# The Miller indices- searching for a proof

1. May 6, 2015

### antonni

Hi all, first let me post this (from "Elementary Crystallography An Introduction to the Fundamental Geometrical Features of Crystals" by Buerger):
https://www.physicsforums.com/attachments/1-png.82644/ [Broken]
Can someone please explain me the proof of Lemma 1? I just can not see it with the "mini proof" provided. Maybe a rigorous mathematical proof?

Thank you,

Anton

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2. May 12, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. May 12, 2015

### antonni

don't know really how to reword it....but others can try

4. May 27, 2015

### dipstik

i tried for quite a while to derive the results using a*(x-x_0)+b*(y-y_0)+c*(z-z_0)=0 equations, but got B*C+B^2*C/A+C^2*B/A planes to reach A*B*C along the x axis...

there may be a more elegant approach considering the number of latice points within the quadrant (from origin to rational plane) where each point is where a new parallel plane would originate. but then you would have to remove all the degenerate planes

here is another place that states the same and does a rough sketch: https://books.google.com/books?id=SHzeQ49ZlH4C&pg=PA12&lpg=PA12&dq=ABC+planes+miller&source=bl&ots=QLFbVXZoyf&sig=RJbIjR6Nd4Gm_AJx0QClHio1GFU&hl=en&sa=X&ei=pDFmVcKoCsXUsAWiuID4DA&ved=0CDkQ6AEwAw#v=onepage&q=ABC planes miller&f=false

5. May 31, 2015

### antonni

Thanks for the reply.....yes, just one of those things everyone takes for granted and think its basic knowledge, but not straight forward at all

ill try it again