Defects population

On the other side of stoichiometry, we know from experiment that the constitutional defect in NiAl is the vacancy, so we can assume that Cva dominatej he defect populations. In this case we obtain the solution ... 

Note that in Regimes II and III, pair-creation of defects does riot take place rather the defect population gradually dwiridles by pair-annihilation during collisions. Numerical simulations suggest that the average number of defects decreases... 

As well as these intrinsic structural defect populations, electronic defects (excess electrons and holes) will always be found. These are also intrinsic defects and are present even in the purest material. When the equilibria among defects are considered, it is necessary to include both structural and electronic defects. 

The mechanical consequences of defect populations are less frequently considered than optical or electronic aspects, but they are of importance in many ways, especially when thin films or nanoparticles are considered. 

Calculate the theoretical density for alternative point defect populations. 

Such changes in the defect population can be critical in device manufacture and operation. For example, a thin him of an oxide such as SiO laid down in a vacuum may have a large population of anion vacancy point defects present. Similarly, a him deposited by sputtering in an inert atmosphere may incorporate both vacancies and inert gas interstitial atoms into the structure. When these hlms are subsequently exposed to different conditions, for example, moist air at high temperatures, changes in the point defect population will result in dimensional changes that can cause the him to buckle or tear. 

Ionic conductors, used in electrochemical cells and batteries (Chapter 6), have high point defect populations. Slabs of solid ceramic electrolytes in fuel cells, for instance, often operate under conditions in which one side of the electrolyte is held in oxidizing conditions and the other side in reducing conditions. A signihcant change in the point defect population over the ceramic can be anticipated in these conditions, which may cause the electrolyte to bow or fracture. 

Point defect populations profoundly affect both the physical and chemical properties of materials. In order to describe these consequences a simple and self-consistent set of symbols is required. The most widely employed system is the Kroger-Vink notation. Using this formalism, it is possible to incorporate defect formation into chemical equations and hence use the powerful methods of chemical thermodynamics to treat defect equilibria. 

In the knowledge that the Gibbs energy of a crystal containing a small number of intrinsic defects is lower than that of a perfect crystal, the defect population can be treated as a chemical equilibrium. In the case of vacancies we can write... 

In order for the battery to function, the lithium iodide must be able to transfer ions. Lil adopts the sodium chloride structure, and there are no open channels for ions to use. In fact, the cell operation is sustained by the Schottky defect population in the... 

The Schottky defect population in the electrolyte is rather too low for practical purposes. To overcome this problem the Lil is sometimes doped with Cal2. The extra I- ions extend the Lil structure, and the Ca2+ ions form substitutional impurity defects on sites normally reserved for Li+ ions. The consequence of this is that each Ca2+ ion in Lil will form one cation vacancy over and above those present due to Schottky defects in order to maintain charge neutrality. This can be written... 

The actual current drain that these batteries can support is low and is limited by the point defect population. However, the cell has a long life and high reliability, making it ideal for medical use in heart pacemakers. 

The estimation of the number of Frenkel defects in a crystal can proceed along lines parallel to those for Schottky defects by estimating the configurational entropy (Supplementary Material S4). This approach confirms that Frenkel defects are thermodynamically stable intrinsic defects that cannot be removed by thermal treatment. Because of this, the defect population can be treated as a chemical equilibrium. For a crystal of composition MX, the appropriate chemical equilibrium for Frenkel defects on the cation sublattice is... 

The formation of latent images is a multistage process, involving the Frenkel defect population. The major steps in the formation of the latent image follow a path similar to that originally suggested by Gurney and Mott (1938) ... 

Lithium iodide pacemaker batteries use lithum iodide as the electrolyte, separating the lithium anode and the iodine anode. The function of the electrolyte is to transport ions but not electrons. Lithium iodide achieves this by the transport of Li+ ions from the anode to the cathode. This transport is made possible by the presence of Li vacancies that are generated by the intrinsic Schottky defect population present in the solid. Lithium ions jump from vacancy to vacancy during battery operation. 

