Crystals hexagonal close packed

Hexagonal close-packed crystals to melting point at 923 K. Boiling point at 1366.1 K. 

Grayish metal hexagonal close-packed crystal system, lattice constant, a=2.286 A and c=3.584 A density 1.85 g/cm permeable to x-rays highly ductile modulus to weight ratio very high, elastic modulus 44.5 x 10 at 25°C (for hot-pressed block and sheet) melting point 1,287°C vaporizes at 2,471°C sound transmission velocity 12,600 m/sec reflectivity (white hght) 55% thermal neutron absorption cross-section 0.0090 barns/atom electrode potential, Be/Be2+(aq) 1.85 V electrical resistivity 3.36 x 10-i° ohm.m (at 20°C). 

Silvery white metal soft and malleable hexagonal closed pack crystal system transforms to face-centered cubic crystals at 310°C which further transforms to a body-centered cubic allotropic modification at 868°C density 6.166 g/cm3 Brinnel hardness (as cast) 37 melts at 918°C vaporizes at 3,464°C vapor pressure 1 torr at 2,192°C electrical resistivity 56.8 x 10 ohm-cm at 25°C Young s modulus 3.84 x lO- dynes/cm Poisson s ratio 0.288 thermal neutron cross section 8.9 bams. 

Hard silvery-white metal hexagonal close-packed crystal structure density 12.41 g/cm3 at 20°C melts at 2,334°C vaporizes at 4,150°C electrical resistivity 7.1 microhm-cm at 0°C hardness (annealed) 200-350 Vickers units Young s modulus 3.0x10 tons/in magnetic susceptibility 0.427 cm /g thermal neutron absorption cross section 2.6 barns insoluble in water, cold or hot acids, and aqua regia can be brought into aqueous phase by fusion of finely divided metal with alkaline hydroxides, peroxides, carbonates and cyanides. 

It is an unusual problem to construct a homogeneously distorted two-dimensional domain structure which allows us to cover the range of the hexagonal closely packed crystal up to a two-dimensional gas. For example, the concept of the paracrystal is based on the philosophy that every state of condensed matter has at least a micro-paracrystalline arrangement of segments within a distorted lattice of arbitrary symmetry with a defined coordination number. 

STRONTIUM. [CAS 7440-24-6], Chemical element, symbol Sr, at. no. 38, at. wt. 87.62. periodic table group 2, mp 769°C, bp 1384°C, density 2.54 g/cm- (20°C). Below 215°C, elemental strontium has a face-centered cubic crystal structure between 215-605 C. a hexagonal close-packed crystal structure and above 605°C, a body-cen tered cubic crystal structure. 

Hexagonal close packed crystals are often characterized using four lattice vectors. In this case four Miller indices (h k i l) are used correspondingly, where the fourth index is related to the first two indices by i = — (h + k). 

Woodcock, L., Entropy difference between the face-centred cubic and hexagonal close-packed crystal structures. Nature, 385, 141, 1997. 

Fig. 12. Adsurbale structures on (11 1) faces of face-centered cubic crystals [e g. Ni( 111) or (100) faces of hexagonal close packed crystals [e.g. Ru(100)]. The adsorption sites form a regular triangular lattice. Ordered structures that are discussed are (i/fxv JRSO0 (coverage e = 1/3), p(2x2) (0 - 1/4), p(2x 1) (0 = 1/2) and (2x2)-3H (0 = 3/4), respectively.

Dark-gray metallic powder hexagonal close-packed crystal lattice, d 9.062. mp 1497. E (aq) EH+ZEr —230 V (calc). Similar to the other rare earth metals, possesses two reduction potentials 1.770 and 1.875 volts (ref to the normal calomel electrode), Noddack, Brukl, Angew. Chem, 50, 362 (1937). Radioactivity induced by neutron bombardment Sugden. Nature 135,469 (1935) McLennan, Rann, ibid 136, 831 (1935). Spectrum Eder. Ber. Wien. Akad. [2aJ 124, 790 (1915) deGramont, Compt. Rend. 171, 1106 (1920) Mott, McDonald. Trans. Roy. Soc. Canada [3] 21, 230 (1927). 

Hexagonal close-packed crystals, black to silver-gray, d 21.02. mp 3180. bp 5900 (estimated). Specific beat 0-2ff 0.03263 cal/g/ C. Specific electrical resistance 0.2] X... 

PHYSICAL PROPERTIES silvery-metallic, lustrous solid darkens on exposure to light forms hexagonal close-packed crystals brittle much harder than zinc soluble in dilute acids and potassium hydroxide solution odorless MP (1522°C, 2772°F) BP (3338°C, 6040°F) DN (4.469 g/cm ) SG (4.47) CP (26.5 J/K-mol crystal at 25°C) VD (NA) VP (0 mmHg at 20°C). 

Figures 4.13 and 4.14 present the Brillouin zones for cubic crystal lattices. One can see the Brillouin zone for hexagonal close-packed crystal lattice in Figure 4.15.

Table 4.1 Points and directions of high symmetry in the first Brillouin zones, fee is the face-centered cubic crystal lattice bcc is the body-centered cubic crystal lattice hep is the hexagonal close-packed crystal lattice.

Figure 4.15 First Brillouin zone of the hexagonal close-packed crystal lattice, kx.ky, kz are the axes of the Cartesian coordinate system in fe-space. The symmetry points and symmetry lines are indicated. See Table 4.1 for details.

As the name implies, the hexagonal close-packed crystal has the highest possible packing density. Its stacking sequence (cf. figure 1.9) differs from that of the face-centred cubic lattice. Only the 0001 -basal planes are close-packed. They contain the three (1120) close-packed directions, resulting in only three independent slip systems (figure 6.16). 

It would have been much simpler to solve the exercise using the following argument The face-centred cubic and the hexagonal close-packed crystal are close packed with each atom having 12 nearest neighbours. Therefore, the relative density must be the same in both cases and the result for the face-centred cubic lattice can be used. 

Fig. 3. The surface and bulk Brillouin zone of bulk hexagonal close packed crystals. The surface Brillouin zone is shown for the (0001) basal face.

In any close-packed arrangement, each interior atom is surrounded by 12 nearest-neighbor atoms. The number of nearest-neighbor atoms of an atom is called its coordination number. Thinking of atoms as hard spheres, one can calculate that the spheres occupy 74% of the space of the crystal. There is no way of packing identical spheres so that an atom has a coordination number greater than 12 or the spheres occupy more than 74% of the space of the crystal. All the noble-gas solids have cubic close-packed crystals except helium, which has a hexagonal close-packed crystal. 

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