Band 222, Heft 6

. The Al−Mg phase diagram has been reinvestigated in the vicinity of the stability range of the Samson phase, β-Mg 2 Al 3 ( cF 1168). For the composition Mg 38.5 Al 61.5, this cubic phase, space group Fd -3 m (no 227), a = 28.242(1) Å, V = 22526(2) Å 3 , undergoes at 214 °C a first-order phase transition to rhombohedral β′-Mg 2 Al 3 ( hR 293), a = 19.968(1) Å, c = 48.9114(8) Å, V = 16889(2) Å 3 , ( i.e. 22519 Å 3 for the equivalent cubic unit cell) space group R 3 m (no 160), a subgroup of index four of Fd -3 m . The structure of the β-phase has been redetermined at ambient temperature as well as in situ at 400 °C. It essentially agrees with Samson's model, even in most of the many partially occupied and split positions. The structure of β′-Mg 2 Al 3 is closely related to that of the β-phase. Its atomic sites can be derived from those of the β-phase by group-theoretical considerations. The main difference between the two structures is that all atomic sites are fully occupied in case of the β′-phase. The reciprocal space, Bragg as well as diffuse scattering, has been explored as function of temperature and the β- to β′-phase transition was studied in detail. The microstructures of both phases have been analyzed by electron microscopy and X-ray topography showing them highly defective. Finally, the thermal expansion coefficients and elastic parameters have been determined. Their values are somewhere in between those of Al and Mg.

The crystal structures of the gallosilicate sodalites Na 8 [GaSiO 4 ] 6 Cl 2 , Na 8 [GaSiO 4 ] 6 Br 2 and Na 8 [GaSiO 4 ] 6 I 2 were refined from X-ray powder data in the space group P -43 n : a = 894.70 pm, V = 0.7162 nm 3 , R WP = 0.066, R P = 0.050, R I = 0.011, a = 900.83 pm, V = 0.73102 nm 3 , R WP = 0.066, R P = 0.051, R I = 0.016 and a = 908.36 pm, V = 0.74951 nm 3 , R WP = 0.050, R P = 0.036, R I = 0.013 for 4000 data points and 14 variable positional parameters in each case for the chloride, bromide and iodide compound, respectively. The gallium and silicon atoms on the tetrahedral framework positions are totally ordered, the halide anions were found at the centre of the sodalite cage coordinated by four sodium atoms. The recorded infrared and Raman spectra show absorption bands typical for the sodalite structure, but indicate also clearly the difference between chloride, bromide and iodide incorporation in the sodalite cage by different absorption band in the FIR range. Heating X-ray investigations show the expected increases of lattice parameters for all three sodalites with increasing temperature and no phase transition was detected. But for the freshly prepared bromide sample a different nearly linear increase of the lattice parameter was observed up to 770 K and above 870 K with an invariant behaviour between these temperatures. The tilt and T—O—T angle as well as the interatomic Si—O and Ga—O distances show an expected temperature dependent behaviour as found by Rietveld calculations of the high-temperature X-ray data. The angles in the tetragonal distorted SiO 4 tetrahedra show values comparable to those found in alumosilicate sodalites but seem to be temperature dependent. Additionally, the corresponding GaO 4 angles indicate a disappearance of the tetragonal tetrahedron distortion around the temperature where the discontinuity was observed for the lattice parameter. The GaO 4 tetragonal tetrahedron distortion is close to zero during the formation of the framework which leads to different distortion direction. This different distortion direction could be relaxed by heating the sample or a self relaxing occurs within several months at room temperature.

A series of three homologous amino acids derivatives: N -acetyl- N -methyl-α,β–dehydroalanine N ′-methylamide ( 1 ), N -acetyl- N -methyl-L-alanine N ′-methylamide ( 2 ), and N -acetyl- N -methyl-DL-alanine N ′-methylamide have been synthesised. The racemic species undergoes spontaneous separation into L and D-enantiomers. From these two chiral forms, the structure of L-enantiomer ( 3 ) was analysed. The molecules of 1 – 3 adopt the cis arrangement of the N-terminal amide bond. The molecular conformations are similar for 1 (φ, ψ = 94.6(1)°, −1.7(1)°) and 3 (φ, ψ = 111.5(1)°, −23.8(1)°), and also 2 (φ, ψ = −114.8(2)°, 29.5(2)°), if inversion through the chiral C2 carbon is considered. They are stabilised by intramolecular N—H…N hydrogen bond. In the case of 1 , the π—electron conjugation resulting from the planar arrangement of the C2—C21 double bond and C-terminal amide group is another stabilising force of this conformation. Thus, the N -methyldehydroalanine residue should promotes trans-cis isomerisation to a greater extend than the saturated analogue. The compounds 1 – 3 reveal similar associative pattern and form centrosymmetric dimers linked by the intermolecular N—H…O hydrogen bonds.

WinLALS series is a software package to solve crystal structures of helical polymers based on the linked-atom least-squares (LALS) method and consists of three independent programs: PreLALS workbench, WinLALS program and new developed PostLALS program. The PostLALS program is newly developed and this becomes very easy to use LALS users.

In April 1991 the Commission on Aperiodic Crystals [1] adopted the following definition of a crystal:“[In the following] by ‘crystal’ we mean any solid having an essentially discrete diffraction diagram , [and by ‘aperiodic crystal’ we mean any crystal in which three-dimensional lattice periodicity can be considered to be absent.]”This definition has, in my opinion, two flaws. …

What is a crystal? The Commission on Aperiodic Crystals, in a recent report, listed three statements “that each by itself might characterize the crystalline state”:(1) a solid with an essentially discrete diffraction diagram;(2) a solid with an atomic structure with long range order;(3) a solid with an atomic structure that can be obtained as a section of an n-dimensional periodic structure (n = 3, 4, …). The report noted that “advantages of and problems with each of these definitions were discussed.”…

When in the seventies and eighties materials were analysed which did not show lattice periodicity but were very similar to the then known crystals the IUCr decided to extend the definition of ‘crystal’. This resulted in the well known definition which is a bit vague but points to a spectrum with essentially Bragg peaks. By being a bit vague one could also include crystals with defects and finite sizes. Of course, it was well known that there are other notions of order. …

To clearly define the objects one is working with is a prerequisite for sound scientific work. In particular, a comparison of results is impossible without. In this view, one needs a clear-cut definition of what a crystal is supposed to be. Moreover, in view of the large community of people working with them, it is desirable to even have a well accepted definition. Neither property seems to be satisfied with the present fuzzy definition of a crystal, and the reasons are manifold. …

Almost 25 years have passed since Shechtman discovered quasicrystals, and 15 years since the Commission on Aperiodic Crystals of the International Union of Crystallography put forth a provisional definition of the term crystal to mean “any solid having an essentially discrete diffraction diagram.” Have we learned enough about crystallinity in the last 25 years, or do we need more time to explore additional physical systems? There is much confusion and contradiction in the literature in using the term crystal. Are we ready now to propose a permanent definition for crystal to be used by all? I argue that time has come to put a sense of order in all the confusion.

A look back into history tells us that crystallography was developed without a definition of a crystal, or more precise: the definition has grown with the knowledge about an only vaguely described object. This is painful for mathematicians but not for physicists. Physicists can show the material they deal with, it exists as soon as they have shown, named and described it, mathematicians have to define it: it does not exist as long as it is not defined. …