The Defect Solid State

Wherever there is a defect in a crystal lattice, interatomic forces will remain unbalanced and the free energy will be less negative than elsewhere in the crystal, although generally the lattice will deform locally to smooth this out. Nevertheless, defect sites (especially of the extended variety) tend to be more chemically reactive than the bulk crystal and tend to be active sites for crystal growth, dissolution, corrosion, and catalytic activity. 

Point defects. Point defects (Fig. 5.1) are limited to a single point in the lattice, although the lattice will buckle locally so that the influence of point defects may spread quite far. A Frenkel defect consists of a misplaced interstitial atom and a lattice vacancy (the site the atom should have occupied). For example, silver bromide, which has the NaCl structure, has substantial numbers of Ag+ ions in tetrahedral holes in the ccp Br array, instead of in the expected octahedral holes. Frenkel defects are especially common in salts containing large, polarizable anions like bromide or iodide. 

Defects in which both a cation and sufficient anions to balance the charge (or vice versa) are completely missing from the lattice are called Schottky defects. Schottky defects result in a density that is lower than that calculated on the basis of unit cell dimensions, whereas Frenkel defects do not affect this density. Titanium(II) oxide, for example, also has the NaCl structure, but, even when its composition is TiOi.oo (which it rarely is see Section 5.4), about one-sixth of the Ti2+ and 02 sites are vacant. 

The existence of Schottky or Frenkel defects, or both, within an ionic solid provides a mechanism for significant electrical conductance through ion migration from site to empty site (leaving, of course, a fresh empty site behind).4 Solid /3-AgI provides a classic example of a nonmetallic solid with substantial electrical conductivity at elevated temperatures at 147 °C, it undergoes a transition to a-Agl in which the silver ion sublattice is disordered and consequently allows for relatively free movement of Ag+ and 

Line defects. Line defects extend in one dimension and may originate in an incomplete layer of atoms (an edge dislocation, Fig. 5.2) or from 

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There is a scarcity of oxygen-transport data for oxygen-deficient actinide oxide systems. Because of this, our understanding and predictive capabilities of the effect of the defect solid state on the properties of reactor fuel systems, as well as on the chemical state of fission products in these systems, are limited. 

Rees, A. L. G., Chemistry of the Defect Solid State, Methuen, London, 1954. 

The usefulness of quadrupolar effects on the nuclear magnetic resonance c I 7 yi nuclei in the defect solid state arises from the fact that point defects, dislocations, etc., give rise to electric field gradients, which in cubic ciystals produce a large effect on the nuclear resonance line. In noncubic crystals defects of course produce an effect, but it may be masked by the already present quadrupole interaction. Considerable experimental data have been obtained by Reif (96,97) on the NMR of nuclei in doped, cubic, polycrystalline solids. The effect of defect-producing impurities is quite... 

Most metals acquire an oxide film or scale on their surfaces on exposure to oxygen or air, especially at elevated temperatures.5-7 The kinetics and mechanism of formation of such films provide examples of applications of the concepts of the defect solid state outlined above, and indeed of solid-state kinetics in general.8... 

Each of the four cases delineated [(ci), (cv), (ai), and (av)] is developed individually in such a way that it is self-contained. Each theoretical development is preceded by a formulation of the relevant equations for the defect solid-state reactions [63, 64] occurring at the phase boundaries separating the oxides. That is, balanced chemical equations involving... 

A thermodynamic description of the defect solid state of linear high polymers. Polymer 5, 125—134 (1964). 

The properties of the defect solid state are fundamental to our understanding of all reacting systems involving a solid in fact, there is little of the metallurgical and chemical industries which is not based on the chemical properties of defect solids. A little reflection will make this so obvious that there is no necessity to enumerate specific examples even the electrical industry depends on the ability to produce materials having controllable defect properties, e.g. luminescent materials for fluorescent lamps and cathode-ray tube screens, oxide materials for cathode coatings, a variety of semi-conductors for resistors, rectifiers, detectors and photoelectric devices. 

For the fundamentals of statistical thermodynamics the reader is referred elsewhere (14) however, it is possible from a knowledge of classical thermodynamics and an acceptance of the manner in which the classical thermodynamic functions can be specified in terms of observable quantities to show how statistical theory can be usefully applied to the defect solid state. 

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