= Crystal basis structure factor
{title2=$F_{hkl}$}
The crystal basis structure factor is the coherent sum of scattering contributions from the <atomic basis of a crystal> at a chosen <reciprocal lattice> vector $\mathbf G$:
$$
F(\mathbf G)=\sum_s f_s(\mathbf G)e^{i\mathbf G\cdot\mathbf r_s}.
$$
The positions $\mathbf r_s$ lie within a cell and $f_s$ are the corresponding scattering amplitudes. Fractional coordinates give $F_{hkl}=\sum_s f_s e^{2\pi i(hx_s+ky_s+lz_s)}$.
The <Bravais lattice> sum fixes possible Bragg-peak positions, while this basis sum controls their amplitudes and can cancel some exactly. Two identical sites separated by half a cubic body diagonal give a factor $1+(-1)^{h+k+l}$, extinguishing odd sums. Replacing one site by a different species generally prevents that cancellation. The intensity involves $|F|^2$, so amplitudes must be added before squaring.
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