Associated defects

Afzelius, B. (1985). The inunotile-cilia syndrome A micronibule-associated defect. CRC Crit. Rev. Biochem. 19, 63-87. 

Note that we have also specified these equilibrium constants in terms of the activity of the associated defects. We can also write thermodynamic equations for these defects ... 

Thus, if Frenkel Defects predominate in a given solid, other defects are usually not present. Likewise, for the Schottky Defect. Note that this applies for associated defects. If these are not present, there will still be 2 types of defects present, each having an opposite effect upon stoichiometry. 

Our study has led us to the point where we can realize that the primary effect of impurities in a solid is the formation of defects, particularly the Frenkel and Schottky types of associated defects. Thus, the primary effect... 

An effective charge relative to the host lattice is possible with any defect. These are added as superscripts to the appropriate symbol VM, Vx, M , Mx and associated defects such as (VMVX). 

Associated defects (vacancy pair) (VMVr) Associated defects with positive effective charge (VmVp) ... 

The high conductivity of (3-alumina is attributed to the correlated diffusion of pairs of ions in the conduction plane. The sodium excess is accommodated by the displacement of pairs of ions onto mO sites, and these can be considered to be associated defects consisting of pairs of Na+ ions on mO sites plus a V N l on a BR site (Fig. 6.12a and 6.12b). A series of atom jumps will then allow the defect to reorient and diffuse through the crystal (Fig. 6.12c and 6.12d). Calculations suggest that this diffusion mechanism has a low activation energy, which would lead to high Na+ ion conductivity. A similar, but not identical, mechanism can be described for (3"-alumina. 

Figure 6.12 Correlated diffusion in (3-alumina (a) the Na+ positions in the conduction plane of ideal NaAlnOi7 (b) the creation of associated defects by location of pairs of Na+ ions on mO sites (c) the ionic jumps involved in diffusion of an associated defect and (d) the final position of the defect.

Point defects of opposite charges tend to be reciprocally attracted, forming the so-called associate defects. 

Let us consider the general case of two point defects A and B forming an associate defect (AB) according to the process... 

If we imagine that both defects A and B and associate defect (AB) are distributed in conditions of complete configurational disorder, and if we substitute thermodynamic activity for the molar concentration, we have... 

For the simple associate defect (AB), cr = 1 and the relative concentrations of associate defect (AB) and free defects A and B are ruled by... 

Figure 4.4 plots relative concentrations of associate defect (AB) and free defects A and B calculated as functions of AHj IkT for various values of c, with Z = 4 and / = 1. Note that when the enthalpy change connected with the association process is low (and/or T is high) all defects are practically free, whereas for high (negative) values of AHj IkT all defects are associated. The dashed line in figure 4.4 represents the equality condition outlined by equation 4.65. 

Figure 4,4 Relative concentrations of free and associate defects for various values of total defect concentration c, with Z = 4 and/ = 1 (from Kroger, 1964 redrawn). Dashed line equality conditions in populations of free and associate defects.

In general terms the relations between possible compound phases in any system are determined by the usual tangent relation between their free energy surfaces. The free energy of any phase is a function of the temperature, activity of the components, number of lattice sites and relative numbers of atoms of each kind in the crystal, concentrations of vacancies, interstitials and substitutions of each kind, concentrations of associated defects, energies of lattice disorder, of defect interactions, of valence change, of ionization, etc. ... 

Associated defects Point defects that are associated or clustered are indicated by enclosing the components of such a group in parenthesis. For example, (VmVx) would represent a defect in which two vacancies are associated as a vacancy pair. 

This may be taken into account by modifying the activation energy of Eq. 2.21 and adding another enthalpy contribution AH, as the enthalpy of formation of associated defects... 

Reimer KA, Jennings RB, Hill ML (1981) Total ischemia in dog hearts, in vitro. 2. High energy phosphate depletion and associated defects in energy metabolism, cell voliune regulation, and sarcolemmal integrity. Circ Res 49 901-911... 

Drugs that effectively treat human disease states by restoring disease-associated defects in signal transduction can act either by replacing endogenous transmitters, e.g., 1-dopa treatment to replace the dopamine (DA) lost... 

In examining the defect state of real crystals such as AgBr, we find that we can write, using equilibrium constants and defect thermodsmamlcs derived from Statistical Mechanics and classical Thermodynamics, valid equations for the numbers and tjrpes of various associated defects present. However, we also find that we cannot solve for the value of the unknown quantities in a set of simultaneous equations since the equations are not linearly solvable. The equations can be written, but the set of equations cannot be easily solved. It is for this reason that we have resorted to graphical method like that of Brouwer, even though it is not entirely satisfactory in its solutions to the numbers and types of defects present in real crystals. 

Our study has led us to the point where we can realize that the primary effect of impurities in a solid is the formation of defects, particularly the Frenkel and Schottky types of associated defects. Thus, the primary effect obtained in purifying a solid is the minimization of defects. Impurities, particularly those of differing valences than those of the lattice, cause charged vacancies and/or interstitials. We can also increase the reactivity of a solid to a certain extent by making it more of a defect crystal by the addition of selected impurities. 

We can thus make an important deduction from our studies, namely that associated defects hove definite effects iqKm the eneigy hand structure of solids. It is not surprising, then, that reactivity of solids depends considerably upon the degree of purity of the solid itself. 

Kav equilibrium of formation of associated defects with oxygen vacancies,... 

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