Electron Diffraction, and General X-Ray (EBSD- Kikuchi lines)

[antonni]

Hi guys, new here.
We all know the famous "Bragg Law" and the attached schematic drawing that goes along with it of a couple of planes with a distance `d` between them. Then, a DP occurs cause of constructive interference and destructive interference which happens due to planes deep in the crystal (B.D Culity book). That holds for X-Rays.

Q: Is there, in the same time as the above, diffraction from the same plane? I mean if we look at the famous drawing and the `d` is now the interatomic distance while the `dots` are actually the scatterers of the same plane ( or a diff. plane if you change your reference frame and the `depth axis`). How it relates to the "regular" diffraction phenomena?

The reason I am asking is that I have to understand EBSD nowdays, and I want to know that is the situation for electrons, cause e's interact strongly with matter (not like X-Rays) and do not penetrate too deep and I need to understand how we get diffraction from an EBSD schematic: high tilt to the e-beam in the SEM for a good BSE yield and the kikuchi lines on the detector's screen. Everywhere I saw it is described by Bragg simple formula, but these are electrons & the under these conditions the interaction onion is nanometric! where is the deep interaction which causes destructive interference? Is it diffraction a couple of planes on the "top" ? OR DIFFRACTION FROM SAME PLANE AND THE `d` IS INTERATOMIC DISTANCE?

Will also post it in "Engineering>Materials & Chemical Engineering"
(not native English)
Than x
Anton

 

[DrDu]

Either I haven't understood your question or you haven't understood completely the physics behind Braggs law: Obviously, the waves from atoms in the same plane interfere, too, but as there is no path difference, the interference is always constructive.

 

[antonni]

Perhaps (well..probably) I have not, will be grateful for clarification.
"but as there is no path difference"- Hmm, if the angle of incidence equals the angle of reflection, which is a condition for Bragg's law...I guess so. Do not know if I'm allowed to "link" here...but here (from min. 11:30 onwards for like 25 sec.)
the profeesot draws 90 deg. electron "rays" and the reflection is not 90 deg. (obviously)- then we do get a path difference. Can this situation happen in electron diffraction? Or it will not be proper diffraction anymore, at least not Bragg's diffraction?

Now I am more confused when ever about this all. I stopped trying to understand what happens to two electron waves that "distruct" each other (where do the electrons "go" to "vanish"), as I am not a physicist. With X-rays (photons) I think I can see the infinite (stretches to all space) EM field, a.k.a the wave-front with the direction of propagation normal to the detector's "sensitive screen" at certain angles will have different amplitudes- we get a pattern. With electrons I can not see it, instead of EM field we have probability!? Or the Electrons hit the screen, the normal of the specimen surface points to the center of the screen, as particles?
What "diffraction" we can talk about in the classic sense (Bragg's law) in EBSD? We do not have enough thickness for destructive Bragg interference to occur, yet bragg's law appears everywhere in my literature survey on EBSD, there is path difference to the screen (bright Vs deficient kikuchi lines)...Well, if anyone knows EBSD here I will be glad for some "theoretical" help. .. :) guess I can not link electron diffraction in EBSD with "regular" XRD analysis.

thank x

 

[M Quack]

A surface is a two-dimensional entity, unlike a bulk crystal that is 3-dimensional.

Therefore the Fourier transform of the atoms on a surface gives an array of rods perpendicular to the surface. These are called crystal truncation rods.
With (low energy) electron diffraction (LEED) you measure these.

http://en.wikipedia.org/wiki/X-ray_crystal_truncation_rod

http://en.wikipedia.org/wiki/Low-energy_electron_diffraction