Symmetrical polyhedra (simple crystal forms) as orbits of noncrystallographic point symmetry groups

Simple crystal forms are analyzed as the orbits of noncrystallographic point symmetry groups on a set of smooth or structured (“hatched”) planes of crystal space. Polyhedra with symmetrically equivalent faces, obtained using noncrystallographic point symmetry groups, are considered. All possible versions of simple forms for all noncrystallographic groups are listed in a unified table.     

Complete scheme of four-dimensional crystallographic symmetry groups

One of the main problems of four-dimensional geometric crystallography is considered; i.e., the complete scheme of four-dimensional crystallographic symmetry groups is presented, and the number of symmetry groups characterizing the 12 different categories entering this scheme is indicated for each of these categories.     

Some geometric characteristics of four-dimensional crystallographic point symmetry groups and their subgroups

Using three-dimensional point and tablet antisymmetry groups and also rosette and zero-dimensional groups of generalized antisymmetry that model all possible subgroups of four-dimensional crystallographic point groups, we determined the number of various symmetry groups forming the four-dimensional crystallographic classes for each category of such subgroups. These results allowed us to establish (without the use of the complete catalogue of the groups themselves) that 168 four-dimensional crystallographic classes preserve not only the point but also some other geometrical objects. The remaining 103 classes preserve only one invariant point of the four-dimensional Euclidean space.     

On a number of some categories of the limiting groups of multidimensional plane crystallographic point groups of symmetry

Many categories of multidimensional crystallographic plane point groups of symmetry are established with the aid of two-and three-dimensional point groups of symmetry and the groups of simple and multiple antisymmetry generated by these point groups and the groups of rosette, tablet, hypertablet, crystallographic, and hypercrystallographic P symmetries. The numerical characteristics of all the categories of such groups are given and, for each of these groups, the numbers of the limiting groups of multidimensional symmetry (whose subgroups they are) are determined for each category based on the limiting symmetry groups of the classical point groups and the generalizing groups of l-tuple antisymmetry and the indicated particular cases of the P symmetry.     

Structure of Tl18Pb2Ti7S25 as a masterpiece of crystallographic symmetry

A crystallographic analysis of the cubic structure of Tl₁₈Pb₂Ti₇S₂₅ has established the arrangement of all cations and anions according to the law of the 27-fold (with respect to volume) structure type of PbS(NaCl) with strictly fixed anionic vacancies. The nonintersecting axes of symmetry \(\bar 3\) of four directions organizing the structure distribute cations differing in sizes, charges, and amounts over general and particular sites of the sp. gr. Pa3 to form a high-symmetry design in the simple atomic matrix.     

Information patterns of point groups of symmetry

An algorithm for calculating information entropy of regular point systems in crystallographic point groups has been described. The information patterns visualizing the information properties of the groups are described.     

Application of the periodic bond chain method for calculating sapphire crystallographic forms

The application of the periodic bond chain method for calculating the sequence of the development of corundum single crystal faces is considered. The key role of the faces of pinacoid, high rhombohedron, and hexagonal prisms is demonstrated. The calculated data are compared with the experimental results on faceting of the lateral surface of cylindrical sapphire single crystals grown by the Stepanov technique and with the faceting data on flux-grown and natural crystals.     

General concept of increasing crystal symmetry with an increase in temperature

A general concept of the symmetry transformation of a material during its thermal expansion and final polymorphic transition is proposed based on numerous experimental data. Within this concept, the atomic nature of the transformation of the crystal structure with a change in temperature is considered. Particular attention is paid to the thermal expansion of materials, along with the well-known tendency of a thermally induced increase in the crystal symmetry, which is generally considered to be the directionality of material transformation during polymorphic transitions.     

Complete derivation of space groups of magnetic symmetry of crystals by numerical construction

The solution is given to the problem regarding the derivation of the so-called space groups of magnetic symmetry with crystallographic angles of rotation of the spin vector, which was formulated as far back as the early 1970s. The crystallographic P-symmetries that should be used in the generalization with the three-dimensional space Fedorov groups G ₃ are revealed. The space groups G ₃ are generalized with each of these P-symmetries.     

Growth investigations of single crystal sulphates containing molecular glycine groups

Investigations on the optimalisation of the growth conditions of single crystals containing molecular glycine groups were performed and depending on the pH-value of the solution, crystals of triglycine sulphate, diglycine sulphate or diglycine sulphate monohydrate can be grown. The optimal pH-value for triglycine sulphate growing was found to be 1.5.     

Syntheses and crystal structures of two isomeric pyrazoles with ferrocenyl groups

Ferrocenoylacetone I reacts with terephthaloyl hydrazide in the presence of a catalytic amount of p-toluenesulfonic acid to afford complex 1 whereas acylation of 3(5)-ferrocenyl-5(3)-methylpyrazole II with terephthaloyl chloride leads to an isomer of complex 1, viz. complex 2. Two new complexes have been characterized by elemental analyses and IR,¹H NMR, UV spectra and structurally characterized by single-crystal X-ray crystallography. Complex 1 (C₃₆H₃₀Fe₂N₄O₂) crystallizes in the monoclinic space group P2₁/c, with lattice constants: a = 11.593(2) ?, b = 12.9962(17) ?, c = 10.0030(17) ?, β = 113.227(4)°, V = 1462.1(4) ?³, Z = 4, D _c = 1.505 g·cm⁻³, F(000) = 684, R ₁ = 0.0307, wR ₂ = 0.0739. Complex 2 (C₃₆H₃₀Fe₂N₄O₂) crystallizes in the monoclinic space group P2₁/n, with lattice constants: a = 12.2388(18) ?, b = 7.3200(15) ?, c = 17.288(4) ?, β = 90.89(3)°, V = 1466.9(5) ?³, Z = 2, D _c = 1.500 g·cm⁻³, F(000) = 684, R ₁ = 0.0410, wR ₂ = 0.1247. Supplementary material Full crystallographic data (CCDC No. 602174 for complex 1 and CCDC No. 602175 for complex 2) have been deposited at the Cambridge Crystallographic Database Centre and are available on request from the Director, CCDC, 12 Union Road, Cambridge, CB2 1EZ, UK (Fax: +44-1223-336-033; Email:deposit@ccdc.cam.ac.uk or http://www.ccdc.cam.ac.uk).     

