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I'm trying to understand how electron diffraction works, but I'm not really getting it. Here's an image

enter image description here

Here are a couple of questions about it that I can't figure out.

Why is the angle of the beam $2\theta$ instead of just $\theta$?
Why are there exactly two beams (outer and inner) when the experiment is performed? I would expect there to be several that got dimmer as they went out from the center.

If someone could explain the concepts in basic language to me, including the specific questions I've asked here, I'd be very appreciative.

Thanks.

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  • $\begingroup$ You already got everything right as far as I can tell. The picture does not specify why its author chose to name the diffraction (or illumination?) angle $2\,\vartheta$. Just as with any diffraction, you can (in theory) expect multiple diffraction orders but note that even observing the first one is sufficiently challenging that not everyone may consider any but the +/- 1st ones worthy of being pointed out! $\endgroup$ – pyramids Mar 27 '15 at 0:46
  • $\begingroup$ I think it means that it's twice the incident angle. I'm not sure why that would be though. $\endgroup$ – Bob Dylan Mar 27 '15 at 1:06
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I can only answer in terms of Bragg's Law. There are more correct models out there, but this one is easiest to work with :) n * Lambda = 2* d * sin(theta) where n is the "order" of the diffraction. Diffraction does get weaker at higher n, as you predict. First order (n=1) is usually focused on because the angles are smaller, the points are brighter, and higher order spots contain mostly redundant information about the crystal structure.
Lambda is the wavelength. For 200 keV electrons, the wavelength (lambda = h*c/E; lambda = 1240/200000 nm) is crazy short.
d is the repeated spacing in the sample creating diffraction. Usually around 1-10 Angstrom.

The picture I think of for this equation is a theta-theta X-ray diffraction setup. In this picture you can see that the incoming "beam" is bent by 2-theta. It's hard to picture it applied to electron diffraction. As you saw if you started playing with the Bragg Law, in this case the diffraction angle is tiny. The schematic you posted is not drawn to scale :) Anyway- in electron diffraction, electrons are diffracted by planes essentially parallel to the incident beam. I picture electrons that find themselves flying through a hallway in the structure of the sample veering through the walls (like the Kool Aid man) at an angle of 2-theta.
Awwwwww I just noticed this thread is nearly 4 years dead :(

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