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Although W. L. Bragg's law can be easily derived for beginners in the field of crystallography, its interpretation however seems to cause some difficulties which lies essentially in the relation between the concept of lattice planes and the unit cell constants characterizing the lattice periodicity of the crystal structure. Our approach is certainly not new and is based on a more physical approach where every single point in the crystal participates in the diffraction process. From the early stages of developing a model of diffraction, we make abundant use the dual reference frames namely the direct and reciprocal reference frames. With this approach, W. L. Bragg's law can be reformulated directly in terms of the reciprocal unit cell constants avoiding thus the necessity to introduce a priori the notion of lattice planes. Following the derivation of the diffraction law, different steps and methods leading to the complete determination of a crystal structure are derived. We present also some simulation tools to explain in particular the crystal diffraction phenomenon based on the Ewald sphere and the solution of crystalline structures based on the dual space iteration techniques which are currently used. [ABSTRACT FROM AUTHOR]

The rapid development of the Internet has created new opportunities for teaching in general and it is our aim to show how the current evolution can best be exploited for crystallography education in particular. Currently, we can find a very large selection of media dedicated to crystallographic education extending from plain text and videos to the most elaborate forms of interactive simulations. However, due to the lack of criteria for ranking educational materials, it is difficult to select the most appropriate information for educational purposes. In this article, we propose a modular approach to the teaching of crystallography along the lines of the Kahn Academy in the field of mathematics. Each module can be an interactive application (applet), a short video or any other form of media which can be used by teachers and learners to illustrate the fundamental concepts of crystallography. This includes, among others, topics on the symmetry of periodic objects, diffraction phenomena, the Fourier methods of density calculations and the representation of structures depending on the physical or chemical phenomena that one would like to stress. The modular approach resides in the freedom given to the teachers in selecting the topics which are best suited according to their visions, needs and pedagogical aims. [ABSTRACT FROM AUTHOR]

Diaqua (15-crown-5) copper (II) dinitrate is an organic salt presenting an one-dimensional commensurate modulation. The diffraction pattern is characterized by strong Bragg reflections and weaker superstructure reflections (satellites). The structure is described in the superspace formalism as a modulated structure in (3+1) dimensions with occupational and displacive modulation functions. [ABSTRACT FROM AUTHOR]

A molecular dynamics simulation of 4, 4′-dichlorobiphenyl sulfone was carried out in order to study the phase transition from a normal to incommensurate modulated phase observed experimentally. Agreements of simulated and experimental diffraction patterns and lattice constants indicates that the simulation is able to well reproduce the normal-incommensurate phase transition. The incommensurate modulation is found to originate from large-scale fluctuations in the displacements of the molecules. [ABSTRACT FROM AUTHOR]

In order to perform a molecular dynamics (MD) simulation of the incommensurate crystalline structure hexamethylenetetramine suberate (C 6 H 12 N 4 )(HOOC-(CH 2 ) 6 -COOH), we present in a first step the separate simulations of the crystalline structure of each of the two pure components, hexamethylenetetramine (HMT) and suberic acid. The domain decomposition parallel MD program ddgmq is used for this purpose. A second-generation consistent force field (CFF91) is employed to describe the interactions between atoms. Starting from experimental crystal structures, both pure components were heated from low to high temperatures. Our MD results show that the HMT system can be well represented by CFF91. In the case of suberic acid the layered structure of the crystal is largely preserved although deviations in the unit cell lengths from the experimental values are ∼10%. Rather than attempt a complex re-parametrisation of CFF91 we chose to impose a fixed compensating external pressure tensor to correct for the deficiencies of the chosen force field. After optimising this compensating external pressure tensor at one temperature we find that experimental lattice constants and angles can be well reproduced over a range of temperatures. [ABSTRACT FROM AUTHOR]