Calculating 2θ for XRD Pattern of a FCC Lattice

[SherlockOhms]

Homework Statement

A wavelength of 0.7107 Angstroms is used to analyse a polycrystalline sample with a known FCC lattice structure. The interplanar spacing of the first peak is 0.3 A. Calculate 2θ for the first 3 peaks on the XRD pattern. First 3 peaks occur at (111), (200) and (220).

Homework Equations

nλ = 2dsinθ.
d = a/sqrt(h^2 + k^2 + l^2)

The Attempt at a Solution

I used d = a/sqrt(h^2 + k^2 + l^2) to find the lattice parameter. You're given d for the (111) plane. I then used this value for a to find d for the remaining planes, followed by the diffraction angle for these planes. Was I correct in assuming that a is the same for each and every set of miller indices? I can't see any other way of doing this than this way.

 

[jbsteele]

(111) plane: a = d/sqrt(1), d = 0.3 A, nλ = 2(0.3)sinθ, θ = 10.7 degrees. (200) plane: a = 0.3/sqrt(2), d = 0.212 A, nλ = 2(0.212)sinθ, θ = 18.4 degrees.(220) plane: a = 0.3/sqrt(4), d = 0.174 A, nλ = 2(0.174)sinθ, θ = 21.4 degrees.