Body-centered cubic lattice structure

Gray, heavy, and very hard metal malleable and ductile body-centered cubic lattice structure the density of the metal 16.65 g/cm at 20°C and that of powder 14.40 g/cm melts at 2,996°C vaporizes around 5,458°C electrical resistivity 13.1 microhm-cm at 25°C modulus of elasticity 27x10 psi Poisson s ratio 0.35 magnetic susceptibility 0.849x10 cgs units at 25°C insoluble in water, alcohol and practically all acids soluble in hydrofluoric acid... 

When cooled, pure iron solidities at about 1.5.1b C as delta iron, having a body-centered cubic lattice structure. This form changes allmropically to... 

Figure 5.19 Small-angle neutron scattering intensity obtained with a styrene-butadiene diblock copolymer having spherical butadiene microdomains. The peaks at very small q are due to a body-centered cubic lattice structure of ordered microdomains. The solid curve is the calculated intensity of independent scattering from solid spheres of mean radius 124 A. (From Bates etal.34)...

After the fused iron catalysts with Fe304 or Fei xO as precursor are reduced, in which the oxygen anions are removed out and the iron cations form the a-Fe crystallites with body centered cubic lattice structures as shown in Fig. 3.76. Both... 

Blue phases I and II show cubic 3D lattice stmctures. Figure 8.14a-d shows the unit cell structures of blue phases 1 and n, respectively. Blue phases I and II have a body-centered cubic lattice structure and a simple cubic lattice structure, respectively, with lattice constants of several 100 nm. 

FIG. 5 A crystalline structure. The particles are located near preferred lattice sites. A body-centered cubic (bcc) structure is shown. 

The /3-alloys are different in nature from the 7-alloys and the a-manganese and /3-manganese structures discussed above, in that they are not complex structures, but are simple, being based upon the body-centered arrangement. /3-Brass, for example, has either a disordered structure, above 480°K, the copper and zinc atoms in essentially equal number being distributed largely at random over the points of a body-centered cubic lattice, or an ordered structure, below 300°K, with copper and zinc at the positions 000 and, respectively, of the cubic unit. Moreover, the physical properties of /3-brass are not those that indicate a filled zone structure. 

Although the comer atoms must move apart to convert a simple cube into a body-centered cube, the extra atom in the center of the stracture makes the body-centered cubic lattice more compact than the simple cubic structure. All the alkali metals, as well as iron and the transition metals from Groups 5 and 6, form ciystals with body-centered cubic structures. 

A theoretical interpretation relating the valence electron concentration and the structure was put forward by H. Jones. If we start from copper and add more and more zinc, the valence electron concentration increases. The added electrons have to occupy higher energy levels, i.e. the energy of the Fermi limit is raised and comes closer to the limits of the first Brillouin zone. This is approached at about VEC = 1.36. Higher values of the VEC require the occupation of antibonding states now the body-centered cubic lattice becomes more favorable as it allows a higher VEC within the first Brillouin zone, up to approximately VEC = 1.48. 

Figure 9.2 is schematic diagram of the crystal structure of most of the alkali halides, letting the black circles represent the positive metal ions (Li, Na, K, Rb, and Cs), and the gray circles represent the negative halide ions (F, Cl, Br, and I).The ions lie on two interpenetrating face-centered-cubic lattices. Of the 20 alkali halides, 17 have the NaCl crystal structure of Figure 9.1. The other three (CsCl, CsBr, and Csl) have the cesium chloride structure where the ions lie on two interpenetrating body-centered-cubic lattices (Figure 9.3). The plastic deformation on the primary glide planes for the two structures is quite different.

A simple icosahedral structure 1 is that of MoAlx, WAlia, and (Mnr Cr)Alu. In this structure, based on a body-centered cubic lattice,... 

Assuming the same crystal structure, explain why the density of vanadium (6.11 g-cm-3) is significantly less than that of chromium (7.19 g-cm-3). Both vanadium and chromium crystallize in a body-centered cubic lattice. 

