Rhombohedral structure

Boron carbide is a non-metallic covalent material with the theoretical stoichiometric formula, B4C. Stoichiometry, however, is rarely achieved and the compound is usually boron rich. It has a rhombohedral structure with a low density and a high melting point. It is extremely hard and has excellent nuclear properties. Its characteristics are summarized in Table 9.2. 

Further effects seen with the substitution of Cl for T in the [(Zr6Z)Ii2] type are a reduction of inter-cluster I I repulsions which allows for a reduction in Zr-I inter-cluster bond lengths. The [110] section of this rhombohedral structure is shown in Fig. 5.3 and illustrates that the clusters can be described as a cubic-close-packed array, with the 3 axes running vertically through Z. Phase widths found are 0[Pg.63]

It is usually difficult to discuss unambiguously on the role of the formation of sulphate, which may explain the deactivation. Their formation can equally occur on the support and on the noble metals. The poisoning effect of S02 has been reported by Qi el al. on Pd/Ti02/Al203 [112], However, in the presence of water, the stabilisation of hydroxyl groups could inhibit the adsorption of S02 [113], Burch also suggested a possible redispersion of palladium oxide promoted by the formation of hydroxyl species [114], Such tentative interpretations could correctly explain the tendencies that we observed irrespective to the nature of the supports, which indicate an improvement in the conversion of NO into N2 at high temperature. Nevertheless, the accentuation of those tendencies particularly on prereduced perovskite-based catalysts could be in connection with structural modifications associated with the reconstruction of the rhombohedral structure of... 

Also known for some time is a phase transition at low temperature (111K), observed in studies with various methods (NQR, elasticity measurement by ultrasound, Raman spectrometry) 112 temperature-dependent neutron diffraction showed the phase transition to be caused by an antiphase rotation of adjacent anions around the threefold axis ([111] in the cubic cell) and to lower the symmetry from cubic to rhombohedral (Ric). As shown by inelastic neutron scattering, this phase transition is driven by a low-frequency rotatory soft mode (0.288 THz 9.61 cm / 298 K) 113 a more recent NQR study revealed a small hysteresis and hence first-order character of this transition.114 This rhombohedral structure is adopted by Rb2Hg(CN)4 already at room temperature (rav(Hg—C) 218.6, rav(C—N) 114.0 pm for two independent cyano groups), and the analogous phase transition to the cubic structure occurs at 398 K.115... 

Rhombic prism lattice, 8 114t Rhombohedral structure, of ferroelectric crystals, 11 95, 96 Rhombohedron lattice, 8 114t Rhomboidal symmetry, 8 114t Rhone-Poulenc process, 24 482, 485 Rhovanil extra pure vanillin, 25 548t, 549-550... 

The results of a similar analysis of the intermetallic hexagonal structure types have been reported by Daams and Villars (1994). Of 442 structure types, 315 (clearly intermetallic and correctly refined) were considered. In this case too it was observed that a small group of atomic environments is greatly preferred. The 23 AET most frequently occurring in the 315 hexagonal structure types are reported in the following list (to be compared with those previously reported for cubic and rhombohedral structure types) ... 

According to Pearson (1972) the rhombohedral structure of these elements can be considered a distortion of a simple cubic structure in which the d2/d ratio would be 1. The decrease of the ratio on passing from As to Bi, and the corresponding relative increase of the strength of the X-X interlayer bond (passing from a coordination nearly 3, as for the 8 — eat rule, to a coordination closer to 6) can be related to an increasing metallic character. 

Pinkish-red translucent crystals hexagonal-rhombohedral structure refractive index 1.597 density 3.70 g/cm hardness 3.8 Mohs decomposes above 200°C slightly soluble in water Ksp2.24xl0-ip soluble in dilute acids. 

Colorless crystalline solid rhombohedral structure decomposes at 73.5°C decomposes in water soluble in sulfuric acid. 

Colorless transparent crystals or white granular or crystalline powder rhombohedral structure density 2.11 g/cm at 20°C melts at 334°C decomposes at 400°C evolving oxygen soluble in cold water, 13.3 g/lOOmL at 0°C highly soluble in boiling water, 247 g/lOOmL at 100°C lowers the temperature of water on dissolution very slightly soluble in ethanol soluble in glycerol and liquid ammonia. 

Colorless crystalline solid saline taste trigonal, and rhombohedrals structure density 2.257g/cm3 refractive index 1.587 (trigonal) and 1.336 (rhombo-... 

Ternary fluorides Cs2MeF4 on the other hand, containing the large cesium ions, are known of several transition element ions Me +. They crystallize in rhombohedral structures with large sizes of the unit cells z = 14) 8). Detailed information about the coordination of Me and Cs in these compounds is not yet available. 

Unique is the compound MnFg, subjected to the Jahn-Teller effect, by which the MnFg-octahedra are strongly distorted. Three different Mn—F-distances (1.79 and 1.91 and 2.09 A) are displayed and the pseudo-rhombohedral structure of this compound represents a distorted version of the VF3-t5q)e (138). 

FIGURE 9.16 Distortions of TiOe octahedra in (a) the tetragonal structure, (b) the orthorhombic, and (c) the rhombohedral structures of barium titanate. 

High-temperature modifications generally have lower coordination numbers, just as low-pressure modifications do. Structures of certain metals such as Zn, Cd and Hg do not conform to this pattern. Mercury has a rhombohedral structure in which each atom is six-coordinated following the (8 — N) rule indicating the presence of the covalent... 

