# How do I determine the $n$ integer in the Bragg's law?

I'm studying X-rays crystallography. The basic assumption is that if I let some X-rays scatter on a crystal the atoms act as sources of new waves. Considering two waves that hit two "neighbouring" planes of the crystal I can have a constructive interference then if the phase difference between the two waves is equal to an integer multiple of the wavelenght:

$$n\lambda=2d\sin{\theta}$$

where d is the distance between the two planes of the crystal. My question is: how can I practically determine the value of n? If I need to get to know the value of d I can't just put a random n in the equation as the value of d will change and give me an uncorrect result. Thank you in advance for the help.

## 1 Answer

Since $\lambda$ is fixed by the incoming light you send, each $n$ gives you a different angle $\theta_n$ such that $n \lambda = 2d~\sin\theta_n$. All of these secondary waves will be present because the incoming wave is scattered in all directions but only the directions $\theta_n$ verifying the above equation will interfere constructively.

Therefore each direction $\theta_n$ will correspond to a Bragg peak on your area detector. So the game is then to index those peaks, i.e. to find which value of $n$ correspond to each peak. But nobody does indexing by hand anymore: this will be performed by the software provided by the manufacturer of your diffractometer.

• I think you might want to elaborate on OP's question as to how to actually determine an $n$ for a specific peak or sth along those lines ... – Sanya Jul 8 '17 at 12:32
• Or am I totally off here? Are you doing some kind of "school" project for which you are suppose to do everything "by hand"? – user154997 Jul 8 '17 at 14:48
• @LucJ.Bourhis Thank you for your answer. I still don't get why each n should give me a different angle $\theta$, I'm sure I'm missing something. – Federico Mastellone Jul 8 '17 at 16:06
• @LucJ.Bourhis to me, your edited answer explains a lot more :) – Sanya Jul 9 '17 at 12:37
• You can thank @Alexis Prel for that: he authored the changes! – user154997 Jul 9 '17 at 22:27