BCC crystal structure

It is relatively common for DFT calculations to not explicitly include electron spin, for the simple reason that this approximation makes calculations faster. In materials where spin effects may be important, however, it is crucial that spin is included. Fe, for example, is a metal that is well known for its magnetic properties. Figure 8.10 shows the energy of bulk Fe in the bcc crystal structure from calculations with no spin polarization and calculations with ferromagnetic spin ordering. The difference is striking electron spins lower the energy substantially and increase the predicted equilibrium lattice constant by 0.1 A. 

Molybdenum, niobium, and tantalum (bcc crystal structure) form a continuous series of solid solutions with tungsten, but only Nb and Ta additions lead to a strong straining effect. Higher additions of Nb and Ta raise the recrystallization temperature but also increase the DBTT and thus decrease the workability. Therefore, none of these binary or ternary tungsten base alloys developed in the past [6.2] has attained commercial importance. The only important tungsten-base solid-solution alloy today is tungsten-rhenium. 

Pure barium is a silvery-white metal, although contamination with nitrogen produces a yellowish color. The metal is relatively soft and ductile and may be worked readily. It is fairly volatile (though less so than magnesium), and this property is used to advantage in commercial production. Barium has a bcc crystal structure at atmospheric pressure, but undergoes solid-state phase transformations at high pressures (2,3). Because of such transformations, barium exhibits pressure-induced superconductivity at sufficiendy low temperatures (4,5). 

Table 2.4. Canonical bandwidths (P scale) obtained from the second moment wjv s the canonical bands (Tables 2.1,2) w, and the Wigner-Seitz rule (2.23) ww, for fee and bcc crystal structures ... 

An interesting phenomenon has been observed on reduction of iron. The surfactant chemistry has influenced the iron crystal structure. If the anionic surfactants (such as AOT) are used, we obtain a-Fe with a body-centered (bcc) crystal structure [198]. If the nonylphenol polyethoxylate surfactant is used, the crystals with the face-centered (fee) lattice are formed [199]. Similar data are known for metallic alloys. For this purpose, a mixture of metal salts has been subjected to the joint reduction [200]. It is essential that the reduction happens simultaneously with the formation of multication phases. 

Figure 3.12 Schematic of the unit cell of a cubic body-centered (bcc) crystal structure.

Figure 1 Metals tend to crystallize as vay simple structures. For example (a) Al, Ca, Ni, Cu, Ag, Au, Pt, and Pb adopt cubic close-packing (ccp) (b) Be, Mg, Ti, Zr, Co, Zn, and Cd hexagonal close-packing (hep) and (c) Cr, Fe, Mo, W, and aU alkali metals body-centered cubic (bcc) crystal structures.

There is a similarity between the hexagonal close-packed (HOP) and body-centered cubic (bcc) crystal structures. 

Figure 3.1. Surfaces of the fee and bcc crystal structures (from Niemantsverdriet, 1993).

The irradiation embrittlement of ferritic steel is a special manifestation of low-temperature brittleness. A transition from ductility to brittle failure with decreasing temperature is observed for many metals and alloys, but primarily for those with the body-centred cubic (bcc) crystal structure. This phenomenon was first explained via Ioffe s well-known scheme (Figure 4.18). In this scheme, the nature of brittle failure is determined by the ratio between the temperature-dependent flow stress (yield stress CTy) and the temperature-independent brittle fracture stress (cTbf), which characterise the material s resistance to the cleavage. 

However, none of the proposed mechanisms satisfactorily explain all experimental findings ([48] and references therein). For instance, it was experimentally observed that some bcc alloys, such as the V-5Fe alloy, exhibit swelling rates which can be as high as 2%/dpa [53], which is not consistent with the hypothesis of an intrinsic swelling resistance of the bcc crystal structure. 

Working and machining characteristics. The cold-working properties of niobium are excellent. Because of its body-centered cubic (bcc) crystal structure, niobium is a very ductile metal that can undergo cold reductions of more than 95% without failure. The metal can be easily forged,... 

Another common metallic crystal structure also has a cubic unit cell with atoms located at all eight corners and a single atom at the cube center. This is called a body-centered cubic (BCC) crystal structure. A collection of spheres depicting this crystal structure is shown in Figure 3.2c, whereas Figures 3.2a and 3.2b are diagrams of BCC unit cells with the atoms represented by hard-sphere and reduced-sphere models, respectively. Center... 

The coordination number for the BCC crystal structure is 8 each center atom has as nearest neighbors its eight corner atoms. Because the coordination number is less for BCC than for FCC, the atomic packing factor is also lower for BCC—0.68 versus 0.74. 

The atomic arrangement for a crystallographic plane, which is often of interest, depends on the crystal structure. The (110) atomic planes for FCC and BCC crystal structures are represented in Figures 3.12 and 3.13, respectively. Reduced-sphere unit cells are also included. Note that the atomic packing is different for each case. The circles represent atoms lying in the crystallographic planes as would be obtained from a slice taken through the centers of the full-size hard spheres. 

Calculate the radius of a tantalum (Ta) atom, O given that Ta has a BCC crystal structure, a... 

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