Hexagonally closest packed lattice

Construct a third close-packed layer of seven spheres as shown in Diagram Ic. Reverse (invert) the first and second layer, and place the third layer on top so each sphere in the top layer is directly above a sphere in the bottom layer. You have constructed three planes of a hexagonally closest-packed lattice. Additional layers would pack a,b,a,b,a,b,a,b,a,b,... 

Figure 7.1 Three common crystal lattices adopted by elements (a) body-centred cubic packing, (b) cubic closest packed (or face-centred cubic) and (c) hexagonal closest packed...

Berkelium metal exhibits two stable crystallographic modifications, double hexagonal closest packed (dhcp) and face-centered cubic (fee). Thus it is isostructural with the two preceding elements, all of which exhibit the fee structure at high temperature. The room-temperature lattice constants of the dhcp form are ao = 0.3416 0.0003 nm and c0 = 1.1069 0.0007 nm, yielding a calculated density of 1.478 x 104 kg/m3 and a metallic radius (CN = 12) of 0.170 nm (119). The room-temperature fee lattice parameter is a0 = 0.4997 0.0004 nm from which the... 

Translation of ions within crystals is less frequently observed than is rotation. Perhaps one of the most interesting cases is that of silver iodide which may actually be said to melt in halves. When this solid is heated to 145.8° C, the crystal structure then changes and the ionic conductivity increases tremendously the iodide ions are hexagonally closest-packed below the transition temperature but at this temperature they rearrange to form a more open structure, and the silver atoms are allowed to move within the lattice. At 555° C, the network of iodide ions collapses, and the compound becomes a liquid. The solids Cul and Ag2Se show similar behavior. 

The closest analogues of thiols, alkaneselenols R—SeH, were found to form well-packed monolayers on the Au(lll) surface. The structure of these layers was studied by X-ray diffraction. An oblique unit cell was revealed, indicating a distorted hexagonal close-packed lattice of selenol molecules . Benzeneselenol and diphenyl diselenide form identical monolayers on gold, as shown with STM microscopy. Monolayers of benzeneselenol do not have vacancy pits typical for thiolate monolayers, but show the presence of small islands of gold (20-200 A) which were absent before deposition . 

The zinc blende lattice Is named after its parent compound, ZnS. Zinc sulfide also exists in a different structure known as the wurtzite lattice. Molecules that can exist in more than one type of crystalline form exhibit polymorphism. The wurtzite lattice is comprised of one type of ion forming a hexagonal closest-packed unit cell, with the other type of ion occupying half of the tetrahedral holes. The following molecules can assume the wurtzite lattice ZnO, ZnS, ZnSe, ZnTe, BeO, Agl, CdS, MnS, SiC, AIN, and NH4F. Both types of lattices consist of corner-shared tetrahedrons, but the tetrahedrons in wurtzite are canted in alternating layers. 

FIGURE 13.8 The structure of the face-centered cubic, hexagonal closest packing, and body-centered cubic lattices. To form each lattice, start with the first layer (green atoms), add the second layer as shown (blue atoms), and then the third layer (yellow atoms). The cycle repeats, with every other layer being identical in each lattice. One face of one unit cell is outlined on the first layer of each lattice. This representation illustrates the (100) surface of each lattice. 

Assuming the tungsten particles are located on a hexagonal close-packed lattice (HOP) and have a radius of 0.02 mm, the closest distance between tungsten spheres is 0.0114 mm for 35-volume-percent tungsten in HMX. If the tungsten sphere radius is 0.03 mm, the closest distance between spheres is 0.0170 mm. 

The computational grid contained 24 x 22 by 36 cells, each 1 x 10 cm on a side. The 36 air holes were described by 4 cells per sphere diameter. Numerical tests with 2 to 6 cells per sphere diameter showed the results were independent of grid size for more than 3 cells per sphere diameter. The air holes were located on a hexagonal close-packed lattice (HCP). The closest distance for the HCP matrix between holes was 3.8 x 10 " cm. The time step was 1 X 10 /rsec. 

Some crystal lattices can also be depicted as closest-packed structures, including the hexagonal closest-packing structure (not cubic) and the cubic closest-packing structure (which has a face-centered cubic unit cell). 

We can describe the structures of metals as the closest packing of spheres, first discussed in Section 11.11. Elemental metals generally crystallize in one of the basic types of crystal lattices, including face-centered cubic, body-centered cubic, and hexagonal closest packed. The crystal structure of a metal may change, however, as a function of temperature and pressure. Table 23.2 lists the crystal structures for the 3d transition metals at attnospheric pressure. 

Like rhenium and ruthenium it crystallizes in a closest packed hexagonal lattice with the metal atoms having the coordination number 12. In Table 2 some properties of technetium are compared with those of manganese and rhenium. 

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