Landolt-Börnstein - Group III Condensed Matter Simplifications and calculations


As the main method for obtaining information about atom positions remains full dynamical calculation, this chapter introduces many simplifications to shorten the computer time and core requirements. One of the most efficient and widely-used approximation is called "renormalized forward scattering" (RFS). In the approximations, perturbative schemes are often used to avoid inversion of the very large matrix involved in the theory by developing it in an infinite series and keeping just a few terms. Another approximation often used is called "layer doubling". In this method, the forward and backward scattering by a couple of layers is solved exactly and from this a new set of scattering matrices are derived, describing the scattering of this double layer. The cluster approach was also re-elaborated using a kinematic approximation with renormalized atomic scattering factors in a form suitable for large unit cells. A new formulation was also performed in the transfer-matrix method in the case of small interplanar distances. Finally, a completely different formalism was used to express the scattering which has cylindrical instead of spherical waves as a set of base functions. The method is called the "chain method" because the multiple scattering within a single layer is constructed from the scattering of a linear chain of atoms.

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Title Simplifications and calculations
Book Title
Interaction of Charged Particles and Atoms with Surfaces
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Landolt-Börnstein - Group III Condensed Matter
  • G. Chiarotti
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  • E. Zanazzi
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