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