I Is it Possible to Index a Cubic Lattice with h^2+k^2+l^2=7?

[elevenb]

Hi everyone,

I've been given a problem where I have to index reflections from a cubic lattice, the procedure is simple enough but I'm getting a case where I get :

h^2+k^2+l^2=7

I've taken to many books, but most either don't mention the topic or say they are simply 'forbidden' reflections. I have also seen where I should double hkl before indexing but I haven't seen a concrete example of this.

I don't think irrational miller indices are the solution here either.

Any contribution would be so helpful.

 

[DrDu]

I never did index a crystal, but the situation appears to be quite trivial. Specifically, I was looking at the table "Selection Rules for Reflections in Cubic Crystals" here
http://www.khwarizmi.org/system/files/activities/146/csd1.pdf
I suppose your substance is BCC. Then you don't observe the peak (100) with h^2 +k^2 +l^2=1, because it is forbidden for a BCC lattice. Instead, the first peak you observe is (110) with h^2 +k^2 +l^2=2. If you wrongly assign it as (100) , you will assign also the following peaks wrong. You don't realize this immediately, because all peaks with h^2+k^2+l^2 odd are forbidden, too. So you will assume for them with h^2 +k^2 +l^2=n instead of 2n. The first time you notice is with the peak (321) for which you obtain h^2+k^2+l^2=7 instead of 14, but 7 never occurs in any cubic pattern.