The Fourier transform of the structure factors gives us an expression for scattering density, which will be in the form of electrons for x-ray scattering, but will be in the form of nuclear scattering power with neutron structure factors.
\[\rho (x,y,z) = \frac {1}{V} \sum _{hkl} F_{hkl} \exp [-2\pi i(hx + ky + lz)] \] This equation might imply that once we have measured the structure factors, we can apply this equation to find where atoms are located. However, we can measure only \(|F_{hkl}|\), without phase information, this equation cannot be applied directly without knowing the phases. Nevertheless, it is quite useful as will be discussed much later when Fourier maps are considered in §20.2. It should be understood that for x-ray scattering \(\rho (x,y,z)\) has units of electrons/\(\mathring {\text {A}}^3\) and must be either zero or positive. Since some isotopes have negative scattering lengths for neutrons, \(\rho (x,y,z)\), can be positive or negative when any of those types of atoms are present when neutron scattering factors are used. This equation is only exact when an infinite number of terms is used, but in practice the summation is terminated, which produces “ripples” on the intensities known as truncation errors.