For crystals, the scattering density of electron scattering, X-ray scattering, or neutron scattering can be given by the Fourier series,
         ------------------------------ [1845a]
where,
         V_c -- The unit cell volume.
         F_h (or F_hkl) -- The structure factors (or called Fourier coefficients).
         h -- The reciprocal space coordinate system (normally given by (h k l)).

The Fourier transform of Equation 1845a gives the structure factor from the scattering density,
         ------------------------------ [1845b]
F(h) is normally a complex quantity.

In the XRD and electron diffraction analyses of a Hf crystal (a crystal with Hf elements), assuming that x % of Hf is randomly substituted by atom A, the structure factor F_hkl of the (h k l) reflection is then given by

where,
        f_A, f_Hf, and f_O -- The atomic scattering factors of A, Hf, and O, respectively.