Hexagonal system

Dividing each sin 6 values sequentially by integers 1,3,4,7,9. the match for X /2a giving constant values is then indexed and the indexed (/ A0) lines are to be sorted out and the lattice parameter a is to be calculated. For rest of the lines (/ 0), we get 

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Fig. 4. Inclusion cage of Dianin s compound (5). The matrix is constructed via a cyclic H-bonded hexagonal system of host molecules (on top and on bottom of the macrocage O atoms as bold dots, H-bonds as dotted lines) bulky parts of the host molecules interlock (equatorial of the cage). The cage can be filled with molecules of fitting size (e.g. one molecule of chloroform) (Adapted from Ref. 16)...

The Miller indices of planes in crystals with a hexagonal unit cell can be ambiguous. In order to eliminate this ambiguity, four indices, (hkil), are often used. These are called Miller-Bravais indices and are only used in the hexagonal system. The index i is given by... 

In reality this third index is not needed. However, it does help to bring out the relationship between the planes. Because it is a redundant index, the value of i is sometimes replaced by a dot, to give indices (hkl). This nomenclature emphasizes that the hexagonal system is under discussion without actually including a value for i. 

Notice that, for reasons of symmetry, in the hexagonal system a somewhat redundant index type may be used for plane identification. It is customary to define an auxiliary axis u at 120° to x and y and 90° to z (and with the same unit length of the x and y axes). As a consequence instead of indices (hid) for a face, indices (h, k, i, l) are used, where the index / is related to the axis u in the same way... 

Bluish-white lustrous soft metal closed-packed hexagonal system density 8.69 g/cm3 Brinnel hardness 21 melts at 321.1°C vaporizes at 767°C vapor pressure 5 torr at 455°C electrical resistivity 6.8 microhm-cm at 0°C insoluble in water. 

Figure A.1.2. Miller-Bravais axes in the hexagonal system.

Since a subsidiary axis is assumed in addition to the and axes in the hexagonal system (and in the hexagonal expression of the trigonal system), the index is expressed by four indices for a general face (hktl). This is called the Miller-Bravais index. For example, in Fig. A.3.1(b) a face ACB cuts the + and + axes at 1 (= OA, OB), and the - axis at 0C = 0D = OB/2. Therefore this face is indexed as (1120). From geometry, h(l) + k(l) = i(2). 

In Section 11.4 the fourteen 3D lattices (Bravais lattices) were derived and it was shown that they could be grouped into the six crystal systems. For each crystal system the point symmetry of the lattice was determined (there being one point symmetry for each, except the hexagonal system that can have either one of two). These seven point symmetries are the highest possible symmetries for crystals of each lattice type they are not the only ones. 

The Swedish mineral finnemanite 4 contains lead orthoarsenite in combination with lead chloride, the composition being 3Pb3(As03)2. PbC l2 (see p. 15). It occurs in dark grey or black prismatic crystals belonging to the hexagonal system and of axial ratio a c = 1 0-6880. 

ALUNITE. The mineral alunite, KAl3(S04)2(0H)t , is a basic hydrous sulfate of aluminum and potassium a variety called natroalunite is rich in soda. Alunite crystallizes in the hexagonal system and forms rhombohedrons with small angles, hence resembling cubes. It may be in fibrous or tabular forms, or massive. Hardness, 3.5-4 sp gr, 2.58-2.75 luster, vitreous to pearly streak white transparent to opaque brittle color, white to grayish or reddish,... 

I/15,000 1.6.000. which in lowest terms arc 3 2 5. These smallest integers are the Miller indices of the family lo which this plane belongs, and the family is thus designated (325). The family (2011 is parallel to the Y axis but intersects the X and Z axes. (The hexagonal system has four Bravais-Miller indices lor each plane-family. I... 

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