Electron-Density Distributions Determined by X-Ray Diffraction Methods

Electron-Density Distributions Determined by X-Ray Diffraction Methods 

The Relationship between the Electron-Density Distribution in a Crystal and the X-Ray Scattering Amplitudes from a Single Crystal 

At present the X-ray diffraction method is used mostly to determine atomic positions in a crystal. However, X-ray scattering amplitudes depend directly on the electron-density distribution in a crystal, from which atomic positions can be derived on the assumption of coincidence of the nuclear positions and the center of gravities of total electron densities around atomic nuclei. 

The scattering amplitude is given by the absolute value of the following expression, which is a Fourier transform of the total electron-density distribution in a unit cell and is called a crystal structure factor  

In this case, the phase problem reduces to a question of the sign of the structure factor. Since the sign of the structure factor can be evaluated more reliably than the phase angle, the electron density in a centrosymmetric crystal can be evaluated more accurately than that in an acentric crystal (93), Equation (2) implies that total, time-averaged electron density can be determined by the diffraction method. 

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