Shapes triclinic

One of the intensively discussed topics was the question about the shape of atoms - a question with also high educational relevance, if we think of some students preconceptions. We can focus on two main positions One group of chemists observed that crystals always broke to parts with similar shapes to those of the original crystal. Therefore, their theory was that the smallest particles of atoms must have also the same shape as the macroscopic crystal. If we follow Domenico Guglielmini (1655-1710), the particles of sodium chloride would be cubic, those of calcspar would be triclinic. Hexagonal-prismatic and trigonal-prismatic crystals... 

Two macromolecular computational problems are considered (i) the atomistic modeling of bulk condensed polymer phases and their inherent non-vectorizability, and (ii) the determination of the partition coefficient of polymer chains between bulk solution and cylindrical pores. In connection with the atomistic modeling problem, an algorithm is introduced and discussed (Modified Superbox Algorithm) for the efficient determination of significantly interacting atom pairs in systems with spatially periodic boundaries of the shape of a general parallelepiped (triclinic systems). 

The examples cited above represent part of an increasing body of structural information on chlorophylls, chlorins, bacteriochlorins and isobacteriochlorins (10-14 and references therein) that points to the remarkable flexibility of these molecules This ability of the macrocycle to adjust is not limited to hydroporphyrins but is also observed in porphyrins 5,10,15,20-tetra-n-propylporphinato lead (II) assumes a "roof" shape by folding along an axis defined by two opposite methine carbons with the two planes of the "roof" inclined at 22 to one another (15) In contrast, triclinic 5,10,15, 20-tetraphenylporphinato cobalt (II) is distinctly saddle shaped with the 3 carbons of adjacent pyrrole rings lying 40 66 and -0 66A above and below the plane of the four nitrogens (16) ... 

Block-shaped black crystals with a distinct metallic luster are formed which upon crystallographic study are found to crystallize in the triclinic system with lattice constants as follows a = 7.786 (1) A, fe = 13.033 (3) A, c = 18.590 (4) A, a = 110.09 (2)°, 0 = 90.21 (2)°, y = 105.27 (2)°, and Vc = 1699.8 (6) A3. These lattice parameters indicate that the crystals contain 0.5 molecules of TCE in the formula unit as is the case for isostructural (BEDT-TTF)2ClO4(TCE)0 5 in which Vc = 1689.8 A3.10 The electrical properties of this material indicate that they are metallic from room temperature to 90 K at which point a metal-insulator transition occurs. 

The lattice points of a triclinic crystal may be joined in various ways to form differently shaped unit cells (see p. 151). It is usually most convenient to use the cell with the shortest edges, unless there is some special feature which recommends some other direction as a unit cell edge. Donnay (1943) recommends that the shortest axis shall be called c and the longest b and that the angles a and ft shall be obtuse. 

Where there is more than one cell of the same volume (and shape appropriate to the crystal system) which will account for all the reflections, as in monoclinic and triclinic orystals (see Fig. 76), the most nearly rectangular cell will usually prove the most convenient to accept. There has been much discussion of conventions in the triclinic system the convention recommended bj" International Tables (1952) is that all three angles of the cell should be obtuse, and the direction cosines of the axes with the fill] zone axi should all be positive. 

An example of a polymer crystal is given in Figure 4.12, namely of PE, in which the chains should be imagined to lie in zig-zag shape perpendicular to the plane of drawing the figure gives the projection of the C- and H-atoms. The crystal is orthorhombic with a = 0.740 nm, b = 0.493 nm the vertical dimension of the cell, c = 0.253 nm. Also other polymers can crystallize with extended chains, such as PA-6 (monoclinic) and PA-6.6 (triclinic). 

Cellulose I(S and cellulose II have monoclinic, two-chain unit cells. Cellulose IIIj has a monoclinic one-chain cell [227], and the one-chain unit cell of la is triclinic with no 2i symmetry. Still, all of the chain shapes are very similar to each other. It had been speculated that cellulose chain linkage geometries would alternate between the quite different linkages found in crystalline p-cellobiose and in methyl 3-cellobioside [196]. That idea is now obsolete. Such a departure from symmetry would be far greater than indicated by the above high-resolution studies. When molecules from the high-resolution structures for all of the polymorphs are superimposed, differences in their backbone structures are barely visible. 

X-ray diffraction is the most common and most accurate method used to determine the polymorphic form of a sample. A change in the diffraction profile (e.g., a change in peak shape or position) indicates a change in polymorphism. The wide-angle reflections, (also called short-spacings ) are used to characterize the polymorphism of a lipid. These reflections correspond to in-plane ordering of the fatty acyl chains on the TAG molecule. Common polymorphic forms include the hexagonal, a form (d = 4.15A), the orthorhombic perpendicular P form (J = 3.8 and 4.2A) and the triclinic P form (d=4.6A) (Larsson 1966). 

Particle shape sub-angular Crystal structure monoclinic to triclinic ... 

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