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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]

A detailed synchrotron X‐ray diffraction (XRD) study performed with a single crystal of BaVS3 (barium vanadium trisulfide) in the temperature range between 10 and 295 K is reported. Aside from the known tetragonal–orthorhombic (240 K) and orthorhombic–monoclinic (69 K) phase transitions, in the 130 < T ≤ 295 K range the overall structure can be viewed as a host–guest (H–G) composite. The BaS3 matrix is the host, while the V‐chains form the guest. The two subsystems lock in at TLOCK = 130 ± 20 K. This temperature is marked by a symmetry change from orthorhombic to monoclinic. This results in the formation of twins, implying a structural phase transition identified here for the first time. From the refined structural data, it is possible to follow, starting already at 295 K downwards, the stepwise transformation of VS6 octahedra into VS5 tetragonal pyramids as the origin of the structure evolution. The new findings will yield a better understanding of the complex electronic phase diagram of BaVS3. [ABSTRACT FROM AUTHOR]

The H2 antagonist cimetidine forms many polymorphs, several of which have resisted structural analysis thus far. Using single-crystal X-ray measurements obtained from synchrotron radiation, the crystal structure of cimetidine form C has been solved. This layered structure crystallizes in space group C2/ c with an unusually large lattice parameter, a = 82.904 Å. The thickness of each layer L is equal to a′ = a/6 = 13.82 Å, and a = 6 a′ originates from a sixfold LLLL′ L′ L′ sequence with L and L′ differing by 0.5 b. This packing is reminiscent of polytypic stacking in metals. A (3 + 1)-dimensional superspace model is derived and used to explain and predict many polytypic modifications. This model is characterized by (i) the (3 + 1)-dimensional symmetry group X2/ c(α0γ)00, where X = 00; (ii) the lattice parameter a′ and modulation vector q = 1/ n( a′*); (iii) the atomic positions of a single molecule of cimetidine form C; (iv) the primary variable, 1/ n. The model reproduces the previously solved structure, the 6M polytype, and generates the related polytypes nM with lattice parameter anM = na′ for n = 1, 2, 3, 4 and 5. A comparison of powder X-ray diffraction patterns available for cimetidine form C with those simulated for the nM polytypes suggests that the powder samples published previously probably contain a mixture of various polytypes. [ABSTRACT FROM AUTHOR]

A detailed synchrotron X‐ray diffraction (XRD) study performed with a single crystal of BaVS3 (barium vanadium trisulfide) in the temperature range between 10 and 295 K is reported. Aside from the known tetragonal–orthorhombic (240 K) and orthorhombic–monoclinic (69 K) phase transitions, in the 130 < T ≤ 295 K range the overall structure can be viewed as a host–guest (H–G) composite. The BaS3 matrix is the host, while the V‐chains form the guest. The two subsystems lock in at TLOCK = 130 ± 20 K. This temperature is marked by a symmetry change from orthorhombic to monoclinic. This results in the formation of twins, implying a structural phase transition identified here for the first time. From the refined structural data, it is possible to follow, starting already at 295 K downwards, the stepwise transformation of VS6 octahedra into VS5 tetragonal pyramids as the origin of the structure evolution. The new findings will yield a better understanding of the complex electronic phase diagram of BaVS3. [ABSTRACT FROM AUTHOR]