Ectrostatic Potentials in Crystals

Abstract

In an X-ray diffraction experiment, the integrated Bragg intensities can be reduced to structure factor amplitudes, $\left| {{F_{\vec H}}} \right|$, which may be accurate to a few percent. Data reduction models include deviations from kinematic scattering conditions (extinction models), inelastic scattering due to phonons in the crystal (thermal diffuse scattering) and current density contributions (anomalous scattering). The relative success of the correction terms can be improved on occasion with controlled experimental parameters such as reduced crystal size, reduced temperatures or higher-frequency X-rays. The phases of $\left| {{F_{\vec H}}} \right|$ are determined exclusively by model calculations and are generally more reliable for centric crystal structures than acentric ones. If the crystallographer has pursued these sundry steps from the measured, scattered X-ray photons to a set of ${F_{\vec H}}$ with success, then these data may be used to map out a crystal structure at atomic resolution. The ${F_{\vec H}}$, in principle, are the Fourier components of the thermal average electron density in the crystallographic unit cell. If, in addition, the mean thermal nuclear distribution is known (as from a neutron diffraction experiment) then the total charge density distribution can be determined to within the resolution of the experiment, which is restricted to the finite size of the Ewald sphere with radius 1/λ where λ is the wavelength of the X-ray.