The Ewald dynamical diffraction theory--ninety years later.

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.

Is the border surface of a crystal indeed the weakest point of the dynamical theory of diffraction?

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.

A note on the problem of scattering from a single atomic plane and a stack of planes. Differences between the Ewald and other diffraction theories.

The scattering of a scalar plane wave (neutrons) from a single atomic plane consisting of any two-dimensional lattice with a basis is studied using the Ewald dynamical theory of diffraction. Formulae for the reflection and transmission coefficients obtained by evaluating the optical plane lattice sums are valid for general geometries, including nonsymmetrical and noncoplanar diffractions. The approach adopted is different from and more general than that by Yashiro & Takahashi [Acta Cryst.

The Darwin procedure in optics of layered media and the matrix theory.

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.