Orthorhombic crystal lattice

Tetravinylmethane (TVM) is a very interesting compound with respect to its conformational and structural parameters. All the assumptions on the symmetry of TVM are based on D2d and S4 conformations10,11. Surprisingly, none of these conformations is observed in the crystalline state instead, C symmetry was found in an orthorhombic crystal lattice (space group Pbca). If one of the vinyl groups (C3-C8-C9) is rotated by ca 150°, the Ci symmetry can be transferred to S4 symmetry (or vice versa). This is evident from Figure 2 where DVC is also shown in the same projection which demonstrates that the C1 symmetry is no coincidence of packing effects. 

The CBD method can also be used to fabricate 8b2 Bi 83 (Eg = 1.6-2.4eV) which is a mixed composition of 8b283 and Bi283 compounds, both of which have an orthorhombic crystal lattice. These isomorphous compounds can form solid solutions of a desired mixed composition, giving materials of variable bandgaps [275]. These films were similar to the one described for growth of 8b283 except... 

The degree of crystallinity and spheralite density of PLA also increased with an increase in the number of branches. This view is not supported by other works in the field. The presence of short chain branches in polyethylene delayed the onset of nucleation and the growth of crystalline stractures. Star-chain branched PA-11 had low crystallization rate because star-branched core and its adjacent chains were unable to crystallize. Methyl groups may still be included in the PE orthorhombic crystal lattice, but with increased methyl group content, polymer gradually looses its ability to crystalUze when the methyl content reaches 20 wt%. If short-chain brarrches increase in size to 1-butane, 1-hexane, 1-octane, the crystallization is even more severely hampered. ... 

Brookite [12188-41-9], which exhibits an orthorhombic crystal lattice, is more difficult to produce than rutile and anatase, and for that reason it has never been used industrially, especially in the white pigment industry. 

The orthorhombic crystal lattice itself is not too important technically because there are only a small number of materials crystallising in this structure. Composites (chapter 9), however, frequently have the same symmetry because they may contain aligned fibres. Materials with the same symmetry as an orthorhombic crystal are called orthotropic. 

Fig. 79. (a) c-base centered orthorhombic CrB type-crystal structure. Spheres with and without pattern show the B atoms and the Cr atoms, respectively, (b) Brillouin zone of the c-base centered orthorhombic crystal lattice for arectangular parallelepiped which is equivalent to the Brillouin zone is shown by the dashed lines. 

The theoretical tensile modulus of polyethylene is 180-340 GPa. [165, 166] The extremely high tensile modulus of polyethylene is due to the small cross-sectional area of the chain, no side groups, and the planar zig-zag conformation in the orthorhombic crystal lattice. The theoretical tensile strength calculated from the C-C bond energy is in the order of 20-60 GPa. These theoretical values for polyethylene can happen if all the C-C bonds fracture simultaneously. This requires defect free, chain-extended structure, and infinite polymer chains which is a completely different situation from which is encountered [167]. 

Scandium orthophosphate contains two water molecules and is isomorphic with the corresponding iron and aluminum compounds having an orthorhombic crystal lattice (Komissarova et al., 1965a Eshchenko et al., 1979). 

The many commercially attractive properties of acetal resins are due in large part to the inherent high crystallinity of the base polymers. Values reported for percentage crystallinity (x ray, density) range from 60 to 77%. The lower values are typical of copolymer. Poly oxymethylene most commonly crystallizes in a hexagonal unit cell (9) with the polymer chains in a 9/5 helix (10,11). An orthorhombic unit cell has also been reported (9). The oxyethylene units in copolymers of trioxane and ethylene oxide can be incorporated in the crystal lattice (12). The nominal value of the melting point of homopolymer is 175°C, that of the copolymer is 165°C. Other thermal properties, which depend substantially on the crystallization or melting of the polymer, are Hsted in Table 1. See also reference 13. 

Texture. All limestones are crystalline, but there is tremendous variance in the size, uniformity, and arrangement of their crystal lattices. The crystals of the minerals calcite, magnesite, and dolomite are rhombohedral those of aragonite are orthorhombic. The crystals of chalk and of most quick and hydrated limes are so minute that these products appear amorphous, but high powered microscopy proves them to be cryptocrystalline. Hydrated lime is invariably a white, fluffy powder of micrometer and submicrometer particle size. Commercial quicklime is used in lump, pebble, ground, and pulverized forms. 

