Triclinic unit cells

Altogether there are 14 possible types of unit cell and we call these the Bravais lattices. For dmgs there are three common types of unit cell triclinic, monoclinic and orthorhombic. 

The unit cell parameters, the lengths (a, b, c) as well as the angles (a, fi, y) of the unit cell are also determined from the crystal structure. There are seven classes of unit cells triclinic, monoclinic, orthorhomic, tetragonal, hexagonal, rhombo-hedral, and cubic. For pharmaceutics, only triclinic (a b c, a P y 90°), monoclinic a b c, a y 90°, P = 90°), and orthorhombic a b c, a = P = y = 90°) unit cells are commonly observed. 

Figure C2.3.3. Molecular packing of SDS monohydrate viewed as projected on the ac plane. This polymoriDh crystallizes in a triclinic cell with unit cell constants a, b and c of 10.423 A, 5.662 A and 28.913 A, respectively, and with a = 86.70°, (3 = 93.44°, y = 89.55°. There are four molecules per unit cell. Adapted from figure 2 of [18].

Properties of PET Molding Resins. The fliU crystal stmcture of poly(ethylene terephthalate) has been estabhshed by x-ray diffraction (134—137). It forms triclinic crystals with one polymer chain per unit cell. The original cell parameters were estabhshed in 1954 (134) and numerous groups have re-examined it over the years. Cell parameters are a = 0.444 nm, b = 0.591 nm, and c = 1.067 nm a = 100°, (3 = 117°, and 7 = 112° and density = 1.52 g/cm. One difficulty is determining when crystallinity is fliUy developed. PET has been aimealed at up to 290°C for 2 years (137). 

Wess, T.J., et al. Type 1 collagen packing, conformation of the triclinic unit cell. J. Mol. Biol. 248 487-493, 1995. 

The translational direction of the lattice (c), which is the direction that the crystallite axis is not, because of the triclinic crystallographic system, is perpendicular to the plane of the unit cell base (ab). 

This is, for instance, the case of PTFE, which at atmospheric pressure presents two reversible first-order transitions at 19 °C and 30 °C [67], In the transition at 19 °C the molecular conformation changes slightly, from a 13/6 to a 15/7 helix and the molecular packing changes from an ordered structure with a triclinic unit cell (corresponding to a positioning of the chain axes nearly hexagonal) toward a partially disordered structure (partial intermolecular rotational disorder) with a... 

Figure 3.5 Changing spacing of unit cell with temperature as measure with WAXS.20 Transition from triclinic (a-stmeture, with two spacings) to pseudohexagonal (/-structure, with one spacing) can be seen.

The second choice is a simpler solution. According to Sarko and Muggli,66 all 39 observed reflections in the Valonia X-ray pattern are indexable by a two-chain triclinic unit cell with a = 9.41, b =8.15 and c = 10.34 A, a = 90°, 3 = 57.5°, and y = 96.2°. Ramie cellulose, on the other hand, is completely consistent with the two-chain monoclinic unit cell. Also, there are significant differences between their high-resolution solid-state l3C NMR spectra, indicating that Valonia and ramie celluloses, the two most crystalline forms, reflect two distinct families of biosynthesis. On this basis, the Valonia triclinic and the ramie monoclinic forms are classified69 as Ia and Ip, respectively. It has been shown from a systematic analysis of the NMR spectra by these authors, and from electron-dif-... 

Hartung and Rapthel [64] described the crystal structure of the mesogenic 2-methylthio-5-(4 -n-butyloxyphenyl)-pyrimidine which forms a monotropic smectic A phase. The chemical structure of this compound is presented in Fig. 5. The compound crystallises in the triclinic space group PI with two molecules per unit cell. The molecules adopt a fully stretched and nearly planar form. The pyrimidine ring is nearly planar. The dihedral angle between the phenyl and the pyrimidine rings is 22.7°. The molecules are arranged parallel to each other. 

Finally, we note that, to the best of our knowledge, only one report exists about EPR spectra of non-Kramers lanthanide ions in molecular magnets. In 2012, Hill and coworkers [51] performed a multifrequency study on powder and single crystal samples of NagHofWgOj H20, in both the pure form and when doped into the isostructural Y3+ derivative. While crystallizing in a triclinic unit cell, the symmetry of the lanthanide ion in this family is very close to Did. For this reason, susceptibility data had been previously fitted by a purely axial Hamiltonian [50]. 

In the paramagnetic regime, the evolution of the EPR line width and g value show the presence of two transitions, observed at 142 and 61 K in the Mo salt, and at 222 and 46 K in the W salt. Based on detailed X-ray diffraction experiments performed on the Mo salt, the high temperature transition has been attributed to a structural second-order phase transition to a triclinic unit cell with apparition of a superstructure with a modulation vector q = (0,1/2, 1/2). Because of a twinning of the crystals at this transition, it has not been possible to determine the microscopic features of the transition, which is probably associated to an ordering of the anions, which are disordered at room temperature, an original feature for such centrosymmetric anions. This superstructure remains present down to the Neel... 

The unit cell considered here is a primitive (P) unit cell that is, each unit cell has one lattice point. Nonprimitive cells contain two or more lattice points per unit cell. If the unit cell is centered in the (010) planes, this cell becomes a B unit cell for the (100) planes, an A cell for the (001) planes a C cell. Body-centered unit cells are designated I, and face-centered cells are called F. Regular packing of molecules into a crystal lattice often leads to symmetry relationships between the molecules. Common symmetry operations are two- or three-fold screw (rotation) axes, mirror planes, inversion centers (centers of symmetry), and rotation followed by inversion. There are 230 different ways to combine allowed symmetry operations in a crystal leading to 230 space groups.12 Not all of these are allowed for protein crystals because of amino acid asymmetry (only L-amino acids are found in proteins). Only those space groups without symmetry (triclinic) or with rotation or screw axes are allowed. However, mirror lines and inversion centers may occur in protein structures along an axis. 

Seven crystal systems as described in Table 3.2 occur in the 32 point groups that can be assigned to protein crystals. For crystals with symmetry higher than triclinic, particles within the cell are repeated as a consequence of symmetry operations. The number of asymmetric units within the unit cell is related but not necessarily equal to the number of molecules in a unit cell, depending on how the molecules are related by symmetry operations. From the symmetry in the X-ray diffraction pattern and the systematic absence of specific reflections in the pattern, it is possible to deduce the space group to which the crystal belongs. 

Figure 2.23 Models of packing of chains in form IV of sPP according to space groups (a) P1148 and (b) C2149. Arrows indicate crystallographic twofold axes, present in (b) and lost in (a). In (a) chains are rotated by 6.5° according to direction indicated by arrows and continuous and dashed lines show triclinic and monoclinic unit cells, respectively.

PET crystallizes in a triclinic crystal structure with unit cell dimensions as follows [44] ... 

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