Rhombohedral block

In the transitional zone between the secondary and tertiary layers, fibres begin to lose their identity by becoming smaller within semi-ellipsoidal hollows coated with membranes. The earliest secretion of the tertiary layer is marked by an encroachment of horizontally disposed granular sheets of calcite across fibres (Fig. 3.2i). The sheets show strong rhombohedral cleavage and fragment as rhombohedral blocks. 

Because a regular triacontahedron can be geometrically decomposed into ten prolate and ten oblate rhombohedra, the 1/1 and 2/1 ACs can also be viewed as two different types of periodic condensations of prolate and oblate rhombohedral building blocks. In this way, a link between AC structures and 3D Penrose tiles [93] used for i-QC modeling becomes evident. Therefore, the local atomic orders within and the linkages among triacontahedra are very useful in QC modeling. 

The spinel blocks in (3-alumina are related by mirror planes that mn through the conduction planes that is, the orientation of one block relative to another is derived by a rotation of 180°. A second form of this compound, called (3"-alumina, has similar spinel blocks. However, these are related to each other by a rotation of 120°, so that three spinel block layers are found in the unit cell, not two. The ideal composition of this phase is identical to that of (3-alumina, but the unit cell is now rhombohedral. Referred to a hexagonal unit cell, the lattice parameters are a = 0.614 nm, c = 3.385 nm. The thickness of the spinel blocks and the conduction planes is similar in both structures.3... 

There are two other phases that are similar to (3- and (3"-alumina but are built from spinel blocks that are six close-packed oxygen layers thick. The material (3" -alumina is the analog of (3-alumina, with the spinel blocks related by 180° mirror-plane (hexagonal) symmetry, while the phase (3""-alumina, the analog of (3"-alumina, has blocks related by 120° rotation and rhombohedral symmetry. 

These observations led to the concept of a unit cell. Haiiy was able to build realistic models of calcite crystals by stacking rhombohedral building blocks of uniform size (each with interfacial angles of 75°). Clearly, the interfacial angles are important dimensions of the exteriors of crystals. The Law of the Constancy of Interfacial Angles was first proposed by Steno. It states that in all crystals of a givpn... 

McDonald and Stull (5) measured enthalpies in a copper block drop calorimeter, 20 points in the range 282.8 to 1667.8 K. The sample was reported to be the 0-rhombohedral form (based on X-ray data) with a metallic impurity of 0.59%. Stout et al. (6), also using a copper block drop calorimeter, measured enthalpies, five data points in the range 1820-2218 K. The sample was reported to have 0.04% metallic impurities and to contain 300 ppm 0 and 6300 ppm C. No information as to crystalline form was given. Wise et al. (9) measured the enthalpy of two crystalline boron samples (each reportedly containing some of the 0-modificatlon) in the temperature range 515-1103 K. 

V elements (N, P, As, Sb and Bi) adopt several orthorhombic and rhombohedral phases. Additional structural complexity is ushered in as a result of the fact that in certain cases, the basic building blocks are no longer individual atoms, but rather molecules. The most stunning example of this effect is revealed in S which has a room temperature orthorhombic crystal structure built up of 16 Ss molecules in each unit cell. 

Fig. 12.5 Part of one layer of the infinite lattice of a-rhombohedral boron, showing the Bn-icosahedral building blocks which are covalently linked to give a rigid, infinite lattice.

Fig. 12.6 The construction of the Bg4-unit, the main building block of the infinite lattice of P-rhombohedral boron.

Hydrous kaolins, standard GCC, rhombohedral PCC, talc and titanium dioxide may be considered products that comprise discrete particles. These filler products typically range from plates to spheres to blocks of varying uniformity. 

Structures of powdered P-rhombohedral boron and amorphous boron were investigated with pulsed neutron diffraction techniques (Delaplane et al. 1988). To avoid intensive neutron absorption by °B nuclei, samples were "B isotopically enriched up to 97.1% and 99.1%, respectively. Earlier neutron diffraction studies based on nuclear reactor data did not permit the derivation of a meaningful radial distribution of atoms in amorphous material due to limited range of the neutron wave vector (<10.8 A" ). The obtained static structural factor and derived radial distribution function supported a structural model of amorphous boron based on building blocks of B,2 icosahedra resembling those found in p-rhombohedral boron, but with disorder occupying in the linking between ico-sahedral subunits. The intensity data indicated that amorphous samples contained 5% of a mixture of crystalline a- and p-rhombohedral boron. 

VM Fig. 13.6 The construction of the Bg -unit, the main building block of the infinite lattice of P-rhombohedral boron, (a) In the centre of the unit is a B] 2-icosahedron, and (b) to each of these twelve, another boron atom is covalently bonded, (e) A B o-cage is the outer skin of the Bg4-unit. (d) The final Bg -unit can be described in terms of covalently bonded sub-units (Bi2)(Bi2)(Bgo). 

It is remarkable that hollow calcite spheres, but with less expressed surface rhombohedra, have been reported when the same block copolymer was used together with the SDS surfactant [245]. These rhombohedral surface structures are very similar to those reported by Tremel et al. when Au nanocolloids... 

The synthesis of one- and two-dimensional polymers has been achieved by Wang et al. via the self-assembly of dicarboxylic acids with trimethyltin chloride. Scheme 55 shows the synthesis of a two-dimensional sheet polymer (223) consisting of dimeric dicarboxylato-telra-organodistannoxane secondary building blocks via reaction of diphenic acid (220) with trimethyltin chloride (221) under hydrothermal conditions. The synthesis of a rhombohedral grid polymer with te/ni-organodistan-noxane units has also been synthesized by reaction of 4-hydroxy-3-methoxybenzoic acid with trimethyltin chloride. ... 

Fig. 36. Block stacking for the hexagonal and rhombohedral nT4+5 structural series, after Parthe and Lemaire (1975). 24 denotes a R2T4 block as found in the Laves phase structures and 15 a RT5 block with an atom arrangement as in the CaCuj-type.

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