Structure of crystalline boron

Boron is unique among the elements in the structural complexity of its allotropic modifications this reflects the variety of ways in which boron seeks to solve the problem of having fewer electrons than atomic orbitals available for bonding. Elements in this situation usually adopt metallic bonding, but the small size and high ionization energies of B (p. 222) result in covalent rather than metallic bonding. The structural unit which dominates the various allotropes of B is the B 2 icosahedron (Fig. 6.1), and this also occurs in several metal boride structures and in certain boron hydride derivatives. Because of the fivefold rotation symmetry at the individual B atoms, the B)2 icosahedra pack rather inefficiently and there 

The lattice parameters showed considerable variation from one crystal to another with average values a 875 pm, c 506 pm this is now thought to arise from variable composition depending on the precise preparative conditions used. 

The interatomic distances involving the single 4-coordinate atoms at 2(b) were only 160 pm this is unusually short for B-B but reasonable for B-C or B-N distances. 

The structure requires 160 valence electrons per unit cell computed as follows internal bonding within the 4 icosahedra (4 x 26 = 104) external bonds for the 4 icosahedra (4x12 = 48) bonds shared by the atoms in 2(b) positions (2x4 = 8). However, 50 B atoms have only 150 valence electrons and even with the maximum possible excess of boron in the unit cell (0.75 B) this rises to only 152 electrons. The required extra 8 or 10 electrons are now supplied by 2C or 2N though the detailed description of the bonding is more intricate than this simple numerology implies. 

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, 

2-centre B-B bonds at 171 pm (directed rhombohedrally, 3 above and 3 below the icosahedron). B units in the layer above are centred over 1 and those in the layer below are centred under 2. 

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This applies for instance to the boron (Ill)-halides for which nearly the same Db-b values are obtained (Table 1). With dH/=dH/ assumed to be valid, Eq. (12) is applicable. For BFsand BCI3 with JHB2(St- g) = 0 and /JHcpd (St - -g) = 0, the result is = 0, and for BBra with f dHB2 (St- g) = 11.1 and dHcp(j(St g) =7.3, one obtains dHm= —3.8. This negative value for appears unreasonable. Values dHnj = 0 do exist in case of the diamond modification of C, Si, Ge and Sn for the tetra-valent sp -hybridized state of these elements. For sp -hybridized boron, dH = 0 is improbable in view of the comphcated structures of crystalline boron. 

AC Switendick. The electronic structure of crystalline boron carbide I B12 icosahedra and C—B—C chains. In R Freer, ed. The Physics and Chemistry of Carbides, Nitrides and Borides. Dordrecht Kluwer, p 525, 1990. 

A characteristic feature of the structuie of most electron-deficient substances is that the atoms have ligancy that is not only greater than the number of valence electrons but is even greater than the number of stable orbitals.66 Thus most of the boron atoms in the tetragonal form of crystalline boron have ligancy 6. Also, lithium and beryllium, with four stable orbitals and only one and two valence electrons, respectively, have structures in which the atoms have ligancy 8 or 12. All metals can be considered to be electron-deficient substances (Chap. 11). 

Boron prepared in this way appears as black crystals having a density of 2.34 g cm-3. The structure of the boron unit cell in the crystalline material is a regular icosahedral structure containing 20 equilateral triangles meeting at 12 vertices. Figure 8.1 shows the structure of the B12 icosahedron (4 symmetry). 

We have described the structures of some boron-rich borides in which there are extensive 3D systems of B—B bonds. At the other extreme there are crystalline borides with low boron content in which there are isolated B atoms, that is, B atoms surrounded entirely by metal atoms as nearest neighbours. With increasing boron content the B atoms link together to form first B2 units, then chains, layers, or 3D frameworks extending throughout the whole crystal (Table 24.3). 

