The structure factor formalism in terms of atomic densities

4 The Structure Factor Formalism in Terms of Atomic Densities 

The structure factor F can be simplified by approximating the unit cell density distribution by a summation over atomic densities, each centered at the nuclear 

To obtain the corresponding structure factor expression, the Fourier convolution theorem is applied, or 

The Fourier transform of the spherical atomic density is particularly simple. One can select S to lie along the z axis of the spherical polar coordinate system (Fig. 1.4), in which case S-r = Sr cos. If pj(r) is the radial density function of the spherically symmetric atom, 

5 Spherical atom scattering factors for the isoelectronic F and Na ions. 

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