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Patterns with octagonal and icosahedral symmetries obtained from periodic two‐dimensional (2D) 8‐grids and three‐dimensional (3D) 12‐grids by the dual method are shown to be superstructures of the Beenker pattern and the 3D Penrose pattern with the same edge length. The superstructures are...
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...
The effect of the limited alignment of hydrated molecules is considered in a laser‐aligned molecular beam, on diffraction patterns taken from the beam. Simulated patterns for a protein beam are inverted using the Fienup–Gerchberg–Saxton phasing algorithm, and the effect of limited alignment on...
A systematic use of binary codes derived from the Hägg symbol are used to study close‐packed polytypes. Seitz operators acting over the corresponding binary codes are defined and used. The number of non‐equivalent polytypes of a given length are calculated through the use of the Seitz operators....
The problem of coincidences of planar lattices is analyzed using Clifford algebra. It is shown that an arbitrary coincidence isometry can be decomposed as a product of coincidence reflections and this allows planar coincidence lattices to be characterized algebraically. The cases of square,...
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