Anhydrite also has several common classifications. Anhydrite I designates the natural rock form. Anhydrite 11 identifies a relatively insoluble form of CaSO prepared by high temperature thermal decomposition of the dihydrate. It has an orthorhombic lattice. Anhydrite 111, a relatively soluble form made by lower temperature decomposition of dihydrate, is quite unstable converting to hemihydrate easily upon exposure to water or free moisture, and has the same crystal lattice as the hemihydrate phase. Soluble anhydrite is readily made from gypsum by dehydration at temperatures of 140—200°C. Insoluble anhydrite can be made by beating the dihydrate, hemihydrate, or soluble anhydrite for about 1 h at 900°C. Conversion can also be achieved at lower temperatures however, longer times are necessary. 

Also deoxycholic acid (6) crystallizes in an inclusion lattice with channel-shaped cavities 13). Figure 3 shows that they are formed by facing molecules of deoxycholic acid, 4). This characteristic structural unit is a double layer of head-to-tail linked deoxycholic acid molecules at which specific H-bridges between hydroxy and carboxy groups are the decisive fact. The channels as such (e.g. in case of the orthorhombic crystal, see Fig. 3) are lined with lipophilic groups. Thus only van der Waals contacts are kept between the included guest molecules (also for polar molecules like acetone, Fig. 3) and the molecules of the channel wall. 

Figure 8.11 Transformation of a tetragonal crystal, with lattice parameters aT = bT, into a multiply twinned orthorhombic crystal with lattice parameters a0, bQ. The twinned regions are often called domains and the boundaries may occur on a variety of crystallographic planes.

Electron diffraction study indicates that the unit cell is orthorhombic with lattice parameters a = 3.85 A, b = 3.86 A and c = 11.5 A. The [010] plane group of the crystal is pImm [30]. 

Thus the reciprocal lattice axes are perpendicular to the (100), (010) and (001) planes in the real-space lattice. In cubic, tetragonal and orthorhombic crystals it is also trae that they are parallel to the [100], [010] and [001] directions, but this is not tme in other crystal classes. The general formulae for the reciprocal space... 

As Is well known, the shape of MgS0 7H20 Is an orthorhombic crystal with three different lattice parameters(5), 11.86, 11.99, and 6.858. From these values, the shape factor can be calculated as 0.778. This value closely matches the upper lines of Figure 6. If crystals having a shape factor of 0.778 are wanted, the lower values should be raised so that the amplitude becomes more narrow and the... 

Vibrational spectra of solid samples are also influenced by the packing of the molecules in the crystal lattice. For instance, the spectra of orthorhombic a-Sg and monoclinic P-Sg are somewhat different. Thus it was found by Raman spectroscopy that Sy crystallizes as four and S, as two allotropes which consist of identical molecules but must have different crystal structures. 

Orthorhombic crystals are similar to both tetragonal and cubic crystals because their coordinate axes are still orthogonal, but now all the lattice parameters are unequal. There are four types of orthorhombic space lattices simple orthorhombic, face-centered orthorhombic, body-centered orthorhombic, and a type we have not yet encountered, base-centered orthorhombic. The first three types are similar to those we have seen for the cubic and tetragonal systems. The base-centered orthorhombic space lattice has a lattice point (atom) at each comer, as well as a lattice point only on the top and bottom faces (called basal faces). All four orthorhombic space lattices are shown in Figure 1.20. 

Indexing rotation photographs by reciprocal lattice methods. Orthorhombic crystals. First of all, the coordinates and for each reflection on the photograph (Fig. 86) are found in one of the ways just described these coordinates may be plotted as in Fig. 87 a to form the reciprocal lattice rotation diagram. The problem now is to decide which point of the reciprocal lattice itself corresponds to each spot on the rotation diagram. 

Fic. 87. a. Reciprocal lattice rotation diagram corresponding to Fig. 86. b. Graphical determination of values for an orthorhombic crystal. 

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