Body-centered structure

Iron (Fe) has the body-centered structure at 298 °K and a density of 7.86 gm with a lattice spacing of a = 2.876 A. Calculate Avogaddro s number from these data. 

Although the correlation between ionic porosity and diffusivity is imperfect, there is a rough trend that oxygen diffusivity in the minerals increases with increasing IP. The trend is useful in qualitative estimation of closure temperature (among other applications). Extending the relation to metallic systems, one prediction is that diffusion in face-centered cubic structure (25.95% free space) is slower that that in body-centered structure (31.98% free space) of the same metal composition. To avoid the issue of anisotropy, it would be worthwhile to reexamine the relations between diffusivity and ionic porosity using only isometric minerals. 

Many metals crystallize in the relatively simple cubic (either primitive, face-centered, or body-centered) structures. 

A previous examination of a synthetic calcium mordenite 15) revealed an orthorhombic cell. A synthetic strontium mordenite 16) had a C-centered orthorhombic cell although Kerr 12) reported that a few crystals giving electron diffraction patterns corresponding approximately to the body-centered structure Immm) have been synthesized hydro-thermally from aluminosilicate gels containing strontium similar to those gels which yielded a strontium-mordenite. ... 

These are the first observations of intergrowths in the Cmcm mordenite structure. They show, in the first case, that the Cmmm structure exists as discrete regions intergrown with the usual Cmcm structure while in the second, the body-centered structures only exist as very narrow regions or stacking faults. An intergrowrth of cither Cmmm or Immm and the Cmcm structure would also account for the incompleteness of the c-glide plane observed in some of the previous studies. 

Figure 6. Cubic structures in lipid-water systems based on space-filling polyhedra. The data from the monoglyceride-water cubic phases fit with the body-centered structure to the right.

Tetrakis(hydroxymethyl)methane, [C(CH20H)4, also known as pen-taerythritol], is one of the simpler substitution products of methane for which structures have been determined. The tetragonal cell contains two molecules, S4,14, a0 6.083, c0 = 6.726 A. The structure shown in Figure 11.10 is body centered, 3 2PTOT(t). At higher temperatures, between 179.5 and 260.5°C, this body-centered structure is transformed to a face-centered cubic structure. The cubic cell (a0 = 8.963 A at 230°C) contains four molecules. It has been proposed that at the higher temperature the molecules achieve a statistical orientation that makes them effectively spherical crystallographically. The notation is 3P. 

The structure of C(CH20N02)4, like C(CH20H)4, the alcohol from which it is formed, has a bimolecular tetragonal unit cell, D2l/4, P42iC, a0 = 9.33, c = 6.66 A. The body-centered structure, 3 2PTOT(t), is shown in Figure 11.11. The compact molecule with high symmetry packs efficiently in the body-centered structure. 

The position of a point inside the primitive unit cell is determined by a fraction of the axial length, a, b, c. For example, in a body-centered structure, the position of the central point is 411. ... 

The rutile structure is tetragonal (see Figure 2.9). That is, it is formed by a cationic framework of a tetragonal body-centered structure with the Ti4+ cation, located in the lattice sites and the O2 anions arranged as a TiOe octahedron connected through opposite edges alongside the c-axis. 

Taylor and Roy s Na-Pt (13), and possibly represent various degrees of distortion (displacive transformation) of the cubic body-centered structure. B6 is quite similar to Bi except for doubleting of peaks near 18°, 28°, and 34° 20(CuK ). Be probably represents the least distortion from the cubic structure (Bi) of all the other B zeolites. Zeolites B2 and B5... 

Another common arrangement of spheres that occurs in a few metals is the body-centered cubic (bcc), which is built up of layers having the arrangement shown in Fig. 27.4. The second layer fits in the notches of the first and the pattern of layers repeats, xyxy. In these layers the number of nearest neighbors around any sphere is four, as compared with six in the close-packed layers. In the body-centered structure the overall coordination number is eight there are four nearest neighbors within the most closely packed layer, two... 

Assuming the body-centered structure (bee) of metal (M), which of the following compounds MX or MX2 (where X = C, N) is more likely to progress its structure to hexagonal or face-centered cubic ... 

CH3)2Hg + 2Na 2CH3Na + Na/Hg These materials are used as catalysts for polymerization reactions. The metal itself has a body-centered structure. 

For a more familiar view of these structures we now turn to the unit cells. The tetragonal crystal structure of MoSi2 (space group lAlmmm) is presented in Fig. 21. It may also be considered as derived from the body-centered structure of... 

Size effects in the films depend essentially on substrate type. Namely, iron epitaxial film crystallizes into body centered structure on Ag(lOO) substrate independently of film thickness. For the films thicker than five monolayers, Curie temperature Tc coincides with its bulk value Tc = 1,017 K) so that ferromagnetic order appears diiT [Pg.68]

At r = 30 K the fllms with three or four iron monolayers are magnetized perpendicularly to the film surface, while the magnetization of thicker and thinner films lays in the film plane. Epitaxial iron film on Cu( 1,000) substrate has the face-centered structure up to 15 monolayers thickness, while the bulk samples have body-centered structure. The Curie temperature for the films containing three and five monolayers is equal to 390 K, which possibly corresponds to 7). of face-centered bulk iron, while for monolayer Tc = 230 K [68]. The saturation magnetization decreases linearly with temperature near 7),. At room temperature, three and five monolayers films have no magnetization, but at 7 = 30 K, the hysteresis loops have been observed with coercive fields 350 and 650 Oe respectively. The direction of the easy magnetization axis is perpendicular to the film plane. There was no hysteresis even at low temperatures in a monolayer film. 

Figure 11.40 lists the structures of the metallic elements. With few exceptions, they have either a close-packed or a body-centered structure. 

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