Defects in Ionic and Molecular Crystals

All the defects and impurities described for metals are seen in ionic and molecular compounds as well. Because ionic compounds contain both cations and anions rather than only neutral atoms, however, they exhibit additional types of defects that are not possible in metals.

The most straightforward variant is a substitutional impurity in which a cation or an anion is replaced by another of similar charge and size. For example, Br⁻ can substitute for Cl⁻, so tiny amounts of Br⁻ are usually present in a chloride salt such as CaCl₂ or BaCl₂. If the substitutional impurity and the host have different charges, however, the situation becomes more complicated. Suppose, for example, that Sr²⁺ (ionic radius = 118 pm) substitutes for K⁺ (ionic radius = 138 pm) in KCl. Because the ions are approximately the same size, Sr²⁺ should fit nicely into the face-centered cubic (fcc) lattice of KCl. The difference in charge, however, must somehow be compensated for so that electrical neutrality is preserved. The simplest way is for a second K⁺ ion to be lost elsewhere in the crystal, producing a vacancy. Thus substitution of K⁺ by Sr²⁺ in KCl results in the introduction of two defects: a site in which an Sr²⁺ ion occupies a K⁺ position and a vacant cation site. Substitutional impurities whose charges do not match the host’s are often introduced intentionally to produce compounds with specific properties.

Virtually all the colored gems used in jewelry are due to substitutional impurities in simple oxide structures. For example, α-Al₂O₃, a hard white solid called corundum that is used as an abrasive in fine sandpaper, is the primary component, or matrix, of a wide variety of gems. Because many trivalent transition metal ions have ionic radii only a little larger than the radius of Al³⁺ (ionic radius = 53.5 pm), they can replace Al³⁺ in the octahedral holes of the oxide lattice. Substituting small amounts of Cr³⁺ ions (ionic radius = 75 pm) for Al³⁺ gives the deep red color of ruby, and a mixture of impurities (Fe²⁺, Fe³⁺, and Ti⁴⁺) gives the deep blue of sapphire. True amethyst contains small amounts of Fe³⁺ in an SiO₂ (quartz) matrix. The same metal ion substituted into different mineral lattices can produce very different colors. For example, Fe³⁺ ions are responsible for the yellow color of topaz and the violet color of amethyst. The distinct environments cause differences in d orbital energies, enabling the Fe³⁺ ions to absorb light of different frequencies.

Substitutional impurities are also observed in molecular crystals if the structure of the impurity is similar to the host, and they can have major effects on the properties of the crystal. Pure anthracene, for example, is an electrical conductor, but the transfer of electrons through the molecule is much slower if the anthracene crystal contains even very small amounts of tetracene despite their strong structural similarities.

If a cation or an anion is simply missing, leaving a vacant site in an ionic crystal, then for the crystal to be electrically neutral, there must be a corresponding vacancy of the ion with the opposite charge somewhere in the crystal. In compounds such as KCl, the charges are equal but opposite, so one anion vacancy is sufficient to compensate for each cation vacancy. In compounds such as CaCl₂, however, two Cl⁻ anion sites must be vacant to compensate for each missing Ca²⁺ cation. These pairs (or sets) of vacancies are called Schottky defectsA coupled pair of vacancies—one cation and one anion—that maintains the electrical neutrality of an ionic solid. and are particularly common in simple alkali metal halides such as KCl (part (a) in Figure 1.1). Many microwave diodes, which are devices that allow a current to flow in a single direction, are composed of materials with Schottky defects.

Occasionally one of the ions in an ionic lattice is simply in the wrong position. An example of this phenomenon, called a Frenkel defectA defect in an ionic lattice that occurs when one of the ions is in the wrong position., is a cation that occupies a tetrahedral hole rather than an octahedral hole in the anion lattice (part (b) in Figure 1.1). Frenkel defects are most common in salts that have a large anion and a relatively small cation. To preserve electrical neutrality, one of the normal cation sites, usually octahedral, must be vacant.

Frenkel defects are particularly common in the silver halides AgCl, AgBr, and AgI, which combine a rather small cation (Ag⁺, ionic radius = 115 pm) with large, polarizable anions. Certain more complex salts with a second cation in addition to Ag⁺ and Br⁻ or I⁻ have so many Ag⁺ ions in tetrahedral holes that they are good electrical conductors in the solid state; hence they are called solid electrolytesA solid material with a very high electrical conductivity.  In response to an applied voltage, the cations in solid electrolytes can diffuse rapidly through the lattice via octahedral holes, creating Frenkel defects as the cations migrate. Sodium–sulfur batteries use a solid Al₂O₃ electrolyte with small amounts of solid Na₂O. Because the electrolyte cannot leak, it cannot cause corrosion, which gives a battery that uses a solid electrolyte a significant advantage over one with a liquid electrolyte.