Crystal Engineering最新文献

In this paper, crystallographic aspects of ancient, medieval and modern Turkish ornaments are dealt with. Crystallographic patterns (CPs) are considerably different from other patterns. The following are characteristic of CPs: the edge of ornament elements draws the edge of the figure; maximal compactness of the ornament elements; lack of background or transformation of background to ornament elements; minimization of the variety of ornament elements; symmetry is not used for form creation. In the process of the construction of CPs, symmetry appears as a result of combination, not as a means of its formation that is characteristic of other ornaments. Their symmetries are analogous to symmetries of natural objects. The atoms and molecules dispose themselves in crystals just as elements arrange themselves in CPs. In other words, CPs are constructed according to the same principles of crystal formation, i.e. the principle of tight packing. The similarity (isomorphism) of crystals and ornaments enables us to describe the ornaments with structural analysis terms, and the similarity between ornaments and crystal structures can be also used in chemistry education. This will bring an aesthetical aspect to education. An invisible part of nature can be studied as ornament creation. Each newly created CP is the structural scheme of a number of possible compounds. The familiarity with such ornaments and the ability to create them are important for solving compound structures. Similarity of patterns with some crystal structures enables us to reach the following conclusions: mankind may make use of the principles from which nature was created, and he may achieve a resemblance to the creation of nature in ideal; mankind may create nothing whose prototype does not exist in nature.

Fibonacci phyllotaxis is one of many examples that demonstrate the relationship of biological growth patterns with the golden mean and self-similar symmetry, also observed in scale–rotational crystal growth. An equivalent relationship of natural-number patterns with the structure and periodicity of atomic matter is demonstrated. A generalized, closed periodic law that reveals the hidden symmetry in the periodicity of atomic matter is derived and related to the variability of electronic configuration of atoms, as a function of thermodynamic conditions, to nuclear synthesis and to the DNA code. Implications on space-time structure are discussed.

The artifacts under investigation (three red clay shards, two gray clay shards and a red clay teapot) are from the J A Van Tilburg museum at the University of Pretoria (UP). The large red clay shard was recovered from the 1552 Portuguese shipwreck, São João, found in the region of Port Edward, South Africa. The other shards were recovered from the 1622 Portuguese shipwreck, the São João Baptista, which sank around Kenton-on-sea off the South African coast. The results from these are compared to those obtained from the analysis of a red-brown teapot. The oldest of this type of teapot was made in China during the second half of the 18th century. Raman spectroscopy has proven to be a useful tool for qualitative determination of the composition of these clay artifacts. The red clays were characterized by the presence of hematite, kaolin, quartz, amorphous carbon and aluminosilicates. The results of the clay teapot differed from those of red clay shards in that no quartz Raman bands were observed for the clay teapot. The gray clay shards were characterized mainly by the presence of quartz, kaolin, amorphous carbon and aluminosilicates. The presence of mullite in all samples could not be ascertained unambiguously using Raman spectroscopy. The pigments found in the investigated samples are hematite (α-Fe₂O₃) (for red samples) and amorphous carbon (for both red and gray samples).

Although the number patterns generated by the integer solutions of equations such as$\text{h}{}^{\mathrm{<mtext>2</mtext>}}\text{+k}{}^{\mathrm{<mtext>2</mtext>}}\text{+l}{}^{\mathrm{<mtext>2</mtext>}}\text{=n}$are of fundamental importance in crystallography, little work has been done to apply number theory, perhaps the most famous and fundamental area of mathematics, to problems involving the three-dimensional lattices on which crystal structures are based. The relevance of the work of such giants as Euler, Riemann, Dirichlet and Erdos to some crystallographic questions are discussed.

Pressure-induced structural changes in molecular crystals that are not accompanied by a change in space group symmetry are considered. Anisotropic structural strain of the same polymorph and isosymmetric polymorphic transition are two possibilities which are illustrated in the examples of Co(III)nitropentaammine chloride, the monoclinic and ortho rhombic polymorphs of paracetamol, the α- and γ-polymorphs of glycine, benzoquinone (anisotropic structural strain) and sodium oxalate (isosymmetric polymorphic transition). The experiments described were carried out in diamond anvil cells, and the structural changes were monitored by X-ray powder and single crystal X-ray diffraction, and IR and Raman spectroscopy.

After studying more than 100 different samples of calaverite Au_1-pAg_pTe₂ (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.

Illustrative examples are provided of infrequent situations arising in the chiral or achiral crystal structures formed of chiral or achiral molecules. For absolute-configuration determination by way of structure analysis, it is demonstrated how powerful characterization of enantiomers by way of CD spectra and enantioselective chromatography can be when working on the single crystal used in the diffraction analysis. Common misunderstandings in the description of non-centrosymmetric achiral crystal structures are clarified. Further attention is given to questions of nomenclature.

The published structural data of pseudo-square-pyramidal and pseudo-octahedral transition metal complexes with tetra- and pentadentate bispidine ligands (2,4-, 2,3,4- and 2,4,7-substituted 3,7-diazabicyclo[3.3.1]nonane, pyridine or 6-methylpyridine substituents), primarily with copper(I), copper(II) and iron(II) is reviewed, together with few molecular mechanics and DFT calculations, and in the light of the specific and uncommon molecular properties of bispidine coordination compounds. One of the main features is that, while the ligands are very rigid, there is a high degree of elasticity of the coordination geometries. That is, the potential energy surfaces of the complexes are flat; in addition, there are various shallow minima, and this leads to uncommon types of isomerism. These structural features, the emerging reactivities and possibilities to tune them are discussed in detail.

Varied aspects of breaking of symmetry in crystalline and molecular conditions are considered. Distributions of electronic density about atomic centres of Li and H in crystalline LiH and isolated diatomic molecules of that compound en route to dissociation are discussed in relation to symmetry.

The properties of the homodimers of the covalent hydrides of the elements from lithium to fluorine and from sodium to chlorine have been computed by means of ab initio molecular orbital theory. These properties show some interesting discontinuities, illustrating the significant differences between the natures of the dimers of the hydrides of the metals and metalloids of groups 1–3, and those of the electronegative non-metals of groups 5–7. The dimers of the group 1–3 hydrides are very strongly bound, featuring two bridging hydrogen atoms per dimer molecule, in structures similar to that of the well-known diborane species. Those of the hydrides of groups 6 and 7 are stabilized by conventional, almost linear, hydrogen bonds. The same is true of the ammonia dimer, but that of phosphine contains two equivalent pairs of bridging hydrogen atoms in a very weakly bound, doubly bifurcated hydrogen-bonded aggregate. The methane and silane dimers are found to be barely bound at all.