Defects, types

The type of disorder may be determined by conductivity measurements of electronic and ionic defects as a function of the activity of the neutral mobile component [3]. The data are commonly plotted as Brouwer diagrams of the logarithm of the concentration of all species as a function of the logarithm of the activity of the neutral mobile component. The slope is fitted to the assumption of a specific defect-type model. 

Figure 8 Measure of delocalisation of each defect type predicted by resonance theory. The loops enclose centres which have numbers of classical structures larger than. 74 times the greatest number in the type. The cut-off point for type bi (or type 63) centres is particularly arbitrary since the delocalisation is spread around the equator. The small circles are the point of muonium attachment. The dotted circle is coincident with the equator of Cra-...

Defect Type Notation Defect Type Notation... 

There is no obvious reason why only one defect type should occur in a crystal, and several different species would be expected to be present. However, the formation energy of each defect type is different, and it is often a reasonable approximation to assume that only one or a small number of defect types will dominate the chemical and physical properties of the solid. 

Despite the fact that not all details of the photographic process are completely understood, the overall mechanism for the production of the latent image is well known. Silver chloride, AgBr, crystallizes with the sodium chloride structure. While Schottky defects are the major structural point defect type present in most crystals with this structure, it is found that the silver halides, including AgBr, favor Frenkel defects (Fig. 2.5). 

Photochromic behavior depends critically upon the interaction of two point defect types with light Frenkel defects in the silver halide together with substitutional Cu+ impurity point defects in the silver halide matrix. It is these two defects together that constitute the photochromic phase. 

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. 

The important quantities AH and AS are assumed to be temperature independent. This is often quite a good approximation, but the vibrational component of the entropy, which has been neglected altogether, will become increasingly important at high temperatures. The effects of these factors can cause the major defect type present to change as the temperature increases. Near to the transition temperature a complex equilibrium between both defect types will be present. 

The favored defect type in strontium fluoride, which adopts the fluorite structure, are Frenkel defects on the anion sublattice. The enthalpy of formation of an anion Frenkel defect is estimated to be 167.88 kJ mol-1. Calculate the number of F- interstitials and vacancies due to anion Frenkel defects per cubic meter in SrF2 at 1000°C. The unit cell is cubic, with a cell edge of 0.57996 nm and contains four formula units of SrF2. It is reasonable to assume that the number of suitable interstitial sites is half that of the number of anion sites. 

There are two overriding considerations to keep in mind when discussing diffusion in solids the structure of the matrix across which diffusion occurs and the defects present. In a normal crystalline solid, diffusion is mediated by the defects present, and the speed of diffusion will vary significantly if the predominant defect type changes. This is because diffusion involves the movement of a species from a stable position, through some sort of less stable position or bottleneck, to another stable position. Any disorder in the solid due to defects will make this process easier. 

More than one point defect species may be present in a crystal at any temperature, and the amount of matter transported by diffusion will depend upon the number of each defect type present. In general, therefore, the overall apparent diffusion coefficient, D, will be the sum of the individual contributions, for example ... 

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. 

Figure 7.9 Brouwer diagram for a phase MX in which Schottky defects are the main point defect type (a) initial points on the diagram, (b) variation of defect concentrations in the near-stoichiometric region, (c) extension to show variation of defect concentrations in the high partial pressure region, (d) extension to show variation of defect concentrations in the low partial pressure region, and (e) complete diagram.

Finally, it is apparent that the principal defect type may change as the temperature increases, so that, for example, electronic defects may become more important than ionic defects. In such cases the diagram will change appreciably. 

It is necessary to write the electroneutrality equation in terms of just two variables, a defect type and the partial pressure, to obtain a polynomial capable of solution. For example, the equation for the concentration of holes, [h ], is obtained thus Electroneutrality ... 

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. 

Which of these possibilities is preferred can be answered by experiment. A plot of the strontium content, x, in Lai - Sr CoOs-s, versus the oxygen content, 3 8, for the two possibilities, Vo or Co 0, can be drawn and compared with experimental measurements, which show that both defect types are present with vacancies dominating (Fig. 8.15). The material is a mixed conductor. 

The relative solubilities reported are very crude estimates based on equilibrium solubility products. These estimates do not take into account variations in solubility as a function of pH, ionic strength, activities of various solution species (e.g., HCO "), redox state, particle size, surface defect types and concentrations, the concentration of various types of adsorbates, including natural organic matter, on mineral surface, or the presence of different types of bacteria or microbial biofilms on mineral surfaces. 

Table 1.4.12 Fed and fasting state for a patient affected with a pyruvate carboxylase defect (type B)...

Fig. 2.2.1 Outline of homocysteine metabolism in man. BMT Betaine methyltransferase, cblC cobalamin defect type C, cblD cobalamin defect type D, GNMT def glycine N-methyltransferase deficiency, MAT methionine adenosyl transferase, MeCbl methylcobalamin, Met Synth methionine synthase, MTHFR methylenetetrahydrofolate reductase, SAH Hyd dc/S-adenosylhomocys-...

Since the ratio of number of anions to cations in a unit cell for the Fluorite structure is 1 to 2, the compound Zro.gsCao isOj 5 can be said to be non-stoichiometric. The possible defect types are anion vacancies or interstitial cations. X-ray diffraction studies have definitely confirmed that the former type of defect structure is dominant therefore, there exist oxygen vacancies up to 7.5 per cent. The concentration of oxygen vacancies must depend on Po., as is usual for the metal oxides. 

That electronic changes occur when the catalyst is brought into contact with N20 has been well established from semiconductivity measurements, while the use of catalysts containing known amounts of foreign oxides, i.e., of controlled defect type and concentration, has enabled Hauffe 3, 56) to distinguish in some cases between the possible rate-determining steps in the above set of reactions. The present position is admirably summarized by Hauffe (3, 56) and by Stone (3). 

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