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Tony Gardner · Daedalian Member

[materials science mode]

Does anyone know if there's a general formula to compute the multiplicity of a certain (hkl)-reflection for a given type of crystal structure? I'm writing a bit of Matlab code and I want to include a computation of the multiplicity of the reflection I'm looking at. I could go with something like:

if h==k==l
M=6
elseif h==k or k==l or h==l
|
|
|
|
end

but I'd like it to be cleaner than that. So, can anyone help me out? Btw I'm interested in fcc and bcc structures.

[/materials science mode]

Lepton* · Guest

I hate to see a good question with no replies, but I cannot help. I'll check with some people today..

Sumudu* · Guest

Could you explain how "multiplicity" is related to "(hkl)"? I'd like to help, but I don't know any materials science Revenge most foul!

I guess a start would be filling in your program above to cover all the cases.

Tony Gardner · Daedalian Member

Okay, a quick lesson on crystal diffraction. For a certain crystal type,Bragg's Law describes the relation between the spacing between the atomic planes, and the angles under which incident photons of a certain wavelength produce diffraction maxima after passing. These angles depend on the plane off which the incident photons reflect; this plane is identified using hkl-indices. The multiplicity indicates how many different hkl-combinations, i.e. how many different planes, result in the same diffraction angle.

But I've already sort of solved this issue. Thanks anyways!