Interstitial pair formation

From a thermodynamic point of view the formation of an interstitial pair obeys the chemical equilibrium (Kittel, 1968)... 

Fig. 4.3 Schematic representation of interstitial cationic pair formation (a) and migration from one non bridging oxygen to another in a cation conducting glass (b).

Fig. 4.7 A schematic representation of a cationic displacement along a polymeric chain above its Tg. (a) An initial activated step (ft) allows the formation of an interstitial pair, the migration of which (c) and (d) is assisted by local free volume redistribution.

Self-diffusion of Ag cations in the silver halides involves Frenkel defects (equal numbers of vacancies and interstitials as seen in Fig. 8.116). In a manner similar to the Schottky defects, their equilibrium population density appears in the diffusivity. Both types of sites in the Frenkel complex—vacancy and interstitial— may contribute to the diffusion. However, for AgBr, experimental data indicate that cation diffusion by the interstitialcy mechanism is dominant [4]. The cation Frenkel pair formation reaction is... 

The ES-mechanism of Frenkel-pair formation as a result of excitation of Rydberg atomic states was confirmed by recent molecular dynamics calculations [28,29]. After the bubble formation the surrounding ground state atoms appear to have moved to the second shell. It was found that the second-nearest neighboring vacancy-interstitial pairs could create the permanent defects, which remain in the lattice after exciton annihilation (Fig.Sb) [29],... 

AGPrenkel represents the Gibbs free energy of formation of the interstitial pair... 

We mentioned above the collision cascade producing displaced atoms in a solid target. If we consider a single collision event in a crystalline solid, we can see that this displacement of atoms leads to the preferential formation of point defects. The most important types of point defects are a single vacancy (one atom or ion is missing), a single interstitial (an additional atom), a vacancy-interstitial pair (Frenkel pair). 

Note that in LRC, the stable Frenkel pairs may be formed (e.g., under irradiation). The energy spectrum of Frenkel pair formation is somewhat spread due to the spread in energies of vacancies and interstitials formation. The width of this spectrum as well as variations in energy of vacancies and interstitials formation may amount to some eV, and the typical values of the threshold energy of Frenkel pair formation in metallic glasses as well as in crystals may amount to about 25-30 eV. To point defects of a cluster one may attribute also the interstitial and substitutional impurities that locally break the topological and compositional order. 

In compound crystals, balanced-defect reactions must conserve mass, charge neutrality, and the ratio of the regular lattice sites. In pure compounds, the point defects that form can be classified as either stoichiometric or nonstoichiometric. By definition, stoichiometric defects do not result in a change in chemistry of the crystal. Examples are Schottky (simultaneous formation of vacancies on the cation and anion sublattices) and Frenkel (vacancy-interstitial pair). 

The quotient of electrical conductivity a and thermal conductivity X is inversely proportional to the temperature. The ionic conductivity of solids depends on the lattice type and the type of the defects. The conductivity increases with temperature. This property is used to distinguish the ion conductor from the electron conductor. For vacancies and interstitials in the ion lattice, conductivity depends on the formation enthalpy for vacancy-interstitial pairs, Afo v. 

The formation of a PKA as a result of particle impingement is equivalent to the formation of a vacancy-interstitial pair lattice defect, and is a basic structural defect... 

The extent of reaction for this process is determined by a trade-off between enthalpy and entropy. The perfect lattice is energetically favorable. To form this vacancy-interstitial pair, we need to overcome the bond energy of a zinc atom in its lattice site. However, when the crystal exists in a perfectly ordered lattice, every atom has a designated place to be it can have only one configuration. Therefore, its entropy is low. Formation of... 

A variety of techniques has been employed to investigate aliovalent impurity-cation vacancy pairs and other point defects in ionic solids. Dielectric relaxation, optical absorption and emission spectroscopy, and ionic thermocurrent measurements have been most valuable ESR studies of Mn " in NaCl have shown the presence of impurity-vacancy pairs of at least five different symmetries. The techniques that have provided a wealth of information on the energies of migration, formation and other defect energies in ionic solids are diffusion and electrical conductivity measurements. Electrical conductivity in ionic solids occurs by the motion of ions through vacancies or of interstitial ions. In the case of motion through vacancies, the conductivity, a, is given by... 

Fig. 4.22 On the surface of a solid, there are a wide variety of atomic processes. A formation of a surface vacancy-adatom pair, or their recombination B association or dissociation of adatoms with an atomic cluster and cluster diffusion C diffusion of a surface vacancy, especially toward the lattice step D falling off a lattice step of an adatom E diffusion of a substitutional or interstitial impurity atom and its interaction with an adatom F diffusion of an adatom and its long range interactions with other adatoms G diffusion, dissociation and activation of a ledge atom H dissociation and activation of a kink atom into an adatom, a ledge atom, or an adatom on the layer above.

A cation vacancy may be paired with a nearby cation interstitial. This is called a Frenkel pair. An example is the formation of Zn+2 vacancies and Zn+2 interstitials in ZnO. This is illustrated in Figure 5.2B. In principle, paired anion vacancies and interstitials are possible, but this is less likely because of the larger size of the anions. 

Hence the statistical and thermodynamical theory of the lattice hydrogen solubility in fee fullerite with consideration for the hydrogen atoms distribution over the interstitial sites of different types has allowed us to explain and justify the formation of HX hydrofullerites with high hydrogen concentration when 0 < x < 18. It has been found that hydrogen solubility depends on the fullerite composition, its temperature, the order parameter in i = C6o, 2 = C70 fullerenes distribution over the lattice sites, the energetic constants characterizing the interaction between H- pairs at the different distances. 

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