Crystalline boron-rich boron nitrides of the compositions B25N up to B53N as well as amorphous phases of the composition B3N and B5N have also been synthesized by CVD methods [120,121]. The formation of a rhombohedral structure of the boron-rich nitride, B4N, is described in [122]. The films deposited at 1200°C on hBN substrates by a tungsten hot filament assisted vapor-phase reaction... 

Figure 6.1 The icosahedron and some of its symmetry elements, (a) An icosahedron has 12 vertices and 20 triangular faces defined by 30 edges, (b) The preferred pentagonal pyramidal coordination polyhedron for 6-coordinate boron in icosahedral structures as it is not possible to generate an infinite three-dimensional lattice on the basis of fivefold symmetry, various distortions, translations and voids occur in the actual crystal structures, (c) The distortion angle 0, which varies from 0° to 25°, for various boron atoms in crystalline boron and metal borides.

Figure 6.4 Crystal structure of ar-tetragonal boron. This was originally thought to be B50 (4Bi2 + 2B) but is now known to be either B50C2 or B50N2 in which the 2C (or 2N) occupy the 2(b) positions the remaining 2B are distributed statistically at other vacant sites in the lattice. Note that this reformulation solves three problems which attended the description of the or-tetragonal phase as a crystalline modification of pure B ...

Reaction of methyl a-L-rhamnopyranoside with triphenylboroxole gave a syrupy boronate ester which was characterized as a crystalline phenyl-carbamate. Removal of the phenylboronic acid residue gave a product identified as methyl a-L-rhamnopyranoside 4-N-phenylcarbamate, since it was identical with that resulting from removal of the ketal group from methyl 2,3-O-isopr opylidene-a-L-rhamnopyranoside 4-N-phenylcarbamate (12). This establishes the structure of the original ester as methyl a-L-rhamnopyranoside 2,3-phenylboronate (24). 

The atomic and crystalline structure of the two non-metallic carbides, boron and silicon carbides, is less complex than that of the... 

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 structure of CaB contains bonding bands typical of the boron sublattice and capable of accommodating 20 electrons per CaB formula, and separated from antibonding bands by a relatively narrow gap (from 1.5 to 4.4 eV) . The B atoms of the B(, octahedron yield only 18 electrons thus a transfer of two electrons from the metal to the boron sublattice is necessary to stabilize the crystalline framework. The semiconducting properties of M B phases (M = Ca, Sr ", Ba, Eu, Yb ) and the metallic ones of M B or M B5 phases (Y, La, Ce, Pr, Nd ", Gd , Tb , Dy and Th ) are directly explained by this model . The validity of these models may be questionable because of the existence and stability of Na,Ba, Bft solid solutions and of KB, since they prove that the CaB -type structure is still stable when the electron contribution of the inserted atom is less than two . A detailed description of physical properties of hexaborides involves not only the bonding and antibonding B bands, but also bonds originating in the atomic orbitals of the inserted metal . ... 

Boron nitride may be obtained in three primary crystalline modifications (2) a, j3, and y. The most commonly encountered a form has a graphitic structure (hexagonal cell, a = 2.504 A, c = 6.661 A). For many years, this modification has been prepared from combinations of cheap boron and nitrogen containing reagents, e.g. B(0H)3 and (NH2)C0, B(0H)3, C and N2 or KBH4 and NH4C1 (3-5). More... 

Furthermore, we believe that the stabilizing influence of boron in the structure of graphite is connected with enhancement of its acceptor properties, which manifest themselves when Boron atoms substitute carbon atoms in the crystalline structure (hexagon ring) of carbon. Such effects are mentioned in the literature for some types of carbon materials [3] and the influence of boron on TEG can be the similar. 

Figure 13 shows typical results of the degradation of crystalline Si solar cells having a back surface field and reflector structure (Si-BSFR), which were qualified by National Space Development Agency of Japan (NASDA) for space usage, when irradiated by 10-MeV protons and 1 -MeV electrons. The pn junction of the cell samples, with a size of 2 cm x 2 cm X 50 pm, was fabricated by phosphorus (P) doping to a depth of 0.15 pm into boron... 

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