Sodium chloride solid state structure, 167

The elucidation of the factors determining the relative stability of alternative crystalline structures of a substance would be of the greatest significance in the development of the theory of the solid state. Why, for example, do some of the alkali halides crystallize with the sodium chloride structure and some with the cesium chloride structure Why does titanium dioxide under different conditions assume the different structures of rutile, brookite and anatase Why does aluminum fluosilicate, AljSiCV F2, crystallize with the structure of topaz and not with some other structure These questions are answered formally by the statement that in each case the structure with the minimum free energy is stable. This answer, however, is not satisfying what is desired in our atomistic and quantum theoretical era is the explanation of this minimum free energy in terms of atoms or ions and their properties. 

Fig. 4.1 Crystal structures of two 1 1 ionic compounds (a) unit cell of sodium chloride, cubic, space group Fm3m (b) unit cell of cesium chloride, cubic, space group Fm3m. [From Ladd, M.F C Structure and Bonding in Solid State Chemistry, Wiley New York, 1979. Reproduced with permission.]...

Upon evaporation of (lie sulvent, the salt is obtained as such, frequently as crystals, sometimes with and sometimes without water of crystallization. A salt, when dissolved in an ionizing solvent, or fused (e.g., sodium chloride in water), is a good conductor of electricity and when rn the solid state forms a crystal lattice (e.g., sodium chloride crystals possess a definite lattice structure tor both sodium cations (Na+) and chloride anions (Cl-), determinable by examination with x-rays). 

An ionically bonded molecule (NaCl). (a) A sodium atom (Na) can donate the one electron in its valence shell to a chlorine atom (Cl), which has seven electrons in its outermost shell. The resulting ions (Na+ and CP) bond to form the compound sodium chloride (NaCl). The octet rule has been satisfied, (b) The ions that constitute NaCl form a regular crystalline structure in the solid state. 

Another troublesome borderline area is that between ionic solids and three-dimensional polymers. The distinction cannot be made from the structure alone. Electrical conductivity in the molten state does not, as already mentioned, necessarily demonstrate the presence of ions in the solid state and such a test is inapplicable where, as often happens, the substance sublimes or decomposes before melting. There can rarely be any objective means of assigning a compound to one category or the other. We are often persuaded towards one description on aesthetic grounds. For example, the structure of sodium chloride cannot easily be rendered in terms of localised, electron-pair bonds (but this is true also of many unequivocally covalent compounds). Its structure is eminently plausible for an array of cations and anions, however. 

Since the Braggs first determination, thousands of structures, most of them far more complicated than that of sodium chloride, have been determined by x-ray diffraction. For covalently bonded low molecular weight species (such as benzene, iodine, or stannic chloride), it is often of interest to see just how the discrete molecules are packed together in the crystalline state, but the crystal structures affect the chemistry of such substances only to a minor degree. However, for most predominantly ionic compounds, for metals, and for a large number of substances in which atoms are covalently bound into chains, sheets, or three dimensional networks, their chemistry is very largely determined by the structure of the solid. 

Ionic compounds, like sodium chloride, are normally considered insulating in the solid state. This is due to the marked difference in electronegativity of the cations and anions, which creates a large band gap of typically 6-12 eV between the valence and conduction bands. Therefore, ionic solids have a band structure similar to an insulator (Figure 5.15). The ions and their associated electrons can be thought of as fixed on their lattice sites. 

We are all familiar with sodium chloride as table salt. It is a typical ionic compound, a brittle solid with a high melting point (801 °C) that conducts electricity in the molten state and in aqueous solution. The structure of solid NaCI is shown in Figure 2.12. 

A closely analogous state of affairs is seen in the systems NiTe2-NiTe and TiTe2-TiTe, in which the AB2 compound has the cadmium iodide structure and the AB compound that of nickel arsenide. In both of these structures the B atoms are arranged as in hexagonal close-packing, but in other respects the relationship between them is precisely the same as that between the cadmium chloride and sodium chloride structures, so that solid solution can take place by the same mechanism. Examples such as this, and many others which could be quoted, emphasize that solid solution is in no sense a satisfactory criterion for isomorphism, and that substances may form solid solution even if their structures are formally quite different. 

So-called ternary or mixed oxide systems based on the rock salt structure are well established. Thus LiFe02 exists both in a disordered form in which Li and Fe are randomly distributed on the metal sites, and as an ordered variant with tetragonal symmetry. Rhombohedral distortions are found for LiNi02, LiV02, and NaFe02 in which the cations are ordered on different sublattices. The HCP counterpart of the sodium chloride structure, the so-called Nickel Arsenide stucture (5ee Chalcogenides Solid-state Chewistr, is found only for the heavier members of the Oxygen family. 

Clearly, the treatment of a solid involving of the order of 10 3 electrons is even a more complicated matter than that of an isolated molecule or complex in spite of the simplifications introduced by symmetry, and the use of effective potentials, and thus of a band theoretical approach, is probably not adequate in the discussion of wave function sensitive parameters such as spin distributions. But many important properties of solids reflect the electronic energy levels, rather than the finer details of the electronic distributions, and in spite of the fact that band calculations are rarely carried through to self consistency, band structures and energies of simple compounds may be determined sufficiently well to provide a good comparison with experimental data. The main effort has been directed to metals, where the valence electrons are weakly bound, and to simple compounds of high symmetry with the sodium chloride or diamond-like structure. In the latter case this effort also reflects the importance of these compounds in solid state physics and electronics and the elucidation of the band structure was essential for an understanding of many of the important properties of these materials. 

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