Types of Point Defects

Ttiiis, the charge compensation mechanism represents the single 

Because of this, the number and types of defects, which can appear in the solid, are limited. This restricts the number of defect types we need to consider, in both elemental (all the same kind of atom) and ionic lattices (having both cations and anions present). We have shown that by stacking atoms or propagation units together, a solid with specific symmetry results. If we have done this properly, a perfect solid should result with no holes or defects in it. Yet, the 2nd law of thermodynamics demands that a certain number of point defects (vacancies) appear in the lattice. It is impossible to obtain a solid without some sort of defects. A perfect solid would violate this law. The 2nd law states that zero entropy is only possible at absolute zero temperature. Since most solids exist at temperatures far from absolute zero, those that we encounter are defect-solids. It is natural to ask what the nature of these defects might be, particularly when we add a foreign cation (activator) to a solid to form a phosphor. 

Consider the surface of a solid. In the interior, we see a certain s nnmetry which depends upon the structure of the solid. As we approach the surface from the interior, the symmetry begins to change. At the very surface, the surface atoms see only half the symmetry that the interior atoms do. Reactions between solids take place at the surface. Thus, the surface of a solid represents a defect in itself since it is not like the interior of the solid. 

In a three-dimensional solid, we can postulate that there ought to be 

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Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

This type of point defect formation is summarized by the general notation due to Kroger and Viirk in tire equivalent form... 

Fig. 20.27 (a) Schematic illustration of two types of point defect and (b) three stages in diffu-... 

Types of Point Defects Expected in a Homogeneous Solid... 

On the left, in 3.1.1., are the two types of point defects which involve the lattice itself, while the others involve impurity atoms. Indeed, there do not seem to any more than these four, and indubitably, no others have been observed. Note that we are limiting our defect family to point defects in the lattice and are ignoring line and volume defects of the lattice. These four point defects, given above, are illustrated in the following diagram, given as 3.1.2. on the next page. 

Intrinsic Defects The simplest 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 and Frenkel defects. A Schottky defect consists of a pair of vacant sites a cation vacancy and an anion vacancy. A Schottky defect is... 

One type of point defect that cannot be entirely eliminated from a solid compound is the substituted ion or impurity defect. For example, suppose a large crystal contains 1 mole of NaCl that is 99.99 mole percent pure and that the 0.01% impurity is KBr. As a fraction, there is 0.0001 mole of both K+ and Br ions, which is 6.02 X 1019 ions of each type present in the 1 mole of NaCl Although the level of purity of the NaCl is high, there is an enormous number of impurity ions that occupy sites in the lattice. Even if the NaCl were 99.9999 mole percent pure, there would still be 6.02 X 1017 impurity cations and anions in a mole of crystal. In other words, there is a defect, known as a substituted ion or impurity defect, at each point in the crystal where some ion other than Na+ or Cl- resides. Because K+ is larger than Na+ and Br is larger than Cl-, the lattice will experience some strain and distortion at the sites where the larger cations and anions reside. These strain points are frequently reactive sites in a crystal. 

A somewhat different situation is found in the type of point defect known as a Frenkel defect. In this case, an atom or ion is found in an interstitial position rather than in a normal lattice site as is shown in Figure 7.17. In order to position an atom or ion in an interstitial position, it must be possible for it to be close to other lattice members. This is facilitated when there is some degree of covalence in the bonding as is the case for silver halides and metals. Accordingly, Frenkel defects are the dominant type of defect in these types of solids. 

The potassium ions that are produced occupy cation lattice sites, but no anions are produced so electrons occupy anion sites. In this situation, the electron behaves as a particle restricted to motion in a three-dimensional box that can absorb energy as it is promoted to an excited state. It is interesting to note that the position of the maximum in the absorption band is below 4000A (400nm, 3.1 eV) for LiCl but it is at approximately 6000 A (600 nm, 2eV) for CsCl. One way to explain this observation is by noting that for a particle in a three-dimensional box the difference between energy levels increases as the size of the box becomes smaller, which is the situation in LiCl. Schottky, Frenkel, and F-center defects are not the only types of point defects known, but they are the most common and important types. 

The various types of point defect found in pure or almost pure stoichiometric solids are summarized in Figure 1.17. It is not easy to imagine the three-dimensional consequences of the presence of any of these defects from two-dimensional diagrams, but it is important to remember that the real structure of the crystal surrounding a defect can be important. If it is at all possible, try to consult or build crystal models. This will reveal that it is easier to create vacancies at some atom sites than others, and that it is easier to introduce interstitials into the more open parts of the structure. 

