Predominant defect

The third term in Eq. 7, K, is the contribution to the basal plane thermal resistance due to defect scattering. Neutron irradiation causes various types of defects to be produced depending on the irradiation temperature. These defects are very effective in scattering phonons, even at flux levels which would be considered modest for most nuclear applications, and quickly dominate the other terms in Eq. 7. Several types of in-adiation-induced defects have been identified in graphite. For irradiation temperatures lower than 650°C, simple point defects in the form of vacancies or interstitials, along with small interstitial clusters, are the predominant defects. Moreover, at an irradiation temperatui-e near 150°C [17] the defect which dominates the thermal resistance is the lattice vacancy. 

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. 

The defect structure of wiistite can be discussed from the view of a quasi-chemical equilibrium among defects, similar to the case of Nij O. Assuming that the predominant defects are iron ion vacancies, we obtain the following equations ... 

Cdi) and Cd vacancies (VC(l), and an excess of one over the other gives Cd-rich or Te-rich CdTe. In CdS it was presumed that Cd vacancies and sulfur vacancies (Vs) are the predominant defects and here again nonstoichiometric compositions arise from an excess of one type of defect over the other. Other combinations of interstitials and vacancies are possible and in Bi2Te3 (15) indications are that stoichiometric deviations arise from the presence of one type or atom upon the sublattice of the other (BiTe and TeBi ). 

It is thus seen that whether the type of predominating defects are structural or electronic, the resulting catalytic effect may be only a qualitative... 

It is worth noting here that the exact solution of a set of nonlinear equations for more complicated equilibria is often unachievable. In such cases, the approximation method implying a simplification of the overall electroneutrality condition using the only pair of predominant defects can be useful. This approach can be illustrated on the basis of the above example of a Si crystal. As the equilibrium constants (Equations (3.15-3.17)) are functions of temperature, the concentrations of different defects can alter in different ways, depending on the value of the pre-exponential factor K° and the enthalpy of the defects reaction, AH . As a result, it is possible to choose a temperature range where the overall electroneutrality condition (Equation (3.18)) can be approximated by pairing the predominant defects. In this case, two possible approximations can be suggested ... 

The advantage of such an approximation method becomes clear when complex systems with a number of unknown parameters must be analyzed. It is very convenient to present the results graphically, using log [i] —1/T plots, and one such example, comparing the exact solution and the approximation method mentioned above, is shown in Figure 3.4. As can be seen from these data, the electrons and holes represent the predominant defects in silicon at low temperatures, whereas silicon vacancies and holes dominate at high temperatures. 

Region 1. At relatively high oxygen pressures, the process of Equation (3.32) should dominate, whereas the reaction Equation (3.33) is suppressed. As a result, the pair of predominant defects in this region includes vacancy in the metal sublattice and free hole, with the electroneutrality condition... 

Impurities introduced into the crystal lattice can strongly affect the defect equilibria [9, 15-19]. This influence can be illustrated by the example of MO oxide matrix doped with Me2O3, assuming that predominant defects in pure MO are vacancies in the metal and oxygen sublattices (Vm, V ) in accordance with Equation (3.30). The dissolution of Me2O3 is also assumed to occur via a substitution mechanism, that is, Me atoms incorporate into the M-sublattice ... 

As with oxygen ion-conducting electrolytes, proton conduction in these electrolytes occurs only within a limited range of hydrogen partial pressures. In addition, as they are oxides, oxygen defects can occur. Figure 13.6 shows the predominant defects in indium-doped calcium zirconate, which were calculated based on an extrapolation of conductivity measurements [79]. Hydrogen conduction occurs by interstitials H ... 

Undoped PbS is an -type semiconductor and crystallizes in the NaCl structure. The predominant defects are Frenkel defect pairs on the Pb sublattice. 

A Lorentzian-like line shape indicates random defect distribution across the surface. The oscillation of the rocking curve width as a function of Lri is a direct result of constructive and destructive interference conditions that are alternately satisfied as the momentum transfer perpendicular to the surface, Qz, increases. The vertical extent of the defects, h, is revealed through the relation h = 27dbQz = Chid/5L where 8Q is the characteristic period of the oscillations. The periods of oscillations in Figures 26C and 26D are 80 = 2 / for both surfaces, implying that for each surface the predominant defects correspond to unit-cell-high steps, with h = 7.2 A and 3.4 A on the (001) and... 

Predominant defects in these compounds, which represent one limiting condition,... 

Mrowec and Stoldosa and Mrowec et al have investigated the oxidation of Cu to CU2O over a range of temperatures and oxygen partial pressures and their results are shown in Figure 3.12. From this it is clear that the exponent is very close to 1 /4, indicating that neutral cation vacancies are the predominant defect species in CU2O. 

Manganous Sulfide Nonstoichiometry and defect concentrations are very low in Mni yS of the order of that in nickel oxide. The predominant defect equilibrium is... 

Atlas and Schlehman have measured the variation of oxygen content and electrical conductivity with oxygen pressure in the temperature range from 1100 to 16(X)°C (87). From the pressure dependence of the electrical conductivity, they inferred that the defects in Pu02 j are constituted of predominantly interstitial plutonium ions, and discussed the change of the form of defects with temperature. However, measurements by the same authors on the density of the PuOj-j. phases (277) led to the conclusion that oxygen vacancies are the predominant defects in the PUO2 phase. 

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