Molecular solids and covalent networks

X-ray diffraction studies of solids reveal a huge amount of information, including interatomic distances, bond angles, stereochemistry, and vibrational parameters. In this section we can do no more than hint at the diversity of types of solids found when molecules pack together or atoms link together in extended networks. In covalent network solids, covalent bonds in a definite spatial orientation link the atoms in a network extending through the crystal. The demands of directional bonding, which have only a small effect on the structures of many metals, now override the geometrical problem of packing spheres together, and elaborate and extensive structures may be formed. Examples include silicon, red phosphorus, boron nitride, and— very importantly—diamond, graphite, and carbon nanotubes, which we discuss in detail.

Diamond and graphite are two allotropes of carbon. In diamond each sp3-hybridized carbon is bonded tetrahedrally to its four neighbours (Fig. 20.43). The network of strong C-C bonds is repeated throughout the crystal and, as a result, diamond is the hardest known substance. In graphite, σ bonds between sp2-hybridized carbon atoms form hexagonal rings which, when repeated throughout a plane, give rise to sheets (Fig. 20.44). Because the sheets can slide against each other when impurities are present, graphite is used widely as a lubricant. Carbon nanotubes are thin cylinders of carbon atoms that are both mechanically strong and highly conducting (see Impact I20.2). They are synthesized by condensing a carbon plasma either in the presence or absence of a catalyst. The simplest structural motif is called a single-walled nanotube (SWNT) and is shown in Fig. 20.45. In a SWNT,sp2-hybridized carbon atoms form hexagonal rings reminiscent of the structure of the carbon sheets found in graphite. The tubes have diameters between 1 and 2 nm and lengths of several micrometres. The features shown in Fig. 20.45 have been confirmed by direct visualization with scanning tunnelling microscopy (Impact I9.1). A multi-walled nanotube (MWNT) consists of several concentric SWNTs and its diameter varies between 2 and 25 nm. Molecular solids, which are the subject of the overwhelming majority of modern structural determinations, are held together by van der Waals interactions (Chapter 18). The observed crystal structure is Nature’s solution to the problem of condensing objects of various shapes into an aggregate of minimum energy (actually, for T > 0, of minimum Gibbs energy). The prediction of the structure is a very difficult task, but software specifically designed to explore interaction energies can now make reasonably reliable predictions. The problem is made more complicated by the role of hydrogen bonds, which in some cases dominate the crystal structure, as in ice (Fig. 20.46), but in others (for example, in phenol) distort a structure that is determined largely by the van der Waals interactions.

Fig. 20.43 A fragment of the structure of diamond. Each C atom is tetrahedrally bonded to four neighbours. This framework-like structure results in a rigid crystal.

Fig. 20.45 In a single-walled nanotube (SWNT),sp2-hybridized carbon atoms form hexagonal rings that grow as tubes with diameters between 1 and 2 nm and lengths of several micrometres.

Fig. 20.44 Graphite consists of flat planes of hexagons of carbon atoms lying above one another. (a) The arrangement of carbon atoms in a sheet; (b) the relative arrangement of neighbouring sheets. When impurities are present, the planes can slide over one another easily.

Fig. 20.46 A fragment of the crystal structure of ice (ice-I). Each O atom is at the centre of a tetrahedron of four O atoms at a distance of 276 pm. The central O atom is attached by two short O-H bonds to two H atoms and by two long hydrogen bonds to the H atoms of two of the neighbouring molecules. Overall, the structure consists of planes of hexagonal puckered rings of H₂O molecules (like the chair form of cyclohexane).

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مواضيع ذات صلة

Light emission by solid-state lasers and light-emitting diodes

Light absorption by molecular solids, metallic conductors, and semiconductors

Insulators and semiconductors

The occupation of orbitals

The formation of bands

Energetics

Structure

Close packing

Structure refinement

The phase problem

Bragg’s law

X-ray diffraction