# Homework Help: Solid state-problem with difraction

1. Oct 6, 2015

### Frank Einstein

1. The problem statement, all variables and given/known data
Hi everybody. I am triying to do the next exercice:
Given a unit cell of Ice X and knowing the positions of the atoms on it, find the expression of the structure factor for a difraction peak as a function of its Miller's index and the atomic form factors fO and fH.

Will there be a systematic extinction?

Would there be more extinctions if fO=fH

2. Relevant equations
F=Σfi*erjHhkl

In the ice X, there are two atoms of oxygen (0,0,0) and (0.5, 0.5, 0.5); the atoms of hydrogen are at (1/4, 1/4, 1/4), (3/4, 3/4, 1/4), (3/4, 1/4, 3/4) and (1/4, 3/4, 3/4)

3. The attempt at a solution

F=fO*(1+expπ[h+k+l])+fH*(exp[(π/2)(h+k+l)]+exp[(π/2)(3h+3k+l)]+exp[(π/2)(3h+k+3l)]+exp[(π/2)(h+3k+3l)])

Here is where I don't know how to keep going; I have never seen something with two different atomic form factors.
In theory we have seen the case where only the firs term is; in that case, I would say h+k+l=2n+1 so that 1+expπ[h+k+l] becomes zero; but I don't know how to solve this with a second kind of atom.