Practical Electron Microscopy and Database

An EBSD pattern consists of a number of Kikuchi bands. Each band comprises a pair of parallel Kikuchi lines. The incident electron beam is directed to the point of interest (POI) on the sample surface and thus, the elastic scattering of the electron beam induces the electrons to diverge from a point just below the sample surface and to impinge on crystal planes in all directions. Backscattered electrons that satisfy Bragg's law for a given plane generate two diffraction cones from the front and back surfaces of the plane. These cones are produced for each family of lattice planes. When these cones intersect the phosphor screen or camera thin bands are formed. These bands are called Kikuchi lines. The Kikuchi lines appear as almost straight lines because the cones are very shallow due to the small Bragg angle (order 1°) with a very small electron wavelength. EBSD software can automatically analyze the individual Kikuchi lines by comparing them with the theoretical Kikuchi lines in database.

The two diffraction cones are generated due to the geometry of the diffraction process, which involves backscattered electrons and the crystalline lattice planes of the sample:

---------------------------------------------- [2334a]

where,

n is the order of diffraction.
λ is the electron wavelength.
d is the interplanar spacing.
θ is the Bragg angle.

Note that Bragg's Law itself does not include any explicit directional components.

• Diffraction from Atomic Planes: The diffraction process generates a cone of scattered electrons around the direction of the atomic planes that satisfies Bragg's law. Because the atomic planes are spread throughout the sample, two sets of diffraction cones are generated:

  • Front Surface: When the incident electron beam interacts with the atomic planes from one side, a cone of diffracted electrons is formed from this surface.
  • Back Surface: The electron beam can also pass through the crystal and interact with the same atomic planes from the opposite side, generating another cone of diffraction.
• Two Diffraction Cones: The two cones are produced because the atomic planes in a crystal are periodic and extend throughout the material, allowing for diffraction to occur from both sides of the planes. Electrons are diffracted in two opposite directions: one towards the front (towards the incident beam direction) and the other towards the back (opposite to the incident beam direction). This gives rise to two cones of diffracted electrons for each family of planes.
• Shallow Cones and Kikuchi Lines: Since the Bragg angle for electron diffraction is very small (due to the very short wavelength of electrons), the cones formed are shallow. When these cones intersect with the phosphor screen or detector in an Electron Backscatter Diffraction (EBSD) setup, they appear as almost straight bands, which are the Kikuchi lines.

For better understanding, Figure 2334 (a) and (b) shows the formation of Kikuchi lines and electron backscatter diffraction pattern in different ways.

Figure 2334 (a) and (b). The formation of Kikuchi lines and electron backscatter diffraction pattern in different ways.

Traditional EBSD methods use Hough transforms to determine the position of Kikuchi bands on the phosphor screen. [1 - 2] The Hough transform provides a proper technique for obtaining the parameters of a straight line and thus the positions of Kikuchi bands in an EBSP (electron backscatter diffraction pattern). Lines in the pattern are converted to spots in Hough Space.

[1] Krieger Lassen, N.C., Conradsen, K. & Juul Jensen, D. (1992). Image-processing procedures for analysis of electron back scattering patterns. Scanning Microsc 6(1), 115–121.
[2] Adams, B.L.,Wright, S.I. & Kunze, K. (1993). Orientation imaging: The emergence of a new microscopy. Metall Trans A 24A(4), 819–831.