Vacancy pair diffusion

When divalent cation impurities (e.g. Cd, Sr ) are present in an ionic solid of the type MX consisting of monovalent ions, the negatively charged cation vacancies (created by the divalent ions) are bound to the impurity ions at low temperatures. Similarly, the oppositely charged cation and anion vacancies tend to form neutral pairs. Such neutral vacancy pairs are of importance in diffusion, but do not participate in electrical conduction. The interaction energy of vacancy pairs or impurity-vacancy pairs decreases with the increase in distance between the two oppositely charged units. 

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... 

We use our previous results for the return and recombination probabilities of the vacancy, and consider the random walk of the tracer-vacancy pair on the bond lattice. Let p(r, re) denote the probabihty that the tracer-vacancy pair is at position r at instance n, where re counts the number of moves the tracer-vacancy pair has already made. Since the subsequent moves of the pair are independent, we can write an effective diffusion equation for the evolution of p(r, n) ... 

At high temperatures, terraces appear to produce most adatoms. Activation energies for mass transfer diffusion are therefore higher than at low temperatures. Evidence for this effect comes from molecular dynamics simnlations for self-diffusion on Lennard-Jones solids [94Sunl] and semi-conductors [96Sunl, 96A111]. The simulations show that the number of adatom-vacancy pairs produced from terraces increases... 

A comparison with ionic conductivity data revealed an excess diffusion of 10 to 20%. This was tentatively attributed to the effect of vacancy pairs. 

Li and H vacancies (diffuses slowly barrier -40-90 kJ/mol) Li+ and H- interstitials (diffuses quickly barrier -7-25 kJ/mol) LiH vacancy pairs, etc. 

The defects generated in ion—soHd interactions influence the kinetic processes that occur both inside and outside the cascade volume. At times long after the cascade lifetime (t > 10 s), the remaining vacancy—interstitial pairs can contribute to atomic diffusion processes. This process, commonly called radiation enhanced diffusion (RED), can be described by rate equations and an analytical approach (27). Within the cascade itself, under conditions of high defect densities, local energy depositions exceed 1 eV/atom and local kinetic processes can be described on the basis of ahquid-like diffusion formalism (28,29). 

In this diagram, we have shown both charged ions involved in the migrational diffusion process as well as charged vacancies which also add to the overall diffusion process. We must have electroneutrality in diffusion, i.e.- pairs of defects, and using the above example, we can write nine equations, of which the following is just one case ... 

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.

In a molecular dynamic simulation147 of bulk atomic diffusion by a vacancy mechanism, two atoms may occasionally jump together as a pair. The temperature of the simulation is close to the melting point of the crystal. In FTM studies of single atom and atomic cluster diffusion, the temperature is only about one tenth the melting point of the substrate. All cluster diffusion, except that in the (1 x 1) to (1 x 2) surface reconstruction of Pt and Ir (110) surfaces already discussed in Section 4.1.2(b), are consistent with mechanisms based on jumps of individual atoms.148,149 In fact, jumps of individual atoms in the coupled motion of adatoms in the adjacent channel of the W (112) surface can be directly seen in the FTM if the temperature of the tip is raised to near 270 K.150... 

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... 

Figure 9.9 Calculated atom jumps in the core of a E5 symmetric (001) tilt boundary in b.c.c. Fe. A pair-potential-molecular-dynamics model was employed. For purposes of clarity, the scales used in the figure are [130] [310] [001] = 1 1 5. All jumps occurred in the fast-diffusing core region. Along the bottom, a vacancy was inserted at B, and subsequently executed the series of jumps shown. The trajectory was essentially parallel to the tilt axis. Near the center of the figure, an atom in a B site jumped into an interstitial site at I. At the top an atom jumped between B, I and B sites. From Balluffi et al. [14],...

At small radiation doses (the number of radiation-produced defects), the mean distance l between components of such geminate pairs (the vacancy and an interstitial atom) is much less than the mean distance between different pairs Iq = n-1/3, where n is defect concentration. The initial defect distribution is described by the distribution function f(r). Below a certain temperature (typically < 30 K for interstitial atoms and 200 K for vacancies in alkali halides), defects are immobile. With a temperature increase, the defects perform thermally activated random hops between the nearest lattice sites. This is usually considered to be continuous diffusion. 

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