Miller index, structure factor

The structure of the y phase is characterized by diffraction lines which are indexed by mixed Miller indices, such as (110), (112), (310), (114), etc. The expression for the structure factor is ... 

The crystallographic planes and their representation through Miller indices were rationalized in this section at the level of Ewald sphere of diffraction in the reciprocal space. This complements the structure factors, and implicitly the electronic densities, equally expressed in the previous section through the Miller indexing. However, the electronic localization is made around their attraction centers and the diffraction model should contain also the atomic representation, as basic structural unit. Accordingly, the atomic information should be contained in the diffraction description, and then into the determination of the crystalline structure type, towards the molecular and bio-molecular structural determination by crystallization, as will be eiqiosed in the next section. 

The theory of diffraction can be found in any crystallography book. The so-called structure factor F(h,k,l), where h, k, and / are the Miller indexes for the diffraction spots, is the Fourier transformation of the electron densities inside... 

The atomic scattering factors are the Fourier transforms of the spherical atomic electron distributions. They are considered as known from quantum-chemical calculations. The site occupation parameters may assume values different from unity if the structure is disordered. The Debye-Waller factors allow for the atomic thermal motions. They are functions of the atomic displacement parameters W. Omitting the atom index n and representing the Miller indices and lengths of the reciprocal lattice vectors by and a, respectively ... 

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