Monoclinic symmetry

These systems can be described in terms of their symmetry elements. A triclinic crystal has only a center of symmetry. Monoclinic crystals have a single axis of twofold rotational symmetry. Orthorhombic crystals have three mutually perpendicular axes of twofold symmetry. With tetragonal symmetry, there is a single axis of fourfold symmetry. Cubic crystals are characterized by four threefold axes of symmetry, the <111> axes. There is a single axis of threefold symmetry in the rhombohedral system. The hexagonal system involves a single axis of sixfold symmetry. 

The structure of ThC2 is very similar to the CaC2 structure but of lower symmetry (monoclinic). The similarity to the NaCl structure is not readily seen from the conventional diagram showing a unit cell of the structure, but can be seen from Fig. 22.7 where the relation to the monoclinic axes is indicated. 

Compound or mineral Approximate formula Symmetry monoclinic Space group a (pm) b (pm) Lattice constants c (pm) a (°) y °) Interlayer distance (pm) References... 

Figure 6-3. Top Structure of the T6 single crystal unit cell. The a, b, and c crystallographic axes are indicated. Molecule 1 is arbitrarily chosen, whilst the numbering of the other molecules follows the application of the factor group symmetry operations as discussed in the text. Bottom direction cosines between the molecular axes L, M, N and the orthogonal crystal coordinate system a, b, c. The a axis is orthogonal to the b monoclinic axis.

Since the first structure determination by Wadsley [56] in 1952 there has been confusion about the correct cell dimensions and symmetry of natural as well of synthetic lithiophorite. Wadsley determined a monoclinic cell (for details see Table 3) with a disordered distribution of the lithium and aluminium atoms at their respective sites. Giovanoli et al. [75] found, in a sample of synthetic lithiophorite, that the unique monoclinic b-axis of Wadsley s cell setting has to tripled for correct indexing of the electron diffraction patterns. Additionally, they concluded that the lithium and aluminum atoms occupy different sites and show an ordered arrangement within the layers. Thus, the resulting formula given by Giovanelli et al. 

The layered structure of Li12V308 was first determined by Wadsley in 1956 [83] (Fig. 9a) it has monoclinic symmetry (space group P2, /m). 

Physical Properties. According to Lagowski (Ref 32), X-ray analysis of a single crystal of nitric acid shows a monoclinic unit cell (symmetry P21/a-Cfh) the following dimensions a=16.23, b=8.57, and c=6.3lA, and 0=90°. The unit cell contains 16 molecules, and the calc d is 1.895g/cc at —41.6°... 

For instance, in the three crystalline forms (a, 3, y) of i-PP the chains are always in the conformation of threefold helix (s(3/l)l symmetry) but are packed in different ways in monoclinic [24], hexagonal [25], and orthorhombic [26] unit cells, respectively. The X-ray diffraction spectra of unoriented samples in the crystalline forms a, P, y are reported in Fig. 6. 

In the monoclinic crystals of cyc/o-decasulfur the molecules occupy sites of C2 symmetry although the molecular symmetry is close to D2 [151, 158]. In-... 

CycZo-tridecasulfur S13 was first prepared in 1982 and vibrational spectra served to identify this monoclinic allotrope as a new phase of elemental sulfur [160]. Later, the molecular and crystal structures were determined by X-ray diffraction [162]. The S13 molecules are of C2 symmetry but occupy sites of Cl symmetry. The vibrational spectra show signals for the SS stretching modes between 385 and 500 cm and the bending, torsion and lattice vibrations below 290 cm [160, 162]. For a detailed list of wavenumbers, see [160]. The vibrational spectra of sohd S13 are shown in Fig. 25. 

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