Main Types of Crystal Defects

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 Ti and 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). 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-AgI 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 

Crystal surfaces. Crystal surfaces may be viewed as vast defects inasmuch as the lattice forces are incompletely balanced. The effects of this imbalance are partially offset by distortion of the crystal lattice near the surface, but crystal surfaces still show a strong tendency to adsorb other 

---

The two main types of line defect which can play an important role in the model of crystal growth are the edge and screw dislocations. Both of these are responsible for slip or shearing in crystals. Large numbers of dislocations occur in most crystals they form readily during the growth process under the influence of surface and internal stresses. 

Crystal defects can take several forms and be classified in a number of ways. The solid state electrochemist, however, is mainly concerned with five types of crystal defect as follows ... 

Intrinsic defects such as lattice vacancies or interstitials are present in the pure crystal at thermodynamic equilibrium. The simplest of these crystalline defects involve single or pairs of atoms or ions and are therefore known as point defects. Two main types of point defect have been identified Schottky defects,in which an atom or ion pair are missing from the lattice (Figure 3.35a), and Frenkel defects, in which an atom or ion is displaced from its ideal lattice position into an interstitial site (Figure 3.35b). 

Interpretation of the WAXS patterns of native starch is often difficult because of the low crystallinity, small size, defects and the multiple orientations of the amylopectin crystallites (Waigh et al, 1997). Two main types of X-ray scattering patterns have been commonly observed (A and B). Potato starch has been shown to crystallize in a hexagonal unit cell in which the amylopectin molecules twist in a double helix (the B structure) (Lin Jana Shen, 1993). Between adjacent helices a channel is formed in which 36 water molecules can be located within the crystal unit cell. By means of heat treatment this structure can be transformed into a more compact monoclinic unit cell (the A structure) (Shogren, 1992). Amylose (the linear and minor component of starch) can be crystallized from solution in the A and B structures (Buledn etal, 1984), yielding X-ray diffraction patterns similar to those of amylopectin but with higher orientation. 

In atomic or molecular sohds, common types of point defects are the absence of an atom or molecule from its expected position at a regular lattice site (a vacancy), or the presence of an atom or molecule in a position which is not on the regular lattice (an interstitial). In ionic solids, these point defects occur in two main combinations. These are Schottky defects, in which there are equal numbers of cation and anion vacancies within the crystal, and Frenkel defects, in which there are cation vacancies associated with an equal number of "missing" cations located at non-lattice, interstitial positions. Both are illustrated in Figure 1.1. Point defects are also found in association with altervalent impurities, dislocations, etc., and combinations of vacancies with electrons or positive holes give rise to various types of colour centres (see below). 

For the purposes of the discussion given here, we will only consider point defects in crystalline solids. Our main objective in this section is to provide the semantic backdrop for the remainder of the chapter. Our starting point is the perfect crystal since this is the reference state against which the defected crystal is measured. In fig. 7.9, we provide a visual catalog of some of the key types of point defects that can perturb the uninterrupted regularity of the perfect crystal. 

The solid state chemist approaches the problem in a different way(2). His main interest focus on the phase composition of the solid, type of crystal planes exposed, presence of additives and impurities, oxidation states of the cations and their changes in the course of the reaction, type of defects in the oxide lattice, etc. Correlation is sought between these parameters and the activity and selectivity of the oxide system in the given reaction, but little attention is usually paid to the type of interactions between the hydrocarbon molecule and the surface and to the possible transition states. When these two approaches are integrated, several general conclusions may be formulated, but also a number of important yet unanswered questions emerge. 

Very few crystals are perfect. Indeed, in many cases they are not required to be, since lattice imperfections and other defects can confer some important chemical and mechanical properties on crystalline materials. Surface defects can also greatly influence the process of crystal growth. There are three main types of lattice imperfection point (zero-dimensional, line (one-dimensional) and surface (two-dimensional). 

Bap2. Two main types of relaxation are found in this material, corresponding to dipole moments caused by association of substitutional lanthanum with an interstitial fluorine along the <100> and <111> crystal axes, respectively. Loss peaks are seen at low levels of doping corresponding to both defects. Calculation of the respective dipole moments allows calculation of the concentration of defects from the strengths of the losses (i.e. from the associated values of C2). 

Whether Schottky or Frenkel defects are found in a crystal depends in the main on the value of A//, the defect with the lower A// value predominating. In some crystals it is possible for both types of defect to be present. 

The common feature of the internal reactions discussed so far is the participation of electronic defects. In other words, we have been dealing with either oxidation or reduction. We now show that reactions of the type A+B = AB can take place in a solvent crystal matrix as, for example, the formation of double oxides (CaO +Ti02 = CaTi03) in which atomic (ionic) but no electronic point defects are involved. Although many different solvent crystal matrices can be thought of (e.g., metals, semiconductors, glasses, and even viscous melts and surfaces), we will deal here mainly with ionic crystal matrices in order to illustrate the basic features of this type of solid state reaction. 

This process is obviously a natural scattering process in polycrystalline materials, since polycrystalline films exhibit a high concentration of crystallographic defects, especially dislocations [133,134]. However, this process is rarely used to explain experimental data of carrier transport in polycrystalline semiconductors and especially transparent conducting oxides [88], which is mainly due to the fact that in most works on transport properties of polycrystalline films the density of defects was not determined. Podor [135] investigated bended n-type Ge crystals with a dislocation density around 107 cm 2... 

The large vacancy clusters are called voids. At higher temperatures these voids may collapse and form loops. These loops may be regarded as a special type of dislocation. Dislocations are present in every non-ideal material and determine its mechanical properties. The two main types are the edge and the screw dislocations. Defects are called edge dislocations when one plane of atoms in the lattice is missing or supernumerary screw dislocations are formed when a part of the crystal is displaced by an atomic layer. Fig. 14 illustrates the two types of dislocation. 

---