Brouwer Diagrams Electronic Defects

BROUWER DIAGRAMS ELECTRONIC DEFECTS 7.6.1 Electronic Defects... 

Sketch a full Brouwer diagram (log defect concentrations vs log P02) for an oxide MO2 dominated by fully ionised oxygen and metal vacancies at under- and overstoichiometry, respectively. Assume that intrinsic electronic equilibrium predominates close to stoichiometric conditions. (Hint the main goal is to obtain and illustrate the po2-dependencies. Use the rules we listed for such constmctions of Brouwer diagrams.)... 

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 7.10 Brouwer diagram for a phase MX in which electronic 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) the complete diagram.

Frenkel and Schottky defect equilibria are temperature sensitive and at higher temperatures defect concentrations rise, so that values of Ks and Kv, increase with temperature. The same is true of the intrinsic electrons and holes present, and Kc also increases with temperature. This implies that the defect concentrations in the central part of a Brouwer diagram will move upward at higher temperatures with respect to that at lower temperatures, and the whole diagram will be shifted vertically. 

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. 

Brouwer diagrams plot the defect concentrations in a solid as a function of the partial pressure of the components of the material and are a convenient way of displaying electronic properties (Sections 7.6-7.9). These can be readily extended to include the effects of doping by acceptors or donors. 

The discussion of Brouwer diagrams in this and the previous chapter make it clear that nonstoichiometric solids have an ionic and electronic component to the defect structure. In many solids one or the other of these dominates conductivity, so that materials can be loosely classified as insulators and ionic conductors or semiconductors with electronic conductivity. However, from a device point of view, especially for applications in fuel cells, batteries, electrochromic devices, and membranes for gas separation or hydrocarbon oxidation, there is considerable interest in materials in which the ionic and electronic contributions to the total conductivity are roughly equal. 

Fig. 2. (a) Sketch of the relations between defect concentrations and partial pressure (Brouwer diagram) of a pure oxide MO In regime II the intrinsic Schottky disorder determines the concentration, whereas in I and III non-stoichiometry prevails, (b) Dependence of the hole and electron concentration on the frozen-in oxygen vacancy concentration in a negatively (acceptor) doped oxide. 

For a defect situation in an oxide dominated by doubly charged oxygen vacancies and electrons, sketch the van t Hoff plot (Logarithm of defect concentration vs 1/T) and a double-logarithmic plot of defect concentrations vs po2 (Brouwer diagram). 

Figure 4-4. Brouwer diagram of the effects of a higher valent cation impurity/dopant on the concentration of point and electronic defects as a function of oxygen pressure in a metal deficient oxide predominantly containing singly charged metal vacancies.

We assume that the amount of MIO added is well below the solubility so that [Ml ] = constant. Fig. 4.5 shows a Brouwer diagram of the defect situation as a function of oxygen partial pressure when the level of aliovalent dopant is higher than the level of intrinsic disorder. At the lowest the oxide is oxygen-deficient and oxygen vacancies and electrons predominate. As these defects decrease with increasing pg we hit the level of the acceptor dopant. From here... 

We can examine point defects, defects that occur at single atomic site, by applying the principles of chemical reaction equilibrium from this chapter. Atomic point defects include vacancies, interstitials, substitutional impurities, and misplaced atoms. Electronic point defects include mobile electrons and holes. From this approach, we can study carrier concentrations in semiconductors and see the effect of gas partial pressure on defect concentrations at equilibrium. The Brouwer diagram is a particularly useful tool in seeing the effect of gas partial pressure on defect concentration over many orders of magnitude. 

Construct a Brouwer diagram, including regions of low pg, intermediate pg, and high pg,. In the region of intermediate pg, assume that the concentration of electronic defects is greater than the vacancy concentration. When is this material intrinsic When is it n-type When is itp-type ... 

In Example 9.23 we assumed that in the intermediate region, the concentration of electronic defects is greater than the atomic defects. Draw a Brouwer diagram for the case where the concentration of atomic defects is greater than the electronic defects. 

The data shown in Fig. 6 represent values of the conductivities of CuCl coexisting with copper. However, the electronic and ionic conductivities may both depend on the stoichiometry fixed by the chemical potentials of the constituents. Shown in Fig. 7 are two schematic graphs [18] for the behavior of CaF2 The upper graph shows the isothermal variation of the defect concentration with partial pressure of fluorine (a Brouwer or Kroger-Vink diagram) and the lower one shows the corresponding behavior of the conductivities. 

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