Rhombohedral Boron

The physical properties of elemental boron are significantly affected by purity and crystal form. In addition to being an amorphous powder, boron has four crystalline forms a-rhombohedral, P-rhombohedral, a-tetragonal, and -tetragonal. The a-rhombohedral form has mp 2180°C, sublimes at approximately 3650°C, and has a density of 2.45 g/mL. Amorphous boron, by comparison, has mp 2300°C, sublimes at approximately 2550°C, and has a density of 2.35 g/mL. 

Boron is an extremely hard refractory soHd having a hardness of 9.3 on Mohs scale and a very low (1.5 x 10 ohm cm ) room temperature electrical conductivity so that boron is classified as a metalloid or semiconductor. These values are for the a-rhombohedral form. 

The a-rhombohedral form of boron has the simplest crystal stmcture with slightly deformed cubic close packing. At 1200°C a-rhombohedral boron degrades, and at 1500°C converts to P-rhombohedral boron, which is the most thermodynamically stable form. The unit cell has 104 boron atoms, a central B 2 icosahedron, and 12 pentagonal pyramids of boron atom directed outward. Twenty additional boron atoms complete a complex coordination (2). 

Lower Oxides. A number of hard, refractory suboxides have been prepared either as by-products of elemental boron production (1) or by the reaction of boron and boric acid at high temperatures and pressures (39). It appears that the various oxides represented as B O, B O, B22O2, and B23O2 may all be the same material ia varying degrees of purity. A representative crystalline substance was determined to be rhombohedral boron suboxide, B12O2, usually mixed with traces of boron or B2O3 (39). A study has been made of the mechanical properties of this material, which exhibits a hardness... 

Properties. Boron carbide has a rhombohedral stmcture consisting of an array of nearly regular icosahedra, each having twelve boron atoms at the vertices and three carbon atoms ia a linear chain outside the icosahedra (3,4,6,7). Thus a descriptive chemical formula would be [12075-36-4]. 

Each boron atom is bonded to five others ia the icosahedron as well as either to a carbon atom or to a boron atom ia an adjacent icosahedron. The stmcture is similar to that of rhombohedral boron (see Boron, elemental). The theoretical density for B22C2 is 2.52 g/mL. The rigid framework of... 

Rhombohedral boron nitride can be prepared by heating a mixture of NaBH and NH Cl rapidly to 750—1000°C (15). The presence of NaCl appears to favor the rhombohedral form. 

The cubic 2inc blende form of boron nitride is usually prepared from the hexagonal or rhombohedral form at high (4—6 GPa (40—60 kbar)) pressures and temperatures (1400—1700°C). The reaction is accelerated by lithium or alkaline-earth nitrides or amides, which are the best catalysts, and form intermediate Hquid compounds with BN, which are molten under synthesis conditions (11,16). Many other substances can aid the transformation. At higher pressures (6—13 GPa) the cubic or wurt2itic forms are obtained without catalysts (17). 

Figure 6.2 Basal plane of a-rhombohedral boron showing close-packed arrangement of B 2 icosahedra. The B-B distances within each icosahedron vary regularly between 173-179 pm. Dotted lines show the 3-centre bonds between the 6 equatorial boron atoms in each icosahedron to 6 other icosahedra in the same sheet at 202.5 pm. The sheet-s are slacked so that each icosahedron is bonded by six 2-centre B-B bonds at 171 pm (directed rhombohedral ly, 3 above and 3 below the icosahedron). B12 units in the layer above are centred over 1 and those in the layer below are centred under 2.

The thermodynamically most stable polymorph of boron is the /3-rhombohedral modification which has a much more complex structure with 105 B atoms in the unit cell (no 1014.5 pm, a 65.28°). The basic unit can be thought of as a central Bn icosahedron surrounded by an icosahedron of icosahedra this can be visualized as 12 of the B7 units in Fig. 6.1b arranged so that the apex atoms form the central Bn surrounded by 12 radially disposed pentagonal dishes to give the Bg4 unit shown in Fig. 6.3a. The 12 half-icosahedra are then completed by means of 2 complicated Bjo subunits per unit cell,... 

The determination of precise physical properties for elemental boron is bedevilled by the twin difficulties of complex polymorphism and contamination by irremovable impurities. Boron is an extremely hard refractory solid of high mp, low density and very low electrical conductivity. Crystalline forms are dark red in transmitted light and powdered forms are black. The most stable ()3-rhombohedral) modification has mp 2092°C (exceeded only by C among the non-metals), bp 4000°C, d 2.35 gcm (a-rhombohedral form 2.45gcm ), A77sublimation 570kJ per mol of B, electrical conductivity at room temperature 1.5 x 10 ohm cm- . 

