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.     

Effect of the seed crystallographic orientation on AlN bulk crystal growth by PVT method

The growth of AlN crystals by PVT method was investigated using TaC crucible in the temperature range of 2250‐2350 °C. AlN boules with 30 mm in diameter were successfully grown on the crucible lid by self‐seeded growth. The AlN boules consist of the spontaneously nucleated AlN single crystal grains with the {1010} natural crystalline face. The fast growth rate of more than 1 mm/h was achieved. AlN crystals grown on (11 0)‐, (10 0)‐, and (0001)‐face AlN seeds were investigated. Different experimental phenomena have been observed under particular condition. The crystal grown on (11 0)‐face seed has different natural crystalline face from the seed. For the crystal grown on (10 0) or (0001) seed, the crystal natural crystalline face is same as the crystallographic orientation of the seed. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Effect of pH value on the growth morphology of KH2PO4 crystal grown in defined crystallographic direction

KH₂PO₄ single crystals were grown in aqueous solution at different pH values by using “point seeds” with a defined crystallographic direction at 59 degree to the Z axis. Atomic Force Microscope (AFM) was applied to observe the surface morphology of (100) face. It was found that at the same supersaturation, the larger steps appeared at the lower pH value before appearance of 2D nucleus. We found that 2D nucleus was occurred at σ ≤ 0.04 when pH value is <2.8. The occurrence of 2D nucleus was caused by the decreasing step‐edge free energy with the decreasing of pH value in the growth solution. In this paper, we observed the morphologies of (100) faces of KDP crystals which grew in solutions with different pH values. 2D nucleuses appeared on the terrace of growth steps when pH value down to 2.8 and 3.2 at supersaturation of 0.04, while pH value down to 2.4, only 2D nucleation control the growth. Therefore, the pH value can change the growth mechanism of KDP crystals.     

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.     

On the equilibrium crystal habit as predicted by the Gibbs-Curie principle

It is pointed out that there is no physical mechanism for the change, dictated by the Gibbs-Curie principle, from a nonequilibrium habit of a macroscopic faceted crystal to the equilibrium habit. The reason why this principle is inapplicable to such a crystal is established.     

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.     

Growth and forms of spherulitic crystal pattern in a Belousov‐Zhabotinski type reaction system

The growth of spherulitic like crystal patterns in a dual substrate Belousov–Zhabotinski (BZ) reaction system has been studied. The solution phase reaction has been found to show concentric ring like wave pattern. A colloidal phase consisting of numerous fine solid particles have also been observed during reaction process, which initially forms the solid phase nucleation centers of dendritic character, and subsequently grow into spherulitic like crystal patterns. The reaction mechanism has been proposed, which illustrate possible reaction products formed during solution phase reaction that are inevitably involved in the formation of the dendritic nucleation centers. The spherulitic crystal pattern has been found to show transition in morphology by substituted organic substrate.The transition behaviour of crystal pattern has also been described and discussed. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.