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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.