Electron Gun diffraction and undeflected spot diameter

In summary, the angle of 2 phi in electron gun diffraction is the result of two symmetric waves with the same accident angle but negative, causing all other rays to cancel each other. This is similar to the rotation of an optical mirror, where the image moves twice as much as the mirror rotation. For Bragg scattering, constructive interference only occurs in certain directions determined by the spacing d. There is a mathematical proof behind this, as it can be thought of as a diffraction grating with many crystal cells involved. The analogy to a mirror is due to the equal angles on each side of the normal for constructive interference. Moving the mirror by an extra angle φ results in the reflected beam moving by 2φ.
  • #1
rashida564
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Hi I am doing an electron gun diffraction right now and I wonder why the angle below is 2 phi.
pXasrzc.png

What I think about it that it's actually the results of two waves one is shown below and the other is a wave
with the same accident angle but negative "those two rays will be symmetric around the lattice plane" and all other rays will cancel each other. Thus will image in the screen is the result of the two rays and the angle between them will be 2phi.
Even-though this makes sense to me, but I want to know is it true. and is there a proof that all the other rays"other than the twos" will cancel each other
SqNKbop.png
 

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  • #2
If the ϑ in the top diagram is the θ in the bottom then the change of direction in the bottom is θ+θ. This is general and is true for rotation of an optical mirror. The image moves twice as much as the mirror rotation.
For Bragg scattering, the only directions where you get constructive interference is determined by the spacing d. So for other values of θ you are not at a max.
 
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  • #3
sophiecentaur said:
If the ϑ in the top diagram is the θ in the bottom then the change of direction in the bottom is θ+θ. This is general and is true for rotation of an optical mirror. The image moves twice as much as the mirror rotation.
For Bragg scattering, the only directions where you get constructive interference is determined by the spacing d. So for other values of θ you are not at a max.
Is there a mathmatecal proof behind this
 
  • #4
Like why is it possible to think about it as a rotates mirror
 
  • #5
rashida564 said:
Is there a mathmatecal proof behind this
rashida564 said:
Like why is it possible to think about it as a rotates mirror
There are two mechanism involved, if you like. Firstly, in the direction of a maximum, you need the path lengths through successive layers to be a whole number of wavelengths (as with Youngs Slits etc. etc.). In other directions there is no constructive interference. You need to remember that there are many (hundreds) of crystal cells involved so that the analogy is more with a diffraction grating than with just two slits. That makes the reflections very 'directive' and with narrow beams.
Why is it like a mirror? Because the angles each side of the normal are equal (for constructive interference on the way in and on the way out). So the total deviation is twice the incoming angle. Google Mirrors and Laws of reflection for pictures and ideas but, if you accept that Incident and Reflected angles are equal (about the normal) then moving the mirror by an extra angle φ from the original θ, the change new direction will be 2(φ+θ), i.e. reflected beam will move by 2φ. A simple bit of Maths there.
 

1. What is an electron gun?

An electron gun is a device that generates a beam of electrons. It is commonly used in electron microscopes and televisions to produce images by directing a focused beam of electrons onto a fluorescent screen.

2. What is electron diffraction?

Electron diffraction is a phenomenon that occurs when a beam of electrons is directed at a sample, causing the electrons to scatter and interfere with each other. This interference pattern can be used to analyze the structure and composition of the sample.

3. How does an electron gun produce an electron beam?

An electron gun typically consists of a heated cathode, which releases electrons, and a series of electrodes that accelerate and focus the electrons into a beam. The electrons are then directed towards the sample using electromagnetic lenses.

4. What is the significance of the undeflected spot diameter in electron gun diffraction?

The undeflected spot diameter refers to the size of the electron beam before it is directed towards the sample. It is an important factor in determining the resolution and quality of the diffraction pattern obtained from the sample.

5. How is the undeflected spot diameter controlled in electron gun diffraction?

The undeflected spot diameter can be controlled by adjusting the voltage and current in the electron gun, as well as the strength of the electromagnetic lenses. The higher the voltage and current, the smaller the spot diameter will be, resulting in a more focused and intense electron beam.

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