Interstitial pair migration

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.

The 2.2 eV in equation 57 may represent the migration enthalpy of the phosphorus-self-interstitial pair (56) with the excess self-interstitials produced by damage annealing. 

Ionic transport in crystals usually involves migration of defects (vacancies, interstitial ions, interstitial pairs). Haven and Verkerk [46] argued that when the ionic motion involves defect mechanisms the experimental difihision coefficient, D, is different (because of correlation effects) from the calculated one, D, which obeys the Nemst-Einstein equation... 

Ko within which any vacancy-interstitial pair will spontaneously recombine and (ii) to subthreshold energy transfers inducing athermal migration and annihilation of interstitials (with a cross-section Frenkel-pair production rate obeys the following relation ... 

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).

There are also other mechanism which can lead to desorption. For example, the generation of electron hole pairs by either photons or electrons can produce desorption from some insulators and semiconductors. The holes are believed to reach the surface where they neutralize adsorbed negative ions which are subsequently desorbed into the gas phase. It is also possible that other defects (such as migrating H centers in the alkali halides) may cause desorption when they reach the surface . Moreover, interstitial atoms generated within the solid may diffuse to the surface where they are desorbed . 

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... 

The relationship between jump rate and diffusivity in Eq. 8.3 can be obtained by an alternate method that considers the local concentration gradient and the number of site-pairs that can contribute to flux across a crystal plane. A concentration gradient of C along the y-axis in Fig. 8.86 results in a flux of C atoms from three distinguishable types of interstitial sites in the a plane (labeled 1, 2, and 3 in Fig. 8.8). The sites are assumed to be occupied at random with small relative populations of C atoms that can migrate between nearest-neighbor interstitial sites. If d is the number of C atoms in the a plane per unit area, the carbon concentration on each type of site is c /3. Carbon atoms on the types 1 and 3 sites jump from plane a to plane (3 at the rate (c /3)T. The jump rate from type-2 sites in plane a to plane (3 is zero. The contribution to the flux from all three site types is... 

For ceramic materials, defects within the lattice are inextricably linked with transport properties. The diffusion of a cation in a ceramic, for example, involves the formation of vacancy or interstitial states within the crystal, and the migration of these species leads to a net transport of material through the lattice. These processes may be modeled by means of ion pair potentials in conjunction with the Mott-Littleton defect approach, direct molecular dynamics techniques, 24 or Monte Carlo methods to describe overall transport on the basis of calculated individual process statistics. 

When a positron enters a solid, it thermalizes in a time much shorter (few picoseconds) than its lifetime (few hundred of picoseconds). At the time of annihilation, the positron has diffused over a certain distance (few hundreds of nm). This diffusion process is critical to determine the state of the electron-positron pair at the time of annihilation the positron migrates in a region energetically favorable, namely the interstitial region of the lattice. The positron might also be trapped if it reaches a defect and experiences a longer lifetime. Otherwise, it annihilates with an electron in the valence or conduction band. Observing the annihilation radiation provides information on the electronic structure in momentum space. 

The migration of a lattice atom/ion into an available interstitial site will leave behind a vacancy (Figure 2.49) the formation of such an interstitial/vacancy pair is known as a Frenkel defect. In contrast, Schottky defects are formed through the migration of a cation-anion pair from the crystal lattice framework, leaving behind two vacant lattice sites. For ionic crystals, the overall charge of the crystal must be charge-balanced. That is, if trivalent ions such as La are substituted with divalent cations such as Ca, there must be concomitant placements of divalent anions... 

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