Packing hexagonal close

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...

Figure Bl.21.1 shows a number of other clean umeconstnicted low-Miller-index surfaces. Most surfaces studied in surface science have low Miller indices, like (111), (110) and (100). These planes correspond to relatively close-packed surfaces that are atomically rather smooth. With fee materials, the (111) surface is the densest and smoothest, followed by the (100) surface the (110) surface is somewhat more open , in the sense that an additional atom with the same or smaller diameter can bond directly to an atom in the second substrate layer. For the hexagonal close-packed (licp) materials, the (0001) surface is very similar to the fee (111) surface the difference only occurs deeper into the surface, namely in the fashion of stacking of the hexagonal close-packed monolayers onto each other (ABABAB.. . versus ABCABC.. ., in the convenient layerstacking notation). The hep (1010) surface resembles the fee (110) surface to some extent, in that it also...

Figure C2.17.3. Close-packed array of sub-micrometre silica nanoparticles. Wlren nanoparticles are very monodisperse, they will spontaneously arrange into hexagonal close-packed stmcture. This scanning electron micrograph shows an example of this for very monodisperse silica nanoparticles of -250 nm diameter, prepared in a thin-film fonnat following the teclmiques outlined in [236].

Fig. 3.8 Some basic Bravais lattices (a) simple cubic, (b) body-centred cubic, (c) face-centred cubic and (d) simple hexagonal close-packed. (Figure adapted in part from Ashcroft N V and Mermin N D 1976. Solid State Physics.

As with other related rare-earth metals, gadolinium is silvery white, has a metallic luster, and is malleable and ductile. At room temperature, gadolinium crystallizes in the hexagonal, close-packed alpha form. Upon heating to 1235oG, alpha gadolinium transforms into the beta form, which has a body-centered cubic structure. 

Eig. 1. SoHd—Hquid phase diagram for ( ndashrule ) He and (—) He where bcc = body-centered cubic, fee = face-centered cubic, and hep = hexagonal close-packed (53). To convert MPa to psi, multiply by 145. 

Sohd hydrogen usually exists in the hexagonal close-packed form. The unit cell dimensions are = 378 pm and Cg = 616 pm. SoHd deuterium also exists in the hexagonal close-packed configuration, and = 354 pm, Cg = 591 pm (57—59). 

Thin films (qv) of lithium metal are opaque to visible light but are transparent to uv radiation. Lithium is the hardest of all the alkaH metals and has a Mohs scale hardness of 0.6. Its ductiHty is about the same as that of lead. Lithium has a bcc crystalline stmcture which is stable from about —195 to — 180°C. Two allotropic transformations exist at low temperatures bcc to fee at — 133°C and bcc to hexagonal close-packed at — 199°C (36). Physical properties of lithium are Hsted ia Table 3. 

DpopE related to SpQpp, which is in turn related to the closeness of packing of the powder. The number of particles adjacent to a given particle is represented by The maximum packing density for monosize spheres occurs at hexagonal close packing, where = 12 and = 0.2595 for... 

Bismuth Triiodlde. Bismuth(Ill) iodide is a greenish black crystalline powder. The iodines are in a hexagonal close-packed array with each bismuth having six nearest-neighbor iodines at 0.32 nm (21). This suggests that the lone pair on bismuth is stereochemicaHy inactive and that the compound is largely ionic in character. 

The hexagonal-close-packed (hep) metals generally exhibit mechanical properties intermediate between those of the fee and bcc metals. For example Zn encounters a ductile-to-brittle transition whereas Zr and pure Ti do not. The latter and their alloys with a hep structure remain reasonably ductile at low temperatures and have been used for many applications where weight reduction and reduced heat leakage through the material have been important. However, small impurities of O, N, H, and C can have a detrimental effect on the low temperature ductihty properties of Ti and its alloys. 

---