Vacancy-dopant associates

Here AH , is the enthalpy of vacancy migration, A//y is the enthalpy of vacaney formation, and A//a is the enthalpy of vacancy-dopant association, e.g. ... 

Extensive atomistic simulation work " has provided valuable insights into the nature of defect association and migration. It is generally recognized that both attractive coulombic interactions and attractive or repulsive elastic lattice relaxation play a major role in the energetics of ionic transport. The atomistic simulations conclude that for small dopants, the oxide ion vacancies preferentially associate with dopant ions, whereas for large dopants the oxide ion vacancies tend to associate with Ge host cations. The switchover is estimated to occur at a rare-earth dopant ionic radius similar to that of Gd, which offers a rational for the minimum in activation energy and the maximum in ionic conductivity observed for Gd- or Sm-doped Andersson et con-... 

Sohd solutions of ceria with trivalent ions, eg, Y and La, can readily be formed. The ions substitute for the tetravalent Ce and introduce one oxygen vacancy for every two ions. The dopant ions and the oxygen vacancies form charge associates. The resulting defect-fluorites have good oxide... 

A silicon surface, no mater how well it is prepared, is not perfectly flat at the atomic scale, but has surface defects such as surface vacancies, steps, kinks sites, and dopant atoms. The dissolution of the surface is thus not uniform but modulated at the atomic scale with higher rates at the defects and depressed sites. The micro roughness of the surface will increase with the amount of dissolution due to the sensitivity of the reactions to surface curvature associated with the micro depressed sites. These sites, due to the higher dissolution rates, will evolve into pits and eventually into pores. Depending on the condition, a certain amount of dissolution is required before the initiation of pores on all types of materials. 

So far, we have dealt with optically active centers based on dopant ions, which are generally introduced during crystal growth. Other typical optically active centers are associated with inhinsic lattice defects. These defects may be electrons or holes associated with vacancies or interstitials in ionic crystals, such as the alkali halide matrices. These centers are nsually called color centers, as they prodnce coloration in the perfect colorless crystals. 

The activation energy for oxide ion conduction in the various zirconia-, thoria- and ceria-based materials is usually at least 0.8 eV. A significant fraction of this is due to the association of oxide vacancies and aliovalent dopants (ion trapping effects). Calculations have shown that the association enthalpy can be reduced and hence the conductivity optimised, when the ionic radius of the aliovalent substituting ion matches that of the host ion. A good example of this effect is seen in Gd-doped ceria in which Gd is the optimum size to substitute for Ce these materials are amongst the best oxide ion conductors. Fig. 2.11. 

Figure 16. Concentrations of vacancies and interstitial particles in a positively doped Frenkel-disordered material taking account of association between cationic vacancies and dopant ions. The...

Hie main experimental techniques used to study oxygen migration in doped cerias are based on the AC impedance analysis of the measured electrical conductivity. It is found that the oxygen ion conductivity of ccria-bascd oxides depends strongly upon the dopant size and concentration. Both these factors are related to defect association between oxygen vacancies (the charge carriers) and other defects (mainly dopant substitutionals) which were discussed in section 8.3.2,. 

Y,Zrj -,O2 /2 ceramics, the maximum conductivity is obtained for x 0.10. Higher concentrations of dopant cations decrease conductivity by the effect of their progressive association with oxygen vacancies. The working temperature range extends from 400 to 1600°C for partial pressures of oxygen between 10 ° and 10 bar. 

An important aspect concerning the defects in ceria-based materials is their tendency to associate to form clusters of various complexity, which was mentioned in the previous section. The most studied defect clusters have been those formed by lower-valent (acceptor) dopant cations and oxygen vacancies. The reason for this is that these associations are widely considered to be responsible for the observed variation of the electrical conductivity of ceria-based oxides with dopant size, concentration and temperature. ... 

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