Solid Brouwer diagrams

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. 

A number of factors must be taken into account when the diagrammatic representation of mixed proton conductivity is attempted. The behavior of the solid depends upon the temperature, the dopant concentration, the partial pressure of oxygen, and the partial pressure of hydrogen or water vapor. Schematic representation of defect concentrations in mixed proton conductors on a Brouwer diagram therefore requires a four-dimensional depiction. A three-dimensional plot can be constructed if two variables, often temperature and dopant concentration, are fixed (Fig. 8.18a). It is often clearer to use two-dimensional sections of such a plot, constructed with three variables fixed (Fig. 8.18h-8.18<7). 

The Brouwer diagram approach can be illustrated with reference to the perovskite structure oxide system BaYbvPr VC>3, which has been explored as a potential cathode material for use in solid oxide fuel cells. The parent phase... 

Niekel oxide NiO is metal deficient with cation vacancies predominating. If it is doped with Li, which goes into solid solution on the regular Ni lattice sites, develop equations for the defect equilibria and constract the Brouwer diagram. 

Describe the process of doping by a set of chemical reactions of the appropriate defects. Construct a Brouwer diagram to illustrate the effect of gas partial pressure on the concentration of defects in a solid. 

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