The geometry of formation of Kikuchi lines (discovered by S. Kikuchi in 1928) is traditionally explained by Bragg diffraction of inelastically scattered electrons of the diffuse background. This is well described in the classical TEM literature [1,2].

I could be wrong, but I always interpreted Kikuchi band formation in terms of electron channeling, as observed also in the SEM. This can perhaps be explained by the superposition of Bloch waves undergoing multiple scattering events. I have not studied this in any detail. However, a quick search revealed recent articles by S. Zaefferer [3,4] that may be useful for a deeper understanding.

1. PB Hirsh, A Howie, RB Nicholson and G Thomas: "Electron Microscopy of Thin Films", Butterworths London 1969.

2. M von Heimendahl: "Electron Microscopy of Materials", Academic Press 1979.

3. S. Zaefferer: "On the formation mechanisms, spatial resolution and intensity of backscatter Kikuchi patterns", Ultramicroscopy 107, 254-266, (2007).

4. S Zaefferer and NN Elhami: "Theory and application of electron channelling contrast imaging under controlled diffraction conditions.", Acta Materialia 75, pp. 20-50 (2014).

Thank you Pal,

I have got the same supposal, so I hope you are right. Inelastic scattering for Kikuchi lines and elastic scattering for Kikuchi bands. Just remains to understand it well. I am going to check the articles 3 and 4 you recommended.

I would recommend another publication which compares the different approaches for Kikuchi band formation : A. Winkelmann et al. "Physics-based Simulation Models for EBSD: Advances and Challenges"  (2016) IOP Conf. Ser.: Mater. Sci. Eng. 109 012018

http://arxiv.org/pdf/1505.07982.pdf

 While TEM,   the electrons are inelastically scattered in all directions and hence  the diffracted electrons will form a cone, not a beam. As a result of this  we observe Kikuchi lines.In the TEM,these lines are  used to set the orientation of a crystal  to an accuracy of 0.01 deg.

Firstly, the pair of Kikuchi lines equals to  ‘Kikuchi band’ to include the lines and the region between them. So we only need to figure out where Kikuchi lines come from.  The attached picture is the origin of kikuchi lines from the book 'Transmission Electron Microscopy' by David B. Williams and C. Barry Carter.

The electrons are generated above the specimen and travel through the specimen. Of course, they will scatter at all directions.Some of these electrons will travel at an angle theta B to the hkl planes. Due to bragg diffraction,the diffracted beam will lie on one of two cones.They are called kossel cones. They are parabolas. Since the screen/detector is flat and nearly normal to the incident beam, the Kossel cones appear as parabolas.

If we consider regions close to the optic axis, these parabolas appear as two parallel lines.

Reference: Transmission Electron Microscopy' by David B. Williams and C. Barry Carter.

Dear Hansheng,

thank you for your reply, but I am not sure if you are right. Kikuchi lines and Kikuchi bands are not equal. I am well familiarized with this book, but scheme you attached desribe only Kikuchi lines. Did you ever tried to construct Kikuchi map? If not, please, find the figure 19.6A on page 316 in book you cited (2nd ed.). I think what we can see on Kikuchi map are bands with the rims of the same intesity, no excess and deficient lines.

In the simplest case, the Kikuchi patterns are interpreted with the help of the gnomonic projection of Kossel cones which are formed by all possible directions of Bragg reflection from a lattice plane with normals (h k l) and (h k l). This does not include any information about band intensities.The angle-dependent Kikuchi band profile intensity can be described by a function B(v), where v is measured from the relevant lattice plane. The general form of B(v) is determined by the distance of v to the Bragg angle. For large angles, we observe the average background intensity, since we are away from diffraction effects which are strongest near the Bragg angle.

In the region near the Bragg angle, the Kikuchi band intensity is modulated and can go below or above the background for different angles. To approximate the complicated  Kikuchi band profile, a constant intensity I can be empirically assigned to the full geometrical band width.

Here from figure (a) to (b) to (c), one can clearly see the formation of the Kikuchi band from the Kikuchi lines. It is purely based on geometry.

Technically, in case (c) - the amplitude of inelastically scattered electrons becomes equal for the Bragg reflections 1 and 2. Which was not in the case (a).

Dear Girman,

I read all answers, but I can not understand why Kikuchi bands are surrounded by two dark lines in EBSD? I see two lines darker than the background!

Have you ever found any simple answer to this question?