Reactions defect

The formation of the various point defects can be described by chemical reactions for which the following rules have to be followed  

This does not imply that the ratio has to be maintained for the number cf atoms or ions, but only for the number of sites. 

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Furthermore, equilibria hold for ions and electrons. In every case, the Gibbs energy of the defect reaction has to provide a minimum for the equilibrium concentrations ... 

Returning to the subject of lattice defect formation, we can now proceed to write a series of defect reactions for the defects which we found for our plane net ... 

In this case, we use 6 as a small fraction since the actual number of defects is small in relation to the overall number of ions actually present. For the F-Center, the brackets enclose the complex consisting of an electron captured at an anion vacancy. Note that these equations encompass all of the mechanisms that we have postulated for each of the individual reactions. That is, we show the presence of vacancies in the Schottlqr case and interstitial cations for the Frenkel case involving either the cation or anion. The latter, involving an interstitlcd anion is called, by convention, the "Anti-Frenkel" case. The defect reaction involving the "F-Center" is also given. 

Actually, the formation of an F-center is more complicated than this. Although F-centers can be formed by severed methods, the best way to do so is by exposing a sodium chloride ciystal to sodium metal vapors. In that case, the following defect reactions have been observed to take place ... 

In a non-stoichiometric crystcd, the lattice may have either excess charge or excess cations and/or anions situated in the lattice. Consider the semiconductor, Ge. It is a homogeneous solid and is expected to contain excess charge. The defect reactions associated with the formation of p-type and n-type lattices are ... 

They are usually joined along the 110 plane of the lattice of the face-centered salt crystal, although we have not shown them this way (The 100 plane is illustrated in the diagram). Note that each vacancy has captured an electron in response to the charge-compensation mechanism which is operative for all defect reactions. In this case, it is the anion which is affected whereas in the "F-center", it was the cation which was affected (see equation 3.2.8. given above). These associated, negatively-charged, vacancies have quite different absorption properties than that of the F-center. 

Another genre is the so-called homotype impurity system. One example is the substance, nickelous oxide, which is a pale-green insulator when prepcired in an inert atmosphere. If it is reheated in air, or if a mixture of NiO and Li+ is reheated in an inert atmosphere, the NiO becomes a black semi-conductor. This is a classical example of the effect of defect reactions upon the intrinsic properties of a soUd. The defect reactions involved are ... 

Having Introduced these examples, let us now examine a method of symbolism useful in characterizing defect reactions in solids. 

Whether you recdize it or not, we have already developed our own symbolism for defects and defect reactions based on the Plane Net. It might be well to compeu e our system to those of other authors, who have also considered the same problem in the past. It was Rees (1930) who wrote the first monograph on defects in solids. Rees used a box to represent the cation vacancy, as did Libowitz (1974). This has certain advantages since we can write equation 3.3.5. as shown in the following ... 

Before we proceed to analyze defect reactions by a mathematical approach, let us consider an applications of solid state chemistry. In this example, the effect of a defect on the properties of the solid is described. 

The explanation lies in the defect reactions controlling the formation of the phosphor itself. The defect reactions occurring were found to be the substitution of a trlvalent cation on a divalent site and the defects reactions thereby associated. This is shown in the following table which compares these two methods of preparing such materials. In this case, the increase in brightness was found to be related to the amount of activator actually being incorporated into the lattice. It is well known that phosphor brightness is proportional to the numbers of Sb3+ ions (activators) actually incorporated into cation sites of the pyrophosphate structure. 

Defect Reactions Which Occur in the Phosphor (Ca.99, Sb.oi )2P2C>7)-... 

Note that we have written two defect reactions for the case of vacancy formation in Table 3-2. Pyrophosphate is an insulator and the formation of a positively-charged vacancy is much less likely than the vacancy plus a free positive charge. This brings us to a rule found in defect chemistry that seems to be universal, namely ... 