The structures of boron-rich borides (e.g. MB4, MBfi, MBio, MB12, MBe6) are even more effectively dominated by inter-B bonding, and the structures comprise three-dimensional networks of B atoms and clusters in which the metal atoms occupy specific voids or otherwise vacant sites. The structures are often exceedingly complicated (for the reasons given in Section 6.2.2) for example, the cubic unit cell of YB e has ao 2344 pm and contains 1584 B and 24 Y atoms the basic structural unit is the 13-icosahedron unit of 156 B atoms found in -rhombohedral B (p. 142) there are 8 such units (1248 B) in the unit cell and the remaining 336 B atoms are statistically distributed in channels formed by the packing of the 13-icosahedron units. 

Another compound which is even more closely related to /l-rhombohedral boron is boron carbide, B4C this is now more correctly written as but the phase can vary... 

Heteroatom fullerene-type clusters — The possibility of incorporation of hetero atoms into C clusters has excited the attention of both theoreticians and experimentalists since the earliest days of fullerene chemistry, particularly in view of the known stability and ubiquity of organic heterocycles. The structural relationship between Ceo and /3-rhombohedral boron has already been alluded to (p. 142). 

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. 

Poly crystalline boron nitride films, with a structure similar to rhombohedral boron carbide and a ratio of boron to nitrogen of 3 1, were produced by hot-filament CVD. This work indicates the possible existence of other boron-nitride structures. 

The interpretation proposed for the LnB phases can be extended to alkaline-earth and potassium hexaborides. These dissociate through metal evaporation, yielding a j3-rhombohedral boron residue at the mp for CaB , SrB5 and BaB , and at 750°C for KBft. 

Several of the claimed crystalline modifications of boron are not truly boron modifications but consist of phase mixtures or B-rich compounds formed under favorable kinetic conditions. The existence of the a- and /3-rhombohedral (a-rh and... 

The materials for solid solutions of transition elements in j3-rh boron are prepared by arc melting the component elements or by solid-state diffusion of the metal into /3-rhombohedral (/3-rh) boron. Compositions as determined by erystal structure and electron microprobe analyses together with the unit cell dimensions are given in Table 1. The volume of the unit cell (V ) increases when the solid solution is formed. As illustrated in Fig. 1, V increases nearly linearly with metal content for the solid solution of Cu in /3-rh boron. In addition to the elements listed in Table 1, the expansion of the unit cell exceeds 7.0 X 10 pm for saturated solid solutions " of Ti, V, (2o, Ni, As, Se and Hf in /3-rh boron, whereas the increase is smaller for the remaining elements. The solubility of these elements does not exceed a few tenths at %. The microhardness of the solid solution increases with V . Boron is a brittle material, indicating the accommodation of transition-element atoms in the -rh boron structure is associated with an increase in the cohesion energy of the solid. 

Table 1. Data on Solid Solutions in -Rhombohedral Boron ...

S. Solid Solution of Transition and Inner Transition Metals 6.7.2.5.3. Data on Solid Soiutions of -Rhombohedral Boron. 

S.3. Crystallographic Data on Solid Solutions of p-Rhombohedral Boron. 

Boron is as unusual in its structures as it is in its chemical behavior. Sixteen boron modifications have been described, but most of them have not been well characterized. Many samples assumed to have consisted only of boron were possibly boron-rich borides (many of which are known, e.g. YB66). An established structure is that of rhombohedral a-B12 (the subscript number designates the number of atoms per unit cell). The crystal structures of three further forms are known, tetragonal -B50, rhombohedral J3-B105 and rhombohedral j3-B 320, but probably boron-rich borides were studied. a-B50 should be formulated B48X2. It consists of B12 icosahedra that are linked by tetrahedrally coordinated X atoms. These atoms are presumably C or N atoms (B, C and N can hardly be distinguished by X-ray diffraction). 

The structural similarity of Al22Br2o 12(THF) 6 to (3-rhombohedral boron with the familiar B84 unit raises the question whether another, more covalent, form of aluminum in addition to the metallic a-form exists, similar to the geometry of the Al atoms in the Al12 icosahedra of 6. The mild conditions applied for the synthesis of Al22Br20 might also favor the formation of such a modification. In order to support this hypothesis, we investigated the structural competition between the fee and ff-B type for Al by means of ab initio full-potential calculations, with the results shown in Fig. 15.52... 

The structure of oxygen hexaboride illustrates the flexibility of boron. In this case, the boron atoms form iscosahedra (12 faces) instead of octahedra (eight faces). This requires a rhombohedral (hexagonal) array of the oxygen atoms and the icosahedra. Figure 11.10 shows the arrangement in one layer of this structure. Two other layers have the same form but are rotated 60° relative to one another, and the fourth layer repeats the position of the first layer. 

There are several ways of arranging the almost spherical B12 units. Three of these result in the forms of boron known as tetragonal, a-rhombohedral, and (3-rhombohedral. All of the structures are very rigid, which results in boron having a hardness of 9.3 compared to the value of 10.0 for diamond (Mohs scale). 

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