Monoclinic lattices

Properties. Physical properties of titanium tetrachloride are given ia Table 17. la the vapor phase, the titanium tetrachloride molecule is tetrahedral and has a Ti—Cl bond length of 218 pm. The regular tetrahedral coordination is retained ia the soHd, although each of the chlorines is crystaHographicaHy differeat ia the monoclinic lattice (131). 

The telluride halides crystallize in monoclinic lattices, but only In-TeBr and InTel are isotypic 162). InTeCl forms a layer type of structure, as do InSCl and its analogs, but, owing to the size of the Te atom and the enhanced covalency of the In-Te bond, only a coordination number of 4 for indium is realized. The structure is built up of strongly distorted, InTesraCli/j tetrahedra that share the corners and edges occupied by Te atoms. The Cl atoms are coordinated to one tetrahedron each, and do not take part in the layer formation 324, 325). 

The XRD powder patterns of V-containing silicalite samples indicate in all cases the presence of only a pentasyl-type framework structure with monoclinic lattice symmetry, characteristic of silicalite-1 no evidence was found for the presence of vanadium oxide crystallites. The analysis of cell parameters of VSU545 does not indicate significant modifications with respect to those found for pure silicalite-1. This is in agreement with that expected on the basis of the small amount of V atoms present in V-containing silicalite. 

We next turn to monoclinic lattices, of which there are two types. A monoclinic lattice is one in which we require one vector to be perpendicular to the plane of the other two. The lattice then has twofold rotational symmetry about this unique vector and planes of symmetry perpendicular to it. A monoclinic lattice (so-called because there is only one nonorthogonal pair of... 

Note that there would be nothing to gain in defining a C-centered monoclinic cell since the resulting lattice would still be a primitive monoclinic lattice with shorter a and b translation vectors, a smaller volume, and the same symmetry. 

Figure 11.13. Alternate ways of choosing a unit cell for the centered monoclinic lattice, a, fi, c, define the body-centered (/) cell a, b c define the A-centered cell a, fi, c define the F-centered cell.

A 3D lattice can be built up by stacking 2D lattices. If a 2D lattice is defined by two translation vectors, t, and t2, we need to introduce a third translation vector, t3, that defines the stacking pattern. For example, if we stack a set of (identical) oblique lattices (defined by t, and t2) employing a vector t3 that is not orthogonal to the 2D lattice planes, we generate the triclinic lattice, while if we require t3 to be orthogonal to the 2D lattice planes and connect each plane with a point in the nearest neighboring plane we get the primitive monoclinic lattice. 

For a monoclinic lattice (primitive or centered) the unique axis, that is, the one perpendicular to both of the others is a twofold symmetry axis. When the inversion property is added to this, we have the point symmetry group Qyr... 

Write a matrix that converts an (incorrectly) C-centered monoclinic lattice to the proper primitive one. 

A crystal lattice is an array of points arranged according to the symmetry of the crystal system. Connecting the points produces the lattice that can be divided into identical parallelepipeds. This parallelepiped is the unit cell. The space lattice can be reproduced by repeating the unit cells in three dimensions. The seven basic primitive space lattices (P) correspond to the seven systems. There are variations of the primitive cells produced by lattice points in the center of cells (body-centered cells, I) or in the center of faces (face-centered cells, F). Base-centered orthorhombic and monoclinic lattices are designated by C. Primitive cells contain one lattice point (8 x 1/8). Body-centered cells... 

Figure 4. Variation of the monoclinic lattice constants with composition for compounds in the LaPl"XVx 4 an< CePl-xvx04 systems.

Isotactic vinyl polymers -(CH2-CHX)- can, because of sterical hindrance, in most cases not lie in zig-zag shape the chain then takes, as the most regular conformation, a helical shape. An example is given in Figure 4.13, again as a projection on the plane of drawing, for PP, which as a helix crystallizes in a monoclinical lattice. 

The crown-shaped molecule Se8 has long been known to crystallize in two monoclinic lattices termed a- and jS-Se8, respectively (see Table II). Crystals of various sizes have been obtained from CS2 solutions prepared by dissolution of either red amorphous Se (22) or of vitreous selenium in CS2 and subsequent cooling or evaporation of the solvent (3a,b, 4a, 5). Red amorphous Se is readily soluble in CS2, but since both vitreous and red amorphous Se do not contain more than small amounts of Se8, the dissolution must be accompanied by a chemical interconversion. It has, however, been reported (26) that the dissolution of red amorphous Se in CS2 requires illumination with photons of energies in excess of 2.3 eV, ambient room light levels being sufficient. 

Zirconium oxide, an n-type oxide, has a monoclinic lattice and has excess metal. The vacant sites are compensated by electrons to maintain electroneutrality. In this case electron current is carried by the electrons and ion transport by the oxide ion. The addition of Ca2+ ions to the zirconium system results in a disposition such that Ca2+ ions fit into the monoclinic lattice, which is schematically shown in Figure 1.39. 

Bayerite has a monoclinic lattice, P2,/a, its parameters being a = 0.562, b = 0.867, c = 0.471 nm, p = 90.26° [10]. It is based on AB packet composed of two tightly packed layers of hydroxyl ions with a layer of aluminium cations located between them. The arrangement of packets in bayerite can be expressed as ABAB [8]. The packets are perpendicular to the axis C and held between each other by hydrogen bonds. The average distance between two layers in a packet is equal to 0.207 nm while the distance between two neighbouring layers from different packets is 0.260 nm. 

All crystals as grown from toluene solution have monoclinic lattice. 

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