Let us now turn to the structure factors of Eq. (16-5), to determine them first for the perfect crystal. What we do here is formulate the diffraction theory for crystal lattices, since the interaction of the electron waves with the crystal is a diffraction phenomenon. A perfect crystal is characterized by a set of lattice translations T that, if applied to the crystal, take every ion (except those near the surface) to a position previously occupied by an equivalent ion. The three shortest such translations that arc not coplanar are called pihuitive translations, t, Tj, and Tj, as indicated in Section 3-C. For the face-centered cubic structure, described also in Section 3-A, such a set is [011]a/2, [101]u/2, [ll0]a/2. The nearest-neighbor distance is d = n 2/2. Replacing one of these by, for example, [0lT]a/2, would give an equivalent set. For a body-centered cubic lattice, such a set is [Tll]u/2, [lTl]a/2, and [11 l]ti/2, and the nearest-neighhor distance is For each of these struc-... 

That is, among the pure iron forms, only ferrite (a, bcc) is magnetic. This is intriguing, as the 5-Fe form also exhibits a body-centered cubic crystal structure. This must indicate that in addition to the simple 3D arrangement of lattice iron atoms, their individual magnetic dipoles must also be suitably aligned in order to yield a particular magnetic behavior. 

Manganese crystallizes in a structure that has a body-centered cubic lattice. What is the coordination number (number of nearest neighbors) for Mn in this structure, and how many atoms are there in each unit cell ... 

Documentation exists in the literature as to the observation of anomalies in the temperature dependence of some physical properties of vanadium in the range 175-325 K. Although the anomaly was attributed by different workers to an antiferromagnetic transition, a small distortion of the body-centered cubic crystal structure, and impurities, Finkel et al. ( ) recently ascribed the anomaly to a second order phase transition at 230 K. Using low temperature x-ray diffraction techniques in the study of a single crystal of vanadium, Finkel et al. observed a decrease in crystal lattice symmetry form body-centered cubic (T > 230... 

The alkali metals crystallize in the body-centered cubic (bcc) structure at atmospheric pressure (Fig. 21.12). A unit cell of this structure contains two lattice points, one at the center of the cube and the other at any one of the eight corners. A single alkali-metal atom is associated with each lattice point. An alternative way to visualize this is to realize that each of the eight atoms that lie at the corners of a bcc unit cell is shared by the eight unit cells that meet at those corners. The contribution of the atoms to one unit cell is therefore 8 X = 1 atom, to which is added the atom that lies wholly within that cell at its center. 

Sketch a two-dimensional plane of the reciprocal lattice for a body-centered cubic (BCC) structure with a plane normal as [001],... 

OL-Tungsten is the only stable modification. It has a body-centered cubic lattice of space group - Im3m (No. 229). A diffraction pattern is shown in Fig. 1.7, together with a crystal structure model. 

Fig. 27 a-c. Some coloring problems, a) Attachment of donors and acceptors to square cyclobutadiene, b) Two arrangements of the B and N atoms over the graphite net in BN. (Only the fully alternating one is found in practice), c) The CsCl and CuTi structures which result from the body centered cubic lattice... 

In the X-ray studies of Luo et al. the j8-Po phase could be observed up to at least 212 CiPa, the highest pressure achieved in the experiments [200]. From an analogy of the ratio of the lattice constants da in Se and Te (-0.72), at pressures where the body-centered cubic bcc) structure is reached, a similar transition for sulfur was estimated to take place around 700 GPa [200]. 

Fig. 69. (a) Part of the body-centered cubic lattice ordered in the B2 structure (left part) and in the Dtp structure (right part). Left part shows assignment of four sublattices a, b, c and d, In the B2 structure (cf. also fig. 66a), the concentrations of A atoms are the same at the a and c sublatticcs, but differ from the concentrations of the b, d sublattices, while in the DOj structure the concentration of the b sublattice differs from that of the d sublatlice, but both differ from those of the a, c sublattices (which are still the same). In terms of an Ising spin model, these sublattice concentrations translate into sublattice magnetizations mu, mu, mc, m,i, which allow to define three order parameter components / = ma + mL- — mu — m,/, fa = m - mc + mu — m,j, and fa = -ma + m., + mu — nij. 

It is shown, that chromium and molybdenum coatings have ultra-fine grain structure (Fig. 1). So, the grains size in 80 and 400 nm thickness chromium and molybdenum coatings are equal to 40 -50 nm and 20 nm accordingly. The diffraction pattern shows that only lines corresponding to lines body-centered cubic lattices chromium and molybdenum are precisely fixed, additional lines are not revealed. 

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