Calculating Diffraction Intensities

[Stupid_Ben]

Hi,

I'll start with the background so perhaps you can understand my problem better.

I want to write some requirements for diffraction with electrons.

I know that typically an electron diffraction pattern would need ~1e6 electrons, I could justify this because I also know (and can show that) an image needs 1e8, and a diffraction pattern uses about 100 times less pixels or the beam is 100 times less spread out.

However I started trying to understand the diffraction process a little more, and I figured it should be possible to calculate the intensity of the diffraction peaks and then I could say something about how many electrons, and the have lots of nice information about the angles etc.

It seems a little worthless to try and calculate the intensities of an electron diffraction pattern as all the books say the intensities vary too much with thickness etc.

However because X-rays scatter much less their intensities can be reasonably well calculated and I can find example calculations.
--I guess that X-ray diffraction patterns and electron diffraction patterns are similar enough that if I can use one to make justifications about the other (on at least an order of magnitude level).--

So I have all the peaks and intensity for a KCL powder difrraction, great, But what I can not get however is the zero order peak intensity, where nearly 100% of the signal goes.

Does anyone have any suggestions on this?

I don't really want to have to use a computer program, as it's nice to have easily manipulatable analytical equations?

Thanks for your

Help!

Ben

 

[eljose79]

Hello Ben,

Thank you for sharing your background and the problem you are facing. As a scientist who specializes in electron diffraction, I am happy to offer some suggestions and insights.

Firstly, your approach in calculating the intensity of the diffraction peaks is valid. However, as you mentioned, the intensity of the peaks can vary greatly depending on factors such as thickness and crystal orientation. This is due to the complex nature of electron diffraction and the interactions between the electrons and the sample.

One way to estimate the intensity of the zero order peak is by using the kinematical theory of electron diffraction. This theory assumes that the electrons interact with the sample as classical particles, without taking into account their wave nature. This simplifies the calculations and can provide a rough estimate of the zero order peak intensity.

Another approach is to use the dynamical theory of electron diffraction, which takes into account the wave nature of the electrons. This theory is more complex and requires the use of computer programs, but it can provide more accurate results.

In terms of justifying the number of electrons needed for a diffraction pattern, it is important to consider the signal-to-noise ratio. This means that the number of electrons should be high enough to produce a strong signal, but not too high that it causes excessive noise in the pattern. Generally, 1e6 electrons is a good starting point, but it may need to be adjusted depending on the specific sample and experimental conditions.

In conclusion, while it is possible to estimate the intensity of the zero order peak using analytical equations, it may be more accurate to use computer programs that take into account the complex nature of electron diffraction. I hope this helps and feel free to reach out if you have any further questions.

Best of luck with your research!