Miller Indices for FCC and BCC and XRay Diffraction Peaks

[LukeD]

In my Physics lab, I'm doing X-Ray diffraction and attempting to determine the crystal structure of some common salts. To do this, I first need to determine the Miller Indices for the crystal structures that I'm considering. I can then match the location of peaks in X-Ray data (we're using monochromatic light) to the Miller Indices. (via Bragg's law)

I, however, only have a rough idea of how to find the Miller Indices of all of the planes I should be considering.


Relevant equations
By Bragg's law, we have that for two peaks in our X-Ray data located at $$\theta_1$$ and $$\theta_2$$
$$\frac{\sin^2 (\theta_1)}{\sin^2 (\theta_2)}=\frac{h_1^2+k_1^2+l_1^2}{h_2^2+k_2^2+l_2^2}$$

The attempt at a solution

For the simple cubic lattice, which is one of the structures I'm considering, I know that I have the planes (100),(110),(111) and various permutation of those optionally involving minus signs.

I can figure out the Miller Indices of a plane if I can see clearly where the plane intersects the axes (and in my lab, we have some models of crystals, so I was using that), but I can't seem to figure out the planes or Miller Indices or anything from just the description of a crystal structure.

If I know the locations of all of the atoms, how can I calculate the Miller Indices of the planes that touch these atoms?

 

[Astronuc]

Hopefully, by now, one has learned how to determine Miller indices for various planes in a crystal lattice.
Some notes on crystal lattices and Miller indices.

https://msestudent.com/miller-indices/

https://web.iit.edu/sites/web/files...demic-resource-center/pdfs/Miller_Indices.pdf

http://clay.uga.edu/courses/8550/millerindices.html

https://www.ocf.berkeley.edu/~mwg/lab/Miller