Orthorhombic lattice

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. 

Observed first-order reflections from planes with one or two indices even, with the sum of all three indices even, and with the sum of any two indices even (Table II) require6 that the lattice underlying the structure be the simple orthorhombic lattice To- The types of prism planes giving first-order reflections (Table III) are such as to eliminate definitely all of the holohedral space groups7 VJ, to V, 6 (2Di—1 to 2Di—16) based on this lattice except V, V, Vj,3 and V 6. 

The presence of first-order reflections from all types of pyramidal planes (Table II) eliminates from consideration all space-groups based on any but the simple orthorhombic lattice r0. Of these the following are further definitely eliminated ) by the occurrence of first-order reflections from the prism planes given in Table III ... 

The small difference in energy between S4 and Ci forms caused speculations as to whether a second crystalline form might exist which has S4 symmetry. These assumptions were fed by the fact that an X-ray powder diffractogram revealed another orthorhombic lattice with half of the volume. This polymorphic form emerged when cooling below the... 

The calcium ion is of such a size that it may enter 6-fold coordination to produce the rhombohedral carbonate, calcite, or it may enter 9-fold coordination to form the orthorhombic carbonate, aragonite. Cations larger than Ca2+, e.g., Sr2+, Ba2+, Pb2+, and Ra2 only form orthorhombic carbonates (at earth surface conditions) which are not, of course, isomorphous with calcite. Therefore these cations are incapable of isomorphous substitution in calcite, but may participate in isodimorphous or "forced isomorphous" substitution (21). Isodimorphous substitution occurs when an ion "adapts" to a crystal structure different from its own by occupying the lattice site of the appropriate major ion in that structure. For example, Sr2+ may substitute for Ca2 in the rhombohedral lattice of calcite even though SrC03, strontianite, forms an orthorhombic lattice. Note that the coordination of Sr2 to the carbonate groups in each of these structures is quite different. Very limited miscibility normally characterizes such substitution. 

Munoz-Guerra also studied stereoregular polyamides fully based on d- and L-tartaric acid [73]. The bispentachlorophenyl esters of both 2,3-di-(9-methyl-tartaric acids (22 and 23) were condensed with (2S, 3S )-2,3-dimethoxy-l,4-butanediamine (41) to obtain optically active (PTA-LL) and racemic (PTA-LD) polytartaramides. Fiber-oriented and powder X-ray studies of these polyamides demonstrated that PTA-LL crystallized in an orthorhombic lattice, whereas PTA-LD seemed to adopt a tricUnic structure. In both cases, the polymeric chain appears to be in a folded conformation more contracted than in the common y form of conventional nylons. 

Fig. 21.7 Hull-Davey chart for determining the unit cell dimensions of an orthorhombic lattice.

We can continue to apply restrictions to the defining vector set so as to obtain an orthorhombic lattice in which all three vectors are of different lengths, but are required to be orthogonal. The lattice now has considerable symmetry, namely, three mutually perpendicular sets of twofold axes, and three sets of mutually perpendicular reflection planes. 

If in addition to orthogonality of the translation vectors we also require two vectors to be of equal length, say a = b, we have a tetragonal lattice. This now has the same mirror planes and twofold axes as an orthorhombic lattice but has fourfold axes parallel to the c direction. In this case there is only one form of centering possible, namely, / centering. 

For the orthorhombic lattices, each translation vector lies on a C2 axis. These three axes plus the center of inversion result in the point symmetry group Djh. 

The carbon chain is in a planar zigzag orientation and forms an orthorhombic lattice with interpenetration of adjacent chains.61 As a result of this structure, ETFE has an exceptionally low creep, high tensile strength, and high modulus compared to other thermoplastic fluoropolymers. Interchain forces hold this matrix until the alpha transition occurs at about 110°C (230°F), where the physical properties of ETFE begin to decline and more closely resemble perfluoropolymers properties at the same temperature. Other transitions occur at -120°C (-184°F) (gamma) and about -25°C (-13°F) (beta).62... 

The valence electron density of the tetragonal-phase polymer is shown in Fig. 10a [37]. It is evident from the figures that this tetragonal phase should have different in-plane lattice constants (a and b) if the stacking is a simple AA type with a body-centered lattice. It has been reported recently that it is actually the case in this polymer, and the material has a pseudo-tetragonal orthorhombic lattice [38]. 

The amorphous phase appearing above 20 GPa at room temperature (see above) has also recently been studied by X-ray diffraction [135] and Raman scattering [132,133]. Serebryanaya et al. [135] identify the structure as a three-dimensionally polymerized Immm orthorhombic lattice, but find that compression above 40 GPa gives a truly amorphous structure. In contrast to the orthorhombic three-dimensional polymer structure discussed in the last section, the best fit here is found for (2+2) cycloaddition in two directions, with (3+3) cycloaddition in the third, and thus some relationship to the tetragonal phase. From the in situ X-ray data a bulk modulus of 530 GPa is deduced, about 20% higher than for diamond. Talyzin et al. [132, 133] find that this phase depolymerizes on decompression into linear polymer chains, unless the sample is heated to above 575 K under pressure. A strong interaction with the diamond substrate is also noted, such that only films with a thickness of several hundred nm are able to polymerize fully [ 132]. Hardness tests were also carried out on the polymerized films, which were found to be almost as hard as diamond and to show an extreme superelastic response with a 90% elastic recovery after indentation [133]. 

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