Corrosion resistance of sapphire surface as a function of its crystallographic characteristics

Corrosion resistance of a sapphire surface has been studied as a function of various technological factors (growth method, presence of impurities, growth medium), the density of structural defects (pores, vacancies, dislocations), and the crystallographic characteristics. It is shown that the main contribution to the corrosion resistance depends on the type of the mechanical treatment and the crystallographic characteristics of the surfaces and that the resistance of different crystallographic planes to aggressive media can differ up to seven times.     

Using the <Emphasis Type="Italic">P</Emphasis>-symmetry space groups of crystals to investigate 6D symmetry groups

All P symmetry space groups of crystals in the geometric classification that are allowed by the general theory of P symmetry have been investigated. The number of different symmetry groups of a 6D Euclidean space that retain the invariant 3D plane has been revealed using the different (disregarding enantiomorphism) symmetry space groups and crystallographic P symmetries generated by these groups.     

Investigation of 5D point symmetry groups with an invariant 3D plane and immobile point on it

To reveal the structure of 5D point symmetry groups with an invariant 3D plane and immobile point on it, we review in detail the catalog of 1208 3D point groups of ten rosette P-symmetries at P ? G ₂₀, which interpret (accurate to the structure) the aforementioned symmetry groups of the 5D Euclidean space of the category G ₅₃₀, where the numbers in the index 530 indicate successively the dimension of space and the dimensions of invariant subspaces in this space.     

Studies in molecular structure,symmetry and conformation. IX. Crystal and molecular structure of the mixed crystal of L-threonine and L-allothreonine

The mixed crystal ofL-threonine andL-allothreonine is orthorhombic, space groupP2₁2₁2₁, witha = 13.60(1),b = 7.87(1),c = 5.16(1) Å andZ = 4. The structure, which is closely isomorphous with that ofL-threonine, was solved from photographic data and refined to anR of 11.6%. The structure is spatially disordered, containing the molecules in bothL- andL-allo forms.Contribution No. 394 from the Centre of Advanced Study in Physics, University of Madras, Guindy Campus, Madras-600025, India.     

Polymorphs of nitrofurantoin. I. Preparation and X-ray crystal structures of two monohydrated forms of nitrofurantoin

The preparation and X-ray crystal structures of two monohydrates of the antibacterial drug nitro furantoin are reported. MonohydrateI crystallizes in the monoclinic space groupP2₁ n and monohydrateII in the orthorhombic space group Pbca. The nitrofurantoin molecule maintains the same, planar conformation in both crystals. The molecular packing arrangements inI andII are distinctly different,I possessing a layer structure while inII the packing is based on a herring bone motif. Hydrogen bonds of the type O-HO, N-HO, O-HN and C-HO stabilize the crystal structures.     

Polymorphs of nitrofurantoin. 2. Preparation and X-ray crystal structures of two anhydrous forms of nitrofurantoin

The preparation and X-ray crystal structures of two polymorphs of the antibacterial drug nitrofurantoin are reported. The -polymorph is triclinic, space groupP¯1 witha=6.774(1),b=7.795(1),c=9.803(2)Å, =106.68(1),=104.09(2), =92.29(1)°,Z=2. The-polymorph is monoclinic, space groupP2₁/n witha=7.840(5),b=6.486(1),c=18.911(6)Å,=93.17(3)°,Z=4. The nitrofurantoin molecules adopt the same, planar conformation in both polymorphs. Both crystal structures are built up from layers held together by van der Waals forces. In each polymorph, intralayer cohesion is effected by N-HO and C-HO hydrogen bonds, but their arrangements differ in the two crystals. The significance of the C-HO hydrogen bond, now known to occur in four modifications of nitrofurantoin, is discussed.     

Optical and crystallographic evidence for the choice of space group,nature of the crystal phase change and high birefringence in Ln(Apy)6I3

Reexamination of the structures and electronic spectra of Ln(antipyrene)₆I₃ crystals indicates that the series is isomorphous [space groupR3, (No. 146);Z=1] at room temperature despite spectral evidence of a centric ligand field for the Ln ions. High birefringence and phase changes at lower temperatures (<60 K for Ln=Pr) limit the possibilities for CD meaurement.     

Anisotropic properties of Nd:ReCOB (Re=Y,Gd):A low symmetry self-frequency doubling crystal

The anisotropy of low symmetry Nd:YCOB and Nd:GdCOB crystals, including their linear and nonlinear optical properties, as well as their laser and SFD properties, are discussed in detail, for the first time, in this paper. We have found the optimum directions of doubling-frequency for these crystals are not in the principle planes.