Crystal structures Body-centered cubic structure

With the exception of manganese and urauium, all true metals have one of the following crystal structures body-centered cubic (sodium, potassium, molybdenum), iron face-centered cubic (copper, silver, gold), iron close-packed hexagonal (beryllium, magnesium, zirconium). 

Crystal Structure. Body-centered cubic single-phase p is obtained in the solution treated condition. Close-packed hexagonal o) phase and cph phase a are precipitated dining aging below 400 °C (750 °F) and above 450 C (840 °F), respectively. Omega phase is usually avoided because it causes embrittlement. 

Crystal Structure. Body-centered cubic P phase is obtained after solution treating in the p temperature region and quendiing. Close-padded hexagonal a phase and co phase precipitate dialing aging above and below 425 (795 F), respectively. Compared with Ti-15Mo-5Zr, embrittlement caused by co phase does not occur as predominantly because the amount of q> phase is reduced by the 3% aluminum additions. 

Crystal structure, body centered cubic (bcc) A crystal structure where the basic building block is a cubic unit cell having atoms at each comer and one in the center of the cell. 

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. 

Disordered alloys may form when two metals are mixed if both have body-centered cubic structures and if their atomic radii do not differ by much (e.g. K and Rb). The formation of ordered alloys, however, is usually favored at higher temperatures the tendency towards disordered structures increases. Such an arrangement can even be adopted if metals are combined which do not crystallize with body-centered cubic packings themselves, on condition of the appropriate composition. /J-Brass (CuZn) is an example below 300 °C it has a CsCl structure, but between 300 °C and 500 °C a A type transformation takes place resulting in a disordered alloy with a body-centered cubic structure. 

Figure 5.8 Interstitial diffusion (a) interstitial diffusion involving the direct migration of an interstitial atom to an adjacent site in the crystal (b, c) some of the octahedral and tetrahedral interstitial sites in the body-centered cubic structure of metals such as iron and tungsten and (d) the total number of octahedral and tetrahedral sites in a unit cell of the body-centered cubic structure. Diffusion paths parallel to the unit cell edges can occur by a series of alternating octahedral and tetrahedral site jumps, dashed line.

If you try to draw an electron-dot structure for a metal, you ll quickly realize that there aren t enough valence electrons available to form an electron-pair bond between every pair of adjacent atoms. Sodium, for example, which has just one valence electron per atom (3s1), crystallizes in a body-centered cubic structure in which each Na atom is surrounded by eight nearest neighbors (Section 10.8). Consequently, the valence electrons can t be localized in a bond between any particular pair of atoms. Instead, they are delocalized and belong to the crystal as a whole. 

Potassium metal crystallizes in a body-centered cubic structure. Draw one unit cell, and try to draw an electron-dot structure for bonding of the central K atom to its nearest-neighbor K atoms. What is the problem ... 

When we determined the crystalline structure of solids in Chapter 4, we noted that most transitional metals form crystals with atoms in a close-packed hexagonal structure, face-centered cubic structure, or body-centered cubic arrangement. In the body-centered cubic structure, the spheres take up almost as much space as in the close-packed hexagonal structure. Many of the metals used to make alloys used for jewelry, such as nickel, copper, zinc, silver, gold, platinum, and lead, have face-centered cubic crystalline structures. Perhaps their similar crystalline structures promote an ease in forming alloys. In sterling silver, an atom of copper can fit nicely beside an atom of silver in the crystalline structure. 

Adamantane, a structural analog of hexamethylenetetramine, crystallizes at room temperature in the cubic space group Fm3m with ac = 944.5 pm and Z = 4. The structure is disordered, not ordered in space group F43m (no. 216, multiplicity = 96) as described in a previous report. The cubic close-packed arrangement of (CH2)6(CH)4 is favored over the body-centered cubic structure... 

Just as the body-centered cubic structure can be considered as made of two interpenetrating simple cubic lattices, the face-centered cubic structure can be made of four simple cubic lattices. There are some interesting cases of ordered alloys with this crystal structure and ratios of approximately one to three of the two components. An example is found in the copper-gold system, where such a phase is found in the neighbor-... 

This completes the specification of the pseudopotential as a perturbation in a perfect crystal. We have obtained all of the matrix elements between the plane-wave states, which arc the electronic states of zero order in the pseudopotcntial. We have found that they vanish unless the difference in wave number between the two coupled states is a lattice wave number, and in that case they are given by the pseudopotential form factor for that wave number difference by Eq. (16-7), assuming that there is only one ion per primitive cell, as in the face-centered and body-centered cubic structures. We discuss only cases with more than one ion per primitive cell when we apply pseudopotential theory to semiconductors in Chapter 18. Tlicn the matrix element will be given by a structure factor, Eq. (16-17),... 

I lGURK 20-2 The body-centered cubic structure. The central atom sits at the center of a cube formed by k,r. its eight nearest neighbors, shaded to distinguish them, though every atom and its environment (in the extended crystal) is identical. The six second neighbors lie a distance 15 percent further away. We construct a Bloch sum with wave number in the z-direction, giving phase factors shown for atoms in each plane of constant z. 

Plan Because an atom is spherical, we can find its radius from its volume. If we multiply the reciprocal of density (volume/mass) by the molar mass (mass/mole), we find the volume of 1 mol of Ba metal. The metal crystallizes in the body-centered cubic structure, so 68% of this volume is occupied by 1 mol of the atoms themselves (see Figure 12.26C). Dividing by Avogadro s number gives the volume of one Ba atom, from which we find the radius. 

FOLLOW-UP PROBLEM 12.4 Iron crystallizes in a body-centered cubic structure. The volume of one Fe atom is 8.38X10 cm, and the density of Fe is 7.874 g/cm. Calculate an approximate value for Avogadro s number. 

Solid chromium adopts a body-centered cubic structure and crystallizes in the space group Irnim with a = 288.46pm its density is 7.19gcm (at 293K). The metal melts at 2130 ( 20) K and boils at 2945 K the corresponding enthalpies are A//fusion = 15.3kJmoU and AT/vap = 348.78 kj mol Values of various thermodynamic functions are listed in Table 2. Some other values are thermal conductivity 93.7 W m (at 300 K), electrical resistivity 12.7 X 10 m (at 273 K), magnetic susceptibility 3.5 x... 

PHYSICAL PROPERTIES steel-gray metallic pieces, powder, and flakes gray crystals blue-white hard metal body-centered cubic structure ductile odorless chromium (III) compounds are sparingly soluble in water chromium (IV) compounds are readily soluble in water soluble in acids (except nitric) and strong alkalis exists in active and passive forms Cr ion forms many coordination compounds MP (1890°C, 3434°F) BP (2672°C, 4841.6°F) DN (7.14 gW at 20°C) SG (7.14) ST (50 mN/m in air at MP) CP (5.58 cal/g-atom deg at 25°C) HV (81.7 kcal/g-atom) VD (7.1) VP (ImmHg at 1616°C). 

Diffusivity and diffusion coefficient are synonymous [25]. In dense membranes, diffusivity is associated with the rate of movement of dissociated hydrogen from site to site within a crystal lattice. In general, diffusivity of hydrogen is greater in metals with the body centered cubic structure (bcc) relative to metals with the face centered cubic stmcture (fee) [26]. According to Wipf, dissociated hydrogen occupies tetrahedral interstitial sites in bcc metals and hops between such sites. Tetrahedral interstitial sites are only 1.01-1.17 A apart in common bcc metals [26]. This relatively short distance permits quantum mechanical tunneling, which accord-... 

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