Bands antibonding

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 . ... 

Fig. 2-3. Formation of electron energy bands in constructing a solid crystal X from atoms of X ro = stable atom-atom distance in crystal BB = bonding band ABB = antibonding band e, = band gap.

Fig. 2-12. Electron energy band formation of silicon crystals from atomic frontier orbitals number of silicon atoms in crystal r = distance between atoms rg = stable atom-atom distance in crystals, sp B8 = bonding band (valence band) of sp hybrid orbitals sp ABB = antibonding band (conduction band) of sp hybrid orbitals.

Most metal oxides are ionic crystals and belong to either the class of semiconductors or insulators, in which the valence band mainly comprises the frontier orbitals of oxide ions and the conduction band contains the frontier orbitals of metal ions. In forming an ionic metal oxide ciTstal from metal ions and oxide ions, as shown in Fig. 2-21, the crystalline field shifts the frontier electron level of metal ions to higher energies to form an antibonding band (the conduction... 

As shown in Figure 5.6, the dz2 and pz orbitals can hybridize to form a o-bonding band and a o-antibonding band. The dxz and dyz orbitals hybridize with the pA and pv orbitals to produce a jr-bonding band and a jt-antibonding band. The dxy and dxi y2 do not hybridize with any p-orbitals and so produce a metallic 6-band in the gap between the hybridized covalent orbitals. 

If the two-sublattice condition does not exist, there can be no electron correlations that avoid exclusion of electron charge from the region between positive atomic cores. Therefore the bottom of the valence-electron band should be less stable than that of a corresponding bonding band, the top more stable than that of a corresponding antibonding band. Such a band is called metallic as it is characteristic of the close-packed metals. 

Fig. 81. Simplified density of states curve for ferromagnetic a-Fe. Energy scale is referred to bottom of 8-p band. The [eg -f t2g (antibonding)] bands each contain 3.5 electrons per atom. Bonding t2g band held same as in Figure 80 and magnetic-electron band drawn to give 104yei = 12 cal/mole/deg2.

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