I want to compute the distance between two (111) planes in a cubic crystalline structure, in order to do some computations involving Bragg reflection.

I have a sketch of which the (111) planes are, however I don't know what these Miller-indices really tell me. Could you explain this to me?

Furthermore, is there an easy way to compute the distance between such planes in general, given the distance of two adjacent atoms?

  • 2
    $\begingroup$ To me the wikipedia page answers this very well. $\endgroup$
    – Nic
    Jan 14, 2014 at 11:31
  • $\begingroup$ I found the answer to the second question. The distance between $(nk\ell)$-planes is $a\cdot (n^2+k^2+\ell^2)^{-1/2}$, where $a$ is the lattice constant. However, I'm still not aware how to interpret the miller indices. $\endgroup$ Jan 14, 2014 at 11:45
  • 1
    $\begingroup$ Again, the wikipedia page explains it pretty well right at the beginning. I find a Google search also returns pretty good explanations $\endgroup$ Jan 14, 2014 at 16:23

2 Answers 2


The miller indice is the inverse of the distance between the planes, in the direction of that indice. The higher the index, the more planes in the unit volume.

In the case of $(1,1,1)$, $n=1$,$k=1$ and $l=1$.


If you have the distance between atoms in a cubic lattice, then the (1,1,1) planes are the planes you get when you move one atom in X, one in Y, and one in Z.

There is a nice presentation on this at https://nanohub.org/resources/5488/download/ch3_p3.pdf

The following picture is taken from that presentation, and answers your question exactly: enter image description here


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