How Do Bragg Peak Intensity Ratios Differ in Ca and CaF2 X-Ray Diffraction?

[Ichimaru]

Question statement: We are given that Ca and CaF2 are both Ca face-centred cubic lattices, and that in the case of CaF2 there is a basis of F ions at +/-(1/4, 1/4, 1/4). Then explain qualitatively how the ratio of the (2 0 0) and (4 0 0) Bragg peak intensities in the X-ray diffraction patterns of Ca and CaF2 would differ.

Attempt at Solution: The main difference I can think of is that the planes defined by (4 0 0) would go through the F ions as well as Ca ions in the CaF2 lattice whereas the (2 0 0) planes would not intersect any F ions. In contrast the (4 0 0) planes and (2 0 0) planes in Ca would intersect the same atoms, and there would be empty planes in the (4 0 0) case.

However when I try to compute the ratios I get that they are the same, as the extra structure factor in the case of CaF2 just cancels itself out when comparing the (4 0 0) and (2 0 0) structure factors.

Any input would be appreciated.

 

[nasu]

Are you sure you put all the terms in the structure factor formula? How many fluorine atoms have you considered in the conventional cell?