Figure 1.42 Structure of M MOgXg Chevrel phases (a) the MOgXg building unit and (b) the stacking of eight MogXg units in the rhombohedral structure. The cube-shaped cavity at the centre is occupied by the large M atom. (After Yvon, 1979.)...

The structure of presolar silicon carbide grains can provide information about the conditions of formation. Crystalline silicon carbide is known to form about 100 different polytypes, including cubic, hexagonal, and rhombohedral structures. Presolar silicon carbide exists in only two of these, a cubic (fi-SiC) polytype and a hexagonal (a-SiC) polytype (Daulton et al.,... 

Intriguing forms of competition between superconductivity and ferromagnetism have recently been reported for the elements carbon and iron, where the two cooperative phenomena are related to different crystallographic structures. As discussed in section 1.1 pristine C60 consisting of dominantly van der Waals bounded molecules becomes superconducting if doped by electrons or holes. On the other hand, under sufficiently high pressure and temperature, a layered rhombohedral structure of Cft) forms where, within the layers, the C60 molecules are covalently bound. This phase is metastable at room temperature and ambient pressure. It shows a spontaneous magnetization, which is assumed to be based on unpaired electrons created by structure defects (Makarova et al. 2001 Xu and Scuseria 1995). 

Properties. Boron carbide has a rhombohedral structure consisting of an array of nearly regular icosahedra, each having twelve boron atoms at the vertices and three carbon atoms in a linear chain outside the icosahedra (3,4,6,7). Thus a descriptive chemical formula would be B12C3 [12075-36 4], Each boron atom is bonded to five others in the icosahedron as well as either to a carbon atom or to a boron atom in an adjacent icosahedron. The structure is similar to that of rhombohedral boron (see Boron, elemental). The theoretical density for B12C3 is 2.52 g/mL. The rigid framework of... 

Crystal Structure. Silicon carbide may crystallize in the cubic, hexagonal, or rhombohedral structure. There is a broad temperature range where these structures may form. The hexagonal and rhombohedral structure designated as the a-form (noncubic) may crystallize in a large number of polytypes. 

Chromium(III) oxide crystallizes in the rhombohedral structure of the corundum type space group D3d-R3c, Q 5.2 g/cm3. Because of its high hardness (ca. 9 on the Mohs scale) the abrasive properties of the pigment must be taken into account in certain applications [3.44], It melts at 2435 °C but starts to evaporate at 2000 °C. Depending on the manufacturing conditions, the particle sizes of chromium oxide pigments are in the range 0.1-3 pm with mean values of 0.3-0.6 pm. Most of the particles are isometric. Coarser chromium oxides are produced for special applications, e.g., for applications in the refractory area. 

This hydrolysis of the anhydrous fluoride can be easily effected by heating it at 800° C in a current of moist air. All rare earth oxyfluorides except CeOF, have the rhombohedral structure (LaOF type). The lattice constants for EuOF are a = 6.827 0.002 A and a = 33.05 0.02°. 

The most common valence states of arsenic are —3, 0, +3, and +5 (Shih, 2005), 86. The —3 valence state forms through the addition of three more electrons to fill the 4p orbital. In the most common form of elemental arsenic (As(0)), which is the rhombohedral or gray form, each arsenic atom equally shares its 4p valence electrons with three neighboring arsenic atoms in a trigonal pyramid structure ((Klein, 2002), 336-337 Figure 2.1). The rhombohedral structure produces two sets of distances between closest arsenic atoms, which are 2.51 and 3.15 A (Baur and Onishi, 1978), 33-A-2. The +3 valence state results when the three electrons in the 4p orbital become more attracted to bonded nonmetals, which under natural conditions are usually sulfur or oxygen. When the electrons in both the 4s and 4p orbitals tend to be associated more with bonded nonmetals (such as oxygen or sulfur), the arsenic atom has a +5 valence state. 

The index usually indicates the sequence cubic (3), hexagonal (2), or double hexagonal (4) for the ABAC sequence. The Pearson symbols (Table 2.5) can clarify cases such as hexagonal structures with an ABC sequence and a = 3 for the index. The symbols t for tetragonal, o for orthorhombic, m for monoclinic, and h for hexagonal, rhombohedral, or trigonal indicate the type of distortion of an idealized structure. Without distortion, a = 3 is for a cubic structure and a = 2 is for a hexagonal (or rhombohedral) structure. 

The notation is IP 5y3PA1. Figure 9.20 shows two layers of four cells of the hexagonal structure of WAI5 with two molecules per cell, a0 = 4.902 and c0 = 8.851 A. Each atom has CN 12. There are no W—W close neighbors. M0AI5 has a rhombohedral structure related to WAI5. 

Besides orthorhombic f/ and O phases, the defected LaMn03 is observed in monoclinic and rhombohedral phases [5]. The monoclinic one is observed at low temperatures and with an increase of temperature it transforms to rhombohedral structure. 

The rhombohedral structure, obtained via the optimization of crystal energy [equation (1)] without the JT term inclusion or setting IVj = 0, is stable with respect to deformations of the crystal. The experimental and calculated structure parameters are listed in Table 2. As the temperature decreases down to about 400 K [5,8] the crystal symmetry changes to monoclinic phase. The major difference between the monoclinic and rhombohedral phases is the presence of JT distortions and a doubled primitive cell. The local values of JT distortions on different Mn3+ ions could be obtained via the projection of oxygen ions coordinates onto the normal local Eg modes of each [Mn06] octahedra (the numbering of Mn3+ is carried out according to Fig. 1). 

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