Determining Type of Lattice from Powder Diffraction

1. The problem statement, all variables and given/known data

In a powder diffraction measurement, we obtain a measure of Bragg angles θ. (A powder sample contains small crystallines with all possible random orientations.) In a particular experiment with Al powder, the following data is obtained when X-ray radiation with wavelength λ = 1.5417 Angstroms is used:



19.48°, 22.64°, 33.00°, 39.68°, 41.83°, 50.35°, 57.05°, 59.42°



Use this to determine the type of lattice for the Aluminum.





2. Relevant equations

[itex]\lambda = 2 d sin(\theta)[/itex]

[itex]\vec{T} = u_1 \vec{a_1} + u_2 \vec{a_2} + u_3 {a_3}[/itex]







3. The attempt at a solution

Solving the first equation for d, [itex]d = \lambda/(2 sin(\theta))[/itex]. So I can plug the thetas into this equation to find the distances d between parallel planes cutting the lattice at various orientations:



2.331, 2.00252, 1.41534, 1.20728, 1.15583, 1.00116, 0.918613, 0.89538 [all in Angstroms]



The problem is, once I have these values, I have no idea how to use them to find what type of lattice the Aluminum is. Any ideas?