Cover illustration: Electron-density isosurface of silicon coloured with electrostatic potential (red for lowest and blue for highest), together with a convergent-beam electron-diffraction (CBED) pattern of silicon. The red regions between neighbouring atoms indicate that the electrostatic potential is lowered due to the excess (bonding) electrons. The electrostatic potential and electron density were determined using a CBED structure-refinement method [Ogata et al. (2008), Acta Cryst. A64, 587-597]. The figure was drawn using VESTA [Momma & Izumi (2008), J. Appl. Cryst.41, 653-658].
The mystery of observing films that are much thinner than the resolution limit of a reflectivity measurement is explained within the bounds of the kinematic approximation. Although never encountered in crystal structure determination (hence it is not widely known and even seems counter-intuitive to crystallographers), the phenomenon is in no way limited to reflectometry, which could not be described without invoking dynamic scattering theory.
Tables of the abelianizations of all the n-dimensional space groups for n = 1, 2, 3 are provided. The exponent of the torsion subgroup of the abelianization of an arbitrary n-dimensional space group is shown to divide the order of its point group.
In addition to the diverse parameter-retrieval algorithms commonly used for multilayer structure determination, a dynamic Newton–gradient-direction-type algorithm is proposed. It works well and provides the absolute minimum of the error functional even when the initial values of the search parameters are rather far from the true ones.