Structure types body-centred cubic

WoWj/2 the body-centred cubic structure of W (1 atom in 0, 0, 0 and 1 atom in A, A, /) corresponds to a sequence of type 1 and type 4 square nets at the heights 0 and A, respectively. Note, however, that for a fall description of the structure, either in the hexagonal or the tetragonal case, the inter-layer distance must be taken into account not only in terms of the fractional coordinates (that is, the c/a axial ratio must be considered). For more complex polygonal nets, their symbolic representation and use in the description, for instance, of the Frank-Kasper phases, see Frank and Kasper (1958) and Pearson (1972). 

Another contribution is represented by an investigation of a cubic thallium cluster phase of the Bergmann type Na13(TlA.Cdi A.)27 (0.24 < x <0.33) (Li and Corbett 2004). For this phase too the body centred cubic structure (space group Im 3, a = 1587-1599 pm) may be described in terms of multiple endo-hedral concentric shells of atoms around the cell positions 0, 0, 0, and 14,14,14. The subsequent shells in every unit are an icosahedron (formed by mixed Cd-Tl atoms), a pentagonal dodecahedron (20 Na atoms), a larger icosahedron (12 Cd atoms) these are surrounded by a truncated icosahedron (60 mixed Cd-Tl atoms) and then by a 24 vertices Na polyhedron. Every atom in the last two shells is shared with those of like shells in adjacent units. A view of the unit cell is shown in Fig. 4.38. According to Li and Corbett (2004), it may be described as an electron-poor Zintl phase. A systematic description of condensed metal clusters was reported by Simon (1981). 

Their normal crystal structure, at ambient conditions, corresponds to the body-centred cubic cI2-W-type structure. At very low temperatures, the close-packed hexagonal hP2-Mg-type structure has been observed for Li and Na, while for Rb and Cs the face-centred cubic close-packed cF4-Cu-type structure is known at high pressure. No polymorphic transformation has been reported for potassium. 

The body-centred cubic W-type structure. The W-type structure is another important structure of metallic elements it is common to a number of metals Li, Na, K, Rb, Ba, Cs, Eu, Cr, Mo, Y Ta, W, etc. (as the only room temperature stable form), Be, Ca, Sr, several rare earth elements, Th, etc. (as a high-temperature form) and a and 8 Fe forms. The data relevant to the prototype are reported in the following. 

The W body-centred cubic structure can be compared with the simple cubic CsCl-type structure (which can be obtained from the W type by an ordered substitution of the atoms) and with the MnCu2Al-type structure ( ordered superstructure of the CsCl type) see Fig. 3.31 and notice the typical eight (cubic) coordination. 

The In cell may be considered a distortion of the Cu type, face-centred cubic, cell. The unconventional face-centred tetragonal cell (equivalent to the tI2 cell), corresponds to a = aJY = 459.8, c = c = 494.7 and c /a = 1.076. Protactinium has a similar structure, which however with a c/a value lower than one, can be considered a distortion of the body-centred cubic structure. 

Fig. 1.1 The three commonest elemental structure types (a) face-centred cubic, (b) hexagonal close-packed, and (c) body-centred cubic. From Wells (1986).

The ten most commonly occurring structure types in order of frequency are NaCl, CsCl, CrB, FeB, NiAs, CuAu, cubic ZnS, MnP, hexagonal ZnS, and FeSi respectively. Structures cF8 (NaCl) and cP2 (CsCl) are ordered with respect to underlying simple cubic and body-centred cubic lattices respectively, as is clear from Figs 1.10(a) and 1.11(a). The Na, G sites and Cs, Cl sites are, therefore, six-fold octahedrally coordinated and fourteen-fold rhombic dodecahedrally coordinated, respectively, as indicated by the Jensen symbols 6/6 and 14/14. 

In body-centred cubic coordination, the eight ligands surrounding a transition metal ion lie at the vertices of a cube (cf. fig. 2.6a.). In one type of dodecahedral coordination site found in the ideal perovskite structure (cf. fig. 9.3), the 12 nearest-neighbour anions lie at the vertices of a cuboctahedron illustrated in fig. 2.6b. The relative energies of the eg and t2g orbital groups in these two cen-trosymmetric coordinations are identical to those of the e and t2 orbital groups... 

Amphiphilic lipopeptides with a hydrophobic paraffinic chain containing from 12 to 18 carbon atoms and a hydrophilic peptidic chain exhibit lyotropic meso-phases and good emulsifying properties. The X-ray diffraction study of the mesophases and of dry lipopeptides showed the existence of three types of mesomorphic structures lamellar, cylindrical hexagonal and body-centred cubic. Two types of polymorphism were also identified one as a function of the length of the peptidic chain and the other as a function of the water content of the mesophases. The emulsifying properties of the lipopeptides in numerous pairs of immiscible liquids such as water/ hydrocarbons and water/base products of the cosmetic industry showed that small amounts of lipopeptides easily give three types of emulsions simple emulsions, miniemulsions and microemulsions. 

The crystal structure of the elements is given in Table CXXXVIII in which the type of structure is indicated in the following way Ai cubic close packed (face centred), A2 body centred cubic, A3 hexagonal close packed and A4 diamond. The interatomic distances and the number of atoms at that distance are also given. 

First preliminary variants of DDM were applied in the full-profile X-ray diffraction structure analysis of a series of new silica mesoporous materials and ordered nanopipe mesostructured carbons. DDM allowed stable back-ground-independent full-profile refinement of the structure parameters of these advanced nanomaterials, a result that was unattainable by any other method. To date, DDM has been applied to many various mesoporous and mesostructured substances. The structural parameters of a series of face-centred cubic (Fm3m), body-centred cubic Im3m), and two-dimensional hexagonal (pGmm) mesoporous silicates were determined by DDM from synchrotron XRD. A comprehensive structural analysis of mesoporous silicates SBA-16 (cage-type cubic Irriim), their carbon replicas, and silica/carbon composites was performed by applying DDM. The structure of MCM-48 mesoporous silicate materials was analysed in detail by DDM from different laboratory and synchrotron XRD data. The pore wall thickness of both as-made and... 

By examining Figures 3.7 and 3.32, we note that the caesium cations sit on a primitive cubic unit cell (lattice type P) with chloride anion occupying the cubic hole in the body centre. Alternatively, one can view the structure as P-type lattice of chloride anions with caesium cation in cubic hole. Keep in mind that caesium chloride does not have a body centred cubic lattice although it might appear so at a first glance. The body centred lattice has all points identical, whereas in CsCl lattice the ion at fte body centre is different from those at the comers. 

Most pure metals adopt one of three crystal structures, Al, copper structure, (cubic close-packed), A2, tungsten structure, (body-centred cubic) or A3, magnesium structure, (hexagonal close-packed), (Chapter 1). If it is assumed that the structures of metals are made up of touching spherical atoms, (the model described in the previous section), it is quite easy, knowing the structure type and the size of the unit cell, to work out their radii, which are called metallic radii. The relationships between the lattice parameters, a, for cubic crystals, a, c, for hexagonal crystals, and the radius of the component atoms, r, for the three common metallic structures, are given below. 

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