ALTHOUGH MORE THAN ONE DEFECT REACTION MAY BE APPLICABLE TO A GIVEN SITUATION, ONLY ONE IS USUALLY FAVORED BY THE PREVAILING THERMODYNAMIC AND ELECTRON-COMPENSATION CONDITIONS. 

Given the strontium chloride crystal, write the defect reaction(s) expected if lithium chloride is present as an impurity. Do likewise for the antimony chloride impurity. Also, write the defeet reactions expected if both impurities are present in equal quantities. 

Write equations for as many of the thirty (30) defects reactions of your "PU" plane-net as you can. Do not forget the defect-pairs. 

The last defect is one involving two nearest neighbor cation lattice-sites The following Table presents the defect reactions governing this case. 

If we have thermal disorder at room temperature (I do not know of any crystal for which this is not the case), then we can expect the following defect reaction relations ... 

The following gives the standard Enthalpy and Entropy of these defect reactions, according to Kroeger (1965) ... 

Difiusion mechanisms involve the following defect reactions ... 

Chapter 3).The following defect reactions would then be operative as shown ... 

One of the results of this variety in hydrogen-defect reaction pathways is that it largely clouds one of the hopes of the hydrogenation experiments, namely that the susceptibility of deactivation could provide information on the defect microstructure and the nature of the bonding with hydrogen. 

The description theoretical study of defects frequently refers to some computation of defect electronic structure i.e., a solution of the Schrodin-ger equation (Pantelides, 1978 Bachelet, 1986). The goal of such calculations is normally to complement or guide the corresponding experimental study so that the defect is either properly identified or otherwise better understood. Frequently, the experimental study suffices to identify the basic structure of the defect this is particularly true when the system is EPR (electron paramagnetic resonance) active. However, if the computational method properly simulates the defect, we are provided with a wealth of additional information that can be used to reveal some of the more basic and general features of many-electron defect systems and defect reactions. 

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. 

Of course, it is possible to write other and more complex defect reactions, which may be equally compatible with the results. In all of these examples, therefore, direct evidence is desirable before the mechanisms can be regarded as proven. 

To construct such a diagram, a set of defect reaction equations is formulated and expressions for the equilibrium constants of each are obtained. The assumption that the defects are noninteracting allows the law of mass action in its simplest form, with concentrations instead of activities, to be used for this purpose. To simplify matters, only one defect reaction is considered to be dominant in any particular composition region, this being chosen from knowledge of the chemical attributes of the system under consideration. The simplified equilibrium expressions are then used to construct plots of the logarithm of defect concentration against an experimental variable such as the log (partial pressure) of the components. The procedure is best illustrated by an example. 

The Gibbs energy of this defect reaction defines the degree of disorder through the equilibrium constant. 

Analyses of the defect chemistry and thermodynamics of non-stoichiometric phases that are predominately ionic in nature (i.e. halides and oxides) are most often made using quasi-chemical reactions. The concentrations of the point defects are considered to be low, and defect-defect interactions as such are most often disregarded, although defect clusters often are incorporated. The resulting mass action equations give the relationship between the concentrations of point defects and partial pressure or chemical activity of the species involved in the defect reactions. 

The relation between Co Co and V may be expressed by the following defect reaction and equilibrium with increasing temperature ... 

Using the spin integration method described above, it was also determined that at an average formal valence of +4 Xu = 0) both Mn and Co undergo a simple tetrahedral defect reaction... 

Assume that ionic diffusion in Fei.xO occurs via cation vacancies. A defect reaction that conserves charge and atoms can be written as... 

Write balanced defect reaction equations using Kroger-Vink notation. 

Defect Reaction Equilibrium Constants. Recall that a Frenkel disorder is a self interstitial-vacancy pair. In terms of defect concentrations, there should be equal concentrations of vacancies and interstitials. Frenkel defects can occur with metal... 

Write a defect reaction equation for the substitution of a CaCl2 molecule into a KCl lattice. 

Solution There are actually two ways that CaCl2 can be placed in the KCl lattice substitutionally and interstitially. The defect reaction equation for substitution is... 

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