The number of different types of point defects found in a pure monatomic crystal is ... 

N is here the number of lattice defects (vacancies or interstitials) which are responsible for non-stoichiometry. AHfon is the variation of lattice enthalpy when one noninteracting lattice defect is introduced in the perfect lattice. Since two types of point-defects are always present (lattice defect and altervalent cations (electronic disorder)), the AHform takes into account not only the enthalpy change due to the process of introduction of the lattice defect in the lattice, but also that occurring in the Redox reaction creating the electronic disorder. 

The second type of point defect is called an impurity. Impurities can occur in two ways as an interstitial impurity, in which an atom occupies an interstitial site (see Figures 1.21, 1.22, and 1.29) or when an impurity atom replaces an atom in the perfect lattice (see Figure 1.29). In the first instance, either the same atom as in the lattice, or an impurity atom, can occupy an interstitial site, causing considerable lattice strain as the atomic planes distort slightly to accommodate the misplaced atom. The amount of strain created depends on how large the atom is relative to lattice atoms. It... 

We have to evaluate the diffusion coefficient or any other transport coefficient with the help of point defect thermodynamics. This can easily be done for reaction products in which one type of point defect disorder predominates. Since we have shown in Chapter 2 that the concentration of ideally diluted point defects depends on the chemical potential of component k as d lncdefec, = n-dp, we obtain quite generally... 

The current majority opinion is that both types of point defects are important. Thermal equilibrium concentrations of point defects at the melting point are orders of magnitude lower in Si than in metals. Therefore, a direct determination of their nature by Simmons-Balluffi-type experiments (26) has not been possible. The accuracy of calculated enthalpies of formation and migration is within 1 eV, and the calculations do not help in distinguishing between the dominance of vacancies or interstitials in diffusion. The interpretation of low-temperature experiments on the migration of irradiation-induced point defects is complicated by the occurrence of radiation-induced migration of self-interstitials (27, 28). 

If both types of point defects are important, then diffusion processes may involve both types, and the following relation applies... 

In summary, a variety of ab initio and DFT methods can be applied for different types of model clusters. A comparison of the results of different methods with available experimental data should be carried out and, based on this comparison, a proper theoretical procedure should be chosen for each particular type of point defect in Si02 and Ge02. 

The concept of a zero-dimensional intrinsic point defect was first introduced in 1926 by the Russian physicist Jacov Il ich Frenkel (1894-1952), who postulated the existence of vacancies, or unoccupied lattice sites, in alkali-halide crystals (Frenkel, 1926). Vacancies are predominant in ionic solids when the anions and cations are similar in size, and in metals when there is very little room to accommodate interstitial atoms, as in closed packed stmctures. The interstitial is the second type of point defect. Interstitial sites are the small voids between lattice sites. These are more likely to be occupied by small atoms, or, if there is a pronounced polarization, to the lattice. In this way, there is little dismption to the stmcture. Another type of intrinsic point defect is the anti-site atom (an atom residing on the wrong sublattice). 

The most prevalent type of point defect that occurs at metal oxide surfaces is an oxygen vacancy (Henrich, 1983, 1985), and this is illustrated for MgO(lOO) and TiOjlllO) in Figs. 8.13 and 8.16. At such defects, there is a reduction of the ligand coordination of adjacent surface cations, generally from five to four. Removal of an oxygen anion also reduces the... 

We mentioned above the collision cascade producing displaced atoms in a solid target. If we consider a single collision event in a crystalline solid, we can see that this displacement of atoms leads to the preferential formation of point defects. The most important types of point defects are a single vacancy (one atom or ion is missing), a single interstitial (an additional atom), a vacancy-interstitial pair (Frenkel pair). 

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). 

Schottky and Frenkel defects do not alter the stoichiometry of the material as they are intrinsic. In non-stoichiometric materials, both types of point defect occur, but ... 

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. 

In this diagram, we see three types of point defects. In addition to the vacancy, we also see two types of substitutional defects. Both are direct substitutions in the "lattice", or arrangement of the atoms. One is a smaller atom, while the other is larger than the atoms comprising the lattice. Note the difference, due to size of the impurity, upon the ordering... 

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