The following model describes the principle features of pattern formation and collection for EBSD analysis. A beam of electrons is directed at a point of interest on a tilted crystalline sample. The atoms in the material inelastically scatter a fraction of the electrons, with a small loss of energy, to form a divergent source of electrons close to the surface of the sample. Some of these electrons are incident on atomic planes at angles which satisfy the Bragg equation:

where n is an integer, λ is the wavelength of the electrons, d is the spacing of the diffracting plane, and θ the angle of incidence of the electrons on the diffracting plane.

These electrons are diffracted to form a set of paired large-angle cones that correspond to each diffracting plane. The image produced on the phosphor screen contains characteristic Kikuchi bands which are formed where the regions of enhanced electron intensity intersect the screen (Figure 1). The pattern seen is a gnomonic projection of the diffracted cone, making the band edges appear hyperbolic.

### Band intensity

The mechanisms giving rise to the Kikuchi band intensities and profile shapes are complex. As an approximation, the intensity of a Kikuchi band for the plane (hkl) is given by:

where fi(θ) is the atomic scattering factor for electrons and ( xi yi zi ) are the fractional coordinates in the unit cell for atom i. A collected diffraction pattern should be compared with a simulated pattern calculated using this equation. This ensures only planes that produce visible Kikuchi bands are used when solving the diffraction pattern.