Ionic crystals defects

N. N. Greenwood, Ionic Crystals. Defects and Non-Stoichiometry, Butterworths, London, 1968. 

In ionic crystals, defects in one partial lattice must be compensated by defects in the second partial lattice to fulfill the law of electroneutrality. Therefore, one can distinguish (Hauffe ) among... 

Crystal structure, crystal defects and chemical reactions. Most chemical reactions of interest to materials scientists involve at least one reactant in the solid state examples inelude surfaee oxidation, internal oxidation, the photographie process, electrochemieal reaetions in the solid state. All of these are critieally dependent on crystal defects, point defects in particular, and the thermodynamics of these point defeets, especially in ionic compounds, are far more complex than they are in single-component metals. I have spaee only for a superficial overview. 

Fig. 5.20. The shock-induced polarization of a range of ionic crystals is shown at a compression of about 30%. This maximum value is well correlated with cation radius, dielectric constant, and a factor thought to represent dielectric strength. A mechanically induced point defect generation and migration model is preferred for the effect (after Davison and Graham [79D01]).

These observations were the basis for the proposal that polymers, like ionic crystals, exhibit shock-induced polarization due to mechanically induced defects which are forced into polar configurations with the large acceleration forces within the loading portion of the shock pulse. Such a process was termed a mechanically induced, bond-scission model [79G01] and is somewhat supported by independent observations of the propensity of polymers to be damaged by more conventional mechanical deformation processes. As in the ionic crystals, the mechanically induced, bond-scission model is an example of a catastrophic shock compression model. 

Ionic solids, such as lithium fluoride and sodium chloride, form regularly shaped crystals with well defined crystal faces. Pure samples of these solids are usually transparent and colorless but color may be caused by quite small impurity contents or crystal defects. Most ionic crystals have high melting points. 

Because of the high electrostatic energy required to maintain them in an ionic crystal such as AgBr, we can safely ignore the following possible defects ... 

The point defects are decisive for conduction in solid ionic crystals. Ionic migration occurs in the form of relay-type jumps of the ions into the nearest vacancies (along the held). The relation between conductivity o and the vacancy concentration is unambiguous, so that this concentration can also be determined from conductivity data. 

In addition to the thermal vacancies, impurity-related vacancies will develop in ionic crystals. When impurity ions have a charge different from ions of like charge which are the crystal s main constituents, part of the lattice sites must remain vacant in order to preserve electroneutrality. Such impurity-type defects depend little on temperature, and their major effects are apparent at low temperatures when few thermal vacancies exist. 

In some ionic crystals (primarily in halides of the alkali metals), there are vacancies in both the cationic and anionic positions (called Schottky defects—see Fig. 2.16). During transport, the ions (mostly of one sort) are shifted from a stable position to a neighbouring hole. The Schottky mechanism characterizes transport in important solid electrolytes such as Nernst mass (Zr02 doped with Y203 or with CaO). Thus, in the presence of 10 mol.% CaO, 5 per cent of the oxygen atoms in the lattice are replaced by vacancies. The presence of impurities also leads to the formation of Schottky defects. Most substances contain Frenkel and Schottky defects simultaneously, both influencing ion transport. 

For Schottky defects in an ionic crystal with a cubic lattice, the diffusion coefficient is given by the relationship, e.g. for a cation,... 

Although several types of lattices have been described for ionic crystals and metals, it should be remembered that no crystal is perfect. The irregularities or defects in crystal structures are of two general types. The first type consists of defects that occur at specific sites in the lattice, and they are known as point defects. The second type of defect is a more general type that affects larger regions of the crystal. These are the extended defects or dislocations. Point defects will be discussed first. 

Although this is a small fraction, for 1 mole of lattice sites, this amounts to 5.6 X1018 Schottky defects. The ability of ions to move from their sites into vacancies and by so doing creating new vacancies is largely responsible for the conductivity in ionic crystals. 

FIGURE 7.16 An illustration of Schottky defects in an ionic crystal. 

Figure 1.15 Balanced populations of point defects in an ionic crystal of formula MX (schematic) (a) Schottky defects and (b) Frenkel defects.

Figure 1.16 Antisite point defects in an ionic crystal of formula MX (schematic) (a) A on B sites, AB (b) B on A sites, BA (c) Na+ on a Cl- site in sodium chloride, Na and (d) Cl- on an Na+ site in sodium chloride, Cl a.

When writing defect formation equations, the strategy involved is always to add or subtract elements to or from a crystal via electrically neutral atoms. When ionic crystals are involved, this requires that electrons are considered separately. Thus, if one considers NiO to be ionic, formation of a VNi would imply the removal of a neutral Ni atom, that is, removal of a Ni2+ ion together with two electrons. Similarly, formation of a VQ would imply removal of a neutral oxygen atom, that is, removal of an O1 2- ion, followed by the addition of two electrons to the crystal. An alternative way to express this is to say the removal of an O2- ion together with 2h. Similarly, only neutral atoms are added to interstitial positions. If ions are considered to be present, the requisite number of electrons must be added or subtracted as well. Thus, the formation of an interstitial Zn2+ defect would involve the addition of a neutral Zn atom and the removal of two electrons. 

A single anion Frenkel defect in an ionic crystal of formula MX2 needs to be balanced by ... 

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