Point defects compounds

Some good papers have been published recently. Unfortunately the corresponding experimental data are most often lacking. The point-defect properties calculated from the electronic structure will have to be integrated in a proper thermodynamic theory. Such knowledge will also allow study in important fields that are practically unexplored up to now in intermetallic compounds point defect-impurity interaction, point defect-dislocation interaction, and consequences on the mechanical properties, etc. Considerable work is still required. 

It is not necessary for a compound to depart from stoichiometry in order to contain point defects such as vacant sites on the cation sub-lattice. All compounds contain such iirndirsic defects even at the precisely stoichiometric ratio. The Schottky defects, in which an equal number of vacant sites are present on both cation and anion sub-lattices, may occur at a given tempe-ramre in such a large concentration drat die effects of small departures from stoichiometry are masked. Thus, in MnOi+ it is thought that the intrinsic concentration of defects (Mn + ions) is so large that when there are only small departures from stoichiometry, the additional concentration of Mn + ions which arises from these deparmres is negligibly small. The non-stoichiometry then varies as in this region. When the departure from non-stoichio-... 

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. 

We will be considering primarily inorganic solids but must keep in mind that the same principles also apply to organic solids. Therefore, we intend to examine the nature of point defects in terms of their thermodynamics, equilibria and the energy required for their formation. It will be seen that point defects follow the same physical chemistry laws that apply to inorgcuiic compounds and physical properties in general. 

Now, suppose that we have a solid solution of two (2) elemental solids. Would the point defects be the same, or not An easy way to visualize such point defects is shown in the following diagram, given as 3.1.3. on the next page. It is well to note here that homogeneous lattices usually involve metals or solid solutions of metals (alloys) in contrast to heterogeneous lattices which involve compounds such as ZnS. 

A considerable body of scientific work has been accomplished in the past to define and characterize point defects. One major reason is that sometimes, the energy of a point defect can be calculated. In others, the charge-compensation within the solid becomes apparent. In many cases, if one deliberately adds an Impurity to a compound to modify its physical properties, the charge-compensation, intrinsic to the defect formed, can be predicted. We are now ready to describe these defects in terms of their energy and to present equations describing their equilibria. One way to do this is to use a "Plane-Net". This is simply a two-dimensional representation which uses symbols to replace the spherical images that we used above to represent the atoms (ions) in the structure. 

We have Investigated the structure of solids In the second chapter and the nature of point defects of the solid in the third chapter. We are now ready to describe how solids react. This will Include the mechanisms Involved when solids form by reaction from constituent compounds. We will also describe some methods of measurement and how one determines extent and rate of the soUd state reaction actually taking place. We will also show how the presence and/or formation of point defects affect reactivity In solid state reactions. They do so, but not In the memner that you might suspect. We will also show how solid state reactions progress, particularly those involving silicates where several different phases appear as a function of both time and relative ratios of reacting components. 

Cul) is not due to point defects but to partial occupation of crystallographic sites. The defective structure is sometimes called structural disorder to distinguish it from point defects. There are a large number of vacant sites for the cations to move into. Thus, ionic conductivity is enabled without use of aliovalent dopants. A common feature of both compounds is that they are composed of extremely polarizable ions. This means that the electron cloud surrounding the ions is easily distorted. This makes the passage of a cation past an anion easier. Due to their high ionic conductivity, silver and copper ion conductors can be used as solid electrolytes in solid-state batteries. 

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. 

No material is completely pure, and some foreign atoms will invariably be present. If these are undesirable or accidental, they are termed impurities, but if they have been added deliberately, to change the properties of the material on purpose, they are called dopant atoms. Impurities can form point defects when present in low concentrations, the simplest of which are analogs of vacancies and interstitials. For example, an impurity atom A in a crystal of a metal M can occupy atom sites normally occupied by the parent atoms, to form substitutional point defects, written AM, or can occupy interstitial sites, to form interstitial point defects, written Aj (Fig. 1.4). The doping of aluminum into silicon creates substitutional point defects as the aluminum atoms occupy sites normally filled by silicon atoms. In compounds, the impurities can affect one or all sublattices. For instance, natural sodium chloride often contains... 

Figure 1.3 Point defects in a crystal of a pure compound, MX, VM, a metal vacancy Vx a nonmetal vacancy Mj, a metal (self-)interstitial and Xs a nonmetal (self-)interstitial.

Compounds are made up of atoms of more than one chemical element. The point defects that can occur in pure compounds parallel those that occur in monatomic materials, but there is an added complication in this case concerning the composition of the material. In this chapter discussion is confined to the situation in which the composition of the crystal is (virtually) fixed. Such solids are called stoichiometric compounds. (The situations that arise when the composition is allowed to vary are considered in Chapter 4 and throughout much of the rest of this book. This latter type of solid is called a nonstoichiometric compound.) The composition problem can be illustrated with respect to a simple compound such as sodium chloride. 

A point defect is a localized defect that consists of a mistake at a single atom site in a solid. The simplest point defects that can occur in pure crystals are missing atoms, called vacancies, or atoms displaced from the correct site into positions not normally occupied in the crystal, called self-interstitials. Additionally atoms of an impurity can occupy a normal atom site to form substitutional defects or can occupy a normally vacant position in the crystal structure to form an interstitial. Other point defects can be characterized in pure compounds that contain more than one atom. The best known of these are Frenkel defects, Schottky defects, and antisite defects. 

At all temperatures above 0°K Schottky, Frenkel, and antisite point defects are present in thermodynamic equilibrium, and it will not be possible to remove them by annealing or other thermal treatments. Unfortunately, it is not possible to predict, from knowledge of crystal structure alone, which defect type will be present in any crystal. However, it is possible to say that rather close-packed compounds, such as those with the NaCl structure, tend to contain Schottky defects. The important exceptions are the silver halides. More open structures, on the other hand, will be more receptive to the presence of Frenkel defects. Semiconductor crystals are more amenable to antisite defects. 

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