# Finding unit cell dimensions of iron or copper

1. Mar 31, 2013

### CAF123

1. The problem statement, all variables and given/known data
The research notes from an x-ray diffraction experiment were damaged and information was lost. The wavelength of the x-rays used in the experiment, and measurements of the three smallest Bragg angles (θ) from the sample were all that remained: they were 0.71Å, 10.1°, 14.4°, 17.7°. Using this information determine whether the samples was iron or copper, giving the steps in your reasoning.

2. Relevant equations
Bragg's Law: $n \lambda = 2 d \sin \theta$.
Distance between planes in a lattice structure.

3. The attempt at a solution

I know the distance between the Miller planes is, for a cubic unit cell, $d = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$. Using Bragg's Law, I can calculate the value of d given the angle and the wavelength. Since for each angle, I attain a different value for d, I take it then that the angles in question are the angles that the incident xray radiation make with 3 different families of planes. (e.g for angle 10.1, we have an intensity maximum (at n = 1) for a family of planes at some spacing d, for 14.4, this corresponds to another intensity maximum (at n=1) to another family of planes with a different spacing d.) At least, that is how I interpret the fact that the three angles give a different d.

If all three angles gave the same interplanar spacing, then (I think) I could conclude that the three angles correspond to the three smallest orders of intensity maxima for one family of planes. (e.g 10.1 for n =1, 14.4 for n =2 etc..). Are these correct interpretations?

I am not sure how to use what I have above to determine the unit cell dimensions. I know given a d, I can relate this to h,k,l and then I thought, since I was given three angles and three unknowns (h,k,l) I could solve, but when I tried this, I ended up with a contradiction.

Many thanks,