Solid state structures borides

A typical building block used to construct several solid-state structures (boron-rich borides and allotropes of elemental boron) is the B12 icosahedron. According to King, (1993) an icosahedral B12 building block in which each of the 12 vertices contributes a single electron for an external two-electron two-centre (2e, 2c) bond to an external group implies the following electron count ... 

The second example comes from solid-state chemistry, and the coimection with cluster chemistry is less obvious. Despite this, it is an excellent example of how E/M variation can lead to systematic variation in structure and, consequently, to properties. Although the example is taken from solid-state metal borides, the silicides see Silicon Inorganic Chemistry) and phosphides (see Phosphides Solid-state Chemistry) could have been used. 

The metal borides are one of the five major classes of boron compounds (1). In the following we review the geometric and electronic structural data with an emphasis on the transition metal borides. Because the structures of transition metals and elemental boron provide end points, we begin by reviewing the solid state structures of these elements. A brief survey of the range of metal boride structures in general is followed by some more detailed consideration of the problems of electronic structure raised by the geometries of the transition metal borides. 

Table 12.3 Classification of the structures of solid state metal borides. 

Fehlner, T.P. Molecular models of solid state metal boride structure. J. Solid State Chem. 154, 110-113 (2000)... 

Borides Sohd-state Chemistry Carbides Transition Metal Solid-state Chemistry Electronic Structure of Sohds Quasicrystals Structure Property Maps for Inorganic Solids Superconductivity Zintl Compounds. 

This article covers only a part of the chemistry of boron. Boron-carbon compounds are covered in other articles in this volume see Boron Organoboranes Boron Metallacarbaboranes, and Boron Polyhedral Carboranes). The main subject of the latter two articles, and the separate one on Boron Hydrides is the extensive chemistry of the multicenter bonded boron-hydride systems. This area has been a major focus of boron research for the past 60 years. There is some direct overlap between the two articles Borides Solid-state Chemistry and Borates Solid-state Chemistry, and this more general one covering the inorganic chemistry of boron. Boron-Nitrogen Compounds are also covered separately. These articles should be consulted for more detailed discussions of the structure, bonding, and properties of borides, solid-state borates, and boron-nitrogen compounds. 

Fhst, the number of valence functions (or frontier orbitals) and valence elechons (frontier orbital occupancy) determines the tendency toward cluster bonding. It is instructive to recall that the structural motif in elemental boron is the icosahedron with six-connected boron atoms see Borides Solid-state Chemistry), it is the tetrahedral carbon atom in the diamond form of elemental carbon with four-coimected carbon atoms and it is three-connected phosphorus atoms in the sheets of elemental black phosphorus (see Phosphides Solid-state Chemistry). Boron has more valence orbitals than valence elechons, naturally leading to orbitally rich cluster formation for example, BH has three orbitals and two elechons and forms... 

Finally, the structural modifications of elemental boron exhibit complex extended lattices of cages in the solid state, whereas those of metals possess much simpler close-packed atomic lattices. These differences are a direct reflection of atomic properties and result in the respective nonmetallic and metallic behavior. However, boron combines with most other elements including metals. There are a wide range of metal borides known with stoichiometric as well as nonstoi-chiometric atomic ratios. The amazingly varied interpenetration of the two characteristic structural motifs and the subtly balanced competition between the two modes of solid state bonding found in the metal borides constitutes further justification of our theme. This is discussed in some detail in Section II,C. 

We have already pointed out that the most stable forms of the solid state bonding of elemental boron and metals differ in an essential aspect. Hence, in the solidification of a melt containing a random mixture of metal and boron atoms the observed structure will be determined by a balance between the tendencies for boron to form a covalently bound network and the metal to form a close-packed lattice. Among other things, this competition will depend on relative metal and boron concentrations and one expects in proceeding from the metal-rich to the boron-rich borides that the B-B bonded network will become more extensive and dominant. 

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