Crystalline system Cubic

The various groups of planes arc identified using indices in three dimensions h. k, and /, related to the directions of axes defining the crystalline system. Thus, for example, in a cubic system, the (100) family, in this case equivalent by a 90 rotation to the (010) and (001) families, corresponds to the planes parallel to the edges of the cube. The notation (110) denotes planes on the diagonal, (111) corresponds to planes perpendicular to the major diagonal, etc. (sec Fig. 10.2). 

Cubic liquid crystalline systems have been described as clear, stiff gelsJ As such, they show shear thinning after an apparent yield stress has been exceeded. The viscoelastic properties are also typical for the gel character a broad linear viscoelastic range and a frequency-independent elastic component, which is considerably higher than the viscous component, are observed. ... 

Rizwan SB, Dong YD, Boyd BJ, Rades T, Hook S (2007) Characterisation of biconti-nuous cubic liquid crystalline systems of phytantriol and water using cryo field emission scanning electron microscopy (cryo FESEM). Micron 38 478M 85... 

Primitive three-dimensional lattices have been classified into seven crystalline systems triclinic, monoclinic, orthorombic, tetragonal, cubic, trigonal, and hexagonal. They are different in the relative lengths of the basis vectors as well as in the angles they form. An additional seven nonprimitive lattices, belonging to the same crystalline systems, are added to the seven primitive lattices, which thus completes the set of all conceivable lattices in ordinary space. These 14 different types of lattices are known as Bravais lattices (Figure 3). 

Crystalline kris-ta-bn [ME cristallin, ft. MF L MF, fr. L crystallines, fr. Gk krys-tallinos, fr. krystallos] (15c) adj. A substance (usually solid but can be liquid) in which the atoms or molecules are arranged in a definite pattern that is repeated regularly in three dimensions. Crystals tend to develop forms bounded by definitely oriented plane surfaces that are harmonious with their internal structure. They may belong to any of six crystal systems cubic, hexagonal, tetragonal, orthorhombic, monoclinic, or triclinic. 

The relative developments (growths or cleavages) on the external aspect of a crystalline structure generate the so-called crystalline habitus (the set of shapes for a system), see Table 2.7. For example, the cube and the octahedron are two different forms of habitus, but belong to the same crystalline system, the cubic one, according with Figure 2.34. 

As another example, let us take a look at copper-zinc alloys. Table 2.1 shows quite different characteristics of the two elements in particular, they crystallize in two different crystalline systems (centered cubic faces for copper and hexagonal compact for zinc). Although the 15% rule is respected (there is a difference of 4%), these two metals are not miscible in all proportions, which shows that this rule is not sufficient, alone, to ensure total solubility. In addition, we can see that zinc is more soluble in copper than vice versa. This is attributable to the fact that the valences of the two metals are different - the valence of zinc is 2, whereas that of copper is 1. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

Since the discovery by researchers at Mobil of a new family of crystalline mesoporous materials (1), a large effort has been expended on synthesis, characterization, and catalytic evalrration (2). MCM-41 is a one-dimerrsiorral, hexagonal structure. MCM-48 is a cubic structine with two, norrintersecting pore systems (3). MCM-50 is a layered stractme with silica sheets between the layers (4). Many scientists also looked into other mesoporous materials, of note the HMS (Hexagonal Molecular Sieve) family (5) and SBA-15 (acronym derived from Santa Barbara University) (6), bnt to date few materials have been both catalytically significant and inexpensive to synthesize. 

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