2π/k, θ is the angle between the incident beam and the crystal planes perpendicular
to G, and d is the separation between the plane and the origin.