Otto Litzman

The crystal truncation rod scattering of neutrons and the multiwave dynamical theory of diffraction

The influence of the Bragg diffractions on the coplanar and non-coplanar crystal truncation rod scattering is studied using the Ewald multiwave dynamical theory of diffraction. The resulting formulae are compared with the approximate ones of the kinematical theory and geometrical optics approximations.

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.

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 Laues theory is performed.

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. (2000), A56, 1663–167]. The structure factor yielded by this procedure differs from that used in the kinematical or Laue dynamical diffraction theories.

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

In Laues 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 Ewalds theory based on the microscopic discrete model of a crystal, where no boundary conditions are needed.

Multiple wave scattering on a bordered crystal. Translation symmetry breaking and forbidden reflections

The interaction of a scalar wave (thermal neutrons) with a single Si crystal is treated using Ewalds self-consistent field method. Considering from the very beginning the two-dimensional translation symmetry of the problem, the reflectivities of allowed and forbidden reflections in the Bragg geometry valid for both coplanar and non-coplanar cases are derived. It is shown that there exists a very narrow reflectivity peak of the forbidden reflection as a result of the symmetry breaking due to a crystal surface.

Total reflection at grazing incidence as a special case of the Bragg reflection in Ewald's extended theory

The quantum mechanical version of Ewalds extended dynamical theory of diffraction is used for the study of the transmission and reflection of neutrons by a crystal. It is shown that the total reflection of neutrons at grazing incidence on a crystal is formally equivalent to the total reflection at the Bragg reflection position. Ewalds quantum mechanical and Fresnels classical formulae for reflection and transmission at grazing incidence are compared.