X-ray and the Electronic Density

The stmcture factor is the wave resulted by diffraction at the level of unit cell, thus being expressible through a complex number, with an amplitude and a phase, without dimension, but having the number of electrons 

When the diffraction picture is recorded from an object containing more electrons located in various points (e.g., a crystal), the waves scattered by each electron contribute to diffraction by summing the individual stmcture factors (5.13) in the total stmcture factor  

FIGURE 5.9 Schematic connections between the real and the ditfraction spaces characteristics. 

In these conditions, the Eq. (5.15) will be rewritten as the equation for the stmcture factor  

Based on the Fourier inverse transformations properties, the inverse Fourier transformation of Eq. (5.17) involves only the inversion of the sign in the appeared exponential. Generally, the Fourier transformation of integral form has a inverse transformation still as an integral form, yet, in this case being about the electronic density in a crystal, i.e., presenting a periodicity. Thus, the inverse transformation of the Eq. (5.17) will be written as a sum, generating the electronic density equation  

---