B, bonding

Metals A and B form an alloy or solid solution. To take a hypothetical case, suppose that the structure is simple cubic, so that each interior atom has six nearest neighbors and each surface atom has five. A particular alloy has a bulk mole fraction XA = 0.50, the side of the unit cell is 4.0 A, and the energies of vaporization Ea and Eb are 30 and 35 kcal/mol for the respective pure metals. The A—A bond energy is aa and the B—B bond energy is bb assume that ab = j( aa + bb)- Calculate the surface energy as a function of surface composition. What should the surface composition be at 0 K In what direction should it change on heaf)pg, and why ... 

There is the possibility of building up an extensive systematic chemistry of compounds containing boron-nitrogen bonds, analogous to the chemistry of carbon-carbon bonds but the reactivity of the B—bond is much greater than that of the C—C bond, so that we get physical, but not chemical, resemblances between analogous compounds. 

Boranes are typical species with electron-deficient bonds, where a chemical bond has more centers than electrons. The smallest molecule showing this property is diborane. Each of the two B-H-B bonds (shown in Figure 2-60a) contains only two electrons, while the molecular orbital extends over three atoms. A correct representation has to represent the delocalization of the two electrons over three atom centers as shown in Figure 2-60b. Figure 2-60c shows another type of electron-deficient bond. In boron cage compounds, boron-boron bonds share their electron pair with the unoccupied atom orbital of a third boron atom [86]. These types of bonds cannot be accommodated in a single VB model of two-electron/ two-centered bonds. 

Figure 2-60. Soine examples of electron-deficient bonds a) diborane featuring B-H-B bonds b) diborane in a tentative RAMSES representation c) the orbital in a B-B-B bond (which occurs in boron cage compounds),...

Vibrational emission spectra iadicate that the B2O2 molecule has a linear 0=B—B=0 stmcture. Values of 782 and 502 kj/mol (187 and 120 kcal/mol) were calculated for the respective B=0 and B—B bond energies (36). 

Fig. 5. Modes of M—H—B bonding where M—H—B represents a three-center hydrogen bridge bond for (a), (b), (c) tetrahydroborates and for (d), (e), (f)...

The valence theory (4) includes both types of three-center bonds shown as well as normal two-center, B—B and B—H, bonds. For example, one resonance stmcture of pentaborane(9) is given in projection in Figure 6. An octet of electrons about each boron atom is attained only if three-center bonds are used in addition to two-center bonds. In many cases involving boron hydrides the valence stmcture can be deduced. First, the total number of orbitals and valence electrons available for bonding are determined. Next, the B—H and B—H—B bonds are accounted for. Finally, the remaining orbitals and valence electrons are used in framework bonding. Alternative placements of hydrogen atoms require different valence stmctures. 

Boron haUdes have also been shown to insert into B—B bonds to give initial products with the new boryl moiety in a bridge position (80). 

Fig. 7.7. Solid-solution structures. In interstitial solutions small atoms fit into the spaces between large atoms. In substitutional solutions similarly sized atoms replace one another. If A-A, A-B and B-B bonds hove the some strength then this replacement is random. But unequal bond strengths con give clustering or ordering.

In the case of a strongly exothermic reaction the final term turns into an absorbing wall, and the transition is completed whenever the distance AB reaches a certain value and the A-B bond is broken. The intra- and intermolecular coordinates Q and q are harmonic and have frequencies (Oo and oji, and reduced masses mo and mi. At fixed intermolecular displacement the tunneling probability equals... 

Disconnection of non-building-block rings which are embedded in a skeleton and also centrally located, either by breaking one bond or a pair of bonds. The one-bond disconnections which are of value are (a) bonds between C and N, O or S and (b) bonds leading to a totally symmetrical, locally symmetrical, or linear skeleton. The bond-pair disconnections which are most effective in simplification are those which generate two structures of roughly equal complexity. 

Figure 5.11 Schematic representation of the three laws of comminution. B, Bond, K, Kick, R, Rittinger...

Fig. 5. Possible bond-alternation patterns of CNTs (a) Isodistant (Iso), (b) bond-altemant 1 (Alt 1), (c) bond-alternant 2 (Alt 2) and (d) Kekuld patterns.

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 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. 

The B3Hg ion (p. 166) is a triangular cluster of Cj (rather than C2 ) symmetry (see Fig. 6.15a) the bridging atoms are essentially in the B3 plane with Ht above and below. While it has been conventional to represent the cluster bonding in terms of two BHB and one B-B bond (Fig. 6.15b), recent high-level computations suggest the presence of a 3-centre BBB bond, as depicted approximately in Fig. 6.15c. 

The neutral m do-borane B Hio (structure 10) has a basal B-B bond (see p. 159) and this enables it to act as a ligand by displacing ethene from Zeise s salt (p. 930). 

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