Cover illustration: An octagonal mosaic from the Kasbah de Telouet, High Atlas, Morocco, based on a modified quasilattice. The underlying quasilattice can best be seen in the blue-and-black portions of the pattern where the `standing' lozenges define bars of unit width and the diagonally positioned lozenges define bars with a width equal to 2. Four orientations of the bar scheme, 45° apart, and phason shifts (alternation of bars in the sequence) are present. Picture taken by Emil Makovicky during the 24th European Crystallographic Meeting 2007.
X-ray rocking curves in the Bragg–Laue case have been measured using a high-resolution optical system. Calculations using Wagner's approach based on Laue's dynamical theory reproduced the rocking curves observed in the experiment.
HK codes representing close-packed polytypes are studied as operators forming a group. The symmetry of the HK codes can be related to the space group of the corresponding polytype. Equivalent polytypes correspond to bracelet equivalent classes in the binary HK code. An algorithm for bracelet generation, with execution time constant per generated object, is modified to exhaustively generate all non-equivalent polytypes of a given length.
A model of independent random faulting in face-centered-cubic and hexagonal close packing considering single deformation faults or twin faulting is revisited. The approach allows the analysis, within the random model, of the whole range of faulting probabilities. Several descriptions of the underlying faulting process are presented which allows the derivation of different properties of the faulted sequences. The probability of finding two layers of the same type Δ layers apart is derived. It is shown that previous generalizations did not account for mixed terms in the final probability expressions.
A triplet relation using an unbiased joint probability distribution of the atomic vectors is derived based on the observation that the distribution of the probability density of an atomic vector is a sum of delta functions.
A quartet relation using an unbiased joint probability distribution of the atomic vectors is derived based on the observation that the distribution of the probability density of an atomic vector is a sum of delta functions.
A method called symbolic asymptotic development (SAD) is proposed for calculating joint probability distributions of structure factors using a general joint probability distribution of the random vector variables.