Family crystal

Crystal family Symbol Crystal system Crystallographic point groups (crystal classes) Number of space groups Conventional coordinate system Bravais lattices... 

Crystal family Unit cell symmetry Unit cell shape/parameters... 

Crystal family Standard unit cell choice Alternative unit cell choice... 

The introduction of lattice centering makes the treatment of crystallographic symmetry much more elegant when compared to that where only primitive lattices are allowed. Considering six crystal families Table 1.12) and five types of lattices Table 1.13), where three base-centered lattices, which are different only by the orientation of the centered faces with respect to a fixed set of basis vectors are taken as one, it is possible to show that only 14 different types of unit cells are required to describe all lattices using conventional crystallographic symmetry. These are listed in Table 1.14, and they are known as Bravais lattices. ... 

Careful measurement of mineral specimens allowed crystals to be classified in terms of six crystal families, called anorthic, monoclinic, orthorhombic, tetragonal, hexagonal and isometric. This classification has been expanded slightly by crystallographers into seven crystal systems. The crystal systems are sets of reference axes, which have a direction as well as a magnitude, and hence are vectors1. The crystal families and classes are given in Table 1.1. 

Crystal family Crystal system Axial relationships... 

Symmetry elements are operators. That is, each one describes an operation, such as reflection. When these operations are applied to the crystal, the external form is reproduced. It was found that all crystals fell into one or another of 32 different groups of symmetry operations. These were called crystal classes. Each crystal class could be allocated to one of the six crystal families. These symmetry elements and the resulting crystal classes are described in detail in Chapters 3 and 4. 

Another important member of the liquid crystal family is the solution of amphiphilic molecules. The amphiphilic molecules are tadpole-like. A polar, hydrophilic group is at one end of the amphiphilic molecule while a nonpolar, hydrophobic group is at the other end. Two examples are shown in Figure 1.3. Soap in solution, for example, is a liquid crystal. One end of this molecule, -COO-Na+ is a polar group and is soluble in water, while the other end is a hydrocarbon paraffin group CH3(CH2)i4, dissolved in water. 

In this liquid crystal phase, the molecules have non-symmetrical carbon atoms and thus lose mirror symmetry. Otherwise optically active molecules are doped into host nematogenic molecules to induce the chiral liquid crystals. The liquid crystals consisting of such molecules show a helical structure. The most important chiral liquid crystal is the cholesteric liquid crystals. As discussed in Section 1.2, the cholesteric liquid crystal was the first discovered liquid crystal and is an important member of the liquid crystal family. In some of the literature, it is denoted as the N phase, the chiral nematic liquid crystal. As a convention, the asterisk is used in the nomenclature of liquid crystals to mean the chiral phase. Cholesteric liquid crystals have beautiful and interesting optical properties, e.g., the selective reflection of circularly polarized light, significant optical rotation, circular dichroism, etc. 

Therefore in order to avoid any confusion between these fairly chemically different famihes, and taking into account that a large number of these liquid crystals occur naturally in nature, we think that the use of the old fashioned but adequate mineral adjective taken sensus largo is more specific that an alternative such as purely inorganic , to name this subclass of the inorganic liquid crystals family. 

Walba, D.M. Slates, S.C. Thurmes, W.N. Clark, N.A. Handschy, M.A. Supon, F. Design and synthesis of a new ferroelectric liquid crystal family. Liquid crystals containing non-racemic 2-alkoxy-l-propoxy unit., 1. Am. Chcm. Soc. 1986, 108 (17). 5210-5221. 

Since 3m and 6/mmm are included in the same point lattice, they are sometimes subsumed into the hexagonal crystal family. So there are seven crystal systems but six crystal families. Note further that rhombohedral symmetry is a special case of centering (/J-centering) of the trigonal crystal system and offers two equivalent possibilities for selecting the cell parameters hexagonal or rhombohedral axes (see Table 1.3-4 again). 

Tablel.3-b Crystal families, crystal systems, crystallographic point groups, conventional coordinate systems, and Bravais lattices in three dimensions. Lattice point symmetries (holohedries) are given in bold...

Liquid Crystals (Family Number Tl). Ferroelectric and antiferroelectric liquid crystals are very useful as fast display elements. 

A. Ferroelectric liquid crystals (family number 71A). Ferroelectric liquid crystals are defined as liquid... 

B. Antifermelectric liquid crystals (family number 71B). The phase denoted by Sm (e.g. of MH-POBC) exhibits a double hysteresis of the type shown in Fig. 4.5-2, and a liquid crystal showing this phase is called antiferroelectric [5.53]. 

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