The simplest way to account for composition variation is to include point defect populations into the crystal. This can involve substitution, the incorporation of unbalanced populations of vacancies or by the addition of extra interstitial atoms. This approach has a great advantage in that it allows a crystallographic model to be easily constructed and the formalism of defect reaction equations employed to analyze the situation (Section 1.11). The following sections give examples of this behavior. 

These point defect models need to be regarded as a first approximation. Calculations for stoichiometric GaAs suggest that balanced populations of vacancies on both gallium and arsenic sites, VGa and VAs, exist, as well as defect complexes. Calculation for nonstoichiometric materials would undoubtedly throw further light on the most probable defect populations present. 

The continuous sinusoidal composition change that occurs during spinodal decomposition can be considered to be a modulation of the solid structure. It is now known that many structures employ modulation in response to compositional or crystallographic variations, and in such cases the material flexibly accommodates changes without recourse to defect populations. (Other modulations, in, for example, magnetic moments or electron spins, although important, will not be discussed here.)... 

Movement through the body of a solid is called volume, lattice, or bulk diffusion. In a gas or liquid, bulk diffusion is usually the same in all directions and the material is described as isotropic. This is also true in amorphous or glassy solids and in cubic crystals. In all other crystals, the rate of bulk diffusion depends upon the direction taken and is anisotropic. Bulk diffusion through a perfect single crystal is dominated by point defects, with both impurity and intrinsic defect populations playing a part. 

When the random-walk model is expanded to take into account the real structures of solids, it becomes apparent that diffusion in crystals is dependent upon point defect populations. To give a simple example, imagine a crystal such as that of a metal in which all of the atom sites are occupied. Inherently, diffusion from one normally occupied site to another would be impossible in such a crystal and a random walk cannot occur at all. However, diffusion can occur if a population of defects such as vacancies exists. In this case, atoms can jump from a normal site into a neighboring vacancy and so gradually move through the crystal. Movement of a diffusing atom into a vacant site corresponds to movement of the vacancy in the other direction (Fig. 5.7). In practice, it is often very convenient, in problems where vacancy diffusion occurs, to ignore atom movement and to focus attention upon the diffusion of the vacancies as if they were real particles. This process is therefore frequently referred to as vacancy diffusion... 

When Schottky defects are present in a crystal, vacancies occur on both the cation and anion sublattices, allowing both cation and anion vacancy diffusion to occur (Fig. 5.12a). In the case of Frenkel defects interstitial, interstitialcy, and vacancy diffusion can take place in the same crystal with respect to the atoms forming the Frenkel defect population (Fig. 5.12b). 

Just as one point defect type may dominate the defect population in a crystal, so one diffusion coefficient may be dominant, but the other diffusion coefficients can sometimes make an important contribution to the overall transport of atoms through a solid. It is by no means easy to separate these contributions to a measured value of D, and, as well as theoretical assessments, the way in which the diffusion coefficient varies with temperature can help. 

In very pure crystals, the number of intrinsic defects may be greater than the number of defects due to impurities, especially at high temperatures. Under these circumstances, the value of D0 will be influenced by the intrinsic defect population and may contribute to the observed value of the activation energy. 

VARIATION OF DEFECT POPULATIONS WITH PARTIAL PRESSURE 315... 

Models describing the point defect population can be used to determine how the electronic conductivity will vary with changes in the surrounding partial pressure. 

Defect populations and physical properties such as electronic conductivity can be altered and controlled by manipulation of the surrounding atmosphere. To specify the exact electronic conductivity of such a material, it is necessary to specify its chemical composition, the defect types and populations present, the temperature of the crystal, and the surrounding partial pressures of all the constituents. Brouwer diagrams display the defect concentrations present in a solid as a function of the partial pressure of one of the components. Because the defect populations control such properties as electronic and ionic conductivity, it is generally easy to determine how these vary as the partial pressure varies. 

---