Body-cubic

The rocksalt stmcture is illustrated in figure Al.3.5. This stmcture represents one of the simplest compound stmctures. Numerous ionic crystals fonn in the rocksalt stmcture, such as sodium chloride (NaCl). The conventional unit cell of the rocksalt stmcture is cubic. There are eight atoms in the conventional cell. For the primitive unit cell, the lattice vectors are the same as FCC. The basis consists of two atoms one at the origin and one displaced by one-half the body diagonal of the conventional cell. 

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 A2.5.18. Body-centred cubic arrangement of (3-brass (CiiZn) at low temperature showing two interpenetrating simple cubic superlattices, one all Cu, the other all Zn, and a single lattice of randomly distributed atoms at high temperature. Reproduced from Hildebrand J H and Scott R L 1950 The Solubility of Nonelectrolytes 3rd edn (New York Reinliold) p 342.

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]-...

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851. 

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.

At 31OC, lanthanum changes from a hexagonal to a face-centered cubic structure, and at 865C it again transforms into a body-centered cubic structure. 

The metal has a bright silvery metallic luster. Neodymium is one of the more reactive rare-earth metals and quickly tarnishes in air, forming an oxide that spalls off and exposes metal to oxidation. The metal, therefore, should be kept under light mineral oil or sealed in a plastic material. Neodymium exists in two allotropic forms, with a transformation from a double hexagonal to a body-centered cubic structure taking place at 863oC. 

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. 

Mole fraction basis 7x Body-centered cubic bcc... 

Molybdenum hexafluoride [7783-77-9] MoF, is a volatile liquid at room temperature. It is very moisture sensitive, hydrolysing immediately upon contact with water to produce HF and molybdenum oxyfluorides. MoF should therefore be handled in a closed system or in a vacuum line located in a chemical hood. The crystals possess a body-centered cubic stmcture that changes to orthorhombic below —96° C (1,2). The known physical properties are Hsted in Table 1. 

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. 

Fig. 1. Iron—carbon phase diagram, where a is the body-centered cubic (bcc) a-iron, y is the face-centered cubic y-iron, and Fe C is iron carbide(3 l)...

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

Lithium magnesium alloys, developed during World War 11, have found uses in aerospace appHcations. Lithium alters the crystallization of the host magnesium from the normal hexagonal stmcture to the body-centered cubic stmcture, with resultant significant decreases in density and increases in ductibiHty. 

Iron (qv) exists in three aHotropic modifications, each of which is stable over a certain range of temperatures. When pure iron free2es at 1538°C, the body-centered cubic (bcc) 5-modification forms, and is stable to 1394°C. Between 1394 and 912°C, the face-centered cubic (fee) y-modification exists. At 912°C, bcc a-iron forms and prevails at all lower temperatures. These various aHotropic forms of iron have different capacities for dissolving carbon. y-Iron can contain up to 2% carbon, whereas a-iron can contain a maximum of only about 0.02% C. This difference in solubHity of carbon in iron is responsible for the unique heat-treating capabilities of steel The soHd solutions of carbon and other elements in y-iron and a-iron are caHed austenite and ferrite, respectively. 

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