Diffraction

Background

Crystalline, polycrystalline and amorphous materials.

The crystal lattice: unit cell and point lattices. The seven crystal systems. Space groups. Miller indices and Unit vectors. Reciprocal space.

Some diffraction properties and conditions

• Elastic scattering (no energy loss).
• The wavelength of the radiation should be comparable to the interatomic spacing of the material.

Bragg's law

• Condition: The planes of atoms responsible for a diffraction peak have to behave as a specula mirror, so that the angle of incidence \theta equals the angle of reflection.
• Bragg's law

<math> n\lambda=2dsin\theta </math>

where n is an integer, \lambda is the wavelength of the radiation, d is the spacing of the crystal lattice planes and \theta is is the reflection angle.

• Allowed and forbidden reflections

In the FCC (face-centered cubic) lattice the Miller indices have to be all odd or all even.\ In the BCC (body-centeres cubic) lattice the sum of h+k+l must be odd for an allowed reflection.