Hexagonal closest packed hep structure

The aba arrangement has the hexagonal unit cell shown in Fig. 16.14, and the resulting structure is called the hexagonal closest packed (hep) structure. The abc arrangement has a face-centered cubic unit cell, as shown in Fig. 16.15 on page 779, and the resulting structure is called the cubic closest packed (ccp) structure. Note that in the hep structure the spheres in every other layer occupy the same vertical position (ababab. . . ), while in the ccp structure the spheres in every fourth layer occupy the same vertical position (abcabca. . . ). A characteristic of both structures is that each sphere has 12 equivalent nearest... 

Hess s law in going from a particular set of reactants to a particular set of products, the enthalpy change is the same whether the reaction takes place in one step or in a series of steps in summary, enthalpy is a state function. (9.5) Heterogeneous equilibrium an equilibrium involving reactants and/or products in more than one phase. (6.5) Hexagonal closest packed (hep) structure a structure composed of closest packed spheres with an ababab arrangement of layers the unit cell is hexagonal. (16.4)... 

Hexagonal closest packed (hep) structure a structure composed of closest packed spheres with an ababab arrangement of layers the unit cell is hexagonal. (10.4)... 

The aba arrangement has the hexagonal unit cell shown in Fig. 10.14, and the resulting structure is called the hexagonal closest packed (hep) structure. The abc arrangement has a face-centered cubic unit cell, as shown in Fig. 10.15, and the resulting structure is... 

There are two possibilities for C, the third layer (Fig. 12-39a). In one arrangement, called hexagonal closest packed (hep), all the tetrahedral holes are covered. Layer C is identical to layer A, and the structure begins to repeat itself. In the other arrangement, called cubic closest packed, all the octahedral holes are covered. The spheres in layer C (blue) are out of line with those in layer A. Only when the fourth layer is added does the structure begin to repeat itself. 

A FIGURE 12-41 The hexagonal closest packed (hep) crystal structure... 

Crystal Structures— Some crystal structures can be described in terms of the packing of spheres. Depending on the way in which the spheres are packed, different unit cells are obtained (Fig. 12-37). The hexagonal unit cell is obtained with hexagonal closest packed (hep)... 

The 17 rare-earth metals are known to adopt five crystalline forms. At room temperature, nine exist in the hexagonal closest packed structure, four in the double c-axis hep (dhep) structure, two in the cubic closest packed structure and one in each of the body-centered cubic packed and rhombic (Sm-type) structures, as listed in Table 18.1.1. This distribution changes with temperature and pressure as many of the elements go through a number of structural phase transitions. All of the crystal structures, with the exception of bep, are closest packed, which can be defined by the stacking sequence of the layers of close-packed atoms, and are labeled in Fig. 18.1.1. 

Use the diagram of the unit cell for the hexagonal closest packed structure in Fig. 16.14 to determine the net number of atoms in the hep unit cell. 

The densest ABAB close-packing structure is also known as the hexagonal closest packing structure (hep) because of its hexagonal elementary unit. It can be found in metals like magnesium and zinc Magnesium Type (see Fig. 5.6). 

Mg type Crystal structure isotypic to Mg, space group P63/mmc, Mg in 2c 1/3, 2/3, 1/4 in the literature also called hep (hexagonal closest packed). 

Study Figure 12-40 and you will see that the cubic closest packed structure has a face-centered cubic unit cell. The unit cell of the hexagonal closest packed structure is shown in Figure 12 1. In both the hep and fee structures, holes account for only 25.96% of the total volume. For the simple cubic and bcc unit cells, holes account for a higher percentage of the total volume. In the bcc unit cell, holes account for 31.98% of the total volume. The best examples of... 

The Hume-Rothery types listed in Table 4.6 include structures of different complexity ranging from the simple close-packed (fee and hep) and bcc structures to the more complex Mn-type and 7-brass type structures. As for the hexagonal hep structures, notice that for this type several variations are known three branches of this structure are generally considered. The (-hep corresponds to the true closest packing with the value of the axial ratio da close to the ideal one ((8/3) = 1.6329. .. (see 3.7.4 and Fig. 3.16). The e-hex corresponds to da ranging around 1.55 to 1.58 and the r/ phase to c/a values of about 1.77 to 1.88. As observed by Lee and Hoistad (1995), the various hexagonal types can be considered genuinely different. 

The crystal structure of antimony pentachloride, SbCls, is hexagonal (D (, P63 jmmc, a0 = 7.49, and c0 = 8.01 A) with two molecules in the cell. The molecules are hep giving the simple notation 2P(h). In Figure 4.26, we see that the trigonal bipyramidal molecules have their C3 axes parallel to c0, the packing direction. The axial Sb—Cl distance is 2.34 A and that in the equatorial plane is 2.29 A. The closest Cl—Cl distances (3.33 A) are between axial Cl atoms between adjacent molecules. 

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