Monoclinic crystal lattice

At present, isotactic polypropylene (i-PP) is commercially by far the most important system of the three modifications mentioned above. During crystallisation from the melt, i-PP is usually in the a form, which has a monoclinic crystal lattice with a Tm-value of about 160°C. The occurrence of a S form (with a hexagonal lattice and a Tm-value of about 152°C) is also possible during crystallisation under stress. Besides, a third (gamma) form with a triclinic crystal lattice is possible under exceptional circumstances [11]. 

Figure 2.43. Comparison between a real monoclinic crystal lattice (a = b c) and the corresponding reciprocal lattice. Dashed lines indicate the unit cell of each lattice. The magnitudes of the reciprocal lattice vectors are not in scale for example, la l = 1/dioo, lc l = 1/dooi, IGioil = dioi, etc. Note that fra-orthogonal unit cells (cubic, tetragonal, orthorhombic), the reciprocal lattice vectras will be aligned parallel to the real lattice vectors. 2009 From Biomolecular Crystallography Principles, Practice, and Application to Structural Biology by Bernard Rupp. Reproduced by permission of Garland Science/ Taylor Francis Group LLC.

The detailed structures of P0X4 are unknown. Some properties are in Table 16.5. P0F4 is not well characterized. P0CI4 forms bright-yellow monoclinic crystals which can be melted under an atmosphere of chlorine, and PoBr4 has a fee lattice with aq = 560 pm. These compounds and P0I4 can be made by direct combination of the... 

Monoclinic crystal system, 8 114t Monoclinic parallelepiped lattice, 8 114t Monoclinic sulfur, 23 565 Monoclinic symmetry, 8 114t Monoclonal antibodies, 3 847 72 150, 475 cell culture technologies used for,... 

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. 

Sulfur exists in two crystalline forms, rhombic and monoclinic, the latter comprising three axes of unequal length, two of which intersect at right angles. The bonding within each crystal lattice is covalent and with an electronic structure approaching the configuration of an inert gas atom, the element shows purely nonmetallic chemistry. 

The crystal descriptions become increasingly more complex as we move to the monoclinic system. Here all lattice parameters are different, and only two of the interaxial angles are orthogonal. The third angle is not 90°. There are two types of monoclinic space lattices simple monoclinic and base-centered monoclinic. The triclinic crystal, of which there is only one type, has three different lattice parameters, and none of its interaxial angles are orthogonal, though they are all equal. 

Fig. 88. Reciprocal lattice (hOl plane) of monoclinic crystal. The b projection of the real cell is also shown (a, c, ),...

Fig. 92. Part of reciprocal lattice rotation diagram for monoclinic crystal rotated round c axis, constructed by measurement of Fig. 91.

If a triclinic crystal is rotated round any axis of the real cell (Fig. 93), the photograph exhibits layer lines (since the various levels of the reciprocal lattice are normal to the axis of rotation), but not row lines, since none of the points on upper or lower levels are at the same distance from the axis of rotation as corresponding points on the zero level. The indices for points on the zero level are found in the same way as for photographs of monoclinic crystals rotated round the 6 axis for the zero level of a triclinic crystal rotated round c, a net with elements a, 6, and y is constructed (Fig. 94), and distances of points from the origin are measured. The other levels, projected on to the equator, are displaced with regard to the zero level in a direction which does not lie along an equatorial reciprocal axis the simplest way of measuring values is, as before, to use the zero level network,... 

For triclinic crystals the expression is so unwieldy that it is not worth while attempting to use it a graphical method based on the conception of the reciprocal lattice should be used (see pp. 154 ff). The reciprocal lattice method is also more rapid than calculation for monoclinic crystals. 

The same procedure is followed for all crystals. In dealing with photographs of monoclinic crystals oscillated round a or c, or triciinic crystals oscillated round any axis, care should be taken to use the appropriate origin for each reciprocal lattice level. (See Figs. 91 and 94.) As an example, the procedure for the first (hfcl) level of a triclinic crystal is illustrated in Fig. 98. 

Fractional Coordinates. In specifying the location of a point in a crystal lattice it is customary to employ coordinates, jt, y, z, that give the fraction of each principal vector distance (a, b, c), which define the unit cell. Thus, a point at the origin has the fractional coordinates 0,0,0 while the center of the cell has the coordinates 3,2,5. The face centers are 0, , , ,0, and , ,0 for the a, b, and c faces, respectively. It is to be emphasized that these fractional coordinates are not Cartesian except for isometric cells and are not even orthogonal for triclinic, monoclinic, or hexagonal lattices. 

Only fourteen space lattices, called Bravais lattices, are possible for the seven crystal systems (Fig. 328). Designations are P (primitive), / (body-centered), F (face-centered),34 C pace-centered in one set of laces), and R (rhombohedral) Thus our monoclinic structure P2Jc belongs to the monoclinic crystal system and has a primitive Bravais lattice. 

We can now complete our answer to the question, What information is conveyed when we read that the crystal structure of a substance is monodime P2JC7" The structure belongs to the monoclinic crystal system and has a primitive Bravais lattice. It also possesses a two-fold screw axis and a glide plane perpendicular to it. The existence of these two elements of symmetry requires that there also be a center of inversion. The latter is not specifically included in the space group notation as it would be redundant. 

X-ray crystallographic studies have been carried out on four compounds belonging to three different pseudoazulene systems.9-61129 All studied compounds crystallized in monoclinic or orthorhombic space groups, a situation requiring Cs symmetry of each molecule. The size of the unit cells of the crystal lattice strongly depends upon the pseudoazulene system. The atoms of the pseudoazulene skeleton are all coplanar to within <5 ... 

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... 

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