Body-centered cubic pattern

Powder patterns of cubic substances can usually be distinguished at a glance from those of noncubic substances, since the latter patterns normally contain many more lines. In addition, the Bravais lattice can usually be identified by inspection there is an almost regular sequence of lines in simple cubic and body-centered cubic patterns, but the former contains almost twice as many lines, while a face-centered cubic pattern is characterized by a pair of lines, followed by a single line, followed by a pair, another single line, etc. 

For additional symbols of further packings cf. [38, 156], T (triangular) refers to hexagonal layers, Q to layers with a periodic pattern of squares. The packing Qs yields a primitive cubic lattice (Fig. 2.4), Qf a body-centered cubic lattice (cf. Fig. 14.3, p. 153). Sometimes the symbols are set as superscripts without the angular brackets, for example Ti[Ca03]c. 

The chemistry of Scheme 2 produces a cubic pore structure with long-range periodicity and unit cell parameter (Ko) of 8.4 nm. The material show a relatively large number of Bragg peaks in the X-ray diffraction (XRD) pattern, which can be indexed as (211), (220), (321), (400), (420), (332), (422), (431), (611), and (543) Bragg diffraction peaks of the body-centered cubic Ia-3d symmetry (Fig. 1). 

Phase analysis and texture of the metal particles. Iron powders are constituted of the a-Fe phase with a body-centered cubic (bcc) lattice, whereas Fe-Co powders appear as a mixture of three phases that are quite similar to those of pure metals (bcc for a-Fe and a mixture of hep and fee for cobalt) (6). In the Fe.Nil(m system, a single fee phase is observed over the whole available composition range U s 25) with a linear dependence of the lattice parameter versus z, which shows the existence of a fee solid solution as already evidenced for the Co.rNiu)o-. system (33). The XRD patterns of the Fe [CovNi(1()o -,v)] i - powders depend on the composition An fee phase is always observed either as a single phase or as the main phase a second hep phase with weak and broad lines appears for a cobalt content x > 35 a third body-centered cubic (hcc) phase can be evidenced when x > 80. 

Lyotropic liquid crystals form in solutions of polar molecules such as soap in water. One end of the molecule is hydrophilic and the other end is hydrophobic. The molecules are aligned such that the hydrophilic end is exposed to water and the hydrophobic end is shielded from the water. There are several forms. The molecules may be arranged in lamellae or spherical units (Figure 16.7). The spherical units tend to be arranged in body-centered cubic arrays. The lamellae may be flat or rolled up to form columns that are arranged in hexagonal patterns. 

H3PW12O40 is one of the most common heteropoly compounds. A distinct X-ray diffraction pattern is seen for H3PWi2O40.6H2O, where the Keggin units are linked by H+(H20)2 bridges, resulting in a body-centered cubic structure and hence the X-ray diffraction pattern. The water molecules can be easily replaced by a number of polar molecules such as alcohols and amines (Misono, 1987). 

In general terms, transition metals are those which have incompletely filled d-bands. The progression in the filling of the d-band in the first long-transition metal series is as follows Ti(HCP), V(BCC), Cr(BCC), Fe(BCC), Co(FCC), Ni(FCC), Cu(FCC), Zn(HCP), and is not highly influenced by the structural difference between the body-centered cubic (BCC) and face-centered cubic (FCC) lattices. However, this is not the case for the hexagonal close-packed (HCP) lattice [10], An analogous pattern is expected for the second and third series. 

Refers to the Miller indices (Shkl) values) that are absent from the diffraction pattern. For instance, a body-centered cubic lattice with no other screw axes and glide planes will have a nonzero intensity for all reflections where the sum oi Qi + k + 1) yields an odd number, such as (100), (111), etc. other reflections from planes in which the sum of their Miller indices are even, such as (110), (200), (211), etc. will be present in the diffraction pattern. As these values indicate, there are three types of systematic absences three-dimensional absences (true for all hkl) resulting from pure translations (cell centering), two-dimensional absences from glide planes, and one-dimensional absences from screw axes.[261... 

X-ray Diffraction of Pure MoFe, High Temperature Form. X-ray diffraction powder photographs of MoFe taken at 10 °C. can be indexed on the basis of a body-centered cubic unit cell with a lattice constant, a = 6.23 zb 0.01 A. The similarity of the MoFe diffraction pattern to that of molybdenum metal indicates that the molybdenum atoms in the hexafluoride, as in the metal, are located at the body center and comers of a cube. 

Sketch diffraction patterns of single crystals in a TEM for (a) a face-centered cubic (FCC) crystal with transmitted beam direction (B) parallel to [001], and (b) a body-centered cubic (BCC) crystal with B= [001],... 

Changes of this nature are not uncommon among phase transformations and ordering reactions. For example, the powder pattern of slowly cooled plain carbon steel shows lines due to ferrite (body-centered cubic) and cementite (FcsC,... 

This ratio is so low that the superlattice lines of ordered CuZn can be detected by x-ray diffraction only under very special circumstances. (The powder pattern of this alloy, ordered or disordered, ordinarily appears to be that of a body-centered cubic substance.) The same is true of any superlattice of elements A and B which differ in atomic number by only one or two units, because the superlattice-line intensity is generally proportional to (/a — /b). ... 

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. 

Properties XRD pattern between those of Y2O3 (body-centered cubic) and CeO2 (face-centered cubic), IR spectrum available, particle diameter 80 nm, specific surface area 15 m /g [2154]. 

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. 

Fig. la-c. X-Ray diffraction patterns of the body centered cubic (Aspect No. 8) phase from hydrated monoolein recorded on X-ray sensitive film (a) and monoelaidin recorded on Kodak image plates (b). A 360° radial average of the scattered X-ray intensity recorded in (b) is shown in (c) at relative magnifications of xl and x3.2. Radial position is shown in units of mm corresponding to the actual distance on the image plate from the center of the pattern. The patterns in (a) and (b) were recorded with exposures of 15 min and lO s, respectively... 

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