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Basics of EBSD
Interpreting the diffraction pattern
The centre lines of the Kikuchi bands correspond to the projection of the diffracting planes on the phosphor screen. Hence, each Kikuchi band can be indexed by the Miller indices of the diffracting crystal plane which formed it. Each point on the phosphor screen corresponds to the intersection of a crystal direction with the screen. In particular, the intersections of the Kikuchi bands correspond to the intersection of zone axes in the crystal with the phosphor screen. These points can be labelled by the crystal direction for the zone axis (Figure 4).
The pattern is a gnomonic projection of the diffracted cones of electrons onto the phosphor screen. The semi-angle of the diffracted cones of electrons is (90 - θ) degrees. For EBSD this is a large angle so the edges of the Kikuchi bands approximate to straight lines. For example, the wavelength of 20 kV electrons is 0.00859 nm and the spacing of the (111) plane in aluminium is 0.233 nm making the cone semi-angle 88.9°.
The width w of the Kikuchi bands close to the pattern centre is given by:
where l is the distance from the sample to the screen (Figure 5). Hence, planes with wide d-spacings give thinner Kikuchi bands than narrow planes.
Because the diffraction pattern is bound to the crystal structure of the sample, as the crystal orientation changes the resultant diffraction pattern also changes. The positions of the Kikuchi bands can therefore be used to calculate the orientation of the diffracting crystal (Figure 6).
Click here for an interactive Java applet showing the relationship between the crystal structure and the diffraction pattern.
Click here to see figure 6 as an animation.
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