Monoclinic system lattices

Crystals of the dihydrate belong to the monoclinic system and have lattice parameters a = 659 pm, b = 1020 pm, and c = 651 pm. The anhydrous crystal belongs to the cubic system, a = 596 pm. Other physical properties of the anhydrous salt are Hsted iu Table 1. The anhydrous salt is hygroscopic but not dehquescent. 

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,... 

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. 

For the monoclinic system it is essential to have one twofold axis, either 2(C2) or 2(m), and it is permitted, of course, to have both. When both are present the point group is that of the lattice, 2lm Cy). There are no intermediate symmetries. By proceeding in this way, we can arrive at the results shown in column 4 of Table 11.4, where each of the 32 crystallographic point groups (i.e., crystal classes) has been assigned to its appropriate crystal system. 

From the foregoing prefactory remarks, we can describe the task of finding all of the space groups in the monoclinic system in the following explicit terms. For each lattice type (P or A) we must add one or more of the allowed symmetry elements, which, for this system are the various forms of twofold symmetry 2, 2 (ssm) and their related translational elements 2, and a glide, plane a (or b) or n. 

In addition to the simple (primitive) space lattices listed on page 310, the following are known monoclinic system—base centered... 

There are only two combinations possible for the triclinic system. They are named PI and PI. For the monoclinic system three point groups are to be considered and two lattice types. Combining P and I lattices, on one hand, and point group 2 and symmetry 2 on the other hand, the four possible combinations are P2, P21 72, and 72 The latter two, however, are equivalent only their origins differ. 

Sodium bromide [7647-15-6] NaBr, the most common and available alkali bromide, is a salt of hydrobromic acid (see Bromine COMPOUNDS). Sodium bromide crystallizes from aqueous solution as a di ydj 2LX.e[13466-08-5] NaBr-2H20, below 51 C. Above 51°C, it crystallizes as the anhydrous compound. Crystals of the dihydrate belong to the monoclinic system and have lattice parameters a = 659 pm, b = 1020 pm, and c = 651 pm. The anhydrous crystal belongs to the cubic system, a = 596 pm. Other physical properties of the anhydrous salt are Hsted in Table 1. The anhydrous salt is hygroscopic but not dehquescent. 

Stated by Dana (75] were used in selection of axial lengths corresponding to the a, b, and c axes. For orthorhombic and triclinic systems, the c axis is shorter than the a axis, and the a axis is shorter than the b axis, oir c < a < b. For monoclinic systems, the c axis is shorter than the a axis dimension, or c < a. The A axial ratio is the quotient of the a axis dimension divided by the b axis dimension. In this report the A axial ratios of the compounds of the trace elements were divided by the A axial ratio of gypsum to give a number for each compound, indicative of the extent to which the crystal lattice of the compound matched that of gypsum. These numbers are listed in Table 13 in Column 6. The percent absorbed is defined as 100 minus the percent leached and is also given in Table 13. These data were fitted to Eq 3... 

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]. 

For the monoclinic system, a new lattice can be obtained by centering a monoclinic P-cell along the face defined by the plane formed by the intersection of the a and b crystal axes. This is because it is not... 

Asymmetrical molecules occur very frequently in organic chemistry. We would, at first, be inclined to expect, therefore, that the triclinic crystal system would be frequently met with, but actually nearly all asymmetrical molecules crystallize in the monoclinic system their lattices possess diagonal screw axes or slip-surface planes of symmetry. 

Information about the crystallographic data is contained in column 8 the crystallographic system, the lattice parameters a, b, c and, in the monoclinic system, the angle between the axes a and c are included. 

Here only the results of the structure analyses are presented. Table II shows the crystal data of the two hydrates. Both phases crystallize into the monoclinic system of space group C2/c. There are eight monomeric units and twelve water molecules (the mole ratio is 1/1.5) in the sesquihydrate unit cell, and four monomeric units and eight water molecules (the mole ratio is 1/2) in the dihydrate unit cell. The theoretical values of water content of the crystal lattices are 38.6 wt. for the sesquihydrate and 5-5 wt. for the dihydrate, and these values are accordance well with the observed water contents for a whole sample, ca. i+0 wt.% and more than 5 wt., respectively (Table l). The fiber period is 7.36 A in both hydrates, which corresponds to the length of two monomeric units taking the planar zigzag conformation. 

P"Ga203, though indexed in the monoclinic system, has many similarities with the spinel structure with an approximately cubic close-packed oxygen lattice. From their X-ray powder-diffraction patterns the 8- and 0- phases appear to be more crystalline than the y-phase. All these structural studies generally neglect the fact that the metastable aluminas are not pure oxides and contain water in the form of hydroxyl species [24,25]. 

Where the details of a crystal structure are required, e.g. for the determination oi Ki,K2 and K3, this information is given as cross-reference in the remarks column, indicated by C.S. and followed by the reference number to the crystal structure bibliography of section 1.1.9. If reported in conjunction with the quoted magnetic data, information about the crystallographic system, the lattice parameters a, b, c and, e.g., in the monoclinic system, the angle JS between the axes a and c, is included in column 5. 

Fig. 4.4. (Continued) (a) The addition of base-centered points in cubic cell results in primitive tetragonal space lattice. The resultant lattice is shown by heavy lines, a = b c and a = /3 = 7 = 90°. The resultant tetragonal lattice is shown by bold lines, (b) The addition of base-centered points in primitive tetragonal cell results in primitive tetragonal space lattice and does not yield to a new lattice, (c) The addition of face-centered lattice points in tetragonal lattice results in body-centered tetragonal space lattice points and thus does not give a new lattice and resultant lattice, that is, body-centered tetragonal shown by heavy lines) is already considered as a new lattice, (d) The face-centered lattice in Rhombohedra system is equivalent to primitive rhombohedra lattice. The corner points are not shown and the resultant lattice is shown by heavy lines, (e) The figure shows the equivalence between body-centered rhombohedra and the primitive rhombohedra lattice. The resultant lattice is shown by heavy lines, (f) The figure shows the equivalence between base-centered and primitive shown by heavy lines) lattices in monoclinic system. No corner atoms are shown, (g) (h) The equivalence between bcc (g) and fee (h) monoclinic with C (base) centered monoclinic. This shows that only primitive and C face-centered monoclinic lattices are possible, rest are repetitions and redundant. No corner atoms are shown...

Monoclinic System It has two Bravais lattices, i.e., primitive (P) and base-centered C, and three point groups 2, m, and 2/m. In detailed study of symmetry, the array of atoms that constitutes the structure of the crystal, a macroscopic mirror plane m, might be a glide plane c, while twofold rotation axis might be a screw axis as 2i. Considering these aspects of possible symmetry, the complete set is given as follows ... 

A particular crystal system has some definite number of point groups and for this monoclinic system it has symmetry operations like 2, m, and 2/m, that is, twofold rotation, a mirror plane, and twofold with mirror plane of symmetries. Now, for three-dimensional crystal the possible symmetry elements will include also screw axes and glide planes, and when screw axes and glide planes are added to the point group of symmetries for this system, we can say that different possibilities that may exist are 2, 2i, m, c, 2/m, 2i/m, 2/c, and 2j/c. Now each of these symmetry groups are repeated by lattice translation of the Bravais lattices of that system. As monoclinic system has only primitive P and C, all the symmetry possibilities may be associated with both P and C. Therefore, if they are worked out, they come out to be 13 in number and they are Pm, Pc, Cm, Cc, P2, P2i, C2, P2/m, P2i/m, C2/m, P2/c, P2i/c, C2/c, etc. 

---