I tried to treat FCC lattice with a lattice constant a, as a monoatomic lattice. The reciprocal lattice is a BCC with a lattice constant 2pi/a. And the structure factor is 1. But I can treat FCC lattice with a lattice constant a, as a simple cubic lattice, with 4 atoms in each unit cell. As one can see in Wikipedia: Now the distance between adjacent planes in the reciprocal lattice is as in a simple cubic: a/sqrt(h^2+k^2+l^2),and I cannot see how I can get the same wavelengths,according to Bragg's diffraction.