Hexagonal crystal systems

Steel-gray crystalline brittle metal hexagonal crystal system atomic volume 13.09 cc/g atom three allotropes are known namely, the a-metaUic form, a black amorphous vitreous solid known as P-arsenic, and also a yellow aUotrope. A few other allotropes may also exist but are not confirmed. Sublimes at 613°C when heated at normal atmospheric pressure melts at 817°C at 28 atm density 5.72 g/cc (P-metallic form) and 4.70 g/cm (p-amor-phous form) hardness 3.5 Mohs electrical resistivity (ohm-cm at 20°C) 33.3xlCh (B—metallic polycrystalline form) and 107 (p—amorphous form) insoluble in water. 

Colorless glassy solid or vitreous crystal hexagonal crystal system slightly hitter taste hygroscopic density 2.55 g/cm melts at 450°C vaporizes at 1,500°C slightly soluble in cold water (3.3%), soluble in alcohol and boiling... 

White to yellowish powder or flakes hexagonal crystal system hygroscopic density 5.192g/cm3 melts at 568°C vaporizes at 844°C soluble in water, alcohol, ether, acetone, and hquid ammonia. 

Colorless powder or crystal hexagonal crystal system hygroscopic density 4.047 g/cm3 melts at 560°C vaporizes at 960°C highly soluble in water (140 g/lOOg at 20°C), also soluble in acetone slightly soluble in alcohol insoluble in ether. 

White powder or crystal trigonal or hexagonal crystal system density 4.79 g/cm3 decomposes slowly at 130°C dehydration completes at 300°C insoluble in water (2.6 mg/L at 20°C) soluble in dilute acids. 

White, very fine powder hexagonal crystal system heptahydrate is yellow orthogonal crystal and hygroscopic density of anhydrous salt 3.97 g/cm melts at 817°C vaporizes at 1,727°C heptahydrate begins to lose water above 90°C and becomes anhydrous at about 230°C soluble in water and alcohol hexahydrate has greater solubility in these solvents. 

Green hexagonal crystal system corundum type structure density 5.22 g/cm3 melts at 2,330°C vaporizes above 3,000°C insoluble in water and alcohol. 

Soft, lustrous metal silver-like appearance close-packed hexagonal crystal system density 8.78 g/cm paramagnetic magnetic moment 11.2 Bohr magnetons melts at 1,472°C vaporizes at 2,694°C electrical resistivity 195 microhm-cm at 25°C Young s modulus 6.71xl0n dynes/cm2 Poisson s ratio 0.255 thermal neutron cross section 64 barns insoluble in water soluble in acids (with reactions). 

Cinnabar is a red crystalline or powdery substance hexagonal crystal system refractive index 2.854 density 8.10 g/cm sublimes at 583.5°C color changes to brown at 250°C and converts to black sulfide at 386°C reverts to red color on cooling insoluble in water, alcohol and nitric acid soluble in aqua regia and solutions of alkali metal sulfides decomposed by hot concentrated sulfuric acid. 

Metallic appearance in massive form, black to metallic color in powdered state or in electrodeposited form hexagonal crystal system density 20.53 g/cm3 hardness (Brinell) 250 melts at 3,180°C vaporizes at 5,627°C (estimated) vapor pressure 4.6x10- torr at 2,500°C electrical resistivity 19.14 microhm -cm modulus of elasticity 67x10 psi at 20°C specific magnetic susceptibility 0.369x10 thermal neutron absorption cross section 86 barns/atom superconductivity transition temperature 1.7°K insoluble in water and hydrochloric acid soluble in dilute nitric acid and hydrogen peroxide slightly soluble in sulfuric acid. 

Heteropoly anions. 760-764 Hexagonal crystal system, 75. 78 Hexanuclear dusters. 816 VtexgonsA closest packed (hep)... 

Trigonal, tetragonal, and hexagonal crystal systems have three, four and sixfold axes of symmetry, respectively, while the cubic crystal contains four threefold axes along with diagonals of the cube as well as two-fold axes passing through the faces (see Fig. 15-14). 

As Figure 16.5 shows, z is also a C6 axis. From Figure 16.5, the hexagonal crystal system is defined by... 

Use these drawings to compare the cubic, monoclinic, and hexagonal crystal systems. (13.3)... 

Clearly, there are two choices for placing each plane, and an infinite number of crystal structures can be generated that have the same atomic packing density. The two simplest such structures correspond to the periodic layer sequences abcabcab. . . and abababa.. . . The first of these is the fee structure already discussed, and the second is a close-packed structure in the hexagonal crystal system termed hexagonal close-packed (hep). In each of these simple structures, atoms occupy 74.0% of the unit cell volume, as the following example shows. (Atoms that crystallize in the bcc structure occupy only 68.0% of the crystal volume, and the packing fraction for a simple cubic array is only 52.4%.)... 

Heteropoly anions, 760-764 Hexagonal crystal system, 75, 78 Hexanuclear clusters, 816 Hexgonal closest packed (hep) system, 120 Hieber, Walter, 643 Highest occupied molecular orbital (HOMO). 351, 428, 721, 722... 

As seen in Table 1.10, there is one powder Laue class per crystal system, except for the trigonal and hexagonal crystal systems, which share the same powder Laue class, 6/mmm. In other words, not every Laue class can be established from a simple visual analysis of powder diffraction data. This occurs because certain diffraction peaks with potentially different intensities (the property which enables us to differentiate between I ue classes 4/m and 4/mmm 3, 3m, 6/m and 6/mmm m3 and m3m) completely overlap since they are observed at identical Bragg angles. Hence, only Laue classes that differ from one another in the shape of the unit cell (see Table 1.11, below), are ab initio discernible from powder diffraction data without complete structure determination. 

In the hexagonal crystal system, a total of four Miller indices are sometimes used to designate a plane (htdl), where i = - h + k). See Figure 1.37 for details. 

Figure 1.37. Three possibilities to select the crystallographic basis in hexagonal and trigonal crystal systems and the family of (1120) crystallographic planes in the hexagonal crystal system. Indices are shown in the unit cell based on the vectors b and c. Three additional symmetrically related families of planes have indices (1120), (1210) and (2110) in the same basis and we leave their identification to the reader.

Table 1.20. Selected symmetry elements in trigonal and hexagonal crystal systems, their orientation and corresponding symmetry operations in the algebraic form as augmented matrices (see Figure 1.51). ...

Based on the symmetry of the unit cell shape, the proper table (crystal system) must be selected. Only in one case, i.e. when the unit cell is primitive with a-b c,a = = 90° and y = 120°, both trigonal and hexagonal crystal systems should be analyzed. 

Table 2.15. Reflection conditions for the hexagonal crystal system. There are no space groups...

The quadratic form of Eq. 5.2 in the hexagonal crystal system is found in Eq. 5.4 and its analogue in the tetragonal crystal system is... 

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