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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]

SUPERFLIP is a computer program that can solve crystal structures from diffraction data using the recently developed charge-flipping algorithm. It can solve periodic structures, incommensurately modulated structures and quasicrystals from X-ray and neutron diffraction data. Structure solution from powder diffraction data is supported by combining the charge-flipping algorithm with a histogram-matching procedure. SUPERFLIP is written in Fortran90 and is distributed as a source code and as precompiled binaries. It has been successfully compiled and tested on a variety of operating systems. [ABSTRACT FROM AUTHOR]

The charge-flipping method tends to fail if applied to an incomplete diffraction data set. The reason is artifacts induced in the density maps by Fourier transforming the data. It is shown that the missing data can be sufficiently well approximated on the basis of the Patterson map of the unknown structure optimized by the maximum entropy method (MEM). Structures that could not be solved by the original charge-flipping algorithm can be solved by the proposed method. The method has been tested on experimental data of one inorganic and two organic structures and on several types of missing data. In many cases, up to 50% of missing reflections, or even more, can be tolerated and the structure can still be reconstructed by charge flipping. [ABSTRACT FROM AUTHOR]

After studying more than 100 different samples of calaverite Au1-pAgpTe2 (p < 0.15) three famous mineralogists declared in a well documented 1931 publication the invalidity of the law of rational indices. What could lead them to draw such an extreme conclusion from the observation law of Hauÿ dating from more than two centuries? Their observations remained unexplained for the next forty years. In the 1970''s, the room temperature structure of γ-Na2CO3 resisted any attempt for a precise structural analysis. The appearance of satellite reflections was noted on single crystal diffractograms which led to the generalisation of the concept of crystal. This generalisation consisted in using at least four integers to fully characterise each individual diffractions peaks. The theory of periodic crystals in space of higher dimension, i.e. the superspace was then developed to deal with the new experimental observations. Later, a new class of materials called composite crystals and still later, the discovery of quasicrystals only reinforced the validity of the superspace concept to describe any material requiring more than three integers to index their diffraction pattern.What is the essence of superspace to describe crystalline structures? Any crystal structure requesting more than three integers to index its diffraction pattern can be described as a periodic object in superspace with dimension equal to the number of required integer. The structure observed in our real word is a three dimensional cut of the superspace description. In general this cut is irrational and consequently the crystal is aperiodic. Calaverite and γ-Na2CO3 are examples of aperiodic crystals which includes incommensurately modulated crystals, composite and quasi-crystals. Rational cuts are also possible. In this case, the structure is periodic and is usually called a superstructure. [Copyright &y& Elsevier]

Urotropin (U) and azelaic acid (AA) form 1:1 co-crystals (UA) that give rise to a rather complex diffraction pattern, the main features of which are diffuse rods and bands in addition to the Bragg reflections. UA is characterized by solvent inclusions, parasite phases, and high vacancy and dislocation densities. These defects compounded with the pronounced tendency of U to escape from the crystal edifice lead to at least seven exotic phase transitions (many of which barely manifest themselves in a differential scanning calorimetry trace). These involve different incommensurate phases and a peritectoid reaction in the recrystallization regime (T[sub h] > 0.6). The system may be understood as an OD (order-disorder) structure based on a layer with layer group P(c)c2 and cell a[sub o] ... 4.7, b ... 26.1 and c ... 14.4 Å. At 338 K the layer stacking is random, but with decreasing temperature the build-up of an orthorhombic MDO (maximal degree of order) structure with cell a[sub 1] = 2a[sub o], b[sub 1] = b, c[sub 1] = c and space group Pcc2 is begun (at ∼301 K). The superposition structure of the OD system, at T = 286 (1)K with space group Bmmb and cell â = 2a[sub o], &bcirc; = b and ĉ = c/2 owes its cohesion to van der Waals interactions between the AA chains and to three types of hydrogen bonds of varied strength between U-U and U-AA. Before reaching completion, this MDO structure is transformed, at 282 K, into a monoclinic one with cell a[sub m] = -a[sub o] +c/4, b[sub m] = b, c[sub m] = -2(a[sub o] + c/2), space group P2[sub 1]/c, spontaneous deformation ~2°, and ferroelastic domains. This transformation is achieved in two steps: first a furtive triggering transition, which is not yet fully understood, and second an improper ferroelastic transition. At ∼233 K, the system reaches its ground state (cell a[sub M] = a[sub m], b[sub M] = b, c[sub M] = c[sub m] and space group P2[sub 1]/c) via an irreversible transition. The phase... [ABSTRACT FROM AUTHOR]

presents a computer program for the simultaneous refinement of orientation matrix and modulation vector. Orientation matrix of the main reflections from a single-crystal diffraction; Estimates of the modulation vector; Calculation on the standard uncertainties of refined parameters.

The structure of room-temperature ZrP2O7 is shown to be orthorhombic by a combination of high-resolution synchrotron powder diffraction and single-crystal synchrotron diffraction data. Small nontwinned single crystals were obtained by synthesizing the compound using solvothermal methods at temperatures below the cubic to orthorhombic phase transition. The average P-O-P angle is 146°. DFT calculations (B3LYP/AUG-cc-pVDZ) on the isolated P2O74- anion yield a P-O-P angle of 153.42° and indicate that the barrier to inversion is of the order 3.6 kJ mol-1. [ABSTRACT FROM AUTHOR]