Biomedical subjects
Publications and source records attributed to P Dub.
Diffraction on a crystalline slab formed by point-like scattering centres is treated as a multiple scattering problem based on the Ewald equations. Using general results expressed in a lucid matrix form, the two-beam solution for both coplanar and non-coplanar cases valid near and far from Bragg peaks is found and a detailed comparison of the final formulae obtained with those following from Laue's theory is performed.
In Laue's dynamical theory of diffraction, the boundary conditions claim to introduce a mathematical plane instead of the discrete atomic surface of the crystal. This assumption is analysed from the point of view of Ewald's theory based on the microscopic discrete model of a crystal, where no boundary conditions are needed.
The Darwin dynamical theory of diffraction for two beams yields a nonhomogeneous system of linear algebraic equations with a tridiagonal matrix. It is shown that different formulae of the two-beam Darwin theory can be obtained by a uniform view of the basic properties of tridiagonal matrices, their determinants (continuants) and their close relationship to continued fractions and difference equations. Some remarks concerning the relation of the Darwin theory in the three-beam case to tridiagonal block matrices are also presented.